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HEAT TRANSFER ANALYSIS AND MODELING OF A PARABOLIC TROUGH SOLAR RECEIVER IMPLEMENTED IN ENGINEERING EQUATION SOLVER by Russell Edward Forristall B.S. University of Colorado at Denver, 1997 A thesis submitted to the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Science Mechanical Engineering 2003
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This thesis for the Master of Science degree by Russell Edward Forristall has been approved by LA/_
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Forristall, Russell Edward (M.S., Mechanical Engineering) Heat Transfer Analysis and Modeling of a Parabolic Trough Solar Receiver hnplemented in Engineering Equation Solver Thesis directed by Associate Professor Sean Wright ABSTRACT This report describes the development, validation, and use of a heat transfer model implemented in Engineering Equation Solver (EES). The model determines the performance of a parabolic trough solar collector's linear receiver, also called a heat collector element (HCE). All heat transfer and thermodynamic equations, optical properties, and parameters used in the model are discussed. The modeling assumptions and limitations are also discussed, along with recommendations for model improvement. The model was implemented in EES in four different versions. Two versions were developed for conducting HCE design and parameter studies, and two versions were developed for verifying the model and evaluating field test data. Both a onedimensional and twodimensional energy balance was utilized in the codes, where appropriate. Each version of the codes is discussed briefly, which includes discussirig the relevant EES Diagram Windows, Parameter Tables, and Lookup Tables. Detailed EES software instructions are not included; however, references are provided. Model verification and a design and parameter study to demonstrate the model versatility are also presented. The model was verified by comparing the field test versions of the EES codes with HCE experimental results. The design and parameter study includes numerous charts showing HCE performance trends based on different design and parameter inputs. Based on the design and parameter study, suggestions for HCE and trough improvements and further studies are given. The HCE perfomiance software model compared well with experimental results and provided numerous HCE design insights from the design and parameter study. The two design versions of the EES codes of the HCE performance model are provided in the appendix. This abstract accurately represents the content of the candidate's thesis. I recommend its publication. Signed 111
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ACKNOWLEDGEMENT I would like to thank my advisor, Associate Professor Sean Wright, for his guidance and patience during this thesis. I also would like to thank my supervisor at the National Renewable Energy Laboratory (NREL), Hank Price, for providing the opportunity to work on this project and his patience along the way. Further thanks go to Sandia National Laboratories (SNL) and Kramer Junction Operating Corporation for hosting visits to witness the solar trough in action and for providing test data to verify the software model. Finally, I would like to thank all those people who were kind enough to take time out of there busy schedules to answer questions I had during my work on this thesis; specifically, Rod Mahoney, Tom Mancini, and Tim Reynolds of SNL; Mark Mehos, JoAnn Fitch, Mary Jane Hale, Tim Wendelin, and Vahab Hassani ofNREL; and Professor Sam Welch of the University of Colorado at Denver (UCD).
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CONTENTS Figures ............................................................................................................................... ix Tables ............................................................................................................................... xiii Symbols ............................................................ ; ............................................................... xv Chapter 1. Introduction .................................................................................................................... 1 1.1 Background .................................................................................................................. 2 1.2 Motivation .................................................................................................................... 6 2. HCE Performance Model. .............................................................................................. 8 2.1 OneDimensional Energy Balance Model ................................................................... 8 2.1.1 Convection Heat Transfer between the HTF and Absorber .................................... 11 2.1.1.1 Turbulent and Transitional Flow Cases ............................................................... 12 2.1.1.2 Laminar Flow Case .............................................................................................. 13 2.1.1.3 Annulus Flow Case .............................................................................................. 13 2.1.2 Conduction Heat Transfer through the Absorber Wall ........................................... 14 2.1.3 Heat Transfer from the Absorber to the Glass Envelope ........................................ 15 2.1.3.1 Convection Heat Transfer .................................................................................... 16 2.1.3.1.1 Vacuum in Annulus .......................................................................................... 16 2.1.3.1.2 Pressure in Annulus .......................................................................................... 18 2.1.3.2 Radiation Heat Transfer ....................................................................................... 19 2.1.4 Conduction Heat Transfer through the Glass Envelope .......................................... 19 v
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2.1.5 Heat Transfer from the Glass Envelope to the Atmosphere ................................... 20 2.1.5.1 Convection Heat Transfer .................................................................................... 20 2.1.5.1.1 No Wind Case ................................................................................................... 21 2.1.5.1.2 Wind Case ......................................................................................................... 22 2.1.5.2 Radiation Heat Transfer ....................................................................................... 22 2.1.6 Solar Irradiation Absorption ................................................................................... 23 2.1.6.1 Optical Properties ................................................................................................ 23 2.1.6.2 Solar Irradiation Absorption in the Glass Envelope ............................................ 26 2.1.6.3 Solar Irradiation Absorption in the Absorber ...................................................... 27 2.1.7 Heat Loss through HCE Support Bracket.. ............................................................. 27 2.1.8 No Glass Envelope Case ......................................................................................... 29 2.2 TwoDimensional Energy Balance Model... .............................................................. 30 2.3 Assumptions and Simplifications .............................................................................. 34 2.4 Model Limitations and Suggested Improvements ..................................................... 41 3. EES Codes ................................................................................................................... 44 3.1 OneDimensional Heat TransferEES Codes ............................................................. 45 3.1.1 OneDimensional Design Study Version ................................................................ 45 3.1.1.1 Lookup Tables ..................................................................................................... 45 3 .1.1.2 Diagram Window ................................................................................................. 46 3 .1.1.3 Parametric Table .................................................................................................. 49 3.1.2 AZTRAK Test Data Version .................................................................................. 49 3.1.2.1 Diagram Window ................................................................................................. 50 vi
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3.1.2.2 Parametric Table .................................................................................................. 51 3.2 TwoDimensional Heat TransferEES Codes ............................................................ 53 3.2.1 TwoDimensional Design Study Version ............................................................... 53 3.2.1.1 Diagram Window ................................................................................................. 53 3.2.1.2 Parametric Table .................................................................................................. 54 3.2.2 KJC Testloop Data Version ................................................................................... 57 3.2.2.1 Diagram Window ................................................................................................. 57 3.2.2.2 Parametric Table .................................................................................................. 58 4. Comparison between the One and TwoDimensional Models .................................... 61 5. Comparison with Experimental Data ........................................................................... 65 5.1 Comparison with SNL AZTRAK Data ..................................................................... 66 5.2 Comparison with KJC Data ....................................................................... 74 6. Design and Parameter Studies ..................................................................................... 83 6.1 Absorber Pipe Base Material ..................................................................................... 86 6.2 Selective Coating ....................................................................................................... 89 6.3 Annulus Gas Type ..................................................................................................... 92 6.4 HCE Condition and Wind Speed ............................................................................... 94 6.5 Annulus Pressure ....................................................................................................... 96 6.6 Mirror Reflectance ..................................................................................................... 99 6.7 Solar Incident Angle ................................................................................................ 102 6.8 Solar Insolation .......................... : ............................................................................. 104 6.9 H'fF Flow Rate ........................................................................................................ 107 vii
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6.10 HTFType ............................................................................................................... l09 6.11 Glass Envelope Outer Diameter ............................................................................ 111 6.12 Parameter Variation along Receiver Length .......................................................... 113 6.13 Recommendations .................................................................................................. 115 7. Conclusion ................................................................................................................. 1 I 9 Appendix A. Lookup Table References ......................................................................................... 121 B. Optical and Material Property References ................................................................ 122 C. Heat Transfer Fluid Change in Enthalpy ................................................................... 124 D. Radiation Heat Transfer Zonal Analysis for the Glass Envelope ............................. 126 E. OneDimensional Design Study Version of EES Code ............................................ 133 F. TwoDimensional Design Study Version ofEES Code ............................................ 155 References ....................................................................................................................... 180 viii
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FIGURES Figure 1.1 Aerial view of five 30 MW SEGS solar plants at Boron, California. (source: [Price 2002]) ................................................................................................................ 3 1.2 Process flow schematic of largescale parabolic trough solar power plant with thermal storage capability. (source: Flabeg Solar International) ................................. 4 1.3 Parabolic trough solar collector assembly (SCA) located at a solar research test facility in Spain. (source: Plataforma Solar de Almeria) ............................................. 5 1.4 Schematic of a heat collector element (HCE). (source: Solei Solar Systems Ltd.) ..... 6 2.1 a) Onedimensional steadystate energy balance and b) thermal resistance model for a crosssection of an HCE .................................................................................... 10 2.2 Chart of heat loss per unit length of receiver as a function of annulus pressure ........ 16 2.3 Examples of solar trough receiver support brackets .................................................. 29 2.4 Closeup of receiver support bracket attachment to absorber tube ............................ 29 2.5 Schematic of the twodimensional heat transfer model. ............................................ 32 3.1 Diagram window from the Design Study Version of the heat transfer code ............. 4 7 3.2 Diagram window from the AZTRAK Test Data Version of the heat transfer code .. 50 3.3 Diagram window from the TwoDimensional Design Study Version of the heat transfer code ............................................................................................................... 54 3.4 Diagram window from the KJC Testloop Data Version of the heat transfer code ... 57 4.1 Heat loss chart for different receiver length step sizes .............................................. 62 4.2 a) Heat gain and b) efficiency charts comparing the one and twodimensional models for different HfF temperatures ..................................................................... 63 ix
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4.3 Heat loss chart comparing the one and twodimensional models for different H1F temperatures ...................................................................................................... 64 5.1 AZTRAK rotating test platform located at SNL in Albuquerque, NM. An LS2 type collector module is shown installed on the platform ......................................... 65 5.2 a) Efficiency and b) heat loss charts comparing the EES HCE Code and SNL AZTRAK test data for Luz Cermet selective coating ................................................ 69 5.3 Heat loss comparison chart between the EES HCE Code and SNL AZTRAK test data for the offsun case and Luz Cermet selective coating ...................................... 70 5.4 a) Efficiency and b) heat loss chart comparing the EES HCE Code and SNL AZfRAK test data for Luz Black Chrome selective coating .................................... 71 5.5 Heat loss comparison chart between the EES HCE Code and SNL AZTRAK test data for the offsun case and Luz Black Chrome selective coating ........................... 72 5.6 a) Efficiency trend and b) heat loss trend charts comparing the EES HCE Code and SNL AZTRAK test data for varying wind speeds and no glass envelope .......... 73 5.7 a) Heat gain and b) outlet temperature charts comparing the EES HCE Code and KJC testloop data for 010201 ................................................................................ 76 5.8 a) Heat gain and b) outlet temperature charts comparing the EES HCE code and KJC testloop data for 032201. ............................................................................... 77 5.9 a) Heat gain and b) outlet temperature charts comparing the EES HCE code and KJC testloop data for 062101 ................................................................................ 78 5.10 Power loss components and solar insolation chart from the KJC testloop data for 010201 ............................................................................................................. 79 5.11 Power loss components and solar insolation chart from the KJC testloop data for 032201 ............................................................................................................. 80 5.12 Power loss components and solar insolation chart from the KJC testloop data for 062201 ............................................................................................................. 81 5.13 Average HTF temperature above ambient for each KJC testloop data set. ............ 82 6.1 a) Efficiency and b) heat loss charts comparing different HCE absorber pipe base material types ............................................................................................................. 88 X
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6.2 Energy rate components chart for each selective coating type .................................. 90 6.3 a) Efficiency and b) heat loss charts comparing different HCE types ....................... 91 6.4 a) Efficiency and b) heat loss charts comparing different annulus gas types ............ 93 6.5 a) Efficiency and b) Heat loss charts comparing different HCE conditions as functions of wind speed ............................................................................................. 95 6.6 Heat loss chart as a function of annulus pressure for air and hydrogen as the annulus gas ................................................................................................................. 96 6.7 a) Efficiency and b) heat loss charts for different annulus pressures and air as the annulus gas ................................................................................................................. 97 6.8 a) Efficiency and b) heat loss charts for different annulus pressures and hydrogen as the annulus gas ...................................................................................................... 98 6.9 Energy rate components chart for different solar weighted reflectivities ................ 100 6.10 a) Efficiency and b) heat loss charts comparing different solar weighted reflectivities. Both the one and twodimensional model results are included for comparison ............................................................................................................. 101 6.11 Energy rate components chart as a function of different solar incident angles ..... 102 6.12 a) Efficiency and b) heat loss charts comparing different solar incident angles .... 103 6.13 Chart showing solar incident angles for three different times of year from actual data for a northsouth oriented SEGS plant in Kramer Junction, California ............................................................................................................... 104 6.14 Energy rate components chart for different solar insolation values ....................... 105 6.15 a) Efficiency and b) heat loss charts for different solar insolation values ............. 106 6.16 a) Efficiency and b) heat loss charts comparing different flow rates and including both the one and twodimensional models ............................................ 108 6.17 a) Efficiency and b) heat loss charts comparing different HTF types and including both the one and twodimensional models ............................................ 110 6.18 a) Efficiency and b) heat loss charts comparing different glass envelope diruneters ................................................................................................................ 112 xi
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6.19 HCE crosssection temperatures chart at position along receiver length ............... 114 6.20 Energy rate components chart as a function of position along receiver (total receiver length= 779.5 m) ..................................................................................... 115 D.1 Zone definitions for the generalized zone analysis of the radiation heat loss from the receiver .................................................................................................... 126 D.2 Line segments used for the string method approximation for view factors ............ 129 D.3 Radiation heat loss comparison chart showing difference between modeling the radiation loss with and without the collector effects .............................................. 132 xii
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TABLES Table 21 Heat Flux Definitions ................................................................................................ 11 22 Nusselt Number for Laminar Annulus Flow with Uniform Heat Flux ..................... 14 23 Heat Transfer Coefficients and Constants for Each Annulus Gas ............................. 18 24 Estimates of Effective Optical Efficiency Terms [Price 2002] ................................. 24 25 Optical Properties for Each Selective Coating .......................................................... 25 26 Temperature Dependent Emittance Equations .......................................................... 26 27 Assumptions and Simplifications made in the HCE Performance Models ............... 35 31 Part of the Lookup Table for Therminol VPl ........................................................... 46 32 Parametric Table for the Design Study Version of the Heat Transfer Code ............. 49 33 Parametric Table from the AZTRAK Test Data Version of the Heat Transfer Code ........................................................................................................................... 52 34 Collector and Test Type Receiver Lengths ............................................................... 54 35 Parametric Table from the TwoDimensional Design Study Version of the Heat Transfer Code ............................................................................................................ 56 36 Parametric Table from the KJC Testloop Data Version of the Heat Transfer Code ........................................................................................................................... 59 41 Iteration Time for Different Receiver Step Sizes ...................................................... 62 5l Mirror Reflectivity and Optical Efficiency for Each Test Type ................................ 67 52 List of Figures and Comments for the AZTRAK Test Platform Data Comparison .. 67 53 List of Figures and Comments for the KJC TestLoop Data Comparison ................ 75 xiii
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54 Daily Average Losses per Receiver Length .............................................................. 79 55 Estimated Heat Loss Percentages due to HCE Support Brackets .............................. 81 61 HCE Design and Parameter Study Summary ............................................................ 83 62 Recommendations from HCE Design and Parameter Study ................................... 117 D1 Radiation Heat Transfer Zonal Analysis Parameters and Results .......................... 131 xiv
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SYMBOLS a = accommodation coefficient of annulus gas Acs = absorber pipe crosssectional flow area [m2 ] Acs,b = minimum crosssection of receiver support bracket [m2 ] Ai = circumferential area of receiver segment "i" [m2 ] b = interaction coefficient of annulus gas C,m,n = constants Cave,i = H1F specific heat at average temperature of receiver segment "i" [OC] Dz = inside diameter of absorber pipe [m] D3 = outside diameter of absorber pipe [m] D4 = inside diameter of glass envelope [m] Ds = outside diameter of glass enveope [m] Db = hydraulic diameter of absorber pipe [m] Dp = outside diameter of absorber pipe flow restriction insert pipe (or cylinder) [m] f = Darcy friction factor fz = friction factor for the inner surface of the absorber pipe g = gravitational constant, 9.81 rn/s2 h. = convection heat transfer coefficient for the H1F at T1 [W/m 2 K] h34 = convection heat transfer coefficient of annulus gas at T34 [W/m 2 K] hs6 = convection heat transfer coefficient of air at T56 [W/m 2 K] hb. = convection heat transfer coefficient of air evaluated at the ,I average receiver support bracket film temperature for receiver segment "i" [W/m 2 K] hi,in = enthalpy at inlet of receiver segment "i" [J/kg] hi,out = enthalpy at outlet of receiver segment "i" [J/kg] K = incident angle modifier kt = thermal conductance of H1F at T 1 [W /mK] k23 = thermal conductance of absorber wall at T23 [W/mK] k34 = thermal conductance of annulus gas at T 34 [W /mK] ks6 = thermal conductance of air at T56 [W/mK] kb = conduction heat transfer coefficient of air evaluated at the average receiver support bracket film temperature for receiver segment "i" [W/mK] kstd = thermal conductance of annulus gas at standard temperature and pressure [W/mK] m = mass flow rate [kgls] ni = number of receiver support brackets on receiver segment "i" XV
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Nu02 = Nusselt number of HTF based on D 2 Nuns = Nusselt number of air based on D5 Pa = annulus gas pressure [mmHg] pb = exterior perimeter of receiver support bracket [m] Pinlet,i = HTF pressure at inlet of receiver segment "i" [0C] Poutlet,i = HTF pressure at outlet of receiver segment "i" [0C] Pr1 = Prandtl number of HTF evaluated at T 1 Pr2 = Prandtl number of HTF evaluated at T 2 Pr34 = Prandtl number of annulus gas at T 3 4 Prs = Prandtl number of air at T 5 Prs6 = Prandtl number for air at T 56 Pr6 = Prandtl number of air at T 6 Pw = absorber pipe inner wetted surface perimeter [m] I = convection heat transfer rate between the heat transfer fluid and qi2conv inside wall of the absorber pipe per unit receiver length [W/m] I = conduction heat transfer rate through the absorber pipe wall per q23cond unit receiver length [W/m] I = solar irradiation absorption rate into the absorber pipe per unit q3So/Abs receiver length [W /m] I = incident solar irradiation absorption rate into the absorber pipe of q3So/Abs,i receiver segment "i" per unit segment length [W/m] I = convection heat transfer rate between the outer surface of the q34conv absorber pipe to the inner surface of the glass envelope per unit receiver length [W/m] I = convection heat transfer rate for receiver segment "i" between the qJ4COIIV,i outer surface of the absorber pipe to the inner surface of the glass envelope per receiver segment length [W/m] I = radiation heat transfer rate between the outer surface of the q34rad absorber pipe to the inner surface of the glass envelope per unit receiver length [W/m] I = radiation heat transfer rate for receiver segment "i" between the q34rad,i outer surface of the absorber pipe to the inner surface of the glass envelope per receiver segment length [W/m] I = convection heat transfer rate between the outer surface of the q36conv absorber pipe to the atmosphere per unit receiver length [W/m] I = convection heat transfer rate between the outer surface of the q36conv,i absorber pipe to the atmosphere per unit receiver segment length for receiver segment "i" [W/m] I = radiation heat transfer rate between the outer surface of the glass q51rad envelope to the sky per unit receiver length [W/m] I = radiation heat transfer rate between the outer surface of the q31rad,i absorber pipe to the sky per unit receiver segment length for receiver segment "i" [W/m] xvi
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I q45cond I q5So/Abs I q5So1Abs,i I q56conv I q37rad q cond ,bracket,i q cond ,bracket ,total,i I qHeatLoss ., q HeatLoss,i ., q Heat Loss ,total,i ., qi I qsi ., q So/arAbs ,i Ra03 Raos Reo2 Reo2,ave,i Reos T Tz T23 T3 T34 T4 Ts Ts6 T6 T1 Tbase,i = = = = = = = = = = = = = = = = = = = = = = = = = = = = = conduction heat transfer rate through the glass envelope per unit receiver length [W/m] solar irradiation absorption rate into the absorber pipe per unit receiver length per unit receiver length [W/m] incident solar irradiation absorption rate into the glass envelope of receiver segment "i" per unit segment length [W/m] convection heat transfer rate between the outer surface of the glass envelope to the atmosphere per unit receiver length [W/m] radiation heat transfer rate between the outer surface of the absorber pipe to the sky per unit receiver length [W/m] conductive heat loss through each receiver support bracket on receiver segment "i" [W] total conductive heat losses through all receiver support brackets on receiver segment "i" [W] total heat loss rate from the heat collecting element to the surroundings [W/m] heat loss rate per unit circumferential area to the atmosphere from receiver segment "i" (excluding bracket losses) [W/m 2 ] total heat loss rate per unit circumferential area from receiver segment "i" [W/m 2 ] net heat flux per unit circumferential area of receiver segment "i" [W/m2 ] solar irradiance per receiver unit length [W/m] incident solar irradiation absorption rate per unit circumferential area of receiver segment "i" [W/m 2 ] Rayleigh number of annulus gas based on 03 Rayleigh number of air based on 05 Reynolds number of HTF based on 0 2 Reynolds number based on 02 and evaluated at the average HTF bulk temperature of receiver segment "i" Reynolds number of air based on D5 mean (bulk) temperature of the HTF [0C] absorber pipe inner surface temperature [0C] average absorber wall temperature, (T 2 + T 3)/2 [0C] absorber pipe outer surface temperature [0C] average temperature of annulus gas, (T 3+ T 4)/2 [0C] glass envelope inner surface temperature [0C] glass envelope outer surface temperature [0C] average temperature of air, (T5 + T6)/2 [0C] atmosphere temperature [0C] estimated effective sky temperature [0C] temperature at base of receiver support bracket for receiver segment "i" [C] XVII
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Tinlet,i Toutlet,i Vs6 Vi,in Vi,out L\bi = = = = = = HlF temperature at inlet of receiver segment "i" [0C] H1F temperature at outlet of receiver segment "i" [0C] kinematic viscosity of air at T56 [m2/s] bulk fluid velocity at inlet of receiver segment "i" [J/kg] bulk fluid velocity at outlet of receiver segment "i" [J/kg] change in enthalpy through receiver segment "i" (hinlet.ihoutlet,i) [J/kg] LlLaperture = receiver segment length [m] APi = dTi = Pave,i = change in HlF pressure through receiver segment "i" (Pinlet.i P outlet,i) [Pa] change in H1F temperature through receiver segment "i" (Tinlet,i T outlet,i) [K] H1F density at average temperature of receiver segment "i" [kg/m3 ] Greek Letters (l Clabs Clenv f3 E E'# E3 E4 Es llave,i y T\abs T\env A. 1t 0' 'tenv = = = = = = = = = = = = = = = = = thermal diffusivity of air at T56 [m2/s] absorptance of the absorber selective coating absorptance of the glass envelope volumetric thermal expansion coefficient of annulus gas or air [ 1/K] molecular diameter of annulus gas [em] equivalent surface roughness [m] optical efficiency terms emissivity of absorber selective coating emissivity of inner surface of glass envelope emissivity of outer surface of glass envelope dynamic fluid viscosity of HlF at the average temperature of receiver segment "i" [Ns/m2 ] ratio of specific heats of annulus gas effective optical efficiency at the absorber effective optical efficiency at the glass envelope meanfreepath between collisions of a molecule of annulus gas [em] ratio of the circumference to diameter of a circle, 3.14159 StefanBoltzmann constant [W/m2K4 ] transmittance of the glass envelope EES Lookup and Parametric Tables Design Study Version: c = specific heat [J/kgK] xviii
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Tlcol = collector efficiency [%] k = thermal conductance [W /mK] ll = dynamic viscosity [kglms] Pv = vapor pressure [kPa] qHeatGain = HTF heat gain per unit receiver length [W/m] qHeatl..oss = heat loss per unit receiver length [W/m] p = density [kglm3 ] T = temperature [0C] Tlave = average bulk HTF temperature between the receiver inlet and outlet [0C] AZTRAK Test Data Version: Tlcoi = collector efficiency [%] Ib = direct normal incident solar irradiation per unit area [W/m2 ] qHeatGain = heat gain per unit receiver length [W/m] qheat,Ioss,col,area = heat loss per projected collector area [W/m2 ] T 6 = ambient temperature [0C] TdiffAir = temperature difference between the average HTF temperature and ambient temperature [0C] Tin = HTF inlet bulk temperature [0C] Tout = HTF outlet bulk temperature [0C] v1 = HTF inlet volumetric flow rate [Limin] v6 = wind speed [rnls] KJC Testloop Data Version: LlP = HTF pressure drop through receiver [Pa] Tlcoi = collector efficiency [%] Ib = direct normal incident solar irradiation per unit area [W/m2 ] e = solar incident angle from the normal to the projected collector area [degrees] qcond,bracket = total conductive losses through receiver support brackets [W] qHeatGain = HTF heat gain per receiver length [W/m] qHeatLoss = heat loss per receiver length [W/m] qheat.loss,HCE.lengt = heat loss per receiver length [W /m] h qoptLoss qopt,loss qopt,loss,K Tunlet Tloutlet T6F Time TinF = = = = = = = = total optical loss per receiver length [W/m] total optical loss per receiver length [W/m] optical losses due to solar incident angle per receiver length [W/m] HTF bulk inlet temperature [0C] HTF bulk outlet temperature [0C] ambient temperature [Dp] local time HTF bulk inlet temperature [0F] xix
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ToutF = RTF bulk outlet temperature [F] ToutletF = RTF bulk outlet temperature [F] VJinlet = RTF bulk inlet velocity [rnls] VJoutlet = RTF bulk outlet velocity [rnls] V!Volg = RTF volumetric inlet flow rate [gpm] VI volg,outlet = RTF volumetric outlet flow rate [gpm] V6mph = wind speed [mph] XX
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1. Introduction This report describes the development, validation, and use of a heat transfer model implemented in Engineering Equation Solver (EES). The model detennines the performance of a parabolic trough solar collector's linear receiver, also called a heat collector element (HCE). All heat transfer and thermodynamic equations, optical properties, and parameters used in the model are discussed; along with all model inputs and outputs. Inputs include collector and HCE geometry, optical properties, heat transfer fluid (HTF) properties, HTF inlet temperature and flow rate, solar insolation, wind speed, and ambient temperature. Outputs include collector efficiency, outlet HTF temperature, heat gain, and heat and optical losses. Modeling assumptions and limitations are also discussed, along with recommendations for model improvement. The model was implemented in EES in four different versions: OneDimensional Design Study Version, TwoDimensional Design Study Version, AZTRAK Test Data Version, and K.JC TestLoop Data Version. The two design study versions were developed for conducting HCE design and parameter studies. The two test data versions were developed for verifying the model and evaluating field test data. Both onedimensional and twodimensional energy balances were utilized in the codes. When evaluating long receiver lengths, the twodimensional model becomes necessary. The onedimensional model is valid for short receiver lengths and for conducting design and parameter comparisons. The onedimensional version offers faster convergence times. Each version of the codes is discussed briefly, which includes the EES Diagram Windows, Parameter Tables, and Lookup Tables. Detailed EES software instructions are not included; however, references are provided. Model verification and a design and parameter study to demonstrate the model versatility are also presented. The model was verified by comparing the field test versions of the EES codes with experimental results. The field tests included data from a collector test platform at Sandia National Laboratories in Albuquerque, New Mexico, and data from a testloop of collectors in an operating solar plant in Kramer Junction, California. The design and parameter study section includes numerous charts showing HCE performance trends based on different design and parameter inputs. Based on the design and parameter study, suggestions for further studies and trough improvements are discussed. Additional model development analysis is provided in the Appendix, along with a copy of the two design study versions of the EES codes, and numerous analysis and parameter references. The AZTRAK and K.JC TestLoop Data versions of the code are not included; however, they are very similar to the design study versions of the code. They differ slightly due to the required inputs and output comparisons. As will be shown, the HCE performance software model compared well with the receiver field test results and provided numerous HCE design insights from the design and parameter study.
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1.1 Background Concentrating Solar Power (CSP) has been around for over a hundred years. Initially, CSP was used for smallscale solar thermalmechanical applications, with outputs up to 100 kW, and used mainly for water pumping [Duffie and Beckman 1991]. It wasn't until after the energy crises of 1973 that the idea of largescale solar power plants got its start [Thomas and Guven 1993]. Starting in the late 1980's, nine Solar Electric Generating Systems (SEGS) have been built and operated in the Mojave Desert of southern California. These SEGS plants range in size from 30 MW to 80 MW and total 354 MW of peak generating power for the Southern California Edison utility company, enough electricity for over 300,000 residents and displacing the use of over 2 million barrels of oil a year [Solel2002]. Five SEGS are shown in an aerial view in Figure 1.1. The SEGS pictured are located in Kramer Junction, California and are operated by the Kramer Junction Corporation Operating Company (KJCOC). The plants shown are natural gas supplemented steam Rankine turbine/generator systems. The natural gas supplements the required energy input during times of low solar insolation and allows the plants to operate 24 hrs a day at peak output. The buildings shown in the middle of the collector fields contain the heat exchangers, natural gas boilers, and pumping and generating equipment. There are other SEGS plant designs that are solar only, and others that have thermal storage capability. A schematic of a SEGS power plant is shown in Figure 1.2. As shown, the plant consists ofrows of troughs that collect the sun's thermal energy, a storage system that stores the thermal energy (optional), heat exchangers that generate superheated steam, and a standard power cycle that converts the thermal energy to electricala supplemental boiler system may also exist (a gas boiler in this case). The solar energy is captured by a Heat Transfer Fluid (HTF) which could be synthetic oil, or molten salt and transferred to heat exchangers for thermal storage or for steam generation. The thermal storage collects the solar energy during periods of high solar insolation, and supplements the heat input during periods of low insolation. The natural gas boiler would be used to further modulate the heat input and allow for 24 hr plant operation. Typically, the trough field is designed to provide enough heat input to raise the temperature of a HTF to around 400 C a temperature high enough to generate superheated steam for a standard Rankine steam generating plant. The outlet temperature is maintained by the HTF flow rate, the thermal storage (if applicable), and the natural gas heater (if applicable). A row of solar troughs or solar collector assemblies (SCA's), from an experimental solar test facility in Spain is shown in Figure 1.3. The figure illustrates the major components of a solar trough. As shown, it consists of the parabolic trough reflector, steel support structure, absorber pipe (HCE), and a singleaxis drive mechanism. The trough reflector provides an aperture about five meters in width and can extend for several thousand meters depending on the number of SCA' s and plant requirements. The HCE is about 115 mm in diameter and four meters in length between the support braces that support it at the focal line. Each individual SCA system can move independently from 2
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the rest of the collector field. This allows for maintenance and a control mechanism for controlling the HTF temperature, since one or a number of SCA's can be taken off sun during operation, which effectively controls the solar input. Figure 1.1 Aerial view of five 30 MW SEGS solar plants at Boron, California. (source: [Price 2002]) A diagram of an HCE is shown in Figure 1.4. The HCE consist of an absorber inside a glass envelope with bellows at either end. The absorber is typically a stainless steel tube about 70 mm in diameter with a special coating on the outside surface to provide the required optical properties. The selective coating has a high absorptance for radiation in the solar energy spectrum, and low emittance in the long wave energy spectrum to reduce thermal radiation losses [Duffie and Beckman 1991]. As will be shown in Section 6.2, the selective coating type has a strong influence on the HCE performance. The glass envelope protects the absorber from degradation and reduces heat losses. It is typically made from Pyrex, which maintains good strength and transmittance under high temperatures. To reduce reflective losses, the glass envelope goes through an antireflective treatmentbasically a slight chemical etching. The annulus space between the absorber and glass envelope is under vacuum to further reduce thermal losses and add 3
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additional protection to the selective coating [Price 2002]. The getter bridge installed in the annulus consists of metallic compounds designed to absorb hydrogenwhich naturally permeates from the HTF and if left in the annulus would decrease the HCE performance (see Sections 6.3 and 6.5). The getter is a vacuum loss indicator consisting of barium, which turns white when exposed to oxygen Solar field Solar superheater Steam turbine Figure 1.2 Process flow schematic of a largescale parabolic trough solar power plant with thermal storage capability. (source: Flabeg Solar International) The bellows provide a glasstometal seal and allow thermal expansion between the metal absorber and glass envelope. The bellows also allow the absorber to protrude beyond the glass envelope so that HCE's can be butt welded together to form a continuous receiver. Furthermore, the space between bellows provides a place where the HCE support brackets can be attached (see Figure 2.6 in Section 2.2). For years, a combination of operating problems, collector cost, and low oil prices has restricted the growth of CSP [Duffie and Beckman 1991 ]. With recent improvements in materials, optics, structures, and controls along with a renewed awareness of the importance of cleaner energy sources CSP has become a more viable option for large scale electricity generation. Leading the technology has been parabolic trough solar 4
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technology, which has been the most proven and lowest cost largescale CSP technology available today [Price 2002]. Figure 1.3 Parabolic trough solar collector assembly (SCA) located at a solar research test facility in Spain. (source: Plataforma Solar de Almeria) 5
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II 1. Bellow 4. Getter 2. Glass Tube (Envelope) 5. Getter Bridge 3. Absorber Tube (Pipe) Figure 1.4 Schematic of a heat collector element (HCE). (source: Solei Solar Systems Ltd.) 1.2 Motivation Early on in the parabolic trough technology development, inefficient HCE' s were one of the principle sources of poor SEGS performance [Price 2002]. Therefore, a priority was placed on improving the HCE. Part of this priority included designing a software model to evaluate HCE performance, which could be used to evaluate new and existing HCE designs. This effort was originally undertaken in the early 1990's and resulted in a version of a software model that was later upgraded. The software proved useful and played a part in HCE improvements. And, the HCE improvements have proven to be the primary reasons for increases to the SEGS plants performance [Price 2002].However, there is still room for additional HCE improvements, and the HCE performance software used has proven to be problematic. The first version of the performance model was developed by Virtus Energy Research Associates in 1992 and written in Microsoft QuickBasic [Cohen, et al. 1999]. It (along with the later version and this current version) was based on a methodology proposed by Sandia National Laboratories (SNL) [Final Report . 1993]. Because QuickBasic had become obsolete, Sandia National Laboratories developed a second version in 1999 written in Microsoft Excel Visual Basic. The second version improved algorithms and the userinterface. However, it used a numerical solution technique that 6
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often could not converge on a solution and, due to simplifications in the heat transfer model, could not model many of the desired receiver configurations. In conjunction with an expanded R&D effort to develop higher performance parabolic trough receivers, the National Renewable Energy Laboratory (NREL) funded by the U.S. Department of Energy (DOE) decided an improved HCE performance model was needed, which will be used to meet the analysis needs of the expanded parabolic trough R&D program. This thesis work, sponsored by NREL, consists of the development and documentation of this improved HCE performance model. The new HCE performance model implemented in EES improves the heat transfer analysis, improves the versatility and speed of computation, provides additional model detail (twodimensional energy balance model, HCE support bracket losses, pressure losses, etc .. ), improves the model robustness (valid for larger ranges of HTF flow properties, imbedded warning messages if correlations or HTF properties are used out of range of validity), and improves the modeling input and output capabilities. Furthermore, the model was developed independently from the previous two models so it validates the heat transfer methodology originally proposed by SNL and all the changes to the original methodology (more detailed Nusselt Number correlations, HCE support bracket losses, twodimensional model etc .. ). Finally, the new model has been developed in a more powerful programming environment that is more amendable to model changes and improvements. This new HCE performance model is described in this report and, as will be demonstrated, is an accurate development tool for improving the HCE performance. 7
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2. HCE Performance Model The HCE performance model is based on an energy balance about the collector and HCE. The energy balance includes the direct normal solar irradiation incident on the collector, optical losses from both the collector and HCE, thermal losses from the HCE, and the heat gain into the HTF. For short receiver lengths(< 100m) a onedimensional energy balance gives reasonable results; whereas, for longer receiver lengths a two dimensional energy balance becomes necessary. All the equations and relationships used in both the onedimensional and twodimensional HCE performance models are described below. 2.1 OneDimensional Energy Balance Model The onedimensional HCE performance model uses an energy balance between the HTF and the atmosphere, and includes all equations and correlations necessary to predict the terms in the energy balance, of which depend on the collector type, HCE condition, optical properties, and ambient conditions. Figure 2.1 a shows the onedimensional steadystate energy balance for a cross section of an HCE, with and without the glass envelope intact, and Figure 2.1 b shows the thermal resistance model and subscript definitions. For clarity, the incoming solar energy and optical losses have been left out of the resistance model. The effective incoming solar energy is the energy absorbed by the glass envelope ( and absorber selective coating ( q;soiAbs ). Some of the energy that gets absorbed into the selective coating is conducted through the absorber ( and transferred to the HTF by convection ( q;zconv) while remaining energy is transmitted back to the glass envelope by convection ( q;4conv) and radiation ( q;4rad) and lost through the HCE support bracket through conduction ( q;ond,bracket ). The energy from the radiation and convection then passes through the glass envelope by conduction ( q;scond) and along with the energy absorbed by the glass envelope ( ) is lost to the environment by convection ( q;6conv) and radiation ( q;7rad ). If the glass envelope is missing, the heat loss from the absorber is lost directly to the environment. Note that the model assumes all temperatures, heat fluxes, and thermodynamic properties are uniform around the circumference of the HCE. Also note all flux directions shown in Figure 2.1 a are positive. With the help of Figure 2.1, the energy balance equations are determined by conservation of energy at each surface of the HCE crosssection, both with and without the glass envelope intact. 8
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with the glass envelope: I I q 12conv = q 23cond ., ., ., q3So/Abs = q34conv + q34rad + q23cond + qcond,bracket I I I q34conv + q34rad = q45cond I I I I q45cond + q5So/Abs = q56com + q51rud ' ' q HeaiUJSS = q 56conv + q 51 rad + q cond,bracker without the glass envelope: I I q12conv = q23cond I I I I I q3So/Abs = q36com + q31rad + q23cond + qcond,hracket I I I I q Heat Loss = q 36com + q 37 rud + q cond .bracket (2.la) (2.1 b) (2.lc) (2.ld) (2.le) (2.2a) (2.2b) (2.2c) Note that in the case without the glass envelope Equations (2.lc) and (2.ld) drop out, and the subscripts for the convection and radiation from the absorber change to 6 and 7, respectively, since the heat loss from the absorber outer surface escapes directly to the environment instead of through the glass envelope. All the terms in Equations 2.1 and 2.2 are defined in Table 21. Note that dotted variables indicate rates and the prime indicates per unit length of receivera double prime will indicate per unit normal aperture area. The solar absorptance q;So/Ahs and are treated as heat flux terms. This simplifies the solar absorption terms and makes the heat conduction through the absorber pipe and glass envelope linear. In reality, the solar absorption in the glass envelope (semi transparent material) and absorber (opaque, metal material) are volumetric phenomena. However, the majority of the absorption in the absorber occurs very close to the surface (about 6 angstroms) [Ozisik 1973], and although solar absorption occurs throughout the thickness of the glass envelope, the absorptance is relatively small (a= 0.02). Therefore, any error in treating solar absorption as a surface phenomenon should be relatively small. 9
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a) Onedimensional energy balance With Glass Envelope Without Glass Envelope b) Thermal resistance model conduction (HCE support bracket) I radiation radiation convection conduction conduction ( ) convection convectiOn (I) heat transfer fluid (2) absorber inner surface (3) absorber outer surface ( 4) glass envelope inner surface (5) glass envelope outer surface (6) surrounding air (7) sky Figure 2.1 a) Onedimensional steadystate energy balance and b) thermal resistance model for a crosssection of an HCE 10
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Table 21 Heat Flux Definitions Heat Flux Heat Heat Transfer Path (W/m)* Transfer From To Mode convection inner absorber pipe surface heat transfer fluid ql2conv conduction outer absorber pipe surface inner absorber pipe surface q23cond solar irradiation incident solar irradiation outer absorber pipe surface q3So/Abs absorption convection outer absorber pipe surface inner glass envelope surface q34conv radiation outer absorber pipe surface inner glass envelope surface q34rad conduction inner glass envelope surface outer glass envelope surface q45cond solar irradiation incident solar irradiation outer glass envelope surface q5So/Abs absorption convection outer glass envelope surface ambient q56conv radiation outer glass envelope surface sky q57rad convection outer absorber pipe surface ambient q36conv radiation outer absorber pipe surface sky q37rad conduction outer absorber pipe surface HCE support bracket q cond ,bracket convection ., and heat collecting element ambient and sky qHeatlo.vs radiation Per unit aperture length. 2.1.1 Convection Heat Transfer between the HTF and Absorber From Newton's Law of Cooling, the convection heat transfer from the inside surface of the absorber pipe to the HTF is (2.3) with 11
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where, h. Dz T Tz Nuoz kl = = = = = = HTF convection heat transfer coefficient at T1 (W/m2K) inside diameter of the absorber pipe (m) mean (bulk) temperature of the HTF (0C) inside surface temperature of absorber pipe (0C) Nusselt number based on D2 thennal conductance of the HTF at T 1 (W /mK) (2.4) In the above equations, both T1 and T2 are independent of angular and longitudinal HCE directions, as will be all temperatures and properties in the onedimensional energy balance model. The Nusselt number depends on the type of flow through the HCE. At typical operating conditions, the flow in an HCE is well within the turbulent flow region. However, during offsolar hours or when evaluating the HCE heat losses on a test platfonn, the flow in the HCE may become transitional or laminar due to the viscosity of the HTF at lower temperatures. Therefore, to model the heat losses during all conditions, the model includes conditional statements to determine type of flow. The Nusselt Number used for each flow condition is outlined below. 2.1.1.1 Turbulent and Transitional Flow Cases To model the convective heat transfer from the absorber to the HTF for turbulent and transitional cases (Reynold's number> 2300) the following Nusselt Number correlation developed by Gnielinski is utilized [Gnielinski 1976]. (2.5) with (2.6) where, f2 = friction factor for the inner surface of the absorber pipe 12
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Pr1 = Prandtl number evaluated at the HTF temperature, T 1 Pr2 = Prandtl number evaluated at the absorber inner surface temperature, T 2 Along with being valid for turbulent pipe flow, this Nusselt number correlation accounts for transitional flow states for Reynolds numbers between 2300 and 4000. Furthermore, the correlation adjusts for fluid property variations between the absorber wall temperature and bulk fluid temperature. The correlation is valid for 0.5 < Pr1 < 2000 and 2300< Re02 < 5E6. If used out of this range of validity, the code will display a warning message. With the exception of Pr2 all fluid properties are evaluated at the mean HTF temperature, T 1 Furthermore, the correlation assumes uniform heat flux and temperature, and assumes the absorber has a smooth inner surface. 2.1.1.2 Laminar Flow Case An option to model the flow as laminar is included in all the onedimensional energy balance versions of the HCE heat transfer codes. When the laminar option is chosen and the Reynolds Number is lower than 2300, the Nusselt number will be constant. For pipe flow, the value will be 4.36 [lncropera and DeWitt 1990]. For annulus flow, the value will be dependent on the ratio between the pipe insert diameter and absorber inside diameter, Dpf02 (see Section 2.1.1.3 below). Both pipe and annulus flow values were derived assuming constant heat flux. If the laminar option is not chosen and the Reynolds number is less than 2300 the code will still use the turbulent flow model described above in Section 2.1.1.1, but will display the following warning message ''The result may not be accurate, since 2300 < Re02 < (5E6) does not hold. See Function fq_12conv. Re02 = (value)". 2.1.1.3 Annulus Flow Case One possible use of the HCE performance model will be to evaluate HCE testing conducted on an AZTRAK testing platform located at SNL (see Section 3.1.2). The test platform is essentially a scaled down version of a trough plant. Unfortunately, the test platform does not have the same volumetric pumping capability and collector lengths as a trough plant. Therefore, to simulate field heat transfer characteristics, a pipe is inserted in the center of the HCE during testing [Dudley, et al. 1994]. This decreases the cross sectional flow area of the HTF, increasing the flow velocities, and thus increasing the Reynolds number. To be applicable to this type of HCE testing, the code is setup to model the HTF flow as annulus flow when prompted. The same turbulent pipe flow correlations described in Section 2.1.1.2 can be used for annulus flow by substituting the inside pipe diameter, D2 with the following hydraulic diameter [lncropera and De Witt 1990]. 13
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where, D 4As D D hp 2 p w Acs = flow crosssectional area (m2 ) Pw = wetted perimeter (m) Dp = outside diameter of pipe insert (m) D2 = inner diameter of absorber pipe (m) (2.7) For Laminar flow through an annulus, as stated above, the Nusselt number depends on the ratio Dp102 Table 22 lists Nusselt numbers for various diameter ratios. The table is a modified version of a table for heat flux occurring at both the inner and outer surfaces ofthe annulus [Incropera and DeWitt 1990]. Table 22 Nusselt Number for Laminar Annulus Flow with Uniform Heat Flux DJ02 Nuoh 0 4.364 0.05 4.792 0.10 4.834 0.20 4.833 0.40 4.979 0.60 5.099 0.80 5.24 1.00 5.385 2.1.2 Conduction Heat Transfer through the Absorber Wall Fourier's Law of conduction through a hollow cylinder describes the conduction heat transfer through the absorber wall [Incropera and De Witt 1990]. (2.8) where, 14
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k23 = absorber thermal conductance at the average absorber temperature, (T 2+ T 3)/2 (W /mK) T 2 = absorber inside surface temperature (K) T3 = absorber outside surface temperature (K) D2 = absorber inside diameter (m) D3 = absorber outside diameter (m) In this equation the conduction heat transfer coefficient is constant, and is evaluated at the average temperature between the inner and outer surfaces. Also, the coefficient is dependent on the absorber material type. Currently the HCE performance model includes three stainless steels, 304L, 316L, and 321H, and one copper, B42. If 304L or 316L is chosen, the conduction coefficient is calculated with the following equation. (2.9a) If 321H is chosen, k23 = (0.0153)7'23 +14.775 (2.9b) Both these equations were determined by linearly fitting data from "Alloy Digest SourcebookStainless Steels" [Davis 2000]. If copper is chosen, the conduction coefficient is a constant of 400 W/mK [ASM Handbook Committee 1978]. Note that conductive resistance through the selective coating has been neglected. 2.1.3 Heat Transfer from the Absorber to the Glass Envelope Convection and radiation heat transfer occurs between the absorber and the glass envelope. The convection heat transfer mechanism depends on the annulus pressure [Final Report ... 1993]. At low pressures ( < 1 torr), the heat transfer mechanism is molecular conduction. At higher pressures (> 1 torr), the mechanism is free convection. Radiation heat transfer occurs due to the difference in temperatures between the outer absorber surface and inner glass envelope surface. The radiation heat transfer calculation assumes the glass envelope is opaque to infrared radiation and assumes both surfaces are gray (p = a). 15
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2.1.3.1 Convection Heat Transfer Two heat transfer mechanisms are evaluated to determine the convection heat transfer between the absorber and glass envelope ( ), freemolecular and natural convection [Final Report ... 1993]. In the HCE performance model, both calculations are done and the larger of the two values is chosen. This results in a smooth transition between the two heat transfer modes, as shown in Figure 2.2. Heat Loss Vs. Annulus Pressure i i /i /I / i I I J i _.____.., I I 0.0001 0.001 0.01 0.1 10 100 1000 Annulus Preeaure (torr) Figure 2.2 Chart of heat loss per unit length of receiver as a function of annulus pressure. 2.1.3.1.1 Vacuum in Annulus When the HCE annulus is under vacuum (pressure < I torr), the convection heat transfer between the absorber and glass envelope occurs by freemolecular convection [Ratzel, et al.l979]. 16
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(2.10) with, kstd 4 (D3/2ln(D4/DJ+bA.(D3/D4 +1)) (2.11) b = (2a)(9y5) 2a(y+1) (2.12) A,_ 2.331E(20)(T34 +273.15) (Pa02 ) (2.13) where, D3 = outer absorber surface diameter (m) D4 = inner glass envelope surface diameter (m) h34 = convection heat transfer coefficient for the annulus gas at T 34 (W/m2K) T3 = outer absorber surface temperature (0C) T4 = inner glass envelope surface temperature (0C) ksrd = thennal conductance of the annulus gas at standard temperature and pressure (W /mK) b = interaction coefficient A. = meanfreepath between collisions of a molecule (em) a = accommodation coefficient 'Y = ratio of specific heats for the annulus gas T34 = average temperature, (T 3 + T 4)/2 (0C) Pa = annulus gas pressure (mmHg) 0 = molecular diameter of annulus gas (em) This correlation is valid for Ra04 < (D 4 I (D 4 D3 )) 4 but slightly over estimates the heat transfer for very small pressures ( < 0.0001 torr). The molecular diameters of the gases, o, were obtained from the Gas Encyclopedia [Marshal1976] and are shown in Table 23. Table 23 also compares the convection heat transfer coefficients (h34) and other parameters that are used in the calculation for each of the three gasses currently included in the HCE performance model. 17
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Table 23 Heat Transfer Coefficients and Constants for Each Annulus Gas Annulus kstct b A. 'Y h34 Gas [W/mK] [em] Lcml [W/m2K] Air 0.02551 1.571 88.67 1.39 3.53E8 0.0001115 Hydrogen 0.1769 1.581 191.8 1.398 2.4E8 0.0003551 Arg_on 0.01777 1.886 76.51 1.677 3.8E8 0.00007499 T1ave = 300 C, Insolation= 940 Wlm2 2.1.3.1.2 Pressure in Annulus When the HCE annulus losses vacuum (pressure > 1 torr), the convection heat transfer mechanism between the absorber and glass envelope occurs by natural convection. For this case, Raithby and Holland's correlation for natural convection in an annular space between horizontal cylinders is utilized [Bejan 1995]. 2.425k34 T4 XPr Ram/{0.861 + Pr34 ))'14 q34conv = (1 + {D3 / D 4 )3/5 't4 (2.14) R gp(T3 T4 )D/ avJav (2.15) For an ideal gas P=ITavg (2.16) k34 = thermal conductance of annulus gas at T 34 (W /mK) T3 = outer absorber surface temperature (0C) T4 = inner glass envelope surface temperature (0C) 03 = outer absorber diameter (m) 04 = inner glass envelope diameter (m) Pr34 = Prandtl number Ra03 = Rayleigh number evaluated at 03 = volumetric thermal expansion coefficient (1/K) T34 = average temperature, (T3 + T 4)/2 (0C) 18
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This correlation assumes long, horizontal, concentric cylinders at uniform temperatures, and is valid for Ra04 > (D4 / (D4 D3)) 4 Furthermore, all physical properties are evaluated at the average temperature, (T 3 + T 4)/2. 2.1.3.2 Radiation Heat Transfer The radiation heat transfer between the absorber and glass envelope ( ) is estimated with the following equation [Incropera and De Witt 1990] where, mdJ3 (r3 4 T4 4) q34rad(1/&3 +(1&JD3j(E4D4)) a = StefanBoltzmann constant (W/m2K4 ) D3 = outer absorber diameter (m) D4 = inner glass envelope diameter (m) T3 = outer absorber surface temperature (K) T4 = inner glass envelope surface temperature (K) E 3 = absorber selective coating emissivity f4 = glass envelope emissivity (2.17) Several assumptions were made in the derivation of Equation (2.17). Specifically, the equation assumes a nonparticipating gas in the annulus, gray surfaces, diffuse reflections and irradiation, and long concentric isothermal cylinders. Also, it is assumed that the glass envelope is opaque to infrared radiation. Not all these assumptions are completely accurate. For instance, neither the glass envelope nor the selective coatings are gray. Furthermore, the glass envelope is not completely opaque for the entire thermal radiation spectrum [Touloukian and DeWitt 1972]. However, any errors associated with the assumptions should be relatively small. 2.1.4 Conduction Heat Transfer through the Glass Envelope The conduction heat transfer through the glass envelope uses the same equation as the conduction through the absorber wall described in Section 2.1.2. It is assumed that the antireflective treatment on the inside and outside surfaces of the glass envelope does not introduce thermal resistance, nor have any effect on the glass emissivity. This should be fairly accurate since the treatment is a chemical etching and does not add additional elements to the glass surface [Mahoney 2002]. As in the absorber case, the temperature 19
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distribution is assumed to be linear. Furthermore, the thermal conductance is assumed constantas explained in Section 2.1 with a value of 1.04 (Pyrex glass) [Touloukian and DeWitt 1972]. 2.1.5 Heat Transfer from the Glass Envelope to the Atmosphere The heat transfer from the glass envelope to the atmosphere occurs by convection and radiation. The convection will either be forced or natural, depending on whether there is wind or not. Radiation heat transfer will always occur and will depend on the sky temperature, which in the code is taken as eight degrees Celsius below the ambient temperature. The equations utilized for both convection and radiation heat transfers are listed below. 2.1.5.1 Convection Heat Transfer The convection heat transfer from the glass envelope to the atmosphere ( is the largest source of heat loss, especially if there is a wind. From Newton's Law of cooling where, T5 T6 h56 k56 D5 NuD5 = = = = = = glass envelope outer surface temperature (0C) ambient temperature COC) convection heat transfer coefficient for air at (T 5 T 6)/2 (W/m2K) thermal conductance of air at (T 5 T 6 )/2 (W /mK) glass envelope outer diameter (m) average Nusselt number based on the glass envelope outer diameter (2.18) (2.19) The Nusselt number depends on whether the convection heat transfer is natural (no wind) or forced (with wind). Both cases are described below. 20
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2.1.5.1.1 No Wind Case If there is no wind, the convection heat transfer from the glass envelope to the environment will be by natural convection. For this case, the correlation developed by Churchill and Chu will be utilized to estimate the Nusselt Number [Incropera and De Witt 1990]. where, Raos g as6 Prs6 Vs6 Ts6 { } 2 1/6 N = 0 60 0.387 Ravs Um + n [1 + (0.559/Pr56 )9116 rl P=1 Ts6 = = = = = = = Rayleigh number for air based on the glass envelope outer diameter, Ds gravitational constant (9.81) (rnls2 ) thermal diffusivity for air at T56 (m2/s) volumetric thermal expansion coefficient (ideal gas) (1/K) Prandtl number for air at T 56 kinematic viscosity for air at T56 (m2/s) film temperature (T 5 + T 6 )/2 (K) (2.20) (2.21) (2.22) (2.23) The above correlation is valid for 105 < Ra00 < 1012, and assumes a long isothermal horizontal cylinder. Also, all the fluid properties are determined at the film temperature, (Ts + T6)/2. 21
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2.1.5.1.2 Wind Case If there is wind, the convection heat transfer from the glass envelope to the environment will be forced convection. The Nusselt number in this case is estimated with Zhukauskas' correlation for external forced convection flow normal to an isothermal cylinder [Incropera and DeWitt 1990]. with, and, c 140 0.75 401000 0.51 1000200000 0.26 2000001000000 0.076 n = 0.37, for Pr <=10 n = 0.36, for Pr > 10 (2.24) m 0.4 0.5 0.6 0.7 This correlation is valid for 0.7 < Pr6 < 500, and 1 < Re05 < 106 And, all the fluid properties are evaluated at the atmospheric temperature, T6 except Pr5 which is evaluated at the glass envelope outer surface temperature. 2.1.5.2 Radiation Heat Transfer As mentioned above, the useful incoming solar irradiation is included in the solar absorption tenns (see Section 2.6). Therefore, the radiation transfer between the glass envelope and sky, discussed here, is the radiation transfer due to the temperature difference between the glass envelope and sky. To approximate this radiation transfer, the envelope is assumed to be a small convex gray object in a large blackbody cavity (sky). The net radiation transfer between the glass envelope and sky becomes [Incropera and De Witt 1990] (2.25) 22
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where, cr = StephanBoltzmann constant (5.670E8) (W/m2K4 ) D5 = glass envelope outer diameter (m) e5 = emissivity of the glass envelope outer surface T5 = glass envelope outer surface temperature (K) T7 = effective sky temperature (K) It should be noted that the sky, especially during less than clear conditions, does not act like a blackbody; however, it is common practice to model it as a blackbody and to use an effective sky temperature to compensate for the difference [Duffie and Beckman 1991]. As stated by Duffie and Beckman, "the effective sky temperature accounts for the fact that the atmosphere is not at a uniform temperature and that the atmosphere radiates only in certain wavelength bands." Furthermore, as they stated, "the atmosphere is essentially transparent in the wavelength region from 8 to 14 J.lm, but outside of this 'window' the atmosphere has absorbing bands covering much of the infrared spectrum." Several relations have been proposed to relate the effective sky temperature for clear skies to measured meteorological data; however, to simplify the model, the effective sky temperature is approximated as being 8 C below the ambient temperature. 2.1.6 Solar Irradiation Absorption The optical losses and solar absorption given the direct normal solar irradiation, solar angle, and optical properties of the trough mirrors and HCE components is very difficult to model accurately with a set of equations that can be solved with a software program like EES. Because of this, optical efficiency terms are estimated, and then combined to form an effective optical efficiency, which is then used to determine the optical loss and solar absorption terms. 2.1.6.1 Optical Properties The optical properties used in the HCE performance model were obtained from a combination of sources. Some of the terms used to estimate the effective optical efficiencies were determined by SEGS plant performance modeling completed by NREL. The absorber selective coating and glass envelope optical properties were determined by tests conducted by SNL, and Solei Solar Systems Ltd. of Israel the prime HCE manufacturer. Furthermore, some of the optical terms were evaluated and revised with ray tracing software developed by NREL. Table 24lists some of the terms used to estimate the effective optical efficiencies. The table was generated from data published in a report by NREL [Price 2002], which in tum was based on field tests [Dudley, et al. 1994], and software performance modeling The first three terms e' 1. e' 2 and E' 3 and the last term e' 6 are 23
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strictly estimates. The clean mirror reflectance Pel is a known value, and the two dirt effect approximations E' 4 and E'5 are as recommended by Duffie and Beckman [Duffie and Beckman 1991]. Note that the data in the table is only valid for solar incidence irradiation normal to the collector aperture. An incident angle modifier term is added to account for incident angle losses, which includes trough end shading, changes in reflection and refraction, and selective coating incident angle effects. Table 24 Estimates of Effective Optical Efficiency Terms [Price 2002] E'1 = HCE Shadowing (bellows, shielding, supports) 0.974 E' 2 = Tracking Error 0.994 E'3 =Geometry Error (mirror alignment) 0.98 Pel = Clean Mirror Reflectance 0.935 E'4 =Dirt on Mirrors* reflectivity/l)el E' s = Dirt on HCE (1 + E'4)/2 E'6 =Unaccounted 0.96 reflectivity is a user input (tyJ!ically_ between 0.88 and 0.93) As shown in Table 24, there are terms for collector geometric effects (shadowing, tracking, alignment), mirror and glass envelope transmittance effects (mirror reflectance, and dirt), and a term for unexplained differences between field test data and modeled data. Testing continues to refine all these values and to better understand the optics of the HCE's. In the EES codes for the HCE performance model, the optical efficiency terms can also be manually entered (see Section 3). In addition to the effective optical efficiency terms listed in Table 24, another term is needed for cases when the solar irradiation is not normal to the collector aperture. This term has been given the name "incident angle modifier'' and is a function of the solar incidence angle to the normal of the collector aperture. The equation was determined from HCE testing conducted at SNL [Dudley, et al. 1994]. K = cos(8) + 0.00088480.0000536982 (2.26) Other optical properties include the glass envelope absorptance, emittance, and transmittance; and the selective coating absorptance and emittance. The glass envelope absorptance and emissivity are constants (independent of temperature) and are constant for all selective coating types (a= 0.02, E = 0.0.86). The transmittance and the selective coating properties coincide with the selective coating types and are listed in Table 25. 24
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Note that both the envelope transmittance and the coating absorptance are constants; whereas, the coating emittance is a function of temperature. All the selective coating types listed in Table 25 are included in the EES codes. The "Solei UV AC Cermet avg" selective coating is the reference value used in all the design study and comparison charts shown in this report, unless stated otherwise. Table 25 Optical Properties for Each Selective Coating Selective Coating Envelope Coating Coatin2 Emittance Transmittance Absorptance @ toooc @ 400C Luz Black Chrome 0.935 0.94 0.11 0.27 LuzCermet 0.935 0.92 0.06 0.15 Solei UVAC 0.965 0.96 0.07 0.13 Cermet a Solei UVAC 0.965 0.95 0.08 0.15 Cermetb Solei UVAC 0.965 0.955 0.076 0.14 Cermetavg Solei UVAC 0.97 0.98 0.04 0.10 Cermet Proposed a Solei UVAC 0.97 0.97 0.02 0.07 Cermet Proposed b The emittance equations used in the codes are shown in Table 26, and coincide with the emittance values in Table 25. For all the coating types, the emittance values between the two reference points, 400 C and 100 C, are nearly linear. However, more test data was available for the UV AC (Universal Vacuum Air Collector) Cermets, so that data uses a 2nd order polynomial fit; whereas, the other coating emittance values use linear fits. Also, it should be noted, that the two proposed selective coatings (Solei UV AC Cermet Proposed a and Solei UV AC Cermet Proposed b) were specified by the manufacturer for a single temperature of 400 C; therefore, these functions were approximated with a slope and intercept to resemble the trends of the results for the Cermet tested by SNL. 25
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Table 26 Temperature Dependent Emittance Equations Coatin2 Type Coating. Emittance* Luz Black Chrome 0.0005333 (T + 273.15)0.0856 LuzCermet 0.000327 (T + 273.15)0.065971 Solei UV AC Cermet a + (1.039E4)T + 5.599E2 Solei UV AC Cermet b + (1.376E4)T + 6.966E2 Solei UV AC Cermet avg (1.907E7)T2 + (1.208E4)T + 6.282E2 Solei UV AC Cermet (2.084E4)T + 1.663E2 Proposed a Solei UV AC Cermet (1.666E4)T + 3.375E3 Proposed b All temperatures are in degrees Celsius. 2.1.6.2 Solar Irradiation Absorption in the Glass Envelope As stated earlier, to simplify the model, the solar absorption into the glass envelope is treated as a heat flux (see Section 2.1). Physically this is not true. The solar absorption in the glass envelope is a heat generation phenomenon and is a function of the glass thickness. However, the heat flux assumption introduces minimal error since the solar absorptance coefficient is small for glass, 0.02 [Touloukian and DeWitt 1972], and the glass envelope is relatively thin, 6 mm. Also, as stated earlier, an optical efficiency is estimated to calculate the solar absorption. With this stated, the equation for the solar absorption in the glass envelope becomes with where, q;; = solar irradiation per receiver length (W/m) 1'\nv = effective optical efficiency at the glass envelope CXenv = absorptance of the glass envelope (Pyrex glass) K = incident angle modifier (as defined by Equation (2.26)) 26 (2.27) (2.28)
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All terms in Equation (2.28), except for K, are from Table 24. The solar irradiation term ( q;;) in Equation (2.27) is determined by multiplying the direct normal solar irradiation by the projected normal reflective surface area of the collector (aperture area) and dividing by the receiver length. Note that all terms in both equations are assumed to be independent of temperature. 2.1.6.3 Solar Irradiation Absorption in the Absorber The solar energy absorbed by the absorber occurs very close to the surface; therefore, as stated earlier, it's treated as a heat flux (see Section 2.1). The equation for the solar absorption in the absorber becomes with where, ' q 3So1Abs = q sl/ abs a abs 1J abs = 1J env 'r e11v Ttabs = effective optical efficiency at absorber
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The bracket heat loss is estimated with the following equation [Incropera and DeWitt 1990]. where, hb = average convection coefficient of bracket (W/m2K) Pb = perimeter of bracket (m) kb = conduction coefficient (W/mK) A = minimum crosssectional area of bracket (m2 ) T base = temperature at base of bracket (0C) T 6 = ambient temperature (0C) LHcE = HCE length (m) (2.31) The perimeter of the bracket Pb in Equation (2.31) is the perimeter around the two 1"x I" square tubes (0.2032 m) that run from the absorber attachment bracket to the collector structure (see Figure 2.4). And, the crosssectional area is the crosssectional area of the two connection tabs, 1" x 1/8" (1.613E4 m2), connecting the square tubes to the absorber attachment bracket. These dimensions were chosen because the square tubes are the part of the support brackets that are exposed to convection heat transfer to the environment, and the two connection tabs are the smallest crosssection area near the base of the support bracket (fin) where conduction heat transfer occurs from the absorber pipe. The conduction coefficient (kb) for the HCE support bracket is a constant equal to 48.0 W/mK (plain carbon steel at 600 K). The film coefficient hb in Equation (2.31) depends on the wind speed. If there is no wind(<= 0.1 m/s), the film coefficient is estimated with the same Churchill and Chu correlation described in Section 2.1.5 .1.1 for natural convection from a long isothermal horizontal cylinder. If there is wind(> 0.1 m/s), the film coefficient is estimated with Zhukauskas' correlation described in Section 2.1.5 .1.2. For both cases, two inches is used as the effective diameter of the HCE support brackets and the average isothermal bracket temperature is estimated as (Tbase + T6 ) /3the bracket base temperature plus the ambient temperature, divided by three. This estimate is only based on intuition; however, the calculations gave reasonable results (see Section 5.2). Also, during the comparison with experimental data, the film coefficient was within expected values, 225 w/m2K for free convection and 25250 w/m2K for forced convection [Incropera and DeWitt 1990]. 28
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Figure 2.3 Examples of solar trough receiver support brackets. Figure 2.4 Closeup of receiver support bracket attachment to absorber tube. 2.1.8 No Glass Envelope Case As mentioned in the discussion of the onedimensional energy balance model, the HCE is modeled with and without the glass envelope. Most of the equations discussed so far are for the glass envelope intact case. When the glass envelope is missing, the five energy balance equations, Equation (2.1), collapse down to three (as shown in Section 2.1 ). The equations for and q;Jcond remain unchanged for the two cases. Without the glass envelope, the convection and radiation heat transfer equations for the absorber are calculated with the same equations given in Section 2.1.5. Also, the solar absorption term for the absorber is adjusted to account for the solar flux that is no longer lost with the 29
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glass envelope. In this case Tlabs equals Tlenv as defined above in Section 2.1.6.2, without the 5 term, which accounted for particulate matter on the HCE. 2.2 TwoDimensional Energy Balance Model The twodimensional energy balance model was constructed by dividing the length of the receiver into "N" segments of equal length, with temperature continuity at the bounding surfaces (Figure 2.5). The radial heat fluxes are assumed uniform and normal to the surfaces for each segment and are evaluated at the average temperature between the left and right side of the segment ((Tnght.i+Tieft.i)/2). The longitudinal temperature is assumed to be nearly linear (see Section 6.12) and the conduction coefficient constant. Therefore, the right and left side longitudinal conduction terms cancel out, and only the HTF will transfer energy in the longitudinal direction. With these assumptions, the radial heat transfer terms can be modeled with the onedimensional energy balance described above, and the steadystate energy balance for the receiver can be estimated with the following equation. (2.32) where, .. net heat flux per unit area (W/m2 ) qi = Ai = circumferential area of segment "i" (m2 ) riz = mass flow rate (kg/s) h = enthalpy (Jikg) v = bulk fluid velocity (rnls) In this equation, potential energy is neglected, and mass flow is constant. The kinetic energy is retained due to the thermal expansion of the HTF, especially for long receiver lengths (> 700 m). Furthermore, the velocity will be needed for the pressure drop and local Reynolds number calculations, which are used to determine the flow energy and radial HTF heat convection terms, respectively (see below and Section 2.1 ). For a receiver segment "i" of length M....aperrure, the energy balance becomes (2.33) 30
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The net heat flux (q;) in Equations (2.32) and (2.33) includes solar absorption and heat loss. '"'A ., A ., A qi i = qSolarAbs,i iqHetJil.oss,i i The solar absorption term includes both the absorber (ti;soiAbs,i) and the glass envelope contributions. o/1 A o/ 8L o/ 8L qSolarAbs,i i = q3So/Abs,i aperture + q5So/Abs,i aperture The solar absorption tenns are described in Sections 2.1.6.2 and 2.1.6.3. (2.34) (2.35) The heat loss in Equation (2.34) includes both the radiation and convection heat losses from the glass envelope and the conductive losses through the support brackets . ,. A 8L ., 8L qHeatl.oss,i i = q51rtJJ!,i aperture +q56conv,i aperture +qcond,bracket,tota/,i (2.36) where, q cond ,bracket,lota/,i = n i q cond ,bracket,i (2.37) Again, both the radiation and convection tenns are evaluated with the average longitudinal temperatures for each receiver segment. They are described in Sections 2.1.5 .1 and 2.1.5.2. The conductive heat loss through the bracket is described in Section 2.1.7 and is also evaluated with the average longitudinal temperature for each segment. The parameter n; is the number of brackets attached to the HCE segment "i" and is a function of the segment length D.Laperture Assuming the HlF density is only a function of temperature (incompressible with pressure); the change in enthalpy in Equation (2.33) can be approximated with the following equation. (2.38) where, fl.T; = (T;nlet,i Toutlet,i) and, 31
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fll'; = (P;nlet,ipoutlet,i) The specific heat in Equation (2.38) (Cave,i ) and the density (Pave,i ) are evaluated at the average HTF temperature along the length of the receiver segment. A complete derivation of Equation (2.38) is given in Appendix C. i= 2 3 (N 2) """'"""""""""o"b"""""""""'""""ob"""""o"""""""o"b"""""ooo I I I I I I I I I I I I ............. ..,. .............. ..,. .............. ..,. .......... Lapenure _, A q Heat Loss ,i i (N I) q;o/arAbs,iAil i i niqcondbrackeji N Figure 2.5 Schematic of the twodimensional heat transfer model. 32
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Substituting all the above results into Equation (2.33) gives 0 ( I I I I = q3so1Abs,i + q5so1Abs,i q34rad.i q34conv,i aperture +m[cave,;(T;n,i Tour,;)+M';j Pave,i + (v;.,; v:u,J]ticond,bracket,total,i And, solving for the outlet temperature gives (( I I I I ) T q3so1Abs,i + qSsoiAbs,i q34rad,i q34conv,i apenure,i qcond,bracket,total,i OUI,i ( ) mcave,i (2.39) (2.40) In this equation, the inlet velocity ( V;n,i) is determined from the absorber crosssectional area and volumetric flow rate, both of which are inputs. The remaining velocities are calculated from conservation of mass and continuity at the segment boundaries. VOIII,i = A Pout,i cs (2.41) V;n,(i+i) = Vout,i (2.42) The change in pressure {M'; ) in Equation (2.40) is estimated with an equation to calculate pressure loss in a horizontal pipe with fully developed turbulent flow [Munson, et. al. 1990]. (2.43) Where, f is the Darcy friction factor, and can be estimated for turbulent pipe flow with the following Colebrook equation [Munson, et. al. 1990]. 33
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1 2Lo [Yn2 2.51 J .J1 =g D + Re D2,ave,i .J1 (2.44) Here, E is the equivalent roughness ( 1.5E6 m for drawn pipe), and Re02,ave,i is the Reynolds number calculated at the average axial HTF bulk temperature for each receiver segment. P .v .D2 R ave ,1 ave ,t eD2,ave,i = f.Lave,i (2.45) with, f.Lave,i =dynamic fluid viscosity (Ns/m2 ) With the above equations, the outlet temperature, outlet velocity, pressure drop, heat gain, and heat loss can be determined. If the calculations are done without the glass envelope, then the following substitutions are made. I 0 q5solAbs,i 7 I I q57rad,i 7 q37rad,i I I q56conv,i 7 q36conv,i 2.3 Assumptions and Simplifications Numerous assumptions and simplifications made in the modeling of the HCE performance model are listed in Table 27. Many have already been discussed, but are included for completeness. Some listings in Table 27 warrant further discussion. For instance, the model assumes that the flow is uniform; however, because of the nonuniform solar flux around the circumference of the HCE, the flow will be heated asymmetrically and thus will be nonuniform. To accurately predict the convective heat transfer rate for this type of flow, a computational fluid dynamics model would need to be utilized. The extent of the flow nonuniformity and how much that affects the heat transfer will require further study. For now, this is assumed to be a negligible effect. 34
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Table 27 Assumptions and Simplifications made in the HCE Performance Models Model Component Assumptions and Simplifications T 1 is the bulk temperature. convection heat transfer between Uniform flow. the HTF and absorber (Section 2.1.1) For laminar flow in an annulus, uniform flux was assumed. Linear in radial direction. Negligible conduction in circumferential and conduction heat and longitudinal HCE directions. transfers through the absorber wall and Negligible thermal resistance from glass envelope (Section 2.1.2 and 2.1.3.3) absorber coating and glass envelope antireflection treatment. Constant thermal conductance. Constant convection heat coefficient. convection heat transfer between At low pressures (<0.0001), the heat the absorber and glass envelope (Section transfer may be slightly over estimated. 2.1.3.1) Long, horizontal, concentric cylinders at uniform temperatures. Annulus gas is nonparticipating. Both surfaces are gray. radiation heat transfer between the Diffuse irradiation and reflections. absorber and glass envelope (Section Surfaces are formed from long concentric 2.1.3.2) isothermal cylinders. Glass envelope is opaque to radiation in the infrared range. convection heat transfer between Wind direction is normal to the axis of the HCE. the glass envelope and atmosphere (Section 2.1.4.1) Long isothermal horizontal cylinders. 35
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Table 27 (cont.) Model Component Assumptions and Simplifications Effective sky temperature is eight degrees below the ambient temperature. radiation heat transfer between Small convex gray object in a large the glass envelope and sky (Section blackbody cavity. 2.1.4.2) Collector has a 5 % effect on radiation leaving glassenvelope outer surface. Uniform properties. Negligible degradation with time. Antireflection treatment has negligible affect on glass envelope emittance. optical properties (Section 2.1.6.1) Incident angle modifier is the same for each HCE and each collector type. Optical properties don't vary from HCE to HCE. \ Optical properties are independent of temperature, except for the selective coating emissivity. tl;soLAbs and (Section 2.1.6.2 and Can be treated as heat fluxes. 2.1.6.3) Uniform along HCE circumference and q;; (Section 2.1.5.2) length. Neglected HCE and bracket shadowing. 36
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Table 27 (cont.) Model Component Assumptions and Simplifications Estimated as an infmite fin. Wind is normal to the bracket axis. Convection and conduction coefficients are constant. Conduction crosssectional area is at the two 1 "x l/8"connection tabs from the square tubes to the absorber connection q;ond.bracket (Section 2.1.5) bracket. Convection perimeter is the perimeter of the two 1" x 1" square tubes. Convection coefficient is estimated by treating the bracket as a long horizontal isothermal cylinderwith a 2" diameter. Base temperature is estimated as (T 3 10) and average temperature is estimated as (T base + T 6)/3. Minimal interpolation and extrapolation errors. thermalphysical property data HTF data is based on average test data at saturation pressures. The HTF thermalphysical properties could change over time. 37
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Table 27 (cant) Model Component Assumptions and Simplifications Temperature continuity between receiver segment lengths. Heat transfer analysis for each receiver segment assumes a onedimensional model evaluated at the average temperatures along the length of the segment. HTF density is only a function of temperature. twodimensional model (Section 2.2 and Appendix) Constant specific heat for each segment. Absorber pipe inner surface is smooth. Conduction in the longitudinal direction is negligible. All heat fluxes are normal to the surfaces. Constant mass flow. Negligible change in potential energy. Heat losses through cross piping are not included. HCE endlosses from shielding and solar incident angle are not included. general Shadowing from adjacent troughs is neglected. All heat fluxes, optical properties, thermodynamic properties, and temperatures are uniform around circumference and length of HCE segments. 38
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Another effect of the nonuniform solar flux would be nonuniform temperature profiles around the circumference. The profiles would be nonlinear with the maximum temperatures closest to the collector and the minimum temperatures on the opposite side of the HCE, which would not receive any concentrated solar at all. The error associated with assuming uniform circumferential temperatures requires further study; however, assuming uniformity in the flow and temperature profiles should cause the heat fluxes to be overestimated and not underestimated, if there is much difference at all. The model neglects the radiation heat transfer influence from the collector, ground, and surrounding troughs. A simply radiation zonal analysis was conducted to determine a first approximation to this error (see Appendix D). The results showed that neglecting these influences could add an error of 5 to 10 % to the radiation heat transfer from the glass envelope. However, since the error results in the radiation heat transfer being over predicted, it was decided to leave the simplification in place. This was justified because the radiation loss is relatively small compared to the convective loss, and since the model typically under predicts losses (see Section 5). Many of the correlations in the model are based on a uniform temperature in the longitudinal direction. However, because the heat gain per unit length is going to decrease as the HTF temperature increases, and because the radiation heat loss is nonlinear, the true temperature profile will be nonlinear (see Section 6.12). Assuming a uniform temperature or using a linear averaged temperature may over predict the heat gain and under predict the heat loss; however, assuming uniform temperature profiles allows all the heat fluxes to be treated as onedimensional and thus significantly simplifies the model. The film coefficients used to estimate forced convection from the HCE and HCE support brackets are based on a correlation that assumes the wind acts normal to the axis. In practice, the wind will be very turbulent and nonuniform in both magnitude and direction throughout a SEGS plant. Therefore, modeling the wind as normal to axis of the HCE and support bracket should result in the worstcase scenario for forced convection heat loss, and would still answer some questions a designer may have about the effect of heat loss due to wind on an HCE. As shown in Section 6.4, when the annulus between the absorber and glass envelope is under vacuum, the heat losses are fairly insensitive to wind speed. As mentioned earlier, the optical properties are estimates based on experimental data and software models (see Section 2.1.6.1). Unfortunately, the testing has been limited, and the variation of the optical properties is not very well known. Tests have shown, however, that there is some variation, even over a single HCE. Therefore, the assumption in the HCE performance model that the optical properties are uniform may not be valid. Furthermore, in the model, the absorptance terms and glass envelope transmittance and emittance are assumed to be independent of temperature. This is also known not to be true; although, it is assumed there dependence on temperature is weak. Other optical property assumptions made in the model include the incident angle modifier term (K) is the same for each HCE and collector type, and that the selective coating emissivities follow the experimentally determined temperature functions. As mentioned earlier, the modifier is based on one set of test data conducted on a UV AC HCE on a LS2 type collector, and most likely is different for different HCE and collector 39
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types. The selective coating emittance functions were determined from experimental measurements on HCE's at temperatures lower than normal HCE SEGS operating temperatures [Dudley, et al. 1994]. Therefore, the emissivity functions may not be accurate at elevated temperatures (The error, if any, associated with this is not completely known. Additional optical testing is planned to answer this question.). The heat transfer model assumes q;; is uniform both around the circumference (see Section 2.1) and along the length of the HCE. The actual solar flux pattern on the HCE will depend on the collector geometry, alignment errors, tracking errors, and any optical aberrations in the mirrors. The true solar flux profile around the circumference will be similar to an asymmetric normal distribution with the maximum at the point closest to the collector and the minimum located on the HCE side opposite the collector1 The profile along the length of the HCE will include hot points where the flux overlaps due to mirror misalignments and aberrations. The influence of the "true" solar flux profile still requires more study to better understand the loss in performance due to these effects. As one can see by the number of assumptions associated with q;ond,bracket, the calculation of the conduction losses through the HCE support brackets is a rough approximation. For instance, both the bracket base temperature and the bracket average temperature are based on calculated guesses. However, the estimated bracket film coefficient and resulting losses are within expected values2 to 25 W/m2K for free convection and 25 to 250 W/m2K for forced convection [lncropera and DeWitt 1990], and the comparisons with the KJC testloop data revealed the bracket losses to contribute 1 to 4% of the total HCE thermal losses, depending on the ambient conditions and HTF temperature (see Section 5.2). Thermalphysical property data is based on tables in brochures provided by the manufacturer (see Lookup Table References in Appendix A). However, the manufacturer has warned that there could be variation in properties from batch to batch, and that properties do change over time, especially after numerous thermalcycles and mechanical agitation. Furthermore, the thermalphysical property data is based on experiments conducted at saturation pressure. The actual pressures will be higher, depending on the pumping requirements of a particular SEGS plant on a particular day. Furthermore, the EES program interpolates and extrapolates the thermalphysical data from lookup tables. Nonetheless, errors associated with all these HTF property factors should only have a small influence on the data (see Section 6.10), and only be a factor when using the HCE performance model to compare with actual field data, whose HTF properties could be a little different then the data in the code. A few general assumptions warrant further explanation. The model does not include losses through crossover piping. In an actual SEGS plant, as shown in Figure 1.1, the solar field can consist of numerous rows of collectors, and can cover many acres of 1 Thomas and Guven provide good examples of the flux distribution around the circumference of the absorber based on collector mirror optical errors [Thomas and Guven 1994]. 40
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land. The actual lengths of crossover piping can become very large, and how well the piping is insulated will vary; therefore crossover piping can result in a fairly significant source of heat loss from the HTF. The model does not account for any of these losses. In addition, in a SEGS plant one row of troughs can partially shade another during morning and late afternoon operations. Also, during the mornings and afternoons, the troughs at the end of rows will experience some end shadowing. These factors are also not accounted for in the model. However, like the HTF property variations, the crossover piping losses, trough to trough shading, and end losses only become significant when using the model to evaluate actual SEGS data. 2.4 Model Limitations and Suggested Improvements The HCE performance model described above has numerous limitations. For instance, because the model neglects the nonuniformity in the solar insolation around the circumference and length of the HCE, these effects cannot be evaluated. This also means that asymmetric design changes cannot be evaluated such as adding a reflective coating to part of the inside surface of the glass envelope to reflect back to the absorber some of the concentrated solar flux that misses the absorber and to reduce some of the absorber thermal radiation loss2 The HCE performance model simplifies other analysis, which limits the amount of information that can be gained. For instance, the model simplifies the heat transfer analysis between the absorber and HTF. This prevents using the model for evaluating HTF heat transfer enhancement devices such as helical coil and twisted tape inserts, or machined longitudinal fins and helical ribs on the inside surface of the absorber pipe3 Also, as mentioned in Section 2.1.5.1, the wind effects are simplified. The wind is modeled as blowing normal to the receiver axis with no obstructions, so the model is not much help in evaluating actual wind losses that may occur as the wind blows from all directions and around adjacent SCA's. Furthermore, the model neglects the receiver radiation heat loss effects from the collector (see Appendix D), ground, and surrounding SCA's, and assumes an effective sky temperature for the radiation heat transfer loss (see Section 2.1.5.2), so studies ofthese effects also cannot be conducted with this model. The HCE performance model also does not calculate location or time dependent parameters, or initial guesses or parameter bounds, so these values have to be manually changed when needed. One time and location dependent parameter is the solar incident angle. For the evaluation of the KJC testloop data, the solar incident angle was calculated with a separate program and included as an input in the parameter table (see Sections 2.1.6.1, 3.2.2, and 5.2). Having to manually input the solar incident angle makes it 2 See Duke Solar Energy's technical report Subtask 1.2 Final Report, A NonImaging Secondary Reflector for Parabolic Trough Concentrators for an example of such a study. 3 See samples on pages 504 and 505 in Incropera's and DeWitt's Fundamentals of Heat and Mass Transfer, 3rd ed. 41
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difficult to conduct studies on changing the tilt of the CSA' s or changing the outer surface properties of the absorber. Also, since the model doesn't calculate initial guesses or parameter bounds, these values have to be manually input into the EES variable information window. And for some design changes, the variable information window may have to be updated to get the model to converge. Changing the guesses and bounds can become tedious especially when dealing with a long receiver length with a relatively small segment step size (resulting in large parameter arrays). The HCE performance model also does not do optimization or exergy analysis, both of which would help identify HCE performance limitations. However, an incremental optimization parameter study, similar to Section 6.11 for the glass envelope outer diameter, can be conducted. As shown in Section 2, the HCE performance model is based on first law analysis. This type of analysis provides values for collector efficiency, heat gain, and heat losses; however, it does not provide information on what the limitations are on improving these values. Exergy analysis not only could provide second law efficiencies to identify improvement limitations, but could also help identify collector and HCE components that have the most room for improvement. Or, as stated by Bejan, "With exergy analysis a designer can better focus effort so that losses are effectively pinpointed and reduced" [Bejan ]. The HCE performance model can be improved, if deemed necessary, to eliminate or reduce some of the model limitations just mentioned. For instance, the angular direction of the HCE crosssection could be modeled in discreet segments, similar to the two dimensional model described in Section 2.2. The solar flux for each segment could be approximated with a weighted average of the expected profile4 at the segment location. This would allow some analysis of the influence of the nonuniformity of the solar insolation around the HCE circumference. It would be best, however, to make this modification to the current onedimensional version of the HCE performance model and not the twodimensional, since a threedimensional model may tend to have convergence problems and require long iteration times. Additional meteorological data, date, time, and location inputs could be added to the HCE performance model to give a better representation of actual field test data results. By adding wind direction, for example, an effective wind speed could be approximated by using the component of the wind vector that is normal to the receiver axis in the forced convection calculations. Also, knowing additional meteorological data will allow a calculation for a more accurate approximation of the effective sky temperature5 And with the date, time, and location inputs the solar incident angle could be calculated instead of inputted (see Section 5.2). 4 The expected profile can be estimated from previous results listed in the literature (such as the results discussed by Thomas and Guven [Thomas and Guven 1994]) or from predictions with Ray Tracing techniques. 5 Duffie and Beckman list several references for relations to estimate an effective sky temperature based on different meteorological data [Duffie and Beckman 1991]. 42
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Other improvements could include adding addition logic to smooth the transition between the turbulent and laminar models and adding a manual input for the receiver length. Currently, if the laminar selection is chosen, the model switches to the laminar Nusselt Number when the Reynolds number drops below 2300. This will cause a discontinuity in the HTF convection calculation. Additional logic could be added to smooth out this transition, similar to the logic that was used for the convection heat transfer from the absorber to the glass envelope. The receiver length is currently dependent on the test type and collector type (see Table 34). To manually enter a receiver length additional logic would need to be added along with a "userdefined" entry similar to the "userdefined" option for the absorber selective coating option in the two dimensional design version of the code (see Section 3.2.1). Additional model improves could also include adding temperature dependent optical properties, changing the solar absorption terms to heat generation terms, and adding exergy analysis. Currently, as discussed in Section 2.1.6.1, the absorptance terms are independent of temperature, and the emissivities were detennined at temperatures lower than the HCE will see during normal operation. Once additional testing has been completed, improved temperature dependent functions may be detennined. If so, then these updated properties can easily be added to the HCE performance models. As mentioned in Section 2, the solar absorption is actually a heat generation phenomena. This is especially true for the glass envelope, since the heat absorption occurs throughout its volume. The model could be changed to incorporate this effect; however, the thermal conductance would also need to reflect this change. Finally, an internal procedure or external procedure (written in another software code such as DynamicC) could be utilized to add exergy analysis to the HCE performance model. This would allow component exergy generations terms, and an overall second law efficiency to be outputted, to give a better indication of the availability for HCE performance improvement and to help prioritize design changes to improve trough performance. 43
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3. EES Codes The HCE performance model described above has been coded into Engineering Equation Solver (EES). The basic function of EES is solving algebraic equations. EES is unique from other software because it automatically identifies all unknowns and groups the equations for the most efficient solution. Once a solution is found, the solution to all the unknowns can be viewed. This includes solutions to arrays. EES also supports user defined procedures and functions, similar to FORTRAN, and provides built in mathematical and thermalphysical property functions. Furthermore, EES supports user generated property Lookup Tables, and Parametric Tables. The Lookup Tables provide an easy means for adding user defined thermalphysical properties, or any other data needed in the equations in the code. The Parametric Tables are similar to spreadsheets and are convenient for conducting parametric studies, for instance, heat losses as a function of HTF inlet temperature. EES also has a diagram window, which can be used for easy selection of input variables and can support simple drawings, such as a schematic of a thermodynamic flow cycle. EES can also solve differential and complex equations, and supports optimization, linear and nonlinear regression, uncertainty propagation, and generates user defined plots. It can also be integrated with external functions and procedures written in a highlevel language such as PASCAL, C, or FORTRAN. A complete EES user manual, provided by FChart Software, can be downloaded from the web site http://fchart.com/. [Klein 2002] Four versions of the EES code were written for solving the HCE performance model. Two of the versions include the onedimensional energy balance model and two include the twodimensional model. Each can be used to evaluate and refine optical properties and HCE design parameters. In addition, each version is tailored for a different task. The version titled the "Design Study Version" is best suited for evaluating HCE design changes, such as, evaluating a proposed new selective coating or a new envelope material. It can also be used to evaluate the effects of damage to an HCE, like lost vacuum, or missing glass envelope. Another version titled the "AZTRAK Test Data Version" was written specifically for evaluating the data from the AZTRAK test platform at SNL. This version is compatible with the AZTRAK and weather data output files and calculates the resulting heat loss and efficiency based on the inputted weather and HTF flow properties. In this version the energy absorbed in the glass envelope is included as part of the optical loss and not the heat loss. This makes it possible to compare with the heat loss as it is reported from the testingthe thermal energy leaving the absorber, not the glass envelope. The results from this version can be used to evaluate the AZTRAK test data; thus, used as a tool to better explain the resulting heat losses and efficiencies. A version titled "KJC TestLoop Version" can be used to evaluate the data from two rows of collectors (testloop) at a SEGS plant located in Kramer Junction, California and operated by KJCOC. This version, like the AZTRACK test data version, is compatible with the field test data and weather data outputs (type, units, etc.), and can be used to help 44
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understand the test data results. Lastly, a twodimensional version titled ''Two Dimensional Design Study Version" was written to evaluate the effects of the pressure drop and RTF temperature changes along the length of the RCE. This version is valuable for evaluating effects associated with receiver lengths, and predicting the outlet temperature and velocity based on a given set of inlet data. These last three versions (AZfRAK Test Data Version, KJC Testloop Version, and TwoDimensional Design Study Version) can also be used to evaluate effects of design changes and RCE conditions with actual field criteria (wind speed, ambient temperatures, solar incident angles, solar insolation, flow rates, etc.). A brief description of each version of the codes is discussed below, and the two design study versions are provided in Appendices E and F. 3.1 OneDimensional Heat TransferEES Codes The EES codes titled "OneDimensional Design Study" and "AZTRAK Test Data" only include the onedimensional heat transfer analysis. These codes can be used to evaluate the RCE efficiencies for short receivers lengths(< 500 m, see Section 4), or when the effects of receiver length are not needed, for instance, when evaluating relative changes due to different selective coating properties. In the case of the AZTRAK test data, receiver lengths are limited by the size of the rotating platform, which is only about ten meters; therefore, RTF properties have little variation along the length of the receiver and a twodimensional model makes little difference in comparison to the onedimensional model. 3.1.1 OneDimensional Design Study Version The onedimensional design study version of the EES program is useful for evaluating relative design and parameter effects on the RCE performance (See Section 6). For instance, it can also be used for evaluating existing or proposed selective coatings by selecting or manually inputting the optical properties for the case in study. Also, this version can be used to evaluate the effects of damage to the RCE's, such as lost vacuum or missing glass envelope. 3.1.1.1 Lookup Tables As stated above, EES supports user generated Lookup Tables. The design study version, as well as the other versions, has Lookup tables for various heat transfer fluids (RTF's) and for argon gas. The RTF's tables include Therminol VPl, Syltherm 800, Xceltherm 600, Water, Salt (60% NaN03, 40% KN03), and Ritec XL. Part of the Therminol VPl Lookup Table is shown as Table 31. As shown, the properties include temperature (0C), density (kglm\ vapor pressure (Pa), specific heat (JikgK), dynamic 45
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viscosity (kg/ms), and thennal conductance (W/mK). All the data in the HTF Tables are based on laboratory tests conducted by the manufacturers and were taken at the HTF saturation pressure. Therefore, small variances in the properties can be expected from sample to sample and due to pressures effects. However, temperature has the strongest influence on the properties. If the program evaluates properties outside the recommended HTF temperature range, a warning message will appear. Additional HTF' s can easily be added by inserting a Lookup table with the appropriate properties and making a few changes to the code. Table 31 Part of the Lookup Table for Therminol VP1 .. ;:, : __ ::,_ :_; .. .. . _: ..: 172 938 9.97 1970 0.000486 0.118 182 929 13.8 2000 0.00045 0.1165 192 920 18.9 2030 0.000418 0.115 'Riu120::. 202 911 25.3 2050 0.000389 0.1135 Ruh.2l' 212 902 33.5 2080 0.000364 0.1119 222 893 43.7 2110 0.000341 0.1103 Argon gas is included as a Lookup Table for evaluating the effects of argon in the HCE annulus space between the absorber and the glass envelope (see Section 6.3). Pressurizing this space with argon has been proposed as an option to a vacuum or as a temporary fix if vacuum is loss. The properties in the argon table were compiled for a constant pressure of 1 00kPa. The properties of the other two annulus gases (air and hydrogen) are already provided in the EES program as embedded thennalphysical property tables. For more infonnation on the HTF fluids or argon data see the references listed in Appendix A. 3.1.1.2 Diagram Window Figure 3.1 shows the Diagram Window used in the design study version of the EES HCE heat transfer code. The window provides the ability to manually input data from pulldown menus and the keypad. As shown, the diagram window is divided into seven 46
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sections: Ambient Conditions, HCE and Collector Properties, Optical Properties, Modeling Properties, Heat Transfer Fluid Properties, "UserDefined" Absorber Selective Coating Properties, and "UserDefined" Collector Type Properties. The Ambient Conditions section includes direct normal incident solar irradiation, wind speed, ambient temperature, and solar incident angle. All these inputs can be typed in by right clicking the curser on the input boxes. Be aware that none of the inputs are bounded; typing in an erroneous value will either cause the program to fail or produce erroneous results. !mli!il!!l IOS!!!ditis!!ll Mocleli!Jq ProDertiel Orecl N:H'nal hcdent SOilr tradialion = rwlm2 ] HTF Flow Type= @]1111lhl HTF AmuU.Imer Oiarreler = lo.05081Jni Ant>tont T""""'ature = j1q (onfV vali:t lor annuk.e tn'F lbw type) nckJde larmar llow rTDde/1 E) Solor ncdent Angle From Aperture to>lector Type= IL&2 I t Transfer Fl.ri:i Flow Rota= (gpni Absorbe< Material = 1321 H I Haal Transfer AJd = Thermlnol VP1 I Absort>er SeloclrYo Coa!Olg =1r WAC Cermet (SN. teotavg) I Gas il A.nnUus = "!.!U[!1liD!!II" !121!![111[ !i!lll!i:lil!!l10211i!!a Pr!!li!!lrli!ll Anm.U A.bsokl1e Presstxe = )o.oocn) (torr) (Only Vola I At.orber SeloclrYe Coamg = "LaorDollll8d") Gae& Envelope hlact? I Y j Coamg Aboorpl.llnco = QRII!ill ft!!RIIllll too"q= B Solar Weighted Mrror Rot tocllvily = Coatllg ( 0 400 q = @J Total Opti:al = 74.131"' Glaas Envelope Transrritlance = Total(lpti:al Loea llilllenglh = 1229 [Winj "!.!ur!;!ltiDI!I" 102111!<1!!' Iml ft!!ll!l!li!ll (Only Vaii: I Coloctor Type= "LaorOotined'") lilllmtiDf Optictl Elfictore;y Term Aboorber mar Oiarretor = lo.0661(1Tj Shadowng = lo.9741 Osan AEtllecWy = )o.935j Aboorbe< Outer Oiarretor = lni Trackilg Error= )o.994) C*'1 on =)0.963) Gloao Envolopo lmer Oiarreter = lo.t09llni Goornotry = General Glua Envoklpo Outer Oiarretor =lo.ttsllni llrtonH:E=Io98tl Projected Apenuro Wldlh =@] (IT"j Figure 3.1 Diagram window from the Design Study Version of the heat transfer code. 47
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The HCE and Collector Properties section has pulldown menus for selecting collector type, absorber material, absorber selective coating, gas in the annulus, and options for whether or not the glass envelope is intact. Clicking on the arrow next to the selection box and highlighting the desired choice selects the option. The collector type choices are LS2, LS3, and 1ST. The first two choices are standard collector types found in SEGS plants, and the 1ST collector type is a proposed smaller collector design. The optical properties and geometry for each collector type are written into the program and are discussed in Section 2.1.6.1. References for the optical properties are listed in the Appendix B. The absorber material choices include three stainless steels (304L, 316L, 321H), and a copper (B42) (see Section 2.1.2). The absorber selective coating has eight choices, which include Luz Black Chrome and Luz cermet coatings, five Solei UV AC cermet coatings, and a userdefined choice. Two of the five Solei UV AC coatings, 0.07 and 0.10 @400 C, are not found in the SEGS plants, but rather are coating types the manufacturer Solei has proposed. All the other optical properties are based on tests conducted by SANDIA (see Section 2.1.6.1). The Solei UV AC Cermets labeled "SNL test a" and "SNL test b" are from two separate test results from either end of a single HCE that was tested. The Solei UV AC Cermet labeled "SNL test avg" is the average of these two results. The last choice, UserDefined, is used for evaluating coating properties input manually. The remaining input in the HCE and Collector Properties window is the annulus absolute pressure, which is typed in. The "Optical Properties" section has an input box for the trough solar weighted mirror reflectivity, and outputs for optical efficiency and the optical loss. The reflectivity value is an estimated value of the mirror solar reflectance, and is an indication of both mirror quality and cleanliness. The two outputs are provided for convenience when trying to match a certain optical efficiency by adjusting the mirror reflectance. The Modeling Properties section includes pulldown windows for HTF flow type and an option for including a laminar flow model in the analysis. The flow type choices are either pipe flow or annulus flow. If the annulus pipe flow is chosen, then a valid annulus diameter needs to be typed in the box provided. The annulus flow type is included because HCE's are sometimes tested with an inner pipe or plug to help simulate Reynolds numbers that are typically achieved in a SEGS plant (see Section 2.1.1.3). The option for laminar flow is included so that losses associated with cooler HTF temperatures ( < 100 0C) can be evaluated. These temperatures could be seen during extended down times and/or during startups or testing. The Heat Transfer Fluid Properties section has an input box for the HTF flow rate and a pulldown menu for the HTF type. Again, there are no restrictions on the value that can be input for the HTF flow rate. Values outside normal operating ranges could result in erroneous outputs. However, there are warnings embedded into the code that will print out if the flow rate results in Reynolds numbers below the minimum in which the equations are valid. The choices for the HTF type are the same as mentioned above for the Lookup tables. The "UserDefined" Absorber Selective Coating Properties section contains input boxes for the coating optical properties and glass envelope transmittance. This section is 48
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only valid if the "UserDefined" selective coating option has been chosen. If one of the other selective coating options has been chosen, then optical properties written in the code are used. 3.1.1.3 Parametric Table The parametric table for the onedimensional design study version of EES is shown as Table 32. As stated above, the parametric table acts as a spreadsheet. It contains both user inputs and program outputs. For this case the input is the HTF temperature, T1ave (C), defined as the average bulk HTF temperature between the inlet and outlet of the receiver. The outputs include the HCE heat loss per receiver length, (W/m); heat gain into the HTF fluid per receiver length, qHeatGain (W/m); and the collector efficiency, 1lco1 (% ). The efficiency is defined as the direct normal solar insolation at the collector aperture per receiver length divided by the total HTF heat gain per receiver length. If any changes are required, the parametric table can easily be modified. It should be noted that changing the input variables might also require one or more variable guesses and/or bounds to be changed. In order for the program to converge, the variable guesses need to be "reasonably" close. Instructions on modifying the table and variable information can be found in the general EES user manual. Table 32 Parametric Table for the Design Study Version of the Heat Transfer Code > Tlave qHeatl.oss qHeatGain 'Ileal 1..7 [C] [W/m] [W/m] [%] Run 1 100 11.03 3510 73.90 Run 2 150 25.81 3495 73.59 Run 3 200 49.83 3471 73.08 Run4 250 87.1 3434 72.30 Run 5 300 142.8 3378 71.13 Run 6 350 223.5 3298 69.43 Run 7 400 337.3 3184 67.03 3.1.2 AZTRAK Test Data Version The AZTRAK test data version of the EES program was put together to help verify the model and to evaluate the data collected from testing HCE's and collectors on 49
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the AZTRAK rotating test platform at SANDIA National Laboratories (see Section 5.1 ). Information on the AZTRAK testing along with sample test results can be found in the technical report titled "Test Results, SEGS LS2 Solar Collector" [Dudley, et al. 1994]. The AZTRAK version of the program is very similar to the onedimensional design study version discussed above. It is also based on the onedimensional heat transfer model. However, the heat loss for this version of the code only includes the heat losses from the absorber and not the glass envelope. This was done because of the way the heat loss was measured during the testing. The solar insolation absorption into the glass envelope is included as an optical loss. The lookup tables are all the same, and the diagram window is only slightly different. Furthermore, conversion statements were added to the code where appropriate, so that output data from the testing could be inputted directly into the parametric table. 3.1.2.1 Diagram Window The diagram window for the AZTRAK test data version of the EES code is shown in Figure 3.2. All the input options shown are the same as discussed above in the design study version. For this version, some of the inputs have been moved to the parametric table, the option for pipe flow has been removed, and the "UserDefined" selective coating is not included. Ambient Condjtions Solar Incident Angle From Apenure Nonnal (D75) HCE and Collector Properties Collector Type = LS.2 I Absorber Material = :] Absorber Selectiw Coating =I Luz Cermet (SNL te) I Gas in Amulus = Anno.llus Absolute Pressure = lo.oocnl [IDtT) Glass Emelope Intact?!!!!] Modeling Properties Include laminar now model?!!!!) Heat Transfer Fluid Properties Heat Transfer Fluid= Sylthenn 800 I Optjcal Propertiee Solar Welglltad Mirror RelectMty = lo.93371 Total OptiCal Ellic1ency = 73.11 [%] Total Optical Loss 1 Area= 242.9 (W/m2 ) Figure 3.2 Diagram window from the AZTRAK Test Data Version of the heat transfer code. 50
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3.1.2.2 Parametric Table As shown as Table 33, the parametric table for the AZTRAK test data version of the EES program contains six inputs and four outputs. The input data is set up to match the data provided by the actual AZTRAK testing conducting at SANDIA. The data includes: direct normal insolation, Ib (W/m2); wind speed, v6 (m/s); ambient temperature, T6 (0C); inlet bulk HTF temperature, Tin (0C); outlet bulk H1F temperature, Tout (0C); and H1F volumetric flow rate, (Lirnin). The output data includes: the difference between the average HTF and the ambient temperature, T diffAir COC); HCE heat loss per collector aperture area, qheat.Ioss, col, area (W/m2); H1F heat gain, qHeatGain (W/m); and collector efficiency, 'Tlcoi (%).All necessary unit conversions are made in the code. 51
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V\ N > 1..8 Run I Run 2 Run 3 Run4 Run 5 Run 6 Run 7 Run 8 Table 33 Parametric Table from the AZTRAK Test Data Version of the Heat Transfer Code lb v6 T6 Tin Tout VI T diffAir qAbsorbertHeatloss,CoiArea qHeatGain 1lco1 [W/m2 ] [m/s] [C] [C] [C] [Limin] [C] [W/m2 ] [W/m] [%] 933.7 2.6 21.2 102.2 124 47.7 91.9 5.616 3402 72.5 968.2 3.7 22.4 151 173. 3 47.8 139.8 9.389 3510 72 1 982.3 2.5 24.3 197.5 219.5 49.1 184.2 15.18 3533 71.6 909.5 3.3 26.2 250.7 269.4 54.7 233.8 24.51 3218 70.4 937.9 I 28.8 297.8 316.9 55.5 278.6 37.86 3256 69.1 880.6 2.9 27 5 299 317.2 55 6 280.6 38.38 3042 68.7 920.9 2.6 29.5 379.5 398 56.8 359.3 76.71 2998 64 8 903.2 4.2 31.1 355.9 374 56.3 333.9 63.35 3000 66.1
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3.2 TwoDimensional Heat Transfer EES Codes The length of a receiver in an operating field can reach hundreds or thousands of meters. At these lengths the change in flow rate (due to the density change) and pressure drop can have an appreciable effect on the heat transfer model (See Section 4). In fact, the lengths of the receivers on the KJC testloops are almost 800 m long, yet only consist of two rows of collectors. Because of this, and to study the effects of receiver lengths, two versions of the EES heat transfer code include a twodimensional heat transfer model. The two versions titled "TwoDimensional Design Study" and "KJC TestLoop Data" and are described below. 3.2.1 TwoDimensional Design Study Version Like the onedimensional design study version, the twodimensional version can be used to evaluate design and parameter changes. In addition, the twodimensional model can give a better picture of property and temperature changes along the length of the receiver (see Section 6.12). 3.2.1.1 Diagram Window The Diagram Window for the TwoDimensional Design Study Version is shown in Figure 3.3. As can be seen, it is very similar to the OneDimensional Design Version. For this twodimensional case, an input for the number of segments to model along the length of the receiver has been added to the Modeling Properties section. Also, the flow type and the "User Defined" collector type properties are not included; however, both can be added if needed. As shown in Section 4 below, the number of segments to use depends on the total length of the receiver. Too few segments result in larger errors in the calculations; too many segments result in excessive iteration times, with little gain in model accuracy. Also, adding more segments requires the initial guesses and bounds of the additional variables to be updated to the Variable Infonnation window, which can become very time consuming for large number of segments. Reducing the number of segments from a previous run usually doesn't require any modifications to the Variable Infonnation window. Note that the current version of the two dimensional model Dynamic Window does not have an explicit input for receiver length. The receiver length used in the model will depend on both the Collector Type and Test Type inputs. Table 34 summarizes the receiver lengths used in the code. A possible future modification to the program could be to add a manual input for the receiver length. 53
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A!Dblent Cond!t!ona Direct Normal lrcident Solar lm1diation = [W/m 2 ) Wind SJed = @] [mph) Ambient Temporal..., = [C) Solar lr>::ideot Angle Frrtn Apon1111 Normal (G75) = @][degrees] HCE and Collector Propert!ea CollectOI' Typo= LS:i] Absorber Material =I 32tH I Absorber Selectne Coating =r::ls"""'ot"""'ei,...,.U:::V::AC:Ce::rme1 ("'S'""NL"""'III..vg"""'l'"'l Gas in AMulus = AMulus Absolute Press11e = lo.OOOtl [IDIT) Glass Enlo8lope Intact? !!!!] Optical propert!ta Solar w .. t;ned Mlm>r Rettectiwty @:!] Tolal Optical Ellciency [%) Tolal Optical LOSS I Flecer.er Length )W/m) Modeling proRtrt!et Test Type (only used with LS2 collectOI') = KJC To Loop I Total Number of Discrete Segments ( of Nodes 1) = !: Heat Transfer Fluid Properties Heat Transler FILid Flow Rale ]IJHTl) Heal Translar Fluid ITherminot VP1 I "Uttr=Oeftned" Abaorblr Selective Coating Properties (Only Valid il Absorber Selectne Coaling userDefined") Coating Absorptar>::e Coating Emmarce (0 tOO 0C). Coat1ng Eminance (0 400 C). Glass Enlo8lope Transmittarce = Figure 3.3 Diagram window from the TwoDimensional Design Study Version of the heat transfer code. Table 34 Collector and Test Type Receiver Lengths Test Type Receiver Leneth (m) LS2 SNL AZTRAK Platform 8.12 LS2 KJC Testloop 779.52 LS3 N/A 97.44 1ST N/A 2.16 3.2.1.2 Parametric Table The parametric table for the twodimensional model is shown as Table 35. In addition to the heat gain, heat loss, and efficiency as shown with the onedimensional 54
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design study version, the table includes the parameters resulting from the flow effects: HTF outlet temperature, T1 outlet (0C); inlet and outlet velocities, VJiniet and VJoutiet (rnls); and the pressure drop, M> (Pa). The table also includes the total losses per receiver length due to optical effects, qoptLoss (W/m). 55
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VI 0\ Table 35 Parametric Table from the TwoDimensional Design Study Version of the Heat Transfer Code > Tlinlel Tloullel VJinlel VJoullel .1P qHealloss. Apenurelens:lh qOptloss qHcaiGain llcol 1..7 [C] lCJ [m/s] [m/s] [Pa] [W/m] [W/m] [W/m] [%] Run I 125 275.7 2.582 2.998 576151 56.5 1185 3340 72 9 Run 2 ISO 298 6 2 582 3 018 551632 73.42 1185 3324 72.53 Run 3 175 3 2 1.7 2 582 3.044 530224 94 12 1185 3303 72.08 Run4 200 344.8 2 582 3.073 510399 119.2 1185 3278 71.53 RunS 225 368 2 582 3.114 492940 149.4 1185 3248 70.87 Run6 250 391.1 2 582 3.165 477001 185.4 1185 3212 70. 09 Run? 275 414 2.582 3.243 462750 227.8 1185 3169 69 .16
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3.2.2 KJC Testloop Data Version The KJC Testloop Data version of the HCE heat analysis software was put together to verify the software model and to evaluate the KJC TestLoop data. The test data can be copied directly from the KJCOC performance spreadsheets and paste into the parametric tables. The code has been written to convert all inputs into the correct units before running the iterations. 3.2.2.1 Diagram Window An example of the Diagram Window for the KJC TestLoop version is shown in Figure 3.4. The main difference between this Diagram Window and the Diagram Window for the twodimension design study version is that some inputs have been moved to the Parametric Table, and like the AZfRAK version, the "UserDefined" selective coating optioned is not included. The inputs that have been moved to the parametric table include all the ambient condition inputs and the HTF flow rate. In addition, the option to select the test type has been removed. HCE and Collector Properties Collector Type= LS2 I AbsOiber Matenal = 1321 H I AbsOiber Selectiw Coaling= 'ISo1el_lN_A_C_C8_rme_t_(S_r.L_te__a_vg,) I Gas in ArnJus = Amulus AbsOlute Pressure= lo.OOOtl [IDrr) Glass Emetope ntact? [YUJ Modeling Properties Total I'Urtlef of Discrete Segnents (# of Nodes ) = Heat Transfer Fluid Properties Heat Trans!EI' Fh.id = ITherminol VP1 I Optical Properties Solar Weigrted Mirror Reftectiloity = lo.9041 Figure 3.4 Diagram window from the KJC Testloop Data Version of the heat transfer code. 57
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3.2.2.2 Parametric Table As shown as Table 36, the parametric table for the KJC Testloop test data version of the heat transfer code contains eight inputs and nine outputs. The inputs coincide with measured data from the KJC Testloops. The HTF temperatures, TinF and ToutF; HTF flow rate, Vtvolg; and ambient conditions, lb. T6F are all copied from the Excel spreadsheets put together by KJCOC to evaluate the testloop data. The Time input is included to reference the data properly and is not used in any calculations. The solar incident angle, 8, has to be calculated independently. The incident angles used to generate the data in this report were copied from an Excel HCE spreadsheet used to evaluate the KJCOC Performance Data and developed by NREL [Price 2000]. All parameter units in the parametric table are converted to metric within the EES code. The output data in the Parametric Table includes the outlet temperature, T1outletF outlet flow rate, Vtvotg.outtet. (gpm); the pressure drop, M> (Pa); the heat loss through the HCE support brackets, Qcond.bracket (W); the optical loss due to the solar incident angle, Qopt.Ioss.K (W/m); the total optical loss, Qopt.Ioss (W/m); heat loss, QHeatLoss. (W/m); heat gain, QHeatGain (W/m); and the collector efficiency, Ttcot All the energy terms on a unit length basis are based on the total receiver length. The optical loss due to the solar incident angle is determined by reducing the solar insolation by the incident angle modifier given in Section 2.1.6.1. However, the optical loss is determined by reducing the solar insolation by the effective optical efficiency, which includes the incident angle modifier term. 58
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VI \0 > 1..288 . Run 190 Run 191 Run 192 Run 193 Run 194 Run 195 Run 196 : Table 36 Parametric Table from the KJC Testloop Data Version of the Heat Transfer Code Time TinF ToutF VIVoiJ! lb T6F e TloutletF V I volj!,outlet [W/m2 ] [deg] ... [F] [F] [gpm] [F] [mph] [C] [gpm] : : : : : : : : . .. 1550 446. 6 587.7 93.8 446.5 64 24 14.72 36. 28 579 5 102 2 ... 1555 443 563 3 93.4 785.2 64.19 13.16 35.57 677.8 110 5 ... 1600 448.4 543.8 93.5 768.7 64.56 15.6 34.87 680.3 110.5 . 1605 454.5 518.7 93.7 757 64.8 15.22 34 .16 684.5 110.8 ... 1610 456.3 505 9 93.9 732.6 64.8 14.54 33.45 681 110.6 ... 1615 452.7 490.3 93.8 699.6 64 7 12.95 32 74 670.5 109.6 ... 1620 447.1 462.4 93 9 681 5 64 56 13.12 32 02 662 109.2 ... : : : : : : : : : . . 
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0\ 0 > 1 .. 288 : Run 190 Run 191 Run 192 Run 193 Run 194 Run 195 Run 196 : .1P ... [Pa] : . 229596 ... 231911 ... 231283 ... 231057 ... 231403 ... 231264 ... 232594 ... . . Table 36 (Cont.) qcond,braclu:I(W] qopl,loss,K [W/m] : 1078 25.27 1963 28 1940 29.7 1928 29.81 1884 29.32 1820 27.82 1795 27.46 . . qopl,loss qlleall.oss qHealGain llcol [W/m] [W/m] [W/m] [%] : : . 109.3 500.6 966.5 50.0 150.2 844.9 1674 51.8 153.2 793.5 1615 52.3 157 748.5 1567 52.8 155.7 693.1 1494 53.3 149.3 632.7 1405 53.9 143.6 588 1349 54.6 : : . .
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4. Comparison between the One and TwoDimensional Models There are advantages and disadvantages to both the one and twodimensional models. The onedimensional model is less complex; therefore, it is easier to modify, requires less iteration time, and has less trouble converging. The twodimensional model is more complex. It consist of many arrays, requires longer iteration times, and can have problems converging, especially if all the array guess values are not within reasonable bounds and sequence. The code can also be more difficult to modify. However, the two dimensional model provides a higher degree of accuracy then the onedimensional model, especially for long receiver lengths. As shown in Section 2.2, the twodimensional model includes HTF pressure losses, HTF velocity changes, and receiver support bracket conduction losses. As the receiver length increases, each of these effects becomes more significant and the error associated with using the onedimensional model increases. But, at what receiver length does the axial direction effects become significant, and when should the twodimensional model be used over the onedimensional model? These questions are explored a bit below. The process followed in comparing the one and twodimensional models was to start with the KJCOC testloop receiver length of 779.52 m (the KJC TestLoop Data Version of the EES Heat Transfer Code uses the twodimensional model) and determine a step size to use with the twodimensional model that resulted in a "reasonable" level of accuracy for a "reasonable" convergence time. Then once the step size was determined, compare the one and twodimensional models using the same average HTF temperature the average between the given HTF inlet temperature and the resulting outlet temperature determined by the twodimensional model. Table 41 and Figure 4.1 shows the results of the step size exercise. Note that "number of steps" in the first column in Table 41 is the same as the number of discrete segments the receiver is broken up into in the axial direction. It should also be noted that the iteration time is heavily dependent on the initial variable guesses. The closer the initial guesses are to the solution, the shorter the iteration time. However, given the same range of guess values, the iteration time will always increase with decreasing step size (or increasing number of steps). The KJCOC testloop receiver length was chosen since it is used when comparing the field test data with the EES heat transfer model results. Actual receiver lengths can be many times greater. The testloop receiver length, however, does help in determining at what receiver length the axial direction effects become significant, 80 m, as shown in Figure 4.1. The number of steps will depend on the total receiver length. Figure 4.2 shows the heat gain and collector efficiency per receiver length and Figure 4.3 shows the heat loss per receiver length, respectively, for both the one dimensional and twodimensional models. The KJC testloop receiver length, 779.52 m, was used in the twodimensional model. Also, the iteration step size used was 39 m and is 61
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based on segmenting the receiver by ten sections. The HTF temperature used in the one dimensional model is the same average of the inlet and outlet temperatures determined with the twodimensional model. Table 41 Iteration Time for Different Receiver Step Sizes Number of Steps Step Size* Time (m) (sec) 100 7.795 91411.5 50 15.59 13200 20 38.98 11819 10 77.95 311 4 194.9 39 I 779.5 6 *Total length of solar receiver= 779.5 m Heat Loss for Different Step Sizes 250 DNI950W/m2 LS2 Collector Solei UVAC Cermet 200 Therminol VPt t40gpm rL=n9.5m i r1i r50 ,11r 0 125 150 175 200 225 250 275 HTF lnllll Tempenrture ("C) 1.795 m .59 m 038.98 m cn.95 m .9 m n9.5 m I Figure 4.1 Heat loss chart for different receiver length step sizes. 62
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a) Heat Gain Comparlaon Between the One and TwoDimensional Models DNI9SOW / m2 Solei UVAC Cermet LS2 Collector 3350 1T hermino l VP1 140 gpm 3300 !. c ; Cl 1 3250 3200 3150 L = 779 .52 m 10 i ncrements 198.8 222.8 246.8 270.9 295 319 342.95 A.ge HTF Tempemure ('C) I TwoDimensional Model OneDimensional Modell b) Efficiency Compariaon Between the One and TwoDimensional Models 74,, "#. >73 72 !! 71 !=! m 70 69 68 198.8 Figure4.2 DNI950 W/m2 LS2 Collector Solei UVAC Cermet rherminol VP1 140 gpm L = 779.52 m r10 increments 222.8 246.8 270.9 295 319 342.95 A.ge HTF Temperature ('C) !TwoDimensional Model oneDimensional Model i a) Heat gain and b) efficiency charts comparing the one and two dimensional models for different HTF temperatures. 63
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Heat Loss Comparison Between the One and TwoDimensional Models 350 DNI950W/m2 LS2 Collector 300 Solei UVAC Cermet Therminol VP1 140 gpm 250 L = 779.52 m 10 increments e !_200 :! __. 'ii 150 J: 100 50 0 198.8 222.8 246.8 270.9 295 319 342.95 AIIWage HTF TMnperwture ("C) I TwoDimensional Model OneDimensional Model Figure 4.3 Heat loss chart comparing the one and twodimensional models for different HTF temperatures. As shown, the onedimensional model over predicts the heat gain and efficiency and under predicts the heat loss. Specifically, the onedimensional model gives heat gain and efficiency values that are approximately 0.5 % different then the twodimensional model, and heat loss values that are approximately 5 to I 0 % different_ The small differences between the one and twodimensional models for heat gain and efficiency values are due to the fact that the optical losses remain the same between the two models and that the heat losses are relatively small in comparison to the optical losses (see Section 5_2)_ The charts also show that the higher the HTF temperature the larger the difference between the one and twodimensional models. It should also be noted that these differences will continue to increase with increasing receiver lengths, and receiver lengths in SEGS plants are many times longer than the lengths used here. Additional comparisons between the onedimensional and twodimensional models are shown in Figures 6.1 0, 616, and 6_17 in Sections 6.6, 6.9, and 6.10 respectively. 64
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5. Comparison with Experimental Data To verify the accuracy of the heat transfer codes, the EES heat transfer codes were compared with two sets of data from HCE field tests. One set was from tests conducted from June 1992 through January 1993 on the AZTRAK Rotating Test Platform located at SNL in Albuquerque, New Mexico. The second set of data consists of three days of test data from a testloop of collectors in a SEGS plant in Kramer Junction, California. A picture of the AZTRAK rotating test platform is shown in Figure 5.1. It consist of a rotating platform, a twoaxis tracking control system, and all associated pumping equipment and instrumentation to test a segment of a trough collector and receiver. The trough shown is an LS2 type collector segment with two Luz Cermet HCE's of 4.06 m each for a total of 8.12 m of receiver length. All the data used in the comparisons and a detailed explanation of the AZTRAK Rotating Test Platform tests are reported in "Test Results, SEGS LS2 Solar Collector" [Dudley, et at. 1994]. Figure 5.1 AZTRAK rotating test platform located at SNL in Albuquerque, NM. An LS2 type collector module is shown installed on the platform. 65
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The second set of data, from a testloop of collectors in a SEGS plant, includes data for 010201,032201, and 062101. The testloop consists of two rows of collectors containing sixteen LS2 type SCA's in series each with twelve Luz Cermet selective coating HCE's at 4.06 min length for a total receiver length of 779.52 m. The testloop is in one of SEGS plants pictured in Figure 1.1. The testloop was instrumented to record HTF flow rates and HTF inlet and outlet temperatures. There was also instrumentation to record the direct normal solar irradiation, ambient temperature, and wind speed. As will be shown below, when using the same HTF input property data and meteorological data as those from the field tests, the EES heat transfer codes gave results that agreed well with the field test data. 5.1 Comparison with SNL AZTRAK Data The eight charts in Figures 5.2 to 5.6 show the comparison between the EES AZTRAK Test Data Version of the heat transfer code and the 1992 data from the AZTRAK Rotating Platform tests [Dudley, et al. 1994]. The data consisted of two different selective coatings, Luz Cermet, and Luz Black Chrome. For each of these selective coatings, four test conditions were compared: onsun and vacuum in the annulus, onsun and no vacuum in the annulus, offsun and vacuum in the annulus, and offsun and no vacuum in the annulus. The no vacuum condition was created simply by drilling small holes into the annulus space at the end of the HCE's to allow air to fill the annulus space. The AZTRAK offsun tests were conducted after sunset with the collectors pointing upward towards the sky. In addition, wind tests were conducted on the Luz Black Chrome HCE with the glass envelope removed, and this test data was also compared with the EES program results. To simulate the test conditions as close as possible with the EES code, the input data from the tests were copied into the parametric tables and the solar weighted reflectivity was adjusted until the optical efficiency calculated with EES matched the field tests results. The reflectivity values used are shown in Table 51. For convenience, all the Figures from the AZTRAK data comparisons along with general comments about the comparisons are listed in Table 52. As revealed in the figures, the onedimensional heat transfer model compares well with the AZTRAK field test data. All trends are followed, and with a few exceptions, the data from the EES program is within the error bounds of the AZTRAK tests data. However, it appears that the spread between data increases with increasing temperature for the Luz Cermet selective coating case. This could be due to either the changes in optical properties with temperature or possible sagging of the HCE's, causing a slight missalignment between HCE and collector. The optical properties used in the code are based on optical tests at lower temperatures. Therefore, it's possible that the optical property equations given in Section 2.1.6.1 are not correct at elevated temperatures for the Luz Cermet casethe Luz 66
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Black Chrome field test data shows better agreement with the EES data. The HTF properties could also explain some of the differences. As the HTF manufactures state in the information sheets, the thermophysical properties could vary slightly from batch to batch and could also change overtime, especially when exposed to thermal cycling (see Appendix A for references). Some of the extraneous points could also be due to typing or recording errors either in the "Test Results, SEGS LS2 Solar Collector" report [Dudley, et al. 1994], actual test data recording, or in the EES parametric tables. Table 51 Mirror Reflectivity and Optical Efficiency for Each Test Type Solar Weighted Mirror Total Optical Test Type Reflectivity Efficiency (%) Luz Cermet, Vacuum 0.9337 73.1 Luz Cermet, Loss Vacuum 0.9353 73.3 Luz Black Chrome, Vacuum 0.9289 74.1 Luz Black Chrome, Loss 0.9221 73.3 Vacuum Table 52 List of Figures and Comments for the AZTRAK Test Platform Data c ompar1son Figure Description Comments Difference between the EES data and AZTRAK data for the Luz Cermet selective coating case tends to increase with increasing temperature. The Luz Black Chrome selective coating resulted in better agreement All All between the EES data and AZTRAK data then the Luz Cermet selective coating. EES data accurately depicts all trends With a few exceptions, the EES data agrees with the AZTRAK data within the instrument error bounds. 67
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Table 52 (coot) Fi2ure Description Comments 5.2a) Luz Cennet, Efficiency for vacuum Two EES data points lay outside the and loss vacuum cases AZTRAK error bounds. Nine EES data points lay outside the AZTRAK error bounds. 5.2 b) Luz Cennet, Heat Loss for vacuum EES data seems to under predict the and loss vacuum cases with solar heat loss. Shows the least agreement between the EES data and AZTRAK data. Luz Cennet, Heat Loss for vacuum One EES data point lies outside the 5.3 and loss vacuum cases without solar AZTRAK data error bounds. Luz Black Chrome, Efficiency for All EES data points are within the 5.4 a) vacuum and loss vacuum cases AZTRAK data error bounds. with solar Luz Black Chrome, Heat Loss for One EES data point lies outside the 5.4 b) vacuum and loss vacuum cases AZTRAK data error bounds. with solar Luz Black Chrome, Heat Loss for One EES data point lies outside the 5.5 vacuum and loss vacuum cases without solar AZTRAK data error bounds. 5.6a) Luz Cennet, Efficiency trend with wind Model tends to over predict losses with 5.6 b) Luz Cennet, Heat Loss trend with increasing wind speed. wind 68
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a) Efficiency Comparison (Luz Cermet Selectlw Coating, Solar (NIP) 800 to 970 Wlm'i LS2 Collector, Synterm 800 Loss Vacuum 100 200 Av.age Tempemure Abow Ambient ("C) i EES HCE COde SNL AZTRAK Tests I b) Heat loBS Comparison 300 (Luz Cermet Selectlw Coating, Solar (NIP) 800 to 970 Wlm'i 400 I LS.2 Collector, Synterm BOO I I!! I "' l ro I I I 100 200 300 350 400 A.ge Tempemu,. Abow Ambient ("C) I EES HCE COde SNL Tests! Figure 5.2 a) Efficiency and b) heat loss charts comparing the EES HCE Code and SNLAZTRAK test data for Luz Cermet selective coating. 69
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Heat Loss Comparison (Luz Cermet Selectl1111 Coating, No Solar) 120.LS2 Collector. Syltherrn 800 .. I 100 1 50 200 250 300 350 Avwge T8IIIJ*BIUI'II Abowt Ambillnl (C) I EES HCE coae SNL AZTRAK Tests j Figure 5.3 Heat loss comparison chart between the EES HCE Code and SNL AZTRAK test data for the offsun case and Luz Cermet selective coating. As shown in Figure 5.6, the heat transfer model overpredicts losses with wind. This is expected, since in the program the wind direction is modeled as normal to the HCE axis, and the input wind speed is assumed to be the speed at the HCE height In reality, the wind will have many obstructions around the collectors and in general won't be normal to the HCE axis. In addition the wind speed anemometer is located well above the collector and any obstructions. As shown in Figure 5.6, the error associated with the wind loss can be as high as 30 % for the missing glass envelope case; however, as will be shown in Section 6.4, the wind has a smaller effect on the heat loss when the glass envelope is in place, especially with a vacuum between the absorber and glass envelope. However, it may be worth reducing the wind effects in the EES codes on a future revision. 70
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a) Efficiency Comparison (BIck Ctrome Slllectlw Colltlng, SOIIIr (NIP) 740 tD 830 W/m2 ) 801 LS2 Colector, S)lllhenn 800 50 100 150 200 250 300 350 400 450 1 EES HCE Coda SNL AZTRAK Tesrs I b) Heat Lou Comparison Ctrome s.lectlv. Collllng, S0111r (NIP) 740 tD 830 W/m2 ) L$2 Collector, Synl'lenn 800 100 150 200 250 AT1111ponturwAmbient ("C) IEES HCE Code SNL AZTRAKTesls I 300 350 400 Figure 5.4 a) Efficiency and b) heat loss chart comparing the EES HCE Code and SNLAZTRAK test data for Luz Black Chrome selective coating. 71
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Heat Loas Comparison (Black Ctvome Selective Coating, No SOlar) L52 Callecler, Synnenn eoo 150 200 250 300 350 400 Avenge T ompenotu,. Abo .. Ambient ("C) IEES HCE Code SNL AZTRAKTesiS I Figure 5.5 Heat loss comparison chart between the EES HCE Code and SNL AZTRAK test data for the offsun case and Luz Black Chrome selective coating. There are many other possible explanations for the differences between the EES data and AZTRAK data. For instance, other unaccounted optical effects could exist during the testing, such as HCE and mirror alignment, aberration in mirrors, deflections in collector structure during tracking, and controller tracking errors. Furthermore, the solar flux along the receiver axial and circumferential directions is not uniform, due to some or all the effects just mentioned and collector geometry, yet the EES model assumes uniformity along both directionsit may be worth investigating this effect in more detail in future research. Another difference between the test data and model data could be due to the vacuum level in the annulus and presence of hydrogen in the annulus both of which are explored more fully in Sections 6.3 and 6.5. Given all the possible sources of inaccuracies, the onedimensional EES Heat Transfer Model does a good job in modeling the HCE performance for a short segment of collector, such as the size that fits on the AZTRAK Rotating Test Platform. 72
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100 90 80 70 l 60 t' j 50 40 30 20 10 0 0 400 1. I I a) Comparison of Efficiency Trend with Increasing Wind Speed (No Gl8u Envelope, SOlar (NIP) 800 to 980 Ls2 Collector, Luz Cermet Selective Coating, Syltherm 800 50 100 150 200 250 300 Aage TperiiiUre Above Ambient rc) [ EES HCE Code SNL AZTRAK Test[ b) Comparison of Heat Loss Trend with Increasing Wind Speed (No GIIM Envelope, No Solar) LS2 Collector, Luz Cermet Selective Coating, Syltherm 800 1: 300 +' 350 I ____________ C I 150+i ____________ J I I 0 400 0 50 100 150 200 250 300 350 Aage Tpereture AboWI Ambient rc) I EES HCE Code SNL AZTRAK Tests I Figure 5.6 a) Efficiency trend and b) heat loss trend charts comparing the EES HCE Code and SNL AZTRAK test data for varying wind speeds and no glass envelope. 73
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5.2 Comparison with KJC Testloop Data Three days of data were used to compare the KJC TestLoop with the EES model, a winter day, a spring day, and a summer day. The testloop data used in this comparison comprised of LS2 type collectors with Luz Cermet HCE' s. In the EES Heat Transfer Model, it was assumed that all HCE's were in good condition and under vacuumthe testloop had a few bad HCE's, however the number was small in comparison to the total number in the testloop. The KJC TestLoop Data Version of the EES Code consists of a twodimensional model to account for the effects of the long receiver (pressure drop, thermal expansion of HTF, HCE support brackets). The EES data compared well with the KJC TestLoop data, as shown in Figures 5.7 through 5.9. As can be seen, both the heat gain and outlet temperatures were compared for each of the three days. Like the AZTRAK test data, there are plenty of reasons to help explain differences in the comparisons. In addition to those already mentioned in Section 5.1, startup and shutdown and cloud transients are not accounted for in the model as well as when a section of collectors may of been taken offline to help control the solar input to the plant. However, both transients and offline collectors are fairly noticeable in the data (i.e. sunrise and sunset periods in all the Figures, and Figure 5.9 around 12:30 PM). Furthermore, with the KJC testloop, the troughs only track from east to west; therefore, end losses and shading explain addition differences. All the figures along with general comments are listed in Table 53. Because the SEGS troughs only track in one axis (east/west) the solar incident angle effect had to be included as an input. As stated earlier, the incident angle was determined with another spreadsheet. The incident angle is the angle between the collector's projected area normal and the direct normal incident solar. The effects of the incident angle are estimated in the model with an equation that was developed from testing at SNL (see Section 2.1.6.1). In addition to the heat gain and outlet temperature comparisons plotted in Figures 5.7 through 5.9, power loss components determined from the model were also plotted and are shown in Figures 5.10 through 5.12. The losses include both heat losses and optical losses. Two components of the optical losses are shown to illustrate how the incident angle effect depends on the time of year incident angle is smallest during the summer months. The plots also reveal that the optical losses are much larger than the heat losses, so any error in the estimated optical losses could overshadow errors in the heat loss. Table 54 further illustrates this point by listing the actual calculated daily average values with percentages of the total losses. It should be noted that part of the reason that heat losses are lower in the winter then the summer is because the plants typically operate at lower HTF temperatures during the winter months, as shown in Figure 5.13, when energy demand is lower. Also shown in the plots is the solar insolation to help indicate transient periods, such as sunrise, sunset, and cloudy conditions 74
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Table 53 List of Figures and Comments for the KJC TestLoop Data Comparison Fi2ure Description Comments Transients explain the larger differences between the EES data and KJC data during startups and All All shutdowns. With the exceptions of the periods of transients, the EES data and KJC data showed good agreement. 5.7 a) 010203, Heat Gain comparison Transients caused by clouds explains 5.7 b) 010203, Outlet Temperature the scattering and increase in comparison differences during late afternoon. 5.8 a) 032201, Heat Gain comparison Increase in difference around 9:30 is most likely due to a collector segment being taken offline. 5.8 b) 032201, Outlet Temperature comparison Brief increase in outlet temperature around 11:30 AM is most likely due to a flow rate adjustment. 5.9 a) 062101, Heat Gain comparison Increase in difference after 12:30 is most likely due to a collector segment being taken off line. 5.9 b) 062101, Outlet Temperature comparison Transients caused by clouds explains the scattering and increase in differences during late afternoon. 75
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3500 3000 2500 a) Heat Gain Comparison (UVAC Data 01..()2..()1) .I 2000 .s Cl I 1500 1000 500 0 500 0:00 2:24 4:48 7:12 9:36 12:00 Time 14:24 16:48 i KJC Tes1Loop Oa1a EES Model Oala I b) Outlet Temperature Comparison (UVAC Data 01..()2..()1) 19:12 1 21:36 0:00 1 _:t1 t. l::r: _________________ 200 r= j 100+0:00 2:24 4:48 7:12 9:36 12:00 Tim. 1424 16:48 I KJC TestLoop Oa18 EES Model Da1al 19:12 21:36 Figure 5.7 a) Heat gain and b) outlet temperature charts comparing the EES HCE Code and KJC testloop data for 010201. 76 0:00
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3500 3000 2500 a) Heat Gain Comparison (UVAC Data # ....... e 2000 ; .. .E 1!1 li :! 1500 1000 500 0:00 2:24 4:48 900 1 # ( 7:12 9:36 12:00 Time 14:24 \& 16:48 19:12 i KJC TestLoop Data EES Model Data 1 b) OuUet Temperature Comparison (UVAC Data 21:36 0:00 : ,. E I S I :: 1 1 0:00 2:24 4:48 7:12 9:36 12:00 TiiM 14:24 16:48 i KJC TestLoop Data EES Model Data I 19:12 21:36 Figure 5 .. 8 a) Heat gain and b) outlet temperature charts comparing the EES HCE code and KJC testloop data for 032201. 77 0:00
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3500 3000 2500 e 2000 = 1500 Cl l1ooo 500 0 ,0:00 2:24 4:48 a) Heat Gain Comparison (UVAC Data 0621.01) .. r ... .. t. .. ... : I _._ ... ,. _:/ 7:12 9:36 12:00 TiiM 14:24 J;l. :. ; 16:48 19:12 j I(JC TestLoop Data EES Model Data I b) Outlet Temperatura Comparison (UVAC Data 0621.01) 21:36 0:00 900 1 ___________ 700 +r 'ft._ fsoo __ _____, E fl . J 0:00 2:24 4:48 7:12 9:36 12:00 Tilm 14:24 16:48 I KJC TestLoop Data EES Model Data I 19:12 21:36 Figure 5.9 a) Heat gain and b) outlet temperature charts comparing the EES HCE code and KJC testloop data for 06210 I. 78 0:00
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Power Lou Components (UVAC Data 01()2..01) 4000 1200 3500 3000 e 2500 !I 2000 ' 11500 1000 500 0 BOO 600 400 200 )( ,i; 0:00 2:24 4:48 7:12 9:36 12:00 14:24 16:48 19:12 21:36 0:00 TirM : Heat Loss Incident Angle Optical Loss Other Optical Losses Total Optical Losses >
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4000 3500 3000 i 2500 !. i!!l 2000 ..... j 0 1500 D. 1000 500 0 Power Loss Components (UVAC Data 03122101) 1200 800 600 400 200 .......... 0 0:00 2:24 4:48 7:12 9:36 12:00 14:24 16:48 19:12 21:36 0:00 Tinw :_ Hea1 Loss lnciden1 Angle Op1ical Loss Other Optical Losses 11 Total Optical Losses x Solar InsolatiOn I c .2 ;; 0 .s Figure 5.11 Power loss components and solar insolation chart from the KJC test loop data for 032201. Another factor that was evaluated with the KJC TestLoop version of the code was the conductive losses through the HCE support brackets. Table 55 lists the results of this study. As shown, on average the brackets can contribute about I to 1.5 % of the total heat losses from the HCE. And, the instantaneous heat loss through the brackets can be higher than 3 %, depending on the operating and ambient conditions. It should be noted that this study assumes that all the brackets are similar in design to those pictured in Figures 2.3 and 2.4 and are not insulated from the HCE absorber. 80
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4000 Power Loss Components (UVAC Data 06121101) ,. )( tJ .. )( )( .. 1200 1000 800 600 400 200 0:00 2:24 4:48 7:12 9:36 12:00 14:24 16:48 19:12 21:36 0:00 Time I Hea1 Loss lnciden1 Angle Optical Loss Other Optical Losses "Total Optical Losses Solar Insolation of c 0 i 0 .5 Figure 5.12 Power loss components and solar insolation chart from the KJC test loop data for 062201. Table 55 Estimated Heat Loss Percentages due to HCE Support Brackets Day Percentage of Total Heat Loss maximum average 01/02/01 3.2% 1.3% 03/22/01 2.8% 0.9% 06/21/01 2.5% 1.5% 81
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Average HTF Temperature Above Ambient 600.0:00 2:24 4:48 7:12 9:36 12:00 Time +112/2001 ....... 312212001 14:24 16:48 19:12 21:36 0:00 6121/2001 I Figure 5.13 Chart comparing average operating HTF temperatures for different times of year. 82
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6. Design and Parameter Studies Numerous examples of design and parameter studies using the HCE performance models implemented in EES are shown below. The examples demonstrate the utility of the software program and identify and prioritize some methods for improving collector and HCE performance. The HCE performance models do not include an optimization routine; but rather, utilizing the EES software, simultaneously solve a set of equations that describe the energy balance between the HfF and surrounding ambient conditions, given a set of inputs (see Section 2). Thus, the results described below were compiled by re running the EES program for each change in a design or parameter variable and then copying the outputs to an EXCEL spreadsheet for comparisons. Twelve different design conditions and parameters were evaluated with the EES HCE Performance Codes. Table 61 summarizes the results, and charts showing the various comparisons are discussed in Sections 6.1 thru 6.12. Table 61 HCE Design and Parameter Study Summary Design Oation or Purpose of Evaluation Results and Comments Parameter Negligible, yet material selection Absorber Pipe Base To determine influence of less is also driven by material Material expensive materials (316L, B42 strength, corrosion properties, (Section 6.1) copper, and carbon steel) on the installation ease, coating HCE performance application, and costs considerations. Chronologically, the improvements in coatings have improved the HCE performance. To compare the differences on Solei's proposed lN AC Cermet Selective Coating HCE performance between all the with emittance of 0.07 @ 400 C (Section 6.2) absorber coatings that have been gives the best HCE performance. used or have been proposed HCE performance would be sensitive to any variance in selective coating optical properties. 83
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Table 61 (cont) Design OJ!tion or Pumose of Evaluation Results and Comments Parameter Vacuum gives the best result. To evaluate the differences on Filling the annulus with an inert Annulus Gas Type HCE performance between (Section 6.3) vacuum, air, argon, and hydrogen gas is better than air. in the HCE annulus Hydrogen permeation can degrade the HCE performance. A broken glass envelope on an HCE gives unacceptable To evaluate the loss in HCE performance results, especially HCE Condition and performance because of loss with windy conditions. Wind Speed vacuum in annulus, or a broken (Section 6.4) glass envelope. The wind has little influence on HCE performance when the annulus vacuum is intact, but does when the vacuum is lost. Vacuum gives the best result. To evaluate the differences on Filling the annulus with an inert Annulus Gas Type HCE performance between (Section 6.3) vacuum, air, argon, and hydrogen gas is better than air. in the HCE annulus Hydrogen permeation can degrade the HCE performance. Vacuum levels less than 0.1 torr show negligible improvements from the 0.0001 torr level. Annulus Pressure To determine sensitivity of HCE HCE performance declines (Section 6.5) performance to the vacuum level appreciably with pressures of 100 inside the HCE annulus torr or greater in the annulus. If hydrogen in present, the HCE performance is even more sensitive to annulus pressure. The trough performance drops To determine sensitivity of trough appreciably with solar weighted Mirror Reflectance reflectivity less than 0.9. (Section 6.6) performance to the mirror reflectance. Keeping mirrors clean is very important to CSA performance. Solar Incident Angle Determine sensitivity of trough Trough performance is very (Section 6. 7) performance to solar incident sensitive to solar incident angle. angle. 84
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Table 61 (coot) Design OJ!tion or PurJ!OSe of Evaluation Results and Comments Parameter Trough performance is very sensitive to solar insolation. Solar Insolation Determine sensitivity of trough Factors such as atmospheric (Section 6.8) performance to solar insolation. pollutants and particulates should be considered when choosing a solar site. HTF Flow Rate Determine sensitivity of trough HCE performance has a weak (Section 6.9) performance to HTF flow rate. dependency to HTF flow rate. Trough performance has a weak To determine sensitivity of HCE dependency to HTF type. HTFType performance to the type of heat (Section 6.1 0) transfer fluid (Therminol VPl, Operation of the HCE at higher Xceltherm 600, Syltherm 800, 60temperatures decreases the HCE 40 Salt, Hitec XL Salt) performance yet increases the power cycle efficiency. Appears to be an optimal diameter that minimizes the heat losses. Glass Envelope Determine sensitivity of trough Influence of diameter on heat loss Diameter performance to glass envelope is more sensitive when the (Section 6.11) diameter. annulus is not under vacuum. Clearance for absorber pipe bowing needs to be included. 85
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Table 61 (cont.) Design O)!tion or Purl!ose of Evaluation Results and Comments Parameter The temperatures along the length of the receiver increase in a slightly nonlinear fashion. The temperature differences between the HTF and absorber (T1 and T2), between the inner and outer absorber pipe surfaces (T 2 and T 3), and between the inner and outer glassenvelope surfaces (T 4 and T 5 ) all remain constant. Temperature and The temperature difference Heat Flux Variation Determine temperature and heat between the absorber and glassalong Receiver flux profiles along length of envelope (T3 and T4 ) changes in a Length receiver. slightly nonlinear fashion. (Section 6.12) Radiation heat transfer fluxes increase nonlinearly. Heat gain per receiver length decreases as the HTF temperature increases. Heat loss per receiver length increases as the HCE crosssectional temperatures increase. Optical losses per unit receiver length remain constant. 6.1 Absorber Pipe Base Material Four different absorber pipe base materials were evaluated; three stainless steels, 321H, 316L, and 304L; and one copper, B42. The materials were chosen to determine the influences of less expensive materials on the HCE performance. All the stainless steels evaluated have been used in HCE' s; however, the copper has not. As shown in Figure 6.1, the differences in efficiency and heat loss between the five different materials are negligible. However, other factors such as material strength, corrosion properties, 86
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installation ease, coating application, and costs weigh in to determine the selection of the absorber pipe base material. The most recent HCE design uses 321H stainless steel as the absorber base material. It was selected for two reasons. First, 321H is very strong and thought to reduce the problem of bending. Second, it slows the hydrogen permeation rate. Both 304L and 316L stainless steels were used in earlier HCE fabrications; however, HCE bowing problems led to the belief that these materials were not strong enough. Later, after the decision to use the more expensive 321H material was made, the bowing problem was thought to be due to the temperature cycling during plant startups rather than a material strength issue. Originally, the cost difference between 316L and 321H was significant. Now that vendors are setup for the 321H polishing process, the cost difference may not be that significant, especially when ordered in large quantities. However, 316L remains a good candidate for HCE's and further investigation may be warranted. [Mahoney 2002; Cohen 2002] Carbon steel is not included in the codes, but can be easily added; however, it has its own problems as being used as an absorber pipe. For instance, carbon steel is very difficult to use with vacuum. If used in a vacuum, the steel would need to go through an expensive and timely process of removing outgassing, which includes keeping the material in an oven at very high temperatures for days. The preparation process for applying selective coatings, including cleaning and polishing, is also long and expensive for carbon steel. Furthermore, carbon steel may pose corrosion problems at the welded joints. In the past, carbon steel in SEGS plants has only been used for very specific applications; for instance, for the vacuum insulated pipes in SEGS VID headers. [Mahoney 2002; Cohen 2002] Although copper pipe may have a lower cost; at current plant operating temperatures, it does not have proper strength and could lead to receiverbowing issues. However, if operating temperatures are reduced in future plants, copper piping may be worth reevaluating as a means to reduce costs. [R. Mahoney 2002; G. Cohen 2002] 87
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a) Efficiency Vs. Absorber Material Type 75 71 1 68 rONI 950 W/m2 "' LS Collec1or Solei UVAC Cerme1 "' 67 1Therminol VP1 '140 gpm . 50 100 150 200 250 300 Awrage KTF Tempemura ("C) 304L and 316L 321H eB42 Copper Pipe I b) Heat Loss Vs. Absorber Material Type 350 400 450 450 ON1950 W/m2 400 1LS2 Collec1or Therminol VP1 / Solei UVAC Cerme1 350 140gpm / l / 250 +7"/:________ __ __ i / .... 200 ___________ I / ______________ so+50 100 150 200 250 300 Avw.ge KTF TempeMure ("C) I304L and 316L 321 H B42 Copper Pipe j 350 400 Figure 6.1 a) Efficiency and b) heat loss charts comparing different HCE absorber pipe base material types. 88 450
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6.2 Selective Coating Six different selective coatings were evaluated to compare HCE performances for all the absorber coatings that have been used or have been proposed. The optical properties for the first four types, Luz Black Chrome, Luz cermet, Solei UV AC cermet (SNL test a), and Solei UV AC cermet (SNL test b), were all determined in testing at SNL. Note that the last two are the same coating. This is because the test results varied when testing either end of the same HCE [Mahoney 2002]. The last two coating types have properties that the manufacturer, Solei, has stated can be manufactured. The results of the selective coating type comparisons are shown in Figures 6.2 and 6.3. The bar chart in Figure 6.2 compares the magnitudes of the heat gain, heat loss, and optical loss for each selective coating. Note that the selective coating type has a strong influence on each of these energy rate components, for each coating has different emittance and absorptance values. Figure 6.3 shows the efficiency and heat loss as a function of HTF temperature. Again, the shapes of the curves reflect the different optical property functions for each selective coating type (see Section 2.1.6.1). As shown in Figure 6.3, the 0.07 @ 400 C proposed coating could increase the efficiency by as much as 8.5% (at 400 C HTF temperature) over current coatings. The Figures also illustrate that significant improvements have been made to the collector efficiency from improvements to the selective coatings. As shown, HCE performance is very sensitive to the optical properties of the selective coatings. Therefore, any manufacturing variances in coatings could result in significant energy losses. Because of this, further variance testing and manufacturing quality checks may be warranted. 89
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Energy Rate Componenta Va. Selective Coating Type f Heat LoS& Heat Gain [] Optical Loss Luz Cermet Solei UVAC Cermet Solei UVAC Cermet Solei UVAC Cermet Solei UVAC Cermel (SNL test a) (SNLb) Proposed (0.07 Proposed (0.10 0400C) 0400C) Figure 6.2 Energy rate components chart for each selective coating type. 90
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a) Efficiency Va. Selective Coating 80 DNI950W/m2 55 L52 Collector Therminol VP1 140gpm 100 200 250 300 A.ge HTF r.("c) 350 400 1Luz Black Chrome Luz Cerme1 i I Solei UVAC Cermet (SNL test a) *""Solei UVAC Cermet (SNL test b) : solei UVAC Cermet Proposed (0.07 0400C) Solei UVAC Cermet Proposed (0.10 0400C)I b) Heat Loss Va. Selective Coating 800 .DNI950W/m' LS2 Collector 700 Therminol VP1 140gpm 3 .... 50 100 150 200 250 300 A.ge HTF T.,.,.,.,.... ("C) Luz Black Chrome Luz Cermet 350 Solei UVAC Cermet (SNL test a) *""Solei UVAC Cermet (SNL test b) 400 Solei UVAC Cermet Proposed (0.07 0400C) Solei UVAC Cermet Proposed (0.10 0400C) Figure 6.3 a) Efficiency and b) heat loss charts comparing different HCE types. 91
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6.3 Annulus Gas Type Figure 6.4 shows the efficiency and heat loss comparison of vacuum, air, argon, and hydrogen in the annulus space between the absorber and glass envelope in the HCE. As shown, a vacuum in the annulus results in the best HCE performance. An inert gas with a low thermal conduction coefficient, such as argon, is the next best option shown. However, it provides only a slight improvement over air (argon is 2.5% gain over air at 400 C HTF temperature). Hydrogen decreases the HCE performance significantly. Currently, the HCE' s are manufactured with the annulus space under a vacuum of 0.0001 torr (various other annulus pressures were evaluated and are discussed in Section 6.5). The problem with a vacuum in the annulus space is maintaining it. Historically, this has been a problem in SEGS plants. The main cause of vacuum loss has been failure of the glasstometal seal. Recent modifications of the glasstometal have shown promising results. Another cause of vacuum loss is hydrogen permeation. An inert gas, such as argon, has been considered as a possible alternative to a vacuum. The thought is that filling the annulus space with an inert gas instead of a vacuum would result in higher reliability and at the same time help mitigate the hydrogen permeation problemfurther study is required to show whether this is true or not. Pumping an inert gas into the annulus space between the absorber and glass envelope, could also be an option to replacing an HCE after the vacuum has been lost. Hydrogen was included in the study because it naturally permeates into the annulus space from the HTF. This potential for a drop in HCE performance due to hydrogen permeation was discovered early on in the HCE development. In fact, over a million dollars has been spent on investigating the hydrogen permeation rate and on developing the getter to absorb the gas [Cohen 2002]. It was determined that at the permeation rates for the current HTF and absorber materials getters have a lifetime of 30 years before they become saturated. It was also pointed out that an attempt was made to implement a hydrogen removal (HR) device to provide a longer lifetime for the HCE's. Unfortunately, the HR device caused HCE glass envelope breakage, and further development had been halted. However, some of the older HCE' s installed in SEGS plants may not have had enough getters to absorb the hydrogen properly [Mahoney 2002]. As this study shows, hydrogen may be one cause why some SEGS run at a lower than expected efficiency. To indicate if a vacuum has been lost, the current HCE design has a barium marker (getter) in the annulus, which turns white when exposed to oxygen. Unfortunately, the barium marker is not sensitive to hydrogen. If the hydrogen getters do not remove the hydrogen sufficiently, it's possible that vacuum could be replaced by hydrogen without an indication. To date, this is not known to be a problem; however, it does bring up the question at what hydrogen concentration and annulus pressure does the HCE performance degrade, and at what pressure and concentration is the getter in equilibrium with the permeation rate (see Section 6.5). Also, this brings up the question of whether a different vacuum loss indicator is needed, such as a temperature indicator on the glass envelope. 92
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a) Eftlciancy Ve. Annulus Gas Type j ,!,! I !. 55 DNI 950 W/m2 L52 Collector Solei UVAC Cermet Therminol VP1 140gpm 50 100 400 450 1Vacuum +Air Argon Hydrogen I b) Heat Lou Ve. Annulus Gas Type 1200ro l DN1950 Wlm' LS2 Collector Solei UVAC Cerme1 1000 I Therminol VP1 : 1140 gpm I 100 200 250 300 A. KTF Tempel'8t\lfW rc) !vacuum +Air Argon Hydrogen i 400 Figure 6.4 a) Efficiency and b) heat loss charts comparing different annulus gas types. 93
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6.4 HCE Condition and Wind Speed The charts in Figure 6.5 compare three HCE conditions, vacuum, loss vacuum, and broken glass envelope, all at different wind speeds. All three of these conditions have been and can be experienced in SEGS plants. As shown, with a vacuum in the annulus the heat losses from the HCE are affected little by wind. Wind has more influence when the vacuum is loss. The model shows that the decrease can be as high as 12% over the vacuum case (@ 400 C HTF temperature and 20 mph wind). If the glass envelope is broken, the HCE performance can drop by as much as 105% over the vacuum case (at 400 C and 20 mph wind). However, as revealed in the comparison with the AZTRAK test data in Section 5.1, this decrease is probably smaller then modeled, since the wind will most likely be obstructed and the wind direction will be something other than normal to the HCE. 94
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a) Efficiency Va. HCE Condition and Wind Speed BOrVacuum so +..._,.___ Loss Vacuum t. I .ll 1: w Broken Envelope 20 LS Collector Solei UVAC 10 Cermet Therminol VP1 140gpm 0 50 100 150 200 300 350 400 450 b) Heat Lou Va. HCE Condition and Wind Speed 4500 4000 LS Collector Solei UVAC Cermet Therminol VP1 3500 140gpm i !. 2500 +:>,L5 Broken Envelope ..I 2000 +:T""::::;j1 Vacuum 0 100 200 300 AV8f'8!111 HTF Tempemu,. ("C) 400 Figure 6.5 a) Efficiency and b) Heat loss charts comparing different HCE conditions as functions of wind speed. 95 450
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6.5 Annulus Pressure Figures 6.6 thru 6.8 show the changes in HCE performance as a function of the pressure in the annulus space between the absorber and glass envelope. Both air and hydrogen as the annulus gas are shown in the charts. The question being explored with this study is at what pressure deviation from the 0.0001 torr (manufactured pressure) does heat loss become a problem? As the charts show, annulus pressures between 0.000 I torr and 0.1 torr have slight influence on the HCE performance. Pressures above 0.1 torr, however, can have a significant affect on the HCE performance, especially if hydrogen has permeated into the annulus space. In fact, partial vacuums from I torr to 760 torr decrease performance from 1% to 8.5% for air (at 400 C), and about triple those values for hydrogen. Heat Lou Vs. Annulus Pressure 900 DNI950W/m2 LS Collector BOO SoleiUVACCermet ______________________ Therminol VP 1 140gpm 350C 700 3 ..... i 500 0.0001 0.001 0.01 0.1 10 100 Annulua p,_re (torr) Figure 6.6 Heat loss chart as a function of annulus pressure for air and hydrogen as the annulus gas. 96 1000
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a) Efficiency Va. Annulus Pressure (Air) j DNI950W/rrl' 59 LS.2 Collector Solei UVAC Cermet 57 Therminol VPt t40 gpm 50 100 150 200 250 300 A.ge HTFT.......("C) 350 400 lo.0001 torr +0.1 torr +1 torr 10 torr 100 torr +400 torr 760 torr I b) Heat Lou Va. Annulus Pressure (Air) 450 800 ,. 700 600 ONI950W/m2 LS2 Collector Therrninol VP1 140gpm ii 400 ..J 50 100 150 200 250 300 HTF Tempet8ture ("C) 350 400 10.0001 torr +0.1 torr +1 torr 10 torr 100 torr +400 torr 760 torr I 450 Figure 6.7 a) Efficiency and b) heat loss charts for different annulus pressures and air as the annulus gas. 97
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a) Efficiency Vs. Annulus Pressure (Hydrogen) 75 I .!i ffi l il ..I I DN1950W/m2 55 LS2 Collector Solei UVAC Cerm!t Tharminol VP t t40gpm 50 tOO t50 200 250 300 350 400 450 A.ge HTF Temperature ("C) 1o.ooot torr ...... o.t torr +t torr to 10rr ....too torr ......._400 torr 760 torr] b) Heat Loss Vs. Annulus Pressure (Hydrogen) t200 DNI950W/m2 LS2 Collector Solei UVAC Cerm!t tOOO Therminol VPt t40gpm 600 400 200 50 tOO t50 200 250 300 Awrage HTF Temperature ('C) 350 400 1o.ooot torr ........ o.t torr +t torr t 0 torr .... t 00 torr ...... 400 torr 760 torr I 450 Figure 6.8 a) Efficiency and b) heat loss charts for different annulus pressures and hydrogen as the annulus gas. 98
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From the evidence poised by the charts, if numerous HCE's installed in the SEGS plants are at partial vacuum, the energy losses could become significant. Since there is no vacuum measurement on the HCE' s, numerous questions go unanswered. For instance, what are the actual pressures in the HCE'sboth when they arrive from the manufacturer and after they've been installed over a period of time, and how much variance is there from HCE to HCE? Also, at what annulus pressure does the barium indicator trigger a lost vacuum, and what is the annulus pressure when the hydrogen concentration is in equilibrium with the getter? Developing a means to measure the annulus pressures could help answer these questionsone such possible means may be to measure the outer glass envelope surface with an infrared camera and compare the results with the model predictions. Being able to answer the previous questions could lead to important HCE performance improvements. For instance, it may be discovered that there needs to be improvement in the manufacturing quality control to tighten the annulus pressure variance from HCE to HCE? Also, it may be found that the barium indicator doesn't tum white until the annulus pressure is close to atmospheric. If this is the case, a more precise vacuum indicator may be warranted. Furthermore, actual HCE annulus pressure measurements could warrant a closer review of the previous getter studies, and thus an improvement on mitigating the hydrogen permeation into the annulus. 6.6 Mirror Reflectance As shown in Figures 6.9 and 6.1 0, mirror reflectance has a strong influence on the collector efficiency. For instance, at a HTF temperature of 400 C, a decrease of 0.15 in reflectance results in efficiency decrease of 24.5%. This indicates that any error in mirror reflectance could easily explain the differences between the model predictions and field data (see Section 5). For example, a 5% error in reflectance could explain a 7% decrease in efficiency (at 400 C). Reflectance is currently measured with an instrument that measures a very small point on the mirror with each reading; therefore, it is trusted that the technician taking the measurements takes a large enough sampling to represent the true average reflectance of a collector, or an entire SEGS plant. A couple questions arise concerning this technique. First, does this give a dependable measure of average mirror reflectance? Second, should a new instrument be developed that takes a reading over a larger surface area to better estimate the overall mirror reflectance, and reduce error associated with the measurement statistical dependency? It should be noted that the HCE heat loss in Figure 6.9 shows only a slight dependence from mirror reflectance (affects the solar absorption terms), and that the heat gain and optical losses are directly impacted. This is only because the average HTF temperature and other parameters that influence the HCE heat loss more strongly were held constant in the model during this study. This wouldn't be completely true in an actual plant. In an actual plant, the HTF temperature would eventually drop with dropping solar 99
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input. Although, small changes in the solar input would be compensated by changing the HTF flow rate. Also note that both the onedimensional and twodimensional model results are shown in Figure 6.1 0. This was done to further illustrate the differences between the two models. The twodimensional model compensates for some of the nonlinearity in the temperature profiles along the longitudinal direction of the HCE, and includes the energy losses associated with the HTF pressure drop and thermal expansion of the HTF. As the total receiver length becomes longer, the difference between the onedimensional and two dimensional models would become more prominent. Energy Rate Components Vs. Solar Weighted Mirror Reflectivity (Average HTF Tempend:ure = 350 "C) 40CO,. 3500 30CO DNI950W/m2 LS Collector Solei UVAC Cermet Thermnol VPI 140 gpm :[ 2500 +s 20CO +1500 +1000 +0.8 0.85 0.9 0.935 Reflectivity I Heat Loss Heat Gain Cl Figure 6.9 Energy rate components chart for different solar weighted reflectivities. This study also hints at the importance of not only keeping the trough mirrors clean, but also keeping the glass envelope on the HCE's clean. 100
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l a) Efficiency Va. Solar Weighted Mirror Reflectivity (Compari8011 the One 8lld Two Dimeneional Models) 80,j u iE ONI 950 W/rrf LS.2 Collector Solei UVAC Cermet =......SS Therminol VP1 140 gpm L=n9.52 m 0 50 tOO 150 200 250 300 350 400 HTF Temperature (C) ........ o.8 ....... o.8s o.9 ........ o.93s ....... o.8 20 ....... o.8s 20 o.9 20 o.93s 20 1 b) Heat Lou Va. Solar Weighted Mirror Reflectivity (Comperi801'1 a.twwn the One Mel TwoDimensiorwlllodels) 450 450 400 350 ONI 950 W/rrf LS2 Collector Solei UVAC Cermet Therminol VP1 140gpm L=n9.52 m so+50 100 150 l0.8 ....... 0.85 200 250 300 HTF Temperature ("C) 350 400 o.9 ........ o.935 ....... o.8 20 ........ o.es 20 20 0.935 20 I Figure 6.10 a) Efficiency and b) heat loss charts comparing different solar weighted reflectivities. Both the one and twodimensional model results are included for comparison. 101 450
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6. 7 Solar Incident Angle The charts in Figures 6.11 and 6.12 show the sensitivity of HCE performance to solar incident angle. Similar to the previous section, the HCE heat loss is only affected slightly in this study, since the average HTF temperature and other parameters directly affecting the heat loss are held constant. However, as shown, the solar incident angle has a large impact on the optical loss and heat gain. Specifically, with an incident angle of 30 the performance is reduced by approximately 15%, and at 60 it's reduced by approximately 65%. For a singleaxis tracking system, like the SEGS plants in California, the solar incident angle is going to depend both on the location and time of year. Figure 6.13, shows the actual solar incident angles for three different seasons for the SEGS plants located in Kramer Junction, California. As shown, the largest incident angles occur during the winter months; whereas, the smallest angles occur during the summer. 4000 3500 3000 e 2soo .. 2000 ,. !!' 1500 1000 500 0 Energy Components Vs. Solar Incident Angle (Average HTF Temperature = 350 "C) DN1950W/m2 LS ColleC1or +Solei UVAC CermetOdeg 10deg 20 deg 30 deg 40deg [ Heat Loss Heat Gain [J Optical Loss [ Therminol VP 1 140 gpm 50 deg 60 deg Figure 6.11 Energy rate components chart as a function of different solar incident angles. 102
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a) Efficiency Va. Solar Incident Angle 80,70 60 ... j 40 .!! = w 30 20 10 0 50 450 400 350 LB2 Collector Therminol VP1 140gpm 100 150 1odeg ....... 1odeg 200 250 300 Awrage HTF Temper8tunl ("C) 350 400 20 deg 30 deg ....... 40 deg 50 deg 60 deg i b) Heat Loaa Va. Sol11r Incident Angle 450 L52 Collector Solei UVAC Therminol VP1 140 gpm 50 100 150 200 250 300 350 400 450 A. HTF ('C) 20 deg ...,._ 30 deg ..... 40 deg 50 deg 60 deg I Figure 6.12 a) Efficiency and b) heat loss charts comparing different solar incident angles. 103
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Incident Angle 70 I 40 0 ... 0:00 2:24 4:48 7:12 9:36 12:00 Time 1424 I 11212001 312212001 s12112001 I 19:12 21:36 0:00 Figure 6.13 Chart showing solar incident angles for three different times of year from actual data for a northsouth oriented SEGS plant in Kramer Junction, California. Although previous studies have showed that tilting the collectors would be cost prohibitive due to the added equipment costs, it may be worth revisiting this now that the actual incident angle losses are better understood. Also, other options to reduce the solar incident angle effects may be worth investigating; such as, changing the outer surface of the absorber pipe by roughening or adding threads [Duffie and Beckman 1991]. 6.8 Solar Insolation Once again, the parameters with the strongest influence on HCE heat loss are held constant, so only the optical losses and heat gain increase significantly with increasing solar insolation, as shown in Figure 6.14. Furthermore, it can be seen that the HCE performance improves with increasing solar insolation, as also shown in Figure 6.15. Therefore, besides clouds, sites with high pollutants and other particulates in the airsuch 104
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as dust and sandwould have a negative impact on the HCE performance. This hints at the importance of choosing a SEGS plant site away from industrial areas with a lot of pollution or areas with high automotive traffic. Nor should a SEGS be built at a site prone to frequent dust storms. Energy Rate Components Vs. Solar Insolation j Heat Loss Heat Gain [J Optical Loss [ 4000 LS Collector Solei UVAC 3500 Cermet Therminol VP1 140 gpm 3000 e 25oo &! 2000 ... !!' 1500 1000 500 0 300 (W/m2) 500 (W/m2) 700(W/m2) 900 (W/m2) 1100 (W/m2) Figure 6.14 Energy rate components chart for different solar insolation values. 105
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a) Efficiency Va. Solar Insolation M.l .. E w LS Collector 55 Therminol VP I 140gpm 50 100 200 300 A.ge HTF Tempermn ("C) 400 1300 (Wtm21 soo (Wtm21 700 (W/m2) 900 (W/m2) 1100 (W/m2) I b) Heat Loaa Va. Solar Insolation LS2 Collector Solei UVAC 400 Therminol VP1 140gpm i 300 !. i .... i 200 +7""''"7"'0,._ 100 150 200 250 300 A.ge HTF Tempemur. ("C) 350 400 1300 (Wtm2) soo (Wtm2l 100 (Wtm2) 900 (Wtm21 1100 (Wtm2) I 450 Figure 6.15 a) Efficiency and b) heat loss charts for different solar insolation values. 106
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6.9 HTF Flow Rate Figure 6.16 shows that the HTF flow rate has little affect on the HCE performance, for the range of flow rates evaluated (I 00 gpm to 160 gpm). The figure includes both the onedimensional and twodimensional model results. As expected, the twodimensional model shows that the HCE performance has a higher dependency on the flow rate then the onedimensional model. This is due to the inclusion of the pressure loss and thermal expansion effects on the HTF in the twodimensional model. A more detailed study of the flow rate affects should include the power cycle side of the plant and losses through pumps and other equipment and piping. Furthermore, an exergy analysis would be more beneficial then the energy analysis for this type of study. 107
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75.74 73 72 a) Efficiency Vs. HTF Flow Rate (Comparl11011 '*the One lllld TwoDimenaionelllloclels) l71 I 70 .. ffi 69 68 67 66 65 50 ONI950W/m2 L52 ColleC10r Therminol VP1 Reflectivity z 0.935 Ln9.52m 100 150 200 250 300 AwragelfTF Temperatura ('C) 350 400 450 !too gpm +120 gpm 140 gpm """*""160gpm ......... 100gpm20 120gpm20 +140gpm20 160gpm20 I b) Heat Loss Vs. HTF Flow Rate (Comparl11011 '*the One and TwoDimenaionallllodels) 450 ,ONI950W/m2 LS2 Colleclor 400 350 Therminol VPt 140 gpm Reflectivity 0.935 L=n9.52 m 50t50 100 150 200 250 300 350 400 450 A.ge lfTF Tempernn ('C) 1100gpm +120gpm 140 gpm """*""160 gpm ......... 100 gpm 20 120 gpm 20 +140 gpm 20 160 gpm20 I Figure 6.16 a) Efficiency and b) heat loss charts comparing different flow rates and including both the one and twodimensional models. 108
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6.10 HTF Type The charts in Figure 6.17 reveal that the HTF type has little effect on the HCE performance. However, each fluid type has a range of recommended operating temperatures, and, as seen in the plot, efficiency drops with increasing HTF temperature. Thus, fluids that can operate at lower temperatures would improve the HCE performance. In addition, each HTF type has other advantages. For instance, HTF types like salts can be used as a thermal storage medium, but also could require additional heating during offsun hours to prevent solidification in piping and equipment. Also, cost and availability could dictate which HTF to use. Furthermore, power cycle efficiencies increase as the working fluid temperature increases, so a complete study would need to include both the solar and power cycle sides. 109
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a) Efficiency Vs. HTF Type (Compariaon betwwn the One and TwoDimensional Modele) 80 75+l >.!! = w 'E i .... :1: 60 ONI950W/m2 L52 Collector Solei UVAC Cermet 55 t40gpm L =n9.52m 50 150 250 350 450 .AW111ge HTF Temper("C) 1Therminol VP1 +Xceijherm 600 Syijherm 800 6040 Salt Thermmol VP1 20 +Xceijherm 600 20 Syijherm 800 20 6040 20 b) Heat Loss Vs. HTF Type (Compariaon 11etwwn the One and TwoDimensional Modela) 550 +Hrtec XL Salt Hrtec XL Saij 20 1200 ONI950W/m2 LS2 Collector 1000 Solei UVAC Cermet 140 gpm I 770 .C:')""' 800 600 400 200 0 0 100 200 300 400 Average HTF Tpemu111 ("C) Therminol VP1 +Xceijherm 600 Syijherm 800 6Q40 Saij herminol VP1 20 +Xceijherm 600 20 Syijherm 800 20 6040 Saij 20 500 +Hitec XL Saij Hitec XL Saij 20 600 Figure 6.17 a) Efficiency and b) heat loss charts comparing different HTF types and including both the one and twodimensional models. 110
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6.11 Glass Envelope Outer Diameter The charts in Figure 6.18 reveal that the glass envelope diameter has an optimal size to minimize heat losses from the HCE. The charts also show that this effect is most sensitive when the annulus is not under vacuum. The optimal diameter reflects the fact that as the diameter is increased, the annulus gap between the absorber and glass envelope increases, which decreases the heat transfer between the absorber and glass envelope, but increases the surface area for heat transfer to the environment. Decreasing the glass envelope diameter increases the heat transfer across the annulus gap, but decreases the surface area for heat transfer to the environment. Another problem with having too small of an annulus gap, however, is that it could cause tolerance problems with the absorber pipe, since the absorber pipe will tend to bow slightly when heated. Therefore, a more detailed glass envelope optimization study would need to include the thermal deflections of the absorber. Ill
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a) Efficiency Va. Glass Envelope Outer Diameter 75.... .2 ffi 59 DNI 950 W/rrf L.S2 Collector Solei IN AC Cermet 57 Thermlnol VP1 0 50 100 150 200 250 300 350 400 450 Awrege HTF Tempemure ('C) 1o.oem o.092m o.105m ....... 0.115m 0.14m ........ 0.165mj b) Heat Loss Va. Glasa Envelope Outer Diameter .50 100 150 200 250 300 Awrege HTF Tempemure ('C) 1o.oem o.092m a. 105m ....... 0.115m 350 400 0.14 m ........ 0.165 m I Figure 6.18 a) Efficiency and b) heat loss charts comparing different glass envelope diameters. 112 450
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6.12 Parameter Variation along Receiver Length The chart in Figure 6.19 shows the temperature variations along the length of the solar receiver (total length of 779.5 m) for each temperature in the crosssection of an HCE (also see Figure 2.1), as modeled with the twodimensional HCE performance model. As expected, the temperatures along the length of the receiver increase in a slightly nonlinear fashion. This is because of the nonlinearity of the radiation heat transfer functions, along with the fact that heat gain per receiver length decreases as the HTF temperature increases, and since the heat loss per receiver length increases as the HCE crosssectiomil temperatures increase. All these heat flux trends can be seen in Figure 6.20. Also, as expected, the temperature differences between the HTF and absorber (T1 and T 2), between the inner and outer absorber pipe surfaces (T 2 and T 3), and between the inner and outer glassenvelope surfaces (T 4 and T 5 ) all remain constant, since the heat transfer coefficients are constants (see Sections 2.1.1, 2.1.2, and 2.1.4). However, the temperature difference between the absorber and glassenvelope (T3 and T4 ) changes in a slightly nonlinear fashion. This is because the selective coating emissivity is a function of temperature (see Section 2.1.6.1) and since the radial heat transfer is nonlinear. The optical loss per unit receiver length is also shown in Figure 6.20. Note that it remains constant; since all the optical properties in the effective optical efficiency terms are assumed to be independent of temperature (see Section 2.1.6.1). 113
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Temperatures Along Length of Receiver 450 c . DNI950W/m2 LS2 Collector 400 'Solei UVAC Cermet Therminol VP 1 350 T 140 gpm l = 779.5 m 300+,E I I! 250 !.200 150 100 50 0 39.0 116.9 194.9 272.8 350.8 428.7 506.7 584.6 662.6 740.5 Figure 6.19 HCE crosssection temperatures chart at position along receiver length. 114
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3500 3000 2500 I 2000 .! ,!2 >!:?' 1500 ., c: w 1000 500 0 rrfr1rr F Energy Rate Components Along Receiver Length , DNI950 W /m2 LS Collector Sole i UVAC Cermet Therm i no l VPt, 1 4 0 gpm L = 779 5 m I 1__.., 11, 11j 111rrrrrrrrr I rrrrIT fi R F 1 JJ ll u ...... 39.0 116.9 194.9 272.8 350.8 428.7 506.7 584.6 662.6 740.5 Position Along Receiver (m) 1 heat loss heat gain C optical loss 1 Figure 6.20 Energy rate components chart as a function of position along receiver (total receiver length= 779.5 m). 6.13 Recommendations Table 62 lists recommendations based on the HCE design and parameter study, many of which have already been mentioned, but some warrant further discussion. As stated in Sections 6.2, 6.3, and 6.5, understanding the manufacturing tolerances and degradation rates of the optical properties and HCE annulus vacuum levels is important. It was mentioned that the selective coating optical properties may vary over the length of the HCE and from HCE to HCE. In fact, what little testing has been done has shown this to be the case. Since the optical properties have a strong influence on the HCE performance, further testing of the selective coating variation is recommended. Furthermore, testing to determine the optical property degradation is also recommended. This testing should include determining what variations would be expected throughout a SEGS plant, especially one that has been operating numerous years. As mentioned in Sections 6.3 and 6.5, some HCE's in a SEGS plant are likely to have annulus pressures higher then the specified 0.000 l torr, either because of manufacturing inconsistencies or hydrogen permeation. If this is found to be the case, one 115
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possible solution might be to fill the HCE annulus with an inert gas. To evaluate this more thoroughly, additional inert gasses can easily be added to the model. In addition, it would be beneficial to develop a means to measure the HCE annulus vacuum on installed HCE's, of which could include measuring the temperature of the outer glass envelope surface using an infrared camera and evaluating the data with the HCE performance model. As discussed in Section 6.4, the model tends to over predict wind induced heat losses. Reducing forced convection effects by Vz in the model may lead to better results, especially for the missing glass envelope case. However, more comparisons with field test data need to be done to verify this. Section 6.6 revealed mirror reflectance has a strong influence on HCE performance. Because of this, it may be worth taking a closer look at how mirror cleaning schedules are determined, and determining the accuracy of current reflectance measurement techniques. Developing instruments that sample a larger mirror surface area may also be warranted. It was also shown that solar incident angle has a strong influence on HCE performance (Section 6.7). Tilting the troughs along the rotating axis a slight amount (5), or possibly changing the absorber surface texture [Duffie 2000] or changing the selective coating properties to be less sensitive to solar incident angle could prove to be cost effective. Conducting more incident angle tests on additional HCE's types could also prove to be beneficial. The HCE performance model could be used to give more insight to these investigations. Section 6.10 discussed how the HTF type has little effect on the HCE performance for anyone temperature; however, the trends did indicate that as the HCE performance decreases with increasing HTF temperature. This indiCates that methods for decreasing the HTF temperature could be beneficial, especially if it could be done in such a way as not to adversely decrease the power cycle efficiency. A possible solution might be to run the power cycle side with a fluid with a lower vapor pressure, such as ammonia or a hydrocarbon. As a final note, it may be worth evaluating heat transfer enhancing mechanisms such as coiled spring inserts, twisted tape inserts, helical ribs, roughening the inner absorber surface, etc .. All of these mechanisms would increase the convection surface area and/or enhance turbulent flow [Incropera and DeWitt 1990]. The current HCE performance model can not be used to evaluate heat transfer enhancing devices without significant changes. However, an option to developing a more complex model may be to do additional field testing. For instance, measuring the radial temperature profile of the HTF and the temperature difference between the absorber inner surface and bulk HTF temperature, which would help determine what improvements, if any, a heat transfer enhancement device could make. H it is determined that there is room for improvement, additional field testing of flow enhancement devices may continue to be less expensive then the development of a more complex heat transfer analysis model. Of course any advantage to increasing the heat gain by an enhancement device would have to be balanced with the increase in pumping losses. 116
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Table 62 Recommendations from HCE Design and Parameter Study Desigg Ontion or Parameter Recommendations Absorber Pipe Base Material Reevaluate 316L. (Section 6.1) Add carbon steel to study. Reevaluate optical properties at elevated temperatures. Update optical properties. Selective Coating (Section 6.2) Determine optical property variation. Evaluate optical property degradation. Determine the manufacturing variances. Add additional inert gasses to study (xenon, neon, etc.) Determine effect of inert gases to hydrogen Annulus Gas Type permeation. (Section 6.3) Develop a better device for determining loss of vacuum (or partial vacuum). Determine hydrogen concentration level when in equilibrium with getter bridge and HTF permeation. Reduce wind effects by approximately HCE Condition and Wind Speed Reevaluate wind effects with different annulus (Section 6.4) pressures. Reevaluate wind effects with hydrogen as the annulus gas. Determine annulus pressure variations throughout a SEGS plant (thermal imaging techniques). Annulus Pressure Determine annulus pressure with hydrogen (Section 6.5) permeation. Determine what the manufacturing variances are. 117
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Table 62 (cont.) Design OJ!tion or Parameter Recommendations Develop improved reflectance measuring Mirror Reflectance techniques. (Section 6.6) Measure true optical errors. Run a study simulating trough tilt angles on actual field test data. Solar Incident Angle Evaluate changes to absorber outer surface on (Section 6.7) reducing incident angle effects (roughening surface, threads, different selective coating characteristics, etc .. ). Develop means to conduct HTF property testing in field. HTFType Evaluate combine cycle operation to reduce RTF temperature (i.e. RTF to ammonia or hydrocarbon (Section 6.10) as the power cycle fluid). Evaluate alternative working fluid to reduce HTF temperature (i.e. Ammonia or hydrocarbon). Glass Diameter Reevaluate sizing now that HCE performance has (Section 6.11) been improved. Temperature and Heat Flux Variation along Receiver Conduct an optimization study on length. Length (Section 6.12) Completing HCE testing with RTF heat transfer General enhancing devices (coiled spring, twisted tape, twisted insert, roughened surface) 118
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7. Conclusion This report described the development, validation, and use of a HCE performance software model implemented in EES. All equations, correlations, and parameters used in the model were discussed in detail. The model was implemented in EES in four different versions. Two versions were developed for HCE design and parameter studies, and two versions were developed for evaluating field test data. Both a onedimensional and two dimensional analysis was used in the codes. Each version of the codes was discussed briefly including discussions on relevant EES Diagram Windows, Parameter Tables, and Lookup Tables. The model was then shown to be accurate by comparing with actual HCE field test data. Following this, the model versatility was demonstrated by conducting various design and parameter studies. This also demonstrated how the HCE performance model implemented in EES could be used as a development tool for improving the HCE performance. Several recommendations were drawn from the design and parameter study and were listed in Table 67 and discussed in more detail where warranted. Several suggestions for improving the HCE performance model were also discussed. 119
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APPENDIX 120
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A. Lookup Table References Argon: Ahlberg, K., ed. (1985) AGA Gas Handbook. Stockholm, Sweden: Almqvist & Wiksell International. HitecXL: Data from EXCEL spreadsheet provided by Mary Jane Hall of NREL and Coastal Chemical Company. "HITEC Heat Transfer Salt." Sales Data Sheet. Pasadena, Texas. Nitrate Salt (60% NaN03 40% KN03): Data from EXCEL spreadsheet provided by Mary Jane Hall ofNREL and Zavoico, A. B. (July 2001). Solar Power Tower, Design Basis Document, Revision 0. SAND20012100. Work performed by Nextant, San Francisco, CA. Albuquerque, NM: SANDIA National Laboratories. Syltherm 800: "Syltherm 800, Silicon Heat Transfer Fluid." (November 2001). Form No. 176014691101 AMS. The Dow Chemical Company, http:// www.dowtherm.com. Therminol VPl: "Therminol, Heat Transfer Fluids, Computed Properties of Therminol VP1 vs. Temperature (Liquid Phase)." (2001). Solutia Inc., www.therminol.com. Xceltherm 600: "Exceltherm 600, Engineering Properties." (1998). Radco Industries, Inc., http://www .radcoind.com. 121
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B. Optical and Material Property References Luz Black Chrome (SNL test): Visual Basic Heat Transfer Code and based on test data from Rod Mahoney of SNL, 8/93. Luz Cermet (SNL test): Visual Basic Heat Transfer Code and based on test data from Rod Mahoney of SNL, 110698. Solei UV AC Cermet (SNL test a), Solei UV AC Cermet (SNL test b), Solei UV AC Cermet (SNL test avg): Tests conducted by Rod Mahoney of SNL and presented in a Power Point presentation dated April23, 2001, "HCE Issues; Cermet Preliminary Results Optical Properties & Construction Forum 2001." Solei UV AC Cermet (0.07 @ 400C), Solei UV AC Cermet (0.15 @ 400C): Table in Price, H. (2002) Concentrated Solar Power Use in Africa. NRELITP. Golden CO: National Renewable Energy Laboratory. Glass Envelope (borosilicate glass): Estimated from Plots in Touloukian, Y. S., D.P. DeWitt, eds. (1972). Radiative Properlies, Nonmetalic Solids. Thermophysical Properties of Matter, Vol. 8, New York: Plenum Publishing. 304L, 316L Stainless Steel: Linear best fit of data from tables in Touloukian, Y. S., R. W. Powell; et al., eds. (1970). Thermal Conductivity, Metallic Elements and Alloys. Thermophysical Properties of Matter, Vol. 1, New York: Plenum Publishing. 321H Stainless Steel: Linear best fit of data from tables in Davis, J. R., ed. (2000). Alloy Digest, Sourcebook, Stainless Steels. Materials Park, Ohio: ASM International. and ASM Handbook Committee (1978). Metals Handbook. Properlies and Selection Stainless Steels, Tool Materials, and Special Purpose Metals, Vol. 3, Metals Park, Ohio: American Society for Metals. 122
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B42 Copper Pipe: ASM Handbook Committee ( 1978). Metals Handbook. Properties and Selection nonferrous alloys and pure metals, Vol. 2, Metals Park, Ohio: American Society for Metals. Gas Molecular Diameters: Marshal, N., trans!. (1976). Gas Encylopedia. New York, NY: Elsevier. 123
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C. Heat Transfer Fluid Change in Enthalpy An estimate for the change in enthalpy for a heat transfer fluid undergoing thermal expansion can be derived by starting with the state postulate that any two independent, intensive, thermodynamic properties are sufficient to establish the stable thermodynamic state of a pure simple compressible substance [Howell and Buckius 1987]. This postulate allows the differential change in enthalpy to be determined as a function of temperature and pressure. dh(T,P) =(ah) dT+(ah) dP aT p aP T (C.l) Substituting the definition of specific heat at constant pressure and taking advantage of one of Maxwell's relations [Cengel and Boles 2002] gives (C.2) where, (C.3) and, (ah) aP T aT p (C.4) If density is independent of pressure and is a weak function of temperature the second term on the right side of Equation (C.2) can be simplified. Specifically, it can then be assumed that the specific volume in the integrand_ will dominate the term. p(T,P)= p(T) v(T,P)= v(T) <
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Furthermore, if the specific heat is treated as a constant evaluated at the average temperature difference, Equation (C.2) can be integrated to give an estimate of the change in enthalpy. /lh ::::::: C P,ave!l.T + V ave/:1P (C.lO) In most cases, for liquids the know specific heat will be Cp. However, if Cv is the known value, then it can be substituted for Cp with out adding much additional error, since the specific heats will not differ much for liquids. 125
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D. Radiation Heat Transfer Zonal Analysis for the Glass Envelope A radiation heat transfer analysis for the glass envelope is conducted below to evaluate the effects of the collector and temperature distribution on the radiation heat losses from the receiver. A generalized zone analysis approach is used in the analysis, and as shown in Figure D.l, the collector and HCE crosssection is separated into four zones. Zone 1 is the half of the receiver closest to the collector. Zone 2 is the receiver half furthest from the collector. Zone 3 is the collector. And, zone four is the sky opposite the collector. \ \ \ 8 "... './ / / / / / ....._sky Figure D. I Zone definitions for the generalized zone analysis of the radiation heat loss from the receiver. With the four zones defined in Figure D.l, four separate cases can be evaluated. Case 1 is with one uniform receiver temperature and no collector (T1 = T2 T3 = T4 = Tsky). Case 2 is with two uniform receiver temperatures and no collector (T1 '#T2 T3 = T4 = Tsky). Case 3 is one uniform receiver temperature and collector present (T1 = T2 T3 = 126
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Tambient T4 = Tsky). And, case 4 is two unifonn receiver temperatures and collector present (T1 T2, T3 = Tambiento T4 = Tsky). Note, the collector temperature is set equal to ambient and the sky temperature is approximated as eight degrees less then ambient. Similar to other generalized zone analysis for radiative exchange in an enclosure, the following assumptions were made for the analysis that follows [Ozisk 1973]. 1. radiative properties are unifonn and independent of direction and frequency 2. surfaces are diffuse emitters and diffuse reflectors 3. radiativeheat flux leaving the surface is unifonn over the surface of each zone 4. surfaces are opaque in the frequency of interest (a.+ p =1) 5. temperatures are unifonn over each surface The first step in the analysis is to define the radiative geometric configuration factors (view factors). For a enclosure with four surfaces there will be sixteen view factors. Four of which can be set to zero, since the receiver surface is convex. =0 (D.la) FI2 =0 (D.1b) F2l = 0 (D.1c) F22 =0 (D.ld) From symmetry, five additional view factors can be eliminated. Fl3 = F24 (D.2a) F23 = FI4 (D.2b) F3l = F42 (D.2c) F32 = F4l (D.2d) F33 = F44 (D.2e) View factor algebra can be used to define two additional view factors, which will be needed in the analysis. FJ(1+2) = F3l + FJ2 F 4(1+2) = F4l + F42 And now, taking advantage of reciprocity, another view factor relationship can be eliminated by symmetry. 127 (D.3) (D.4)
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(D.5) Three additional view factors are defined by taking advantage of view factors cataloged in tables. From A Catalog of Radiation Configuration Factors, by John Howell [Howell 1983] I F(1+2H = z (D.6) F_l4 = ( r(1+2) ] 2 + r(1+2) sin I ( r(1+2) J] '(1+2) (D.8 ) 1t r3 r3 r3 r3 Now, four more relationships are needed to define all the view factors. The first of these relationships can be approximated with the help of Hottel's crossedstring method [Siegel and Howell 2002]. Figure D.2 shows the required line segments for this method. with, +Lhc Lab = f + (Le'h f L JZ1j hc2 L2 = Lrd Led = r3'i And finally, from reciprocity the remaining three view factors can be found. 128 (D.9) (D. lOa) (D. lOb) (D.IOc) (D. tod) (D.IOe)
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F F. 'o+2> _!_ 'o+2> 3(1+2) A (1+2}3 /2 2 (D. II) 3 ,3 ,3 collector \ \ \ \ sky_......... "'"'/ I I I / (0.12) (D. 13) Figure D.2 Line segments used for the string method approximation for view factors. The radiosities and heat fluxes can be determined from the following basic relations for radiative heat exchange in enclosures [Ozisik 1977]. 129
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4 R; =E;dl'/ +P;LRjFij (D.14) j=l (D.15) i = 1,2,3,4 Using Equation (D.l) and treating the sky as a blackbody, gives the following radiosity equations. Rl = E1dl'..4 + P1 (R3F13 + R4F;4) Rz = Ezdl'z4 + Pz (R3F23 + R4Fz4) R3 = e3dl'34 + P3 (Rl F31 + RzF3z + R3F33 + R4F34) R4 = d/'44 Solving for R3 gives (D.16) (D.17) (D.18) (D.19) R 3 = E3dl'34 +F3zTz4)+T44[pe(F31F;4 +F3_zFz_4)+F3_4]} (D.20) 1P3 [p e ( f;_3 F31 + F3z Fz3 ) + F33] The heat flux leaving the glass envelope can be determined by eliminating the summations in Equations (D.14) and (D.15) and summing the heat fluxes from either side of the HCE. (D.21) (D.22) (D.23) Assuming that the emissivity of the glass (pyrex) envelope and collector (low iron glass) is independent of temperature 130
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1 =2 =E'e =0.86 = 0.9 All the required information for solving the four cases is now available. Table D1 shows an Excel spreadsheet used to solve the radiation heat transfer for each case. The results show that by assuming the collector has no effect and that the glass envelope temperature is uniform around the circumference, introduces an error in over predicting radiation heat transfer somewhere between 5 and 10 %. As shown in Figure 0.3, this error is consistent regardless of the temperature difference between the front and back of the HCE assuming the same average temperature around the circumference. Table D1 also shows that neglecting the collector and modeling the glass envelope temperature as non uniform would increase the radiation heat transfer by about 5 %. Table D1 Radiation Heat Transfer Zonal Analysis Parameters and Results Test Criterion Radioaities (W/m1 Heat Fluxes (W/m) R, R R3 q, q. q,.2 %Diff no collector, uniform envelope temperature 785.70 785.70 385.49 72.3 72.3 144.6 0 no collector. two uniform envelope temperatures 1018.26 597.99 385.49 114.3 38.4 152.7 5.6 collector, uniform tem_perature 785.70 785.70 428.33 64.6 64.6 129.1 10.7 collector, two uniform envelope temperatures 1018.26 597.99 428.72 106.5 30.6 137.1 5.2 I"J)II_ta View Factors Collactor Type = L82 F, .. = 0.82212 o..,(m) 0.115 F, .. = 0.17788 o_,.,(m)= 4.803 Fa.o= 0.17788 e..= 0.86 F,..= 0.82212 Penvelope = 0.14 F._,= 0.019685 =0.9 F,.. = 0.004259 ....... = 0.1 F33 = 0.363198 I!. I (1\) = 50 F..,= 0.612859 T ... (K)= 350 r ..... ,(K),. 375 r ...... CKl,. 325 T(K)= 295.15 (K)"' 287.15 a(W/mK1= 5.67E08 131
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190 0 i Comparison of Radiation Heat Loss from the HCE Modeled Wrth and Without the Effect of the Collector i 1 140.o I 110.0 I i 0 10 40 ro Temperatura Dlffarenc:e Betwaen Front and Back Sides of HCE 1+With Collector +Without Collector i 90 100 Figure D.3 Radiation heat loss comparison chart showing difference between modeling the radiation loss with and without the collector effects. 132
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E. OneDimensional Design Study Version of EES Code (Tab settings have been shortened and numerous comment statements have been omitted to reduce length of following code.) .................................................................................................. PROCEDURE Pq_12conv : Convective heat transfer rate from the HTF to the inside of the receiver tube ************************************************************************************************II PROCEDURE Pq_12conv(T _1 ave, T _2, Fluid$: q_ 12conv) $Common D_2, D_p, D_h, L, v_1, Flow_ Type$, lncludeLaminar$ Warning Statements if HTF is evaluated out of recommended temperature ranges" If (Fluid$ = 'Syltherm BOO') Then If (T _1 ave < 40) or (400 < T _1 ave) Then CALL WARNING('The result may not be accurate. since Syltherm BOO fluid properties are out of recommended temperature range, 40 C < T < 400 C. See Function fq_12conv. T _1 ave = XXXA 1', T _1ave) Endlf If (Fluid$ = 'Therminol VP1') Then If (T _1ave < 12) or (400 < T _1ave) Then CALL WARNING('The result may not be accurate, since Therminol VP1 fluid properties are out of recommended temperature range, 12 C < T < 400 C See Function fq_12conv.T _1 ave= XXXA 1', T_1ave) Endlf If (Fluid$= 'Xceltherm 600') Then If (T _1 ave < 20) or (316 < T _1 ave) Then CALL WARNING('The result may not be accurate, since Xceltherm 600 fluid properties are out of recommended temperature range, 20 C < T < 316 C .. See Function fq_12conv.T _1 ave = XXXA 1', T _1ave) Endlf If (Fluid$ = 'Salt (60% NaN03, 40% KN03)') Then If (T _1 ave < 260) or (621 < T _1 ave) Then CALL WARNING('The result may not be accurate, since Salt (60% NaN03, 40% KN03) fluid properties are out of recommended temperature range, 260 C < T < 621 C. See Function fq_12conv.T _1 ave= XXXA 1', T _1 ave) Endlf If (Fluid$ = 'Hitec XL') Then If (T _1ave < 266) or (4BO < T _1ave) Then CALL WARNING('The result may not be accurate, since Hitec XL fluid properties are out of recommended temperature range, 266 C < T < 4BO C. See Function fq_12conv.T _1 ave= XXXA 1', T _1 ave) Endlf If (Fluid$ = 'Water') Then If (T _1 ave< 0) or (100 < T _1ave) Then CALL WARNING('The result may not be accurate, since Water fluid properties are out of recommended temperature range, 0 C < T < 100 C. See Function fq_12conv.T _1ave = XXXA1', T _1ave) 133
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Endlf Thermophysical properties for HTF MU_1 := INTERPOLATE(Fiuid$,'MU','T',T=T_1ave) "[kg/ms]" MU_2 := INTERPOLATE(Fiuid$,'MU','T',T = T _2) "[kglms]" Cp_1 := INTERPOLATE(Fiuid$,'Cp','T',T = T _1 ave) "[JikgK]" Cp_2 := INTERPOLATE(Fiuid$,'Cp','T',T = T _2) "[JikgK]" k_1 := INTERPOLATE(Fiuid$,'k','T',T=T_1ave) "[WimK]" k_2 := INTERPOLATE(Fiuid$,'k','T',T = T _2) "(WimK]" RH0_1 := INTERPOLATE(Fiuid$,'RHO','T' ,T = T _1 ave) "[kglm"3]" Re_D2 := (RH0_1 D_h v_1) I (MU_1) Pr_2 := (Cp_2 MU_2) I k_2 Pr_1 := (Cp_1 MU_1) I k_1 Nusselt Number for laminar flow case if option to include laminar flow model is chosen" If (lncludeLaminar$ ='Yes') and (Re_D2 <= 2300) Then If (Flow_ Type$ = 'Annulus Flow') Then DRatio := D_piD_2 Nu#_D2 := INTERPOLATE(Nu#, 'Nu#_D2','DpiD2', DpiD2=DRatio) "estimate for uniform heat flux case" Else Nu#_D2 := 4.36 "uniform heat flux" Endlf Else "Warning statements if turbulent/transitional flow Nusselt Number correlation is used out of recommended range If (Pr_1 <= 0.5) or (2000 <= Pr_1) Then CALL WARNING('The result may not be accurate, since 0.5 < Pr_1 < 2000 does not hold. See Function fq_12conv. Pr_1 = XXXA1', Pr_1) If (Pr_2 <= 0.5) or (2000 <= Pr_2) Then CALL WARNING('The result may not be accurate, since 0.5 < Pr_2 < 2000 does not hold. See Function fq_ 12conv. Pr_2 = XXXA1', Pr_2) If ( Re_D2 <= (2300)) or (5*1QA6 <= Re_D2) Then CALL WARNING('The result may not be accurate, since 2300 < Re_D2 < (5 1 QA6) does not hold. See Function fq_12conv. Re_D2 = XXXA 1', Re_D2) Turbulent/transitional flow Nusselt Number correlation (modified Gnielinski correlation) f := (1.82 LOG10(Re_D2) 1.64)"(2) Nu#_D2 := (f I 8) (Re_D21000) Pr_1 I (1 + 12.7 (f I 8)"(0.5) (Pr_1"(0.6667) 1 )) (Pr_1 I Pr_2)A0.11 Endlf h_1 := Nu#_D2 k_1 I D_h "[Wim"2K]" 134
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q_12conv := h_1 0_2 PI (T_2T_1ave) "[Wim]" End .................................................................................................. FUNCTION fq_34conv: Convective heat transfer rate between the absorber outer surface and the glazing inner surface ************************************************************************************************II FUNCTION fq_34conv(T _3, T 4) $Common 0_3, 0_ 4, L, P _a, P _6, g, v_6, T _0, T _6, T _std. AnnulusGas$, Glazing Intact$ P _a1 := P _a* CONVERT(torr, kPa) "[kPa]" T _34 := (T _3 + T 4) I 2 "[C]" T _36 := (T _3 + T _6) I 2 "[C]" If (Giazinglntact$ = 'No') Then Thermophysical Properties for air Rho_3 := Oensity(AIR, T = T _3, P=P _6) "[kglm"3]" Rho_6 := Oensity(AIR, T = T _6, P=P _6) "[kglm"3]" If (v_6 <= 0.1) Then MU_36 := viscosity(AIR, T = T _36) "[Nslm"2]" Rho_36 := Oensity(AIR, T = T _36, P=P _6) "[kglm"3]" Cp_36 := CP(AIR, T = T _36) "[kJikgK]" k_36 := conductivity(AIR, T = T _36) "[W lmK]" NU_36 := MU_36 I Rho_36 "[m"2/s]" Alpha_36 := k_36 I (Cp_36 Rho_36 1000) "[m"2/s]" Beta_36 := 1 I (T _36 + T _0) "[1 IK]" Ra_03 := g Beta_36 ABS(T _3 T _6) (0_3)"3 I (Aipha_36 NU_36) Warning Statement if following Nusselt Number correlation is used out of recommended range" If (Ra_03 <= 10"(5)) or (Ra_03 >= 10"12) Then CALL WARNING('The result may not be accurate, since 10"(5) < Ra_03 < 10"12 does not hold. See Function fq_34conv. Ra_03 = XXXA1', Ra_03) "Churchill and Chu correlation for natural convection from a long isothermal horizontal cylinder Pr_36 := NU_36 I Alpha_36 Nu#_bar := (0.60 + (0.387 Ra_03"(0.1667)) I (1 + (0.559 I Pr _36)"(0.5625))"(0.2963) )"2 h_36 := Nu#_bar k_36 I 0_3 "[Wim"2K]" fq_34conv := h_36 PI 0_3 (T _3T _6) "[Wim]" 135
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Else range II Thermophysical Properties for air II MU_3 := viscosity(AIR, T = T _3) 11[Nslm"2]" MU_6 := viscosity(AIR, T = T _6) 11[Nslm"2]11 k_3 := conductivity(AIR, T = T _3) "[W lmK]II k_6 := conductivity(AIR, T = T _6) II[W lmK]11 Cp_3 := CP(AIR, T = T _3) "[kJikgK]" Cp_6 := CP(AIR, T = T _6) "[kJikgK]11 NU_6 := MU_6 I Rho_6 "[m"2/s]" NU_3 := MU_3 I Rho_3 "[m"2/s]" Alpha_3 := k_3 I (Cp_3 Rho_3 1 000) "[m"21s]" Alpha_6 := k_6 I (Cp_6 Rho_6 1 000) 11[m"2/S]11 Re_D3 := v_6 D_3 I NU_6 Pr_3 := NU_3 I Alpha_3 Pr_6 := NU_6 I Alpha_6 "Warning Statements if following Nusselt Number correlation if used out of If (Re_D3 <= 1) or (Re_D3 >= 10"6) Then CALL WARNING('The result may not be accurate, since 1 < Re_D3 < 1 0"6 does not hold. See Function fq_34conv. Re_D3 = XXXA 1', Re_D3) If (Pr_6 <= 0.7) or (Pr_6 >= 500) Then CALL WARNING('The result may not be accurate, since 0.7 < Pr_6 < 500 does not hold. See Function fq_34conv. Pr_6 = XXXA1', Pr_6) Coefficients for external forced convection Nusselt Number correlation (Zhukauskas's correlation) II If (Pr _6 <= 1 0) Then n := 0.37 Else n := 0.36 Endlf If (Re_D3 < 40) Then c := 0.75 m := 0.4 Else If (40 <= Re_D3) and (Re_D3 < 10"3) Then c := 0.51 m :=0.5 Else If (1 0"3 <= Re_D3) and (Re_D3 < 2*1 0"5) Then c := 0.26 m :=0.6 Else If (2*1 0"5 <= Re_D3) and (Re_D3 < 1 0"6) Then 136
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c := 0.076 m :=0.7 Endlf Endlf Endlf Endlf Zhukauskas's correlation for external forced convection flow normal to an isothermal cylinder Nu#_bar := C (Re_03)Am (Pr_6)An (Pr_6 I Pr_3)A(0.25) h_36 := Nu#_bar k_6 I 0_3 "[WimA2K]" fq_34conv := h_36 0_3 PI (T _3T _6) "[Wim]" Endlf Else Thermophysical Properties tor gas in annulus space If (AnnulusGas$ = 'Argon') Then MU_34 := INTERPOLATE('Argon', 'MU', 'T', T = (T _34 + T _0)) "[kglms]" Cp_34 := INTERPOLATE('Argon', 'Cp', 'T', T = (T _34 + T _0)) "[kJikgK]" Cv_34 := INTERPOLATE('Argon', 'Cv', 'T', T = (T _34 + T _0)) "[kJikgK]" Rho_34 := P _a 1 I (0.20813 (T _34 + T _0)) "[kglmA3]" k_34 := INTERPOLATE('Argon', 'k', 'T', T = (T _34 + T _0)) "[W/mK]" k_std := INTERPOLATE('Argon', 'k', 'T', T = (T _std + T _0)) "(WimK]" Else MU_34 := VISCOSITY(AnnulusGas$, T = T _34) "[kglms]" Cp_34 := CP(AnnulusGas$, T = T _34) "[kJikgK]" Cv_34 := CV(AnnulusGas$, T = T _34) "[kJikgK]" k_34 := CONOUCTIVITY(AnnulusGas$, T = T _34) "[WimK]" Rho_34 := OENSITY(AnnulusGas$, T = T _34, P=P _a1) "[kglmA3]" k_std := CONOUCTIVITY(AnnulusGas$, T = T _std) "[WimK]" Endlf Modified Raithby and Hollands correlation for natural convection in an annular space between horizontal cylinders Alpha_34 := k_34 I(Cp_34 Rho_34 1 000) "[mA2/s]" NU_34 := MU_34 I Rho_34 "(mA2/s]" Beta_34 := 1 I (T _34 + T _0) "[11K]" Ra_03 := g Beta_34 ABS(T _3T 4) (0_3)A3 I (Aipha_34 NU_34) Ra_04 := g Beta_34 ABS(T _3T 4) (0_ 4)A3 I (Aipha_34 NU_34) Pr_34 := NU_34 I Alpha_34 Natq_34conv := 2.425 k_34 (T _3T 4) I (1 + (0_31 0_ 4)A(0.6))A(1.25) (Pr_34 Ra_03 I (0.861 + Pr_34))A(0.25) "[Wim]" P := P _a CONVERT(torr, mmHg) "[mmHg]" C1 := 2.331 *1 Ql\( 20) "[mmHgcmA31K]" Freemolecular heat transfer for an annular space between horizontal cylinders" If (AnnulusGas$ = 'Air') Then 137
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Delta:= 3.53 10A(8) "[em]" Endlf If (AnnulusGas$ = 'H2') Then Delta:= 2.4 1()A(8) "[em]" Endlf If (AnnulusGas$ = 'Argon') Then Delta:= 3.8*1()A(8) "[em]" Endlf Lambda := C1 (T _34 + T _0) I (P DeltaA2) "[em]" Gamma := Cp_34 I Cv_34 a:= 1 b := (2 a) I a (9 Gamma 5) I (2 (Gamma + 1)) h_34 := k_std I (D_3 I 2 ln(D_ 4 I D_3) + b *Lambda* (D_3 I D_ 4 + 1 )) 11[W lmA2K)" Kineticq_34conv := D_3 *PI* h_34 (T_3T_4) "[Wim]" II Following compares freemolecular heat transfer with natural convection heat transfer and uses the largest value for heat transfer in annulus If (Kineticq_34conv > Natq_34conv) Then fq_34conv := Kineticq_34conv "[Wim]ll II Warning Statement if freemolecular heat transfer correlation is used out of range II If (Ra_D4 < 10A7) Then CALL WARNING('The result may not be accurate, since (D_ 4 I (D_ 4 D_3))A4 < Ra_D4 < 1 QA7 does not hold. See Function fq_34conv. Ra_D4 = XXXA 1', Ra_D4) Else fq_34conv := Natq_34conv "[Wim]11 Endlf Endlf End .. ************************************************************************************************ FUNCTION fq_34rad :Radiation heat transfer rate between the absorber surface and glazing inner surface ************************************************************************************************ .. FUNCTION fq_34rad(T _3, T 4) $COMMON D_3, D_4, L, T_7, T _0, sigma, EPSILON_3, EPSILON_4, Glazinglntact$ If (Giazinglntact$ = 'No') Then fq_34rad :=EPSILON_3 PI D_3 *sigma* ((T _3 + T _O)A4(T _7 + T _O)A4) II[Wim)" 138
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Else fq_34rad :=PI 0_3 *sigma* ((T _3 + T _0)"4(T 4 + T _0)"4) I (1 I EPSILON_3 + 0_3 I D_ 4 ( 1 I EPSILON_ 41 )) "[Wim]" Endlf END "*********************************************************************************************** FUNCTION fq_56conv: Convective heat transfer rate between the glazing outer surface and the ambient air FUNCTION fq_56conv(T _5, T _6) $Common 0_5, L, P _6, v_6, g, T _0, Glazinglntact$ T _56 := (T _5 + T _6)12 "(C)" Thermophysical Properties for air MU_5 := VISCOSITY(Air,T = T _5) "[kg/ms]" MU_6 := VISCOSITY(Air,T = T _6) "[kg/ms]" MU_56 := VISCOSITY(Air, T = T _56) "[kglms)" k_5 := CONDUCTIVITY(Air,T = T _5) "[WimK)" k_6 := CONDUCTIVITY(Air,T = T _6) "[W lmK)" k_56 := CONDUCTIVITY(Air, T = T _56) "[W lmK]11 Cp_5 := SPECHEAT(Air,T = T _5) 11[kJikgK]11 Cp_6 := SPECHEAT(Air,T = T _6) 11[kJikgK]11 Cp_56 := CP(AIR, T = T _56) 11[kJikgK]" Rho_5 := DENSITY(Air,T = T _5, P=P _6) 11[kglm"3)11 Rho_6 := DENSITY(Air,T = T _6, P=P _6) 11[kglm"3)11 Rho_56 := DENSITY(Air, T = T _56, P=P _6) 11[kglm"3)" II If the glass envelope is missing then the convection heat transfer from the glass envelope is forced to zero by T _5 = T _6 II If (Giazinglntact$ = 'No') Then fq_56conv := (T _5T _6) 11[Wim]11 Else If (v_6 <= 0.1) Then range II II Coefficients for Churchill and Chu natural convection correlation II NU_56 := MU_56 I Rho_56 11[m"2/s]11 Alpha_56 := k_56 I (Cp_56 Rho_56 1000) 11[m"2/s]11 Beta_56 := 1 I (T _56 + T _0) 11[1/K)" Ra_D5 := g *Beta_ 56 ABS(T _5 T _6) (0_5)"3 I (Aipha_56 NU_56) II Warning Statement if following Nusselt Number correlation is used out of 139
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If (Ra_05 <= 1QA(5)) or (Ra_05 >= 10"12) Then CALL WARNING('The result may not be accurate, since 1 QA( 5) < Ra_05 < 1 QA12 does not hold. See Function fq_56conv. Ra_05 = XXXA 1', Ra_05) Churchill and Chu correlation for natural convection for a horizontal cylinder" Pr_56 := NU_561 Alpha_56 Nu#_bar := (0.60 + (0.387 Ra_05"{0.1667)) I (1 + (0.559 I Pr _56)"(0.5625) )"(0.2963) )"2 h_6 := Nu#_bar k_561 0_5 "[Wim"2K]" fq_56conv := h_6 *PI 0_5 (T _5T _6) "[Wim]" Else range II Coefficients for Zhukauskas's correlation Alpha_5 := k_5 I (Cp_5 Rho_5 1 000) 11[m"2/s]11 Alpha_6 := k_61 (Cp_6 Rho_6 1 000) 11[m"2/s]11 NU_5 := MU_51 Rho_5 11[m"2/s]" NU_6 := MU_61 Rho_6 11[m"2/s]" Pr_5 := NU_51 Alpha_5 Pr_6 := NU_61 Alpha_6 Re_05 := v_6 0_5 Rho_61 MU_6 II Warning Statement if following Nusselt Number correlation is used out of If (Pr_6 <= 0.7) or (Pr_6 >= 500) Then CALL WARNING('The result may not be accurate, since 0.7 < Pr_6 < 500 does not hold. See Function fq_56conv. Pr_6 = XXXA1', Pr_6) If (Re_05 <= 1) or (Re_05 >= 10"6) Then CALL WARNING('The result may not be accurate, since 1 < Re_05 < 10"6 does not hold. See Function fq_56conv. Re_05 = XXXA1 ', Re_05) II Zhukauskas's correlation for forced convection over a long horizontal cylinder" If (Pr _6 <= 1 0) Then n := 0.37 Else n := 0.36 Endlf If (Re_05 < 40) Then c := 0.75 m := 0.4 Else If (40 <= Re_05) and (Re_05 < 1 QA3) Then c := 0.51 m :=0.5 Else 140
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If (1 Ql\3 <= Re_D5) and (Re_D5 < 2*1 Ql\5) Then c := 0.26 m:=0.6 Else If (2*1 Ql\5 <= Re_D5) and (Re_D5 < 1 Ql\6) Then c := 0.076 m :=0.7 Endlf Endlf Endlf Endlf Nu#_6 := C Re_DS"m Pr_&"n *(Pr_6/Pr_5)"0.25 h_6 := Nu#_6 k_6 I 0_5 11[W/mA2K]11 fq_56conv := h_6 PI 0_5 (T _5 T _6) "[W /m]11 Endlf Endlf End ............................ ********************************************************************* FUNCTION fq_57rad: Radiation heat transfer rate between the glazing outer surface and the sky .................................................................................................. FUNCTION fq_57rad(T _5, T _7) $COMMON EPSILON_5, 0_5, L, sigma, T _0, Glazinglntact$ II If glass envelope is missing then radiation heat transfer from glass envelope is set to zero; otherwise, radiative heat transfer for a small convex object in a large cavity II If (Giazinglntact$ = 'No') Then fq_57rad := 0 11[W/m]11 Else fq_57rad := EPSILON_5 *PI 0_5 *sigma* ((T _5 + T _0)"4(T _7 + T _0)"4) II[W/m]ll Endlf END II************************************************************************************************ FUNCTION fq_5So1Abs : Solar flux on glazing FUNCTION fq_5So1Abs(q_i) $COMMON Glazinglntact$, Alpha_env, OptEff_env If glass envelope is missing then solar absorption in glass envelope is set to zero; otherwise, solar absorption is estimated with an optical efficiency term II 141
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If (Giazinglntact$ = 'No') Then fq_5So1Abs :=0 "[W/m]11 Else fq_5So1Abs := q_i OptEff_env Alpha_env 11[W/m]11 Endlf END IIW********W************************************************************************************** PROCEDURE Pq_ 45cond : One dimensional energy equation about inside surface of glazing .................................................................................................. PROCEDURE Pq_ 45cond(q_34conv, q_34rad: q_ 45cond) $COMMON Glazinglntact$ II If glass envelope is missing then radial conduction through glass envelope is set to zero; otherwise, the energy balance is used II If (Giazinglntact$ = 'No') Then q_45cond :=0 "[W/m]11 Else q_45cond := q_34conv + q_34rad 11[W/m]" Endlf END II*********************************************************************************************** PROCEDURE Pq_56conv: One dimensional energy equation about outside surface of glazing .................................................................................................. PROCEDURE Pq_56conv(q_ 45cond, q_5So1Abs, q_57rad: q_56conv) $COMMON Glazinglntact$ II If the glass envelope is missing then the convective heat transfer from the envelope is set to zero; otherwise, the energy balance is used II If (Giazinglntact$ = 'Yes') Then q_56conv := q_45cond + q_5So1Absq_57rad 11[W/m]11 Else q_56conv := 0 11[W/m]11 Endlf END 142
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....................................................... FUNCTION fA_cs: Inside cross sectional flow area of absorber ************************************************************************************************ .. FUNCTION fA_cs(D_2, D_p) $COMMON Flow_ Type$ If 'SNL AZTRAK Platform' then the HTF flow area accounts for the inserted plug If (Flow_ Type$ = 'Annulus Flow') Then fA_cs := PI (D_2 "2 D_p "2) /4 "[m"2]" Else fA_cs := PI (D_2 "2/4) "[m"2]" Endlf END .................................................................................................. FUNCTION fETA_Col: Collector efficiency ************************************************************************************************ .. FUNCTION fETA_Col(q_ 12conv, q_i) If the solar insolation is zero or the efficiency is negative, then the collector efficiency is set to zero If (q_i =0) Then fETA_Col := 0 Else If ((q_12conv/q_i)<=0.001) Then fETA_Col := 0 Else fETA_Col :=q_12conv/q_i Endlf Endlf END ........ ****************************************************************************************** FUNCTION fk_23: Absorber conductance ************************************************************************************************ .. { Based on linear fit of data from "Alloy Digest, Sourcebook, Stainless Steels"; ASM International, 2000.} FUNCTION fk_23(T _2, T _3) $COMMON AbsorberMaterial$ T _23 := (T _2 + T _3) I 2 "[C]" If (AbsorberMaterial$ = '304L') or (AbsorberMaterial$ = '316L') Then 143
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fk_23 := 0.013 T _23 + 15.2 "[W /mK]" Endlf If (AbsorberMaterial$ = '321 H') Then fk_23 := 0.0153 T _23 + 14.775 "[W /mK]" Endlf If (AbsorberMaterial$ = '842 Copper Pipe') Then fk_23 := 400 "[W/mK]" Endlf END II******************************************************************************************** PROCEDURE pSelectiveCoatingProperties: Selective Coating Emissivity and Absorptance ************************************************************************************************ .. PROCEDURE pSelectiveCoatingProperties(T _3: EPSILON_3, Alpha_abs, TAU_envelope) $COMMON SelectiveCoating$, T _0, TAU_envelope_UD, Alpha_abs_UD, EPSILON_3_1 OO_UD, EPSILON_3_ 400_UD "Calculates emissivity and determines optical properties for chosen selective coating type If (SelectiveCoating$ = 'UserDefined') Then TAU_envelope := TAU_envelope_UD Alpha_abs := Alpha_abs_UD EPSILON_3 := EPSILON_3_1 OO_UD (EPSILON_3_ 400_UD EPSILON_3_1 OO_UD)/3 + T _3 (EPSILON_3_ 400_UD EPSILON_3_1 OO_UD)/300 End if If (SelectiveCoating$ = 'Black Chrome (SNL test)') Then TAU_envelope := 0.935 Alpha_abs := 0.94 EPSILON_3 := 0.0005333 (T _3+ T _0) 0.0856 If (EPSILON_3 < 0.11) Then EPSILON_3 := 0.11 Endlf End if If (SelectiveCoating$ = 'Luz Cermet (SNL test)') Then TAU_envelope := 0.935 Alpha_abs := 0.92 EPSILON_3 := 0.000327 (T _3+ T _0) 0.065971 If (EPSILON_3 < 0.05) Then EPSILON_3 := 0.05 Endlf 144
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End if If (SelectiveCoating$ ='Solei UVAC Cermet (SNL test a)') Then TAU_envelope := 0.965 Alpha_abs := 0.96 EPSILON_3 := 2.249*1 0"(7)*(T _3)'" + 1.039*1 0"(4)*T _3 + 5.599*1 0"(2) Endlf If (SelectiveCoating$ ='Solei UVAC Cermet (SNL test b)') Then TAU_envelope := 0.965 Alpha_abs := 0.95 EPSILON_3 := 1.565*10"(7)*(T_3)"2 + 1.376*10"(4)*T_3 + 6.966*10"(2) Endlf If (SelectiveCoating$ ='Solei UVAC Cermet (SNL test avg)') Then T AU_envelope := 0.965 Alpha_abs := 0.955 EPSILON_3 := 1.907*10"(7)*(T _3)"2 + 1.208*10"(4)*T _3 + 6.282*1 0"(2) Endlf If (SelectiveCoating$ = 'Solei UVAC Cermet (0.1 0 @ 400C)') Then TAU_envelope := 0.97 Alpha_abs := 0.98 EPSILON_3 := 2.084*1 0"(4)*T _3 + 1.663*1 0"(2) Endlf If (SelectiveCoating$ ='Solei UVAC Cermet (0.07 @ 400C)') Then TAU_envelope := 0.97 Alpha_abs := 0.97 EPSILON_3 := 1.666*10"(4)*T_3 + 3.375*10"(3) Endlf END .................................................................................................. PROCEDURE pHCEdimensions: HCE dimensions based on HCE type ***********************************************************************************************II PROCEDURE pHCEdimensions(CollectorType$: D_2, D_3, D_ 4, D_5, W _aperture) $COMMON D_2_UD, D_3_UD, D_ 4_UD, D_5_UD, W _aperture_UD The following determines the HCE dimensions depending on the HCE type chosen in the Diagram Window If (CollectorType$ = 'UserDefined') Then D_2 := D_2_UD "[m]" D_3 := D_3_UD "[m]" D_ 4 := D_ 4_UD "[m]" D_5 := D_5_UD "[m]" 145
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W _aperture := W _aperture_UD "[m]" Endlf If (CollectorType$ = 'LS2') Then D_2 := 0.066 "[m]" D_3 := 0.070 "[m]" D_4 := 0.109 "[m]" D_5 := 0.115 "[m]" W _aperture := 4.8235 "[m]" Endlf If (CollectorType$ = 'LS3') Then D_2 := 0.066 "[m]" D_3 := 0.070 "[m]" D_4 := 0.115 "[m]" D_5 := 0.121 "[m]" W _aperture := 5.59 "[m]" Endlf If (CollectorType$ = '1ST') Then D_2 := 0.066 "[m]" D_3 := 0.070 "[m]" D_ 4 := 0.075 "[m]" D_5 := 0.0702 "[m]" W _aperture := 3.053 "[m]" Endlf END PROCEDURE pOpticaiEfficiency: Optical Efficiencies based on HCE type ************************************************************************************************ .. PROCEDURE pOpticaiEfficiency(CollectorType$: OptEff_env, OptEtt_abs) $COMMON Glazinglntact$, K, Reflectivity, TAU_envelope, Shadowing_UD, TrackingError_UD, GeomEffects_UD, Rho_mirror_clean_UD, Dirt_mirror_UD, Dirt_HCE_UD, Error_UD The following determines the optical properties depending on the HCE type chosen in the Diagram Window The properties should be modified as better data becomes available If (CollectorType$ ='UserDefined') Then Shadowing:= Shadowing_UD TrackingError := TrackingError_UD GeomEffects := GeomEffects_UD Rho_mirror_clean := Rho_mirror_clean_UD Dirt_mirror := Dirt_mirror_UD Dirt_HCE := Dirt_HCE_UD 146
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Error := Error_UD Endlf If (CollectorType$ = 'LS2') Then Shadowing:= 0.974 TrackingError := 0.994 GeomEffects := 0.98 Rho_mirror_clean := 0.935 Dirt_mirror := Reflectivity/Rho_mirror_clean Dirt_HCE := (1 + Dirt_mirror)/2 Error := 0.96 Endlf If (CollectorType$ = 'LS3') or (CollectorType$ = '1ST') Then Shadowing:= 0.974 TrackingError := 0.994 GeomEffects := 0.98 Rho_mirror_clean := 0.935 Dirt_mirror := Reflectivity/Rho_mirror_clean Dirt_HCE := (1 + Dirt_mirror)/2 Error := 0.96 Endlf following if statement prevents Dirt_mirror and Dirt_HCE from being larger then 1 if the input for Reflectivity is larger then Rho_mirror_clean If (Dirt_mirror > 1) Then Dirt_mirror := 1 Dirt_HCE := 1 Endlf If (Giazinglntact$ = 'No') Then OptEff_env := 0 OptEff_abs :=Shadowing* TrackingError GeomEffects Rho_mirror_clean Dirt_mirror Error K Else OptEff_env := Shadowing TrackingError GeomEffects Rho_mirror_clean Dirt_mirror Dirt_HCE Error K OptEff_abs := OptEff_env T AU_Envelope End if END 147
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II*********************************************************************************************** FUNCTION fD_h: Hydraulic diameter ************************************************************************************************ .. FUNCTION fD_h(Fiow_ Type$) $COMMON 0_2, D_p If 'SNL AZTRAK Platform' is chosen, then the inside absorber diameter accounts for the inserted plug If (Flow_ Type$ = 'Annulus Flow') Then fD_h := 0_2 D_p "[m]" Else fD_h := 0_2 "[m]" Endlf END ...... ******************************************************************************************** FUNCTION fq_cond_bracket: Heat loss estimate through HCE support bracket ************************************************************************************************ .. FUNCTION fq_cond_bracket(T _3) $COMMON T _S, T _0, P _S, v_S, g effective bracket perimeter for convection heat transfer" P _brae := 0.2032 "[m]" effective bracket diameter (2 x 1 in) D_brac := 0.0508 "[m]" minimum bracket crosssectional area for conduction heat transfer" A_cs_brac := 0.0001S129 "[m"2]" conduction coefficient for carbon steel at SOO K" k_brac := 48 "[W /mK]" effective bracket base temperature" T _base := T _3 1 0 "[C]" "estimate average bracket temperature" T _brae := (T _base + T _S) I 3 "[C]" estimate film temperature for support bracket T _braeS := (T _brae + T _S) /2 "[C]" convection coefficient with and without wind" If (v_S <= 0.1) Then MU_bracS := viscosity(AIR, T = T _braeS) "[Ns/m"2]" 148
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Rho_brac6 := Density(AIR, T = T _brac6, P=P _6) "[kglm"3]" Cp_brac6 := CP(AIR, T = T _brac6) "[kJikgK]" k_brac6 := conductivity(AIR, T = T _brac6) "[WimK]" NU_brac6 := MU_brac6 I Rho_brac6 "[m"2/s]" Alpha_brac6 := k_brac6 I (Cp_brac6 Rho_brac6 1 000) "[m"21s]" Beta_brac6 := 1 I (T _brac6 + T _0) "[1 IK]" Ra_Dbrac := g Beta_brac6 ABS(T _brae T _6) (D_brac)"3 I (Aipha_brac6 NU_brac6) "Warning Statement if following Nusselt Number correlation is used out of recommended range If (Ra_Dbrac <= 10"(5)) or (Ra_Dbrac >= 10"12) Then CALL WARNING('The result may not be accurate, since 1 0"( 5) < Ra_Dbrac < 1 0"12 does not hold. See Function fq_cond_bracket. Ra_Dbrac = XXXA1', Ra_Dbrac) Churchill and Chu correlation for natural convection from a long isothermal horizontal cylinder Pr_brac6 := NU_brac6 I Alpha_brac6 Nu#_bar := (0.60 + (0.387 Ra_Dbrac"(0.1667)) I (1 + (0.559 I Pr_brac6)"(0.5625))"(0.2963) )"2 h_brac6 := Nu#_bar k_brac6 I D_brac "[Wim"2K]" Else Thermophysical Properties for air MU_brac := viscosity(AIR, T = T _brae) "[Ns/m"2]" MU_6 := viscosity(AIR, T = T _6) "[Nslm"2]" Rho_6 := Density(AIR, T = T _6, P=P _6) "[kglm"3)" Rho_brac := Density(AIR, T = T _brae, P=P _6) "[kglm"3]" k_brac := conductivity(AIR, T = T _brae) "[W lmK]" k_6 := conductivity(AIR, T = T _6) "[W lmK]" k_brac6 := conductivity( AIR, T = T _brac6) "[W lmK]" Cp_brac := CP(AIR, T = T _brae) "[kJikgK]" Cp_6 := CP(AIR, T = T _6) "[kJikgK]" NU_6 := MU_6 I Rho_6 "[m"21s]" NU_brac := MU_brac I Rho_brac "[m"2/s]" Alpha_brac := k_brac I (Cp_brac Rho_brac 1000) "[m"21s]" Alpha_6 := k_6 I (Cp_6 Rho_6 1 000) "[m"2/s]" Re_Dbrac := v_6 D_brac I NU_6 Pr_brac := NU_brac I Alpha_brac Pr_6 := NU_6 I Alpha_6 "Warning Statements if following Nusselt Correlation is used out of range" If (Re_Dbrac <= 1) or (Re_Dbrac >= 1 0"6) Then CALL WARNING('The result may not be accurate, since 1 < Re_Dbrac < 1 0"6 does not hold. See Function fq_cond_bracket. Re_Dbrac = XXXA1 ', Re_Dbrac) 149
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If (Pr_6 <= 0.7) or (Pr_6 >= 500) Then CALL WARNING('The result may not be accurate, since 0.7 < Pr_6 < 500 does not hold. See Function fq_cond_bracket. Pr_6 = XXXA1', Pr_6) "Coefficients for external forced convection Nusselt Number correlation (Zhukauskas's correlation) If (Pr_6 <= 10) Then n := 0.37 Else n := 0.36 Endlf If (Re_Dbrac < 40) Then c == 0.75 m := 0.4 Else If (40 <= Re_Dbrac) and (Re_Dbrac< 1QI\3) Then c := 0.51 m :=0.5 Else If (1 Ql\3 <= Re_Dbrac) and (Re_Dbrac < 2*1 Ql\5) Then c := 0.26 m :=0.6 Else If (2*1 Ql\5 <= Re_Dbrac) and (Re_Dbrac < 1 Ql\6) Then c := 0.076 m:=0.7 Endlf Endlf Endlf Endlf Zhukauskas's correlation for external forced convection flow normal to an isothermal cylinder Nu#_bar := C (Re_Dbrac)"m (Pr_6)"n (Pr_6 I Pr_brac)"(0.25) h_brac6 := Nu#_bar k_brac6 I D_brac "[Wim"2K]" Endlf estimated conduction heat loss through HCE support brackets I HCE length fq_cond_bracket := SQRT(h_brac6 P _brae* k_brac A_cs_brac) (T _baseT _6)14.06 "[W lm]" END 150
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II*********************************************************************************************** FUNCTION fq_HeatLoss: Heat loss definition ************************************************************************************************II FUNCTION fq_HeatLoss(q_34conv, q_34rad, q_56conv, q_57rad, q_cond_bracket) $COMMON Glazinglntact$ If (Giazinglntact$ = 'Yes') Then fq_HeatLoss := q_56conv + q_57rad + q_cond_bracket "[W/m]" Else fq_HeatLoss := q_34conv + q_34rad + q_cond_bracket "[W /m]" Endlf END II*********************************************************************************************** Constants and conversions ************************************************************************************************u StefanBoltzmann constant sigma= 5.67E8 "[W/m"2K"4]" Used to convert temperature from C to K T _0 = 273.15 "[C]" "Gravitational constant" g = 9.81 "[m/s"2]" Wind speed from MPH to m/s conversion v_6 = v_6mph '* CONVERT(mph, m/s) "[m/s]" IIWW********************************************************************************************* Optical properties ************************************************************************************************II Alpha_env = .02 "Calls procedure that determines optical properties" CALL pSelectiveCoatingProperties(T_3: EPSILON_3, Alpha_abs, TAU_envelope) "Calls procedure that determines effective optical efficiencies at the glass envelope and absorber CALL pOpticaiEfficiency(CollectorType$: OptEff_env, OptEff_abs) Inner and outer glass envelope emissivities (Pyrex)" EPSILON_ 4 = 0.86 EPSILON_5 = 0.86 Incident angle modifier from test data for SEGS LS2 receiver K = COS(THET A) + 0.000884 '* THETA 0.00005369 '* (THET A)"2 151
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.................................................................................................. Heat collector element size .................................................................................................. Calls procedure for determining HCE dimensions based on 'CollectorType' CALL pHCEdimensions(CollectorType$: 0_2, 0_3, 0_ 4, 0_5, W _aperture) .................................................................................................. Ambient conditions .................................................................................................. "Effective sky temperature estimated as 8 C below ambient" T _7 = T _6 8 "[C]" Converts ambient pressure from 0.83 atm to kPa, ambient pressure is treated as a constant" P _6 = 0.83 CONVERT(atm, kPa) "[kPa]11 Standard ambient air temperature II T _std = 25 "(C]11 Incoming solar radiation per aperture length II q_i = l_b W_aperture 11(W/m]11 .................................................................................................. Temporary outputs and inputs .................................................................................................. Space used for any temporary outputs or inputs .................................................................................................. Hydraulic diameter ************************************************************************************************ .. "Calls function to calculate HTF hydraulic diameter II O_h = fD_h(Fiow_ Type$) .................................................................................................. Heat transfer fluid flow rates ************************************************************************************************ .. Calls function to calculate HTF crosssection flow area II A_cs = fA_cs(0_2, O_p) "(mA2]" II Converts HTF flow rate from gpm to mA3/s v_1volm = v_1volg* CONVERT(gpm, mA3/s) 11(mA3/s]11 HTF velocity II v_1 =V_1volm/(A_cs) "[m/s]11 152
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!!************************************************************************************************ q_12conv absorber Convective heat transfer rate between the heat transfer fluid and .................................................................................................. CALL Pq_ 12conv(T _1 ave, T _2, Fluid$: q_12conv) .................................................................................................. q_23cond Conduction heat transfer rate through the absorber ************************************************************************************************ .. "Absorber conductance, temperature and material type dependent" k_23 = fk_23(T _2, T _3) "[W lmK]" q_23cond = 2 *PI k_23 (T _3T _2) I LN(D_31 0_2) "[Wim]" .. ************************************************************************************************ q_34conv Convective heat transfer rate between the absorber pipe and glazing ************************************************************************************************ .. q_34conv = fq_34conv(T _3, T 4) "[Wim]" .................................................................................................. q_34rad Radiation heat transfer rate between the absorber surface and glazing inner surface ************************************************************************************************ .. q_34rad = fq_34rad(T _3, T 4) "[Wim]" .................................................................................................. q_45cond Conduction heat transfer rate through the glazing ************************************************************************************************ .. glass envelope conductivity K_ 45 = 1.04 "[WimK]" q_ 45cond = 2 *PI K_ 45 (T 4T _5) I LN(D_51 D_ 4) "[Wim]" .................................................................................................. q_56conv Convective heat transfer rate from the glazing to the atmosphere ************************************************************************************************ .. q_56conv = fq_56conv(T _5, T _6) "[Wim]" 153
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!!************************************************************************************************ q_57rad Radiation heat transfer rate between the glazing outer surface and the sky 11 q_57rad = fq_57rad(T _5, T _7) "(W/m]" .................................................................................................. q_3So1Abs Solar flux on absorber pipe .................................................................................................. q_3So1Abs = q_i OptEff_abs Alpha_abs "[W/m]" ll********************************************************************************w*************** q_SSoiAbs Solar Flux on glazing Envelope .................................................................................................. q_SSoiAbs = fq_SSoiAbs(q_i) "[W/m]" .................................................................................................. q_cond_bracketHCE support bracket conductive losses .................................................................................................. q_cond_bracket = fq_cond_bracket(T _3) "[W/m]" .................................................................................................. One dimensional (Radial) model ************************************************************************************************II CALL Pq_45cond(q_34conv, q_34rad: q_45cond) "[W/m]" CALL Pq_56conv(q_45cond, q_SSoiAbs, q_57rad: q_56conv) "[W/m]" q_12conv = q_23cond "(W/m]" q_3So1Abs q_23cond q_34conv q_34rad q_cond_bracket = 0 "[W /m]" q_HeatLoss = fq_HeatLoss(q_34conv, q_34rad, q_56conv, q_57rad, q_cond_bracket) "[W/m]" q_OptLoss = q_i (1ETA_EffectiveOptEff/100) "[W/m]" q_HeatGain = q_12conv "(W /m]" .................................................................................................. ETA_ Col Collector efficiency ************************************************************************************************!! ETA_ Col = fETA_Col(q_ 12conv, q_i)*1 00 "[%]" ETA_EffectiveOptEff = (OptEff_abs Alpha_abs + OptEff_env Alpha_env)*100 "[%]" 154
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F. TwoDimensional Design Study Version of EES Code (Tab settings have been shortened and numerous comment statements have been omitted to reduce length of following code.) .. *********************************************************************************************** FUNCTION fq_12conv: Convective heat transfer rate from the HTF to the inside of the receiver tube ************************************************************************************************ .. PROCEDURE Pq_12conv(T_1ave, v_1ave, T_2, Fluid$: q_12conv, Cp_1) $Common D_h, 0_2, L, TestType$ "Warning Statements if HTF is evaluated out of recommended temperature ranges" If (Fluid$= 'Syltherm BOO') Then If (T _1ave < 40) or (400 < T _1ave) Then CALL WARNING('The result may not be accurate, since Syltherm BOO fluid properties are out of recommended temperature range, 40 C < T < 400 C. T _1 ave= XXXA 1', T _1 ave) Endlf If (Fluid$= 'Therminol VP1') Then If (T _1ave < 12) or (400 < T _1ave) Then CALL WARNING('The result may not be accurate, since Therminol VP1 fluid properties are out of recommended temperature range, 12 C < T < 400 C T _1 ave= XXXA 1', T _1 ave) Endlf If (Fluid$= 'Xceltherm 600') Then If (T _1 ave < 20) or (S16 < T _1 ave) Then CALL WARNING('The result may not be accurate, since Xceltherm 600 fluid properties are out of recommended temperature range, 20 C < T < S16 C .. T _1 ave= XXXA 1', T _1 ave) Endlf If (Fluid$= 'Salt (60% NaNOS, 40% KNOS)') Then If (T _1 ave < 260) or (621 < T _1 ave) Then CALL WARNING('The result may not be accurate, since Salt (60% NaNOS, 40% KNOS) fluid properties are out of recommended temperature range, 260 C < T < 621 C. T _1 ave = XXXA 1', T _1 ave) Endlf If (Fluid$ = 'Hitec XL') Then If (T _1ave < 266) or (4BO < T _1ave) Then CALL WARNING('The result may not be accurate, since Hitec XL fluid properties are out of recommended temperature range, 266 C < T < 4BO C. T_1ave = XXXA1', T _1ave) Endlf If (Fluid$= 'Water') Then If (T _1 ave < 0) or (1 00 < T _1 ave) Then CALL WARNING('The result may not be accurate, since Water fluid properties are out of recommended temperature range, 0 C < T < 1 00 C. T _1 ave = XXXA 1', T _1 ave) Endlf Thermophysical properties for HTF MU_1 := INTERPOLATE(Fiuid$,'MU','T',T=T_1ave) "[kg/ms]" 155
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MU_2 := INTERPOLATE(Fiuid$,'MU','T',T = T _2) 11[kglms]" Cp_1 := INTERPOLATE(Fiuid$,'Cp','T',T = T _1 ave) 11[JikgK)" Cp_2 := INTERPOLATE(Fiuid$,'Cp','T',T = T _2) 11[JikgK]11 k_1 := INTERPOLATE(Fiuid$,'k','T',T=T_1ave) 11[WimK]11 k_2 := INTERPOLATE(Fiuid$,'k','T',T = T _2) II[WimK)" RH0_1 := INTERPOLATE(Fiuid$,'RHO','T',T=T_1ave) 11[kg/mA3]11 Re_02 := ABS((RH0_1 O_h v_1ave) I (MU_1)) Pr_2 := ABS(Cp_2 MU_2 I k_2) Pr_1 := ABS(Cp_1 MU_1 I k_1) II Warning statements if Nusselt Number correlation is used out of recommended range II If (Pr_1 <= 0.5) or (2000 <= Pr_1) Then CALL WARNING('The result may not be accurate, since 0.5 < Pr_1 < 2000 does not hold. See Function q_12conv. Pr_1 = XXXA1', Pr_1) If (Pr_2 <= 0.5) or (2000 <= Pr_2) Then CALL WARNING('The result may not be accurate, since 0.5 < Pr_2 < 2000 does not hold. See Function q_12conv. Pr_2 = XXXA1', Pr_2) If ( Re_02 <= (2300)) or (5*10"6 <= Re_02) Then CALL WARNING('The result may not be accurate, since 2300 < Re_02 < (5 1 0"6) does not hold. See Function q_12conv. Re_02 = XXXA1', Re_02) II TurbulenVtransitional flow Nusselt Number correlation (modified Gnielinski correlation) II f_2 := (1.82 LOG10(Re_02)1.64)A(2) Nu#_02 := (f_2 I 8) (Re_021 000) Pr_1 I (1 + 12.7 (f_218)A(0.5) (Pr_1A(0.6667) 1)) (Pr_1 I Pr_2)AQ.11 h_1 := Nu#_02 k_1 I O_h 11[WimA2K]11 q_12conv := h_1 0_2 *PI (T_2T_1ave) 11[W/m]11 End "************************************************************************************************ FUNCTION Convective heat transfer rate between the absorber outer surface and the glazing inner surface ************************************************************************************************ .. FUNCTION fq_34conv(T _3, T 4, AnnulusGas$) $Common 0_3, 0_ 4, L, P _a, P _6, g, v_6, T _0, T _6, T _std, Glazing Intact$ P _a1 := P _a* CONVERT(torr, kPa) 11[kPa]11 T _36 := (T _3 + T _6) I 2 11[C]11 If (Giazinglntact$ = 'No') Then 156
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" Thermophysical Properties for air Rho_3 := Oensity(AIR, T = T _3, P=P _6) "[kglm"3]" Rho_6 := Oensity(AIR, T = T _6, P=P _6) "[kglm"3]" If (v_6 <= 0.1) Then MU_36 := viscosity(AIR, T = T _36) "[Nslm"2]" Rho_36 := Oensity(AIR, T = T _36, P=P _6) "[kglm"3]" Cp_36 := CP(AIR, T = T _36) "[kJikgK]" k_36 := conductivity(AIR, T = T _36) "[WimK]" NU_36 := MU_36 I Rho_36 "[m"2/s]" Alpha_36 := k_36 I (Cp_36 Rho_36 1 000) "[m"2/s]" Beta_36 := 1 I (T _36 + T _0) "[1 IK]" Ra_03 := g Beta_36 ABS(T _3 T _6) (0_3)"3 I (Aipha_36 NU_36) "Warning Statement if following Nusselt Number correlation is used out of recommended range If (Ra_03 <= 10"(5)) or (Ra_03 >= 10"12) Then CALL WARNING('The result may not be accurate, since 1 0"( 5) < Ra_03 < 1 0"12 does not hold. See Function fq_34conv. Ra_03 = XXXA1', Ra_03) Churchill and Chu correlation for natural convection from a long isothermal horizontal cylinder Pr_36 := NU_36 I Alpha_36 Nu#_bar := (0.60 + (0.387 Ra_03"(0.1667)) I (1 + (0.559 I Pr_36)A(0.5625))"(0.2963) )"2 h_36 := Nu#_bar k_36 I 0_3 "[Wim"2K]" fq_34conv := h_36 *PI* 0_3 (T _3T _6) "[Wim]" Else Thermophysical Properties for air MU_3 := viscosity(AIR, T = T _3) "[Nslm"2]" MU_6 := viscosity(AIR, T = T _6) "[Nslm"2]" k_3 := conductivity(AIR, T = T _3) "[WimK]" k_6 := conductivity(AIR, T = T _6) "[WimK]" k_36 := conductivity(AIR, T = T _36) "[W lmK]" Cp_3 := CP(AIR, T = T _3) "[kJikgK]" Cp_6 := CP(AIR, T = T _6) "[kJikgK]" NU_6 := MU_6 I Rho_6 "[m"21s]" NU_3 := MU_3 I Rho_3 "[m"21s]" Alpha_3 := k_3 I (Cp_3 Rho_3 1 000) "[m"2/s]" Alpha_6 := k_6 I (Cp_6 Rho_6 1000) "[m"2/s]" Re_03 := v_6 0_3 I NU_6 Pr_3 := NU_3 I Alpha_3 Pr_6 := NU_6 I Alpha_6 157
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"Warning Statements if following Nusselt Correlation is used out of range" If (Re_03 <= 1) or (Re_03 >= 10"6) Then CALL WARNING('The result may not be accurate, since 1 < Re_03 < 1 0"6 does not hold. See Function fq_34conv. Re_03 = XXXA 1', Re_03) If (Pr_6 <= 0.7) or (Pr_6 >= 500) Then CALL WARNING('The result may not be accurate, since 0.7 < Pr_6 < 500 does not hold. See Function fq_34conv. Pr_6 = XXXA1', Pr_6) Coefficients for external forced convection Nusselt Number correlation (Zhukauskas's correlation) If (Pr_6 <= 1 0) Then n := 0.37 Else n := 0.36 Endlf If (Re_03 < 40) Then c := 0.75 m := 0.4 Else If (40 <= Re_03) and (Re_03 < 1QA3) Then c := 0.51 m :=0.5 Else If (1QA3 <= Re_03) and (Re_03 < 2*1QAS) Then c := 0.26 m :=0.6 Else If (2*1 QA5 <= Re_03) and (Re_03 < 1 0"6) Then c := 0.076 m:=0.7 Endlf Endlf Endlf Endlf Zhukauskas's correlation for external forced convection flow normal to an isothermal cylinder Nu#_bar := C (Re_03)Arn (Pr_6)"n (Pr_6 I Pr_3)"(0.25) h_36 := Nu#_bar k_36 I 0_3 "[Wim"2K]" fq_34conv := h_36 0_3 PI (T _3T _6) "[W/m]" Endlf Else T _34 := (T _3 + T 4) I 2 "[C)" Thermophysical Properties for gas in annulus space If (AnnulusGas$ = 'Argon') Then 158
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MU_34 := INTERPOLATE('Argon', 'MU', 'T', T = (T _34 + T _0)) "[kglms]" Cp_34 := INTERPOLATE('Argon', 'Cp', 'T', T = (T _34 + T _0)) "[kJikgK]" Cv_34 := INTERPOLATE('Argon', 'Cv', 'T', T = (T _34 + T _0)) "[kJikgK]" Rho_34 := P _a 1 I (0.20813 (T _34 + T _0)) "[kglmA3)" k_34 := INTERPOLATE('Argon', 'k', 'T', T = (T _34 + T _0)) "[WimK]" k_std := INTERPOLA TE('Argon', 'k', 'T', T = (T _std + T _0)) "[W lmK]" Else MU_34 := VISCOSITY(AnnulusGas$, T = T _34) "[kg/ms]" Cp_34 := CP(AnnulusGas$, T = T _34) "[kJikgK]" Cv_34 := CV(AnnulusGas$, T = T _34) "[kJ!kgK]" k_34 := CONDUCTIVITY(AnnulusGas$, T = T _34) "[W lmK]" Rho_34 := DENSITY(AnnulusGas$, T = T _34, P=P _a1) "[kglm"3]" k_std := CONDUCTIVITY(AnnulusGas$, T = T _std) "[W lmK]" Endlf "Modified Raithby and Hollands correlation for natural convection in an annular space between horizontal cylinders" Alpha_34 := k_341(Cp_34 Rho_34 1000) "[m"21s]" NU_34 := MU_34 I Rho_34 "[m"2/s]" Beta_34 := 1 I (T _34 + T _0) "[111<]" Ra_D3 := g Beta_34 ABS(T _3T 4) (D_3)"'31 (Aipha_34 NU_34) Ra_D4 := g Beta_34 ABS(T _3T 4) (D_ 4)"'31 (Aipha_34 NU_34) Pr_34 := NU_34 I Alpha_34 Natq_34conv := 2.425 k_34 (T _3 T 4) (Pr _34 Ra_D3 I (0.861 + Pr_34))"(0.25) I (1 + (D_31 D_4)"(0.6))A(1.25) "[Wim]" Freemolecular heat transfer for an annular space between horizontal cylinders" P := P _a CONVERT(torr, mmHg) "[mmHg]" C1 := 2.331 *1 Ql\(20) "[mmHgcm"31K]" If (AnnulusGas$ = 'Air') Then Delta:= 3.53 1QI\(8) "[em]" Endlf If (AnnulusGas$ = 'H2') Then Delta:= 2.4 1QI\(8) "[em]" Endlf If (AnnulusGas$ = 'Argon') Then Delta:= 3.8*1 Ql\(8) "[em]" Endlf Lambda:= C1 (T _34 + T _0) I (P Delta"2) "[em]" Gamma := Cp_34 I Cv_34 a:= 1 b := (2a) (9 *Gamma5) I (2 *a* (Gamma+ 1 )) 159
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h_34 := k_std I (0_3 I 2 ln(D_ 4 I 0_3) + b *Lambda* (0_3 I D_ 4 + 1 )) "[W lm"2K]" Kineticq_34conv := 0_3 *PI* h_34 (T_3T_4) "[Wim]" "Following compares free molecular heat transfer with natural convection heat transfer and uses the largest value for heat transfer in annulus If (Kineticq_34conv > Natq_34conv) Then fq_34conv := Kineticq_34conv "[Wim]" "Warning statement if free molecular correlation is used our of range" If (Ra_D4 < 1QI\7) Then CALL WARNING('The result may not be accurate, since (D_ 4 I (D_ 4 0_3))114 < Ra_D4 < 1 Q/\7 does not hold. See Function fq_34conv. Ra_D4 = XXXA1', Ra_D4) Else fq_34conv := Natq_34conv "[Wim]" Endlf Endlf End .. ************************************************************************************************ FUNCTION fq_34rad: Radiation heat transfer rate between the absorber surface and glazing inner surface ************************************************************************************************ .. FUNCTION fq_34rad(T _3, T 4, i) $COMMON 0_3, D_ 4, L, T _7, T _0, sigma, EPSILON_3[1 .imax], EPSILON_ 4, Glazing Intact$ If (Giazinglntact$ = 'No') Then fq_34rad :=EPSILON_3[i] PI 0_3 *sigma* ((T _3 + T _0)114(T _7 + T _0)114) "[Wim]" Else fq_34rad := PI 0_3 *sigma* ((T _3 + T _0)114(T 4 + T _0)114) I (1 I EPSILON_3[i] + 0_3 I D_ 4 ( 1 I EPSILON_ 41)) "[Wim]" Endlf END .. ************************************************************************************************ FUNCTION fq_56conv: Convective heat transfer rate between the glazing outer surface and the ambient air ************************************************************************************************ .. FUNCTION fq_56conv(T _5, T _6) $Common 0_5, L, P _6, v_6, g, T _0, Glazinglntact$ 160
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T _56 := (T _5 + T _6) I 2 10[C]10 10 Thermophysical Properties for air 10 MU_5 := VISCOSITY(Air,T = T _5) "[kg/ms]" MU_6 := VISCOSITY(Air,T = T _6) "[kg/ms]IO MU_56 := VISCOSITY(Air, T = T _56) IO[kglms]" k_5 := CONOUCTIVITY(Air,T = T _5) "[W lmK]" k_6 := CONOUCTIVITY(Air,T = T _6) "[W lmK]IO k_56 := CONOUCTIVITY(Air, T = T _56) IO[WimK]" Cp_5 := SPECHEAT(Air,T = T _5) IO[kJikgK]" Cp_6 := SPECHEAT(Air,T = T _6) 10[kJikgK]10 Cp_56 := CP(AIR, T = T _56) 10[kJikgK]IO Rho_5 := OENSITY(Air,T = T _5, P=P _6) "[kg/m"3]10 Rho_6 := OENSITY(Air,T = T _6, P=P _6) "[kg/m"3]" Rho_56 := OENSITY(Air, T = T _56, P=P _6) 10[kglm"3]10 10 If the glass envelope is missing then the convection heat transfer from the glass envelope is forced to zero by T _5 = T _6 10 If (Giazinglntact$ = 'No') Then fq_56conv := (T _5T _6) 10[Wim]10 Else If (v_6 <= 0.1) Then range 10 10 Coefficients for Churchill and Chu natural convection correlation 10 NU_56 := MU_561 Rho_56 10[m"2/s]10 Alpha_56 := k_561 (Cp_56 Rho_56 1000) 10[m"2/s]" Beta_56 := 1 I (T _56+ T _0) 10[11K]" Ra_05 := g *Beta_56 ABS(T _5 T _6) (0_5)"31 (Aipha_56 NU_56) 10 Warning Statement if following Nusselt Number correlation is used out of If (Ra_05 <= 10"(5)) or (Ra_05 >= 10"12) Then CALL WARNING('The result may not be accurate, since 10"(5) < Ra_05 < 10"12 does not hold. See Function fq_56conv. Ra_05 = XXXA1', Ra_05) 10 Churchill and Chu correlation for natural convection for a horizontal cylinder 10 Pr_56 := NU_561 Alpha_56 Nu#_bar := (0.60 + (0.387 Ra_05"(0.1667)) I (1 + (0.5591 Pr _56)"(0.5625) )"(0.2963) )"2 h_6 := Nu#_bar k_561 0_5 "[Wim"2K]" fq_56conv := h_6 *PI 0_5 (T _5T _6) 10[Wim]" Else 10 Coefficients for Zhukauskas's correlation 10 Alpha_5 := k_51 (Cp_5 Aho_5 1 000) "[m"2/s]" Alpha_6 := k_61 (Cp_6 Rho_6 1 000) "[m"2/s]" 161
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range" NU_5 := MU_5 I Rho_5 "[m"2/s]" NU_6 := MU_6 I Rho_6 "[m"2/s)" Pr_5 := NU_5 I Alpha_5 Pr_6 := NU_6 I Alpha_6 Re_D5 := v_6 D_5 Rho_6 I MU_6 "Warning Statement if following Nusselt Number coorelation is used out of If (Pr_6 <= 0.7) or (Pr_6 >= 500) Then CALL WARNING('The result may not be accurate, since 0.7 < Pr_6 < 500 does not hold. See Function fq_56conv. Pr_6 = XXXA1', Pr_6) If (Re_D5 <= 1) or (Re_D5 >= 1 0"6) Then CALL WARNING('The result may not be accurate, since 1 < Re_D5 < 1 0"6 does not hold. See Function fq_56conv. Re_D5 = XXXA1 ', Re_D5) Zhukauskas's correlation for forced convection over a long horizontal cylinder" If (Pr _6 <= 1 0) Then n := 0.37 Else n := 0.36 Endlf If (Re_D5 < 40) Then c := 0.75 m := 0.4 Else If (40 <= Re_D5) and (Re_D5 < 10"3) Then c := 0.51 m :=0.5 Else If (1 0"3 <= Re_D5) and (Re_D5 < 2*1 0"5) Then c := 0.26 m :=0.6 Else If (2*1 0"5 <= Re_D5) and (Re_D5 < 1 0"6) Then c := 0.076 m :=0.7 Endlf Endlf Endlf Endlf Nu#_6 := C Re_DS"m Pr_6"n *(Pr_61Pr_5)"0.25 h_6 := Nu#_6 k_6 I D_5 "[Wim"2K]" fq_56conv := h_6 *PI* 0_5 (T _5T _6) "[Wim]" Endlf Endlf 162
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End 11 FUNCTION fq_57rad: Radiation heat transfer rate between the glazing outer surface and the sky FUNCTION fq_57rad(T _5, T _7) $COMMON EPSILON_5, D_5, L, sigma, T _0, Glazinglntact$ II If glass envelope is missing then radiation heat transfer from glass envelope is set to zero; otherwise, radiative heat transfer for a small convex object in a large cavity II If (Giazinglntact$ = 'No') Then fq_57rad := 0 11(W/m]11 Else fq_57rad := EPSILON_5 *PI D_5 *sigma* ((T _5 + T _0)"4(T _7 + T _0)"4) II[W/m]ll Endlf END .................................................................................................. FUNCTION fq_5So1Abs : Solar flux on glazing ************************************************************************************************ .. FUNCTION fq_5So1Abs(q_i) $COMMON Alpha_env, OptEft_env, Glazinglntact$ II If glass envelope is missing then solar absorption in glass envelope is set to zero; otherwise, solar absorption is estimated with an optical efficiency term II If (Giazinglntact$ ='No') Then fq_5So1Abs :=0 "[W/m]11 Else fq_5So1Abs := q_i OptEff_env Alpha_env "[W/m]" Endlf END .................................................................................................. PROCEDURE Pq_ 45cond : One dimensional energy equation about inside surface of glazing ************************************************************************************************ .. PROCEDURE Pq_ 45cond(q_34conv, q_34rad: q_ 45cond) $COMMON Glazinglntact$ 163
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" If glass envelope is missing then radial conduction through glass envelope is set to zero; otherwise, the energy balance is used If (Giazinglntact$ = 'No') Then q_45cond :=0 "[Wim]" Else q_ 45cond := q_34conv+ q_34rad "[W lm]" Endlf END II************************************************************************************************ PROCEDURE Pq_56conv : One dimensional energy equation about outside surface of glazing ************************************************************************************************ .. PROCEDURE Pq_56conv(q_ 45cond, q_5So1Abs, q_57rad: q_56conv) $COMMON Glazinglntact$ If the glass envelope is missing then the convective heat transfer from the envelope is set to zero; otherwise, the energy balance is used If (Giazinglntact$ = 'No') Then q_56conv := 0 "[Wim]" Else q_56conv := q_ 45cond+ q_5So1Abs q_57rad "[W lm]" Endlf END .. ************************************************************************************************ FUNCTION fA_cs :Inside cross sectional flow area of absorber *********************************************************************************************** .. FUNCTION fA_cs(D_2, D_p) $COMMON TestType$ If 'SNL AZTRAK Platform' then the HTF flow area accounts for the inserted plug If (TestType$ = 'SNL AZTRAK Platform') Then fA_cs := PI (D_2 "2 D_p "2) I 4 "[m"2]" Else fA_cs :=PI (D_2 "2 I 4) "[m"2]" Endlf END 164
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II********************************************************************************************* FUNCTION fETA_Col: Collector efficiency ************************************************************************************************ .. FUNCTION fETA_Col(q_12conv, q_i) If heat is leaving the HTF, then the collector efficiency is set to zero" If ((q_ 12conv/q_i) <= 0.001) Then fETA_Col := 0 Else fETA_Col := q_12conv/q_i Endlf END ... *********************************************************************************************** FUNCTION fk_23: Absorber conductance ************************************************************************************************ .. { Based on linear fit of data from "Alloy Digest, Sourcebook, Stainless Steels"; ASM International, 2000.} FUNCTION fk_23(T _2, T _3) $COMMON AbsorberMaterial$ T _23 := (T _2 + T _3)/2 "[C]" If (AbsorberMaterial$ = '304L') or (AbsorberMaterial$ = '316L') Then fk_23 := 0.013 T _23 + 15.2 "[W /mK]" Endlf If (AbsorberMaterial$ = '321 H') Then fk_23 := 0.0153 T _23 + 14.775 "[W /mK]" Endlf If (AbsorberMaterial$ = '842 Copper Pipe') Then fk_23 := 400 "[W/mK]" Endlf END II************************************************************************************************ PROCEDURE pSelectiveCoatingProperties: Selective Coating Emissivity and Absorptance ************************************************************************************************ .. PROCEDURE pSelectiveCoatingProperties(imax, T _3[1 .imax]: EPSILON_3[1 .. imax], Alpha_abs, TAU_envelope) 165
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$COMMON T _0, TAU_envelope_UD, Alpha_abs_UD, EPSILON_3_1 OO_UD, EPSILON_3_ 400_UD, SelectiveCoating$ DoLoop to calculate emissivity for all the HCE increments, and to return optical properties for chosen selective coating type j :=0 repeat j :=j+1 If (SelectiveCoating$ = 'UserDefined') Then TAU_envelope := TAU_envelope_UD Alpha_abs := Alpha_abs_UD EPSILON_3U] := EPSILON_3_1 OO_UD(EPSILON_3_ 400_UDEPSILON_3_1 OO_UD)/3 + T _3[j] .. (EPSILON_3_ 400_UD EPSILON_3_1 OO_UD)/300 2) 2) End if If (SelectiveCoating$ = 'Black Chrome (SNL test)') Then TAU_envelope := 0.935 Alpha_abs := 0.94 EPSILON_3U] := 0.0005333 .. (T _3U]+ T _0) 0.0856 If (EPSILON_3U] < 0.11) Then EPSILON_3U] := 0.11 Endlf End if If (SelectiveCoating$ = 'Luz Cermet (SNL test)') Then TAU_envelope := 0.935 Alpha_abs := 0.92 EPSILON_3U] := 0.000327 .. (T _3[j]+ T _0) 0.065971 If (EPSILON_3[j] < 0.05) Then EPSILON_3U] := 0.05 Endlf End if If (SelectiveCoating$ = 'Solei UVAC Cermet (SNL test a)') Then TAU_envelope := 0.965 Alpha_abs := 0.96 EPSILON_3U] := 2.249'*1QA(7)'*(T _3U])"2 + 1.039'*1 QA(4)'*T _3[j] + 5.599'*1 QA(Endlf If (SelectiveCoating$ ='Solei UVAC Cermet (SNL test b)') Then TAU_envelope := 0.965 Alpha_abs := 0.95 EPSILON_3U] := 1.565'*1 QA(7)'*(T _3U])"2 + 1.376'*1 QA(4)'*T _3U] + 6.966'*1 QA(Endlf 166
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2) If (SelectiveCoating$ ='Solei UVAC Cermet (SNL test avg)') Then TAU_envelope := 0.965 Alpha_abs := 0.955 EPSILON_3U] := 1.907*1QA(7)*(T_3U])"2 + 1.208*1CY'(4)*T_3U] + 6.282*1CY'(Endlf If (SelectiveCoating$ = 'Solei UVAC Cermet (0.1 0 @ 400C)') Then TAU_envelope := 0.97 Alpha_abs := 0.98 EPSILON_3U] := 2.084*1CY'(4)*T_3U] + 1.663*1CY'(2) Endlf If (SelectiveCoating$ ='Solei UVAC Cermet (0.07 @ 400C)') Then TAU_envelope := 0.97 Alpha_abs := 0.97 EPSILON_3U] := 1.666*1 QA( 4)*T _3U] + 3.375*1 QA( 3) Endlf until U>=(imax)) END II************************************************************************************************ PROCEDURE pHCEdimensions: HCE dimensions based on HCE type ************************************************************************************************ .. PROCEDURE pHCEdimensions(HCEtype$: D_ 4, D_5, A_aperture, L_aperture, L_HCE, Number_HCE) $COMMON TestType$ If (HCEtype$ = 'LS2') Then D_5 := 0.115 "[m]" D_4 := 0.109 "[m]" L_HCE := 4.06 "[m]" If (TestType$ = 'SNL AZTRAK Platform') Then A_aperture := 39 "[m"2]" Number_HCE := 2 L_aperture := Number_HCE L_HCE "[m]" Else If (TestType$ = 'KJC Test Loop') Then A_aperture := 235 16 "[m"2]" Number_HCE := 12 16 L_aperture := L_HCE Number_HCE "[m]" End if End if 167
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Endlf If (HCEtype$ = 'LS3') Then D_4:=0.115 "[m]" D_5 := 0.121 "(m]" L_HCE := 4.06 "[m]" A_aperture := 545 "[m"2]" Number_HCE := 24 L_aperture := L_HCE Number_HCE "[m]" Endlf If (HCEtype$ ='1ST') Then D_ 4 := 0.075 "[m]" D_5 := 0.0702 "[m]" A_aperture := 13.19 "(m"2]" L_HCE := 2.16 "[m]" Number_HCE := 1 L_aperture := L_HCE Number_HCE "[m]" Endlf END .... ********************************************************************************************** PROCEDURE pOpticaiEfficiency: Optical Efficiencies based on HCE type ************************************************************************************************ .. PROCEDURE pOpticaiEfficiency(HCEtype$: OptEff_env, OptEff_abs) $COMMON Alpha_abs, Alpha_env, K, Reflectivity, TAU_envelope, Glazinglntact$ All the following optical properties should be modified as updated values are determined If (HCEtype$ = 'LS2') Then Shadowing:= 0.974 TrackingError := 0.994 GeomEffects := 0.98 Rho_mirror_clean := 0.935 Dirt_mirror := Reflectivity/Rho_mirror_clean Dirt_HCE := (1 + Dirt_mirror)/2 Error := 0.96 Endlf If (HCEtype$ = 'LS3') or (HCEtype$ = '1ST') Then Shadowing:= 0.974 TrackingError := 0.994 GeomEffects := 0.98 Rho_mirror_clean := 0.935 Dirt_mirror := Reflectivity/Rho_mirror_clean Dirt_HCE := (1 + Dirt_mirror)/2 168
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Error := 0.96 Endlf following if statement prevents Dirt_mirror and Dirt_HCE from being larger then 1 if the input for Reflectivity is larger then Rho_mirror_clean If (Dirt_mirror > 1) Then Dirt_mirror := 1 Dirt_HCE := 1 Endlf If (Giazinglntact$ = 'No') Then OptEff_env := 0 OptEff_abs := Shadowing TrackingError GeomEffects Rho_mirror_clean Dirt mirror Error K Else OptEff_env :=Shadowing TrackingError GeomEffects Rho_mirror_clean Dirt_mirror Dirt_HCE Error K OptEff_abs := OptEff_env TAU_Envelope End if END .................................................................................................. FUNCTION fD_h: Hydraulic diameter ************************************************************************************************!! FUNCTION fD_h(TestType$) $COMMON D_2, D_p If 'SNL AZTRAK Platform' is chosen, then the inside absorber diameter accounts for the inserted plug If (TestType$ = 'SNL AZTRAK Platform') Then fD_h := D_2 D_p "[m]" Else fD_h := D_2 "[m]" Endlf END II************************************************************************************************ FUNCTION fq_cond_bracket: Heat loss estimate through HCE support bracket ************************************************************************************************ .. FUNCTION fq_cond_bracket(T _3, i) $COMMON L_HCE, Number_HCE, L_aperture, T _6, T _0, P _6, v_6, DEL TAL, imax, g effective bracket perimeter for convection heat transfer" P _brae := 0.2032 "[m]" 169
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" effective bracket diameter (2 x 1 in) D_brac := 0.0508 "[m]" minimum bracket crosssectional area for conduction heat transfer" A_cs_brac := 0.0001S129 "[m"2)" conduction coefficient for carbon steel at SOO K" k_brac := 48 "[WimK]" "effective bracket base temperature" T _base := T _3 1 0 "[C)" estimate average bracket temperature T _brae := (T _base + T _S) I 3 "[C)" estimate film temperature for support bracket T _braeS := (T _brae + T _S) 12 "[C)" convection coefficient with and without wind" If (v_S <= 0.1) Then MU_bracS := viscosity(AIR, T = T _braeS) "[Nslm"2]" Rho_bracS := Density(AIR, T = T _braeS, P=P _S) "[kglm"3)" Cp_bracS := CP(AIR, T = T _braeS) "[kJikgK]" k_bracS := conductivity(AIR, T = T _braeS) "[WimK]" NU_bracS := MU_bracS I Rho_bracS "[m"2/s)" Alpha_bracS := k_bracS I (Cp_bracS Rho_bracS 1000) "[m"2/s]" Beta_ braeS := 1 I (T _braeS + T _0) "[1 IK]" Ra_Dbrac := g Beta_bracS ABS(T _braeT _S) (D_brac)"3 I (Aipha_bracS NU_bracS) Warning Statement if following Nusselt Number correlation is used out of recommended range If (Ra_Dbrac <= 1QI\(5)) or (Ra_Dbrac >= 10"12) Then CALL WARNING('The result may not be accurate, since 1 Ql\( 5) < Ra_Dbrac < 1 Ql\12 does not hold. See Function fq_cond_bracket. Ra_Dbrac = XXXA 1 ', Ra_Dbrac) Churchill and Chu correlation for natural convection from a long isothermal horizontal cylinder Pr_bracS := NU_bracS I Alpha_bracS Nu#_bar := (O.SO + (0.387 Ra_Dbrac"(0.1SS7)) I (1 + (0.559/ Pr _bracS)"(0.5S25) )"(0.29S3) )"2 h_bracS := Nu#_bar k_bracS/ D_brac "[Wim"2K]" Else Thermophysical Properties for air 170
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MU_brac := viscosity(AIR, T = T _brae) "[Nslm"2]" MU_6 := viscosity(AIR, T = T _6) "[Nslm"2]" Rho_6 := Density(AIR, T = T _6, P=P _6) "[kglm"3]" Rho_brac := Density(AIR, T = T _brae, P=P _6) "[kglm"3]" k_brac := conductivity(AIR, T = T _brae) "[WimK]" k_6 := conductivity(AIR, T = T _6) "[WimK]" k_brac6 := conductivity(AIR, T = T _brac6) "[WimK]" Cp_brac := CP(AIR, T = T _brae) "[kJikgK]" Cp_6 := CP(AIR, T = T _6) "[kJikgK]" NU_6 := MU_6 I Rho_6 "[m"21s]" NU_brac := MU_brac I Rho_brac "[m"2/s]" Alpha_brac := k_brac I (Cp_brac Rho_brac 1 000) "[m"2/s]" Alpha_6 := k_6 I (Cp_6 Rho_6 1 000) "[m"2/s]" Re_Dbrac := v_6 D_brac I NU_6 Pr_brac := NU_brac I Alpha_brac Pr_6 := NU_6 I Alpha_6 "Warning Statements if following Nusselt Correlation is used out of range" If (Re_Dbrac <= 1) or (Re_Dbrac >= 1 0"6) Then CALL WARNING('The result may not be accurate, since 1 < Re_Dbrac < 1 QA6 does not hold. See Function fq_cond_bracket. Re_Dbrac = XXXA1', Re_Dbrac) If (Pr_6 <= 0.7) or (Pr_6 >= 500) Then CALL WARNING('The result may not be accurate, since 0.7 < Pr_6 < 500 does not hold. See Function fq_cond_bracket. Pr_6 = XXXA1', Pr_6) "Coefficients for external forced convection Nusselt Number correlation (Zhukauskas's correlation) If (Pr_6 <= 1 0) Then n := 0.37 Else n := 0.36 Endlf If (Re_Dbrac < 40) Then c := 0.75 m := 0.4 Else If (40 <= Re_Dbrac) and (Re_Dbrac< 10"3) Then c := 0.51 m :=0.5 Else If (1 QA3 <= Re_Dbrac) and (Re_Dbrac < 2*1 QA5) Then c := 0.26 m :=0.6 Else If (2*1 QA5 <= Re_Dbrac) and (Re_Dbrac < 1 QA6) Then 171
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c := 0.076 m :=0.7 Endlf Endlf Endlf Endlf Zhukauskas's correlation for external forced convection flow normal to an isothermal cylinder Nu#_bar := C (Re_Dbrac)"m (Pr_6)An (Pr_61 Pr_brac)"(0.25) h_brac6 := Nu#_bar k_brac6 I D_brac "[Wim"2K]" Endlf number of HCE support brackets for each HCE segment If (DEL TAL <= L_HCE) Then index_1 := ROUND(i DEL TAL I L_HCE) index_2 := index_1 L_HCE If (((i 1) *DEL TAL)<= index_2) AND (index_2 <= (i *DEL TAL)) Then n := 1 Else n := 0 Endlf Else n := ROUND(DELTAL/ L_HCE) Endlf If (i = 1) OR (i = imax) Then n := n + 1 Endlf fq_cond_bracket := n SQRT(h_brac6 P _brae k_brac A_cs_brac) (T _base T_6) "[W]" END IIW********************************************************************************************** FUNCTION fHeatLoss: Heat loss term for temperature out equation ***********************************************************************************************" FUNCTION fHeatLoss(q_34rad, q_34conv, q_56conv, q_57rad) $COMMON Glazinglntact$ 172
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If (Giazinglntact$ = 'No') Then fHeatLoss := q_34conv + q_34rad "[W/m]" Else fHeatLoss := q_56conv + q_57rad "[W/m]" Endlf END .................................................................................................. Constants and conversions ************************************************************************************************ .. "StefanBoltzmann constant" sigma= 5.67E8 "[W/m"2K"4]" "Used to convert temperature from C to K" T _0 = 273.15 "(C]" Gravitational constant g = 9.81 "[m/s"2]" Wind speed conversion v_6 = v_6mph CONVERT(mph, m/s) "[m/s]" "Glass envelope conductance II K_ 45 = 1.04 "[W/mK]II Absorber pipe inside surface equivalent roughness factor II e = 1.5E6 "[m]" .................................................................................................. Optical properties ************************************************************************************************ .. II Glass envelope absorbtivity Alpha_env = .02 II Calls procedure that determines optical properties CALL pSelectiveCoatingProperties(imax, T _3(1 .. imax]: EPSILON_3(1 .. imax], Alpha_abs, TAU_envelope) II Calls procedure that determines optical efficiencies at the glass envelope and absorber" CALL pOpticaiEfficiency(HCEtype$: OptEff_env, OptEff_abs) II Inner and outer glass envelope surface emissivities (pyrex)" EPSILON_ 4 = 0.86 EPSILON_5 = 0.86 173
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" Incident angle modifier from test data for SEGS LS2 Receiver K = COS(THETA) + 0.000884 *THETA0.00005369 (THETA)A2 II************************************************************************************************ Heat collector element size ************************************************************************************************" 'SNL AZTRAK Tracker' plug diameter'' D_p = 0.0508 11[m]" II Inner and outer absorber pipe diameters" 0_2 = 0.066 "[m]" 0_3 = 0.070 "[m]" Calls procedure for determining HCE dimensions based on 'HCE Type'" CALL pHCEdimensions(HCEtype$: D_ 4, 0_5, A_aperture, L_aperture, L_HCE, Number_HCE) II*********************************************************************************************** Ambient conditions .................................................................................................. Effective sky temperature estimated as 8 C below ambient T _7 = T _6 8 11[C]" Converts ambient pressure from 0.83 atm to kPa, ambient pressure is treated as a constant" P _6 = 0.83 CONVERT(atm, kPa) "[kPa]" Standard ambient air temperature T _std = 25 "[C]" II Incoming solar irradiance per aperture length" q_i = l_b A_aperture I L_aperture "[W/m]" II************************************************************************************************ Temporary outputs and inputs ************************************************************************************************II Space used for any temporary outputs or inputs II II*********************************************************************************************** Indexes ************************************************************************************************ .. Iteration stepsize along aperture length DEL TAL= (L_aperture)/(imax) "[m]" 174
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.. *********************************************************************************************** Hydraulic diameter ************************************************************************************************ .. Calls function to calculate HTF hydraulic diameter D_h = fD_h(TestType$) .. ************************************************************************************************ Heat transfer fluid flow rates *********************************************************************************************** .. "Calls function to calculate HTF crosssection flow area" A_cs = fA_cs(D_2, D_p) "[m"2]" Converts HTF flow rate from gpm to m"3/s v_1 volm = v_1 volg* CONVERT(gpm, m"3/s) "[m"3/s]" "Calculates HTF velocity" v_1inlet = v_1volm I (A_cs) "[m/s]" "Mass flow rate (conserved)" m_dot = v_1 inlet* RH0_1 inlet* A_cs "[kg/s]" RH0_1 inlet= INTERPOLATE(Fiuid$,'RHO','T',T = T _1 inlet) "[kg/m"3]" .. *********************************************************************************************** ************************************************************************************************* ************************************************************************************************* Doloops for temperatures along aperture length ************************************************************************************************* ************************************************************************************************* ************************************************************************************************ .. "DoLoop to set the inlet temperature and velocity of each increment to the previous increment's outlet temperature and velocity" T _1 in[1] = T _1 inlet "[C]" v_1in[1] = v_1inlet "[m/s]" Duplicate i = 1, (imax1) T _1 in[i+ 1] = T _1 out[i] "[C]" v_1in[i+1]=v_1out[i] "[m/s]" End DoLoop to conduct an energy balance on each increment that determines outlet temperature, heat loss, and efficiency" Duplicate i = 1 ,imax v_1 ave[i] = (v_1 in[i] + v_1 out[i])/2 "[m/s]" 175
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" HTF Densities RH0_1 out[i] = INTERPOLATE(Fiuid$,'RHO','T',T = T _1 out[i]) "[kg/m"3]" RH0_1ave[i] = INTERPOLATE(Fiuid$,'RHO','T',T = T _1ave[i]) "[kglm"3]" MU_1ave[i] = INTERPOLATE(Fiuid$,'MU','T',T = T _1ave[i]) "[kglms]" Re_D2ave[i] = RH0_1 ave[i] v_1 ave[i] D_2 I MU_1 ave[i] "friction factor, f, relation 1 I SQRT(f[i]) = 2.0 LOG10( e I (D_2 3.7) + 2.51 I (Re_D2ave[i] SQRT(f[i]))) .................................................................................................. HTF velocities ************************************************************************************************ .. Outlet velocity of each increment v_1 out[i] = m_dot I (RH0_1 out[i] A_cs) "[mls]" .................................................................................................. Heat loss estimate through HCE support bracket .................................................................................................. q_cond_bracket[i] = fq_cond_bracket(T _3[i], i) "[W]" HTF temperatures ************************************************************************************************ .. "Outlet HTF temperature for each increment" HeatLoss[i] = fHeatLoss(q_34rad[i], q_34conv[i], q_56conv[i], q_57rad[i]) "[Wim]" T _1 out[i] = ((q_SSoiAbs + q_3So1Abs HeatLoss[i] )* DEL TAL q_cond_bracket[i]) I (m_dot Cp_1 ave[i]) +( DEL TAP[i] I RH0_1 ave[i] +((v_1 in[i])"2 (v _1 out[i])"2)12)1Cp_1 ave[i] + T _1 in[i] "[C)" "Average HTF temperature for each increment" T _1 ave[i] = (T _1 in[i] + T _1 out[i])l2 "[C)" DELTAP[i] = ( f[i] *(DEL TAL/ D_2) (m_dot/A_cs)"2) 1(2*RH0_1ave[i]) "[Pa]" II************************************************************************************************ q_12conv[i] Convective heat transfer rate between the heat transfer fluid and absorber ************************************************************************************************II CALL Pq_12conv(T _1 ave[i], v_1 ave[i], T _2[i], Fluid$: q_12conv[i], Cp_1 ave[i]) 176
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.. ***************************************************'******************************************** q_23cond[i] Conduction heat transfer rate through the absorber ************************************************************************************************II Absorber conductance, temperature and material type dependent k_23[i] = fk_23(T _2[i], T _3[i]) "[W lmK]" q_23cond[i] = 2 *PI k_23[i] (T _3[i]T _2[i]) I LN(D_31 D_2) "[Wim]" II*****************************************************************************'***********'****** q_34conv[i] Convective heat transfer rate between the absorber pipe and glazing .................................................................................................. q_34conv[i] = fq_34conv(T _3[i], T 4[i], AnnulusGas$) "[W lm]" .. ************************************************************************************************ q_34rad[i] Radiation heat transfer rate between the absorber surface and glazing inner surface ************************************************************************************************ .. q_34rad[i] = fq_34rad(T _3[i], T 4[i], i) "[W lm]" ............................................................................................... .. q_ 45cond[i] Conduction heat transfer rate through the glass envelope ************************************************************************************************ .. q_45cond[i] = 2 *PI K_45 (T_4[i]T_S[i]) I LN(D_SI 0_4) "[Wim]" "************************************************************************************************ q_56conv[i] Convective heat transfer rate from the glazing to the atmosphere .................................................................................................. q_56conv[i] = fq_56conv(T _S[i], T _6) "[Wim]" .. ************************************************************************************************ q_57rad[i] the sky Radiation heat transfer rate between the glazing outer surface and ************************************************************************************************ .. q_57rad[i] = fq_57rad(T _S[i], T _7) "[Wim]" .. ********************************************************************************'*************** One dimensional (Radial) model *********************************************************************************************** .. CALL Pq_ 45cond(q_34conv[i], q_34rad[i]: q_ 45cond[i]) "[Wim]" CALL Pq_56conv(q_ 45cond[i], q_SSoiAbs, q_57rad[i]: q_56conv[i]) "[Wim]" q_12conv[i] = q_23cond[i] "[W lm]" 177
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q_3So1Abs q_23cond[i] q_34conv[i] q_34rad[i] q_cond_bracket[i] I DEL TAL = 0 "[Wim)" End .................................................................................................. ************************************************************************************************* .................................................................................................. Outlet temperature set equal to the final increment outlet temperature T 1 outlet = T _1 out[imax] "[C)" v_1 outlet= v_1 out[imax] "[mls]" DEL TAP _total = SUM(DEL T APUJ, j=1, imax) "[Pa]" ...... ******************************************************************************************** Average HTF Temperature ************************************************************************************************ .. T _ave= AVERAGE(T _1 ave[1 .imax]) "[C)" .................................................................................................. Effective optical efficiency and optical loss ************************************************************************************************II EffectOptEff = (OptEff_abs Alpha_abs + OptEff_env Alpha_env) Eta_EffectOptEff = EffectOptEff 100 "[%]" q_OptLoss = q_i (1EffectOptEff) "[W lm]" "************************************************************************************************ ETA_Col Collector efficiency ************************************************************************************************ .. "Total HTF convection heat gain equals summation of heat gain for each increment" q_heat_gain = SUM((q_ 12convU] *DEL TAL), j=1 ,imax) I L_aperture "[Wim]" ETA_Col = fETA_Col(q_heat_gain, q_i) 100 "[%]" II************************************************************************************************ q_3So1Abs Solar flux on absorber pipe ************************************************************************************************II q_3So1Abs = q_i OptEff_abs Alpha_abs "[Wim]" 178
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q_5So1Abs Solar Flux on glazing Envelope ************************************************************************************************ .. q_5So1Abs = fq_5So1Abs(q_i) "[Wim]" .. ************************************************************************************************ HCE heat losses ************************************************************************************************ .. q_cond_bracket_total = SUM(q_cond_bracketU], j=1, imax) "[W]" q_cond_bracket_L = q_cond_bracket_total I L_aperture "[Wim]" q_HeatLoss_ApertureLength = SUM((HeatLossU] *DEL TAL), j=1, imax) I L_aperture + q_cond_bracket_L "[Wim]" q_HeatLoss_HCEarea = q_HeatLoss_ApertureLength/(PI*D_5) "[Wim"2]" q_HeatLoss_CoiArea = (q_HeatLoss_ApertureLength L_aperture)IA_aperture "[Wim"2]" 179
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REFERENCES ASM Handbook Committee (1978). Metals Handbook. Properties and SelectionNonferrous Alloys and Pure Metals, Vol. 2, Metals Park, Ohio: American Society for Metals. Bejan, A. (1995) Convection Heat Transfer, Second Edition. New York, NY: John Wiley & Sons. Bejan, A. (1988) Advance Engineering Thermodynamics. New York, NY: John Wiley & Sons. Cohen, G. E. (29 July 2002) Email memorandum. Duke Solar Energy, Raleigh, NC. Cohen, G. E.; Kearney, D. W.; Kolb, G. J. (June 1999) Final Report on the Operation and Maintenance Improvement Program for Concentrating Solar Power Plants. SAND991290. Albuquerque, NM: Sandia National Laboratories. Davis, J. R., ed. (2000) Alloy Digest, Sourcebook, Stainless Steels. Materials Park, Ohio: ASM International. Dudley, V. E.; Kolb, G. J.; Mahoney, A. R.; et al. (December 1994). Test Results: SEGS LS2 Solar Collector. SAND941884. Albuquerque, NM: SANDIA National Laboratories. Duffie, J. A.; Beckman, W. A. (1991) Solar Engineering ofThermal Processes, Second Edition. New York, NY: John Wiley and Sons. Final Report on HCE Heat Transfer Analysis Code. (December 1993) SANDIA Contract No. AB0227. Work performed by KJC Operating Company, Boron. CA. Albuquerque, NM: Sandia National Laboratories. Gnielinski, V. (April 1976) "New Equations for Heat and Mass Transfer in Turbulent Pipe and Channel Flow." International Chemical Engineering (16:2); pp. 359363. Howell, J. R. (1982) A Catalog of Radiation Configuration Factors. New York, NY: McGrawHill. Howell, J. R.; Buckius, R. 0. (1987) Fundamentals of Engineering Thermodynamics. New York, NY: McGrawHill. 180
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Incropera, F.; DeWitt, D. (1990) Fundamentals of Heat and Mass Transfer, Third Edition. New York, NY: John Wiley and Sons. Klein, S.A. (2002) Engineering Equation Solver (EES)for Microsoft Windows Operating System: Commercial and Professional Versions. Madison, WI: FChart Software. (available on the Web at http://www.fchart.com.) Mahoney, R. (September 2002) Phone conversation. Sandia National Laboratories, Albuquerque, NM. Marshal, N., trans!. (1976) Gas Encylopedia. New York, NY: Elsevier. Munson, B. R.; Young, D. F., Okiishi, T. H. (1990) Fundamentals of Fluid Mechanics. New York, NY: John Wiley and Sons. Ozisik, M. N. (1977) Basic Heat Transfer. New York, NY: McGrawHill Book Company. Ozisik, M. N. (1973) Radiative Transfer and Interactions with Conduction and Convection. New York, NY: John Wiley and Sons. Price, H. (1997) Guidlinesfor Reporting Parabolic Trough Solar Electric System Peiformance. NREL/CP55022729. Golden, CO: National Renewable Energy Laboratory. Price, H. (2000) "UV AC Test HCE Heat Loss Model" Excel Spreadsheet. Golden, CO: National Renewable Energy Laboratory. Price, H. (2001) Concentrated Solar Power Use in Africa. NRELITP. Golden, CO: National Renewable Energy Laboratory. Ratzel, A.; Hickox, C.; Gartling, D. (February 1979) "Techniques for Reducing Thermal Conduction and Natural Convection Heat Losses in Annular Receiver Geometries." Journal of Heat Transfer (101:1); pp. 108113. Siegel, R., Howell, J. (2002) Thermal Radiation Heat Transfer, Fourth Edition. New York, NY: Taylor & Francis. Solei Solar Systems Ltd. web pagehttp://www.solel.com. Subtask 1.2 Final Report, A NonImaging Secondary Reflector for Parabolic Trough Concentrators. (November 20, 2001) NREL Subcontract No. NAA13044106. Work performed by Duke Solar Energy, LLC, Arvada, CO.; Golden, CO.: National Renewable Energy Laboratory. 181
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Thomas, A.; H. M. Guven (1993). "Parabolic Trough ConcentratorsDesign, Construction and Evaluation." Energy Conversion Management (34:5); pp. 401416. Thomas, A.; H. M. Guven (1994). "Effect of Optical Errors on Flux Distribution Around the Absorber Tube of a Parabolic Trough Concentrator" Energy Conversion Management (35:7); pp. 401416. Touloukian, Y. S.; DeWitt, D.P., eds. (1972). Radiative Properties, Nonmetalic Solids. Thermophysical Properties of Matter, Vol. 8, New York: Plenum Publishing. 182
