Citation
Numerical study of a Maisotsenko cycle

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Title:
Numerical study of a Maisotsenko cycle
Creator:
Alsadki, Tahani
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
xv, 61 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Evaporative cooling -- Mathematical models ( lcsh )
Heat -- Transmission -- Mathematical models ( lcsh )
Dew point -- Mathematical models ( lcsh )
Maisotsenko Cycle
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (M.A.S.)--University of Colorado Denver, 2011. Mechanical engineering
Bibliography:
Includes bibliographical references (leaves 60-61).
General Note:
Department of Mechanical Engineering
Statement of Responsibility:
by Tahani Alsadik.

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Source Institution:
University of Colorado Denver
Holding Location:
|Auraria Library
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
785955633 ( OCLC )
ocn785955633

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NUMERICAL STUDY OF A MAISOTSENKO CYCLE By TAHANI ALSADIK B.S., University of Omar Almakter, 2004 A thesis Submitted to the University of Colorado Denver In partial fulfillment Of the Requirements for the degree of Master of Applied Science in Mechanical Engineering 2011

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This thesis for the Master of Mechanical Engineering Degree by Tahani Alsadik has been approved by Trapp. John Date

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Alsadik, Tahani (M.S., Mechanical Engineering) Numerical Study of a Maisotsenko Cycle Thesis directed by Associate Professor Peter .E. Jenkins and Samuel W.J. Welch ABSTRACT A new type of evaporative cooling system for sensible cooling of air is proposed and analyzed by using the conservation of energy and the conservation of mass principles. Conventionally, onedimensional differential equations were used to describe the heat and mass transfer processes. In this thesis, analytical and numerical solutions are developed for heat and mass transfer processes to predid the behavior of dew point evaporative systems. The Maisotsenko cycle is present as an alternative to indirect evaporative cooling system, which will improve the performances of the process. The efficiency of the cycle can be increased by utilizing different inlet air conditions. In this thesis, analytical correlations of heat and mass transfer are developed for the dew point evaporative cooling systems, subject to various operating conditions. The analysis is performed for air in contact with water

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various operating conditions. The analysis is performed for air in contact with water film in the wet side and air in the dry side. Validation of the model is performed by comparisons with previous study about the dew point evaporative systems. This abstract accurately represents the content of candidate's thesis. I recommend its publication. Signed __ Peter .E. Jenkins

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ACKNOWLEDGEMENT There are several people I would like to acknowledge for the help they have given to me during the preparation of this thesis. I would not have been able to do it without them; I would like to express my most sincere gratitude and appreciation to my advisors, Professor Samuel W.J. Welch and Professor Peter .E. Jenkins for providing me with unique opportunity to work in this research area, for their expert guidance and mentorship, and for their encouragement and support at all levels. I am grateful to all members all Mechanical Engineering Department especially the program assistant Petrina M. Morgan, the student assistance Rachel Haggerty. I would like to thank my family, and especially my parents ldress and Lila, for supporting me across the oceans and being proud of me without questions. In addition, I would like to thank my brothers and special thanks to my brother Awoth, and my sister Mabroka for support, help, and encouragement. And last but not least, I would like to express my eternal gratitude to my husband, Fawzi. Much honor in this degree belongs to him for his everlasting love

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and support. Thank you for giving me a chance to improve myself though all walks of my life.

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CONTENTS List of Figures -----------------------------------------------x List of Tables ----------------------------------------------xii Nomenclature ---------------------------------------------xiii Chapter !.Introduction -----------------------------------------------1 1.1 Background --------------------------------------------1 1.2 Objective ----------------------------------------------5 1.3 Scientific Method ----------------------------------------7 1.3.1 Basic Concept of Modeling Using Computer Simulation-----------7 2.Description of Dew Point Evaporative------------------------------8 3. Mathematical Model of Dew Point Evaporative Cooling ---------------13 3.1 Differential Equations ----------------------------------14 vii

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3.1.1 Basic equation of heat and mass transfer------------------14 3.1.2 Mass Transfer-------------------------------------15 3.1.3 Heat Transfer to Air---------------------------------17 3.1.4 Total Energy Transfer to Air---------------------------21 3.2 The Cooling Effectiveness -------------------------------24 3.3 Ordinary Differential Equations -----------------------------24 3.4 Heat-Transfer and Mass Transfer Coefficients ------------------26 3.5 Auxiliary Equations ------------------------------------27 4.Simulation Program-----------------------------------------29 4.1 Finite Difference Method-----------------------------------29 4.2Finite difference approximations to the equations-----------------30 S.Results and Discussion -------------------------------------34 5.1 Model validation---------------------------------------34 viii

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5.2 Test Model Design---------------------------------------38 5.2.1 Case 1 -------------------------------------------38 5.2.2 Case 2------------------------------------------43 5.3 Impact of Other Parameters-----------------------------------46 5.3.11mpact of Inlet Air Temperature----------------------------46 5.3.2 Impact of Ratio of Working to Total Air Mass Flow Rate-----------48 5.3.3 Impact of channel length----------------------------------49 5.3.4 Impact of Air Velocity------------------------------------50 5.4 Comparisons the Dew Pointe Evaporative with the Indirect Evaporative Cooling -----------------------------------------------------51 6.Conclusions and Recommendations----------------------------57 References-----------------------------------------------60 ix

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LIST OF FIGURES Figurel. 1 Schematic of heat and mass transfer indirect evaporative cooling----3 Figure 2.1 Schematic of heat and mass transfer in dew point evaporative cooling ------------------------------------------------------9 Figure 2.2 The psychometric processes for the dew point evaporative--------10 Figure 2.3 Schematic of a differential control volume---------------------12 Figure 5.1: Temperature distributions of the process air and the wall surface along the channel length -----------------------------------------35 Figure 5.2: Humidity distributions of the process air along the channel length-------------------------------------------------------36 Figure 5.3: Psychometric indication of heat and moisture transfer in an Indirect evaporative cooling system ---------------------------------------39 Figure 5.4: Temperature distribution of air in the dry channel----------------41 Figure 5.5: Temperature distribution of air in the wet channel----------------41 X

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Figure 5.6: Temperature distribution of air in the wall surface----------------42 Figure 5.7: Humidity distribution of air in the wet channel-------------------43 Figure 5.8: Temperature distribution of air in the dry channel----------------44 Figure 5.9: Temperature distribution of air in the wet channel----------------45 Figure 5.10: Temperature distribution of air in the wall surface---------------45 Figure 5.11: Humidity distribution of air in the wet channel ------------------46 Figure 5.12: Impact of Inlet Air Temperature on cooling effectiveness----------47 Figure 5.13: Impact of ratio of working to total air mass Flow rate on cooling effectiveness-----------------------------------------------48 Figure 5.14: Impact of channel length on cooling effectiveness---------------49 Figure 5.15: Impact of Air Velocity on cooling effectiveness------------------50 xi

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LIST OF TABLES Table 5.1: Operational Conditions for Simulation in Test easel ---------------36 Table 5.2: Problems parameters for the dew point evaporative---------------37 Table 5.3: Numerical results for the indirect evaporative cooling-------------53 Table 5.4: Numerical results for the dew point evaporative cooling------------53 Table 5.5: Performance data for different flow arrangements under different Operations --------------------------------------------------55 xii

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NOMENCLATURE a width, m Cpa Specific heat of dry air, kJ/kgC Cps Specific heat of moist air, kJ/kgC Cpw Specific heat of water vapor, kJ/kgC Cw Specific heat of water, kJ/kgC d Equivalent diameter of the air passage, m h5 Heat transfer coefficient of the air in the wet side, w/m2C ha Heat transfer coefficient of the air in the dry side, w/m2C hm Mass transfer coefficient, kg/m2s htg Latent heat of vaporization at 0C; htg = 2500.8, k] /kg H Specific enthalpy, kj /kg K thermal conductivity of dry air w/m oc L Channel length, m xiii

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Le Lewis number rh5 Mass flow rate of working air in the wet side, kg Is rha Mass flow rate of intake air in the dry side, kg Is rhw Mass flow rate of water, kg Is Nu Nusselt number P Total pressure of air,kN 1m2 Ppw Partial pressure of water vapor in air, kN 1m2 Q Heat flux, W r working air to intake air ratio kg I kg T Temperature, oc W Mass flow rate of water vapor, kg Is Z height of control volume, m Creek Symbols w Humidity ratio xiv

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p Density of air, kgjm3 Effectiveness of efficiency Subscripts a air ,product air pw water vapor w Waterfilm s Secondary air dew Dew point wb Wet bulb XV

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1. Introduction 1.1 Backgrounds In recent years, the use of water evaporative cooling systems has increased substantially and they are now used in almost all new cooling systems. The technology has become easier to use by adding water in the wall of the air supply duct to lower air temperature. The design of evaporative water cooling systems has become more important due to the limitation of fossil fuels and the environmental impact during their use. However, recent reports have pointed to the fact that cooling systems must now reduce greenhouse gas emissions. As a result, the solution must be environmentally friendly and must not use a lot of fuel energy. There have been a number of studies on the development-of methods to provide possible solutions for designing efficient cooling systems. Therefore, this study will provide information about the variables that play a part in determining which cooling system designs have a good level of performance and a high efficiency. The evaporative cooling system is a device that cools the air by the evaporation of water in the air, thus increasing humidity and decreasing the air temperature. Currently there are two types of evaporative cooling systems, which 1

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are known as the direct and indirect evaporative cooling systems. A new system that uses both kinds of evaporative cooling systems together has a good potential for improving the air conditioning performance and for reducing energy costs. Direct evaporative cooling systems cool the air simply by using the latent heat of evaporation. At the same time, the moisture is added directly to the air when the air passes the channel. Therefore, the relative humidity of the air is increasing. The effectiveness of the direct evaporative cooling systems approaches 70-95% [1, 2]. The advantage of using the direct evaporative coolers is that they are more efficient in hot and dry climates. Furthermore, the energy costs of using these kinds of evaporation coolers are very low. However, the direct evaporative cooler has a problem when used in a high air humidity environment and the output temperature becomes uncomfortable when the humidity is over 60%. Therefore, one solution to resolving the problem of high humidity in the direct evaporative cooler is by using a second airstream to avoid direct contact between the air stream and the water. This process is known as indirect evaporative cooling as shown in Figurel.l. 2

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Intake air Outlet air (Ambient) (Product) > Dry channel Qs > Exhausted to Atmosphere wet channel Q, < I < Working air Figure 1.1: Schematic of Heat and Mass Transfer Indirect Evaporative Cooling Indirect evaporative cooling takes advantage of the direct evaporation cooling effects by cooling the outdoor air, but without raising the moisture in the air. The indirect evaporative uses an air-to-air heat exchanger that lowers the air temperature and removes heat from the primary air stream. There are a number of indirect evaporative configurations that could be considered. However, for this research, the configuration used consists of two distinct air passages: the dry channel for the primary air, and the wet channel for the secondary air passage. Thermodynamically, an indirect evaporative air cooler passes the product air in the dry side while the working air passes over the wet channel in the opposite side. The wet side absorbs heat from the dry side by evaporative water, while 3

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cooling the dry side as the latent heat of vaporizing water is given to the wet side of air. In theory, by adiabatic humidification, the air stream in the dry side is cooled and almost reaches the wet bulb temperature of the incoming working air. At the same time, the temperature of working air on wet side will increase to dry bulb temperature of the incoming product air and becomes saturated. In recent years, many studies have been done for indirect evaporative systems to achieve 100% saturation with an incoming working air wet bulb temperature. However, practical systems have proven to be far from ideal systems. They have achieved only 50-60% of incoming working air wet bulb temperature for a typical indirect evaporative cooler [3]. Therefore, a new thermal process has been developed and is called the dew point temperature process, or the Maisotsenko cycle, which will be explained later. 1.2 Objective The main objective of this thesis was to develop and implement a simulation model for the evaporative cooling system. The simulation was used for improving the efficiency of the evaporative cooling system by modifying the counter flow heat and mass exchange in the indirect evaporative system. The modification helped to 4

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lower the product airstream to the dew point temperature of air by taking some fraction of primary air in the dry side, which has the lower dry and wet bulb temperature, to use as working air for the wet side. Therefore, ideally, the working temperature will reach the dew point temperature. This thermal process is called the Maisotsenko cycle. Information on the dew point evaporative cooling systems, for both practical use and modeling use, are limited even though considerable work has already been published on both the simulation and experimental designs. Thus, there is a need for the further development of a model to assist in improving the design of the dew point evaporative cooling systems. The development of an improved model-for the dew point evaporative was the basic driving force behind the work in this thesis. The purpose of this work was to implement a simulation model with enough details to use as a tool for improving the design of the indirect evaporative coolers. Where possible, the results in this thesis are based on validated models, and therefore, a part of this work is devoted to the validation of the model by using these previous studies. 5

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In this thesis, an analytical and numerical solution is used to predict the behavior of the thermal process for the dew point evaporative cooling system with indirect evaporation. The validation of the models involves comparing the model with previous theoretical results obtained from different dew point evaporative cooling studies. In addition, the models were run with different operating inlet air conditions. The analysis of dew point evaporative cooling systems was developed by using the following processes: 1. Developing a complete thermodynamic process for the Maisotsenko cycle. 2. Optimizing the performance of the Maisotsenko cycle. 3. Increasing the efficiency of the cooling system by using mathematical expressions for the wet bulb and dew point effectiveness. 4. Comparing the results of the mathematical model with previous studies of dew point evaporative cooling systems. 6

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1.3 Scientific Method In this thesis, a dew point evaporative system was evaluated by using computer simulations. 1.3.1 Basic Concept of Modeling Using Computer Simulation The development of the computer simulation model is summarized by the following steps: 1. The problem is identified. What are the boundaries of the problem. What should be included into the identification of the problem. 2. A model of the system is created. This model is based on many variables, which are formulated in the mathematical model. 3. The model is run using the Matlab program. A validation was carried out. If the results compared favorably with the previous results, the model was considered validated and could be used for this study. 4. The results from the simulation were then analyzed and compared 7

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2. Description of Dew Point Evaporative A new type of heat and mass exchanger, which is called the dew point evaporative cooler as shown in Figure2.1, has been developed by modifying the process of the heat and mass exchanger in the indirect evaporative cooling system. As a result, the product air in the dry side approaches the dew point temperature of working air. Therefore, the thermal process in the Maisotsenko cycle uses the same wet side and dry side of plate in the indirect evaporative cooler but with different heat and mass exchange. In the dew point evaporative process, a fraction of the outlet air that flows in the dry side of device is taken into the wet channel at the wet side of the evaporative. This arrangement allows the working air to be cooled before entering the wet side by losing heat to the opposite wet surface. After the cooled air is delivered to the wet side, the air will receive additional heat from the dry channel because the total air stream in the dry side is greater than the working air in the wet side. 8

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Intake air Outlet air (Ambient) (Product) Dry channel Q s Exhausted to iii atmosphere INet channel Qt < Working air iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii Figure 2.1: Schematic of Heat and Mass Transfer in Dew Point Evaporative Cooling The psychometric process for the counter flow heat and mass exchanger of a dew point evaporative cooling system is shown in Figure2.2 [4]. The psychometric principle of the system can be explained as follows: the product air passes through the dry side of the plate and then takes a part of product air as working air. The working air is turned to pass over the wet side of the plate and then is exhausted to outside. Ideally, the temperature at the point where the air turns from the dry channel to the wet channel is the dew point temperature. This cooled air is turned 9

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to the wet side at the dew point temperature. The temperature of the working air will increase to a saturated condition as shown on the saturation line in the psychometric chart. As results, for the ideal cycle, the temperature of the working air will leave the wet side equal to the temperature of the entering product air in the dry side. However, practical systems have shown that the working air temperature will be less than the entering air in the dry side. 't .... .. .. I .. I I ., I Figure 2.2: The Psychometric Processes for the Dew Point Evaporative [4) 10

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The effect of cooling the working air in the dry side before it flows into the wet side will lower the working air temperature. Therefore, the working air will be able to absorb additional heat from the dry product airflow. This new process for the evaporative cooling has the advantage that the cooling effectiveness would be higher than the effectiveness of a direct and indirect evaporative cooler. The Maistotsenko cycle heat exchanger process could obtain a wet effectiveness of 110122% and dew point effectiveness of 55-85% [5]. 11

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Ts + dz t -----------:r------------------, I' J-c I dW Typ ion z !I Ji f] r l11 : dQw + I. dQ5 f 'i1 1 I k ,, --------,----------_____________ .L ________ r-1 _________ v ms, Ts, Ws, hs mw + e;:.w) dz ma Figure 2.3: Schematic of a Differential Control Volume 12

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3. Mathematical Model of the Dew Point Evaporative Cooling The schematic diagram of dew point evaporative cooler shown in Figure2.3 shows the process of the heat and mass transfer mechanism along the exchanger wall in the channels. For the development of the mathematical modet the following basic assumptions were made: 1. The Lewis number was unity. 2. The Heat exchange occurs only between the fluids involved in the evaporative cooling process (i.e. adiabatic evaporative cooler). 3. The resistance of heat transfer from water film to its surface was neglected. 4. The thermal conductivity of wall and the temperature difference of wall surfaces between dry and wet side was neglected due to the small thickness [6]. 5. The velocity and properties of all fluids were uniform within the differential control volume. 3.1 Differential Equations Based on the above assumptions, the governing energy equations are formulated for the simultaneous heat and mass transfer to describe the evaporative 13

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cooling process. It was assumed that the product air in the dry side of the evaporative was cooled without added humidity. In addition, the air in the wet side had a different temperature and humidity than the working air. The governing energy balance equations are developed and described below. 3.1.1 Basic equation of heat and mass transfer The heat transfer from the water surface into the secondary air flow was: (3.1) The mass flow of water that is evaporated into the air in the wet channel was obtained as: (3.2) The heat flux transferred from the primary air in the dry side into the water surface was: (3.3) 14

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Using energy and mass conservation, a set of differential equations was obtained for a differential element as shown in Figure2.3 above as follows. 3.1.2 Mass Transfer 1. The water mass balance was written as: . (amw) ( (aw) ) msw + mw = mw dz + ms w -az dz (3.4) Simplifying this equation gave: -=----(3.5) (3.6) where rh5 and rhw are the mass flow rate of air, and mass flow rate of water. The mass flow rate of water evaporating into air was: (3.7) 15

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Thus, the equations for the process that occurs over a differential length dz were written as follows: drhw =-dW (3.8) From equations (6) and (8) it was observed that the water flow rate for the water was not constant due to the process of evaporation. Substituting Equations, (6), (8) into (2) to obtain: (3.9) where hmis the mass transfer coefficient [kg/s.m2] The energy conservation in the dry side required the following: (3.10) By using: 16

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Substituting equations. (10), (11) into (3) to obtain: dTa dz ha a Tw) maCpa 3.1.3 Heat Transfer to Air The conservation of energy at the air-water interface was: After rearrangement of equation (11) to get the following: (3.11) (3.12) (3.13) (3.14) where m5 dw = -d rhw and the heat transfer through the walls in the process have been neglected. Note that the subscript pw refers to saturated liquid water, evaluated at the water temperature. The heat transfer to the water was written as follows: 17

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The specific enthalpy of water vapor is: (3.15) where the subscript h19 is the latent heat of vaporization for water at the reference temperature of 0 C. The specific enthalpy of moist air was determined as follows: (3.16) (3.17) where the subscripts stands for the moist air. The specific enthalpy of water was: (3.18) The specific heat of moist air was: 18

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(3.19) Substituting (19) into (17) to obtain: (3.20) Differentiating equation (20) to obtain: (3.21) After differentiating and substituting equation(19) for the specific heat of moist air into equation (21), the following equations are obtained: (3.22) (3.23) Therefore the heat transfer rate was: (3.24) 19

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The specific heat of dry air as a perfect gas is Cpa = 1.004 kJ/kg K at the reference temperature of 0C. The specific heat of water vapor is Cpw = 1.840 kJ/kg K. The specific enthalpy of saturated water vapor at the reference temperature is htg = 2501KJ/kg. Substituting Equation (24) into Equation (14) and rearranging of the equation gives the following: dT5 dz (3.25) (3.26) The dimensionless is called the Lewis number (Le). Kusuda [7] reviewed Cpshd the available correlations for calculating Le and its' magnitude expresses the relative rates of propagation of energy and mass within a system and is relatively insensitive to temperature variations. For air and water vapor mixtures, the ratio is (0.60/0.71) 20

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or 0.845. At low diffusion rates, where the heat-mass transfer analogy is valid, the Le number for air and water vapor mixtures can be expressed as follows: 3.1.4 Total Energy Transfer to Air The total energy transfer to the air, which includes the heat transfer and mass transfer in the process, was written as follows (refer to Figure2.3): (3.27) The enthalpy of water and intake air was written as: aHa= C (aTa) az pa az (3.28) aHw = C (aTw) az w az (3.29) 21

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By using equations (30} and (29) and then simplifying equation (26), the following equation was obtained: (3.30) By substituting equations (3), (8), (16), and (25} into (30) and rearranging the equations, the following equation was obtained: -(cpwTw + htg) hm a (w(Tw)-w )dz-hs a (TwT5 ) dz (3.31) After rearrangement of equation (31), the water temperature gradient was written as follows: dTw -=-dz (3.32) 22

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In Eq. (32), Tw the water temperature, and, w(Tw), humidity ratio of saturated air are evaluated at the water temperature. In the case under assuming a Lewis factor of unity can be expended as below: The enthalpy of the saturated air at the air water interface evaluated at water film temperature is: (3.33) Substituting Eq.lS into Eq.33 and rearranging gives (3.34) Subtracting Eq.17 from Eq.34 gives (3.35) Substituting Eq.19 into Eq.35 and rearranging gives 23

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(3.36) Substituting Eq.36 into Eq.14 and rearranging gives hs hs ms dHs = -hm(-h-(Hpwa-Hs) + (1-h )Hpw ( w(Tw)-w))dz (3.37) Cps m Cps m Next, by using =1 into Eq.37 gives Cpshm (3.38) 3.2 The Cooling Effectiveness The mathematic expressions of the wet bulb and dew point effectiveness was written as follows [2]: Ta,in -Ta,out Ewb = Ta,in T wb,in Ta,in-Ta,out Ectew = Ta,in-Tdew,in (3.39) (3.40) 24

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where T wb,in and Tdew,in are the dew wet bulb temperature and the wet bulb temperature respectively. 3.3 Ordinary Differential Equations A computer program was developed based on the above equations to determine the air temperatures in the dry and wet sides, the water temperature and the humidity ratio on the wet side. Equations 3.41-3.44 provide a complete description of the system for the dew point evaporative cooling system based on the assumption of the Lewis number=l: dTa ha a (Ta-Tw) dz maCpa (3.41) dT5 hma (T5 Tw) -= dz ma (3.42) dw hma (w(Tw)-w) dz rhs (3.43) (3.44) 25

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3.4 Heat-Transfer and Mass Transfer Coefficients The convection heat transfer coefficient was expressed as follows: Nu ha=kd (3.35) where ha the heat transfer coefficient and k is the thermal conductivity of the dry air. The mass transfer coefficient was determined by using the relation of heat and mass transfer as [2,3, and 7] and was: (3.46) where, ha the defined as the dry heat transfer coefficient which usually less than 20 W/m2k for heat exchanger [3]. 26

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The Nusslet number for fully developed laminar flow inside parallel plates [7] is: Nu = 8.235 3.5 Auxiliary Equations The humidity ratio for saturated air [8] was: Ppw w(Tw) = 0.62198 P P, pw (3.47) (3.48) The saturation pressure of the water vapor for a temperature range of 0 to 200 oc is given [8] as: (3.49) where C8 = -5.800226 + 03 27

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c9 = 1.3914993 + oo C10 = -4.8640239 02 C11 = 4.1764768OS C12 = -1.4452093 08 C13 = 6.54596 73 + oo 28

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4. Simulation Program In order to solve the mathematical equations given in chapter3, a computer program was developed. A finite difference scheme was used to solve the governing equations for the dew point cooling system. The input data of the program included the inlet temperature of air in the dry channel, humidity ratio, fraction of the outlet air (called the working air), which is diverted into the wet channel at the bottom side of the device, and the feed water temperature. The numerical simulation was developed to evaluate the performance of the dew point evaporative cooling, the outlet air condition and cooling effectiveness of the wet bulb and dew point temperature. 4.1 Finite Difference Method The finite difference method used one of several techniques for obtaining numerical solutions to differential equation. In all numerical solutions the derivatives in the partial differential equation are approximated by linear 29

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combinations of function values at grid points. The finite difference method obtains an approximate solution forT( z) at a finite set of uniformly spaced in the interval 0 ::::;; Z ::::;; L such that zk = (k 1)Llz, z = 1,2, .... N Where N is the total number of spatial node, including those on the boundary. Given L and n, the spacing between the zk is computed with L Llz=N-1 4.2 Finite Difference Approximations The finite difference method involves using the backward difference approximation, which is F(z)-F(z-h) F(z) = h ar rK+l-rK az LlZ 30

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The finite difference code is solved the equations 3.41 to 3.44 with boundary conditions Ta(Z = 0) = Tain, and w(z = O) =Wain for the air in the dry side. The boundary conditions for the air in the wet side are w(z = L) = Wain The finite difference code solved the ordinary differential equation for the system by integrating from intake air to outlet in the dry side then from inlet to outlet in the wet side with the boundary conditions. This integration was repeated until the temperatures stop changing as described below: Frist, equations (3.41) and (3.44) were solved to find temperatures of the dry air and temperatures of water in the direction of z. The objective of the numerical solution of the equations was to march the solution at space level k forward in space to space level k+l. The solution was contained in two loops: an 31

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outer loop over all n steps in the opposite direction n and an inner loop over all steps in direction of z, which is k. 11zh a Ta(k) = Ta(k-1); (Ta(k-1)-Tw(k-1)) ma pa w(n + 1)] Notice that values of T5(n + 1) and w(n + 1)from space step n were assumed to be known by guessing values for them so that the equations can be solved. After that, the wet side equations were solved. The first step of our mathematical iteration was the initial guess because the initial value of both the temperature and the humidity in the wet side is unknown. 32

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The initial guess was the starting point for our calculation. The first guess for temperature in the wet side was: 20 Where dT5 =N w(k) = wi These the initial guesses were used in the equations until the values converge. tl.zhma (T5(n-1)-Tw(k + 1)) maCpa hma tl.z(w(Tw (k + 1))-w (n-1)) w(n) = w(n-1)-------.------ms 33

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5. Results and Discussion The main goal of this thesis was to analyze the performance of the heat and mass exchanger of the dew point evaporative cooling system. This chapter deals with the findings and the numerical results of the model developed in the previous chapter, including previous validation results obtained for the Maisotsenko cycle from other studies. Several sensitivity studies were performed to determine the effects of different variables. These were: the effects of inlet air temperature in the dry channel, the water temperature, the mass flow for the product air, the channel length, the ratio of the working to product air mass flow rate, and the air velocity were investigated. A model validation was performed for the dew point evaporative cooling and compared with previous studies to ensure the model was an accurate simulation for the test case. In the analysis, the heat transfer coefficient was assumed constant. 5.1 Model validation The model developed in the previous chapter was validated by comparing the results from previous data for the Maisotsenko cycle with a dew point 34

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evaporative cooling test case. The results from the previous study, as shown in Figure 5.1, were utilized in the first case of the simulation runs in order to test the accuracy of our simulations [9]. The model was set to the same operating conditions of inlet air parameters and flow rate, which were used in the evaporative cooling simulation as shown in TableS.!. 35 Inlet conditio: 21.1 glk1 (humidity) -----------------0.2 0.4 0.6 0.8 1.0 Dimensionless length (lfL) Figure 5.1: Temperature Distributions of the Process Air and the Wall Surface Along the Channel length [9] 35

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0.035 0.030 Inlet (OIIditioa: lSOC. 21.1 elk& (humidity} ell 0.025 -0 0.020 '! 0.015 :.a 0.010 ::c 0.005 0.000 ... profile; in dry ..... llumidity pf(Jfile; i11 cha11nel -.a-<$ 0.0 0.2 n4 n6 ns LO Dimensionless length (z!L) Figure 5.2: Humidity Distributions of the Process Air along the Channel length [9] Table 5.1: Operational Conditions for Simulation in Test Casel Intake air velocity (m/s) 2.4 inlet air dry bulb temp 35 inlet air relative humidity 21 36 inlet air wet bulb feed water temp temp 28 32

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The values for the convective heat transfer coefficient between the air and wall surface, working air to intake air ratio, and the other parameters are shown in Table 5.2. Table 5.2: problems parameters for the dew point evaporative ha (W/mzoq 20 working air to intake air ratio (kg/kg) 0.333 channel length ( m) 1.2 The operating parameters of the dew point evaporative process depicted in Figure 3 are shown in Table 5.2. The test case for the model of the dew point evaporative cooling system was performed to compare the predicted results with previous study. Therefore, the differences between the results were analyzed. Then the model was applied with different operational conditions of the air cooler to get the accuracy of the model, including the wet-bulb and dew point effectiveness. 37

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5.2 Test Model Design 5.2.1 Case 1 The simulation program for the dew point evaporative model was run with the same operating conditions as used in the test cases [9]. The results show there was a close agreement. Tables 5.1 and 5.2 show the temperatures for air, feed water, and the other parameters that were used in the dew point evaporative cooling simulation. The difference between these results and previous study for supply air temperature was about 1.5C. Figure 5.4 shows that the product air temperature decreases along the dry airflow direction by losing heat through the wall due to the temperature difference between the dry and the wet side. As a result, as the supply air stream travels in the dry channel of the device, the humidity of the air does not change because there is no direct contact between the air and the water. On the other hand, the working air temperature in the wet side shows a different orientation. The air steam travels in the wet channel in the opposite direction of the air in the dry channel of the cooling device, as shown in Figure 5.5, resulting in the temperature that initially decreases and then increases. The reason for decrease of the working air temperature in the 38

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wet side before increasing again along the airflow direction can be explained by a psychometric chart in Figure 5.3. Saturation Line_...., Dry Bulb Temperature Figure 5.3: Psychometric Indication of Heat and Moisture Transfer in an Indirect Evaporative Cooling System [10] 39

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As shown in Figure5.3 the outlet air leaves the dry side as saturated air. Therefore, some fraction of this outlet air will be used as working air for the wet channel. The temperature of this working air is higher than the temperature of the wet wall. As a result, the working air at the entrance of channel will lose heat to the water on the wet side of the wall, which will result in more evaporation of the water. The increased evaporation of water in the wet side causes the working air to become saturated along the direction of airstream. As a result, the moisture content of the working air rises gradually until achieving the saturated state from W1 to Wiw' as shown in Figure5.3 [10]. Therefore, the working air absorbs the sensible and latent heat from the dry side and its' temperature increases while the process moves along the saturation line from WiwtoW2 40

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307 306 :>2' :::::1 t:: 305 Q) 0.. E Q) _. 304 303-302 1 0 10 20 30 -------:40=----60 70 80 Dimensionless Lenght Figure 5.4: Temperature Distribution of Air in the Dry Channel 3045c--1 --304-:>2' Q) I '-303':::::1 '@ Q) 0..3025E 2 I 3o1.sl .. 301----, --------, I I -j I __ __j 0 10 20 30 w 70 w 90 100 Dimensionless lenght Figure 5.5: Temperature distribution of Air in the Wet Channel 41

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Figure 5.6 shows that the wall temperature decreases with the length in the airflow direction. Since the air stream travels in the wet region of the evaporative cooling, as shown in figure 5.7, the humidity of air increases as it approaches the end of channel of the evaporative cooling device. Therefore, by decreasing the humidity in the dry side, the more sensible heat is transferred into the wet channel from the dry side. 305 304 303 .a 302: Cl> a. E 3011 Cl> f-300-10 20 30-----40------=a:c::-o-----:oo=-=---Demensionless Lenght Figure 5.6: Temperature Distribution of Air in the Wall Surface 42 I I I 100

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0.027 -c;; ]> 0026:' .Q ; 0.0251 z.. i '6 0.024C. .E ::::l I 0.023i 0.0221 0.021' 0 5.2.2 Case2 10 ----------c:--l. w w 00 70 80 Dimensionless Lenght Figure 5.7: Humidity Distribution of Air in the Wet Channel 90 100 Case 2 studied the effect of changing the humidity levels (21.1 to 8.5 kg/kg) of the air in the dry side, with the same operating parameters as in Case 1, to obtain a different outlet air temperatures in the dry side. The evaporation can be increased by decreasing the inlet humidity of the air. As a result, the increase in the evaporation of water is dependent on the humidity of the air. The effect of humidity ratio was investigated by varying the humidity of inlet air, while keeping the other parameters constant as in Case 1. The results are shown in Figure 5.8 to 5.11. As result, with a decrease of humidity ratio from 21.1 to 8.5 kg/kg, the dry-bulb 43

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temperature of the air in the dry side deceases compared to the outlet temperature in easel. The lower value of the inlet air humidity provides more capacity of the air to absorb more moisture when diverted it into the wet side. Therefore, for lower air inlet humidity, heat that is more sensible is transferred from the dry side process air into the wet channel. The result shows that the low inlet humidity increases the evaporation rate, which indicates there is more energy required to transfer heat from the dry air to the wet air in the wet side. The outlet air temperatures obtained are 29.1 and 19.9C. 308 306-304jg302-:::J ai 3001 a. I 298'-1--296294'292-' 0 10 J.---20 30 40 50 60 70 80 90 100 Dimensionless lenght Figure 5.8: Temperature Distribution of Air in the Dry Channel 44

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.a 295-I 2i E I Q) 1-293-292:-291 r 290----0 10 20 30 40 50 60 70 80 90 Dimensionless lenght Figure 5.9: Temperature Distribution of Air in the Wet Channel i --100 g I Ql I 5 296!' Q) E-294 Q) 1292!290288L_ ____ 0 10 20 30 I __ __[_____ __ 40 50 60 70 80 90 Dimensionless Lenght Figure 5.10: Temperature Distribution of Air in the Wall Surface 45 100

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0.022---0.021 I 0.0181 C -;-+= '6 .E :f 0.012j i o.o1 L 20 30 40 50 60 70 80 90 100 Dimensionless Lenght Figure 5.11: Humidity Distribution of Air in the Wet Channel 5.3 Impact of Other Parameters 5.3.11mpact of Inlet Air Temperature In this section, the impact of inlet air temperature was evaluated and can be seen in Figure 5.12. The same process conditions were applied, as shown in table 1, while the temperature at the inlet of the dry channel was changed between 20 oc and 45C. In this section, the effect of varying the inlet air temperature on the dew point evaporative processes was evaluated. A higher wet bulb effectiveness of the 46

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evaporative cooling required the air temperature to be higher than 30C. For higher inlet air temperatures, the effectiveness values are not significantly increased, which indicates there are some limitations to the inlet air temperature. According to Kumar [9], for inlet air temperature higher than 30C the wet bulb effectiveness does not vary much and ranged between 100 and 115%, and the dew point effectiveness varied between 60 to 90%. This shows that the dew point evaporative cooling systems was more efficient at higher temperatures. 1.3,------1.2Cl Ol1.1c-I t:l 1 ci II 0 9';: 0.8 Q) (.) a5 0.7> "' I 2 0.6, Li:i 0.5 ----. --04"""'25 --------,--------------r I "" I -----------------------------_, ...... -.... -l I wet blib eflrectr..encess _J Dew IXJin eflectr-.encess -I ------30 35 40 45 Inlet air temperature Figure 5.12: Impact of Inlet Air Temperature on Cooling Effectiveness 47

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5.3.2 Impact of Ratio of Working to Total Air Mass Flow Rate This section shows the effects of varying the ratio of working air to intake air from 0.2 to 0.8 (by interval of 0.2) while keeping other parameters constant, as shown in TableS.l. The simulation results are shown in figure 5.13. Both the wet bulb and dew point effectiveness increase by increasing the working to intake air ratio. As a result, with an increase of the ratio, the supply cooled air to the room space is reduced and the increased flow resistance will affect the benefit of the increased effectiveness. ---1.21 0> 1 C\J 0 -,--c) 11 0.8; ----------! ------------------J .. ,_ .... _,.,. en en 0.6c. Ql c: Ql E (.) 2 w 0.2;-, ," ;' , , ; ;' 0--------0 0.1 0.2 0.3 0.4 0.5 Working to intake air ratio(kg/kg) Wet bulb efteclt-.encess Dew pomt eftectt..encess .. .. I --------_ ____]______ ---0.6 0.7 0.8 Figure 5.13: Impact of Ratio of Working to Total Air Mass Flow Rate on Cooling Effectiveness 48

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5.3.3 Impact of channel length In this section, the effects of channel length on the both effectiveness values in the dew point evaporative system are evaluated and are shown in Figure 5.14. By increasing the length of dry channel, the contact time and surface area are significantly increased, which indicated there is more energy require for heat and mass transfer from the air in both sides of the cooler. As a result, both the wet bulb and dew point evaporative effectiveness increase with increasing length of the channel.
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5.3.4 Impact of Air Velocity In this section, a higher velocity of air (4 m/s) was considered while keeping other parameters unchanged. Figure 5.15 shows the effectiveness plotted against the air velocity. It can be observed from the plot that the higher air velocity resulted in a lower dew point and wet bulb effectiveness. The effectiveness values increases by decreasing the intake air velocity and the outlet temperature will decrease. The results show that the air velocity in dry channel should be less than 3m/ s. en en Q) c Q) > "(3 2 Qi 1.1 1-0.9 i oar---------------. --------------0.7-0.6!--1 -----0 5 ---_l __ ;----1.5 2 2.5 3 3.5 Inlet air velocity (m/s) i wet blJb effectiveness =l dew poirt effectivemess -----: -------. --' ______ ., ' 4 4.5 5 Figure 5.15: Impact of Air Velocity on Cooling Effectiveness so

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5.4 Comparisons the Dew Point Evaporative with the Indirect Evaporative Cooling The indirect evaporative cooler as introduced in previous chapter is a device to lower the air temperature by using the latent heat of water: In principle, the process allows the product air to flow over the dry side of plate while the working air to flow opposite wet side of plates, as shown in Figure 1.1. In an ideal operation, the product air temperature in the dry side will reach the value of the wet blub temperature of incoming working air, and the temperature of working air will reach the dry bulb temperature of incoming product air. As a result, the effectiveness of indirect evaporative will be 100%. However, the actual effectiveness of practical systems are far from the ideal, about 50-60% [6]. As result, the indirect evaporative cooling has been studied and developed [6,10], and will effectively improve the cooling effectiveness of the exchanger. Comparing the dew point evaporative system with the indirect evaporative cooling system requires evaluating the performance of the systems in various climates conditions. Numerical calculations were performed for two different evaporative cooling systems by using the same governing equations describing the temperature and the 51

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humidity change of the dew point evaporative cooling and the indirect evaporative cooling used earlier. It can be seen that the indirect evaporative air and the dew point evaporative cooler work in a similar way since the heat and mass transfer processes can be described with the same of set differential equations. The differences are in the mass flow rate and the initial conditions on the wet side. In the indirect evaporative cooler, the mass flow rate is not a fraction of the outlet air, which was used as the working air on the wet side of the dew point evaporative cooler (rh5 =F r rha) The working air on the wet side does not depend on some fraction of diverted air in the dry side to act as the working air in the wet channel. As a result, the initial conditions will be different from the dew point evaporative cooling in the wet side. This means that both channels in the indirect evaporative have the same inlet conditions as the dew point evaporative cooling, and the inlet condition in the wet side was the outlet conditions from the dry side. 52

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Table 5.3: Numerical results for the indirect evaporative cooling Given conditions Numerical results Ta,i(0C) Ts.i(oC) Tw(0C) kg Ta,o(0C) Ts,o(0C) kg w (-) Ws,oCk) S,l kg 35 35 31 0.021 32.2021 31.7777 0.0287 35 35 28 0.0085 29.8275 29.0248 0.0229 35 35 28 0.0162 31.2985 30.7319 0.0264 Table 5.4: Numerical results for the dew point evaporative cooling Given conditions Numerical results Ta,i(oC) Ts.i(0C) TwCOC) kg Ta o(0C) Ts,aCOC) kg w (-) Ws,o(kg) S,l kg 35 27.48 31 0.021 27.48 30.2789 0.0275 35 22.011 28 0.0085 22.01 26.7756 0.0223 35 22.165 28 0.0162 22.165 26.7754 0.0223 53

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The results of simulation model of one-dimensional different equation for both evaporative cooling systems with the same operating condition were compared. The results for the indirect evaporative cooling are presented in Table 5.3, while the results for the dew point evaporative are in Table 5. 4. For discussion, the performance of indirect evaporative cooler and dew point cooler were evaluated by the cooling effectiveness equation to prove that the dew point cooler improves the cooling effectiveness (efficiency) of the exchanger compared with the indirect evaporative cooler. These results could also be seen from the performance data as shown in Table 5.5 that gave the air outlet temperature and effectiveness at different conditions for three different cases. 54

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Table 5.5: Performance Data for Different Flow Arrangements under Different Operations cases Outlet air temperature and effectiveness For indirect evaporative For dew point evaporative Ta,o E Ta,o E Case 1 32.202 0.52814 27.48 1.05714 Case 2 29.8275 0.37359 22.011 0.8526 Case 3 31.29 0.41364 22.165 1.14884 In comparing the results of the indirect evaporative cooler with the dew point evaporative cooler, it was observed that there was a significant different in the outlet temperature of product air and the effectiveness values. The outlet temperature was a key factor for improving the cooling effectiveness of the exchanger by reducing the air temperature. To determine the advantage of using the dew point cooling system, performances of the two models were evaluated for each case and are summarized in Tables 5.3 and 5.4 for both the outlet variables. 55

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Table 5.5 shows samples of data used for testing the performance of the two models i.e. the indirect and dew point evaporative system cooling. The dew point evaporative cooling system was considered better when compared with the indirect evaporative cooler. As can be seen in TableS.S the outlet air temperature of dew point evaporative cooler is below the wet bulb temperature i.e. the new type of M-cycle heat and mass exchanger was able to achieve a higher cooling effectiveness compared with the indirect evaporative cooler. The dew point effectiveness ranged between 85 to 114% whereas the indirect evaporative effectiveness varied between 30 to 58% for various inlet conditions. 56

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Chapter 6 Conclusions and Recommendations The study of the dew point evaporative cooler system (or M-cycle) required the development of a computer model that was able to simulate the thermal process. The work presented in Chapter 2 details the operation and performance of the dew point cooling system. An analytical solution to model the performance of the dew point evaporative system was presented in this thesis. A sensitivity study was performed to examine the effects of changing the values of airflow rate, the ratio of working to intake air flow rates, and the inlet temperature, and the humidity. A potential method for modifying the process of the heat and mass exchanger in an indirect evaporative cooling system to produce a new thermal process called dew point cooling was developed. The dew point evaporative cooling system was used to cool the product air to a temperature below the wet bulb. The evaluation of the dew point cooling process was performed using a numerical analysis. In the numerical analysis for the dew point evaporative cooler system, the temperature distributions of the process air and the water film, humidity 57

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distributions, and the impact of the variables on the cooling effectiveness were obtained. The analysis shows that this new type of exchanger can achieve much higher cooling performance than the indirect evaporative cooler. However, the dew point evaporative cooler system requires more than one channel for dry and wet side to achieve good performance. When the dew point evaporative cooler systems were operated with different climate conditions, a fraction of product air would be used as the working air in the wet side to reduce the outlet air temperature. In this evaporative cooler, results have shown that a higher effectiveness was dependent on changing many variables such as; air velocity, channel length, working to product air ratio, and the inlet air temperature. It was shown that the inlet air temperature should be higher than 30C. As a result, using an inlet air temperature of 30 oc may cause the intake air to have a lower temperature and this increases the effectiveness of the system. Future experimental research is recommended to better understand the M cycle thermal process. In addition, alternative techniques should be investigated that would reduce the outlet air temperature and would improve the effectiveness of the process. Other techniques should be investigated to study the effects of 58

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viscosity, thermal conductivity and pressure loss on the performance of the cooling system. 59

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REFERENCES [1] J.M. Wu, X. Huang, H. Zhang, "Theoretical Analysis on Heat and Mass Transfer in a Direct Evaporative Cooler"; Applied Thermal Engineering ,29(2009)980-984. [2] C. Lertsatitthanakorn, S. Rerngwongwitaya, S. Soponronnarit, "Field Experiments and Economic Evaluation of an Evaporative Cooling System in a Silkworm Rearing House"; Biosystems Engineering ,93 (2) (2006) 213-219. [3] N.J. Stoitchkov, G. I. Dimitrov,"Effectiveness of Crossflow Plate Heat Exchanger for Indirect Evaporative Cooling"; International Journal of Refrigeration, 21 (6) (1998} 463-471. [4] B. Riangvilaikul, S. Kumar, "Numerical Study of a Novel Dew Point Evaporative Cooling System", Energy and Buildings,42 (2010) 2241-2250. [5] ldalex Technologies, Inc., The Maisotsenko Cycle Conceptual. Available from http://www.idalex.com/technology/how it works engineering perspective.htm. [6] Y, A. Cengel, Heat and Mass Transfer: A Practical Approach, McGraw-Hill Companies, Inc., Singapore, 2006. 60

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[7] T. Kusuda, "Calculation of the Temperature of a Flat-plate Wet Surface under Adiabatic Conditions with Respect to the Lewis Relation", Humidity and Moisture, Volume 1: Principles and Methods of Measuring Humidity in Gases, vol., pp. 16-32, 1965. [8] ASHRAE, ASHRAE Handbook of Fundamentals, American society of Heating, Refrigerating and AirConditioning Engineers, Inc., Atlanta, GA, 2009. [9] C. Zhan, X. Zhao, S.B. Riffat, "Numerical Study of M-cycle Cross-Flow Heat Exchanger for Indirect Evaporative Cooling", Building and Environment,46 (2011) 657-668. [10] B. Riangvilaikul, S. Kumar, "Numerical Study of a Novel Dew Point Evaporative Cooling System", Energy and Buildings,42 (2010) 2241-2250. 61