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Numerical and experimental investigation of thermosyphon solar water heater
Energy Conversion and Management xxx (2013) xxx–xxx
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Numerical and experimental investigation of thermosyphon solar water heater Khaled Zelzouli ⇑, Amenallah Guizani, Chakib Kerkeni Thermal Processes Laboratory, (CRTEn), Borj Cedria B.P N°95 2050, Hammam Lif, Tunisia
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Performance collector Storage tank Long-term performance Numerical investigation
a b s t r a c t A glassed flat plate collector with selective black chrome coated absorber and a low wall conductance horizontal storage are combined in order to set up a high performance thermosyphon system. Each component is tested separately before testing the complete system in spring days. During the test period, effect of different inlet water temperatures on the collector performance is studied and results have shown that the collector can reach a high efficiency and high outlet water temperature even for elevated inlet water temperatures. Subsequently, long term system performance is estimated by using a developed numerical model. The proposed model, accurate and gave a good agreement with experimental results, allowed to describe the heat transfer in the storage. It has shown also that the long-term performances are strongly influenced by losses from the storage than losses from the collector. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Solar water heater is one of the most successful solar technologies. Nowadays, world’s demand of energy has dramatically increased; furthermore, process to collect hot water by solar radiation is yet expensive. Most solar water heater designs used for single family are the closed and opened solar water heating systems. These two systems are categorized into two groups: forced circulation and natural convection. The advantages of thermosyphon systems are that they do not rely on pumps and controllers, are more reliable, and have a longer life than forced circulation systems [1]. Thermosyphonic systems are studied intensively by many researches [2–10]. Hasan [11] studied the effect of the hot water storage tank volume and configuration on system efficiency and he concluded that there is no difference between the performances of vertical and horizontal storage tank systems, and concluded that the efficiency of a SWH system can be increased by using a larger hot water storage tank or smaller collectors area. The technical performance and reliability of solar systems are key parameters that can significantly vary the production of thermal energy and thus the cost effectiveness. The two main parameters, to get a reliable system, are the storage insulation and the collector performances. A very good insulated storage and a highly efficient collector leads to a profitable system in all months of the year and mainly in the countries having good sunshine climate. Tunisia is one of these countries which characterized by a temperate and an abundant sunshine for the most periods of the year. A typical flat ⇑ Corresponding author. Tel.: +216 22025245/79325053; fax: 216 79325825. E-mail address: [email protected] (K. Zelzouli).
plate solar collector consists of an absorber in an insulated box with transparent cover sheets (glazing). The absorber is usually made of a metal sheet characterized by a high thermal conductivity with attached or integrated tubes. For the collectors having high performances, its absorbers surfaces are coated with a special selective material to maximize radiant energy absorption while minimizing radiant energy emission. The best selective absorbers present selectivity values over 10, denoting higher sunlight energy absorption and lower thermal energy losses. The insulated box reduces heat losses from the back and sides of the collector. The flat plate collector of selective absorber coated with black chrome is one of best collectors used for heating water. For the complete system, the storage must be insulated with very low thermal conductivity materials. Black chrome for selective absorbers and collector efficiency vs. coating properties are studied in [12–17]. Kalogirou et al. [18] introduced in their study, performance of solar systems employing collectors with colored absorber, that the flat plate collectors of highly selective coatings can reach stagnation temperatures of more than 200 °C and they showed that the colored collectors present lower efficiency than the typical black type collectors. Tripanagnostopoulos et al. [19] studied the solar collectors with colored absorbers and they concluded that selective colored absorbers are efficient in wider range of operating temperatures than absorbers with color paints of high emissivity. Recently, the International Energy Agency issued a Technology Roadmap for Solar Heating and Cooling [20] which estimates the potential for domestic hot water in Africa and the Middle East in the range of 2 Ej/year. For the long term calculation, a number of computer software programs have been developed concerning the modeling and
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simulation of thermal systems. The minimum energy requirement is generally calculated using appropriate software packages (e.g., F-Chart, Transys, T*Sol and Solo) and based on monthly or daily means of climatic data, and the mean storage temperature. Many theoretical models are currently available for the estimation of the thermal stratification within storage tanks, and among the used models, is the one dimensional model. Khalifa and Mehdi [21] studied the verification of the one dimensional heat flow in a horizontal thermosyphon storage tank and they concluded that the heat flow in the tank may be considered one dimensional. Moreover, computer programs are more accurate with smaller time steps. Huang and Hsieh [22] studied the effect of computation time step on temperature distribution with five tank sections choosing 6, 10, 15 and 20 min time steps, and results have shown a good agreement with the experiments. They claimed that the computation time step in simulation can be as large as 15 min with good accuracy even for the worst cases; thus it can save a significant amount of computation time. In this paper, our main objective is to build a high performance solar collector coupled with good insulated storage tank for use in domestic hot water as well as for industrial energy. The storage, of 200 l insulated with polyurethane foam, is located horizontally above a flat plate collector of 1.93 m2 aperture area having a selective absorber coated with black chrome. Long-term prediction of the proposed system will be performed thanks to a numerical model developed in this study. The developed model describes the energy flows within the storage based on a differential equations solution method and the technical characteristics of the proposed system. It yields the hourly, daily, monthly and annual performances. The experimental work is achieved in spring to identify the system efficiency in days characterized by the soft climatic weather. Tests are achieved in the Laboratory of Thermal Processes (L.P.T) in Borj Cedria, Tunis, Tunisia. Numerical results expected are the system drawn water temperature energy, efficiency and system performance. Results are validated with the experimental measurements and they have shown that the model can provide accurate results. 2. System description and test procedure 2.1. System description The experiment is designed to investigate the system performances. Before coupling the collector with the storage, each component is tested separately. In the First days, the collector outputs are obtained. In the next days, the storage loss coefficient is determined. Then, the complete system performance is studied. Fig. 1.1 illustrates the schematic of the amenities used in the experiment. The pyranometer of type KIPP & Zonen CM11, to measure solar radiation, is placed near the top of the solar collector at the same inclination and azimuth of the solar plan. Water temperatures are measured using RTD (Pt100) sensors having the greatest temperature stability and characterized by a good linearity with a sensitiveness ±0.1% °C. Two sensors placed at the inlet and outlet of the collector to measure inlet and outlet fluid temperatures, and another used to determine the draw-off fluid temperature from the tank. The sensor for measuring the ambient temperature is placed at a height of 1.25 m from the surface of the test site. The wind speed is measured by a cup anemometer consisted of three hemispherical cups each mounted on one end of horizontal arms, which in turn were mounted at equal angles to each other on a vertical shaft. The water flow rate is measured by a Flow Meter, of float type, that is installed in the system in the outlet of hot water. The measurements are performed using a Data acquisition type Agilent 34970A.
The collector is titled of 38° to horizontal surface and oriented to the south. It is a selective collector, which has dimensions of 1.98 1.041 0.09 [m] with one glass cover of thickness of 4 mm, an aperture area of 1.93 m2 and 10 risers with inner diameter of 12 mm and outer diameter of 14 mm. The absorber thickness d, absorptance ap, emittance ep and absorption-transmittance sa are 12.103 mm, 0.95, 0.1 and 0.86, respectively. The bottom and edges thickness of the collector are 40 mm with thermal conductivity k of 0.035 W/m K. The horizontal cylindrical water storage tank, of 200 l, is insulated by 4 cm of injected polyurethane foam with density of 40 kg/m3. The polyurethane foam is one of the best insulating materials, having a very low thermal conductivity. The polyurethane thermal conductivity k is in the range of 0.02–0.035 for temperatures below 100 °C [23]. The storage inner area and insulation thickness are 2.1 m2 and 5 cm, respectively. 2.2. Test procedure 2.2.1. Collector performances test A test sequence contains a number of consecutive days of measurements are carried out. Various inlet water temperatures are inserted to acquire information about the collector performance. The experiments were conducted in the months of April and May and the outputs (outlet water temperatures, instantaneous efficiencies, solar radiation and ambient temperature) were recorded. The program used for this test is the HP-VEE; it is designed according to the standards for testing solar collectors following the flow chart below and is as follows: (i) When the program starts, the data logger initializes the different probes, anemometer, flow meter and the pyranometer at a measurement frequency of 10 s. (ii) After assigning the set point temperature, the program always takes the final values given by the data logger and the measures of the difference (Tfo Tfi) should not exceed 0.1 °C and the sunshine G must be greater to 800 W/m2. (iii) Once the gap is stable during 15 min, the program proceeds to the recording of data acquired for 90 successive values and stop recording automatically. The procedure is as follows:
The program automatically opens an excel file; this file shows instantaneous values as ambient temperature Ta; collector inlet, outlet, difference and mean water temperature; solar radiation G (W/m2), the collector efficiency. 2.2.2. Storage loss test sequence This sequence intends to identify the overall store losses. The store overnight heat loss coefficient is obtained in an independent test where the system with a hot storage tank is left to cool down
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Tsout Cup Ananometer Flow Meter
Tfo Pyranometer
Ta
Tfi Thermocouple Fig. 1.1. Schematic of the amenities used in the experiment.
during about 24 h. To calculate the storage heat loss coefficient, the computation strategy consists of:
3. Mathematical model 3.1. Solar collector
(i) Filling the tank with hot water temperature initially at Ti P 70 °C. (ii) The tank is allowed to cool in a room for at least a 24 h period. (iii) The store is brought to uniform temperature using a circulation pump, then measuring the final temperature Tf. The average ambient temperature Ta during the cooling period is calculated by the data logger. The total storage loss coefficient during the 24 h (from 18:00 h to 18:00 the next day) is calculated with a log-mean temperature difference [24,25]:
U¼
qVC p Dt
Log
Ti Ta Tf Ta
ð1Þ
where T i and T f are the initial and final average water temperature during the test period Dt. For the whole system, the storage tank is located horizontally above the collector. The system was heated from 8:00am to 6:00 pm with no draw-off during the charging period. From 6:00 pm, during 1 h, the water is drawn three times the tank volume with a fixed flow rate of 10 l/min. 2.2.3. Store energy test In this stage, the storage is located above the collector (Fig. 1.1) and filled with mains water. During 4 days of measurement, a daily test is effected by allowing the system operates during the period of irradiation and then withdrawing the water at the end of the day. Draw-off temperature profiles are determined for different withdrawn volumes. 2.3. Uncertainty analysis Uncertainty analysis is required to prove the accuracy of the experiments. In this study, errors came from the susceptibility of equipment and measurements explained previously. First, errors due to measurement of temperature are: Susceptibility of data logging system, around ±0.1% °C. Measurement error is ±0.2%. Susceptibility of the thermocouple is ±0.1% °C. The susceptibility was obtained from a catalog of the instruments. Second, errors came from the measurement of the flow rate: the susceptibility of the flow meter is about ±0.1% and errors due to measurement are about ±0.1%.
The collector performance is described by energy balance such as the distribution of incident solar energy and thermal and optical losses. The useful energy output from a collector of area Ac is given by the following equation:
Q_ u
¼ Ac :F R ½ðsaÞG U L ðT fi T a Þ _ p ðT fo T fi Þ ¼ mC
ð2Þ
_ UL and FR denote the collector mass In the above expressions, m, flow-rate, the heat loss coefficient and the collector heat removal factor, respectively. In normal weather conditions, the water specific heat capacity Cp is 4180 J/kg K. Cp is noted in the simulation model, based on the average water temperature Tm in the collector, as Cp = 4206.9–1.1938Tm + 0.01305T 2m in order to reduce errors between numerical and experimental outputs. A and T stand for the area in square meter and temperature in degree Celsius, respectively. Subscripts c, a, fi and fo are the collector, ambient air, the inlet fluid and the outlet fluid from the collector, respectively. The coefficient (sa) is approximately 1% greater than the product of s and a [26]. Duffie and Bekman [26] studied the effective transmittance–absorptance product. They noted that since the surface radiations proprieties are seldom known to within 1%, the effective transmittance–absorptance product can be approximated for collector with an ordinary glass by (sa) = 1.02sa, and by (sa) = 1.01sa for the collectors with covers having negligible absorption. The heat removal factor, FR, is convenient to define a quantity that relates actual useful energy gain of a collector to useful energy gain if the whole collector surface were at the fluid inlet temperature. The collector efficiency is calculated according to the characteristics and dimensions of collector elements such as the distance W between the tubes, the inner diameter Di and the outer diameter D of the tube, the thermal conductivity Cb of the plug fixing the tubes to the absorber and the sheet thickness d. The sheet metal is usually made from copper or aluminum, which have are good conductors of heat. Whillier and Saluja [27] have shown by experiments that simple wiring or clamping of the tubes to the sheet results in low bond conductance and significant loss of performance. They conclude that it is necessary to have good metal-to-metal contact so that the bond conductance is greater than 300 W/m K. The overall loss coefficient UL is the total loss of: the instantaneous rate of energy transferred to the transparent cover above the absorber plate by the process of radiation and convection,
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the instantaneous rate of energy conducted through the insulation below the plate, and the instantaneous rate of energy lost from the plate due to edge effects. UL can be obtained by an empirical equation modified by Klein [28], following the basic procedure of Hottel and Woertz [29] and Klein [30], based on more measurements.
UL ¼ C Tp
FR ¼
h
Ng
1 þ ie þ h1 e v
ðT p T a Þ N g þf
rðT p þ 1 p þ0:00591N g hv
þ
T a ÞðT 2p þ T 2a Þ 2N g þf 1þ0:133:ep eg
_ p Ac F 0 U L mC 1 exp _ p Ac U L mC
Ng
þ U ac
ð3Þ
ð4Þ
F0 is expressed by:
F0 ¼
W
h
1=U L 1 U L ½DþðWDÞF
þ C1 þ pD1i h b
i
ð5Þ
fi
For most collector designs, F is the most important of these vari0 ables in determining F . It is given by the following expression:
th½mðW DÞ=2 with m ¼ F¼ mðW DÞ=2
rffiffiffiffiffiffiffi UL k:d
ð6Þ
where Ng is the number of glass covers;
f ¼ ð1 0:089hv 0:1166hv ep Þð1 þ 0:078N g Þ; e ¼ 0:43ð1 100=T p Þ; C ¼ 520ð1 0:000051b2 Þ
0 < b < 70 b ¼ 70 if b P 70
hv = 5.7 + 3.8Vwind represents the wind convective heat transfer coefficient (W/m2 K), eg the emittance of glass cover, ep the emittance of absorber plate, Tp is the collector stagnation temperature, i.e. the temperature of the absorbing plate when the flow rate is equal to zero. By starting simulation, the first value of Tp is proposed in an iterative manner by assuming the initial temperature of inlet fluid by 10 °C to obtain the first value of UL, F0 , F, FR and Qu. Next values of Tp are calculated using the following equation:
T p ¼ T fi þ
Q u =Ac ð1 F R Þ F R UL
ð7Þ
The collector efficiency is obtained by dividing Qu by (GAc). Therefore, aÞ g ¼ AQc Gu ¼ F R :ðsaÞ F R U L ðT fi T G
_
¼ g0 a
ðT fi T a Þ G
ð8Þ
i ðMC p Þ; i dT dt
_ c C p F Ci ðT h T i Þ þ C m _ L C p F Li ðT L T i Þ ¼m _ T C p ðT i1 T i Þ þ ð1 ci Þm _ T C p ðT iþ1 T i Þ þci m K Sc;i
þ DXw
K Sc;i
i1!i
ðT i1 T i Þ DXw
iþ1!i
ðT i T iþ1 Þ U s Ss; i ðT i T a Þ ð10Þ
_ c is the mass flow rate where M is the fluid mass in the ith node; m _ L is the mass flow rate from load. Ti is the fluid from the collector; m temperature in the ith node of tank; Th is the temperature at the entrance of the tank; TL is the temperature from load. DXi?i+1 and DXi?i1 are the center-to-center distance between node i and the node below and above it, respectively. Sc,i represents a horizontal area of the section i and Ss; i is the lateral area. Moreover, Kw is assumed to be the water thermal conductivity. The left hand side of Eq. (10) describes the change of internal energy with the time. The fluid from the collector enters at the top of storage and the mains water enters at the bottom. At the end of time step any temperature inversions that from these flows are eliminated by mixing appropriate node. The first right side of this equation describes the inflow of water returning from collector into the storage. F ci is defined to determine which node receives the collector return water with a value of 1 if T i 6 T h < T i1 , otherwise it would be zero. The second term describes the inflow of cold water from the mains. F Li determine in a similar manner the liquid returning from the load. F Li = 1 if T iþ1 < T L 6 T i , otherwise it will be zero. The system used in this paper is thermosyphonic and no flow from load, _ L is zero. The value of C is 1 if the draw is used the value of m and zero otherwise. _ T C p ðT i1 T i Þ þ ð1 ci Þm _ T C p ðT i T iþ1 Þ represents The term ci m the resultant intermodal flow into segment i coming from the higher segment i 1 and the lower segment i + 1.
_T ¼m _c Which m
i1 N X X _T >0 1 if m _L F ci m F Li and ci ¼ 0 otherwise j¼1 j¼iþ1
The energy flows in a node i is depicted in Fig. 1.2. Eq. (10) represents a set of N first order ordinary differential equations that can be solved analytically for the temperatures of the N nodes as a function of time. Eq. (10) can be rewritten as:
dT i ¼ ai T i þ bi dt
ð11Þ
ai and bi yield the following equations:
1 h _ c C p F Ci þ C m _ L C p F Li þ ci m _ T C p þ ð1 ci Þm _ T Cp m ðMC p Þ K w Sc;i K w Sc;i þ þ þ U s Ss; i DX i1!i DX iþ1!i
ai ¼
From Eq:ð2Þ; outlet water temperature is : T fo ¼
Q_ u þ T fi _ c Cp m
ð9Þ
3.2. Storage tank model In order to account for the thermal stratification in the storage tank, the model adopted herein is based on the Close model [31], which consists of dividing the storage tank into N layers and feeding water from the collector to the appropriate layer, which is assumed to be fully mixed. In the present work, the model has been implemented for horizontal storage tank assuming that the tank is divided into N equal layers. Applying the energy balance for the ith node and considering the heat conduction between two adjacent nodes for tank without heating element inside it. The temperature distribution of the stratified storage tank is achieved by an energy balance on node i (i = 1 to N) as follows:
Fig. 1.2. Energy flows in a node i.
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K. Zelzouli et al. / Energy Conversion and Management xxx (2013) xxx–xxx
h
K Sc;i
_ T C p þ DXw ¼ ðMC1 p Þ ci m
bi
i
i1!i
þ
K w Sc;i
T i1 þ ðMC1 p Þ ½ð1 ci Þ þ DX
iþ1!i
_ T C p T iþ1 m
_ c C p F C T h þ Cm _ L C p F L T L þU s Ss; i T a m i i MC p
The average draw temperature can be related to Fs, the fraction of the load met by solar energy, through the following expression:
Fs ¼ The simulation algorithm is based in computing the changes in temperature over a time step for each node volume. The Eq. (10) is solved using a forward time step marching technique to obtain the instantaneous value of water temperature. In this technique (dT/dt) is replaced by (Tnew,i Ti)/Dt, where Ti and Tnew,i are the values of water temperature just before and after the time interval Dt. Initial conditions are that the water temperature at each node is equal to the mains temperature. At t + Dt, the algorithm describes the new temperature distribution into the node having the best matching temperature to these returned from the collector. The computed temperature is based on those of the adjacent nodes and the temperature of the environment taking into account the losses from the surroundings. The forward DIFFEQ technical solution method [32] gives the following equation:
bi ai Dt bi e T new;i ¼ T i ðt þ DtÞ ¼ T i ðtÞ þ ai ai
ð12Þ
The average temperature of each node over the time step Dt is defined as:
Ti ¼
1 Dt
Z
Dt
T new;i ðtÞdt ¼
0
1 Dt
Z 0
Dt
bi ai t bi e dt T i ðtÞ þ ai ai
ð13Þ
Integration of equation yields to:
Ti ¼
T i ðtÞ þ baii ai Dt
bi ebi Dt 1 ai
ð14Þ
The number of tank nodes and the time step for the numerical computation should be neatly selected to make a compromise between accuracy and computer processing time and to avoid numerical inaccuracy. As regards the thermal load, the hot water demand varies from one day to another and from one consumer to another. The unsteady consumption requires us to choose a profile of repetitive load. However, the demand volume is higher in summer, and the required temperature is higher during the winter. Therefore, the total thermal energy needs are relatively constant throughout the year. For a typical Tunisian household, the daily volume load is taken equal to the total volume of the tank at a temperature of 50 °C. In order to predict the performance of the system on an annual basis, certain assumptions had to be made: A simple user load profile that concentrates hot water consumption during one period per day is used at 18:00 H in order to know the quantity of energy can be achieved in the storage during the sunshine period. For this profile, the overall daily consumption was normalized to 200 l/day of water at 50 °C. Climatic data for Tunisia are used. The thermal efficiency based on the first law of thermodynamics (gsys) is defined as the ratio between the storage useful energy and the solar radiation incident on the collector surface:
gsys ¼
Qu G Ac
ð15Þ
The daily thermal efficiency of the system is obtained by integrating between t1 and t2 which indicates respectively the initial and the final instances of the charging period:
R t2
gsys ¼ R t2t1 t1
Q u ðtÞdt
Ac GðtÞdt
ð16Þ
5
Q solar Q load
ð17Þ
where
Q solar ¼
Z
_ p ðT draw T mains Þ ¼ M d C p ðT draw T mains Þ mC
ð18Þ
And QLoad = MdCp(Tset Tmains) the energy needed to heat the water if no solar energy is used. Where T draw is the integrated-average draw temperature during periods of draw [°C], Tset the hot water set temperature [°C], Md is the mass of total daily draw [kg]. All component models were implemented in FORTRAN and the overall system model was incorporated in time for an entire year. The FORTRAN program composed of a main algorithm and subroutines dealing the fluid properties, heat transfer, collector losses and pressure drops. The main program controls data entry, all calculations and results. It consists of two parts, the first reserved for the solar collector and the other for energy storage. At the start of simulation, the program read the input data and then manages the equations by beginning with an estimate for the overall loss coefficient UL. This is achieved with estimates of the mean plate temperature Tp. With UL, Qu from Eq. (2) can be resolved with Eq. (3), (4). With Qu, new estimates for the mean absorber temperature Eq. (7) can be computed. The new estimates for the plate temperature are then compared against the previous estimates. The program runs this sequence iteratively until an error criterion is satisfied. When this happens, the program has converged upon the correct UL, and it finishes by using Eq. (9) to calculate the outlet temperature Tfo and the collector efficiency g. The outlet collector temperature enters in the tank (taking into account the losses from the duct) to be received in the node having appropriate temperature as described previously. In the second part of the main program, energy storage, the numerical techniques used to solve for the tank temperature distribution, Eq. (10), is the DIFFEQ solution which returns an analytical solution to Eq. (11) and then the calculation of the temperature of each node over a time step. The volume of draw-off is selected by the user by selecting the local time, the draw-off duration and the load mass flow rate with selecting C = 1. At the end of the time loop (throughout the day), the program displays the daily results. 4. Results and discussion 4.1. Collector results With the technical characteristics of the collector, results such as sunshine, wind speed which is almost constant during the measurement and nearly 0.5 m/s, ambient temperature, cold water temperature are used as input parameters in a developed numerical model. The mass flow rate is of 0.042 kg/s. results are shown in Table 1. In Table 1, experimental measurements show that the solar flat plate collector increases the inlet water temperature to more than 8 °C (DT > 8 °C) with a corresponding efficiency is of 74% for an inlet water temperature nearly 23 °C, ambient temperature of 25 °C and solar irradiance of 937 W/m2. Results shows that varying the inlet water temperature affects the collector’s instantaneous efficiency. An increase in inlet temperature decreases the difference temperature DT between inlet and outlet, and hence reduces the efficiency. For high inlet water temperature (Tfi > 76 °C), DT is less than 5.5 °C and the instantaneous efficiency is below 48%. Here with the increase in inlet fluid temperature, the efficiency of the
Please cite this article in press as: Zelzouli K et al. Numerical and experimental investigation of thermosyphon solar water heater. Energy Convers Manage (2013), http://dx.doi.org/10.1016/j.enconman.2013.08.064
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Table 1 Collector results. DAT
Climatic data
Numerical 2
Experimental
Time
Ta (°C)
Tfi (°C)
G (W/m )
Tfo (°C)
gnum. (%)
Tfo (°C)
gexp. (%)
28-04-2009 29-04-2009 30-04-2009 30-04-2009 02-05-2009 02-05-2009 02-05-2009 03-05-2009 03-05-2009 03-05-2009 03-05-2009 04-05-2009 04-05-2009 04-05-2009 08-05-2009 08-05-2009
11:49:57 12:37:20 10:50:21 11:32:47 10:49:19 12:51:21 13:35:56 10:27:50 11:33:13 12:32:58 13:10:52 11:15:18 11:58:52 12:51:03 12:38:41 13:46:47
27.461 25.411 30.055 30.021 29.922 27.543 25.944 25.805 26.086 26.095 26.122 26.897 27.549 28.324 26.883 26.502
23.835 23.249 31.144 31.823 44.71 55.278 61.904 45.035 55.968 76.544 76.603 78.303 65.682 50.726 77.675 40.226
919.719 937.857 842.523 958.082 878.083 892.878 821.321 865.673 963.42 927.232 882.009 945.129 957.805 922.591 893.55 813.219
31.155 30.439 37.553 39.154 50.863 61.113 66.895 51.026 62.272 81.573 81.395 83.534 71.555 57.015 82.502 46.054
71.79 70.12 68.98 68.69 63.82 59.01 54.95 62.63 58.78 50.68 50.04 50.75 56.17 61.73 49.76 64.9
31.819 31.395 38.06 39.808 51.358 61.688 67.241 51.434 62.769 81.805 81.531 83.738 71.971 57.601 82.838 46.697
72.94 74.01 69.39 69.74 64.31 60.43 54.73 62.37 59.1 49.26 47.82 48.98 56 62.91 49.44 67.19
Ac Ac F R U L T fi ¼ b þ c T fi : T fo ¼ ðg0 G þ F R U L T a Þ þ 1 _ p _ p mC mC In Fig. 2.1b, the line intersects with y-axis where the inlet water temperature equals the ambient temperature and the collector efficiency is at its maximum. The efficiency is zero at the intersection of the line with the horizontal axis. This condition corresponds to a high temperature of the fluid into the collector or to a low radiation level, that heat losses equal solar absorption, and no useful heat delivered. This is called stagnation, which always happens when no fluid flows in the collector. g = 0.71–4.02(Tfi Ta)/G, gives a stagnation temperature of 183 °C. In Fig. 2.1a, the outlet water temperature is linear as function of the inlet temperature with a slope c = 0.95 and a line intercept b equals 9.0. The relation Tfo = 9.0 + 0.95Tfi affords an outlet water temperature equal to the inlet at 180 °C which confirms with the stagnation temperature when the collector efficiency is zero. From Table 2, comparatively with collectors performances C1-7 from the study of Andoh et al. [33], the collector characterized by the smaller heat loss FRUL = 3.55 is the best. The collector of our study (C8) having heat loss of 4.02 occupies the second rank in terms of heat loss. Here, sa represents the fraction of the solar radiation absorbed by the collector and depends mainly on the transmittance of the transparent covers and on the absorbance of the absorber. The
90 80
Tfo= 9.0+0.95.Tfi
70 60 50 40
Numerical
30
experimental
20 20
40
60
80
100
Inlet water temperature [°C] Fig. 2.1a. Collector outlet water temperature.
0.8 0.7 0.6 0.5
η
collector was observed to decrease gradually. This is because of radiation losses from the collector due to higher absorption temperature distribution. For an inlet water temperature of 78 °C, outlet water temperature is of 83 °C with thermal efficiency in order to 49% which implies that flat plate collector of selective absorber coated with black chrome can produce more energy even for very high inlet water temperatures. The instantaneous effiðT T Þ ciency g, plotted in Fig. 2.1b, is expressed as g ¼ 0:71 4:02 fi G a . Were the line intercept 0.71 is the optical behavior FR(sa) of the collector, and the slope 4.02 characterize of the collector thermal loss FRUL. 4.02 is a typical value for flat-plate solar collectors with highly selective absorber coatings. Based on the above equation, the instantaneous efficiency of the collector decreases with an increase in the collector inlet temperature for almost constant in solar radiation and ambient temperature. Fig. 2.1b shows that the selective collector with absorber coated with black chrome can achieve an efficiency up to 70% for a mass flow rate of 0.042 kgs1, a solar radiation in the vicinity of 900 W/m2, an inlet water temperature and an ambient temperature below 30 °C. From the Eqs. (2) and (9), the outlet water temperature is written as
Outlet water temperature [°C]
Day
η = 0.71-4.02x R² = 0.985
0.4 0.3
Efficiency
0.2 0.1 0 -0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
x=(Tfi-Ta)/G Fig. 2.1b. Collector efficiency.
higher this parameter is, the better the collector. UL is the collector overall heat loss coefficient. The smaller this parameter is, the best the collector. Kalogirou et al. [18] compared in their study 4 types of collectors: A (Black collector: a = 0.95, e = 0.1), B (Black collector: a = 0.85, e = 0.1), C (Color collector: a = 0.95, e = 0.9), D (Color collector: a = 0.85, e = 0.9); and results have shown that the black collectors are characterized by FRUL = 4.2 and the color collectors characterized by FRUL = 6.7. They showed also that colored collectors give about 10% lower performance than collectors painted black either for the normal paint or selective. The flat plate C8 is characterized by high performances comparatively with others in literature. 4.2. Storage tank loss coefficient Water temperature used initially is of 82.01 °C, and at the end of the cooling period (Dt = tf ti = 86400 s) it has become 73.07 °C.
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K. Zelzouli et al. / Energy Conversion and Management xxx (2013) xxx–xxx Table 2 Comparative with collectors of different parameters. Collector
Insulation
k (W/m k)
Insul. Thickness (mm)
m (kg/s)
Inst. efficiency
Cl C2 C3 C4 C5 C6 C7 C8 (our study)
Glass wool Polyurethane Polyurethane Glass wool Coconut Coir Glass fiber Glass fiber Polyurethane
0.040 0.035 0.035 0.040 0.074 0.035 0.035 0.035
40 30 40 100 50 50 50 40
0.022 – 0.033 – 0.0085 0.0083 0.002 0.042
n = 0.80–6.55 n = 0.80–9.00 n = 0.68–7.76 n = 0.74–3.55 n = 0.80–5.76 n = 0.66–8.00 n = 0.79–6.65 n = 0.71–4.02
DT/G(sa) DT/G(sa) DT/G(sa) DT/G(sa) DT/G(sa) DT/G(sa) DT/G(sa) DT/G(sa)
C1–C7 [33], C8: our study.
The average ambient temperature Ta, the water density q and the specific heat capacity Cp measured are of 26.5 °C, 0.9791 kg/l and 4189 J/kg/k, respectively. The measured storage loss coefficient is U = 1.67 W/K. The average loss coefficient per unit area is Us = 0.8 W/m2 K. This low average loss coefficient implies that the storage is very good insulated. The polyurethane and fiberglass, having the same thermal conductivity, represents the best insulating materials for heating systems. The measured value Us = 0.8 W/ m2 K is agreement to the study of Cruickshank and Harrison [34].
shown in Table 1, the calculated outlet water temperature and collector efficiency are agreement with those measured. About 0.6 °C deviation of calculated Tfo and 4% deviation of expected collector efficiency from measured were observed. The simulation study for four days of different climatic conditions was carried out. Ambient air, mains water temperature and solar radiation are measured and are used as input parameters in the simulation model. Water temperature is drawn from the top of the cylindrical horizontal storage tank, which corresponds to the temperature T at the node (i = 1). A number of 6 layers gave the best profile temperature with the experimental measurement. Numerical and experimental temperature Tsout and energy cumulated Qsout drawn are observed in the curves Fig. 2.2. We notice from figures (Fig. 2.2a and b) that the values found by simulation are very close to the experimental measurements, which allows us to suggest that the model based on technical characteristics can simulate the operation of the system with a good estimation of the performance of a thermosyphon system. The root mean square error RMSE is defined as
4.3. Thermosyphon system The storage tank is located above the collector, Fig. 1.1, and filled with mains water at morning. The system operates during the sunshine period and then the water temperature is drawn at 6:00 pm. Results in Fig. 2.2a and b have shown that the system may predict in the Spring a hot water temperature in order to 55 °C with a stored energy more than 600 kW h. During the draw from the tank, the water temperature in the top dropped from 55 °C at volume equal to 0 liters to 31 °C at volume equal to 250 l resulting in a loss of stratification. Then, the water temperature fell to 27 °C at 400 l to remains constant for the bigger volumes.
P
ðT num T exp Þ2
1=2
N
RMSE ¼
P
T exp
N
4.4. Model validation
With N the total number of value for temperatures, T, saved in the file. The root mean square error is of 0.046, 0.05, 0.049 and 0.057 for the first, second, third and fourth day of measures, respectively. This indicates that the DIFFEQ technical solution gave a good agreement with the experimental measurements.
Table 1 presents comparisons between measured and calculated Tfo and the efficiency of the collector. For the theoretical calculation, the ambient temperature and inlet water temperature and incident solar radiation are used as input parameters. As
800 600 400
T_amb(°C) G (w/m2)
200
Solar irradiance (w/m2)
ambient temperature (°C)
1000
0 6:43
9:07
11:31
13:55
16:19
18:43
Time (h:mn) T_sout num T_sout exp
50
Energy (kwh)
Temperature (°C)
60
40 30 20 10
Q_sout num Q_sout exp
0 0
200
400
volume draw-off (litres)
600
volume draw-off (litres)
Fig. 2.2. (a) Draw-off temperature profiles and (b) draw-off energy profiles.
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K. Zelzouli et al. / Energy Conversion and Management xxx (2013) xxx–xxx
For the long-term performance, results (in Fig. 2.3) are compared with those obtained by Solo program in Tecsol website [35]. A slight difference in monthly results caused by the difference in incident solar radiation, with an annual difference less than 2%.
5. Long-term performance
10 9 8 7 6 5 4 3 2 1 0
G (KWh/m2.day)
Q_cumul (KWh/day)
Mean daily efficiency (%)
Fs (%)
60 50 40 30 20 10 0
Efficiency \ Solar Fraction
Energy
Tunisia is characterized by a temperate and an abundant sunshine for the most periods of the year. The latitude, longitude, elevation above sea level and of Tunis City are respectively 36°500 N, 10°.110 E, 0 m. From the National Institute of Meteorology, the yearly climatic data for Tunis is characterized by a mean daily solar radiation is more than 2 kW h/m2 in winter and exceeds 6 kW h/m2 in summer (Fig. 2.3). The climatic data file is characterized by a series of 8760 hourly outdoor data giving the solar radiation, mains water temperature, ambient temperature and wind speed. Because a time step of 1 h cannot be used in the numerical model, the climatic data are calculated numerically with a time step of 5 min so that the mean daily values are same to those in the file. The long-term system performances calculated are given in the figure (Fig. 2.3). The results show that for this system, the highest stored energy was almost 3.4 kW h/day in months from April to September, while the lowest was 2 in January and December. This is attributed that during the summer the total incidence solar radiation and ambient temperature are higher that result in higher temperatures in the water storage tank. The highest solar fraction and lowest efficiency are obtained in summer months. The annual cumulated energy, solar fraction and efficiency are of 2.87 kW h/day, 39.04% and 31%, respectively. The annual value of energy supplied by the system under climatic conditions of Tunis City is equal to 3771 MJ. Because it is difficult to measure experimentally the monthly and annual performances, results are compared to those in Tecsol website [35] for the Tunis City using the same parameters of the system discussed in this paper. In the French approach (Tecsol), guaranteed results are calculated with the program Solo 2000, which uses monthly weather, hot water consumption data and system characteristics to calculate the monthly and yearly solar energy yield. A slight difference in monthly results is due to the difference in incident solar radiation on the solar collector. The annual incident solar radiation is the same with that in Tecsol wibsite and the error between the outputs results are less to 2%, which means that the DIFFEQ solution method, with time a step of 5 min, provides accurate results. The good consistency between experiment and simulation has proved that this method is applicable in engineering problems.
6. Effect of the collector and storage tank losses on the system performance The performance of the storage tank with insulation is significantly higher than that of the situation without insulation storage system [36] and the good insulation is one of the important parameters. Its role is to avoid the heat losses. Materials having a very low thermal conductivity are always used for insulating. The increases of heat losses to the environment lead to the decrease of the annual energy performance and economic costs. Stratification in storage tank depends on storage material and wall thermal conductivity [37]. The total storage loss coefficient that is calculated and used previously is 0.8 W/m2 K. In addition, the collector loss coefficient varies according to the collector technical characteristics and climatic data. The losses increase with the raise of the ambient temperature and reach the maximum at the afternoon and then it reduce with the drop of the ambient temperature if it is assumed that the wind speed is constant or zero. The average annual value of UL calculated is 4 W/m2 K. To search the effect of a collector and storage losses on the system performances, UL and Us are used as input parameters in the numerical model to know their effects on temperature profiles within the storage and on the long-term performance. In First, UL assumed to be constant and fixed to 4 W/m2 K and Us is varied from 0.5 to 3 W/m2 K. Results are presented in Figs. 3.1a and 3.2a. Then, Us is kept to 0.8 W/m2 K and UL is varied from 1 to 6 W/m2 K. Results are displayed in Figs. 3.1b and 3.2b. The variation of collector loss coefficient (UL) and storage loss coefficient (Us) causes the variation in the system performances and then the variation of useful energy from which the variation of temperature. In a solar collector, an enhancement of loss coefficient decreases the efficiency, and the useful energy is therefore weakened. The curves Figs. 3.1a and 3.1b show that maximum average water temperature increases respectively from 52 to 66 °C as UL reduced from 6 to 1 W/m2 K, and increases respectively from 43 to 58 °C as Us decreased from 3 to 0.5 W/m2 K. During the sunshine period in the day, water temperature (in Fig. 3.1b) increases to reach the maximum at 16:00 pm then it decreases due to the losses to the environment. From the maximum, at 16:00 pm, the lowering in water temperatures within the storage are with the same slope, which imply that the collector losses emphasize only the amount of energy added to the storage. From the curve Fig. 3.1a it is noted that the use of storage insulation with high losses (high thermal conductivity of material insulating) leads to a low water temperature within the tank. The water temperature reaches the maximum at 14:00 pm for Us of 3 W/ m2 K, and reaches the maximum at 16:00 pm for Us of 0.5 W/ m2 K. This is due to that a storage tank with high losses cannot
Averrage water temperature (°C)
8
Us=0.5 W/m.K Us=1.5 W/m2.K Us=2.5 W/m2.K
70
Us=1 W/m2.K Us=2W/m2.K Us=3 W/m2.K
60 50 40 30 20 6
8
10
12
14
16
18
Local time (h) Fig. 2.3. System performances.
Fig. 3.1a. Temperature profile in a storage tank vs. storage loss coefficient at constant collector loss coefficient.
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Average water temperature (°C)
K. Zelzouli et al. / Energy Conversion and Management xxx (2013) xxx–xxx UL=1W/m2.K UL=3W/m2.K UL=5W/m2.K
70
UL=2W/m2.K UL=4W/m2.K UL=6W/m2.K
60 50 40 30 20 6
8
10
12
14
16
18
Local time (h) Fig. 3.1b. Temperature profile in a storage tank vs. collector loss coefficient at constant storage loss coefficient.
Us=0.5W/m2.K Us=3W/m2.K
Solar fraction (%)
70
Us=1W/m2.K Us=4W/m2.K
Us=2W/m2.K
60 50 40 30 20
Dece …
Annual
Nove …
Septe …
July
Agust
May
June
April
March
January
Febrary
0
October
10
Fig. 3.2a. System performance vs. storage loss coefficient at constant collector loss coefficient of 4 W/m2 K.
Solar fraction (%)
70
UL=1W/m2.K
UL=2W/m2.K
UL=3W/m2.K
UL=4W/m2.K
UL=5W/m2.K
UL=6W/m2.K
60 50 40 30 20
Annual
Dece …
Nove …
October
July
Agust
June
May
April
March
Febrary
January
0
Septe …
10
Fig. 3.2b. System performance vs. collector loss coefficient at constant storage loss coefficient of 0.8 W/m2 K.
store more energy at afternoon. The water temperature is dropped dramatically, at afternoon, if the losses are high. From the two curves, a system having a collector loss coefficient of 6 W/m2 K with a overall storage loss coefficient of 0.8 W/m2 K can reaches a water temperature of 52 °C. By cons, a system having a storage loss coefficient of 3 W/m2 K with a collector loss coefficient of 4 W/m2 K reaches a water temperature of 43 °C. The influence of losses in the system components on the water temperature affects the long-term performances. Figs. 3.2a and 3.2b describe the monthly and yearly systems performances vs. collector and storage losses. From the Fig. 3.1a, the maximum system performance is happened in the months of July and August reaching 62%. It can be
9
seen that Fs is strongly influenced by the storage losses during summer than the winter months and this is due to the higher ambient temperature. If Us varied from 0.5 to 4 W/m2 K, Fs passes from 62% to 33% (dropped by 29%) in the summer months and from 28% to 15% (dropped by 13%) in the winter months. The high falling in summer is due to the elevated ambient temperature. The annual performances decreased from 42.6% to 23.9% when the losses varied from 0.5 to 4 W/m2 K. The tank loss coefficient is desirable in the range 0.5–1 W/m2 K. The annual performance is reduced by 6% if Us varied from 1 to 2 W/m2 K, reduced by 14% if Us varied from 1 to 4 W/m2 K, and reduced by 9% for Us passes from 2 to 4 W/m2 K. Generally, the annual performance dropped by 5% if Us enhanced by 1 W/m2.K. Fig. 3.1b shows that for a collector loss coefficient of 1 W/m2 K, the system may reach a performance of 66% in summer days and 28% in winter days with annual performance of 45%. For a collector loss coefficient of 4 W/m2, the maximum performance (56%) is obtained in August and July and the lower is of 24% in winter days with an annual performance of 38.7%. An increase in collector losses from 1 to 6 W/m2 K lowers the annual system performance from 45% to 36%. The curves suggest that the performance of a system is reduced by 9% if the collector losses increase from 1 to 6 W/ m2 K, and reduced by 6% if UL varied from 1 to 4 W/m2 K. The annual performance is reduced moderately by 2% if UL increased by 1 W/m2 K. The collector and storage loss coefficients are depend on the system materials properties. Heat losses from the collector occur from the top, sides and the bottom. Heat loss from the sides and bottom is dependent on the thermal resistance of the collector that is usually insulated. Current designs are typically insulated such that the thermal conductance level through the back and sides of the collector. The top heat loss depends on the properties of the cover, the absorber coating and the thermal resistance of the air-layer between the absorber and the cover. With the development of selective coatings for the absorber plate, a need was felt for better correlation at the lower values of plate emittance. The good collectors are usually selected according to their instantaneous efficiencies. The best who characterized by the higher value of FR(sa) and the lower value of FRUL. The collector instantaneous efficiency is affected by various factors such as the design of the absorber, materials used, the design of the absorber, the properties of glass cover, weather and operating conditions [38]. Andoh et al. [33] have shown in their study that the collector performance depends on the insulation type and thickness, the insulation thermal conductivity, the fluid flow rate, the fraction (sa) of the solar radiation absorbed by the collector. The fraction (sa), in turn, depends mainly on the transmittance of the transparent covers and on the absorbance of the absorber. Since the storage water temperature depends on the outlet collector temperature, a lofty collector useful energy is very interesting. For collectors operating at a high temperature range and upper medium temperature range, selective absorber coating is worthwhile because it reduces radiation losses significantly. The selective coating absorbers with a high selectivity ratio a/ep are needed that have both high solar absorptance and low thermal emittance to get the high performances, and there are several materials and material combinations considered to have good optical properties for this purpose. Today, the good optical properties for selective surfaces are 90% < a < 98% and 3% < ep < 10%. In addition, the insulated box reduces the heat losses from the back and sides of the collector and hence the insulating material must has very low thermal conductivity. Even, the wind speed has a strong effect on the thermal losses and preferably the system is kept in a location protected from the wind to cut the thermal losses.
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K. Zelzouli et al. / Energy Conversion and Management xxx (2013) xxx–xxx
7. Conclusion A dynamical model for solar domestic water heaters with a horizontal storage tank has been developed. Numerical results show a fairly agreement with experimental measurements. Numerical results showed that DIFFEQ technical solution allows predicting the real performance of the system. Results have shown that the polyurethane is a very good material for insulating thermal systems, and have shown that a very good insulated storage tank coupled with a flat plate collector having selective absorber of FR(sa) = 0.71 and FRUL = 4.02 can yield annual performance of 39%. Results have shown also that the water temperature degradation in thermal storage tank is strongly influenced by the collector and the storage loss coefficients, and showed that performance of the storage tank is more influenced by the losses from the storage than the losses from the flat plate collector. A decrease in collector loss coefficient by 1 W/m2 K increases the annual performances by 2%. The annual performance increases by 5% if the storage loss coefficient reduced by 1 W/m2 K. References [1] Kalogirou SA. Thermal performance, economic and environmental life cycle analysis of thermosiphon solar water heaters. Sol Energy 2009;83:39–48. [2] Uhlemann R, Bansal NK. Side-by-side comparison of a pressurized and a nonpressurized solar water heating thermosiphon system. Sol Energy 1985;34:317–28. [3] Hobson PA, Norton B. Verified accurate performance simulation model of direct thermosyphon solar energy water heaters. J Sol Energy Eng 1988;110(4):282–92. [4] Norton B, Edmonds JEJ, Kovolos E. Dynamic simulation of indirect thermosyphon solar energy water heaters. Renewable Energy 1992;2:283–97. [5] Prapas DE, Psimmenos S, Sotiropoulos BA. Beneficial interconnection of two thermosiphon DHW solar systems. Appl Energy 1994;49:47–60. [6] Helwa NH, Mobarak AM, El-Sallak MS, El-Ghetany HH. Effect of hot-water consumption on temperature distribution in a horizontal solar water storage tank. Appl Energy 1995;52:185–97. [7] Kalogirou SA, Panteliou S. Thermosiphon solar domestic water heating systems: longterm performance prediction using artificial neural networks. Sol Energy 2000;69(2):163–74. [8] Carrillo Andrés A, Cejudo López JM. TRNSYS model of a thermosiphon solar domestic water heater with a horizontal store and mantle heat exchanger. Sol Energy 2002;72(2):89–98. [9] Koffi PME, Andoh HY, Gbaha P, Touré S, Ado G. Theoretical and experimental study of solar water heater with internal exchanger using thermosiphon system. Energy Convers Manage 2008;49:2279–90. [10] Tang R, Cheng Y, Wu M, Li Z, Yu Y. Experimental and modeling studies on thermosiphon domestic solar water heaters with flat-plate collectors at clear nights. Energy Convers Manage 2010;51:2548–56. [11] Hasan A. Thermosyphon solar water heaters: effect of storage tank volume and configuration on efficiency. Energy Convers Manage 1997;38(9):847–54. [12] Mar HYB, Peterson RE, Zimmer PB. Low cost coatings for flat plate solar collectors. Thin Solid Films 1976;39:95–103.
[13] Lampert CM. Coatings for enhanced photothermal energy collection. Solar Energy Mater 1979;1:319–41. [14] Vasudevan N, William Grips VK, Rajagopalan Indira. The present status of black chromium plating. Surf Technol 1981;14:119–32. [15] Shanker K, Holloway PH. Electrodeposition of black chrome selective solar absorber coatings with improved thermal stability. Thin Solid Films 1985;127:181–9. [16] Inal OT, Valayapetre M, Murr LE, Torma AE. Microstructural and mechanical property evaluation of black-chrome coated solar collectors-II. Solar Energy Mater 1981;4:333–58. [17] Driver PM. An electrochemical approach to the characterisation of black chrome selective surfaces. Solar Energy Mater 1981;4:179–202. [18] Kalogirou S, Tripanagnostopoulos Y, Souliotis M. Performance of solar systems employing collectors with colored absorber. Energy Build 2005;37:824–35. [19] Tripanagnostopoulos Y, Souliotis M, Nousia TH. Solar collectors with colored absorbers. Sol Energy 2000;68(4):343–56. [20] Technology Roadmap-Solar Heating and Cooling. IEA, Paris; 2012. [21] Khalifa A-JN, Mehdi MM. On the verification of one dimensional heat flow in a horizontal thermosyphon storage tank. Energy Convers Manage 1999;40:961– 74. [22] Huang BJ, Hsieh CT. A simulation method for solar thermosyphon collector. Sol Energy 1985;35(1):31–43. [23] Engineering toolbox website,. [24] Madhlopa A, Mgawi R, Taulo J. Experimental study of temperature stratification in an integrated collector–storage solar water heater with two horizontal tanks. Sol Energy 2006;80:989–1002. [25] Fooladi F, Taheriani H. Experimental study of a multi tube ICS solar water heating system in mild climates. Appl Solar Energy 2010;46(1):20–8. [26] Duffie JA, Beckman WA. Solar engineering of thermal processes. 3rd ed. New York: John Wiley & Sons; 1993. [27] Whillier A, Saluja G. Effects of materials and of construction details on the thermal performance of solar water heaters. Sol Energy 1965;9:21–6. [28] Klein SA. Calculation of the monthly-average transmittance–absorptance product. Sol Energy 1979;23(6):547–51. [29] Hottel HC, Woertz BB. Performance of flat plate solar heat collectors. Trans ASME 1942;64:91–102. [30] Klein SA. Calculation of flat-plate collector loss coefficients. Sol Energy 1975;17(1):79–80. [31] Close DJA. Design approach for solar processes. Sol Energy 1967;11(2):112–22. [32] Newton BJ. Modelling of solar storage tanks. Wisconsin-Madison: M.S thesis; 1995. [33] Andoh HY, Gbaha P, Koua BK, Koffi PME, Touré S. Thermal performance study of a solar collector using a natural vegetable fiber, coconut coir, as heat insulation. Energy Sustain Dev 2010;14:297–301. [34] Cruickshank CA, Harrison SJ. Heat loss characteristics for a typical solar domestic hot water storage. Energy Build 2010;42:1703–10. [35] Tecsol website, Hot water calculations; 1999. availably on:
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Numerical and experimental investigation of thermosyphon solar water heater Khaled Zelzouli ⇑, Amenallah Guizani, Chakib Kerkeni Thermal Processes Laboratory, (CRTEn), Borj Cedria B.P N°95 2050, Hammam Lif, Tunisia
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Performance collector Storage tank Long-term performance Numerical investigation
a b s t r a c t A glassed flat plate collector with selective black chrome coated absorber and a low wall conductance horizontal storage are combined in order to set up a high performance thermosyphon system. Each component is tested separately before testing the complete system in spring days. During the test period, effect of different inlet water temperatures on the collector performance is studied and results have shown that the collector can reach a high efficiency and high outlet water temperature even for elevated inlet water temperatures. Subsequently, long term system performance is estimated by using a developed numerical model. The proposed model, accurate and gave a good agreement with experimental results, allowed to describe the heat transfer in the storage. It has shown also that the long-term performances are strongly influenced by losses from the storage than losses from the collector. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Solar water heater is one of the most successful solar technologies. Nowadays, world’s demand of energy has dramatically increased; furthermore, process to collect hot water by solar radiation is yet expensive. Most solar water heater designs used for single family are the closed and opened solar water heating systems. These two systems are categorized into two groups: forced circulation and natural convection. The advantages of thermosyphon systems are that they do not rely on pumps and controllers, are more reliable, and have a longer life than forced circulation systems [1]. Thermosyphonic systems are studied intensively by many researches [2–10]. Hasan [11] studied the effect of the hot water storage tank volume and configuration on system efficiency and he concluded that there is no difference between the performances of vertical and horizontal storage tank systems, and concluded that the efficiency of a SWH system can be increased by using a larger hot water storage tank or smaller collectors area. The technical performance and reliability of solar systems are key parameters that can significantly vary the production of thermal energy and thus the cost effectiveness. The two main parameters, to get a reliable system, are the storage insulation and the collector performances. A very good insulated storage and a highly efficient collector leads to a profitable system in all months of the year and mainly in the countries having good sunshine climate. Tunisia is one of these countries which characterized by a temperate and an abundant sunshine for the most periods of the year. A typical flat ⇑ Corresponding author. Tel.: +216 22025245/79325053; fax: 216 79325825. E-mail address: [email protected] (K. Zelzouli).
plate solar collector consists of an absorber in an insulated box with transparent cover sheets (glazing). The absorber is usually made of a metal sheet characterized by a high thermal conductivity with attached or integrated tubes. For the collectors having high performances, its absorbers surfaces are coated with a special selective material to maximize radiant energy absorption while minimizing radiant energy emission. The best selective absorbers present selectivity values over 10, denoting higher sunlight energy absorption and lower thermal energy losses. The insulated box reduces heat losses from the back and sides of the collector. The flat plate collector of selective absorber coated with black chrome is one of best collectors used for heating water. For the complete system, the storage must be insulated with very low thermal conductivity materials. Black chrome for selective absorbers and collector efficiency vs. coating properties are studied in [12–17]. Kalogirou et al. [18] introduced in their study, performance of solar systems employing collectors with colored absorber, that the flat plate collectors of highly selective coatings can reach stagnation temperatures of more than 200 °C and they showed that the colored collectors present lower efficiency than the typical black type collectors. Tripanagnostopoulos et al. [19] studied the solar collectors with colored absorbers and they concluded that selective colored absorbers are efficient in wider range of operating temperatures than absorbers with color paints of high emissivity. Recently, the International Energy Agency issued a Technology Roadmap for Solar Heating and Cooling [20] which estimates the potential for domestic hot water in Africa and the Middle East in the range of 2 Ej/year. For the long term calculation, a number of computer software programs have been developed concerning the modeling and
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simulation of thermal systems. The minimum energy requirement is generally calculated using appropriate software packages (e.g., F-Chart, Transys, T*Sol and Solo) and based on monthly or daily means of climatic data, and the mean storage temperature. Many theoretical models are currently available for the estimation of the thermal stratification within storage tanks, and among the used models, is the one dimensional model. Khalifa and Mehdi [21] studied the verification of the one dimensional heat flow in a horizontal thermosyphon storage tank and they concluded that the heat flow in the tank may be considered one dimensional. Moreover, computer programs are more accurate with smaller time steps. Huang and Hsieh [22] studied the effect of computation time step on temperature distribution with five tank sections choosing 6, 10, 15 and 20 min time steps, and results have shown a good agreement with the experiments. They claimed that the computation time step in simulation can be as large as 15 min with good accuracy even for the worst cases; thus it can save a significant amount of computation time. In this paper, our main objective is to build a high performance solar collector coupled with good insulated storage tank for use in domestic hot water as well as for industrial energy. The storage, of 200 l insulated with polyurethane foam, is located horizontally above a flat plate collector of 1.93 m2 aperture area having a selective absorber coated with black chrome. Long-term prediction of the proposed system will be performed thanks to a numerical model developed in this study. The developed model describes the energy flows within the storage based on a differential equations solution method and the technical characteristics of the proposed system. It yields the hourly, daily, monthly and annual performances. The experimental work is achieved in spring to identify the system efficiency in days characterized by the soft climatic weather. Tests are achieved in the Laboratory of Thermal Processes (L.P.T) in Borj Cedria, Tunis, Tunisia. Numerical results expected are the system drawn water temperature energy, efficiency and system performance. Results are validated with the experimental measurements and they have shown that the model can provide accurate results. 2. System description and test procedure 2.1. System description The experiment is designed to investigate the system performances. Before coupling the collector with the storage, each component is tested separately. In the First days, the collector outputs are obtained. In the next days, the storage loss coefficient is determined. Then, the complete system performance is studied. Fig. 1.1 illustrates the schematic of the amenities used in the experiment. The pyranometer of type KIPP & Zonen CM11, to measure solar radiation, is placed near the top of the solar collector at the same inclination and azimuth of the solar plan. Water temperatures are measured using RTD (Pt100) sensors having the greatest temperature stability and characterized by a good linearity with a sensitiveness ±0.1% °C. Two sensors placed at the inlet and outlet of the collector to measure inlet and outlet fluid temperatures, and another used to determine the draw-off fluid temperature from the tank. The sensor for measuring the ambient temperature is placed at a height of 1.25 m from the surface of the test site. The wind speed is measured by a cup anemometer consisted of three hemispherical cups each mounted on one end of horizontal arms, which in turn were mounted at equal angles to each other on a vertical shaft. The water flow rate is measured by a Flow Meter, of float type, that is installed in the system in the outlet of hot water. The measurements are performed using a Data acquisition type Agilent 34970A.
The collector is titled of 38° to horizontal surface and oriented to the south. It is a selective collector, which has dimensions of 1.98 1.041 0.09 [m] with one glass cover of thickness of 4 mm, an aperture area of 1.93 m2 and 10 risers with inner diameter of 12 mm and outer diameter of 14 mm. The absorber thickness d, absorptance ap, emittance ep and absorption-transmittance sa are 12.103 mm, 0.95, 0.1 and 0.86, respectively. The bottom and edges thickness of the collector are 40 mm with thermal conductivity k of 0.035 W/m K. The horizontal cylindrical water storage tank, of 200 l, is insulated by 4 cm of injected polyurethane foam with density of 40 kg/m3. The polyurethane foam is one of the best insulating materials, having a very low thermal conductivity. The polyurethane thermal conductivity k is in the range of 0.02–0.035 for temperatures below 100 °C [23]. The storage inner area and insulation thickness are 2.1 m2 and 5 cm, respectively. 2.2. Test procedure 2.2.1. Collector performances test A test sequence contains a number of consecutive days of measurements are carried out. Various inlet water temperatures are inserted to acquire information about the collector performance. The experiments were conducted in the months of April and May and the outputs (outlet water temperatures, instantaneous efficiencies, solar radiation and ambient temperature) were recorded. The program used for this test is the HP-VEE; it is designed according to the standards for testing solar collectors following the flow chart below and is as follows: (i) When the program starts, the data logger initializes the different probes, anemometer, flow meter and the pyranometer at a measurement frequency of 10 s. (ii) After assigning the set point temperature, the program always takes the final values given by the data logger and the measures of the difference (Tfo Tfi) should not exceed 0.1 °C and the sunshine G must be greater to 800 W/m2. (iii) Once the gap is stable during 15 min, the program proceeds to the recording of data acquired for 90 successive values and stop recording automatically. The procedure is as follows:
The program automatically opens an excel file; this file shows instantaneous values as ambient temperature Ta; collector inlet, outlet, difference and mean water temperature; solar radiation G (W/m2), the collector efficiency. 2.2.2. Storage loss test sequence This sequence intends to identify the overall store losses. The store overnight heat loss coefficient is obtained in an independent test where the system with a hot storage tank is left to cool down
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Tsout Cup Ananometer Flow Meter
Tfo Pyranometer
Ta
Tfi Thermocouple Fig. 1.1. Schematic of the amenities used in the experiment.
during about 24 h. To calculate the storage heat loss coefficient, the computation strategy consists of:
3. Mathematical model 3.1. Solar collector
(i) Filling the tank with hot water temperature initially at Ti P 70 °C. (ii) The tank is allowed to cool in a room for at least a 24 h period. (iii) The store is brought to uniform temperature using a circulation pump, then measuring the final temperature Tf. The average ambient temperature Ta during the cooling period is calculated by the data logger. The total storage loss coefficient during the 24 h (from 18:00 h to 18:00 the next day) is calculated with a log-mean temperature difference [24,25]:
U¼
qVC p Dt
Log
Ti Ta Tf Ta
ð1Þ
where T i and T f are the initial and final average water temperature during the test period Dt. For the whole system, the storage tank is located horizontally above the collector. The system was heated from 8:00am to 6:00 pm with no draw-off during the charging period. From 6:00 pm, during 1 h, the water is drawn three times the tank volume with a fixed flow rate of 10 l/min. 2.2.3. Store energy test In this stage, the storage is located above the collector (Fig. 1.1) and filled with mains water. During 4 days of measurement, a daily test is effected by allowing the system operates during the period of irradiation and then withdrawing the water at the end of the day. Draw-off temperature profiles are determined for different withdrawn volumes. 2.3. Uncertainty analysis Uncertainty analysis is required to prove the accuracy of the experiments. In this study, errors came from the susceptibility of equipment and measurements explained previously. First, errors due to measurement of temperature are: Susceptibility of data logging system, around ±0.1% °C. Measurement error is ±0.2%. Susceptibility of the thermocouple is ±0.1% °C. The susceptibility was obtained from a catalog of the instruments. Second, errors came from the measurement of the flow rate: the susceptibility of the flow meter is about ±0.1% and errors due to measurement are about ±0.1%.
The collector performance is described by energy balance such as the distribution of incident solar energy and thermal and optical losses. The useful energy output from a collector of area Ac is given by the following equation:
Q_ u
¼ Ac :F R ½ðsaÞG U L ðT fi T a Þ _ p ðT fo T fi Þ ¼ mC
ð2Þ
_ UL and FR denote the collector mass In the above expressions, m, flow-rate, the heat loss coefficient and the collector heat removal factor, respectively. In normal weather conditions, the water specific heat capacity Cp is 4180 J/kg K. Cp is noted in the simulation model, based on the average water temperature Tm in the collector, as Cp = 4206.9–1.1938Tm + 0.01305T 2m in order to reduce errors between numerical and experimental outputs. A and T stand for the area in square meter and temperature in degree Celsius, respectively. Subscripts c, a, fi and fo are the collector, ambient air, the inlet fluid and the outlet fluid from the collector, respectively. The coefficient (sa) is approximately 1% greater than the product of s and a [26]. Duffie and Bekman [26] studied the effective transmittance–absorptance product. They noted that since the surface radiations proprieties are seldom known to within 1%, the effective transmittance–absorptance product can be approximated for collector with an ordinary glass by (sa) = 1.02sa, and by (sa) = 1.01sa for the collectors with covers having negligible absorption. The heat removal factor, FR, is convenient to define a quantity that relates actual useful energy gain of a collector to useful energy gain if the whole collector surface were at the fluid inlet temperature. The collector efficiency is calculated according to the characteristics and dimensions of collector elements such as the distance W between the tubes, the inner diameter Di and the outer diameter D of the tube, the thermal conductivity Cb of the plug fixing the tubes to the absorber and the sheet thickness d. The sheet metal is usually made from copper or aluminum, which have are good conductors of heat. Whillier and Saluja [27] have shown by experiments that simple wiring or clamping of the tubes to the sheet results in low bond conductance and significant loss of performance. They conclude that it is necessary to have good metal-to-metal contact so that the bond conductance is greater than 300 W/m K. The overall loss coefficient UL is the total loss of: the instantaneous rate of energy transferred to the transparent cover above the absorber plate by the process of radiation and convection,
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the instantaneous rate of energy conducted through the insulation below the plate, and the instantaneous rate of energy lost from the plate due to edge effects. UL can be obtained by an empirical equation modified by Klein [28], following the basic procedure of Hottel and Woertz [29] and Klein [30], based on more measurements.
UL ¼ C Tp
FR ¼
h
Ng
1 þ ie þ h1 e v
ðT p T a Þ N g þf
rðT p þ 1 p þ0:00591N g hv
þ
T a ÞðT 2p þ T 2a Þ 2N g þf 1þ0:133:ep eg
_ p Ac F 0 U L mC 1 exp _ p Ac U L mC
Ng
þ U ac
ð3Þ
ð4Þ
F0 is expressed by:
F0 ¼
W
h
1=U L 1 U L ½DþðWDÞF
þ C1 þ pD1i h b
i
ð5Þ
fi
For most collector designs, F is the most important of these vari0 ables in determining F . It is given by the following expression:
th½mðW DÞ=2 with m ¼ F¼ mðW DÞ=2
rffiffiffiffiffiffiffi UL k:d
ð6Þ
where Ng is the number of glass covers;
f ¼ ð1 0:089hv 0:1166hv ep Þð1 þ 0:078N g Þ; e ¼ 0:43ð1 100=T p Þ; C ¼ 520ð1 0:000051b2 Þ
0 < b < 70 b ¼ 70 if b P 70
hv = 5.7 + 3.8Vwind represents the wind convective heat transfer coefficient (W/m2 K), eg the emittance of glass cover, ep the emittance of absorber plate, Tp is the collector stagnation temperature, i.e. the temperature of the absorbing plate when the flow rate is equal to zero. By starting simulation, the first value of Tp is proposed in an iterative manner by assuming the initial temperature of inlet fluid by 10 °C to obtain the first value of UL, F0 , F, FR and Qu. Next values of Tp are calculated using the following equation:
T p ¼ T fi þ
Q u =Ac ð1 F R Þ F R UL
ð7Þ
The collector efficiency is obtained by dividing Qu by (GAc). Therefore, aÞ g ¼ AQc Gu ¼ F R :ðsaÞ F R U L ðT fi T G
_
¼ g0 a
ðT fi T a Þ G
ð8Þ
i ðMC p Þ; i dT dt
_ c C p F Ci ðT h T i Þ þ C m _ L C p F Li ðT L T i Þ ¼m _ T C p ðT i1 T i Þ þ ð1 ci Þm _ T C p ðT iþ1 T i Þ þci m K Sc;i
þ DXw
K Sc;i
i1!i
ðT i1 T i Þ DXw
iþ1!i
ðT i T iþ1 Þ U s Ss; i ðT i T a Þ ð10Þ
_ c is the mass flow rate where M is the fluid mass in the ith node; m _ L is the mass flow rate from load. Ti is the fluid from the collector; m temperature in the ith node of tank; Th is the temperature at the entrance of the tank; TL is the temperature from load. DXi?i+1 and DXi?i1 are the center-to-center distance between node i and the node below and above it, respectively. Sc,i represents a horizontal area of the section i and Ss; i is the lateral area. Moreover, Kw is assumed to be the water thermal conductivity. The left hand side of Eq. (10) describes the change of internal energy with the time. The fluid from the collector enters at the top of storage and the mains water enters at the bottom. At the end of time step any temperature inversions that from these flows are eliminated by mixing appropriate node. The first right side of this equation describes the inflow of water returning from collector into the storage. F ci is defined to determine which node receives the collector return water with a value of 1 if T i 6 T h < T i1 , otherwise it would be zero. The second term describes the inflow of cold water from the mains. F Li determine in a similar manner the liquid returning from the load. F Li = 1 if T iþ1 < T L 6 T i , otherwise it will be zero. The system used in this paper is thermosyphonic and no flow from load, _ L is zero. The value of C is 1 if the draw is used the value of m and zero otherwise. _ T C p ðT i1 T i Þ þ ð1 ci Þm _ T C p ðT i T iþ1 Þ represents The term ci m the resultant intermodal flow into segment i coming from the higher segment i 1 and the lower segment i + 1.
_T ¼m _c Which m
i1 N X X _T >0 1 if m _L F ci m F Li and ci ¼ 0 otherwise j¼1 j¼iþ1
The energy flows in a node i is depicted in Fig. 1.2. Eq. (10) represents a set of N first order ordinary differential equations that can be solved analytically for the temperatures of the N nodes as a function of time. Eq. (10) can be rewritten as:
dT i ¼ ai T i þ bi dt
ð11Þ
ai and bi yield the following equations:
1 h _ c C p F Ci þ C m _ L C p F Li þ ci m _ T C p þ ð1 ci Þm _ T Cp m ðMC p Þ K w Sc;i K w Sc;i þ þ þ U s Ss; i DX i1!i DX iþ1!i
ai ¼
From Eq:ð2Þ; outlet water temperature is : T fo ¼
Q_ u þ T fi _ c Cp m
ð9Þ
3.2. Storage tank model In order to account for the thermal stratification in the storage tank, the model adopted herein is based on the Close model [31], which consists of dividing the storage tank into N layers and feeding water from the collector to the appropriate layer, which is assumed to be fully mixed. In the present work, the model has been implemented for horizontal storage tank assuming that the tank is divided into N equal layers. Applying the energy balance for the ith node and considering the heat conduction between two adjacent nodes for tank without heating element inside it. The temperature distribution of the stratified storage tank is achieved by an energy balance on node i (i = 1 to N) as follows:
Fig. 1.2. Energy flows in a node i.
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K. Zelzouli et al. / Energy Conversion and Management xxx (2013) xxx–xxx
h
K Sc;i
_ T C p þ DXw ¼ ðMC1 p Þ ci m
bi
i
i1!i
þ
K w Sc;i
T i1 þ ðMC1 p Þ ½ð1 ci Þ þ DX
iþ1!i
_ T C p T iþ1 m
_ c C p F C T h þ Cm _ L C p F L T L þU s Ss; i T a m i i MC p
The average draw temperature can be related to Fs, the fraction of the load met by solar energy, through the following expression:
Fs ¼ The simulation algorithm is based in computing the changes in temperature over a time step for each node volume. The Eq. (10) is solved using a forward time step marching technique to obtain the instantaneous value of water temperature. In this technique (dT/dt) is replaced by (Tnew,i Ti)/Dt, where Ti and Tnew,i are the values of water temperature just before and after the time interval Dt. Initial conditions are that the water temperature at each node is equal to the mains temperature. At t + Dt, the algorithm describes the new temperature distribution into the node having the best matching temperature to these returned from the collector. The computed temperature is based on those of the adjacent nodes and the temperature of the environment taking into account the losses from the surroundings. The forward DIFFEQ technical solution method [32] gives the following equation:
bi ai Dt bi e T new;i ¼ T i ðt þ DtÞ ¼ T i ðtÞ þ ai ai
ð12Þ
The average temperature of each node over the time step Dt is defined as:
Ti ¼
1 Dt
Z
Dt
T new;i ðtÞdt ¼
0
1 Dt
Z 0
Dt
bi ai t bi e dt T i ðtÞ þ ai ai
ð13Þ
Integration of equation yields to:
Ti ¼
T i ðtÞ þ baii ai Dt
bi ebi Dt 1 ai
ð14Þ
The number of tank nodes and the time step for the numerical computation should be neatly selected to make a compromise between accuracy and computer processing time and to avoid numerical inaccuracy. As regards the thermal load, the hot water demand varies from one day to another and from one consumer to another. The unsteady consumption requires us to choose a profile of repetitive load. However, the demand volume is higher in summer, and the required temperature is higher during the winter. Therefore, the total thermal energy needs are relatively constant throughout the year. For a typical Tunisian household, the daily volume load is taken equal to the total volume of the tank at a temperature of 50 °C. In order to predict the performance of the system on an annual basis, certain assumptions had to be made: A simple user load profile that concentrates hot water consumption during one period per day is used at 18:00 H in order to know the quantity of energy can be achieved in the storage during the sunshine period. For this profile, the overall daily consumption was normalized to 200 l/day of water at 50 °C. Climatic data for Tunisia are used. The thermal efficiency based on the first law of thermodynamics (gsys) is defined as the ratio between the storage useful energy and the solar radiation incident on the collector surface:
gsys ¼
Qu G Ac
ð15Þ
The daily thermal efficiency of the system is obtained by integrating between t1 and t2 which indicates respectively the initial and the final instances of the charging period:
R t2
gsys ¼ R t2t1 t1
Q u ðtÞdt
Ac GðtÞdt
ð16Þ
5
Q solar Q load
ð17Þ
where
Q solar ¼
Z
_ p ðT draw T mains Þ ¼ M d C p ðT draw T mains Þ mC
ð18Þ
And QLoad = MdCp(Tset Tmains) the energy needed to heat the water if no solar energy is used. Where T draw is the integrated-average draw temperature during periods of draw [°C], Tset the hot water set temperature [°C], Md is the mass of total daily draw [kg]. All component models were implemented in FORTRAN and the overall system model was incorporated in time for an entire year. The FORTRAN program composed of a main algorithm and subroutines dealing the fluid properties, heat transfer, collector losses and pressure drops. The main program controls data entry, all calculations and results. It consists of two parts, the first reserved for the solar collector and the other for energy storage. At the start of simulation, the program read the input data and then manages the equations by beginning with an estimate for the overall loss coefficient UL. This is achieved with estimates of the mean plate temperature Tp. With UL, Qu from Eq. (2) can be resolved with Eq. (3), (4). With Qu, new estimates for the mean absorber temperature Eq. (7) can be computed. The new estimates for the plate temperature are then compared against the previous estimates. The program runs this sequence iteratively until an error criterion is satisfied. When this happens, the program has converged upon the correct UL, and it finishes by using Eq. (9) to calculate the outlet temperature Tfo and the collector efficiency g. The outlet collector temperature enters in the tank (taking into account the losses from the duct) to be received in the node having appropriate temperature as described previously. In the second part of the main program, energy storage, the numerical techniques used to solve for the tank temperature distribution, Eq. (10), is the DIFFEQ solution which returns an analytical solution to Eq. (11) and then the calculation of the temperature of each node over a time step. The volume of draw-off is selected by the user by selecting the local time, the draw-off duration and the load mass flow rate with selecting C = 1. At the end of the time loop (throughout the day), the program displays the daily results. 4. Results and discussion 4.1. Collector results With the technical characteristics of the collector, results such as sunshine, wind speed which is almost constant during the measurement and nearly 0.5 m/s, ambient temperature, cold water temperature are used as input parameters in a developed numerical model. The mass flow rate is of 0.042 kg/s. results are shown in Table 1. In Table 1, experimental measurements show that the solar flat plate collector increases the inlet water temperature to more than 8 °C (DT > 8 °C) with a corresponding efficiency is of 74% for an inlet water temperature nearly 23 °C, ambient temperature of 25 °C and solar irradiance of 937 W/m2. Results shows that varying the inlet water temperature affects the collector’s instantaneous efficiency. An increase in inlet temperature decreases the difference temperature DT between inlet and outlet, and hence reduces the efficiency. For high inlet water temperature (Tfi > 76 °C), DT is less than 5.5 °C and the instantaneous efficiency is below 48%. Here with the increase in inlet fluid temperature, the efficiency of the
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Table 1 Collector results. DAT
Climatic data
Numerical 2
Experimental
Time
Ta (°C)
Tfi (°C)
G (W/m )
Tfo (°C)
gnum. (%)
Tfo (°C)
gexp. (%)
28-04-2009 29-04-2009 30-04-2009 30-04-2009 02-05-2009 02-05-2009 02-05-2009 03-05-2009 03-05-2009 03-05-2009 03-05-2009 04-05-2009 04-05-2009 04-05-2009 08-05-2009 08-05-2009
11:49:57 12:37:20 10:50:21 11:32:47 10:49:19 12:51:21 13:35:56 10:27:50 11:33:13 12:32:58 13:10:52 11:15:18 11:58:52 12:51:03 12:38:41 13:46:47
27.461 25.411 30.055 30.021 29.922 27.543 25.944 25.805 26.086 26.095 26.122 26.897 27.549 28.324 26.883 26.502
23.835 23.249 31.144 31.823 44.71 55.278 61.904 45.035 55.968 76.544 76.603 78.303 65.682 50.726 77.675 40.226
919.719 937.857 842.523 958.082 878.083 892.878 821.321 865.673 963.42 927.232 882.009 945.129 957.805 922.591 893.55 813.219
31.155 30.439 37.553 39.154 50.863 61.113 66.895 51.026 62.272 81.573 81.395 83.534 71.555 57.015 82.502 46.054
71.79 70.12 68.98 68.69 63.82 59.01 54.95 62.63 58.78 50.68 50.04 50.75 56.17 61.73 49.76 64.9
31.819 31.395 38.06 39.808 51.358 61.688 67.241 51.434 62.769 81.805 81.531 83.738 71.971 57.601 82.838 46.697
72.94 74.01 69.39 69.74 64.31 60.43 54.73 62.37 59.1 49.26 47.82 48.98 56 62.91 49.44 67.19
Ac Ac F R U L T fi ¼ b þ c T fi : T fo ¼ ðg0 G þ F R U L T a Þ þ 1 _ p _ p mC mC In Fig. 2.1b, the line intersects with y-axis where the inlet water temperature equals the ambient temperature and the collector efficiency is at its maximum. The efficiency is zero at the intersection of the line with the horizontal axis. This condition corresponds to a high temperature of the fluid into the collector or to a low radiation level, that heat losses equal solar absorption, and no useful heat delivered. This is called stagnation, which always happens when no fluid flows in the collector. g = 0.71–4.02(Tfi Ta)/G, gives a stagnation temperature of 183 °C. In Fig. 2.1a, the outlet water temperature is linear as function of the inlet temperature with a slope c = 0.95 and a line intercept b equals 9.0. The relation Tfo = 9.0 + 0.95Tfi affords an outlet water temperature equal to the inlet at 180 °C which confirms with the stagnation temperature when the collector efficiency is zero. From Table 2, comparatively with collectors performances C1-7 from the study of Andoh et al. [33], the collector characterized by the smaller heat loss FRUL = 3.55 is the best. The collector of our study (C8) having heat loss of 4.02 occupies the second rank in terms of heat loss. Here, sa represents the fraction of the solar radiation absorbed by the collector and depends mainly on the transmittance of the transparent covers and on the absorbance of the absorber. The
90 80
Tfo= 9.0+0.95.Tfi
70 60 50 40
Numerical
30
experimental
20 20
40
60
80
100
Inlet water temperature [°C] Fig. 2.1a. Collector outlet water temperature.
0.8 0.7 0.6 0.5
η
collector was observed to decrease gradually. This is because of radiation losses from the collector due to higher absorption temperature distribution. For an inlet water temperature of 78 °C, outlet water temperature is of 83 °C with thermal efficiency in order to 49% which implies that flat plate collector of selective absorber coated with black chrome can produce more energy even for very high inlet water temperatures. The instantaneous effiðT T Þ ciency g, plotted in Fig. 2.1b, is expressed as g ¼ 0:71 4:02 fi G a . Were the line intercept 0.71 is the optical behavior FR(sa) of the collector, and the slope 4.02 characterize of the collector thermal loss FRUL. 4.02 is a typical value for flat-plate solar collectors with highly selective absorber coatings. Based on the above equation, the instantaneous efficiency of the collector decreases with an increase in the collector inlet temperature for almost constant in solar radiation and ambient temperature. Fig. 2.1b shows that the selective collector with absorber coated with black chrome can achieve an efficiency up to 70% for a mass flow rate of 0.042 kgs1, a solar radiation in the vicinity of 900 W/m2, an inlet water temperature and an ambient temperature below 30 °C. From the Eqs. (2) and (9), the outlet water temperature is written as
Outlet water temperature [°C]
Day
η = 0.71-4.02x R² = 0.985
0.4 0.3
Efficiency
0.2 0.1 0 -0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
x=(Tfi-Ta)/G Fig. 2.1b. Collector efficiency.
higher this parameter is, the better the collector. UL is the collector overall heat loss coefficient. The smaller this parameter is, the best the collector. Kalogirou et al. [18] compared in their study 4 types of collectors: A (Black collector: a = 0.95, e = 0.1), B (Black collector: a = 0.85, e = 0.1), C (Color collector: a = 0.95, e = 0.9), D (Color collector: a = 0.85, e = 0.9); and results have shown that the black collectors are characterized by FRUL = 4.2 and the color collectors characterized by FRUL = 6.7. They showed also that colored collectors give about 10% lower performance than collectors painted black either for the normal paint or selective. The flat plate C8 is characterized by high performances comparatively with others in literature. 4.2. Storage tank loss coefficient Water temperature used initially is of 82.01 °C, and at the end of the cooling period (Dt = tf ti = 86400 s) it has become 73.07 °C.
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K. Zelzouli et al. / Energy Conversion and Management xxx (2013) xxx–xxx Table 2 Comparative with collectors of different parameters. Collector
Insulation
k (W/m k)
Insul. Thickness (mm)
m (kg/s)
Inst. efficiency
Cl C2 C3 C4 C5 C6 C7 C8 (our study)
Glass wool Polyurethane Polyurethane Glass wool Coconut Coir Glass fiber Glass fiber Polyurethane
0.040 0.035 0.035 0.040 0.074 0.035 0.035 0.035
40 30 40 100 50 50 50 40
0.022 – 0.033 – 0.0085 0.0083 0.002 0.042
n = 0.80–6.55 n = 0.80–9.00 n = 0.68–7.76 n = 0.74–3.55 n = 0.80–5.76 n = 0.66–8.00 n = 0.79–6.65 n = 0.71–4.02
DT/G(sa) DT/G(sa) DT/G(sa) DT/G(sa) DT/G(sa) DT/G(sa) DT/G(sa) DT/G(sa)
C1–C7 [33], C8: our study.
The average ambient temperature Ta, the water density q and the specific heat capacity Cp measured are of 26.5 °C, 0.9791 kg/l and 4189 J/kg/k, respectively. The measured storage loss coefficient is U = 1.67 W/K. The average loss coefficient per unit area is Us = 0.8 W/m2 K. This low average loss coefficient implies that the storage is very good insulated. The polyurethane and fiberglass, having the same thermal conductivity, represents the best insulating materials for heating systems. The measured value Us = 0.8 W/ m2 K is agreement to the study of Cruickshank and Harrison [34].
shown in Table 1, the calculated outlet water temperature and collector efficiency are agreement with those measured. About 0.6 °C deviation of calculated Tfo and 4% deviation of expected collector efficiency from measured were observed. The simulation study for four days of different climatic conditions was carried out. Ambient air, mains water temperature and solar radiation are measured and are used as input parameters in the simulation model. Water temperature is drawn from the top of the cylindrical horizontal storage tank, which corresponds to the temperature T at the node (i = 1). A number of 6 layers gave the best profile temperature with the experimental measurement. Numerical and experimental temperature Tsout and energy cumulated Qsout drawn are observed in the curves Fig. 2.2. We notice from figures (Fig. 2.2a and b) that the values found by simulation are very close to the experimental measurements, which allows us to suggest that the model based on technical characteristics can simulate the operation of the system with a good estimation of the performance of a thermosyphon system. The root mean square error RMSE is defined as
4.3. Thermosyphon system The storage tank is located above the collector, Fig. 1.1, and filled with mains water at morning. The system operates during the sunshine period and then the water temperature is drawn at 6:00 pm. Results in Fig. 2.2a and b have shown that the system may predict in the Spring a hot water temperature in order to 55 °C with a stored energy more than 600 kW h. During the draw from the tank, the water temperature in the top dropped from 55 °C at volume equal to 0 liters to 31 °C at volume equal to 250 l resulting in a loss of stratification. Then, the water temperature fell to 27 °C at 400 l to remains constant for the bigger volumes.
P
ðT num T exp Þ2
1=2
N
RMSE ¼
P
T exp
N
4.4. Model validation
With N the total number of value for temperatures, T, saved in the file. The root mean square error is of 0.046, 0.05, 0.049 and 0.057 for the first, second, third and fourth day of measures, respectively. This indicates that the DIFFEQ technical solution gave a good agreement with the experimental measurements.
Table 1 presents comparisons between measured and calculated Tfo and the efficiency of the collector. For the theoretical calculation, the ambient temperature and inlet water temperature and incident solar radiation are used as input parameters. As
800 600 400
T_amb(°C) G (w/m2)
200
Solar irradiance (w/m2)
ambient temperature (°C)
1000
0 6:43
9:07
11:31
13:55
16:19
18:43
Time (h:mn) T_sout num T_sout exp
50
Energy (kwh)
Temperature (°C)
60
40 30 20 10
Q_sout num Q_sout exp
0 0
200
400
volume draw-off (litres)
600
volume draw-off (litres)
Fig. 2.2. (a) Draw-off temperature profiles and (b) draw-off energy profiles.
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For the long-term performance, results (in Fig. 2.3) are compared with those obtained by Solo program in Tecsol website [35]. A slight difference in monthly results caused by the difference in incident solar radiation, with an annual difference less than 2%.
5. Long-term performance
10 9 8 7 6 5 4 3 2 1 0
G (KWh/m2.day)
Q_cumul (KWh/day)
Mean daily efficiency (%)
Fs (%)
60 50 40 30 20 10 0
Efficiency \ Solar Fraction
Energy
Tunisia is characterized by a temperate and an abundant sunshine for the most periods of the year. The latitude, longitude, elevation above sea level and of Tunis City are respectively 36°500 N, 10°.110 E, 0 m. From the National Institute of Meteorology, the yearly climatic data for Tunis is characterized by a mean daily solar radiation is more than 2 kW h/m2 in winter and exceeds 6 kW h/m2 in summer (Fig. 2.3). The climatic data file is characterized by a series of 8760 hourly outdoor data giving the solar radiation, mains water temperature, ambient temperature and wind speed. Because a time step of 1 h cannot be used in the numerical model, the climatic data are calculated numerically with a time step of 5 min so that the mean daily values are same to those in the file. The long-term system performances calculated are given in the figure (Fig. 2.3). The results show that for this system, the highest stored energy was almost 3.4 kW h/day in months from April to September, while the lowest was 2 in January and December. This is attributed that during the summer the total incidence solar radiation and ambient temperature are higher that result in higher temperatures in the water storage tank. The highest solar fraction and lowest efficiency are obtained in summer months. The annual cumulated energy, solar fraction and efficiency are of 2.87 kW h/day, 39.04% and 31%, respectively. The annual value of energy supplied by the system under climatic conditions of Tunis City is equal to 3771 MJ. Because it is difficult to measure experimentally the monthly and annual performances, results are compared to those in Tecsol website [35] for the Tunis City using the same parameters of the system discussed in this paper. In the French approach (Tecsol), guaranteed results are calculated with the program Solo 2000, which uses monthly weather, hot water consumption data and system characteristics to calculate the monthly and yearly solar energy yield. A slight difference in monthly results is due to the difference in incident solar radiation on the solar collector. The annual incident solar radiation is the same with that in Tecsol wibsite and the error between the outputs results are less to 2%, which means that the DIFFEQ solution method, with time a step of 5 min, provides accurate results. The good consistency between experiment and simulation has proved that this method is applicable in engineering problems.
6. Effect of the collector and storage tank losses on the system performance The performance of the storage tank with insulation is significantly higher than that of the situation without insulation storage system [36] and the good insulation is one of the important parameters. Its role is to avoid the heat losses. Materials having a very low thermal conductivity are always used for insulating. The increases of heat losses to the environment lead to the decrease of the annual energy performance and economic costs. Stratification in storage tank depends on storage material and wall thermal conductivity [37]. The total storage loss coefficient that is calculated and used previously is 0.8 W/m2 K. In addition, the collector loss coefficient varies according to the collector technical characteristics and climatic data. The losses increase with the raise of the ambient temperature and reach the maximum at the afternoon and then it reduce with the drop of the ambient temperature if it is assumed that the wind speed is constant or zero. The average annual value of UL calculated is 4 W/m2 K. To search the effect of a collector and storage losses on the system performances, UL and Us are used as input parameters in the numerical model to know their effects on temperature profiles within the storage and on the long-term performance. In First, UL assumed to be constant and fixed to 4 W/m2 K and Us is varied from 0.5 to 3 W/m2 K. Results are presented in Figs. 3.1a and 3.2a. Then, Us is kept to 0.8 W/m2 K and UL is varied from 1 to 6 W/m2 K. Results are displayed in Figs. 3.1b and 3.2b. The variation of collector loss coefficient (UL) and storage loss coefficient (Us) causes the variation in the system performances and then the variation of useful energy from which the variation of temperature. In a solar collector, an enhancement of loss coefficient decreases the efficiency, and the useful energy is therefore weakened. The curves Figs. 3.1a and 3.1b show that maximum average water temperature increases respectively from 52 to 66 °C as UL reduced from 6 to 1 W/m2 K, and increases respectively from 43 to 58 °C as Us decreased from 3 to 0.5 W/m2 K. During the sunshine period in the day, water temperature (in Fig. 3.1b) increases to reach the maximum at 16:00 pm then it decreases due to the losses to the environment. From the maximum, at 16:00 pm, the lowering in water temperatures within the storage are with the same slope, which imply that the collector losses emphasize only the amount of energy added to the storage. From the curve Fig. 3.1a it is noted that the use of storage insulation with high losses (high thermal conductivity of material insulating) leads to a low water temperature within the tank. The water temperature reaches the maximum at 14:00 pm for Us of 3 W/ m2 K, and reaches the maximum at 16:00 pm for Us of 0.5 W/ m2 K. This is due to that a storage tank with high losses cannot
Averrage water temperature (°C)
8
Us=0.5 W/m.K Us=1.5 W/m2.K Us=2.5 W/m2.K
70
Us=1 W/m2.K Us=2W/m2.K Us=3 W/m2.K
60 50 40 30 20 6
8
10
12
14
16
18
Local time (h) Fig. 2.3. System performances.
Fig. 3.1a. Temperature profile in a storage tank vs. storage loss coefficient at constant collector loss coefficient.
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Average water temperature (°C)
K. Zelzouli et al. / Energy Conversion and Management xxx (2013) xxx–xxx UL=1W/m2.K UL=3W/m2.K UL=5W/m2.K
70
UL=2W/m2.K UL=4W/m2.K UL=6W/m2.K
60 50 40 30 20 6
8
10
12
14
16
18
Local time (h) Fig. 3.1b. Temperature profile in a storage tank vs. collector loss coefficient at constant storage loss coefficient.
Us=0.5W/m2.K Us=3W/m2.K
Solar fraction (%)
70
Us=1W/m2.K Us=4W/m2.K
Us=2W/m2.K
60 50 40 30 20
Dece …
Annual
Nove …
Septe …
July
Agust
May
June
April
March
January
Febrary
0
October
10
Fig. 3.2a. System performance vs. storage loss coefficient at constant collector loss coefficient of 4 W/m2 K.
Solar fraction (%)
70
UL=1W/m2.K
UL=2W/m2.K
UL=3W/m2.K
UL=4W/m2.K
UL=5W/m2.K
UL=6W/m2.K
60 50 40 30 20
Annual
Dece …
Nove …
October
July
Agust
June
May
April
March
Febrary
January
0
Septe …
10
Fig. 3.2b. System performance vs. collector loss coefficient at constant storage loss coefficient of 0.8 W/m2 K.
store more energy at afternoon. The water temperature is dropped dramatically, at afternoon, if the losses are high. From the two curves, a system having a collector loss coefficient of 6 W/m2 K with a overall storage loss coefficient of 0.8 W/m2 K can reaches a water temperature of 52 °C. By cons, a system having a storage loss coefficient of 3 W/m2 K with a collector loss coefficient of 4 W/m2 K reaches a water temperature of 43 °C. The influence of losses in the system components on the water temperature affects the long-term performances. Figs. 3.2a and 3.2b describe the monthly and yearly systems performances vs. collector and storage losses. From the Fig. 3.1a, the maximum system performance is happened in the months of July and August reaching 62%. It can be
9
seen that Fs is strongly influenced by the storage losses during summer than the winter months and this is due to the higher ambient temperature. If Us varied from 0.5 to 4 W/m2 K, Fs passes from 62% to 33% (dropped by 29%) in the summer months and from 28% to 15% (dropped by 13%) in the winter months. The high falling in summer is due to the elevated ambient temperature. The annual performances decreased from 42.6% to 23.9% when the losses varied from 0.5 to 4 W/m2 K. The tank loss coefficient is desirable in the range 0.5–1 W/m2 K. The annual performance is reduced by 6% if Us varied from 1 to 2 W/m2 K, reduced by 14% if Us varied from 1 to 4 W/m2 K, and reduced by 9% for Us passes from 2 to 4 W/m2 K. Generally, the annual performance dropped by 5% if Us enhanced by 1 W/m2.K. Fig. 3.1b shows that for a collector loss coefficient of 1 W/m2 K, the system may reach a performance of 66% in summer days and 28% in winter days with annual performance of 45%. For a collector loss coefficient of 4 W/m2, the maximum performance (56%) is obtained in August and July and the lower is of 24% in winter days with an annual performance of 38.7%. An increase in collector losses from 1 to 6 W/m2 K lowers the annual system performance from 45% to 36%. The curves suggest that the performance of a system is reduced by 9% if the collector losses increase from 1 to 6 W/ m2 K, and reduced by 6% if UL varied from 1 to 4 W/m2 K. The annual performance is reduced moderately by 2% if UL increased by 1 W/m2 K. The collector and storage loss coefficients are depend on the system materials properties. Heat losses from the collector occur from the top, sides and the bottom. Heat loss from the sides and bottom is dependent on the thermal resistance of the collector that is usually insulated. Current designs are typically insulated such that the thermal conductance level through the back and sides of the collector. The top heat loss depends on the properties of the cover, the absorber coating and the thermal resistance of the air-layer between the absorber and the cover. With the development of selective coatings for the absorber plate, a need was felt for better correlation at the lower values of plate emittance. The good collectors are usually selected according to their instantaneous efficiencies. The best who characterized by the higher value of FR(sa) and the lower value of FRUL. The collector instantaneous efficiency is affected by various factors such as the design of the absorber, materials used, the design of the absorber, the properties of glass cover, weather and operating conditions [38]. Andoh et al. [33] have shown in their study that the collector performance depends on the insulation type and thickness, the insulation thermal conductivity, the fluid flow rate, the fraction (sa) of the solar radiation absorbed by the collector. The fraction (sa), in turn, depends mainly on the transmittance of the transparent covers and on the absorbance of the absorber. Since the storage water temperature depends on the outlet collector temperature, a lofty collector useful energy is very interesting. For collectors operating at a high temperature range and upper medium temperature range, selective absorber coating is worthwhile because it reduces radiation losses significantly. The selective coating absorbers with a high selectivity ratio a/ep are needed that have both high solar absorptance and low thermal emittance to get the high performances, and there are several materials and material combinations considered to have good optical properties for this purpose. Today, the good optical properties for selective surfaces are 90% < a < 98% and 3% < ep < 10%. In addition, the insulated box reduces the heat losses from the back and sides of the collector and hence the insulating material must has very low thermal conductivity. Even, the wind speed has a strong effect on the thermal losses and preferably the system is kept in a location protected from the wind to cut the thermal losses.
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K. Zelzouli et al. / Energy Conversion and Management xxx (2013) xxx–xxx
7. Conclusion A dynamical model for solar domestic water heaters with a horizontal storage tank has been developed. Numerical results show a fairly agreement with experimental measurements. Numerical results showed that DIFFEQ technical solution allows predicting the real performance of the system. Results have shown that the polyurethane is a very good material for insulating thermal systems, and have shown that a very good insulated storage tank coupled with a flat plate collector having selective absorber of FR(sa) = 0.71 and FRUL = 4.02 can yield annual performance of 39%. Results have shown also that the water temperature degradation in thermal storage tank is strongly influenced by the collector and the storage loss coefficients, and showed that performance of the storage tank is more influenced by the losses from the storage than the losses from the flat plate collector. A decrease in collector loss coefficient by 1 W/m2 K increases the annual performances by 2%. The annual performance increases by 5% if the storage loss coefficient reduced by 1 W/m2 K. References [1] Kalogirou SA. Thermal performance, economic and environmental life cycle analysis of thermosiphon solar water heaters. Sol Energy 2009;83:39–48. [2] Uhlemann R, Bansal NK. Side-by-side comparison of a pressurized and a nonpressurized solar water heating thermosiphon system. Sol Energy 1985;34:317–28. [3] Hobson PA, Norton B. Verified accurate performance simulation model of direct thermosyphon solar energy water heaters. J Sol Energy Eng 1988;110(4):282–92. [4] Norton B, Edmonds JEJ, Kovolos E. Dynamic simulation of indirect thermosyphon solar energy water heaters. Renewable Energy 1992;2:283–97. [5] Prapas DE, Psimmenos S, Sotiropoulos BA. Beneficial interconnection of two thermosiphon DHW solar systems. Appl Energy 1994;49:47–60. [6] Helwa NH, Mobarak AM, El-Sallak MS, El-Ghetany HH. Effect of hot-water consumption on temperature distribution in a horizontal solar water storage tank. Appl Energy 1995;52:185–97. [7] Kalogirou SA, Panteliou S. Thermosiphon solar domestic water heating systems: longterm performance prediction using artificial neural networks. Sol Energy 2000;69(2):163–74. [8] Carrillo Andrés A, Cejudo López JM. TRNSYS model of a thermosiphon solar domestic water heater with a horizontal store and mantle heat exchanger. Sol Energy 2002;72(2):89–98. [9] Koffi PME, Andoh HY, Gbaha P, Touré S, Ado G. Theoretical and experimental study of solar water heater with internal exchanger using thermosiphon system. Energy Convers Manage 2008;49:2279–90. [10] Tang R, Cheng Y, Wu M, Li Z, Yu Y. Experimental and modeling studies on thermosiphon domestic solar water heaters with flat-plate collectors at clear nights. Energy Convers Manage 2010;51:2548–56. [11] Hasan A. Thermosyphon solar water heaters: effect of storage tank volume and configuration on efficiency. Energy Convers Manage 1997;38(9):847–54. [12] Mar HYB, Peterson RE, Zimmer PB. Low cost coatings for flat plate solar collectors. Thin Solid Films 1976;39:95–103.
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Please cite this article in press as: Zelzouli K et al. Numerical and experimental investigation of thermosyphon solar water heater. Energy Convers Manage (2013), http://dx.doi.org/10.1016/j.enconman.2013.08.064