Citation
Assessment of the passive freeze protection of integral collector storage units by natural convection loop

Material Information

Title:
Assessment of the passive freeze protection of integral collector storage units by natural convection loop
Creator:
Darbeheshti, Maryam
Place of Publication:
Denver, Colo.
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
xi, 92 leaves : illustrations ; 28 cm

Thesis/Dissertation Information

Degree:
Master's ( Master of Science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Mechanical Engineering, CU Denver
Degree Disciplines:
Mechanical Engineering
Committee Chair:
Passamaneck, Richard S.
Committee Members:
Burch, Jay D.
Trapp, Josh A.
Rorrer, Ronald A. L.

Subjects

Subjects / Keywords:
Solar water heaters -- Design and construction ( lcsh )
Solar water heaters -- Design and construction ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 91-92).
General Note:
Department of Mechanical Engineering
Statement of Responsibility:
by Maryam Darbeheshti.

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
44075353 ( OCLC )
ocm44075353
Classification:
LD1190.E55 199m .D37 ( lcc )

Full Text
ASSESSMENT OF THE PASSIVE FREEZE PROTECTION
OF INTEGRAL COLLECTOR STORAGE UNITS
BY NATURAL CONVECTION LOOP
by
Maryam Darbeheshti
B.S.M.E., University of Rajasthan, 1988
M.B.A., Industrial Management Institute of Iran, 1992
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
1999


This thesis for the Master of Science
degree by
Maryam Darbeheshti
has been approved
by
Richard S. Passamaneck
Ronald A. L. Rorrer
/2-0
Date


Darbeheshti, Maryam (M.S., Mechanical Engineering)
Assessment of Passive Freeze Protection of Integral Collector Storage Units
by Natural Convection Loop
Thesis directed by Assistant Professor Richard S. Passamaneck
ABSTRACT
The advantages of a passive freeze protection system in solar domestic hot
water units in terms of simplicity, reliability and cost is well recognized. In this study,
a natural convection loop is developed through the piping system of an integral
collector storage unit. This loop is maintained during cold winter conditions in order
to protect the piping system from freezing. The heat source to establish the
thermosyphon flow in the loop is provided by means of an auxiliary tank or a room
heat exchanger. A capillary tube is provided to ensure the required amount of
pressure drop in the loop in order to minimize the heat losses from the tank.
A full-scale residential size test facility has been constructed for testing this
concept and validating theoretical models. The test is performed under five different
capillary geometries. This investigation analyzes the results of testing and also
describes the reasons for a deviation between model predictions and experimental
results.
iii


This abstract accurately represents the content of the candidates thesis. I
recommend its publication.
Signed
Richard S. Passamaneck
IV


ACKNOWLEDGEMENTS
There are several people and organizations that I would like to acknowledge
for supporting me and this research project at the University of Colorado at Denver.
First and foremost is my advisor, Dr. Richard Passamaneck. I thoroughly enjoyed
working with him and appreciate all the advice, support, and guidance he has given
me during my studies. He allowed me to begin my graduate studies in Mechanical
Engineering and I am most grateful for his initial encouragement.
Special thanks are also expressed to the head of the Mechanical Engineering
Department, Dr. James C. Gerdeen for his support and encouragement since the first
day I was admitted to the graduate program at University of Colorado at Denver.
My gratitude and respect go to Senior Physicist, Dr. Jay Burch at the National
Renewable Energy Laboratory (NREL), for his help in coming up with the topic of
this research and his continued guidance during the time it took to complete this work.
I would also like to express my appreciation to Dr. John Trapp and Dr. Ronald
Roirer for serving on my graduate committee and also for their comments and
suggestions for the content of this thesis.
Several other individuals at NREL were also very helpful to me. Thanks to Dr. Keith
Gawlik for his last minute help and guidance on my defense day. Also thanks to my
colleague, Thom Johnson for providing me the information I needed regarding the test
data and instrumentation specifications.
Financial support by the National Renewable Energy Laboratory and
University of Colorado at Denver is appreciated.
Finally, I would particularly like to thank my husband Hamid for his love,
support, and patience as I periodically abandoned my role as loving wife these past
few years.


DEDICATION
This thesis is dedicated to my husband Hamid, our two daughters, Yalda and
Ida, and to the loving memory of my father.


CONTENTS
Figures .................................................................ix
Tables...................................................................xi
Chapter
1. Introduction..........................................................1
LI Conventional Freeze Protection Methods ................................1
1.2 Sequential Freezing for Freeze Protection ............................3
1.3 Solar Thermosyphons With Heat Exchangers..............................4
1.4 Freeze Protection by Natural Convection ..............................5
2. Principles of Natural Convection .....................................6
2.1 Theoretical Concepts..................................................6
2.2 Governing Equations .................................................7
2.3 Natural Convection Loop..............................................9
2.4 Fully Developed Velocity Profile ...................................10
2.5 Fully Developed Temperature Profile ................................11
2.6 Natural Convection from Vertical and Horizontal Pipes ..............14
2.7 Temperature Dependence of Fluid Properties .........................18
2.8 Determination of Pressure Drop and Friction Factor .................20
3. Instrumentation .....................................................25
3.1 Electric Element System; Tank as Heat Exchanger .....................25
3.2 Room Air Heat Exchanger System; (RHX) ..............................31
4. Experimental Data for Electric System ...............................34
4.4 Tank UA from Decay Test Data .....................................35
vii


4.5 Mass Flow Rate in Natural Convection Loop...........................43
5. EES Model for Determination of Design Parameters .....................53
5.1 Capillary Tube Sizing ................................................53
5.2 Mass Flow Rate Through The Bypass Orifice and Collector ............55
5.3 Comparison between Measured Temperatures and Model Predictions......59
5.4 Determination of System Parameters with respect to the Pipe Velocity.66
5.5 Comparison between Measured and Model Values.........................72
6. Conclusions and Recommendations.......................................75
Appendix
A. Derivation of Formula and Details of Tank UA.......................77
B. Uncertainty Analysis..................................................84
C. Mass Row Rate Calculations in Natural Convection Loop.................88
Bibliography..............................................................91
viii


FIGURES
Figure
3.1 Schematic Diagram of Tank Electric Element and RHX Systems...........26
4.1 Decay of Tank Water Temperature versus Time..........................36
4.2 Decay of Tank Water Temperature versus Time.........................37
4.3 Decay of Tank Water Temperature versus Time.........................38
4.4 Comparison of UA Results in Decay Tests 1,2,3.....................40
4.5 Polynomial Fit to UA as a Function of AT in Decay Test 1..........41
4.6 Polynomial Fit to UA as a Function of AT in Decay Test 2..........42
4.7 Polynomial Fit to UA as a Function of AT in Decay Test 3..........42
4.8 Experimental Data for Various Temperatures along the Loop (up)
and the Resulted Mass Flow Rate (down) with 3A Copper Pipe..........45
4.9 Experimental Data for Various Temperatures along the Loop (up)
and the Resulted Mass Row Rate (down) with 3/8 Capillary Tube.......47
4.10 Experimental Data for Various Temperatures along the Loop (up)
and the Resulted Mass Row Rate (down) with 5/16 Capillary Tube.....49
4.11 Experimental Data for Various Temperatures along the Loop (up)
and the Resulted Mass Row Rate (down) with 1/8 Capillary Tube......50
4.12 Experimental Data for Various Temperatures along the Loop (up)
and the Resulted Mass Row Rate (down) with 3/32 Capillary Tube.....51
5.1 Relation between DcaP and Leap for E- System.........................54
5.2 Relation between Orifice Diameter and Row Ratio.....................57
5.3 Comparison of Measured Temperatures with Model Predictions
along the NCL for % Copper Piping...................................61
5.4 Comparison of Measured Temperatures with Model Predictions
along the NCL for 3/8 Capillary Tubing..............................62
IX


5.5 Comparison of Measured Temperatures with Model Predictions
along the NCL for 5/16 Capillary Tubing.............................63
5.6 Comparison of Measured Temperatures with Model Predictions
along the NCL for 1/8 Capillary Tubing..............................64
5.7 Comparison of Measured Temperatures with Model Predictions
along the NCL for 3/32 Capillary Tubing.............................65
5.8 Relation Between Design Parameters and Pipe Velocity................71
5.9 Mass Flow Rate (Measured / Model)...................................72
5.10 AT (Measured / Model)..............................................73
5.11 UA (Measured / Model)............................................74


TABLES
Table
2.1 Constants for Determination of Nu..................................16
2.2 Simplified Equations for Free Convection from Pipes to Air
at Atmospheric Pressure............................................17
2.3 Values for K Corresponding to Ratio A1/A2 for Pipe Entrance........24
3.1 The Piping and Piping Equivalent Measurements for E-System.........29
3.2 Detailed Measurement of the Loop in E-System.......................30
3.3 The Piping and Piping Equivalent Measurements for RHX System.......32
3.4 Detailed Measurement of the Loop in RHX System.....................33
4.1 Tank UA with Tank Average Temperatures...........................37
4.2 Tank UA with RTD Temperatures....................................38
4.3 Tank UA with Method 2............................................39
5.1 Relation Between Dia. and Length of Capillary Tube.................54
5.2 Flow Ratio for Various Orifice Diameters...........................58
5.3 Measured and Model Mass Flow Rates (kg/s)..........................72
5.4 Measured and Model AT (C).........................................73
5.5 Measured and Model UA (W/C).....................................74
XI


1. Introduction
Integral collector storage (ICS) units are an effective way of using solar
energy for domestic hot water systems, which account for 15 percent of residential
energy use or about three percent of all energy used in the United States [1]. ICS is a
passive solar domestic hot water system that has the collector and storage tank all in
one package that requires no pump or controller, making it a potentially effective
system.
Freezing of the potable water piping has limited the deployment of these cost-
effective systems to mild climates, where piping insulation will adequately protect the
piping. Therefore a study of freeze protection analysis is necessary to expand their
use to colder climates. In cold climates, such as the Rocky Mountain Region,
nighttime temperatures are frequently well below freezing, and some form of
automatic freeze protection is essential.
1.1 Conventional Freeze Protection Methods
There are several types of passive and active freeze protection systems that
have commonly been used in the past. A brief description of different systems along
with their advantages and disadvantages follows:
Freeze-tolerant pipe material
Certain plastic pipe materials like polybutylene have been shown to be freeze
tolerant for a limited number of cycles, but their full capacity under the temperature
conditions typical of a solar system are not known. High density polyethylene can
l


expand to accommodate freezing water [1], but the stagnation temperature of the
collector must be considered seriously.
Compressible foam inserts
Inserting a compressible material into the piping will allow the expansion of
water upon freezing without significant pressure on the piping. There are a number of
issues which must be addressed before the viability of this approach can be fully
assessed. The most important is the selection of compressible material. The material
must be able to take up the 10 percent volume expansion, which occurs when water
freezes. It must also be compatible with water and withstand the stagnation
temperature of the collector. The proper distribution of the foam, the change in flow
velocity as the material expands or contracts and its effect on heat transfer are other
important issues that must be considered.
Bypass/shutdown the system in freezing conditions
An indoor bypass pipe between the cold water supply and the auxiliary tank
must exist to ensure flow to the auxiliary tank. This is not a freeze protection concept
and wastes available solar energy in winter.
Use of heat tape
Installation of electrically powered heat tapes on outside pipes will warm the
pipes and prevent freezing. This active method of freeze protection will not work
during a power failure, which is quite common in very cold conditions or heavy snow
falls.
2


Tapered pipes
In this approach the pipes are tapered so that the small end will freeze first
forcing the ice towards the large end instead of bursting the pipe. The problem with
this and any other freeze-tolerant designs is that once the pipes freeze, flow is blocked
and no solar energy can be collected until the ice melts. Also, it has been shown that
tapered piping fails due to complex freeze-melt-freeze cycling. A better solution is to
prevent the system from freezing in the first place.
Continuous circulation of fluid
It has been suggested that a low rate circulation pump would be installed at
the storage tank to prevent freezing, but it has not yet been shown what effect it might
have on system performance. Additionally, a pump failure could have disastrous
effects on the system. The increase in cost of the overall system is another issue to be
considered.
1.2 Sequential Freezing for Freeze Protection
Sequential freezing is accomplished by maintaining a temperature gradient
across the collector so that water is squeezed out of the collector rather than being
trapped by ice at the ends of the tubes. A series of experiments showed that a solar
water heater designed according to the principle of sequential freezing can operate
effectively in winter without drain-down, electricity, or heat exchanger systems [2].
The specific volume of water at 0 C is 1.0002 cm3/g, and for ice it is 1.0901
cm3/g. The expansion on freezing is approximately 9%. If temperature drops
continuously, the specific volume of ice continuously decreases with decreasing
temperature. The expansion of ice is greater than that of copper. The damage to water
containers such as absorbers and tubes is due to the phase change of water at 0C.
3


Once the process of phase change is accomplished, the containers will not break even
though the temperature continues to drop.
The process of water solidification into ice is not instantaneous. If some
measures can be taken to control the process of water freezing in tubes and to make
water in the space occupied previously by ice drain down smoothly, then failure
caused by phase change expansion may be avoided. After the phase change is
finished, the tubes will not be damaged by expansion even though the temperature
continues to drop. This is the basic concept of freeze protection by sequential
freezing.
13 Solar Thermosyphons with Heat Exchangers
Solar thermosyphons have limited use in the United States because of the lack
of effective, reliable freeze protection. One technique for reliable, passive freeze
protection is to use a heat exchanger in the storage tank and a single-phase non-
freezing fluid, such as propylene glycol, in the collector loop. This method of freeze
protection has been used extensively for active systems, but its application to
thermosyphons is not well practiced. For cold climates, this method has an advantage
over other freeze protection systems in that it is safe from hard freeze conditions and
completely passive; it therefore preserves the important attributes of simplicity and
reliability inherent in the thermosyphon concept. Of course the added cost of the heat
exchanger is another issue to be considered. In addition, the reduced system
efficiency due to a second fluid and heat exchanger must be considered.
4


1.4 Freeze Protection by Natural Convection
Natural convection loops (NCL) can carry heat from the auxiliary tank or
room air to prevent freezing. The use of a capillary tube between the cold water inlet
and the auxiliary hot water tank appears to be a practical means of freeze protection
[3]. Because of the very small diameter of the capillary tube, only a small amount of
water can pass by the ICS unit when a load is drawn. However if the solar unit gets
very cold, the temperature difference between it and the auxiliary tank will drive a
small thermosyphon flow sufficient to keep the pipes from freezing. The optimum
tube diameter, to minimize heat loss, yet providing freeze protection needs to be
determined.
An alternate approach is to place a heat exchanger inside the building to
absorb building heat, which then transfers the heat to the solar piping. A convection
loop is created in the piping by introducing a bypass pipe into the system, inside the
heated space. The heat exchanger warms the piping passively, using heat from the
building. The lighter warmed water created in the piping circulates by natural
convection upwards, through the solar piping where it is cooled and returns to the
building below. The design of the loop is the purpose of this study.
5


2. Principles of Natural Convection
2.1 Theoretical Concepts
Several processes of interest and importance, in nature and in technological
applications, are dominated by natural convection mechanism. In other applications,
it exists to either aid or oppose mechanisms that give rise to thermal or material
transport. Natural convection flow is a buoyancy-induced motion resulting from
body forces acting on density gradients, which arise from mass concentration and/or
temperature gradients in the fluid. In this project, we are concerned with the
temperature gradients resulting in natural convection.
The movement of fluid in a natural convection flow occurs because the fluid
density decreases as it heats. Nearby cooler fluid is denser than the heated fluid and
thus sinks to the bottom of the container. The hotter fluid is less dense and thus rises.
In natural convection processes, unlike forced convection, the flow itself rises due to
temperature differences in a body-force field. Therefore, heat transfer and fluid flow
processes are inseparably linked together and must be solved simultaneously.
Natural convection may arise over surfaces or in enclosed areas, called
external and internal natural convection respectively. In internal convection, the
presence of enclosing surfaces has to be considered in determining the flow and the
heat transfer.
The significance of the buoyant free convective forces are described in terms
of the Grashof number:
6


(2.1)
Gr=PliML
V2
where (3 is the coefficient of thermal expansion, and v is the kinematic viscosity, ji/p.
For a pure free convective flow, the ratio Gr/Re2 1 must be satisfied, where
Re is the Reynolds number and given by VDp/p. If the ratio Gr/Re2 ~ 1, the flow is a
special case of mixed free and forced convection. If Gr/Re2 1, the flow is a pure
forced convection.
To determine whether the free convection flow is laminar or turbulent, a non-
dimensional parameter known as Rayleigh number, Ra, is used and is defined as the
product of Grashof and Prandtl numbers. If Ra < 109, the flow is laminar and if Ra >
109, the flow is turbulent.
2.2 Governing Equations
A convective process is governed by the basic conservation principles of
mass, momentum and energy. The governing equations are obtained from application
of these basic principles to a control volume. For the determination of the flow and
temperature fields in a natural convection heat transfer process, the general governing
equations are given as:
Conservation of mass
Dp
^+pv-y = o
Dt r
(22)


Conservation of Momentum
DV u. ,
p = F -VP + pW + f V(V V)
(23)
Conservation of Energy
(2.4)
Where, D/Dx represents the substantial or particle derivative, F is the body force per
unit volume, Q' is the heat generation from an energy source per unit volume, and is
the viscous dissipation [19].
In natural convection flow, the basic driving force arises from the temperature
field. The temperature variation produces a density gradient, which then results in a
buoyancy force due to the presence of the body force field. In a gravitational field, the
body force F = p g where g is the force per unit mass of the fluid. It is the
variation of p that gives rise to the flow and if this variation were neglected, no flow
would result. The temperature field is linked to the flow field and all the above
equations are coupled through density, p. Therefore, these equations have to be
solved simultaneously to yield the distributions of the velocity, pressure and
temperature. Due to this added complexity in the analysis of the flow, several
simplifying assumptions and approximations are made in natural convection to
facilitate a more convenient procedure for obtaining a solution.
In the momentum equation, the local static pressure P is separated into two
terms, one due to the hydrostatic pressure, Pa, and the other due to the motion of the
8


fluid, Pd The former coupled with the body force acting on the fluid constitutes the
driving mechanism for the flow. Therefore, the momentum equation becomes:
where p a is the density of the ambient fluid.
23 Natural Convection Loop
Natural convection in closed loops plays an important role in the design of
thermal energy systems, such as solar heating systems. The configuration of these
systems is characterized by arrangement of a heat source with the heat sink positioned
at some height above the heat source. These components are connected by pipe
forming a closed loop.
The governing equations for NCL need to be modified from the basic
equations of continuity, momentum and energy so that the effect of the flow in a
circular tube is considered employing the cylindrical coordinate system.
Continuity equation
(25)
(2.6)
9


Momentum equation
(2.7)
Energy equation
Note that vr =0 for a fully developed flow, d2t/d§2 = o for a symmetric heat
transfer situation, and d2t I dx2 =o for constant heat flux.
2.4 Fully Developed Velocity Profile
For fully developed laminar flow in a tube, vr = 0 and 3u/3x = 0. Therefore
equation (2.7) becomes, after integration twice with respect to r and applying the
boundary conditions:
(2.9)
Or, in terms of the mean velocity V,
8fJ.\ dx j
(2.10)
10


Knowing the relation between mass flow rate, velocity, density, and area we have:
m = pV Ac
(2.11)
We can calculate pressure drop from equation (2.10). Also eliminating pressure drop
from equation (2.9) and (2.10) yield the velocity in terms of the mean velocity as:
The shear stress at the wall surface can be evaluated from the gradient of the
velocity profile at the wall:
In a fully developed pipe flow, the shear stress varies linearly from a maximum at the
wall surface to zero at the tube center.
2.5 Fully Developed Temperature Profile
A fully developed temperature profile implies that there exists, under certain
conditions, a generalized temperature profile that is invariant with tube length. There
are two conditions to be considered, constant heat flux and constant surface
temperature. The energy equations under these two situations are:
u = 2V 1~~~2
rn
v 'o
(212)
(2.13)
ll


l_d_
r d r
(2.14)
dr) a\dx j
d t ] u (dtm ^
for constant heat flux, and
rdr[ dr) atQ-tm\dx )
1 d r dt' _u tQt fdtm^
(2.15)
for constant surface temperature,
where a is the thermal diffusivity of the fluid, and tm is defined as mixed mean fluid
temperature, sometimes referred as the mass averaged temperature, bulk fluid
temperature, or mixing-cup temperature. This temperature characterizes the average
thermal energy state of the fluid.
To solve the energy equation for the constant heat flux condition, we first
substitute the parabolic velocity profile for u from Eq. (2.12), integrate twice with
respect to r and apply the boundary conditions:
t = t0
and 31 / 3 r = 0
at r = r o,
at r = 0
Therefore the desired temperature profile would be:
a v dx j
(2.16)


The mixed mean temperature can now be found by:
(2.17)
Substituting u and t from Eqs. (2.12) and (2.16), respectively, and integrating yields:
At this point the convective heat transfer coefficient h can be evaluated by use of its
definition:
The surface heat flux can be evaluated in one of two ways. The temperature profile
given in equation (2.16) can be differentiated to give the temperature gradient at the
wall surface, from which the heat flux can be evaluated from the heat conduction
equation. The second method, which is simpler, uses an energy balance on a
differential control volume. Applying the conservation of energy principle, and
solving for the wall surface heat flux, gives:
Combining the last two equations and solving for h gives:
(2.18)
13


(2.21)
where k is the thermal conductivity of the fluid and D is the tube diameter. Note that
h depends only on thermal conductivity k and diameter D and is independent of
velocity, density, specific heat, and so on. However this is only true for laminar flow
and only for the special case of fully developed velocity and temperature profiles.
Equation (2.21) is expressed in non-dimensional form as:
where Nu = hD/k is the Nusselt number.
The energy equation for the constant surface temperature can be solved in the
same manner, giving a Nusselt number that is 16 percent less than the solution for the
constant heat flux:
2.6 Natural Convection from Vertical and Horizontal pipes
For the determination of heat transfer rates, we need to know the heat transfer
coefficient, h, which in turn means the necessity of knowing the Nusselt number, Nu.
Different researchers have come up with different formulations to evaluate the Nu for
a variety of free convection flows.
Nu = 4.364 (constant heat flux)
(2.22)
Nu = 3.658 (constant surface temperature) (2.23)


For the case of natural convection in vertical cylinders, Churchil and Chu
have developed the following formula for determination of the Nusselt number [18]:
Nul = 0.68 + 0.670RaL
1/4
1 +
f0.492 Y711
Pr
-4/9
,for 0 < RaL < 109
(224)
Nul =
(0.492V -8/27'

l Pr ) J
,for RaL > 109 (2.25)
where RaL = GrL Pr. All properties are input at the mean temperature.
The condition under which the above equations can be applied to the free convection
for vertical cylinders is [15]:
D _35
L > GrLl
(2.26)
where D is the diameter of the cylinder, L its length, and Gtl the Grashof number
which has a characteristic dimension L instead of D. Thus, the Grashof number is:
GrL =
L3gP At f LY
D
Grn
(2.27)
The significance of the Prandtl number in the behavior of the fluid inside
tubes is worth mentioning here. The Prandtl number is a non-dimensional group of
fluid transport properties that is defined as Pr = jic/k or if multiplied by density, Pr =
via. If the Prandtl number is greater than one, the velocity profile develops more
rapidly than the temperature profile and vice versa.
15


The following relation is recommended for a wide range of Rao for the free
convection flow in horizontal pipes [14]:
Nud = i 0.60+0.387Ra
1/6
1 +

8/27
10"5 < RaD < 1012 (2.28)
A simpler equation that is only valid for laminar flow is given by:
Nud = 0.36+0.518RaD
1/4
ro.559^ 9/16*
1+
l J
1-4/9
Ra < 109
(2.29)
Besides the above relations, there is another way of finding the average heat
transfer coefficient for a variety of circumstances from the following equation [18]:
Nu = C(RaY
(230)
The values of constants C and m for vertical and horizontal cylinders are given in
Table 2.1.
Table 2.1 Constants for Determination of Nu
Geometry Ra c m
Vertical Cylinders O y^H 1 O 0.59 %
109-1013 0.10 1/3
Horizontal Cylinders 104-109 0.56
109-1012 0.13 1/3
16


Simplified expressions for the free convection heat transfer coefficient from
vertical and horizontal cylinders to air at atmospheric pressure are given in Table 2.2.
These relations may be extended to pressures other than atmospheric by multiplying
by the following factors:
f
y,
P
101.32
V
J
for laminar flow
(2.31)
\2/3
101.32
for turbulent flow
(2.32)
where, p is the pressure in kPa. These simplified relations are only approximations
and therefore should be used with caution [18].
Table 2.2 Simplified Equations for Free Convection from Pipes to
Air at Atmospheric Pressure adapted from table 2.1 10
Surface Laminar Turbulent
104 < Ra < 109 Ra > 109
Vertical cylinder
Horizontal cylinder
h = 1.42
fAry4
~L ,
(a rv'4
h = 1.32
v d j
h = 0.95(A7T)1/3
h = 1.24(AT)1/3
The convective heat transfer coefficient is given by the following expression:
17


(233)
7 £
h = Nuj
L L
And the heat transfer rate is evaluated from the Newtons law of cooling:
q = hizDL At. (234)
2.7 Temperature Dependence of Fluid Properties
The assumption that fluid properties remain constant throughout the flow field
is obviously an idealization. The transport properties of most fluids vary with
temperature and thus vary over the flow cross section within a tube. The general
effect of the variation of the transport properties with temperature is to change the
velocity and temperature profiles, yielding different friction and heat transfer
coefficients than would be obtained if properties were constant. There are methods
whereby the constant property solutions can be corrected in a simple manner to take
into account the influence of temperature.
For most liquids the specific heat and thermal conductivity are relatively
independent of temperature, but the viscosity decreases very markedly with
temperature. This is true for both oils and water. The density of liquids on the other
hand varies little with temperature. The prandtl number of liquids varies with
temperature in much the same manner as the viscosity.
For engineering applications it has been found convenient to employ the
constant property analytic solution, and then to apply some kind of correction to
account for property variation. Fortunately most of the corrections are fairly simple
and apply over a moderate range of temperatures.
18


Two schemes for the correction of the variation of properties are in common
use; the reference temperature method, and die property ratio method. For internal
flow applications, the later is used. In the property ratio method, all the variable
properties are evaluated at the surface temperature, then lumped into a function of
some pertinent property which is then divided by the properties evaluated at the
mixed mean temperature to form the ratio to that property evaluated at the mixed
mean temperature.
For liquids, where the viscosity variation is responsible for most of the effect,
it is found that equations of the following type are often excellent approximations:
Nu St ( fl o ^
NuCP Stcp Jlm
and
_L
fcp
£o

(2.35)
(2.36)
where St = h/(Gc), the Stanton number, and subscript CP refers to the appropriate
constant property solution. The viscosity (io is evaluated at surface temperature, while
Pm is evaluated at mixed mean temperature. The exponents m and n are functions of
geometry and the type of flow. For a laminar flow in a tube, m = 0.50 and n = -0.11
have been suggested.
Fully developed laminar flow in a tube with temperature dependent properties
is a relatively simple analytic problem. Only the variation of viscosity with
temperature is significant. The momentum and energy equations for fully developed
flow in a circular tube with constant heat flux conditions follow directly from
equation (2.37) and (2.38):
19


dx r (2.37)
(2.38)
dx r d r ^ dr
These two equations can be integrated by an iterative procedure in which the
temperature distribution for constant properties is used as a first approximation. Then
using the appropriate viscosity variation with temperature, the momentum equation is
integrated numerically to yield a second approximation for the velocity distribution.
This velocity distribution is employed in a numerical integration of the energy
equation to yield a second approximation for the temperature distribution. The
procedure is repeated until the velocity and temperature distributions converge. The
mean velocity, the mixed mean temperature, the friction factor, and the heat transfer
coefficient is then evaluated as in the constant property solutions.
2.8 Determination of Pressure Drop and Friction Factor
We can express shear stress at the wall in terms of the non-dimensional
friction coefficient, Cf, as:
Now considering equation (2.13), with the absolute value of shear stress, we get:
(2.39)
_ 4Vp/r0 16 16 16
'f ~ pV2/2 ~ DpV/ii ~ DG/p ~ Re
(2.40)
20


where G is the mass flux of the flow, also known as the mass velocity.
It is also necessary to mention that 4cf product is known as the conventional
friction factor, f, used in fluid mechanics in conjunction with the Moody diagram.
Therefore we may rewrite the above equation as:
(2.41)
However, Creveling [12] has studied the steady-state motion and the stability
characteristic of the toroidal loop experimentally and theoretically. They have
obtained and used the following relations for the friction factor, f, in steady laminar
and turbulent flows:
f =
a
Re*
(2.42)
(laminar flow: a=151, b=1.17 turbulent flow: a=0.88, b=0.45)
They have also obtained another correlation, which sets the buoyancy torque
equal to the opposing frictional torque for steady flow:
NuGrR
Pr r
NuGrR
Pr r
= 1260Re1'6
= 1.29 Re
Z56
laminar flow
turbulent flow
(2.43)
(2.44)
where R is the radius of the loop, and r is the tube radius.
The left hand side of the equations (2.43) and (2.44) contains only fluid
properties, system dimensions, and the product of h and At, which is the heat flux.
21


The last four equations make it possible to determine, for each value of the input
heating rate, the steady-state flow conditions and temperature distribution.
The analysis for fully developed turbulent flow in circular tubes is much more
complicated than for laminar flow and must ultimately rely on the use of
experimental results. Friction factors for a wide range of Re are presented in the
Moody diagram. The friction factor is a function of the tube surface condition in
addition to Reynolds number. It is a minimum for smooth surfaces and increases with
increasing surface roughness, e. The friction factor for two ranges of turbulent flow
are:
/ = 0.316Refl'1/4 (Re0 <2xl04) (2.45)
/ = 0.184 Re01/5 (ReD >2xl04) (2.46)
To calculate the pressure drop, one eliminates V from equation (2.10) and
(2.13), which gives the shear stress at the wall surface in terms of dP/dx. Integrating
and substitution of the friction factor results in the pressure drop equation:
A P =
f
rLYpy2>
2 ,
(2.47)
For the laminar flow, the poiseuille formula gives:
A P =
32 nLV
D2
(2.48)
Solving the above two expressions for f gives the well-known relation
between the friction factor and Re, f = 64/Re.
22


A knowledge of the magnitude of pressure loss is important, not only because
of the influence of pressure loss upon the power required to circulate a fluid, but also
because a relationship exists between the pressure loss and the heat transfer between
the tube wall and the fluid stream.
In addition to the pressure loss caused by friction between the fluid and the
pipe wall, losses are also caused by obstructions in the line, changes in direction and
changes in flow area. These losses are called minor losses since they are small when
compared to the total loss. Two methods are used to determine these losses, the
method of equivalent length and the method of loss coefficient.
One way in which pressure losses are expressed, especially in the case of flow
through pipe elbows, valves, etc. is in terms of the additional length of straight run of
pipe that would produce the same resistance as the elbow or any other form of
obstruction. When a fluid flows through an elbow or bend in a pipe, the fluid at the
outer radius of curvature travels a greater distance than that at the inner radius of the
bend. A pressure loss, of greater magnitude than in a straight run of pipe, is expected
because of greater differences in velocities of adjacent fluid particles. Additional
pressure loss also occurs because of the formation of eddy currents, which are
brought about by sudden changes in direction and velocity in portions of the fluid
stream.
For standard elbows used with copper tubing, pressure loss may be expressed
with fair accuracy in terms of the additional equivalent length of straight pipe or
tubing. The method of equivalent length uses a table to convert each valve or fitting
into an equivalent length of straight pipe. This length is added to the actual pipeline
length and then substituted in equation (2.47).
23


The pressure loss at inlet and exit ends of pipes and tubes, is a loss in both
total and static pressure and may be expressed as:
where, V is the velocity of the fluid in the pipe, and K is the loss coefficient, which is
a function of the ratio of the cross-sectional of the pipe Ai to that of the large
enclosure A2 to which it is connected. For the losses at pipe entrance, the values of K
for different ratios of A1/A2 are given in Table 2.3. [17]
Table 23 Values of K corresponding to ratio A1/A2 for pipe entrance
Ai/A2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
K 0.44 0.35 0.29 0.24 0.19 0.15 0.10 0.07 0.04 0.00
For sudden enlargements, and sudden contractions, the values of K are
calculated from the following relations:
(2.49)
2
V /
Sudden Enlargement (2.50)
Sudden Contraction
(2.51)
where Di and D2 are the smaller and larger diameters respectively.
24


3. Instrumentation
3.1 Electric Element System; Tank as Heat Exchanger
This system used the auxiliary tank as a heat source to run the natural
convection loop to freeze protect the system on cold winter days. The tank used in
this system is an A. O. Smith 40 gallon tank Model EES 40 with (2) 4500-Watt
electric elements. Its thermostat is set at 120 F.
The collector used in this system is a 4x 8 collector manufactured by
CopperSun that has (8) 4 diameter copper tubes which hold 40 gallons of water. It is
single glazed with a textured glass that faces up. It is tilted 18.43 from horizontal.
A capillary tube is used in the natural convection loop (thermosyphon loop) to
control pressure drop through the loop in order to obtain the needed flow rate. The
test was performed with five different sets of tubing diameters to determine the flow
rates at different ambient weather conditions below freezing temperatures. This
allows the coldest ambient temperature of the system to be found with no active
freeze-protection. The smaller the diameter of the capillary tube, the higher the
pressure drop across the tube therefore limiting the flow rate and heat loss under cold
conditions.
The connecting pipes are % copper piping and the schematic diagram of the
system is shown in Figure 3.1.
25


to
C\
Capillary Tube
Check Valve, Spring -N-
Expansion Tank | F. |
Flow Meier p*"
Heat Bxchaneer "i 1 =p-
Pressure Gage
Pressure Relief Valve Kl
Solenoid Valve
Strainer
Temperature Probe
Three Way Valve
Gate Valve
Orifice
Mixing Spring ft
-Cj----
Fig 3.1 Schematic Diagram of Tank Electric Element and RHX Systems


Referring to the schematic diagram, Fig 3.1 of the Electric Element system
(ES), the following conventions are used for the thermocouples along the loop:
El Thot,collector
E2 Thounix
E3 Thot^oof
Tclngjiot
Ttank,out
Ttank,avg
Ttankjret
Tcap.tank
E4 :
E5 :
E6
E7 :
Eg :
E9 :
E10
E
E12
cap,wall
Tclng,cold
Tcold,roof
Tcold, collector
Under the normal mode of solar water heating, the city water enters the
system when there is a demand for hot water. The cold city water then passes through
the collector pipes and returns to the indoor auxiliary tank which is located in the
conditioned space inside the house. The hot water will be heated with the electric
element if necessary before leaving the tank at a pre-set temperature.
When there is no draw forcing water through the collector, the water flows in
a reverse thermosyphon loop. In this reverse loop the water need not travel through
the collector pipes since the collector is not subject to freezing. If the water were to
pass through the collector, then there would be a considerable amount of heat loss in
27


the loop which is not necessary. To avoid the heat loss through the collector and yet
allow the NCL flow, we provide a bypass pipe between the entrance and exit pipes of
the collector for the path of the natural convection loop and a check valve preventing
flow through the collector. To ensure the passage of water through the collector in
normal operation, an orifice plate in located in the bypass pipe having a diameter
which is designed so that at least 95% of the water passes through the collector during
the normal operation and only 5% is allowed to enter the bypass line.
The thermosyphon loop causes the tank temperature to drop. Therefore the
electric element comes on to reheat the water and compensate for the heat loss in the
tank. The temperature of water along the loop was measured at various critical points.
The thermocouples were wired into the HP 75000 data acquisition system and were
then transferred to a PC computer for further analysis. The collected data were then
processed and put into separate spreadsheets. The data collected includes the average
temperature of the 40 gallon tank as measured with a linear averaging resistance
temperature device (RTD) which is 38.5 long and a thermocouple tree of (5) Type J
thermocouples. The RTD has a much faster response time giving a much better
indication of temperature changes in the tank as the water is cycled out of the tank
causing the element to turn on and reheat the water. This heat added over time
indicates the relative flow rate with different tubing sizes.
The pressure drop was determined by measuring the effective length of the
piping (valves, fittings, etc. each add effective equivalent pipe length). The piping is
measured on both supply and return sides (different in each installation case) to
determine pressure drops. The supply and return sides are called the hot and cold
legs respectively. The hot leg is measured from the bottom of the tank diptube to
the collector bypass orifice and the cold leg is from the orifice in the bypass to the
bottom of the tank. The piping measurements are summarized in Table 3.1.
28


Table 3.1 Piping and Piping Equivalent Measurements for the E-System
Hot Leg (m) Cold Leg* (m) Total (m)
Pipe 16.15 17.46 33.61
90s (21) 7.04 6.40 13.44
Tees (17) 2.99 4.27 7.26
Branch Tees (4) 3.11 3.11 6.22
BaU Valves (3) 0.14 0.28 0.42
Total 29.43 31.52 60.95
* Hot leg is measured from the bottom of the tank diptube to the collector bypass
orifice.
* Cold leg is measured from the orifice plate in the bypass to the bottom of the tank.
Table 3.1 only shows the total length of the hot and cold legs. In order to
determine the temperature distribution along the pipe we need to know the exact
location of thermocouples along the loop. This will allow us to compare the
experimental data from the instrumentation in the Thermal Test Facility with the
calculated temperatures from our EES Model. To serve our purpose we have divided
the loop into different segments that are separated by 12 thermocouples installed at
various critical positions along the thermosyphon loop. The readings of
thermocouples were sampled every five seconds and five minute averages are stored
through the data acquisition system. The raw data were then processed in separate
spreadsheets. The detailed measurement of the loop segments is given in Table 3.2.
29


Table 3.2 Detailed Measurement of the loop in E-system
Hot Leg (m) Cold Leg (m) Total (m)
Inside Piping:
Dip tube to E5 1.23
E5 to E4 (top of tank to just below ceiling) 3.76
E4 to E3 (below ceiling inside piping) 0.28
Hot leg (inside piping) 5.27
En to E10 (below ceiling inside piping) 0.36
E10 to E9 (ceiling to capillary) 3.22
E9 to Eg (capillary tube) 1.19
Eg to E7 (capillary to bottom of tank inlet) 1.27
Cold Leg (inside piping) 6.04
Total Length of Inside Piping 1131
Outside Piping:
E4 to E3 (above ceiling outside piping) 7.00
E3 to E2 (mid-pipe to Mix TC at top of bypass) 3.49
Eito orifice plate 0.39
Hot Leg (outside piping) 10.88
Orifice plate to E12 0.69
E12 to En (bottom of bypass to mid-pipe outside) 3.48
En to E10 (above ceiling outside piping) 7.25
Cold Leg (outside piping) 11.42
Total Length of Outside Piping 22.30
Total Length of Piping for E-system 33.61
30


3.2 Room Air Heat Exchanger System; (RHX)
This system uses an air-to-water heat exchanger to take heat from the air in a
room which provides the driving temperature for the thermosyphon loop when the
system is in the standby mode and the outdoor temperature is lower than the indoor
temperature. The heat exchanger is a copper-finned piece of pipe. The six fins are
each 0.89 mm thick, 5 cm wide, and 162.5 cm long from top to bottom.
The tank used in this system is a Vanguard 40 gallon tank model 6E721 with
(2) 4500-watt electric elements. The tank is only used during the normal operation of
the system as a water heater and is not used for the circulation of water in the
natural convection loop. This is one of the differences between the two systems.
The collector connected to the system is a Progressive Tube collector by
Thermal Technology Corp. 4x 8with (8) 4 diameter copper tubes in series which
hold 40 gallons of water. It is double glazed (a single layer of untextured glass with a
layer of Teflon film under the glass). The flow rate of the water in the
thermosyphon loop is determined in a different way than the E-system. Here we use
a differential pressure transducer (Celesco model DP31) to determine the flow rate.
The measurements of piping and piping equivalents are done in the same way
as for the other system. There are 13 thermocouples installed at various points for
the data collection, 10 of which are in the thermosyphon loop. Tables 3.3 and 3.4
show the measurements of the hot and cold legs of the loop.
31


Table 33 The Piping and Piping Equivalent Measurements for RHX system
Hot Leg * Cold Leg * Total
(m) (m) (m)
Pipe 15.23 16.19 31.42
90s (19) 5.76 6.40 12.16
Tees (12) 2.13 2.99 5.12
Branch Tees (4) 3.10 3.10 6.20
Ball Valves (2) 0.14 0.14 0.28
Total 2636 28.82 55.18
* Hot leg is measured from the bottom of the heat exchanger to the upper bypass
orifice.
* Cold leg is measured from the orifice plate in the bypass to the bottom of the heat
exchanger.
In chapter 4, the experimental data from the Electric System (ES) is used to
determine the flow rate in the loop. The Heat Exchanger System is only discussed in
theory and the actual tests of the system have not been performed yet. This is due to
the difficulty in establishing the flow in the loop. Therefore, from this point we will
proceed with the analysis of the electric system only.
32


Table 3.4 Detailed Measurement of the loop in RHX system
Hot Leg (m) Cold Leg (m) Total (m)
Inside Piping:
R6 to R5 (bottom to top of HX) 1.78
R5 to R4 (top of HX to TC at inside of ceiling) 3.00
R4 to R3 (below ceiling inside piping) 0.28
Hot leg (inside piping) 5.06
Rio to R9 (below ceiling inside piping) 0.36
R9 to Rg (inside ceiling to west end of capillary) 3.80
Rg to R7 (capillary tube) 0.98
R7 to R$ (east end of capillary to bottom of HX) 0.40
Cold Leg (inside piping) 5.54
Total Length of Inside Piping 10.60
Outside Piping:
R4 to R3 (above ceiling outside piping) 6.29
R3 to R2 (mid-pipe to Mix TC at top of bypass) 3.50
R2to orifice plate 0.38
Hot Leg (outside piping) 10.17
Orifice plate to Rn 0.69
Rn to Rio (bottom of bypass to mid-pipe outside) 3.48
Rio to R9 (above ceiling outside piping) 6.48
Cold Leg (outside piping) 10.65
Total Length of Outside Piping 20.82
Total Length of Piping for RHX system 31.42
33


4. Experimental Data For Electric Element System
As mentioned earlier in chapter 3, the electric element system used the tank as
a heat source to establish the thermosyphon flow in the loop. Therefore, the tank
water temperature was set at a temperature that will be controlled by the electric
element in the tank. The difference in tank supply and tank return temperatures was
then used to determine the flow rate in the loop. It is important to record the
temperature of water along the loop in order to calculate the heat losses and also
compare them with the predicted model temperatures in the loop. The room air
temperature and outside ambient air temperatures were also recorded. The
experimental setup is arranged in such a way that we can easily replace the capillary
tube and perform the same test under different capillary conditions. We started the
experiment with the initial setup which is a 3/4"dia. copper pipe all the way along the
loop. The same test was repeated three times to make sure that we included all the
environmental situations, i.e. sunny, cloudy, mild and freezing conditions in order to
analyze the behavior of the natural convection loop under different circumstances.
For the next experimental setup, a 3/8" dia. Capillary tube was placed in the loop and
the test was then performed with this new capillary tube. The same procedure was
repeated for the other capillary tubes available, i.e. 5/16", 3/32" and 1/8" diameter
polypropylene tubes.
It is also important to mention that when we ran each experiment for several
days, we did not always get a reasonable set of data that could be used for the
calculation of the flow rate in the loop. This is due to the fact that sometimes the
channels in the data acquisition system that collected the data and sent it to the
computer did not function properly. Therefore, we observed an unexpected noise or
34


disturbance in readings of those channels. We ran each set of tests for three times and
had the option to choose the best data available.
4.1 Tank UA From Decay Test Data
In order to determine the tank overall heat transfer coefficient, UA, the tank
is separated from the rest of the system by closing all the pipe connections. The water
temperature of the tank is then raised to about 75C and then allowed to cool for
several hours. This process is called a Decay Test. The same procedure is repeated
three times, first for 25 hours, then for 60 hours and finally for approximately 70
hours. The RTD, TC tree and room ambient temperatures were recorded every five
minutes.
There are two methods used to determine the tank overall heat transfer
coefficient, UA, from the Decay Test Data and are described as follows:
Method 1) Assume Tenv =constant over the range of data acquisition.
In this method we assume Tenv = Temperature average throughout the entire
time the tank is under observation for Decay Tests. To get the best results, the Decay
Tests were repeated three times. Considering the equation of heat transfer rate for the
tank alone we have:
(M cp ^ = -X Q = -UA(T Tem) (4.1)
where M is the mass of water in the tank in kg, Cp is the specific heat at constant
pressure in kJ/kgc, T refers to temperature in C, t is time in seconds, and Q is the
rate of heat transfer in Watts.
35


Solving the above differential equation for T and introducing time constant x,
gives (see Appendix A.l for details):
UA = x M Cp (4.2)
Ati^f
Where x = ----------r
ln(Ar0/A7})
AT0 = T0 Tenv and ATf = Tf Tenv
Figures 4.1, 4.2 and 4.3 show the inside ambient temperature, tank temperature as
measured by RTD (Resistance Temperature Device) and tank temperature by the
average of six thermocouples. There are three different sets of experimental data,
which are labeled as Decay Test 1,2 and 3 respectively.
Tank Decayt Test 1
Fig. 4.1 Decay of Tank Water Temperature versus Time
36


Tank Decay Tset 2
Time (hr)
Fig. 4.2 Decay of Tank Water Temperature versus Time
The value of UA for three sets of Decay Tests are summarized in tables 4.1 and 4.2,
using tank average and RTD temperatures, respectively.
Table 4.1 Tank UA (W/C) With Tank Average Temperatures
To Tf Tenv AT0 ATf At(hr) UA
Decay 1 73.39 58.52 20.87 52.52 37.65 24.5 2.14
Decay 2 71.45 44.77 20.49 50.96 24.28 63.75 1.84
Decay 3 72.20 44.38 21.45 50.75 22.93 69.3 1.81
37


Table 4.2 Tank UA (W/C) With RTD Temperatures
To Tf Tenv AT0 ATf At(hr) UA
Decay 1 73.62 58.38 20.87 52.75 37.51 24.5 2.20
Decay 2 71.60 44.99 20.49 51.10 24.50 63.75 1.82
Decay 3 72.45 44.60 21.45 51 23.15 69.3 1.80
Tank Decay Test 3
Fig. 4.3 Decay of Tank Water Temperature versus Time
38


Method 2) Consider the environmental temperature fluctuations.
In this method, we first determined the temperature gradient with respect to
time, then using the following formula we determined the tank overall heat transfer
coefficient, UA:
JT1
Mcp = -UA(AT) (4.3)
dt
Knowing all the terms in the above equation except UA, we can calculate UA
for each time interval and then take the average of all UAs (Refer to Appendix A for
details, also notice that only a small portion of data for the Decay Test 1 is attached.
The same procedure is repeated for Tests 2 & 3). The results of the spread sheet
calculations are summarized in Table 4.3.
Table 4.3 Tank UA (W/C) with Method 2
UA with T-Tank (avg) UA with T-RTD (avg)
Decay Test 1 2.14 2.03
Decay Test 2 1.82 1.80
Decay Test 3 1.79 1.74
To compare the results of two different methods for UA For Decay Test 1: calculations, we have:
Tank UA (T-Tankavg) Tank UA (RTD)
Method 1 2.14 2.20
Method 2 2.14 2.03
39


For Decay Test 2:
Tank UA (T-Tankavg) Tank UA (RTD)
Method 1 1.84 1.82
Method 2 1.82 1.80
For Decay Test 3:
Tank UA (T-Tank^) Tank UA (RTD)
Method 1 1.81 1.80
Method 2 1.79 1.74
Comparison Between UA's"
in Decay Tests 1,2,3
Tims (Hr*)
---UA1 W/C
---UA2 W/C
UA3 W/C
Fig. 4.4 Comparison of UA Results in Decay Tests 1,2,3
40


For further calculations of mass flow rate in the natural convection loop, we
have plotted UA versus Delta T, and then fit a second order polynomial to it and used
the equation to calculate UA at any given temperature difference.
4.0
3.0
2.0
t
<
p
1.0
0.0
35.0 36.0 37.0 38.0 39.0 40.0
A T (C)
Fig. 4.5 Polynomial Fit to S Note: In order to get the best polynomial fit through the curve, the first five hours of
data in all the three decay tests have been omitted. The noise in the beginning data
might be due to the experimental set up and high temperature difference between tank
and room temperature at the beginning of the tests. Anyway, it is quite reasonable to
ignore this data since our actual working temperature difference would not ever get
that large.
The second order polynomial fit through Decay test 2 is used to determine the
flow rate in the natural convection loop. As it is shown, the UA increases with the
increase in AT and this is in reverse relation with time. Therefore at the beginning of
each test we have the highest AT and highest UA.
-UA=-3.717934 + 0.2988739-DELTA T-0.00394671 -DELTA T2
41


UA" (W/C) *5 "UA" (W/C)
ig. 4.6 Polynomial Fit to UA as a Function of AT in Decay Test 2
Fig. 4.7 Polynomial Fit to UA as a Function of AT in Decay Test 3
42


4.2 Mass Flow Rate in Natural Convection Loop
After the determination of tank UA, we needed to calculate the mass flow
rate in the thermosyphon loop using the tank as a calorimeter.
The energy balance equation of the system is:
-McP ~=QTa71k + mcP (AT) (4.4)
at
where, dT/dt is the slope of the RTD temperature curve versus time, Qrank is the heat
loss of the tank in Watts, m is the flow rate in the natural convection loop in kg/s,
and AT is the total temperature difference between the tank output and tank return
temperatures in C.
As mentioned earlier in chapter 3, the system was tested with four different
capillary tubing sizes along with the original % copper pipe in order to determine the
best combination of capillary tube diameter and length for the thermosyphon loop.
These tests allowed us to get the required flow rate while loosing the minimum
amount of heat. The experiment was performed at least 3 times with each set of
tubing, for a period of several days. The corresponding temperatures of the 12 critical
points in the system were recorded every five minutes. The tank RTD average
temperature is used to calculate dT/dt. The four different sizes of capillary tubing are:
0.75 dia. Copper pipe (1.91 cm)
0.375 dia. Polypropylene tube (0.95 cm)
. 0.3125 dia. Teflon tube (0.79 cm)
0.125 dia. Polypropylene tube (0.32 cm)
0.094 dia. Teflon tube (0.24 cm)
43


The temperature of water at critical points along the loop was measured and
plotted versus time. Also the corresponding mass flow rates were calculated and
plotted versus time. These plots are shown in the next five pages. One set of
experimental data is selected with respect to each capillary tubing for further analysis.
In order to observe the changes in flow rate and the behavior of each channel
with respect to the weather conditions, the outside ambient temperature is recorded
and shown in each plot.
The first test was performed with a 3/4" dia. copper pipe placed as the
capillary in the loop. Actually, in this test the entire loop had the same piping
diameter, whereas in the other four tests the diameter of capillary tube changes and
the rest of the loop stays with its original 3/4" dia. piping. Fig 4.8 shows the
experimental data collected from the first test with 3/4" copper piping (up) and the
resulted mass flow rate calculated from the energy balance equation of the system
(down). This test ran for almost four days. On the first two days of the experiment,
we had relatively higher ambient temperatures as compared to the last two days. As
the sun shines and the temperature goes up, the collector surface becomes very hot
and the thermocouples that are near the collector start to show much higher
temperatures as compared to those far from the collector. This sudden increase in the
water temperature is obvious in readings of thermocouples E2 and Eu This indicates
that there is an unexpected effect of ICS on the loop due to the conduction or simply
mixing of collector water with the water in the loop that was not considered initially
and therefore the loop may behave according to the outside ambient temperature
rather than the natural convection.
44


Temperature (c) Temperature (C)
ES- 3/4" Copper Pipe Test 2
2/7/99-2/11/99
----RTDX
----Tamb.oU X
TcoW.roof X
----TcokJ.coft X
----Thot.mix X
----Thot.roof X
----Tdng.hot X
----Ttank,out X
Ttrk.ret X
TcIng.coW X
Time (hr)
Time (Hr)
Fig. 4.8 Experimental Data for Various Temperatures along the Loop (up)
and the Resulted Mass Flow Rate (down) with % Copper Pipe
45


The flow rate corresponding to the experimental data is shown in Fig. 4.8
(bottom). As the outside ambient temperature increases, the flow rate decreases
dramatically.
The second set of data is from the test with 3/8" capillary tubing and its plot is
shown in Fig. 4.9. This test ran for 21 hours and as you can see from the graph, there
was some channel problem with recording the data and therefore, we neglect that time
of the test and proceed with 17 hours of data.
As the diameter of capillary tube decreases, the pressure drop in the system
increases and therefore we get lower flow rates. Since our five experimental setups
were arranged in such a way that the first test is performed with the largest capillary
tube, then we can expect a decrease in flow rate as we run five sets of experiments.
Fig. 4.10 shows the results of the third test with a 5/16" capillary tube. In this
test we observe some channel disturbance at the beginning of the test and around 20
hours after the starting point Therefore we decided to analyze our available data for
the last 45 hours of the test.
46


Temperature (C) Temperature (C)
80
ES 3/8" Polypropylene Test 1
3/1/99
70
60
50
40
30
20
10
0
-10
-20
----RTD C
----Ttank.out *C
----Tclng.hot C
----Thot.roof C
----Thot.ma C
----TcoW.coB 8C
TcoJd.roof C
----Tdng.cokj C
Ttnk,rel *C
----Tamb.otH C
Time (hr)
----Tamb,out C
DTtank/out C
Flow Rate kg/s
Fig. 4.9 Experimental Data for Various Temperatures along the Loop (up)
and the Resulted Mass Flow Rate (down) with 3/8Capillary Tube
47


The fourth test was run with a 1/8" capillary tube and as you can see from Fig.
4.11, the flow rate is very low and the effect of ICS is to the extent that there is a
reverse flow in the loop. This is obvious from the increase in temperatures along the
loop as flow moves forward instead of the normal reduction of temperature.
Therefore it can be concluded that a 1/8 capillary tube is so small that it drops the
pressure along the loop dramatically and as a result, the flow will not be strong
enough to make it all the way throughout the loop.
The last test was performed with a smaller capillary tube than was used in the
fourth test which resulted in the flow being very close to zero. The readings of
temperatures along the loop do not make any sense at all. For this test a 3/32
capillary tube was used. The experimental data and the corresponding mass flow rates
for the fifth test are shown in fig 4.12. As can be seen from fig 4.12, the temperature
of water in the loop follows the opposite pattern of what it really should be. If we take
a closer look, we find a very unexpected behavior of temperatures along the loop. The
channels E2 and E12 are the readings for the two thermocouples that are closest to the
collector. As the outside ambient temperature increases, these two channels show an
extremely high temperature that is due to their closeness to the ICS unit. If there was
an independent loop, then no temperatures along the loop should have gone higher
than the tank output temperature or lower than the, tank return temperature. The
thermocouples E5 and E4 are 3.76 m apart and they show a 20 C temperature drop
which is quite unusual since they are both inside the conditioned space where the
ambient temperature is about 22 C Also there are two thermocouples E4 and E10
that are 22.3 m apart in the outside ambient temperature and their temperature
difference is almost negligible in the loop. This is the evidence for a reverse flow due
to the heat transfer from the collector to the thermosyphon loop.
48


ES- 5/16* Capillary Tube Test 3
4/14/99-4/19/99
JS
u_
----Tamb,out C
DT C
Flow Rate kg/s
Z
Fig. 4.10 Experimental Data for Various Temperatures along the Loop (up)
and the Resulted Mass Flow Rate (down) with 5/16Capillary Tube
49


Temperature (C) Temperature (C)
ES-1/8" Capillary Tube Test 4
4/6/99
------RTDaC
------Ttank.oU *0
------Tclng.hot C
------Thot.roof C
------Thot.mix C
------Tcdd.coll eC
------Tcotd.roof aC
Tcing.cokl C
Ttnk.ret C
------Tamb.out C




-.V? ' ; :* ,
wSw

JI iup.ni..i. 4krr.;-i I. it_tJgT. jfcafi


mm
10 15
Time (hr)
CC

o
u.
Tamb.out C
0T (Tankout-amb)0 C
Flow Rate kg/8
<0
5
Fig. 4.11 Experimental Data for Various Temperatures along the Loop (up)
and the Resulted Mass Flow Rate (down) with 1/8 Capillary Tube
50


Temperature (C) Temperature (C)
ES 3/32" Tubing Test 2
3/19/99-3/22/99
45
40
35
30
25
20
15
10
Time (hr)

! fy1. .


iM
l
/ *v
i AiV/ 4a.

0 10 20 30 40 50 6
0.0020
0.0018
0.0016
0.0014
0.0012
0.0010
0.0008
- Tamb.out C j
DTtank/out C j
Flow Rate kg/s |
0.0006
4 0.0004
0.0002
0.0000
Time (hr)
Fig. 4.12 Experimental Data for Various Temperatures along the Loop (up)
and the Resulted Mass Flow Rate (down) with 3/32Capillary Tube
51


Based upon the calculated values of mass flow rate for the NCL loop, the
smallest two capillary tubes may not provide enough flow to ensure the existence of
the loop at all times. Also the two biggest tubes may actually waste some of the
valuable energy of the system in the form of heat loss. Therefore the best result,
according to our calculations, would be the third option, i.e. a capillary tube of
approximately 0.8 cm.
The detailed analysis of the mass flow rate calculations is given in Appendix
B. Also, the relative parts of the spread sheet works are attached.
52


5. EES Model For Determination of Design Parameters
The complete set of equations are programmed in EES (Engineering Equation
Solver) to solve for flow rate, one-dimensional temperature distribution, local and
total heat fluxes for given system parameters and environmental specification. This
paper presents the model for the natural convection loop (NCL) driven by heat from
an auxiliary tank located in the conditioned space. The system parameters are
determined by the specific ICS unit which includes the piping dimensions, insulation
specifications, thermal conductivity of piping material, coefficient of heat transfer on
the inside and outside of the pipe and thermal resistance of the system. In the
following sections, the key variables of the system are determined with respect to the
independent variables.
5.1 Capillary Tube Sizing
The EES Model is used to determine the diameter and length of the capillary
tube. Capillary tube diameters are input to the EES Model, which determines the
required tube length.
The initial design length of the capillary tube is one meter long, which is the
actual experimental set up of the system at the Thermal Test Facility (TTF) at the
National Renewable Energy Laboratory (NREL). The length of the tubing required
for different diameters of capillary tube are given in Table 5.1.
53


Table 5.1 Relation between Diameter and Length of Capillary Tube
(mm) Leap (m)
Run 1 1.5 0.3664
Run 2 1.7 0.6044
Run 3 1.9 0.9431
Run 4 2.1 1.407
Run 5 2.3 2.025
Run 6 2.5 2.827
Run 7 2.7 3.846
Run 8 2.9 5.119
Run 9 3.1 6.683
Run 10 3.3 8.582
1.0 2.0 3.0 4.0 5.0 6.0 7.0
Dcapmm [nrun]
Fig. 5.1 Relation between Dcap and L^p for E-system
54


5.2 Mass Flow Rate through the Bypass
Orifice and Collector
In order to have efficient freeze protection and to minimize the heat losses in
the NCL loop, the reversed thermosyphon flow needs to be limited to the bypass pipe
with no flow being allowed to pass through the collector during the standby position.
On the other hand, when there is a demand for hot water in the building, the city
water needs to be able to pass through the collector in order to get the most benefit
from the solar system. Under this condition, the passage of water through the bypass
pipe needs to be minimized to ensure that the solar system is working efficiently.
Therefore, during normal operation our goal is to pass 95% of the water through the
collector and 5% through the bypass pipe. To achieve this goal an orifice plate is
placed in the bypass line that ensures that 95% of the water will go through the
collector during the normal operation of the system.
The flow ratio is defined as the ratio of mass flow rate through the collector to
the total flow rate in the pipe. An EES Model is designed to determine the flow ratio
for a flow of 0.005 kg/s. A parametric table is generated to look at the variation of
mass flow rate with the orifice diameter. The EES Model and the corresponding table
are given here:
{ratio of the flow through the collector and through the bypass for a given
draw...}
{Collector Data}
D_coll = 4*0.0254 {main "big" pipes}
L_coll=92*0.0254 {length of each big pipe}
L_pipecoll = 104*0.0254 {little pipes}
LD_coll = 774
{Bypass data}
C_d = 0.65
Beta = 0.188
D_orifice = Beta*D_pipe
55


mdot_orifice=rho*v_orifice*(pi*D_orificeA2/4)
{Pipe data}
D_pipe = (0.75)*.02547777
P_pipe = 600
f_pipe = 64/Re_pipe
Re_pipe = rho*v_pipe*D_pipe/mu
{Flow data}
mdot_pipe=.005 {kg/s}
mdot_pipe=rho*v_pipe*(pi*D_pipeA2/4)
mdot_coll==rho*v_coll*(pi*D_collA2/4)
How_ratio=(mdot_coU)/(mdot_pipe)
{velocity relationships/mass conservation}
mdot_pipe=mdot_coll + mdot_orifice
v_pipecoll=v_coll*(D_pipeA2/D_collA2)
{Pressure Drop in Collector}
Re_coll=rho*v_coll*D_coll/mu
f_coll=64/Re_coll
DP_coll=0.5*rho*(v_collA2*f_coll*(8*L_coll/D_coll)+v_pipecollA2*f_pipe*(L_
pipecoll/D_pipe+ LD_coll))
{Pressure Drop in Bypass}
DP_orifice = rho*v_orificeA2/(2*C_dA2)*(l/BetaA4 -1)
Dp_orifice=Dp_coll
{Temperature of water at tank exit and tank entrance}
T_set = (120-32)/1.8
T_ret = 0
{W ater properties}
mu = viscosity (WATER, T = (T_set + T_ret)/2, P = P_pipe)
rho = density(WATER, T = (T_set + T_ret)/2, P = P_pipe)
The solution to the above set of equations is:
Beta=0.188
C_d=0.65
DP_coll=0.03227
DP_orifice=0.03227
56


D_coll=0.1016
D_orifice=0.0068 [m]
D_pipe=0.01911
Flow_ratio=0.9987
f_coll=0.9219
f_pipe=0.1732
LD_coll=774
L_coll=2.337
L_pipecoll=2.642
mdot_coll=0.004993
mdot_orifice=0.000006701
mdot_pipe=0.005 [kg/s]
mu=0.0009014
P_pipe=600
Re_coll=69.42
Re_pipe=369.6
rho=998.1
T_ret=0
T_set=48.89
v_coll=0.0006171
v_orifice=0.0001849
v_pipe=0.01747
v_pipecoll=0.00002183
^ortflee In']
Fig. 5.2 Relation between Orifice Diameter and Flow Ratio
57


Table 5.2 Flow Ratio for Various Orifice Diameters
Dorifice Flow Ratio Flow thru Collector
Run 1 0.002 0.9999 0.004999
Run 2 0.0022 0.9999 0.004999
Run 3 0.0024 0.9998 0.004999
Run 4 0.0026 0.9998 0.004999
Run 5 0.0028 0.9998 0.004999
Run 6 0.003 0.9997 0.004999
Run 7 0.0032 0.9997 0.004999
Run 8 0.0034 0.9997 0.004998
Run 9 0.0036 0.9996 0.004998
Run 10 0.0038 0.9996 0.004998
Run 11 0.004 0.9995 0.004998
Run 12 0.0042 0.9995 0.004997
Run 13 0.0044 0.9994 0.004997
Run 14 0.0046 0.9994 0.004997
Run 15 0.0048 0.9993 0.004997
Run 16 0.005 0.9993 0.004996
Run 17 0.0052 0.9992 0.004996
Run 18 0.0054 0.9992 0.004996
Run 19 0.0056 0.9991 0.004995
Run 20 0.0058 0.999 0.004995
Run 21 0.006 0.999 0.004995
Run 22 0.0062 0.9989 0.004994
Run 23 0.0064 0.9988 0.004994
Run 24 0.0066 0.9987 0.004994
Run 25 0.0068 0.9987 0.004993
58


53 Comparison between Measured Temperatures
and Model Predictions
We have already presented the figures showing the measured
temperatures at critical points along the loop obtained from the experimental data.
In this section we will compare that data to the model predictions of the loop.
The model uses the following formula to predict the temperatures along
the loop, given the measured mass flow rates:
nx) =+[ix*=o) rje-"1"
where
A>
ft d Pipe U Pipe
mcp
(5.1)
In the above equations, Upipe is the coefficient of heat transfer per unit area, Tamh
is the air temperature of the room or outside (whichever applies), and T(x=0) is
the temperature at the beginning of the loop. Mass flow rate is calculated using
the energy balance for the tank.
At the beginning of the loop, measured temperatures compare fairly well with
temperatures predicted by the model but as the flow approaches the ICS unit, the
temperature deviates from that predicted by the model and follows the outside
ambient temperature. This unexpected drop in flow temperature results from the
fact that the water in the collector piping has a great influence on the water
temperature in the loop. There is also a possibility of water leakage from the ICS
unit to the loop that eventually mixes with the warm water in the loop.
59


It is also important to mention that for the last two capillary tubing cases,
the flow rate in the loop is so low that the ICS influence totally destroys the
thermosyphon loop which results in a reversed flow of water in the loop. It is
evident from the last two sets of experimental data presented in graphical form
that as the flow moves forward in the loop, the temperature gradient is the
negative of what is expected. Therefore, it is not possible to draw a conclusion
about the model evaluation with these two data sets. For the first three sets of
capillary tubing, the flow rates are large enough to maintain the flow throughout
the loop. Therefore the effect of ICS in these data sets shows a large deviation
between the measured data and predicted model temperatures. This deviation
does not grow as the flow passes through the loop but rather stays constant which
indicates that the model program would work perfectly if the loop was
disconnected from the ICS unit.
The above argument is shown in graphs that are presented in Fig. (5.3)
to (5.7). The temperatures of the critical points along the loop have been
compared using the actual data and model predicted temperatures.
60


Temperature (eC) Temperature (C) Temperature (C)
Measured Temperatures
Model Predictions
Time (hr)
Time (hr)
Hot Leg Ceiling
Cold Collector
Cold Leg Ceiling
TcnkRelun
Fig. 5.3 Comparison of Measured Temperatures with Model Predictions
along the NCL for 3/4" Copper piping
61


Temperature CC) Temperature (C) Temperature (X)
Measured Temperatures
Model Prediction
60
so
40
30
20
10
0
10
~l
TtlMJES B* TlxtiocKTrMfc) E3 Thnt.rnr.itrri) 67 Tka4



i "&> 10 15 20 i 5
Time (hr)
He* Leg Ceiling
coid Leg collector
Cold Leg Ceiling
TnB(lr)
Tark Return
TfTB(h)
Fig. 5.4 Comparison of Measured Temperatures with Model Predictions
along the NCL for 3/8" Capillary Tubing
62


Temperature ("C) Temperature (C) Temperature PC)
Measured Temperatures
Model Predictions
Time (hr)
Time (hr)
Hot Leg Ceiling
Tern (hr)
Cold Leg Collector
Time (hr)
Cold Leg Ceiling
Tank Return
Time (hr)
Fig. 5.5 Comparison of Measured Temperatures with Model Predictions
along the NCL for 5/16" Capillary Tubing
63


Measured Temperatures
Model Predictions
Time (hr)
CddLegCoUeda
Tme(hr)
Fig. 5.6 Comparison of Measured Temperatures with Model Predictions
along the NCL for 1/8" Capillary Tubing
64


Temperature (C) Temperature (C)
Measured Temperatures Model Predictions
Hot Leg Ceiling
Cold Leg Collector
70
60
SO
40
30
20
to
0
S 10 15 20 25 X 36
71ms (hr)
Tune (hr)
Cold Leg Ceiling
Time (hr)
TankFtetim
Fig. 5.7 Comparison of Measured Temperatures with Model Predictions
along the NCL for 3/32" Capillary Tubing
65


5.4 Determination of Flow Parameters
with respect to the Pipe Velocity
Although we are aware of the deviation between the experimental results and
the model predictions, it is still helpful to find out how the model acts under certain
given conditions. At this point we ran the model to solve the set of equations related
to the thermal and hydraulic aspects of the system with the water velocity in the pipe
being the independent variable. The complete set of equations, the solution package
and the related graph is given here:
{Capillary loop equations/piping freeze protection}
{Configuration 1: tank as heat supply, collector not included}
{Problem Parameters}
D_pipe = (0.75)*.02547777
t_pipe = 0.154* .02547777
t_ins = .75* 0254
kjns = .06 {W/m-C}
k_copper = 300
h_in = 130
h_out = 3.5
L_pipeout = 21.3 {m outside distance to/retum colletors}
L_pipein = 9.7 {m inside distance to/retum colletors, thermosyphon loop only}
LD_pipeeq = 1524 {LTD equivalent length for fittings, elbows, etc}
H_pipe = 5 {m}
{Collector data}
D_coll = 4*0.0254
L_coll=92*0.0254
L_pipecoll = 104*0.0254
LD_coll = 774
{Bypass data}
C_d = 0.65
Beta = 0.188
D_orifice = Beta*D_pipe
DP_orifice = rho*v_pipeA2/(2*C_dA2)*(l/BetaA4 -1)
66


T_amb = -10
T_set = (120-32)/1.8
T_ret = 0
U_ics = 3.12
A_ics = 3
P_pipe = 600 {kilo-pascals}
mu = viscosity(WATER, T = (T_set + T_ret)/2, P = P_pipe)
rho = density(WATER, T = (T_set + T_ret)/2, P = P_pipe)
C_p=specheat(WATER,T = T_set, P = P_pipe)
g = 9.8
L_cap = 1
{D_cap = .001}
{Piping heat transfer}
r_pipe = D_pipe/2
Rl=l/(pi*D_pipe*L_pipeout*h_in)
R2=ln((D_pipe+2*t_pipe)/D_pipe)/(2*pi*k_copper*L_pipeout)
R3=ln((D_pipe+2*t_pipe+2*t_ins)/(D_pipe*2*t_pipe))/(2*pi*k_ins*L_pipeout)
R4=l/(pi*(D_pipe+2*t_pipe+2*t_ins)*L_pipeout*h_out)
R = R1+R2+R3+R4 {based on pipe radius, not outside}
UA_pipe = 1/R
Q_pipe =UA_pipe*( (T_hot_avg+ T_cold_avg)/2 T_amb)
Q_ics = U_ics*A_ics*((T_set + T_ret)/2 T_amb)
{Flow rate by setting the heat losses from the pipe to the heat carried by the water
advection:}
v_pipecm=v_pipe*100 {cm/s}
Q_flow_2=Q_pipe
{Q_flow_2 = Q_pipe + Q_ics}
Q_flow_2= (C_p*1000)*rho*v_pipe*(T_set T_ret)*(pi*D_pipeA2/4)
{Head}
Drho = (density (WATER, T=T_cold_avg, P = P_pipe))-(density(WATER, T =
T_hot_avg, P = P_pipe))
Head = Drho*g*H_pipe
67


{Pressure drop in pipes}
Re_pipe = rho*v_pipe*D_pipe/mu
f_pipe = 64/Re_pipe
dpdx_pipe = .5*(rho*v_pipeA2)*f_pipe/D_pipe
DP_ftic_pipe = dpdx_pipe*(L_pipeout+L_pipein+LD_pipeeq*D_pipe)
{Pressure Head equal to system pressure losses:}
Head=DP_Mc_pipe+DP_fric_cap + DP_orifice
{Head = DP_fric_pipe+DP_fric_cap + DP_orifice + DP_coll}
{Capillary tube:}
{f_cap = 64/Re_cap}
{dpdx_cap = .5*(rho*v_capA2)*f_cap/D_cap}
{DP_fric_cap = dpdx_cap*L_cap}
{D_cap=(32*v_cap*mu*L_cap/DP_fric_cap)A0.5}
{combining capillary flow rate and pressure drop equations}
D_cap=(32*v_pipe*D_pipeA2*mu*L_cap/DP_fric_cap)A0.25
D_capmm=D_cap*1000 {mm}
Re_cap = rho*v_cap*D_cap/mu
{Flow rate of capillary tube: mass flow rate in pipe equal to mass flow rate in
capillary}
v_cap=v_pipe* (D_pipeA2/D_cap A2)
v_capcm=v_cap* 100 {cm/s}
{Pressure Drop in Collector}
v_coll=v_pipe*(D_pipeA2/D_collA2)
Re_coll=rho*v_coll*D_coll/mu
f_coll=64/Re_coll
DP_coll=
0.5*rho*(v_collA2*f_coll*(8*L_coll/D_coll)+v_pipeA2*f_pipe*(L_pipecoll/D_pi
pe + LD_coll))
{Temperature profile corrections}
L_pipehot=15.5
L_pipecold=15.5
m_dot=0.005
U_pipe=(UA_pipe)/A_pipe
A_pipe=pi*D_pipe*(L_pipein+L_pipeout)
l/L_0=(pi*D_pipe*U_pipe)/(m_dot*C_p)
68


T_hot_avg=( l/L_pipehot)*((T_amb*L_pipehot)+((T_set-T_amb)* (exp(-
(L_pipehot*( l/L_0)))/(- l/L_0)))-(T_set-T_amb)/(- 1/L_0))
T_cold_avg=(l/L_pipecold)*((T_amb*L_pipecold)+((T_orifice-T_amb)*(exp(-
(L_pipecold*(l/L_0)))/(-l/L_0)))-(T_orifice-T_amb)/(-l/L_0))
T_orifice=T_amb+((T_set-T_amb)*(exp(-(L_pipehot*(l/L_0)))))
The solution set is:
A_ics=3
A_pipe=1.861
Beta=0.188
C_d=0.65
C_p=4.177
dpdx_pipe=0.001662
DP_coll=0.02901
DP_&ic_cap=14.31
DP_Mc_pipe=0.09994
DP_orifice=0.0004181
Drho=0.294
D_cap=0.001984
D_capmm= 1.984
D_coll=0.1016
D_orifice=0.003592
D_pipe=0.01911
f_coll=764.3
f_pipe=143.8
g=9.8
Head= 14.41
h_in=130
h_out=3.5
H_pipe=5
k_copper=300
k_ins=0.06
LD_coll=774
LD_pipeeq= 1524
L_0=0.536
L_cap=l
L_coll=2.337
L_pipecold=15.5
L_pipecoll=2.642
69


L_pipehot=15.5
L_pipein=9.7
L_pipeout=21.3
mu=0.0009014
m_dot=0.005
P_pipe=600
Q_flow_2=1.23
Q_ics=322.4
Q_pipe=1.23
R=0.8279
Rl=0.006016
R2=0.00000857
R3=0.7563
R4=0.06563
Re_cap=4.288
Re_coll=0.08373
Re_pipe=0.4452
rho=998.1
r_pipe=0.009554
T_amb=-10
T_cold_avg=-l 0
T_hot_avg=-7.964
t_ins=0.01905
T_orifice=-10
t_pipe=0.003924
T_ret=0
T_set=48.89
UA_pipe=1.208
U_ics=3.12
U_pipe=0.649
v_cap=0.001952
v_capcm=0.1952
v_coll=7.4428E-07
v_pipe=0.00002104
v_pipecm=0.002104


Tank Heat Exchanger Configuration Outside Ambient = -10 C (No Collector
Fig. 5.8 Relation between Design Parameters and Pipe Velocity
71


5.5 Comparison between Measured and Model
Values for m UA and AT
An EES model is developed to predict the mass flow rate in the loop using the
highest temperature difference from the experimental data. The predicted flow rates
are calculated for each set of capillary tubing and compared with the measured flow
rates. Table 5.3 and Fig. 5.9 show the results.
Table 5.3 Measured and Model Mass Flow Rates (kg/s)
AT (meas.)C m (meas.) m (model)
%Copper Pipe 9.04 0.008 0.0009
3/8 Capillary 8.6 0.006 0.0008
5/16 Capillary 9.16 0.005 0.0009
1/8 Capillary 19.22 0.0003 0.0001
3/32 Capillary 7.84 0.0001 0.0003
Row Rate Comparison
1
I
I
3/4*pipa 3/8* Capaary 5/16* Capaary 1/S* Capaary 3/32* Capaary
Capillary Dia.
Fig. 5.9 Mass Flow Rate (Measured / Model)
72


The model temperature difference in the loop is determined from the
measured mass flow rates. The calculated temperature difference is compared to the
measured temperature difference for each data set. The environmental specifications
are entered into the model from the experimental data. The results are shown in Table
5.4 and Fig. 5.10.
Table 5.4 Measured and Model AT (C)
m (meas.) kg/s AT (meas.) AT (model)
%Copper Pipe 0.008 9.04 1.1
3/8 Capillary 0.006 8.60 1.99
5/16 Capillary 0.005 9.16 2.76
1/8 Capillary 0.0003 19.22 22.97
3/32 Capillary 0.0001 7.84 27.82
Delta T Comparison
3/4*p*a 3^8* CapMary 5/16Ccpaary 1/8* Capaary 3/32*C*>ary
Capillary Dia.
Fig. 5.10 AT (Measured / Model)
73


The third approach is to infer UA from the measured values of mass flow
rate and temperature difference. The results of the EES model are given in Table 5.5
and Fig. 5.11.
Table 5.5 Measured and Model UA (W/ C)
AT (meas.) UA (meas.) UA (model)
%Copper Pipe 9.04 11.81 1.27
3/8 Capillary 8.60 9.07 1.27
5/16 Capillary 9.16 6.9 1.27
1/8 Capillary 19.22 3.33 1.27
3/32 Capillary 7.84 0.41 1.27
UA Comparison

:. : \-N '. i

L D UA (meas.) W/*C UA (modal) W/*C

n
li Ja rJl
3/4'pipe 3/8* Capillary 5/16*Capiary 1/8* Capillary 3/32*Cap*ary
Capillary Dia.
Fig. 5.11 UA (Measured / Model)
74


6. Conclusions and Recommendations
The passive freeze protection of an ICS solar domestic hot water system by a
natural convection loop was studied theoretically and experimentally. A
theimosyphon loop is established using an auxiliary tank as a heat exchanger. The
flow of hot water from the tank to the loop protects the outside pipings from freezing
in extremely cold climates. The idea of NCL has several advantages over the
conventional freeze protection methods which have been practiced for years. It is
simple, reliable and cost effective. It can also be used under a large range of ambient
conditions.
A capillary tube controls the thermosyphon flow by adjusting the pressure
drop along the loop in order to minimize the heat losses from the tank. The
experimental setup was tested with five different capillary tube diameters and the
resulted mass flow rates were analyzed. The best configuration of capillary tubing
that maintained the required flow with minimum heat loss had a diameter of 5/16.
A complete set of equations were developed in EES (Engineering Equation
Solver) and solved simultaneously for flow rate and temperature at critical points
along the loop. There was a deviation between model predicted values and measured
experimental data. This deviation was developed near the ICS readings and stayed
constant all the way back to the tank. This indicates that there is an unexpected
influence of ICS to the loop that causes the fluctuations in flow temperature based on
collector water temperature. There is a possibility that we could have a check valve
that does not function properly and therefore causes a secondary convection loop in
the piping between the collector and bypass. Another possibility for having such a
75


large temperature change in the loop and around the ICS could be that the water from
the thermosyphon loop mixed with the water in the collector piping before it reached
to the orifice plate in the bypass. Thus the cold leg temperature would be much lower
than the hot leg temperature. This would increase heat losses from the tank on cold
winter nights which is not desirable.
In order to eliminate the influence of ICS in the study of a natural convection
loop it is necessary to make sure that the loop piping is completely disconnected from
the ICS piping by means of a high quality check valve. All of the tests should be run
over under the new conditions. Once an ideal thermosyphon flow in the loop has been
established, the model predictions could be adjusted according to experimental data
and then the effect of the ICS on the system could be studied. This effect can not be
ignored since the domestic hot water system piping is attached to the natural
convection loop piping and the design of a freeze protection system would not be
complete if the influence of the ICS unit was not taken into account.
At present the ICS units available on the market do not have a freeze
protection system and therefore their use has been limited to mild coastal climates in
the United States, where the ambient temperatures never goes below 0 C. The idea of
freeze protection by a natural convection loop will make the system suitable for all
environmental conditions. It is a very cost-effective system with an easy installation
procedure.
76


Appendix A. Derivation of Formula and Details of Tank UA
A.1 Determination of TankTJA
from Decay Test Data (Method 1)
The governing equation for the tank alone is:
(Me,)= -Ie = -EM(T-rOT,)
At t = 0, T = To. Defining T = T-Tenv we have:
Utc^.-WT
Solving the above differential equation, we get:
yr/ y/ g(UAfMCp)t
Or
T=TenV+AT0e
-tlx
In
AT t
A T0 T
At,
T =

]n(AT0/ATf)
77


UA = t_1Mcp
Knowing the tank capacity to be 40 gallons, with a 10% uncertainty reported
by some manufacturers, we have:
Vtank = 0.9 x 40 = 36 gals. (0.1363 m3)
p = 998 kg / m3
M = 136 kg, cP = 4.177 kJ/ kg C
Knowing M, cp and t we can determine UA for different Decay Tests (refer to
Tables 4.1 and 4.2).
A.2 UA calculations for table 4.1
For Decay Test 1: r = 24.5x3600 2 55 x 105 s
ln(52.52/37.65)
UA = (136 x 4177) / 2.65 x 10 5 = 2.14 (W/C)
Q = UA(AT) = 2.14x52.52 = 112.4 W
78


For Decay Test 2:
T =
63.73*3600
ln(50.96/24.28)
s
UA = (136 x 4177)/3.1 xl05 = 1.84 (W/C)
Q = UA(AT) = 1.84*50.96 = 93.8 W
For Decay test 3:
69.33*3600
T ln(50.75/22.93)
3.1*105 s
UA = (136x4177)/3.1 x 105 = 1.81 (W/C)
0 = C/A(Ar) = 1.81*50.75 = 91.9 W
A3 UA Calculations for Table 4.2
For Decay Test 1: t =
24.5*3600 c
= 2.6 x 105 s
ln(52.75/37.51)
UA = (136 x 4.177) / 2.6 x 105 = 2.20 W/C
Q = UA(AT) = 2.19863*52.75 = 116 W
79


For Decay Test 2:
63.75 x3600
~ln(51.11/24.50)
=3.1 x 10s
s
UA = (136 x 4.177) / 3.1 x 105 = 1.82 (W/C)
Q = UA(AT) = 1.82x51.11 = 93 W
For Decay Test 3: t = 69-3x3600 ^ s
ln(51/23.15)
UA = (136 x 4177) / 3.2 x 105 = 1.80 (W/C)
Q = UA(AT) = 1.8x51 = 91.8 W
80


A.4 Decay Test 1 analysis for Determination of Tank TJA(Method 2)
Data From Decay Test 1
Time(t) Time(t) T-env Tank(T) RTD(T)
min hrs avg avg avg
0 0.00 23.15 73.39 73.62
5 0.08 23.02 73.31 73.51
10 0.17 23.06 73.25 73.40
15 0.25 23.17 73.21 73.29
20 0.33 23.25 73.16 73.20
25 0.42 23.24 73.09 73.09
30 0.50 23.26 73.05 73.00
35 0.58 23.30 73.00 72.90
40 0.67 23.19 72.96 72.82
45 0.75 22.99 72.89 72.72
50 0.83 22.92 72.82 72.64
55 0.92 22.96 72.77 72.54
60 1.00 23.08 72.73 72.45
65 1.08 23.12 72.70 72.38
70 1.17 23.16 72.64 72.29
75 1.25 23.17 72.57 72.20
80 1.33 23.17 72.54 72.14
85 1.42 23.16 72.48 72.05
90 1.50 23.13 72.41 71.97
95 1.58 23.13 72.34 71.88
100 1.67 23.06 72.29 71.81
105 1.75 23.00 72.25 71.74
110 1.83 22.99 72.20 71.66
115 1.92 22.94 72.14 71.58
120 2.00 22.93 72.08 71.50
125 2.08 22.97 72.05 71.43
130 2.17 23.08 71.99 71.37
135 2.25 23.18 71.95 71.30
140 2.33 23.20 71.91 71.22
145 2.42 23.17 71.84 71.15
150 2.50 23.04 71.77 71.07
155 2.58 22.85 71.72 71.01
160 2.67 22.68 71.68 70.95
165 2.75 22.55 71.64 70.88
170 2.83 22.45 71.58 70.81
175 2.92 22.35 71.52 70.74
180 3.00 22.29 71.48 70.66


Tank "UA" With T(RTD)avg-Method 2
Delta T drat. C(dT/dt) C(dT/dt) UA
C RID kJ/hr W W/C
50.47
50.49 sums
50.34 SWi
50.12 ~~ '- 'J-
49.95 mam -685.09 190.30 3.81
49.85 -668.05 185.57 3.72
49.74 ipppp -647.60 179.89 &62
49.60 -636.24 176.73 3.56
49.63 IIPirCS3 -630.56 175.16 3.53
49.73 HH -612.38 170.11 3.42
49.72 -604.43 167.90 3.38
49.58 liliiii -597.61 166.00 3.35
49.37 mi -583.98 162.22 3.29
49.26 -570.34 158.43 3.22
49.13 ;j5fi(S8SSCSi -562.39 156.22 3.18
49.03 -555.57 154.33 3.15
48.97 mmm -551.03 153.06 3.13
48.89 -546.49 151.80 3.10
48.84 -537.40 149.28 3.06
48.75 wmm -533.99 148.33 3.04
48.75 ie6e -537.40 149.28 3.06
48.74 -527.17 146.44 3.00
48.67 mmm, -514.67 142.96 2.94
48.64 M&BSSt- -502.18 139.49 2.87
48.57 HEiSKSi -501.04 139.18 2.87
48.46 -496.49 137.92 2.85
48.29 wasm -493.09 136.97 2.84
48.12 ~&856tt -486.27 135.07 2.81
48.02 aa&aa&a -478.32 132.87 2.77
47.98 m&ssim -476.04 132.23 2.76
48.03 -474.91 131.92 2.75
48.16 ;iO|?0Sl0| -469.23 130.34 2.71
48.27 -468.09 130.03 2.69
48.33 -462.41 128.45 2.66
48.36 - 48.39 m&m -466.96 129.71 2.68
48.37 wmm -472.64 131.29 2.71
82


In the above spreadsheet, dT/dt is calculated by a LINEST fit through nine
adjacent points, the fit is then considered to be the slope of the line. The above
procedure has been selected for the determination of dT/dt to avoid possible noise.
Also AT is the difference between the RTD tank temperature and the ambient inside
air temperature.
83


Appendix B. Uncertainty Analysis
The uncertainty of any calculated quantity is a function of the uncertainties of
all the measured values that are used to calculate that quantity. The common accepted
formula is the addition of all separate uncertainties in quadrature. In general,
q=f(Xi,i = l,...,N)
Sq =

-il/2
(B.l)
where Sq is the uncertainty in final calculated quantity
da
and is the uncertainty of each element of the function.
OX;
B.1 Tank UA Uncertainties
To determine the uncertainty associated with the tank UA calculations, we
need to determine the uncertainties of each of the variables involved. As mentioned
earlier, the tank UA is a function of ATroom, dT/dt and mass of the water in the tank.
According to the above expression, the tank UA uncertainty is determined as
follows:
UA =
-M cp(dT I dt)
AT
(B.2)
84


2
1/2
8 (UA) =
d(UA) s dT
d(dT/dt) ^dt
+
d(UA)
a (at)
-i2
5 (AT)
d(UA)
d(M)
8 (M)
(B.3)
The substitution of partial derivative of equation (B.2) with respect to each of
its variables into the equation (B.3) gives:
8(UA) =
M cp
3600(AT)
-i2
8(dT Idt)
+
+
Cpi.dTldt)§
3600(A T)
-MCpjdTIdt) IT2
3600 (AT)2 J
>
(fi.4)
where M=136 kg, cp=4.177 kJ/kg C.
AT is the difference of the RTD tank temperature and the ambient room air
temperature in C and it is given in the spreadsheets corresponding to Decay Tests 1,2
and 3.
dT/dt is also calculated in the spreadsheets as the slope of RTD versus time.
The uncertainty 6 (dT/dt) is determined through the array formula which gives the
uncertainty equal to 0.01.
The uncertainty 5 (AT) is estimated to be 0.005 C, and 6 (M) as 3% or 4.08 Kg.
After the substitution of the above values and averaging the uncertainty of all
the data points in three Decay Tests 1,2 and 3, we determined the average uncertainty
in calculation of UA to be 0.07 W/C, which is approximately 3.5% uncertainty.
This is primarily due to the uncertainty in the measured mass of water in the tank. It
should also be noted that the random error estimated by the standard deviation of the
mean of all calculated UA in the spreadsheets has a very small effect on total
uncertainty and therefore can be neglected.
85


B.2 Uncertainty in NCL Mass Flow Rate
The mass flow rate in the natural convection loop is found using the following
formula:
-Mcc
m
'dT\ (dT\
dt
JNCL
\ jNo Loop
CpAlIan*
(B.5)
Therefore the uncertainty in the calculation of mass flow rate is determined by:
8m =
2
dmSM +
dM
-i2
im
d(dT I dt)NCL
-8(dT/dt)
NCL
1/2
-i2 r
dm
d(dT/dt)
-8(dTldt)
No Loop
No Loop
-i2
dm

-8 (AT)
tan k
(B.6)
Substituting the partial derivatives of mass flow rate with respect to each variable in
the above equation gives:
(dT/ dt)NCL (dT dt)NoLoop s m
(AT)
tan k
2 r
M
-i2
1/2
(AD
-8(dT I dt)
NCL
tank
8m -
-M
-8(dT /dt)
No Loop
+
(AD***
-MldTldt)KL-(.dT/dt)^]
-i2
(AD'tan*
8 (AT)
tan k
(B-7)
86


where M is the mass of water in the tank, M = 136 Kg
8 (M) = 3% or 4.08 Kg
(AT)tank is the tank out and tank return temperature difference in C
8 (AT) = 0.005 C
8 (dT/dt) is determined by the array formula in LINEST function of Excell
and is equal to 0.01
cP = 4.177 kJ/kgC
dT/dt and UA values are entered from the spreadsheets.
Substituting the above values into the uncertainty expression and averaging
over all the available data points gives us the following uncertainties for different
capillary tube sizes:
0.75 Copper pipe (1.91 cm), 8 (m) = 1.7x10"* kg/s
0.375 Polypropylene (0.95 cm), 8 (m) = 1.5x10"* kg/s
0.3125 Teflon (0.79 cm), 8 (m) = 1.3X10-4 kg/s
0.125 Polypropylene (0.32 cm), 8 (m) = 3xl0'5 kg/s
0.094 Teflon (0.24 cm), 8 (m) = 7x105 kg/s
87


Appendix C. Mass Flow Rate Calculations in NCL
As mentioned earlier in section 4.2, the mass flow rate in the thermosyphon
loop is determined by the following formula:
dT
M cp QTANK +mcpAT (C.l)
at
DT/dt is determined by a seven point fit through the Temperature curve. It
should also be mentioned that the raw data available included the temperature of RTD
throughout the duration of the experiment. This means that it included the data for the
electric element being both on and off. The time that the electric element turns on is
not related to our experiment, since it is only used to bring the tank temperature back
to it's set temperature to establish the flow. Therefore we filtered that data out of our
farther calculations and used only that portion of the curve that shows a decay in the
tank RTD temperature.
The first page of the spreadsheet calculations is attached here for further
reference.
88


Data From 378" Capillary test 3/1/99
Reading Time RTD Tamb.in Ttank,o ut Ttnk,ret
# hour C c C C
1 0.08 48.45 22.45 41.65 33.25
2 0.17 48.3 22.48 41.47 33.21
3 0.25 48.16 22.48 41.48 33.08
4 0.33 48.02 22.49 41.5 32.96
5 0.42 47.88 22.47 41.73 32.98
6 0.50 47.75 22.48 41.55 33.31
7 0.58 47.61 22.48 41.48 33.17
8 0.67 47.48 22.45 41.42 33.19
9 0.75 47.35 22.45 41.29 33.3
10 0.83 47.47 22.43 41.21 33.12
11 0.92 48.87 22.42 41.76 33.08
12 1.00 49.15 22.43 42.17 33.17
13 1.08 48.99 22.41 41.79 33.24
14 1.17 48.83 22.41 41.75 33.27
15 1.25 48.69 22.38 41.89 33.34
16 1.33 48.55 22.38 41.74 33.35
17 1.42 48.41 22.34 41.79 33.37
18 1.50 48.28 22.33 42.09 33.51
19 1.58 48.15 22.3 41.76 33.66
20 1.67 48.02 22.29 41.62 33.6
21 1.75 47.89 22.26 41.52 33.53
22 1.83 47.75 22.25 41.5 33.43
23 1.92 47.62 22.21 41.59 32.91
24 2.00 47.64 22.19 41.21 33.03
25 2.08 48.97 22.16 41.95 33.14
26 2.17 49.23 22.14 42.07 33.25
27 2.25 49.07 22.11 42.02 33.25
28 2.33 48.92 22.08 41.69 33.32
29 2.42 48.78 22.05 41.84 33.24
30 2.50 48.64 22.01 41.87 33.27
31 2.58 48.51 21.99 41.88 33.36
32 2.67 48.38 21.97 40.83 28.85
33 2.75 48.24 21.94 42.02 32.15
34 2.83 48.1 21.92 41.94 33.06
35 2.92 47.96 21.9 41.62 33.41
36 3.00 47.83 21.88 41.46 33.45
89