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Computer simulation of a two phase thermosyphon solar domestic hot water heating system
PERGAMON
Energy Conversion & Management 40 (1999) 775±793
Computer simulation of a two phase thermosyphon solar domestic hot water heating system Khalid A. Joudi *, Aouf A. Al-tabbakh Department of Mechanical Engineering, Baghdad University, Baghdad, Iraq Received 28 August 1997
Abstract The present work deals with a theoretical analysis by computer simulation of a two phase thermosyphon solar domestic hot water system using R-11 as a working ¯uid. The performance was studied by the aid of a simulation procedure for a typical day period divided into equal time intervals of 15 min. Instantaneous values of solar radiation intensity and ambient temperature were applied at the beginning of each time step. The insolation was calculated according to the procedure suggested by ASHRAE. The variation of ambient temperature during the day was approximated by a sine function. The variation of working ¯uid properties with temperature was also taken into account. The computer program and calculation procedure were ®rst validated by comparing the results with established results of single phase systems. Then, calculations were performed for the two phase thermosyphon system to evaluate mass ¯ow rate, saturation pressure and temperature in the collector and condenser, together with tank temperature, and collector and condenser thermal eciencies. These calculated values were obtained for three cases, namely, the no loading case of no water withdrawal from the tank, continuous loading and intermittent loading. The results obtained showed that, in the two phase system, the saturation pressure and temperature increase continuously during the day and follow the tank temperature pattern. This makes the system pressure dependent on the tank loading. The collector eciency did not reveal a serious change with the loading condition. This behavior diers from that which occurs in the single phase system, where the collector eciency increases considerably with loading. Comparison of the two phase system with a single phase system of the same collector area and tank volume showed a signi®cant increase in collector eciency and tank temperature for the case of the two phase system. # 1999 Elsevier Science Ltd. All rights reserved.
* Corresponding author. 0196-8904/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 9 6 - 8 9 0 4 ( 9 8 ) 0 0 1 1 5 - 0
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Nomenclature Symbols Absorber plate area [m2] AC Collector pipe cross sectional area [m2] A CS Collector pipe surface area [m2] AS Collector plate heat capacity [J/K] CC Collector ¯uid heat capacity [J/K] Cf Speci®c heat [J/(kg K)] Cp Collector plate speci®c heat [J/(kg K)] C pp Water speci®c heat [J/(kg K)] C pw D Diameter [m] F Collector liquid eciency factor Collector boiling eciency factor Fb H Single phase heat transfer coecient [W/(m2K)] Latent heat of vaporization [J/kg] h fg Total solar radiation [W/m2] IT L Collector length [m] Boiling length [m] Lb m System mass ¯ow rate [kg/s] Collector single-pipe mass ¯ow rate [kg/s] mp Loading mass ¯ow rate [kg/s] ml M Collector pipe ¯uid mass [kg] Collector plate mass [kg] MP (MC)T Tank thermal capacity [J/K] n No. of collector pipes P Pressure [Pa] t Time [s] T Temperature [K] U Overall heat transfer coe. [W/(m2K)] Collector overall heat loss coe. [W/(m2K)] UL Boiling overall heat loss coe. [W/(m2K)] Ub Water tank loss factor-surface area product [W/K] (UA)T V Fluid velocity [m/s] W Collector pipe spacing [m] x Fluid quality x Distance along collector [m] Z Distance along pipes (except collector) [m] Collector thermal eciency Z col Condenser thermal eciency Z cond r Density [kg/m3] ta Transmittance±Absorptance product Subscripts 1 Collector inlet 2 Collector outlet
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3 4 a b c d f i l L p sat T u v w
777
Condenser inlet Condenser outlet Ambient Boiling Condensation Downcomer Collector ¯uid (refrigerant) Collector node, or (inside) Load Liquid Collector plate Saturation condition in collector Water tank Upriser Vapor Water property
1. Introduction Solar hot water systems are, by far, the most successful applications of solar energy utilization. They are characterized by ease of manufacturing and installation, suitability for the temperature range and economic feasibility. Most systems are of single phase, whereas two phase solar systems are relatively few for domestic hot water heating applications. The two phase thermosyphon system exceeds the single phase system in some aspects. Among these are the increase in collector thermal eciency, the fastness in response and the inherent protection against fouling and freezing problems. Solar hot water systems that use a boiling working ¯uid have entered the research area relatively late. The ®rst experimental study appeared in 1979 by Soin et al. [1]. They studied a boiling thermosyphon collector containing an acetone and petroleum ether mixture. They developed a modi®ed form of the Hottel± Whillier±Woerts±Bliss (HWWB) equation which accounts for the fraction of the liquid level in a particular collector. Downing and Walden [2] studied experimentally the heat transfer process in boiling solar domestic hot water systems using R-11 and R-114. They concluded that phase change heat transfer ¯uids operate with better eciency and faster response than circulating liquids in solar applications. Schreyer [3] experimentally investigated the use of refrigerant R-11 charged in a thermosyphon solar collector for residential applications. He found that, for two identical collectors, the peak instantaneous eciency of a boiling refrigerant charged collector was 6% greater than that of a hydronic ¯uid circulating solar collector. The ®rst detailed analytical study of a ¯at plate boiling collector was done by Al-tamimi and Clark [4]. They studied the thermal performance of the collector by developing a new generalized heat removal factor FR that may be applied to any ¯at plate collector, whether it is cooled by a single phase or a boiling ¯uid. they concluded from their analysis that the boiling collectors have a thermal eciency that is inherently greater than a nonboiling collector having
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the same dimensions and operating under the same conditions. Similar approaches were pursued by El-assy and Clark [5, 6] in generalizing the HWWB method. Price et al. [7] performed a similar study but took into account the variation of working ¯uid properties with temperature. The eect of installing a heat exchanger in this study was simulated by a modi®ed heat removal factor. Abramzon et al. [8] adopted a dierent approach to analyze the ¯at plate boiling collector. They proposed representing the heat transfer process between the surroundings and the working ¯uid inside tubes by a set of simultaneous equations for each lateral section of the collector and then solving them numerically. They concluded that, during the transition from a single phase to a boiling condition, the eciency increases sharply and reaches a certain limit that does not depend on the working ¯uid nor on the mass ¯ow rate. The emphasis in the above studies was mainly on the solar collector. Other components were not, in general incorporated in the analysis. Simulation procedures for the complete cycle of a two phase system, similar to those of the single phase systems, were not found in the literature. In addition, no report was found on the eect of system loading on the performance of the two phase thermosyphon solar cycle. The present work attempts to study the cycle through a systematic computer simulation procedure for an operating day extending from sunrise till sunset. The system under consideration consisted of a ¯at plate solar collector with selective coating, a coil-type condenser that takes the form of a long coiled pipe immersed directly in the water tank, and the connecting pipes; the upriser and the downcomer. R-11 is used as a working ¯uid in the cycle. This refrigerant is charged initially to occupy 0.6 of the system total volume. Fig. 1 depicts the two phase thermosyphon system under consideration with its components.
Fig. 1. The two phase thermosyphon system.
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2. System component modeling The simulation procedure involves casting mathematical models for each system component and then combining these models consecutively to accomplish the complete simulation. Thermal models compute each component exit temperature and ¯uid quality, whereas hydrodynamic models determine the pressure drop of each component. The solar collector faces south with a tilt angle of 508 at 338 N latitude. The area of the collector is 3.47 m2 and it has 15 risers of 0.012 m diameter each. All other pipes in the system have a diameter of 0.025 m. The lengths of the upriser, the condenser and the downcomer are 1.63, 7 and 3.56 m, respectively. The tank volume is 250 liters. The variation of the working ¯uid properties with temperature is taken into account in this work by using polynomial correlations of the property tables presented by ASHRAE [9]. The solar radiation intensity is calculated according to the procedure suggested by Lunde [10]. The boiling heat transfer coecient is calculated according to the method given by Mathur et al. [11], while the condensation coecient is evaluated using the equation proposed by Chato [12]. 2.1. Thermal analysis 2.1.1. The solar collector The boiling ¯at plate collector is modeled using a system of two simultaneous partial dierential equations. The ®rst describes the thermal behavior of the working ¯uid inside the pipes and the second deals with the absorber plate. These equations describe the thermal processes in the subcooled lower region of the collector. Consider an elemental portion of the collector pipe ¯uid, of length dx as shown in Fig. 2. An energy balance can be applied to evaluate the heat transfer across this element during an elemental period dt:
Fig. 2. Collector plate and pipe element.
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Heat Transfer by Convection
Change of Energy Across Element
0
Change of
1
B C @ Internal Energy A
of Element ÿ H Tp ÿ Tf pD dx dt mp Cp dT dt Cp rAcs L dx dT
divide by dx dt and multiply by L: dT dT Cp rAcs L HpDL Tp ÿ Tf mp Cp L dx dt pDL Collector Pipe Surface Area As rAcs L Collector Pipe Fluid Mass M mp Cp L rAcs VCp L rAcs LCp V MCp V Cf V: So, the equation becomes: Cf
@Tf @Tf Cf V HAs Tp ÿ Tf @t @x
1
Consider now the absorber plate heat transfer process during an elemental time period dt.
Heat Lost to Convection ÿ ÿ the Surroundings Heat to the Fluid Solar Radiation Change of the Plate Mp Cpp dTp FAc taIT dt ÿ HAs Tp ÿ Tf dt ÿ FUL Ac Tp ÿ Ta dt Internal Energy
Incident
Mp Cpp Cc divide by dt and rearrange: @Tp Cc HAs Tf ÿ Tp ÿ FUL Ac Tp ÿ Ta FAc taIT : @t
2
During the operation, most of the collector length is in a boiling state in which the ¯uid temperature is known at the saturation value and does not need a dierential equation to describe it. The equations for the subcooled region of the collector allow the accurate determination of the point at which boiling commences and gives an accurate value of the temperature dierence between the absorber plate and the working ¯uid. This is important in assigning a heat transfer coecient accurately for the various regions of the collector. The analytical solution of these equations is rather dicult. Therefore, they are solved numerically in this work. The partial distance derivative term of the working ¯uid (@Tf /@x) is converted to an ordinary dierence between two adjacent nodes separated by a distance Dx as follows: @Tf Tfi ÿ Tfiÿ1 @X Dx
1EiE20:
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In doing so, the plate and ¯uid temperatures will be functions of time only. Each node will be represented by two ordinary dierential equations for the plate and ¯uid. Thus, the system of two partial dierential equations is converted to a system of several ordinary dierential equations with respect to time. The system can be represented as follows: dTfi a Tpi ÿ Tfi ÿ b Tfi ÿ Tfiÿ1 dt dTpt 3 c Tfi ÿ Tpi ÿ d Tpi ÿ Ta eIT dt where a
HAs V mp HAs FUL Ac FAc ta ; b ; d ; e : ; c Dx rL Acs Dx Cc Cf Cc Cc
The system of resultant equations was tackled by a fourth order Runge±Kutta technique. The details of the method are given by Al-tabbakh [13]. After several attempts, a time interval of 20 s was found sucient to achieve convergence of the solution. The above procedure is valid as long as the ¯uid in the collector is in the subcooled liquid state. When the ¯uid temperature reaches the local saturation temperature, boiling commences and the aforementioned model is no longer valid because the ¯uid temperature will remain practically constant. An energy balance is made to determine the portion of collector necessary to complete boiling. The following equation, which is suggested by Price et al. [7], is used: Lb
mp hfg : Fb W taIT ÿ Ub Tsat ÿ Ta
4
If this length is longer than the remaining length of the collector, the ¯uid will leave the collector as a wet mixture with a quality determined by the following equation: Fb WLb taIT ÿ Ub Tsat ÿ Ta x2 : 5 mp hfg The subscript of x is given as 2 to conform with the temperature designation at the collector exit. Of course, there isn't a quality value x1 at the collector inlet. At times, the collector would be partially occupied by a superheated vapor upstream of the boiling region. In this case, the ¯uid is in a single phase state, and the same approach used for the single phase liquid region can be applied to determine the collector exit temperature but, of course, with diering properties and operating values. The collector pipe may be occupied by an initial liquid phase, then a two phase mixture and then by a vapor along the ¯ow direction. However, the situation depends largely on the operating conditions, particularly the collector inlet temperature and the irradiance. The irradiance that the collector receives and the ambient temperature were introduced
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progressively at their instantaneous values at equal time intervals of 15 min. A complete set of calculations was performed to predict the system behavior at each of these time steps from sunrise till sunset. 2.1.2. Upriser The upriser exit temperature can be determined by adopting the following procedure. Consider a ¯uid element at temperature T ¯owing in a circular pipe and rejecting heat to the surroundings which is at temperature Ta, thereby its temperature reduces continuously. The ¯uid cools from T2 to T3. On the elemental length dx, the following energy balance can be written (Fig. 3): Lost Heat to Change of Energy the Surroundings Across the Upriser pDu Uu T ÿ Ta dx ÿ mCp dT: Integrating the above equation between T2 and T3: Z Lu Z T3 pDu Uu dT ÿ dx T ÿ Ta mC p 0 T2 pDu Uu Lu T3 Ta T2 ÿ Ta exp ÿ : mCp
6
2.1.3. Condenser The condenser is treated here as if it were one long straight pipe. The working ¯uid inside the condenser occupies three dierent consecutive regions which are the vapor, the two phase and the liquid regions. The lengths of these regions change continuously depending on the operation conditions. The length of each region is determined by making energy balances as follows: The length at the beginning of the condenser necessary to bring the vapor to the saturation temperature is found in a similar manner to the upriser (single phase vapor cooling):
Fig. 3. Fluid element in a connecting pipe.
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Convection Heat to the Tank
Change of Energy
783
Across Region
pDc Uc T ÿ TT dx ÿ mCp dT: Integrate the above equation across the vapor region Zc between T3 and T sat at the condenser exit. Z Tsat Z Zc pDc Uc dT ÿ dx mCp 0 T3 T ÿ TT mCp T3 ÿ TT Zc ln : 7 pDc Uc Tsat ÿ TT To determine the length necessary to complete condensation, an energy balance is made between the released amount of heat by condensation and the heat transferred to the water tank through the condenser pipe wall: mhfg Zc pDc Uc Tsat ÿ TT : Thus, Zc
mhfg : pDc Uc Tsat ÿ TT
8
Finally, the condenser exit temperature is determined in a similar way to the upriser using the following equation (single phase liquid cooling): pDc Uc Zc : 9 T4 TT Tsat ÿ TT exp ÿ mCp 2.1.4. Downcomer The refrigerant in the downcomer is always in a liquid state. Once again, the same type of equations used in the upriser and condenser can be used to determine the downcomer exit temperature: pDd Ud Ld T1 Ta T4 ÿ Ta exp ÿ : 10 mCp This temperature represents a new collector inlet temperature. 2.1.5. Water storage tank The tank temperature at the end of each time step of 15 min is determined by making an energy balance between the energy released from the condenser and the energy lost to the load and surroundings. The resulting heat balance equation is as follows: T 00T T 0T
Qv Qc QL ÿ QLoss ÿ QLoad Dt MCT
11
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where Qv mCp T3 ÿ Tsat Qc x3 mhfg QL mCp Tsat ÿ T4 QLoss UAT T 0T ÿ Ta
QLoad ml Cpw T 0T ÿ Tw :
2.2. Hydrodynamic analysis The hydrodynamic analysis calculates the pressure drop across each component. The formulation depends on the phase of the working ¯uid. For single phase ¯ow, the usual approach of the Darci±Weisbach friction coecient is used to determine the pressure drop in the single phase ¯ow in accordance to what is proposed by Morrison and Ranatunga [14]. In two phase ¯ow, there are two models to evaluate the pressure drop. The ®rst is the separated ¯ow model which treats the liquid and vapour as completely separated phases. Each has its properties and occupies a certain fraction of the ¯ow cross sectional area. The second model is the homogeneous model. This model is also known as the friction factor or fog ¯ow model. It considers the two phases to ¯ow as a single phase possessing mean ¯uid properties. The homogeneous model is used in the present study to evaluate the pressure drop in the two phase regions of the system, as proposed by Collier [15]. This model is appropriate for two phase collectors because the boiling process produces the mixing condition that justi®es its use. Also, the accuracy of the homogeneous model is comparable to that of the separated model, and it is easier for computer calculations than the separated model, with reduced program execution time.
2.3. The simulation procedure The main problem in the thermosyphon system simulation is that the mass ¯ow rate induced in the loop is not known a priori. This problem cannot be solved unless an iterative procedure is used. In the iterative calculations, the conservation laws must be satis®ed. The iteration procedure is brie¯y outlined in the following points: 1. Initial guess values of the collector inlet temperature and pressure are assumed, together with the mass ¯ow rate. The initial value of temperature and pressure are taken equal to the saturation values at the initial ambient temperature. The mass ¯ow rate is given an initial value equal to what insolation would evaporate in 15 min with no losses. 2. A thermal analysis is performed to evaluate the exit temperature or exit quality of each component consecutively. The exit temperature of the last component, which is the downcomer, represents a new collector inlet temperature.
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3. In parallel to step 2, a hydrodynamic analysis is performed to evaluate the exit pressure of each component consecutively. The exit pressure of the last component, which is the downcomer, represents a new collector inlet pressure. 4. The new and old values of the collector inlet pressure are compared. If they agree within the imposed tolerance, the simulation skips to the next step. If agreement is not achieved, the entire simulation process for the considered time step is repeated, starting with a modi®ed value of the mass ¯ow rate that is given by the following relation according to Ali and McDonald [16]: P1new : 12 mnew mold P1old 5. Now, the new and old values of collector inlet temperature are compared. If they agree within the imposed tolerance, the simulation skips to another step. If not, the simulation process is repeated, starting with the new obtained temperature.. 6. Finally, the new and old values of the system charge are compared. If agreement is achieved, the simulation stops, and the program prints the results for the considered time step. If not, the process is again repeated, but now, the collector inlet pressure is modi®ed according to the following equation [16]: Old Charge : 13 P1 P1 New Charge The system charge is the quantity of refrigerant volume in the system relative to the total volume. The value of the charge is taken constant in the present treatment, and its value equals 0.6. This means that 0.6 of the system volume is occupied by liquid refrigerant before starting. The above six steps are repeated for each time step of 15 min starting at 8 a.m. to 4 p.m., with outputs of the previous step being the input of the next step.
3. Results and discussion An important property of the two phase thermosyphon system, which assists in understanding the various aspects of its performance, is that it is a sealed system. This makes the pressure in this system change in two coordinates: the time coordinate during the operation period and the position coordinate around the loop. Generally, the collector side represents the high pressure region, while the condenser side is the lower pressure region. The dierence between the collector and condenser pressure establishes a driving potential that maintains the thermosyphonic action as long as the solar irradiance is above a threshold level. The prevailing pressure in the two phase system dominates the thermal processes through the resulting saturation temperatures in the collector and condenser. A high saturation temperature in the collector increases the mean plate temperature and, consequently, the thermal losses to the environment, whereas a low condenser saturation temperature decreases the useful heat
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Fig. 4. Variation of solar irradiance during the simulated period.
released to the water store. The variation of the saturation temperature in the collector and condenser depends largely on the solar radiation intensity and the tank temperature, and there is a strong mutual relation between them, as will be shown from the results. A typical clear day irradiance pattern is shown in Fig. 4, which represents the input to the system. The saturation temperature in the collector and condenser are observed to increase continuously during the simulation period, as shown in Fig. 5. This behavior may be explained by tracking the thermal processes established in the system after exposure to solar radiation. When solar radiation strikes the collector, it raises the temperature and triggers the onset of
Fig. 5. Variation of tank and saturation temperatures during the simulated period.
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Fig. 6. Variation of tank and saturation temperatures during the simulated period.
evaporation. At the same time, condensation commences, as long as the tank temperature is lower than the condensation temperature. So, there is a heat source represented by the collector and a heat sink represented by the condenser and storage tank. This con®guration keeps the collector pressure always greater than the condenser pressure. In fact, the condensation pressure, and the corresponding saturation temperature, is a stimulant that induces the collector to produce a lower or a higher vapor quantity depending on the condenser pressure. The condenser pressure and temperature are, in turn, aected by the tank
Fig. 7. Variation of mass ¯ow rate during the simulated period.
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Fig. 8. Variation of collector and condenser eciency during the simulated period.
temperature. Of course, the condenser temperature cannot be lower than the tank temperature, since this stops condensation. Because of this direct inter-relationship between collector and condenser operation, their saturation temperature and pressure will vary in parallel following the tank temperature pattern, as shown in Fig. 5 for temperature. The dependency on tank temperature renders the system operation largely aected by the loading condition from the tank, as shown in Fig. 6. The mass ¯ow rate through the system was found to follow the irradiance pattern and changes accordingly, as shown in Fig. 7. This is because the mass ¯ow rate is related directly
Fig. 9. Variation of collector and condenser eciency during the simulated period.
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Fig. 10. Comparison between the single and two phase tank temperatures during the simulated period.
to the rates of evaporation and condensation. These rates change in parallel, increasing in the morning and decreasing after solar noon, giving the mass ¯ow rate the trend in Fig. 7. Loading increases the mass ¯ow rate through the system because it increases the condensation rate by introducing a colder ¯uid to the tank, as shown in Fig. 7. The collector thermal eciency can be de®ned as the useful heat collected by the working ¯uid divided by the amount of insolation over the collector.
Fig. 11. Comparison between the single and two phase tank temperatures during the simulated period.
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Fig. 12. Comparison of collector eciency between single and two phase systems.
Zcol
mhfg x2 mCp Tsat ÿ T1 : nWLIT
14
Likewise, the condenser eciency can be de®ned as the heat released from the condenser divided by the insolation value: Zcond
pDc Zc Uc Tsat ÿ TT mCp Tsat ÿ TT : nWLIT
Fig. 13. Comparison of collector eciency between single and two phase systems.
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Fig. 14. Collector eciency curve.
These parameters vary in the manner shown in Figs. 8 and 9 for the cases of no loading and loading, respectively. Comparisons with a single phase system of the same collector area and tank volume shows a clear increase in the collector eciency and tank temperature for the two phase system, as shown in Figs. 10±13. This is an expected result because the latent heat transfer is greater than the sensible heat transfer for the same system geometry and operating conditions. The only experimental results that have been found in the literature for two phase systems that can be compared with the present analysis are the collector eciency curves. These curves
Fig. 15. Collector eciency curve.
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Fig. 16. Collector eciency curve.
were obtained using a ®xed mass ¯ow rate in the collector. They are commonly straight lines that best ®t the scattered experimental readings. Fig. 14 shows a comparison between the present theoretical results and the experimental data of Downing and Waldin [2]. It can be seen that reasonable agreement is obtained between them. In order to make the comparison, the mass ¯ow rate must be ®xed in the simulation. This was done by entering the mass ¯ow rate value of the experimental work in the beginning of the simulation program and eliminating the pressure iteration in the simulation procedure, because this iteration is responsible for modifying the mass ¯ow rate value. In the same manner, other comparisons have been made with Al-tamimi and Clark [4] in Fig. 15,Fig. 15 and Abramzon et al. [8] in Fig. 16. The percentage dierence in these comparisons was within 10%.
4. Conclusions 1. The saturation temperature and pressure in the collector and condenser increase continuously during the day with increasing tank temperature at the no loading condition. Water withdrawal causes a marked eect on the collector and condenser saturation temperatures. 2. The variation in ¯ow rate during the day follows the insolation pattern with a noticeable increase with increased loading. 3. The collector eciency was not seriously aected with loading, whereas the condenser eciency changed clearly with the loading condition. 4. The tank temperature of the two phase system showed a clear improvement over that of a single phase system of the same collector area and tank volume. The improvement was approximately 10%.
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5. The collector eciency of the two phase system is approximately 20% higher than a single phase collector. Also, the response of the two phase system is faster than a single phase system in reaching the maximum tank temperature and maximum eciency. References [1] Soin RS, Sangemeswar K, Rao DP, Rao KS. Performance of ¯at plate solar collector with ¯uid undergoing phase change. Solar Energy 1979;23:69. [2] Downing RC, Waldin VW. Phase change heat transfer in solar hot water heating using R-11 and R-114. ASHRAE Trans. 1980;86:848±56. [3] Schreyer JM. Residential application of refrigerant charged solar collectors. Solar Energy 1981;26:307±12. [4] Al-tamimi AI, Clark JA. Thermal performance of a solar collector containing a boiling ¯uid (R-11). ASHRAE Trans. 1984;90:681±96. [5] El-Assy AY, Clark JA. Thermal analysis of a ¯at plate boiling collector having sub-cooled inlet and saturation exit states. Solar Energy 1989;42:121±32. [6] El-Assy AY, Clark JA. Thermal analysis of ¯at plate collectors in multiphase ¯ows, including superheat. Solar Energy 1988;40:345±61. [7] Price HW, Klein SA, Beckman WA. Analysis of boiling ¯at plate collectors. ASME J. of Solar Energy Engineering 1986;108:150±7. [8] Abramzon B, Yaron I, Borde I. An analysis of a ¯at plate solar collector with internal boiling. ASME J. of Solar Energy Engineering 1983;105:454±60. [9] ASHRAE Handbook. 1985. Fundamentals. . [10] Lunde PJ. Solar thermal engineering. New York: Wiley, 1980. [11] Mathur GD, McDonald TW. Simulation program for a two phase thermosyphon loop heat exchanger. ASHRAE Trans. 1986;92:473±85. [12] Chato JC. Laminar condensation inside horizontal and inclined tubes. ASHRAE J. 1962;4:52±60. [13] Al-tabbakh AA. 1997. Preliminary simulation of a two phase thermosyphon solar domestic hot water heating system. M.Sc. thesis in Mechanical Engineering. Saddam University, Baghdad. . [14] Morrison GL, Ranatunga DBJ. Thermosyphon circulation in solar collectors. Solar Energy 1980;24:191±8. [15] Collier JG. Convective boiling and condensation. London: McGraw±Hill, 1972. [16] Ali AFM, McDonald TW. Thermosyphon loop performance characteristics: part 2. Simulation Program. ASHRAE Trans. 1977;83:260±78.
Energy Conversion & Management 40 (1999) 775±793
Computer simulation of a two phase thermosyphon solar domestic hot water heating system Khalid A. Joudi *, Aouf A. Al-tabbakh Department of Mechanical Engineering, Baghdad University, Baghdad, Iraq Received 28 August 1997
Abstract The present work deals with a theoretical analysis by computer simulation of a two phase thermosyphon solar domestic hot water system using R-11 as a working ¯uid. The performance was studied by the aid of a simulation procedure for a typical day period divided into equal time intervals of 15 min. Instantaneous values of solar radiation intensity and ambient temperature were applied at the beginning of each time step. The insolation was calculated according to the procedure suggested by ASHRAE. The variation of ambient temperature during the day was approximated by a sine function. The variation of working ¯uid properties with temperature was also taken into account. The computer program and calculation procedure were ®rst validated by comparing the results with established results of single phase systems. Then, calculations were performed for the two phase thermosyphon system to evaluate mass ¯ow rate, saturation pressure and temperature in the collector and condenser, together with tank temperature, and collector and condenser thermal eciencies. These calculated values were obtained for three cases, namely, the no loading case of no water withdrawal from the tank, continuous loading and intermittent loading. The results obtained showed that, in the two phase system, the saturation pressure and temperature increase continuously during the day and follow the tank temperature pattern. This makes the system pressure dependent on the tank loading. The collector eciency did not reveal a serious change with the loading condition. This behavior diers from that which occurs in the single phase system, where the collector eciency increases considerably with loading. Comparison of the two phase system with a single phase system of the same collector area and tank volume showed a signi®cant increase in collector eciency and tank temperature for the case of the two phase system. # 1999 Elsevier Science Ltd. All rights reserved.
* Corresponding author. 0196-8904/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 9 6 - 8 9 0 4 ( 9 8 ) 0 0 1 1 5 - 0
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Nomenclature Symbols Absorber plate area [m2] AC Collector pipe cross sectional area [m2] A CS Collector pipe surface area [m2] AS Collector plate heat capacity [J/K] CC Collector ¯uid heat capacity [J/K] Cf Speci®c heat [J/(kg K)] Cp Collector plate speci®c heat [J/(kg K)] C pp Water speci®c heat [J/(kg K)] C pw D Diameter [m] F Collector liquid eciency factor Collector boiling eciency factor Fb H Single phase heat transfer coecient [W/(m2K)] Latent heat of vaporization [J/kg] h fg Total solar radiation [W/m2] IT L Collector length [m] Boiling length [m] Lb m System mass ¯ow rate [kg/s] Collector single-pipe mass ¯ow rate [kg/s] mp Loading mass ¯ow rate [kg/s] ml M Collector pipe ¯uid mass [kg] Collector plate mass [kg] MP (MC)T Tank thermal capacity [J/K] n No. of collector pipes P Pressure [Pa] t Time [s] T Temperature [K] U Overall heat transfer coe. [W/(m2K)] Collector overall heat loss coe. [W/(m2K)] UL Boiling overall heat loss coe. [W/(m2K)] Ub Water tank loss factor-surface area product [W/K] (UA)T V Fluid velocity [m/s] W Collector pipe spacing [m] x Fluid quality x Distance along collector [m] Z Distance along pipes (except collector) [m] Collector thermal eciency Z col Condenser thermal eciency Z cond r Density [kg/m3] ta Transmittance±Absorptance product Subscripts 1 Collector inlet 2 Collector outlet
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3 4 a b c d f i l L p sat T u v w
777
Condenser inlet Condenser outlet Ambient Boiling Condensation Downcomer Collector ¯uid (refrigerant) Collector node, or (inside) Load Liquid Collector plate Saturation condition in collector Water tank Upriser Vapor Water property
1. Introduction Solar hot water systems are, by far, the most successful applications of solar energy utilization. They are characterized by ease of manufacturing and installation, suitability for the temperature range and economic feasibility. Most systems are of single phase, whereas two phase solar systems are relatively few for domestic hot water heating applications. The two phase thermosyphon system exceeds the single phase system in some aspects. Among these are the increase in collector thermal eciency, the fastness in response and the inherent protection against fouling and freezing problems. Solar hot water systems that use a boiling working ¯uid have entered the research area relatively late. The ®rst experimental study appeared in 1979 by Soin et al. [1]. They studied a boiling thermosyphon collector containing an acetone and petroleum ether mixture. They developed a modi®ed form of the Hottel± Whillier±Woerts±Bliss (HWWB) equation which accounts for the fraction of the liquid level in a particular collector. Downing and Walden [2] studied experimentally the heat transfer process in boiling solar domestic hot water systems using R-11 and R-114. They concluded that phase change heat transfer ¯uids operate with better eciency and faster response than circulating liquids in solar applications. Schreyer [3] experimentally investigated the use of refrigerant R-11 charged in a thermosyphon solar collector for residential applications. He found that, for two identical collectors, the peak instantaneous eciency of a boiling refrigerant charged collector was 6% greater than that of a hydronic ¯uid circulating solar collector. The ®rst detailed analytical study of a ¯at plate boiling collector was done by Al-tamimi and Clark [4]. They studied the thermal performance of the collector by developing a new generalized heat removal factor FR that may be applied to any ¯at plate collector, whether it is cooled by a single phase or a boiling ¯uid. they concluded from their analysis that the boiling collectors have a thermal eciency that is inherently greater than a nonboiling collector having
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the same dimensions and operating under the same conditions. Similar approaches were pursued by El-assy and Clark [5, 6] in generalizing the HWWB method. Price et al. [7] performed a similar study but took into account the variation of working ¯uid properties with temperature. The eect of installing a heat exchanger in this study was simulated by a modi®ed heat removal factor. Abramzon et al. [8] adopted a dierent approach to analyze the ¯at plate boiling collector. They proposed representing the heat transfer process between the surroundings and the working ¯uid inside tubes by a set of simultaneous equations for each lateral section of the collector and then solving them numerically. They concluded that, during the transition from a single phase to a boiling condition, the eciency increases sharply and reaches a certain limit that does not depend on the working ¯uid nor on the mass ¯ow rate. The emphasis in the above studies was mainly on the solar collector. Other components were not, in general incorporated in the analysis. Simulation procedures for the complete cycle of a two phase system, similar to those of the single phase systems, were not found in the literature. In addition, no report was found on the eect of system loading on the performance of the two phase thermosyphon solar cycle. The present work attempts to study the cycle through a systematic computer simulation procedure for an operating day extending from sunrise till sunset. The system under consideration consisted of a ¯at plate solar collector with selective coating, a coil-type condenser that takes the form of a long coiled pipe immersed directly in the water tank, and the connecting pipes; the upriser and the downcomer. R-11 is used as a working ¯uid in the cycle. This refrigerant is charged initially to occupy 0.6 of the system total volume. Fig. 1 depicts the two phase thermosyphon system under consideration with its components.
Fig. 1. The two phase thermosyphon system.
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2. System component modeling The simulation procedure involves casting mathematical models for each system component and then combining these models consecutively to accomplish the complete simulation. Thermal models compute each component exit temperature and ¯uid quality, whereas hydrodynamic models determine the pressure drop of each component. The solar collector faces south with a tilt angle of 508 at 338 N latitude. The area of the collector is 3.47 m2 and it has 15 risers of 0.012 m diameter each. All other pipes in the system have a diameter of 0.025 m. The lengths of the upriser, the condenser and the downcomer are 1.63, 7 and 3.56 m, respectively. The tank volume is 250 liters. The variation of the working ¯uid properties with temperature is taken into account in this work by using polynomial correlations of the property tables presented by ASHRAE [9]. The solar radiation intensity is calculated according to the procedure suggested by Lunde [10]. The boiling heat transfer coecient is calculated according to the method given by Mathur et al. [11], while the condensation coecient is evaluated using the equation proposed by Chato [12]. 2.1. Thermal analysis 2.1.1. The solar collector The boiling ¯at plate collector is modeled using a system of two simultaneous partial dierential equations. The ®rst describes the thermal behavior of the working ¯uid inside the pipes and the second deals with the absorber plate. These equations describe the thermal processes in the subcooled lower region of the collector. Consider an elemental portion of the collector pipe ¯uid, of length dx as shown in Fig. 2. An energy balance can be applied to evaluate the heat transfer across this element during an elemental period dt:
Fig. 2. Collector plate and pipe element.
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Heat Transfer by Convection
Change of Energy Across Element
0
Change of
1
B C @ Internal Energy A
of Element ÿ H Tp ÿ Tf pD dx dt mp Cp dT dt Cp rAcs L dx dT
divide by dx dt and multiply by L: dT dT Cp rAcs L HpDL Tp ÿ Tf mp Cp L dx dt pDL Collector Pipe Surface Area As rAcs L Collector Pipe Fluid Mass M mp Cp L rAcs VCp L rAcs LCp V MCp V Cf V: So, the equation becomes: Cf
@Tf @Tf Cf V HAs Tp ÿ Tf @t @x
1
Consider now the absorber plate heat transfer process during an elemental time period dt.
Heat Lost to Convection ÿ ÿ the Surroundings Heat to the Fluid Solar Radiation Change of the Plate Mp Cpp dTp FAc taIT dt ÿ HAs Tp ÿ Tf dt ÿ FUL Ac Tp ÿ Ta dt Internal Energy
Incident
Mp Cpp Cc divide by dt and rearrange: @Tp Cc HAs Tf ÿ Tp ÿ FUL Ac Tp ÿ Ta FAc taIT : @t
2
During the operation, most of the collector length is in a boiling state in which the ¯uid temperature is known at the saturation value and does not need a dierential equation to describe it. The equations for the subcooled region of the collector allow the accurate determination of the point at which boiling commences and gives an accurate value of the temperature dierence between the absorber plate and the working ¯uid. This is important in assigning a heat transfer coecient accurately for the various regions of the collector. The analytical solution of these equations is rather dicult. Therefore, they are solved numerically in this work. The partial distance derivative term of the working ¯uid (@Tf /@x) is converted to an ordinary dierence between two adjacent nodes separated by a distance Dx as follows: @Tf Tfi ÿ Tfiÿ1 @X Dx
1EiE20:
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In doing so, the plate and ¯uid temperatures will be functions of time only. Each node will be represented by two ordinary dierential equations for the plate and ¯uid. Thus, the system of two partial dierential equations is converted to a system of several ordinary dierential equations with respect to time. The system can be represented as follows: dTfi a Tpi ÿ Tfi ÿ b Tfi ÿ Tfiÿ1 dt dTpt 3 c Tfi ÿ Tpi ÿ d Tpi ÿ Ta eIT dt where a
HAs V mp HAs FUL Ac FAc ta ; b ; d ; e : ; c Dx rL Acs Dx Cc Cf Cc Cc
The system of resultant equations was tackled by a fourth order Runge±Kutta technique. The details of the method are given by Al-tabbakh [13]. After several attempts, a time interval of 20 s was found sucient to achieve convergence of the solution. The above procedure is valid as long as the ¯uid in the collector is in the subcooled liquid state. When the ¯uid temperature reaches the local saturation temperature, boiling commences and the aforementioned model is no longer valid because the ¯uid temperature will remain practically constant. An energy balance is made to determine the portion of collector necessary to complete boiling. The following equation, which is suggested by Price et al. [7], is used: Lb
mp hfg : Fb W taIT ÿ Ub Tsat ÿ Ta
4
If this length is longer than the remaining length of the collector, the ¯uid will leave the collector as a wet mixture with a quality determined by the following equation: Fb WLb taIT ÿ Ub Tsat ÿ Ta x2 : 5 mp hfg The subscript of x is given as 2 to conform with the temperature designation at the collector exit. Of course, there isn't a quality value x1 at the collector inlet. At times, the collector would be partially occupied by a superheated vapor upstream of the boiling region. In this case, the ¯uid is in a single phase state, and the same approach used for the single phase liquid region can be applied to determine the collector exit temperature but, of course, with diering properties and operating values. The collector pipe may be occupied by an initial liquid phase, then a two phase mixture and then by a vapor along the ¯ow direction. However, the situation depends largely on the operating conditions, particularly the collector inlet temperature and the irradiance. The irradiance that the collector receives and the ambient temperature were introduced
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progressively at their instantaneous values at equal time intervals of 15 min. A complete set of calculations was performed to predict the system behavior at each of these time steps from sunrise till sunset. 2.1.2. Upriser The upriser exit temperature can be determined by adopting the following procedure. Consider a ¯uid element at temperature T ¯owing in a circular pipe and rejecting heat to the surroundings which is at temperature Ta, thereby its temperature reduces continuously. The ¯uid cools from T2 to T3. On the elemental length dx, the following energy balance can be written (Fig. 3): Lost Heat to Change of Energy the Surroundings Across the Upriser pDu Uu T ÿ Ta dx ÿ mCp dT: Integrating the above equation between T2 and T3: Z Lu Z T3 pDu Uu dT ÿ dx T ÿ Ta mC p 0 T2 pDu Uu Lu T3 Ta T2 ÿ Ta exp ÿ : mCp
6
2.1.3. Condenser The condenser is treated here as if it were one long straight pipe. The working ¯uid inside the condenser occupies three dierent consecutive regions which are the vapor, the two phase and the liquid regions. The lengths of these regions change continuously depending on the operation conditions. The length of each region is determined by making energy balances as follows: The length at the beginning of the condenser necessary to bring the vapor to the saturation temperature is found in a similar manner to the upriser (single phase vapor cooling):
Fig. 3. Fluid element in a connecting pipe.
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Convection Heat to the Tank
Change of Energy
783
Across Region
pDc Uc T ÿ TT dx ÿ mCp dT: Integrate the above equation across the vapor region Zc between T3 and T sat at the condenser exit. Z Tsat Z Zc pDc Uc dT ÿ dx mCp 0 T3 T ÿ TT mCp T3 ÿ TT Zc ln : 7 pDc Uc Tsat ÿ TT To determine the length necessary to complete condensation, an energy balance is made between the released amount of heat by condensation and the heat transferred to the water tank through the condenser pipe wall: mhfg Zc pDc Uc Tsat ÿ TT : Thus, Zc
mhfg : pDc Uc Tsat ÿ TT
8
Finally, the condenser exit temperature is determined in a similar way to the upriser using the following equation (single phase liquid cooling): pDc Uc Zc : 9 T4 TT Tsat ÿ TT exp ÿ mCp 2.1.4. Downcomer The refrigerant in the downcomer is always in a liquid state. Once again, the same type of equations used in the upriser and condenser can be used to determine the downcomer exit temperature: pDd Ud Ld T1 Ta T4 ÿ Ta exp ÿ : 10 mCp This temperature represents a new collector inlet temperature. 2.1.5. Water storage tank The tank temperature at the end of each time step of 15 min is determined by making an energy balance between the energy released from the condenser and the energy lost to the load and surroundings. The resulting heat balance equation is as follows: T 00T T 0T
Qv Qc QL ÿ QLoss ÿ QLoad Dt MCT
11
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where Qv mCp T3 ÿ Tsat Qc x3 mhfg QL mCp Tsat ÿ T4 QLoss UAT T 0T ÿ Ta
QLoad ml Cpw T 0T ÿ Tw :
2.2. Hydrodynamic analysis The hydrodynamic analysis calculates the pressure drop across each component. The formulation depends on the phase of the working ¯uid. For single phase ¯ow, the usual approach of the Darci±Weisbach friction coecient is used to determine the pressure drop in the single phase ¯ow in accordance to what is proposed by Morrison and Ranatunga [14]. In two phase ¯ow, there are two models to evaluate the pressure drop. The ®rst is the separated ¯ow model which treats the liquid and vapour as completely separated phases. Each has its properties and occupies a certain fraction of the ¯ow cross sectional area. The second model is the homogeneous model. This model is also known as the friction factor or fog ¯ow model. It considers the two phases to ¯ow as a single phase possessing mean ¯uid properties. The homogeneous model is used in the present study to evaluate the pressure drop in the two phase regions of the system, as proposed by Collier [15]. This model is appropriate for two phase collectors because the boiling process produces the mixing condition that justi®es its use. Also, the accuracy of the homogeneous model is comparable to that of the separated model, and it is easier for computer calculations than the separated model, with reduced program execution time.
2.3. The simulation procedure The main problem in the thermosyphon system simulation is that the mass ¯ow rate induced in the loop is not known a priori. This problem cannot be solved unless an iterative procedure is used. In the iterative calculations, the conservation laws must be satis®ed. The iteration procedure is brie¯y outlined in the following points: 1. Initial guess values of the collector inlet temperature and pressure are assumed, together with the mass ¯ow rate. The initial value of temperature and pressure are taken equal to the saturation values at the initial ambient temperature. The mass ¯ow rate is given an initial value equal to what insolation would evaporate in 15 min with no losses. 2. A thermal analysis is performed to evaluate the exit temperature or exit quality of each component consecutively. The exit temperature of the last component, which is the downcomer, represents a new collector inlet temperature.
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3. In parallel to step 2, a hydrodynamic analysis is performed to evaluate the exit pressure of each component consecutively. The exit pressure of the last component, which is the downcomer, represents a new collector inlet pressure. 4. The new and old values of the collector inlet pressure are compared. If they agree within the imposed tolerance, the simulation skips to the next step. If agreement is not achieved, the entire simulation process for the considered time step is repeated, starting with a modi®ed value of the mass ¯ow rate that is given by the following relation according to Ali and McDonald [16]: P1new : 12 mnew mold P1old 5. Now, the new and old values of collector inlet temperature are compared. If they agree within the imposed tolerance, the simulation skips to another step. If not, the simulation process is repeated, starting with the new obtained temperature.. 6. Finally, the new and old values of the system charge are compared. If agreement is achieved, the simulation stops, and the program prints the results for the considered time step. If not, the process is again repeated, but now, the collector inlet pressure is modi®ed according to the following equation [16]: Old Charge : 13 P1 P1 New Charge The system charge is the quantity of refrigerant volume in the system relative to the total volume. The value of the charge is taken constant in the present treatment, and its value equals 0.6. This means that 0.6 of the system volume is occupied by liquid refrigerant before starting. The above six steps are repeated for each time step of 15 min starting at 8 a.m. to 4 p.m., with outputs of the previous step being the input of the next step.
3. Results and discussion An important property of the two phase thermosyphon system, which assists in understanding the various aspects of its performance, is that it is a sealed system. This makes the pressure in this system change in two coordinates: the time coordinate during the operation period and the position coordinate around the loop. Generally, the collector side represents the high pressure region, while the condenser side is the lower pressure region. The dierence between the collector and condenser pressure establishes a driving potential that maintains the thermosyphonic action as long as the solar irradiance is above a threshold level. The prevailing pressure in the two phase system dominates the thermal processes through the resulting saturation temperatures in the collector and condenser. A high saturation temperature in the collector increases the mean plate temperature and, consequently, the thermal losses to the environment, whereas a low condenser saturation temperature decreases the useful heat
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Fig. 4. Variation of solar irradiance during the simulated period.
released to the water store. The variation of the saturation temperature in the collector and condenser depends largely on the solar radiation intensity and the tank temperature, and there is a strong mutual relation between them, as will be shown from the results. A typical clear day irradiance pattern is shown in Fig. 4, which represents the input to the system. The saturation temperature in the collector and condenser are observed to increase continuously during the simulation period, as shown in Fig. 5. This behavior may be explained by tracking the thermal processes established in the system after exposure to solar radiation. When solar radiation strikes the collector, it raises the temperature and triggers the onset of
Fig. 5. Variation of tank and saturation temperatures during the simulated period.
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Fig. 6. Variation of tank and saturation temperatures during the simulated period.
evaporation. At the same time, condensation commences, as long as the tank temperature is lower than the condensation temperature. So, there is a heat source represented by the collector and a heat sink represented by the condenser and storage tank. This con®guration keeps the collector pressure always greater than the condenser pressure. In fact, the condensation pressure, and the corresponding saturation temperature, is a stimulant that induces the collector to produce a lower or a higher vapor quantity depending on the condenser pressure. The condenser pressure and temperature are, in turn, aected by the tank
Fig. 7. Variation of mass ¯ow rate during the simulated period.
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Fig. 8. Variation of collector and condenser eciency during the simulated period.
temperature. Of course, the condenser temperature cannot be lower than the tank temperature, since this stops condensation. Because of this direct inter-relationship between collector and condenser operation, their saturation temperature and pressure will vary in parallel following the tank temperature pattern, as shown in Fig. 5 for temperature. The dependency on tank temperature renders the system operation largely aected by the loading condition from the tank, as shown in Fig. 6. The mass ¯ow rate through the system was found to follow the irradiance pattern and changes accordingly, as shown in Fig. 7. This is because the mass ¯ow rate is related directly
Fig. 9. Variation of collector and condenser eciency during the simulated period.
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Fig. 10. Comparison between the single and two phase tank temperatures during the simulated period.
to the rates of evaporation and condensation. These rates change in parallel, increasing in the morning and decreasing after solar noon, giving the mass ¯ow rate the trend in Fig. 7. Loading increases the mass ¯ow rate through the system because it increases the condensation rate by introducing a colder ¯uid to the tank, as shown in Fig. 7. The collector thermal eciency can be de®ned as the useful heat collected by the working ¯uid divided by the amount of insolation over the collector.
Fig. 11. Comparison between the single and two phase tank temperatures during the simulated period.
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Fig. 12. Comparison of collector eciency between single and two phase systems.
Zcol
mhfg x2 mCp Tsat ÿ T1 : nWLIT
14
Likewise, the condenser eciency can be de®ned as the heat released from the condenser divided by the insolation value: Zcond
pDc Zc Uc Tsat ÿ TT mCp Tsat ÿ TT : nWLIT
Fig. 13. Comparison of collector eciency between single and two phase systems.
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Fig. 14. Collector eciency curve.
These parameters vary in the manner shown in Figs. 8 and 9 for the cases of no loading and loading, respectively. Comparisons with a single phase system of the same collector area and tank volume shows a clear increase in the collector eciency and tank temperature for the two phase system, as shown in Figs. 10±13. This is an expected result because the latent heat transfer is greater than the sensible heat transfer for the same system geometry and operating conditions. The only experimental results that have been found in the literature for two phase systems that can be compared with the present analysis are the collector eciency curves. These curves
Fig. 15. Collector eciency curve.
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Fig. 16. Collector eciency curve.
were obtained using a ®xed mass ¯ow rate in the collector. They are commonly straight lines that best ®t the scattered experimental readings. Fig. 14 shows a comparison between the present theoretical results and the experimental data of Downing and Waldin [2]. It can be seen that reasonable agreement is obtained between them. In order to make the comparison, the mass ¯ow rate must be ®xed in the simulation. This was done by entering the mass ¯ow rate value of the experimental work in the beginning of the simulation program and eliminating the pressure iteration in the simulation procedure, because this iteration is responsible for modifying the mass ¯ow rate value. In the same manner, other comparisons have been made with Al-tamimi and Clark [4] in Fig. 15,Fig. 15 and Abramzon et al. [8] in Fig. 16. The percentage dierence in these comparisons was within 10%.
4. Conclusions 1. The saturation temperature and pressure in the collector and condenser increase continuously during the day with increasing tank temperature at the no loading condition. Water withdrawal causes a marked eect on the collector and condenser saturation temperatures. 2. The variation in ¯ow rate during the day follows the insolation pattern with a noticeable increase with increased loading. 3. The collector eciency was not seriously aected with loading, whereas the condenser eciency changed clearly with the loading condition. 4. The tank temperature of the two phase system showed a clear improvement over that of a single phase system of the same collector area and tank volume. The improvement was approximately 10%.
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5. The collector eciency of the two phase system is approximately 20% higher than a single phase collector. Also, the response of the two phase system is faster than a single phase system in reaching the maximum tank temperature and maximum eciency. References [1] Soin RS, Sangemeswar K, Rao DP, Rao KS. Performance of ¯at plate solar collector with ¯uid undergoing phase change. Solar Energy 1979;23:69. [2] Downing RC, Waldin VW. Phase change heat transfer in solar hot water heating using R-11 and R-114. ASHRAE Trans. 1980;86:848±56. [3] Schreyer JM. Residential application of refrigerant charged solar collectors. Solar Energy 1981;26:307±12. [4] Al-tamimi AI, Clark JA. Thermal performance of a solar collector containing a boiling ¯uid (R-11). ASHRAE Trans. 1984;90:681±96. [5] El-Assy AY, Clark JA. Thermal analysis of a ¯at plate boiling collector having sub-cooled inlet and saturation exit states. Solar Energy 1989;42:121±32. [6] El-Assy AY, Clark JA. Thermal analysis of ¯at plate collectors in multiphase ¯ows, including superheat. Solar Energy 1988;40:345±61. [7] Price HW, Klein SA, Beckman WA. Analysis of boiling ¯at plate collectors. ASME J. of Solar Energy Engineering 1986;108:150±7. [8] Abramzon B, Yaron I, Borde I. An analysis of a ¯at plate solar collector with internal boiling. ASME J. of Solar Energy Engineering 1983;105:454±60. [9] ASHRAE Handbook. 1985. Fundamentals. . [10] Lunde PJ. Solar thermal engineering. New York: Wiley, 1980. [11] Mathur GD, McDonald TW. Simulation program for a two phase thermosyphon loop heat exchanger. ASHRAE Trans. 1986;92:473±85. [12] Chato JC. Laminar condensation inside horizontal and inclined tubes. ASHRAE J. 1962;4:52±60. [13] Al-tabbakh AA. 1997. Preliminary simulation of a two phase thermosyphon solar domestic hot water heating system. M.Sc. thesis in Mechanical Engineering. Saddam University, Baghdad. . [14] Morrison GL, Ranatunga DBJ. Thermosyphon circulation in solar collectors. Solar Energy 1980;24:191±8. [15] Collier JG. Convective boiling and condensation. London: McGraw±Hill, 1972. [16] Ali AFM, McDonald TW. Thermosyphon loop performance characteristics: part 2. Simulation Program. ASHRAE Trans. 1977;83:260±78.