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Thermal performance of a solar-aided latent heat store used for space heating by heat pump
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Solar Energy Vol. 69, No. 1, pp. 15–25, 2000 2000 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0038-092X / 00 / $ - see front matter
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THERMAL PERFORMANCE OF A SOLAR-AIDED LATENT HEAT STORE USED FOR SPACE HEATING BY HEAT PUMP MEHMET ESEN† ˘ Turkey Department of Mechanical Education, Fırat University, 23119 Elazıg, Received 11 September 1998; revised version accepted 30 November 1999 Communicated by ERICH HAHNE
Abstract—In this study, the cylindrical phase change storage tank linked to a solar powered heat pump system is investigated experimentally and theoretically. A simulation model defining the transient behaviour of the phase change unit was used. In the tank, the phase change material (PCM) is inside cylindrical tubes and the heat transfer fluid (HTF) flows parallel to it. The heat transfer problem of the model (treated as twodimensional) was solved numerically by an enthalpy-based finite differences method and validated against experimental data. The experiments were performed from November to May in the heating seasons of 1992–1993 and 1993–1994 to measure both the mean temperature of water within the tank and the inlet and outlet water temperature of the tank. The experimentally obtained inlet water temperatures are also taken as inlet water temperature of the simulated model. Thus, theoretical temperature and stored heat energy distribution within the tank have been determined. Solar radiation and space heating loads for the heating seasons mentioned above are also presented. 2000 Elsevier Science Ltd. All rights reserved.
solar heating system. Their main conclusion was that the PCM should be selected on the basis of its melting temperature, rather than its latent heat, i.e. the melting temperature has a significant effect on system performance. Klein and Beckman (1979) described an extensive computer simulation study of a general class of closed-loop solar energy system which can be used for a variety of applications including space heating, absorption air conditioning, and certain types of process heating. The results of this study are presented as a design method so that they can be used to estimate the long-term performance of solar energy systems. Bulkin et al. (1988) suggested a mathematical model for designing a solar heating and hot-water supply system on the basis of solar absorbers and a heat pump with two thermal-storage tanks, taking into account the system’s interaction with the outside climate and with the room being served. Ghoneim (1989) has studied the effect of assumptions in the models of earlier studies on both the fraction of the load met by solar energy, and the required storage capacities. Kaygusuz et al. (1991) developed an experimental model to determine the dynamics of solar-assisted heat pump, collectors, dryer, and energy storage tank used for drying grains. Kaygusuz (1995a) investigated the performance of a dual-source heat pump system for residential heating. Also, Kaygusuz (1995b) conducted an experimental and a theoretical study to determine
1. INTRODUCTION
Energy storage is much more important where the energy source is intermittent such as solar energy. A great disadvantage of this kind of energy shows up immediately, namely the large discrepancy between the supply and the demand. The heat demand is maximum in winter or, in the short term, in the evening when the supply of solar energy is minimal or even zero. This makes heat storage an indispensable element of a solar-powered heat pump system. One way of increasing the economic competitiveness of the heat pump is to integrate it with a thermal energy storage system. The thermal store allows a reduction in the required heat pump size for a given load. This reduces the capital cost of the heat pump. Also, the store reduces the on / off cycling losses of the system because a smaller-sized heat pump will run for longer periods at maximum capacity between cycles to satisfy a given load. Moreover, the store allows the heat pump to operate at lower condensing temperatures leading to a higher steady-state coefficient of performance (COP) (C¸omaklı et al., 1993a). Jurinak and Abdel-Khalik (1978, 1979) have studied the effects of PCM melting temperature and latent heat on the performance of an air-based
†
Fax: 190-424-218-4674; e-mail: [email protected] 15
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M. Esen
the performance of phase-change energy storage materials, and the variation of the outlet fluid temperature with different values of NTU (the number of transfer units of the storage unit) for solar water-heating systems. The performance of a solar energy system varies significantly from day to day and from month to month making it necessary to examine its performance over a long term. The main objectives of the present study have been: (1) to use a theoretical model describing the diurnal transient behaviour of the phase change energy storage (PCES) unit, (2) to perform computer simulations and experiments in order to determine the distribution of energy, and temperature within the PCES unit, and (3) to determine the monthly space heating loads, the monthly stored energy, and monthly total solar insolation on collector surfaces, and to present comparisons of these data.
purposes, a latent heat thermal energy storage tank filled by 1090 kg encapsulated PCM (CaCl 2 .6H 2 O), a heat pump with a water sourced evaporator and an air cooled condenser, a water circulating pump, and measuring equipment. The water cooled solar collectors were installed at an angle of 488 from the horizontal and face due south. Temperatures were measured with copper constantan thermocouples. A Kipp and Zonen pyranometer, mounted in the vertical plane of the solar collectors, was used to measure the solar insolation. Water flow rate was measured by means of two flowmeters. An automatic data logging system was used for data acquisition. Every 25 s all quantities were measured. Solar insolation, water temperatures, ambient air and indoor air temperatures were averaged over each half-hour period. These averaged quantities and the instantaneous values of the remaining quantities were recorded every half-hour.
2.2. Operation modes 2. THE EXPERIMENTAL STUDY
2.1. Experimental set-up The experimental set-up described here is at Trabzon, Turkey (lat. 418109 N; long. 408209 E). Fig. 1 shows a sketch of the set-up. The experimental apparatus consisted of flat plate solar collectors having a total area of 30 m 2 , a laboratory building with 75 m 2 floor area for heating
The two modes of operation were investigated in this system. The first mode occurs when solar radiation is available for collection and there is a space heating load. During this mode, the hot water that receives its energy from the solar collectors first goes to the energy storage tank. It then releases some of its own energy to the CaCl 2 .6H 2 O in the storage tank. After this procedure it is used as a heat source by the water-
Fig. 1. Solar assisted heat pump system with latent heat storage tank.
Thermal performance of a solar-aided latent heat store used for space heating by heat pump
sourced evaporator of the heat pump. Finally, it is sent to the solar collectors by the water circulating pump (Storage and Heating Mode). However, during the night and on cloudy days, when there is low or no solar radiation and the load is not zero, the cold water that comes from the evaporator is sent to the tank instead of the collectors. The cold water extracts heat energy from the PCM in the tank and it flows to the evaporator for use as a heat source. Thus, at night and cloudy times, the stored energy in the tank is used as a heat source for the heat pump. The second mode occurs when solar radiation is available for collection and the space heating load is zero. In this mode, the hot water is circulated between the collectors and the tank (Storage Mode).
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difficulty has been removed by the application of the enthalpy method (Visser, 1986). The relations between the specific enthalpy and the temperature for different ranges are as follows: i(T ) 5 Cp,s T
for T , T m1
r f (T 2 T m1 ) i(T ) 5 Cp,l T 1 ]]]] DT m
(1) for T m1 # T # T m2 (2)
and i(T ) 5 Cp,l T 1 r f
for T . T m2 .
(3)
These equations will be further simplified by using a nondimensional enthalpy and temperature. The nondimensional enthalpy is written as i 2 i m1 H 5 ]] rf
3. THEORETICAL ANALYSIS
3.1. Modelling of the charging process of the PCM The theoretical treatment of this problem is similar to that described by Esen and Ayhan (1996) and Esen et al. (1998). Hence, the subject will be discussed very briefly, and for more details the reader is referred to the full description presented in the references. The energy storage tank (Fig. 2a) consists of cylindrical tubes packed in the vertical direction. Fig. 2b sketches the model for one tube (Esen and Ayhan, 1996; Esen et al., 1998). The storage material (CaCl 2 .6H 2 O) is inside the tubes and the HTF flows parallel to it. We assume that the HTF which is surrounding the cylindrical tubes is situated in theoretical cylinder jackets all around the tubes. The very small spaces between cylindrical jackets were ignored. The packing density is the same everywhere in the tank. The thermophysical properties of various phases of the PCM are different, but are independent of temperature. The PCM is homogeneous and isotropic. In the model development, the following effects were taken into account: the thermal conductivity of the PCM in the axial direction, the thermal conductivity for the PCM in the direction normal to the flow (radial direction) and the local film temperature difference between the HTF and the PCM. During the phase-change process of the storage material, a moving boundary occurs. The moving solid–liquid interface moves continuously with time, and the problem cannot be reduced to a simple solution of the Fourier equation. The
(4)
and the nondimensional temperature as Cp,s (T 2 T m1 ) u 5 ]]]] for T , T m1 rf
(5)
and Cp,l (T 2 T m1 ) u 5 ]]]] for T $ T m1 . rf
(6)
Considering a cylindrical quantity of PCM (Fig. 2c), which is a part of the cylinder, taking a control volume element ( j, k), which is a ring with inner radius R k and outer radius R k 21 , then applying an energy balance on that volume element results in:
U
≠i rVj,k] ≠t
j,k
U U
U U
≠T ≠T 5 2 l A k] 1 l A k 21] ≠R k ≠R ≠T ≠T 1 l A j ] j 2 l A j 21] ≠z ≠z
k 21
j 21
(7)
Eq. (7) is solved by using finite difference approximations for ≠T / ≠R and ≠T / ≠z. Substituting these finite difference equations into Eq. (7), an equation for the enthalpy of a specified element can be written in nondimensional form. An energy balance on the HTF element results in an equation for the temperature distribution of the HTF element. The resulting set of equations is solved using the Gauss–Seidel iteration process.
3.2. The simulated values The energy balance over the PCM is directly coupled with the energy balance over the wall of the pipe, and the HTF. The temperature of HTF flowing from the tank to the heat source on time level (n) is expressed as
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M. Esen
Fig. 2. Energy storage tank packed in vertical direction with cylindrical tubes (a), the model for one cylinder (b) and cylindrical control volume element ( j, k) (c).
T nout,H 5 T nM21,itf 11,1
(8)
The rate of energy flowing from the tank to the heat source circuit can be written as
S
Nt
O
D
1 n ~ in,H ? Cp,f ] T out,H Pout,H 5 m 2 T in,H Nt n51
S
N
OO
D
O OH
M 11N 12
Epcm 5 Epcm,st 1 Nc r r f
nf,itf j,k j,k
V
(11)
j 52 k 53
(9)
where Pout,H 50 on t 5 t M,st . The rate of energy lost to the environment from the tank is calculated as t M 11 1 n,itf Penv 5 A tankU ]] T 2 T env . Nt M n 51 j52 j,1
The energy content with regard to the initial temperature T st of the PCM is given by
where Epcm,st is dependent on the range T st is in the solid, the transition, and the liquid range. The energy content with regard to T st of all cylinder walls together is calculated by
O V (T
M 11
(10)
Ew 5 Nc rw Cp,w
j,2
j 52
nf,itf j,2
2 T st )
(12)
Thermal performance of a solar-aided latent heat store used for space heating by heat pump
and that of all the HTF in the tank by
O V (T
O
M 11
Ef 5 Nc rf Cp,f
j,1
nf,itf j,1
2 T st )
(13)
j52
The energy content of the entire tank is the sum of Eqs. (11), (12), and (13): Etank 5 Epcm 1 Ew 1 Ef
(14)
The percentages in the solid, the transition, and the liquid range of the PCM are calculated as follows. In the solid range: 100 Per s 5 ]] Vpcm,c so that H
OOV
for ( j, k)
j,k
j
nf,itf j,k
k
,0
(15)
in the transition range: 100 Per t 5 ]] Vpcm,c
OOV
j,k
j
for ( j, k)
k
Cp,l DT m so that 0 # H nf,itf # 1 1 ]]] j,k rf
(16)
and in the liquid range: 100 Per l 5 ]] Vpcm,c
OOV
j,k
j
for ( j, k)
k
Cp,l DT m so that H nf,itf . 1 1 ]]]. j,k rf
(17)
Finally, the mean temperature of the pipe wall is given by
O
1 M 11 nf,itf T w,mean 5 ] T M j 52 j,2 and the mean temperature of the HTF by
(18)
1 M 11 nf,itf T f,mean 5 ] T . M j 52 j,1
(19)
The space heating load calculations were made on the basis of the average daily load by month using the effective UA (overall heat transfer3 area) value for the building and (DD) m (number of degree-days per month) (Howell et al., 1982). Thus, the average daily space heating load Q d,sh was calculated using the following equation: UA Q d,sh 5 14(DD) m ]. ND
(20)
The effective UA value for the building is the sum of the products of the overall heat transfer coefficients (Ut ) and buildings areas (A t ) for the building’s various exterior surfaces: slab (floor, ceiling), walls, windows, and roof. The values of UA for window, wall, floor and ceiling area are 315, 96, 187.5 and 150 W K 21 , respectively. So the effective UA value for the heated building is nearly equal to 0.75 kW K 21 . The number of degree-days is the monthly total of all the negative differences between each average daily outdoor temperature and 18.38C. The total heating period in a day is 14 h. Except for these calculated values, temperatures T in,H , T out,H and T f,mean are also measured experimentally.
4. RESULTS AND DISCUSSION
To acquire the theoretical results, the simulation program prepared by Esen (1994) was used. The properties of PCM (CaCl 2 .6H 2 O), the HTF, and other parameters used in this work are listed in Table 1.
Table 1. The properties of PCM, the HTF, and other parameters used in this work Density of PCM (CaCl 2 .6H 2 O) Specific heat of PCM (solid phase) Specific heat of PCM (liquid phase) Thermal conductivity of PCM (solid phase) Thermal conductivity of PCM (liquid phase) Thermal conductivity of PCM (transition phase) Melting temperature of PCM (lower) Melting temperature of PCM (upper) Latent heat of fusion Density of HTF Specific heat of HTF Shape of tank (L /R t,inn ) Inside volume of tank Inside surface area of tank Thermal loss of tank Environment temperature of tank Density of cylinder wall material Specific heat of cylinder wall material Thermal conductivity of cylinder wall material
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1710 kg m 23 1460 J kg 21 K 21 2130 J kg 21 K 21 1.088 W m 21 K 21 0.539 W m 21 K 21 0.7 W m 21 K 21 29.78C 29.858C 187.49 kJ kg 21 1000 kg m 23 4200 J kg 21 K 21 4.923 4.25 m 3 13 m 2 0.55 W m 22 K 21 188C 1200 kg m 23 500 J kg 21 K 21 0.055 W m 21 K 21
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M. Esen
Fig. 3. Variation of T out,H , T w,mean , T f,mean , Per s , Per l , and Per t with time (T st 5188C, Vtank 54.25 m 3 , Lc 53.2 m, Nc 5110).
Fig. 3 shows the variation of T out,H , T w,mean , T f,mean , Per s , Per l and Per t with time. Each curve has been generated for constant values of R c,inn , ~ in,H and T in,H . As seen from the figure, as the m values of Per s and Per t become zero when the whole PCM melts (i.e. at which time maximum energy is stored in the PCM), the value of Per l becomes 100%. The value of Epcm almost remains the same from this point (see Fig. 4). The total of percentages of PCM by volume always become 100% at a given time. Also, in the previous study (Esen and Ayhan, 1996) it was seen that, as the ~ in,H and T in,H increase at a given time, values of m the stored energy in the PCM increases too. When the PCM completely melts, the values T in,H and T out,H approach each other. Throughout the charging process, the values of T f,mean become bigger
than the values of T w,mean . In addition, Esen ~ in,H (1994) determined that, as the value of m increases, the values of T out,H , T f,mean , T w,mean and Epcm increase too. The variation of Penv , Pout,H , Etank , Ef , Ew and Epcm with time is given in Fig. 4. As can be seen from the figure, the values of Ew , Ef , Etank and Penv as well as the value of Epcm almost continues as constant; because the values of T w,mean , T f,mean and T out,H do not increase more when the PCM becomes completely liquid. As shown in the figure, the energy content of the tank always becomes equal to the total of the values of the Epcm , Ew and Ef . Since the value of the Pout,H is the rate of energy flowing from the tank to the heat-source (to the solar collectors), it begins from a negative value, then it approaches zero when the
Fig. 4. Variation of Penv (kJ h 21 ), Pout,H (MJ h 21 ), Etank (MJ), Ef (MJ), Ew (kJ) and Epcm (MJ) with time (T st 5188C, Vtank 54.25 m 3 , Lc 53.2 m, Nc 5110).
Thermal performance of a solar-aided latent heat store used for space heating by heat pump
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Fig. 5. Variation of T in,H , T out,H , T out,H,ex , T f,mean , T f,mean,ex and T w,mean with time of day.
outlet water temperature of the tank begins to increase; because the value of the T out,H approaches the value of the T in,H . The variations of the theoretical and the experimental temperatures with the time of day are depicted in Fig. 5. As seen in the figure, the measured and the calculated values of T out,H and T f,mean are very near each other. As the theoretical values are calculated, the measured values of T in,H were taken as the theoretical values of T in,H . Solar radiation is maximum at around solar noon, and after it begins decreasing from this point, the temperatures T in,H , T w,mean and T out,H decrease too, respectively. The stored energy in the PCM
which extracts the heat of water in the tank becomes maximum towards evening, and the value of Epcm decreases when the value of T f,mean is smaller than the melting temperature of the PCM (see also Fig. 6). Fig. 6 shows the variation of Ii , Epcm , Penv , Pout,H , Per s , Per l and Per t with time of day. The total of Per s , Per l and Per t is always 100% at a given time. This result is the same as seen in Fig. 3. So long as the value of T f,mean increases, Penv increases too. The moment the value of T f,mean begins decreasing, Penv decreases too, because the temperature difference (T f,mean 2T env ) decreases. As soon as T out,H becomes higher than T in,H , the
Fig. 6. Variation of Ii 310 21 (W m 22 ), Epcm (MJ), Penv (kJ h 21 ), Pout,H (MJ h 21 ), Per s (%), Per l (%) and Per t (%) with time of day.
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M. Esen
charging period is finished and the discharging period begins. Because of insufficient insolation, the PCM cannot completely melt, and thus maximum energy storage of PCM cannot be provided. This case shows that the PCM containers (pipes
filled with PCM) made of PVC (polyvinyl chloride) are not as good as some metals (e.g. copper, aluminium, steel, etc.). Therefore, more appropriate pipe wall materials, shapes and dimensions should be selected. The aim of modelling latent
Fig. 7. The variations of I, Q, (Epcm /Q) and (Epcm /I) during the months of the heating season in 1992–1993 and 1993–1994.
Thermal performance of a solar-aided latent heat store used for space heating by heat pump
heat stores is essentially an appropriate selection of the parameters mentioned above (Esen and Ayhan, 1996; Esen et al., 1998). Fig. 7a and b presents the variations of I and Q during the months of the heating season in 1992– 1993 and 1993–1994, respectively. In 1992– 1993, the Q becomes maximum in January, whereas the I becomes maximum in May. In 1993–1994, the Q is maximum in February. For both heating seasons, the values of insolation become smaller than the load values in November, December, January and February. In these months, both the heating and the storage were practised on sunny and warm days. The stored energy in the PCM was released at night. On sunny but cold days only storage was performed, and this stored energy was used for heating during the night. However, on warm days and when solar radiation and a space heating load is available, an air-sourced heat pump and / or a water-to-air heat exchanger can be used. Fig. 7c depicts the variation of the ratio of Epcm /Q during the months of the heating season in 1992–1993 for the storage mode and the storage and heating mode. Whereas the heat pump in the storage mode does not run, both heating and storage are carried out in the storage and heating mode. Naturally, the ratios of Epcm /Q were smaller in the storage and heating mode compared to the ratios in the storage mode. As seen in the figure, the stored energy meets 60% of the load in addition to the energy consumed for space heating in March. While the whole load is almost met by the stored energy in April, the ratio of Epcm /Q nearly becomes 2.5 in May. As the ratios of Epcm /Q are very low from November to February for the storage and heating mode, either the water-sourced (solar-aided) heat pump together with an auxiliary heater should be run, or only storage is performed during daytime, and the water-sourced (store-aided) heat pump together with an auxiliary heater should be run at night. The monthly average outdoor temperatures for November to May in 1992–1993 are 11.5, 7, 5.5, 4.5, 9, 11 and 15.58C, respectively. Although the average outdoor temperature in February is lower than that in January, the heating load in February is smaller than that in January. This is affected by the fact that February has only 28 days. Fig. 7d exhibits the variation of the ratio of Epcm /Q during the months of the heating season in 1993–1994 for the storage mode and the storage and heating mode. The stored energy almost meets half of the load in addition to energy consumed for heating in the first 4 months of the
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season. It is clear that if the space heating had not been carried out, more load would have been met by the stored energy. However, the amount of stored energy is higher than the load in spite of energy consumed for heating in March. The monthly average outdoor temperatures for November to May in 1993–1994 are 8.6, 10, 9.2, 6.1, 8.6, 14.3 and 16.48C, respectively. The ratios of Epcm /Q in 1993–1994 are bigger than those in 1992–1993. This can perhaps be due to two reasons: (1) the average outdoor temperatures in 1993–1994 are higher compared to the values in 1992–1993, (2) using smaller pipe radius in 1993–1994. It is evident that PCM cylinders with smaller radii will melt at a shorter time and these cylinders can store much more heat energy compared to PCM cylinders with thicker radii. The variations of ratios of Epcm /I during the months of the heating season in 1992–1993 and 1993–1994 for the storage mode and the storage and heating mode are shown in Fig. 7e and f, respectively. As seen in Fig. 7e and f, the stored energy is lower than the values of insolation for all the months in both seasons, because some stored energy in the tank is lost to the environment. On the other hand, some energy in the tank is stored in the HTF and the pipe walls. The lost energy occurs both from the tank and from the solar collectors.
5. CONCLUSION
To study the thermal performance of the solaraided latent heat storage tank in the charging and discharging process, a theoretical model was developed, and an experimental system constructed by C ¸ omakli et al. (1993b) was used to validate it. A comparison between mathematical results of the model with experimental data showed reasonable agreement. The following conclusions can be drawn from the results of this study. 1. To show accuracy of the model developed in this study, there is a lot of evidence. • The total of percentages of the PCM by volume in the solid, the transition and the liquid range is always (at a given time) 100%. • The total of Epcm , Ew and Ef is always equal to Etank . 2. Because the outlet water temperature of the tank is low (or constant) at the beginning of the experiments, the heating cannot be performed well. To improve this situation, a
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3.
4.
5. 6. 7.
8.
9.
10.
M. Esen
shorter length of pipes as well as a shorter inside height of the tank should be selected. The thickness of the pipe walls should be thin so that the energy stored in pipes walls becomes minimum. If lots of pipes with small radii are used, the total volume of pipe walls increases; therefore, the whole PCM melting time becomes longer compared to the melting time in the tank which contains fewer pipes with big radius (Esen, 1994). Consequently, the thickness of the pipe walls should be thinner if a lot of pipes with small radius are used. Note that energy released to the heating space by heat pump is not only the energy extracted from the PCM, since the energy (electric energy) consumed to run the heat pump is added to it. The ratio of Epcm /Q is still insufficient especially in the first 4 months of the season. Therefore, availability of seasonal storage should be investigated for Trabzon (placed on the Black Sea side). The choice of modes should be done by checking the temperature T in,H automatically. Other storage materials and storage types should be investigated. The PCM used in the experiments of this study was not changed during two seasons. Thus the most appropriate number of heat cycles should be determined. When the number reaches the value determined, PCM used in the tank should be renewed. The heating space should be insulated very well according to standards of ASHRAE, TSE etc. On cloudy but warm days, a solar assisted heat pump together with air-sourced evaporator can be more efficient. The performance of a solar assisted storage tank used by a heat pump system should be examined over the long term. NOMENCLATURE
A At A tank Cp Cp,f Cp,l Cp,s Cp,w (DD) m Ef Epcm Epcm,st Etank Ew
area (m 2 ) floor area (m 2 ) inside surface area of the tank (m 2 ) specific heat (J kg 21 K 21 ) specific heat of HTF (J kg 21 K 21 ) specific heat of PCM in liquid phase (J kg 21 K 21 ) specific heat of PCM in solid phase (J kg 21 K 21 ) specific heat of cylinder wall material (J kg 21 K 21 ) number of degree-days per month energy content of HTF (J) energy content of PCM (J) initial energy content of PCM (J) energy content of the tank (J) energy content of cylinder walls (J)
H I Ii i itf Lc M ~ in,H m nf N Nc Nt ND Penv Per l Pout,H Per s Per t Q Q d,sh R R c,inn R c,out rf R t,inn T T f,mean T f,mean,ex T in,H T m1 T m2 T out,H T out,H,ex T st T w,mean t t M,st U Ut Vj,k Vpcm,c Vtank z DT m
nondimensional enthalpy monthly total solar insolation on tilted collector surfaces (MJ) instantaneous solar radiation on tilted collector surfaces (W m 22 ) specific enthalpy of PCM (kJ kg 21 ) final iteration level length of cylinder (m) number of axial elements mass flow rate of HTF flowing from heat source to tank (kg s 21 ) final time level inside subroutine number of radial elements number of cylinders number of timesteps inside the subroutine program number of days in a month rate of energy lost to environment (W) percentage of PCM in the liquid range by volume (%) rate of energy flowing from the tank to heat source (W) percentage of PCM in the solid range by volume (%) percentage of PCM in the transition range by volume (%) monthly total space heating load (MJ) average daily space heating load (MJ) radial distance (m) inner radius of PCM cylinders (m) outer radius of PCM cylinders (m) latent heat of fusion (kJ kg 21 ) inner radius of the tank (m) temperature (8C) theoretical mean temperature of HTF in the tank (8C) experimental mean temperature of HTF in the tank (8C) temperature of the HTF flowing from the heat source to the tank (8C) lower melting temperature of the PCM (8C) upper melting temperature of the PCM (8C) theoretical temperature of HTF flowing from the tank to the heat source (8C) experimental temperature of HTF flowing from the tank to the heat source (8C) initial temperature of the tank (PCM, HTF, cylinder walls) (8C) theoretical mean temperature of cylinder walls (8C) time (h) initial time in main program (h) thermal loss of storage tank (W m 22 K 21 ) overall thermal loss coefficient (W m 22 K 21 ) control element volume (m 3 ) one PCM cylinder volume (m 3 ) inside volume of the tank (m 3 ) axial distance (m) transition range width (8C)
Greek letters u nondimensional temperature 21 21 l thermal conductivity (W m K ) ll thermal conductivity of PCM in liquid phase (W m 21 K 21 ) ls thermal conductivity of PCM in solid phase (W m 21 K 21 ) lt thermal conductivity of PCM in transition phase (W m 21 K 21 ) lw thermal conductivity of cylinder wall material (W m 21 K 21 ) r PCM density (kg m 23 ) rf HTF density (kg m 23 ) rw density of cylinder wall material (kg m 23 )
Thermal performance of a solar-aided latent heat store used for space heating by heat pump
REFERENCES Bulkin S. G., Vyrlan P. M. and Pleshka M. S. (1988) Mathematical model of a solar heat-pump system with solar absorbers and two thermal storage tanks. Appl. Solar Energy 24, 41. ¨ Kaygusuz K., Ayhan T. and Arslan F. (1993a) C ¸ omaklı O., Experimental investigation and a dynamic simulation of the solar-assisted energy-storaged heat pump system. Solar Energy 51, 147. ¨ Kaygusuz K. and Ayhan T. (1993b) SolarC ¸ omaklı O., assisted heat pump and energy storage for residential heating. Solar Energy 51, 357. Esen M. (1994). Numerical Simulation of Cylindrical Energy Storage Tank Containing Phase Change Material on the Solar Assisted Heat Pump System and Comparing with Experimental Results, Technical University of Karadeniz, Trabzon, Turkey, Ph.D. thesis. Esen M. and Ayhan T. (1996) Development of a model compatible with solar assisted cylindrical energy storage tank and variation of stored energy with time for different phase change materials. Energy Convers. Mgmt. 37, 1775. Esen M., Durmus A. and Durmus¸ A. (1998) Geometric design of solar-aided latent heat store depending on various parameters and phase change materials. Solar Energy 62, 19. Ghoneim A. A. (1989) Comparison of theoretical models of phase-change and sensible heat storage for air and waterbased solar heating systems. Solar Energy 42, 209.
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Howell J. R., Bannerot R. B. and Vliet G. C. (1982). In 1st edn, Solar-Thermal Energy Systems (Analysis and Design), p. 215, McGraw-Hill, New York. Jurinak J. J. and Abdel-Khalik S. I. (1978) Properties optimization for phase change energy storage in air-based solar heating systems. Solar Energy 21, 377. Jurinak J. J. and Abdel-Khalik S. I. (1979) Sizing phasechange energy storage units for air-based solar heating systems. Solar Energy 22, 355. Kaygusuz K. (1995a) Performance of solar-assisted heat pump systems. Appl. Energy 51, 93. Kaygusuz K. (1995b) Experimental and theoretical investigation of latent heat storage for water based solar heating systems. Energy Convers. Mgmt. 36, 315. ¨ and Ayhan T. (1991) Solar-assisted Kaygusuz K., C ¸ omaklı O. heat pump systems and energy storage. Solar Energy 47, 383. Klein S. A. and Beckman W. A. (1979) A general design method for closed-loop solar energy systems. Solar Energy 22, 269. Visser H. (1986) Energy storage in phase-change materials – development of a component model compatible with the TRNSYS-transient simulation program. In Final report. Contract No. 2462 -84 -09 ED ISPNL, Delft University of Technology, Department of Applied Physics, Delft.
PII: S0038 – 092X( 00 )00015 – 3
Solar Energy Vol. 69, No. 1, pp. 15–25, 2000 2000 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0038-092X / 00 / $ - see front matter
www.elsevier.com / locate / solener
THERMAL PERFORMANCE OF A SOLAR-AIDED LATENT HEAT STORE USED FOR SPACE HEATING BY HEAT PUMP MEHMET ESEN† ˘ Turkey Department of Mechanical Education, Fırat University, 23119 Elazıg, Received 11 September 1998; revised version accepted 30 November 1999 Communicated by ERICH HAHNE
Abstract—In this study, the cylindrical phase change storage tank linked to a solar powered heat pump system is investigated experimentally and theoretically. A simulation model defining the transient behaviour of the phase change unit was used. In the tank, the phase change material (PCM) is inside cylindrical tubes and the heat transfer fluid (HTF) flows parallel to it. The heat transfer problem of the model (treated as twodimensional) was solved numerically by an enthalpy-based finite differences method and validated against experimental data. The experiments were performed from November to May in the heating seasons of 1992–1993 and 1993–1994 to measure both the mean temperature of water within the tank and the inlet and outlet water temperature of the tank. The experimentally obtained inlet water temperatures are also taken as inlet water temperature of the simulated model. Thus, theoretical temperature and stored heat energy distribution within the tank have been determined. Solar radiation and space heating loads for the heating seasons mentioned above are also presented. 2000 Elsevier Science Ltd. All rights reserved.
solar heating system. Their main conclusion was that the PCM should be selected on the basis of its melting temperature, rather than its latent heat, i.e. the melting temperature has a significant effect on system performance. Klein and Beckman (1979) described an extensive computer simulation study of a general class of closed-loop solar energy system which can be used for a variety of applications including space heating, absorption air conditioning, and certain types of process heating. The results of this study are presented as a design method so that they can be used to estimate the long-term performance of solar energy systems. Bulkin et al. (1988) suggested a mathematical model for designing a solar heating and hot-water supply system on the basis of solar absorbers and a heat pump with two thermal-storage tanks, taking into account the system’s interaction with the outside climate and with the room being served. Ghoneim (1989) has studied the effect of assumptions in the models of earlier studies on both the fraction of the load met by solar energy, and the required storage capacities. Kaygusuz et al. (1991) developed an experimental model to determine the dynamics of solar-assisted heat pump, collectors, dryer, and energy storage tank used for drying grains. Kaygusuz (1995a) investigated the performance of a dual-source heat pump system for residential heating. Also, Kaygusuz (1995b) conducted an experimental and a theoretical study to determine
1. INTRODUCTION
Energy storage is much more important where the energy source is intermittent such as solar energy. A great disadvantage of this kind of energy shows up immediately, namely the large discrepancy between the supply and the demand. The heat demand is maximum in winter or, in the short term, in the evening when the supply of solar energy is minimal or even zero. This makes heat storage an indispensable element of a solar-powered heat pump system. One way of increasing the economic competitiveness of the heat pump is to integrate it with a thermal energy storage system. The thermal store allows a reduction in the required heat pump size for a given load. This reduces the capital cost of the heat pump. Also, the store reduces the on / off cycling losses of the system because a smaller-sized heat pump will run for longer periods at maximum capacity between cycles to satisfy a given load. Moreover, the store allows the heat pump to operate at lower condensing temperatures leading to a higher steady-state coefficient of performance (COP) (C¸omaklı et al., 1993a). Jurinak and Abdel-Khalik (1978, 1979) have studied the effects of PCM melting temperature and latent heat on the performance of an air-based
†
Fax: 190-424-218-4674; e-mail: [email protected] 15
16
M. Esen
the performance of phase-change energy storage materials, and the variation of the outlet fluid temperature with different values of NTU (the number of transfer units of the storage unit) for solar water-heating systems. The performance of a solar energy system varies significantly from day to day and from month to month making it necessary to examine its performance over a long term. The main objectives of the present study have been: (1) to use a theoretical model describing the diurnal transient behaviour of the phase change energy storage (PCES) unit, (2) to perform computer simulations and experiments in order to determine the distribution of energy, and temperature within the PCES unit, and (3) to determine the monthly space heating loads, the monthly stored energy, and monthly total solar insolation on collector surfaces, and to present comparisons of these data.
purposes, a latent heat thermal energy storage tank filled by 1090 kg encapsulated PCM (CaCl 2 .6H 2 O), a heat pump with a water sourced evaporator and an air cooled condenser, a water circulating pump, and measuring equipment. The water cooled solar collectors were installed at an angle of 488 from the horizontal and face due south. Temperatures were measured with copper constantan thermocouples. A Kipp and Zonen pyranometer, mounted in the vertical plane of the solar collectors, was used to measure the solar insolation. Water flow rate was measured by means of two flowmeters. An automatic data logging system was used for data acquisition. Every 25 s all quantities were measured. Solar insolation, water temperatures, ambient air and indoor air temperatures were averaged over each half-hour period. These averaged quantities and the instantaneous values of the remaining quantities were recorded every half-hour.
2.2. Operation modes 2. THE EXPERIMENTAL STUDY
2.1. Experimental set-up The experimental set-up described here is at Trabzon, Turkey (lat. 418109 N; long. 408209 E). Fig. 1 shows a sketch of the set-up. The experimental apparatus consisted of flat plate solar collectors having a total area of 30 m 2 , a laboratory building with 75 m 2 floor area for heating
The two modes of operation were investigated in this system. The first mode occurs when solar radiation is available for collection and there is a space heating load. During this mode, the hot water that receives its energy from the solar collectors first goes to the energy storage tank. It then releases some of its own energy to the CaCl 2 .6H 2 O in the storage tank. After this procedure it is used as a heat source by the water-
Fig. 1. Solar assisted heat pump system with latent heat storage tank.
Thermal performance of a solar-aided latent heat store used for space heating by heat pump
sourced evaporator of the heat pump. Finally, it is sent to the solar collectors by the water circulating pump (Storage and Heating Mode). However, during the night and on cloudy days, when there is low or no solar radiation and the load is not zero, the cold water that comes from the evaporator is sent to the tank instead of the collectors. The cold water extracts heat energy from the PCM in the tank and it flows to the evaporator for use as a heat source. Thus, at night and cloudy times, the stored energy in the tank is used as a heat source for the heat pump. The second mode occurs when solar radiation is available for collection and the space heating load is zero. In this mode, the hot water is circulated between the collectors and the tank (Storage Mode).
17
difficulty has been removed by the application of the enthalpy method (Visser, 1986). The relations between the specific enthalpy and the temperature for different ranges are as follows: i(T ) 5 Cp,s T
for T , T m1
r f (T 2 T m1 ) i(T ) 5 Cp,l T 1 ]]]] DT m
(1) for T m1 # T # T m2 (2)
and i(T ) 5 Cp,l T 1 r f
for T . T m2 .
(3)
These equations will be further simplified by using a nondimensional enthalpy and temperature. The nondimensional enthalpy is written as i 2 i m1 H 5 ]] rf
3. THEORETICAL ANALYSIS
3.1. Modelling of the charging process of the PCM The theoretical treatment of this problem is similar to that described by Esen and Ayhan (1996) and Esen et al. (1998). Hence, the subject will be discussed very briefly, and for more details the reader is referred to the full description presented in the references. The energy storage tank (Fig. 2a) consists of cylindrical tubes packed in the vertical direction. Fig. 2b sketches the model for one tube (Esen and Ayhan, 1996; Esen et al., 1998). The storage material (CaCl 2 .6H 2 O) is inside the tubes and the HTF flows parallel to it. We assume that the HTF which is surrounding the cylindrical tubes is situated in theoretical cylinder jackets all around the tubes. The very small spaces between cylindrical jackets were ignored. The packing density is the same everywhere in the tank. The thermophysical properties of various phases of the PCM are different, but are independent of temperature. The PCM is homogeneous and isotropic. In the model development, the following effects were taken into account: the thermal conductivity of the PCM in the axial direction, the thermal conductivity for the PCM in the direction normal to the flow (radial direction) and the local film temperature difference between the HTF and the PCM. During the phase-change process of the storage material, a moving boundary occurs. The moving solid–liquid interface moves continuously with time, and the problem cannot be reduced to a simple solution of the Fourier equation. The
(4)
and the nondimensional temperature as Cp,s (T 2 T m1 ) u 5 ]]]] for T , T m1 rf
(5)
and Cp,l (T 2 T m1 ) u 5 ]]]] for T $ T m1 . rf
(6)
Considering a cylindrical quantity of PCM (Fig. 2c), which is a part of the cylinder, taking a control volume element ( j, k), which is a ring with inner radius R k and outer radius R k 21 , then applying an energy balance on that volume element results in:
U
≠i rVj,k] ≠t
j,k
U U
U U
≠T ≠T 5 2 l A k] 1 l A k 21] ≠R k ≠R ≠T ≠T 1 l A j ] j 2 l A j 21] ≠z ≠z
k 21
j 21
(7)
Eq. (7) is solved by using finite difference approximations for ≠T / ≠R and ≠T / ≠z. Substituting these finite difference equations into Eq. (7), an equation for the enthalpy of a specified element can be written in nondimensional form. An energy balance on the HTF element results in an equation for the temperature distribution of the HTF element. The resulting set of equations is solved using the Gauss–Seidel iteration process.
3.2. The simulated values The energy balance over the PCM is directly coupled with the energy balance over the wall of the pipe, and the HTF. The temperature of HTF flowing from the tank to the heat source on time level (n) is expressed as
18
M. Esen
Fig. 2. Energy storage tank packed in vertical direction with cylindrical tubes (a), the model for one cylinder (b) and cylindrical control volume element ( j, k) (c).
T nout,H 5 T nM21,itf 11,1
(8)
The rate of energy flowing from the tank to the heat source circuit can be written as
S
Nt
O
D
1 n ~ in,H ? Cp,f ] T out,H Pout,H 5 m 2 T in,H Nt n51
S
N
OO
D
O OH
M 11N 12
Epcm 5 Epcm,st 1 Nc r r f
nf,itf j,k j,k
V
(11)
j 52 k 53
(9)
where Pout,H 50 on t 5 t M,st . The rate of energy lost to the environment from the tank is calculated as t M 11 1 n,itf Penv 5 A tankU ]] T 2 T env . Nt M n 51 j52 j,1
The energy content with regard to the initial temperature T st of the PCM is given by
where Epcm,st is dependent on the range T st is in the solid, the transition, and the liquid range. The energy content with regard to T st of all cylinder walls together is calculated by
O V (T
M 11
(10)
Ew 5 Nc rw Cp,w
j,2
j 52
nf,itf j,2
2 T st )
(12)
Thermal performance of a solar-aided latent heat store used for space heating by heat pump
and that of all the HTF in the tank by
O V (T
O
M 11
Ef 5 Nc rf Cp,f
j,1
nf,itf j,1
2 T st )
(13)
j52
The energy content of the entire tank is the sum of Eqs. (11), (12), and (13): Etank 5 Epcm 1 Ew 1 Ef
(14)
The percentages in the solid, the transition, and the liquid range of the PCM are calculated as follows. In the solid range: 100 Per s 5 ]] Vpcm,c so that H
OOV
for ( j, k)
j,k
j
nf,itf j,k
k
,0
(15)
in the transition range: 100 Per t 5 ]] Vpcm,c
OOV
j,k
j
for ( j, k)
k
Cp,l DT m so that 0 # H nf,itf # 1 1 ]]] j,k rf
(16)
and in the liquid range: 100 Per l 5 ]] Vpcm,c
OOV
j,k
j
for ( j, k)
k
Cp,l DT m so that H nf,itf . 1 1 ]]]. j,k rf
(17)
Finally, the mean temperature of the pipe wall is given by
O
1 M 11 nf,itf T w,mean 5 ] T M j 52 j,2 and the mean temperature of the HTF by
(18)
1 M 11 nf,itf T f,mean 5 ] T . M j 52 j,1
(19)
The space heating load calculations were made on the basis of the average daily load by month using the effective UA (overall heat transfer3 area) value for the building and (DD) m (number of degree-days per month) (Howell et al., 1982). Thus, the average daily space heating load Q d,sh was calculated using the following equation: UA Q d,sh 5 14(DD) m ]. ND
(20)
The effective UA value for the building is the sum of the products of the overall heat transfer coefficients (Ut ) and buildings areas (A t ) for the building’s various exterior surfaces: slab (floor, ceiling), walls, windows, and roof. The values of UA for window, wall, floor and ceiling area are 315, 96, 187.5 and 150 W K 21 , respectively. So the effective UA value for the heated building is nearly equal to 0.75 kW K 21 . The number of degree-days is the monthly total of all the negative differences between each average daily outdoor temperature and 18.38C. The total heating period in a day is 14 h. Except for these calculated values, temperatures T in,H , T out,H and T f,mean are also measured experimentally.
4. RESULTS AND DISCUSSION
To acquire the theoretical results, the simulation program prepared by Esen (1994) was used. The properties of PCM (CaCl 2 .6H 2 O), the HTF, and other parameters used in this work are listed in Table 1.
Table 1. The properties of PCM, the HTF, and other parameters used in this work Density of PCM (CaCl 2 .6H 2 O) Specific heat of PCM (solid phase) Specific heat of PCM (liquid phase) Thermal conductivity of PCM (solid phase) Thermal conductivity of PCM (liquid phase) Thermal conductivity of PCM (transition phase) Melting temperature of PCM (lower) Melting temperature of PCM (upper) Latent heat of fusion Density of HTF Specific heat of HTF Shape of tank (L /R t,inn ) Inside volume of tank Inside surface area of tank Thermal loss of tank Environment temperature of tank Density of cylinder wall material Specific heat of cylinder wall material Thermal conductivity of cylinder wall material
19
1710 kg m 23 1460 J kg 21 K 21 2130 J kg 21 K 21 1.088 W m 21 K 21 0.539 W m 21 K 21 0.7 W m 21 K 21 29.78C 29.858C 187.49 kJ kg 21 1000 kg m 23 4200 J kg 21 K 21 4.923 4.25 m 3 13 m 2 0.55 W m 22 K 21 188C 1200 kg m 23 500 J kg 21 K 21 0.055 W m 21 K 21
20
M. Esen
Fig. 3. Variation of T out,H , T w,mean , T f,mean , Per s , Per l , and Per t with time (T st 5188C, Vtank 54.25 m 3 , Lc 53.2 m, Nc 5110).
Fig. 3 shows the variation of T out,H , T w,mean , T f,mean , Per s , Per l and Per t with time. Each curve has been generated for constant values of R c,inn , ~ in,H and T in,H . As seen from the figure, as the m values of Per s and Per t become zero when the whole PCM melts (i.e. at which time maximum energy is stored in the PCM), the value of Per l becomes 100%. The value of Epcm almost remains the same from this point (see Fig. 4). The total of percentages of PCM by volume always become 100% at a given time. Also, in the previous study (Esen and Ayhan, 1996) it was seen that, as the ~ in,H and T in,H increase at a given time, values of m the stored energy in the PCM increases too. When the PCM completely melts, the values T in,H and T out,H approach each other. Throughout the charging process, the values of T f,mean become bigger
than the values of T w,mean . In addition, Esen ~ in,H (1994) determined that, as the value of m increases, the values of T out,H , T f,mean , T w,mean and Epcm increase too. The variation of Penv , Pout,H , Etank , Ef , Ew and Epcm with time is given in Fig. 4. As can be seen from the figure, the values of Ew , Ef , Etank and Penv as well as the value of Epcm almost continues as constant; because the values of T w,mean , T f,mean and T out,H do not increase more when the PCM becomes completely liquid. As shown in the figure, the energy content of the tank always becomes equal to the total of the values of the Epcm , Ew and Ef . Since the value of the Pout,H is the rate of energy flowing from the tank to the heat-source (to the solar collectors), it begins from a negative value, then it approaches zero when the
Fig. 4. Variation of Penv (kJ h 21 ), Pout,H (MJ h 21 ), Etank (MJ), Ef (MJ), Ew (kJ) and Epcm (MJ) with time (T st 5188C, Vtank 54.25 m 3 , Lc 53.2 m, Nc 5110).
Thermal performance of a solar-aided latent heat store used for space heating by heat pump
21
Fig. 5. Variation of T in,H , T out,H , T out,H,ex , T f,mean , T f,mean,ex and T w,mean with time of day.
outlet water temperature of the tank begins to increase; because the value of the T out,H approaches the value of the T in,H . The variations of the theoretical and the experimental temperatures with the time of day are depicted in Fig. 5. As seen in the figure, the measured and the calculated values of T out,H and T f,mean are very near each other. As the theoretical values are calculated, the measured values of T in,H were taken as the theoretical values of T in,H . Solar radiation is maximum at around solar noon, and after it begins decreasing from this point, the temperatures T in,H , T w,mean and T out,H decrease too, respectively. The stored energy in the PCM
which extracts the heat of water in the tank becomes maximum towards evening, and the value of Epcm decreases when the value of T f,mean is smaller than the melting temperature of the PCM (see also Fig. 6). Fig. 6 shows the variation of Ii , Epcm , Penv , Pout,H , Per s , Per l and Per t with time of day. The total of Per s , Per l and Per t is always 100% at a given time. This result is the same as seen in Fig. 3. So long as the value of T f,mean increases, Penv increases too. The moment the value of T f,mean begins decreasing, Penv decreases too, because the temperature difference (T f,mean 2T env ) decreases. As soon as T out,H becomes higher than T in,H , the
Fig. 6. Variation of Ii 310 21 (W m 22 ), Epcm (MJ), Penv (kJ h 21 ), Pout,H (MJ h 21 ), Per s (%), Per l (%) and Per t (%) with time of day.
22
M. Esen
charging period is finished and the discharging period begins. Because of insufficient insolation, the PCM cannot completely melt, and thus maximum energy storage of PCM cannot be provided. This case shows that the PCM containers (pipes
filled with PCM) made of PVC (polyvinyl chloride) are not as good as some metals (e.g. copper, aluminium, steel, etc.). Therefore, more appropriate pipe wall materials, shapes and dimensions should be selected. The aim of modelling latent
Fig. 7. The variations of I, Q, (Epcm /Q) and (Epcm /I) during the months of the heating season in 1992–1993 and 1993–1994.
Thermal performance of a solar-aided latent heat store used for space heating by heat pump
heat stores is essentially an appropriate selection of the parameters mentioned above (Esen and Ayhan, 1996; Esen et al., 1998). Fig. 7a and b presents the variations of I and Q during the months of the heating season in 1992– 1993 and 1993–1994, respectively. In 1992– 1993, the Q becomes maximum in January, whereas the I becomes maximum in May. In 1993–1994, the Q is maximum in February. For both heating seasons, the values of insolation become smaller than the load values in November, December, January and February. In these months, both the heating and the storage were practised on sunny and warm days. The stored energy in the PCM was released at night. On sunny but cold days only storage was performed, and this stored energy was used for heating during the night. However, on warm days and when solar radiation and a space heating load is available, an air-sourced heat pump and / or a water-to-air heat exchanger can be used. Fig. 7c depicts the variation of the ratio of Epcm /Q during the months of the heating season in 1992–1993 for the storage mode and the storage and heating mode. Whereas the heat pump in the storage mode does not run, both heating and storage are carried out in the storage and heating mode. Naturally, the ratios of Epcm /Q were smaller in the storage and heating mode compared to the ratios in the storage mode. As seen in the figure, the stored energy meets 60% of the load in addition to the energy consumed for space heating in March. While the whole load is almost met by the stored energy in April, the ratio of Epcm /Q nearly becomes 2.5 in May. As the ratios of Epcm /Q are very low from November to February for the storage and heating mode, either the water-sourced (solar-aided) heat pump together with an auxiliary heater should be run, or only storage is performed during daytime, and the water-sourced (store-aided) heat pump together with an auxiliary heater should be run at night. The monthly average outdoor temperatures for November to May in 1992–1993 are 11.5, 7, 5.5, 4.5, 9, 11 and 15.58C, respectively. Although the average outdoor temperature in February is lower than that in January, the heating load in February is smaller than that in January. This is affected by the fact that February has only 28 days. Fig. 7d exhibits the variation of the ratio of Epcm /Q during the months of the heating season in 1993–1994 for the storage mode and the storage and heating mode. The stored energy almost meets half of the load in addition to energy consumed for heating in the first 4 months of the
23
season. It is clear that if the space heating had not been carried out, more load would have been met by the stored energy. However, the amount of stored energy is higher than the load in spite of energy consumed for heating in March. The monthly average outdoor temperatures for November to May in 1993–1994 are 8.6, 10, 9.2, 6.1, 8.6, 14.3 and 16.48C, respectively. The ratios of Epcm /Q in 1993–1994 are bigger than those in 1992–1993. This can perhaps be due to two reasons: (1) the average outdoor temperatures in 1993–1994 are higher compared to the values in 1992–1993, (2) using smaller pipe radius in 1993–1994. It is evident that PCM cylinders with smaller radii will melt at a shorter time and these cylinders can store much more heat energy compared to PCM cylinders with thicker radii. The variations of ratios of Epcm /I during the months of the heating season in 1992–1993 and 1993–1994 for the storage mode and the storage and heating mode are shown in Fig. 7e and f, respectively. As seen in Fig. 7e and f, the stored energy is lower than the values of insolation for all the months in both seasons, because some stored energy in the tank is lost to the environment. On the other hand, some energy in the tank is stored in the HTF and the pipe walls. The lost energy occurs both from the tank and from the solar collectors.
5. CONCLUSION
To study the thermal performance of the solaraided latent heat storage tank in the charging and discharging process, a theoretical model was developed, and an experimental system constructed by C ¸ omakli et al. (1993b) was used to validate it. A comparison between mathematical results of the model with experimental data showed reasonable agreement. The following conclusions can be drawn from the results of this study. 1. To show accuracy of the model developed in this study, there is a lot of evidence. • The total of percentages of the PCM by volume in the solid, the transition and the liquid range is always (at a given time) 100%. • The total of Epcm , Ew and Ef is always equal to Etank . 2. Because the outlet water temperature of the tank is low (or constant) at the beginning of the experiments, the heating cannot be performed well. To improve this situation, a
24
3.
4.
5. 6. 7.
8.
9.
10.
M. Esen
shorter length of pipes as well as a shorter inside height of the tank should be selected. The thickness of the pipe walls should be thin so that the energy stored in pipes walls becomes minimum. If lots of pipes with small radii are used, the total volume of pipe walls increases; therefore, the whole PCM melting time becomes longer compared to the melting time in the tank which contains fewer pipes with big radius (Esen, 1994). Consequently, the thickness of the pipe walls should be thinner if a lot of pipes with small radius are used. Note that energy released to the heating space by heat pump is not only the energy extracted from the PCM, since the energy (electric energy) consumed to run the heat pump is added to it. The ratio of Epcm /Q is still insufficient especially in the first 4 months of the season. Therefore, availability of seasonal storage should be investigated for Trabzon (placed on the Black Sea side). The choice of modes should be done by checking the temperature T in,H automatically. Other storage materials and storage types should be investigated. The PCM used in the experiments of this study was not changed during two seasons. Thus the most appropriate number of heat cycles should be determined. When the number reaches the value determined, PCM used in the tank should be renewed. The heating space should be insulated very well according to standards of ASHRAE, TSE etc. On cloudy but warm days, a solar assisted heat pump together with air-sourced evaporator can be more efficient. The performance of a solar assisted storage tank used by a heat pump system should be examined over the long term. NOMENCLATURE
A At A tank Cp Cp,f Cp,l Cp,s Cp,w (DD) m Ef Epcm Epcm,st Etank Ew
area (m 2 ) floor area (m 2 ) inside surface area of the tank (m 2 ) specific heat (J kg 21 K 21 ) specific heat of HTF (J kg 21 K 21 ) specific heat of PCM in liquid phase (J kg 21 K 21 ) specific heat of PCM in solid phase (J kg 21 K 21 ) specific heat of cylinder wall material (J kg 21 K 21 ) number of degree-days per month energy content of HTF (J) energy content of PCM (J) initial energy content of PCM (J) energy content of the tank (J) energy content of cylinder walls (J)
H I Ii i itf Lc M ~ in,H m nf N Nc Nt ND Penv Per l Pout,H Per s Per t Q Q d,sh R R c,inn R c,out rf R t,inn T T f,mean T f,mean,ex T in,H T m1 T m2 T out,H T out,H,ex T st T w,mean t t M,st U Ut Vj,k Vpcm,c Vtank z DT m
nondimensional enthalpy monthly total solar insolation on tilted collector surfaces (MJ) instantaneous solar radiation on tilted collector surfaces (W m 22 ) specific enthalpy of PCM (kJ kg 21 ) final iteration level length of cylinder (m) number of axial elements mass flow rate of HTF flowing from heat source to tank (kg s 21 ) final time level inside subroutine number of radial elements number of cylinders number of timesteps inside the subroutine program number of days in a month rate of energy lost to environment (W) percentage of PCM in the liquid range by volume (%) rate of energy flowing from the tank to heat source (W) percentage of PCM in the solid range by volume (%) percentage of PCM in the transition range by volume (%) monthly total space heating load (MJ) average daily space heating load (MJ) radial distance (m) inner radius of PCM cylinders (m) outer radius of PCM cylinders (m) latent heat of fusion (kJ kg 21 ) inner radius of the tank (m) temperature (8C) theoretical mean temperature of HTF in the tank (8C) experimental mean temperature of HTF in the tank (8C) temperature of the HTF flowing from the heat source to the tank (8C) lower melting temperature of the PCM (8C) upper melting temperature of the PCM (8C) theoretical temperature of HTF flowing from the tank to the heat source (8C) experimental temperature of HTF flowing from the tank to the heat source (8C) initial temperature of the tank (PCM, HTF, cylinder walls) (8C) theoretical mean temperature of cylinder walls (8C) time (h) initial time in main program (h) thermal loss of storage tank (W m 22 K 21 ) overall thermal loss coefficient (W m 22 K 21 ) control element volume (m 3 ) one PCM cylinder volume (m 3 ) inside volume of the tank (m 3 ) axial distance (m) transition range width (8C)
Greek letters u nondimensional temperature 21 21 l thermal conductivity (W m K ) ll thermal conductivity of PCM in liquid phase (W m 21 K 21 ) ls thermal conductivity of PCM in solid phase (W m 21 K 21 ) lt thermal conductivity of PCM in transition phase (W m 21 K 21 ) lw thermal conductivity of cylinder wall material (W m 21 K 21 ) r PCM density (kg m 23 ) rf HTF density (kg m 23 ) rw density of cylinder wall material (kg m 23 )
Thermal performance of a solar-aided latent heat store used for space heating by heat pump
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