- Email: [email protected]
An experimental investigation of the performance boundaries of a solar water heating system
Experimental Thermal and Fluid Science 35 (2011) 1002–1009
Contents lists available at ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
An experimental investigation of the performance boundaries of a solar water heating system I.M. Michaelides, P.C. Eleftheriou ⇑ Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, P.O. Box 50329, 3603 Lemesos, Cyprus
a r t i c l e
i n f o
Article history: Received 18 January 2010 Received in revised form 18 January 2011 Accepted 1 February 2011 Available online 5 February 2011 Keywords: Solar water heating Solar collector Collector efficiency Thermal energy storage Thermal stratification Solar system error analysis
a b s t r a c t This paper presents the performance characteristics of a solar water heating system consisting of a 3 m2 flat plate collector and a 68 L tank, from readings taken over a period of 2 years under real weather conditions. It focuses on the characteristics and the behavior of the system, its response to solar radiation and hot water flow rate through the collector under no load conditions and in the evaluation of the errors associated with the system performance measurements. The system behavior proved to be linear with small relative standard deviations (less than 15%) within the values of the calculated errors and also relatively insensitive to solar radiation fluctuations ranging from 800 to 1100 W/m2. Flow rate variations from 0.07 and up to 0.25 L/s did not produce any noticeable effects on the energy collected in the storage tank of the system under investigation. The calculated absolute errors in the system instantaneous efficiency ranged from 34% for low flow and up to 20% for the high flows. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction The use of solar energy for thermal applications constitutes today one of the most popular engineering applications in the world. According to the European Solar Thermal Energy Industry Federation [1], the average installed capacity in the EU27 and Switzerland in 2006 was 27 kWth per 1000 capita, showing a spectacular growth of 47%. Cyprus with more than 530 kWth per 1000 capita is the distant leader while Austria with 225 and Greece with 208 are in second and third place. Currently, the most widespread solar application is for residential water heating. Today, systems for hot water production in single-family houses are dominant as they are proving economically feasible and viable [2]. The thermal behavior of a solar water heating system, however, constitutes a complex problem involving a number of interrelated parameters such as the solar radiation and other weather conditions, the water flow rate through the collector, the storage tank configuration, the effectiveness of the heat exchanger, and the thermal load. Based on the great number of such systems in operation today a number of researchers have examined the environmental impact of such systems and life cycle assessments have been performed [3,4]. An integrated collector/storage solar water heater was first patented in 1891 [5]. Due to its rather simple and concise structure, this type of system offers a value for money approach to permit ⇑ Corresponding author. Tel.: +357 25002622; fax: +357 25002769. E-mail addresses: [email protected] (I.M. Michaelides), polyvios. [email protected] (P.C. Eleftheriou). 0894-1777/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2011.02.001
the wide scale domestic adoption of solar water heating. Arthur [6] illustrated that a simple cylindrical shape offers a practical solution to maximizing the storage volume to exposed surface area, while Lindsay and Thomas [7] demonstrated that it is necessary to maintain thermal stratification within the store system for an attractive system. Lavan and Thompson [8] indicated that vessels with low aspect ratios promote internal mixing and vessels with a north–south alignment have higher aspect ratios and thus maintaining higher levels of thermal stratification. Reiss and Bainbridge [9] suggested that ‘long thin vessels are more suitable than short squat vessels’ and simulations conducted by Eames and Norton [10] showed that an aspect ratio of 3:1 was a good value to use. Tiller and Wochatz [11] suggested that ‘storage volume/glazing ratio of 51–69 L/m2 operate better for systems in cooler climates’. Theoretical analyses of reflector/collector combinations [12–16] suggest that use of a concentrator improves significantly the system thermal efficiency. As suggested, concentrating reflector increases the solar energy collection of a cylindrical vessel, with a low surface area to volume ratio. The thermal stratification in the storage tank is also an important aspect that affects the system performance and is a desirable phenomenon that improves the collector efficiency since the collector inlet fluid temperature is lower than mixed mean storage temperature. Smyth et al. [17] dealt with the design of the storage itself by examining a number of sleeve design configurations, and proposing an optimized one, while Eames and Norton [10] undertook and experimental investigation of the thermal performance of
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
1003
Nomenclature A c FR I m mw Qu t Ti To Ta Tu TL
solar collector surface area, m2 specific heat of fluid, J/kg °C solar collector heat removal factor intensity of incident solar radiation, W/m2 mass flow rate of fluid through the collector, kg/s mass flow rate of water, kg/s useful energy gain, W time temperature of fluid at collector inlet, °C temperature of fluid at collector outlet, °C ambient air temperature, °C water temperature at the upper zone of the storage tank water temperature at the lower zone of the storage tank
stratified hot water storage and also the effect of inlet and outlet port locations on store performance. Ghaddar [18] observed a substantial increase of up to 20% in the energy delivered when stratification is employed in the storage tank, as compared with fully mixed tank model. A number of studies suggested different types of inserts to the tank for enhancing stratification [19,20] while others elaborate on cases of constant inlet water temperature without any inserts, which is the most usual and practical case [21]. Simulations conducted by Jordan and Furpo [22] showed that the difference between a permanent inlet into a relative storage height of 0.3 compared to a permanent inlet into the very bottom of the tank leads to a decrease of the solar fraction while the annual mean temperature of the lower 15% of the storage height increases by 2.5 K. Numerical simulations have been carried out to investigate how the thermal performance of the systems is influenced by the tank volume for different hot-water consumptions and by mixing in the solar tank during draw-offs [23]. In the present study, the behavior of the solar water heating system and the effect of temperature stratification in the storage tank under real weather conditions along with the effect of solar energy and hot water flow variations are investigated from data recorded over a period of 2 years. The results obtained throughout the test period were evaluated and statistically analyzed to find similarity in behaviors concerning thermal stratification in the storage tank and the collector efficiency, which constitute important parameters in a solar water heating system. 2. Description of the experimental setup The system concerned is a forced circulation solar system within the solar energy e-learning laboratory of the Higher Technical Institute in Nicosia, Cyprus. The schematic diagram of the system is illustrated in Fig. 1, while the system specifications are shown in Table 1. It comprises a pilot solar energy conversion plant which consists of two flat-plate solar collectors having a surface area of 3 m2 located on the flat roof of the laboratory at a slope of 42° from horizontal, an insulated cylindrical thermal storage tank located indoors and other auxiliary equipment and accessories. It is also equipped with all necessary instrumentation, control and communication devices (Table 1) which are needed for remote access, control, and data collection and processing. The storage tank has a capacity of 68 L; it is of the vertical type, made of copper, with an internal height of 600 mm. It is equipped with temperature sensors for the measurement of water temperature at three different levels, bottom (50 mm above bottom), mid-point (300 mm above bottom) and top (550 mm from bottom). The differential controller
UL
a DN DNa DNo
g s RSD
overall heat loss coefficient of the solar collector, W/m2 absorptance difference in the initial and final temperature of the water the temperature difference between the collector inlet temperature (Ti) and the ambient air temperature (Ta) the temperature difference between the collector water inlet temperature (Ti) and the collector water exit temperature (To) instantaneous efficiency of solar collector transmittance relative standard deviation
Fig. 1. System schematic diagram of the experimental setup: (1) Solar collector, (2) pyranometer, (3) pump, (4) storage tank, (5) expansion tank, (6) feed water, (7) and (17) check valves, (8) pressure relief valve, (9) motorised valve, (10) Differential Temperature controller, (11) and (13) water flow meters, (12) drain valve, (14) wind speed and ambient air temperature sensors, (15) and (16) temperature sensors, (18) heat exchanger.
was installed with one of the temperature sensors inserted at the outlet of the collector and the other sensor at the lower part of the storage tank. The installed hard- and software includes features for controlling external devices, responding to events, processing data, creating report files, and exchanging information with other applications. This configuration allows for continuous and remote data collection under any circumstances. The basic data-acquisition system consists of a PC equipped with a 12-bit, high speed, 16-channels multiplexer coupled with a 16-channel sub-multiplexer, which includes cold junction compensation capabilities. In addition to the above the system is connected to an external board which accepts TTL inputs for controlling the various operations of the mechanical system. The controlling PC is also connected to a dedicated server which runs php and a number of other programs such as office applica-
1004
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
Table 1 System specifications. Collector Type: Flat-plate Net surface area: 2.72 m2 (gross area 3 m2) Absorber plate: Copper tubes/plates with selective coating Tilt angle: 42° to horizontal N–S orientation Total system pressure: 2 bar Storage tank Material: Copper, 1 mm thick Height 600 mm Capacity: 68 L Insulation thickness (polyurethane): 50 mm Measuring instrumentation Data logger PC type 16-channel, 12-bit, high speed general board multiplexer 16-channel, 12-bit, temperature board (sub-multiplexer with cold junction compensation) Flow meter Placed at the tank inlet (for water consumption), accuracy: ±1% of reading Placed at pump inlet (for hot water circulation), accuracy: ±5% of reading Storage tank thermocouples T-type copper–constantan thermocouples Placed at 50 mm, 300 mm and 550 mm from bottom Accuracy: ±0.5 °C Resolution: 0.1 °C Radiation Pyranometer accuracy: ±7% of reading Pyranometer resolution: 0.1 W/m2 Fixed at the same inclination as the collector Ambient temperature thermocouple T-type, copper–constantan, air probe, placed at collector side Accuracy: ±0.5 °C Resolution: 0.1 °C Wind speed Accuracy: 3% Resolution: ±0.1 m/s
tions and databases, allowing this way secure communication with the system and offering internet connection. All relevant weather data as well as operational and output data of the system are registered during an experimental session at intervals of 30 s and are temporarily stored in an EXCEL file on the controlling PC and are available for downloading for subsequent calculations and/or documentation. The data includes solar radiation, ambient air temperature, collector inlet and outlet temperatures, water flow rate through the collector, water flow rate to consumption, water temperatures in the storage tank, draw-off water temperature and cold feed water temperature. 3. Experimental procedure The system is allowing the experimentation only within certain hours of the day, when the variables to be measured have reached a rather stable condition. The initialization procedure, which runs automatically checks for the weather and system data and automatically records them on the spreadsheet to be typed. The actual experimental procedure starts only after a number of selections are made by the user (such as temperature differential for the controller). After this initial selection, the system is turned into the acquisition mode and all the relevant variables are recorded in 30 s intervals. There is no need to adjust other system variables during the experimental procedure as those are set at the start. The Differential Temperature controller (DT) compares the temperature at the collector with the lowest storage tank temperature
and accordingly it controls the operation of the circulating pump. The latter is automatically switched on when the collector temperature is higher than the storage tank temperature by an amount equal to the temperature difference set on the controller through the software tool. The pump circulates the heating medium through the collector where it absorbs the incident solar radiation. The solar energy absorbed is converted into thermal energy which is then transferred by the heating fluid to the storage tank heat exchanger. Heat is transferred from the fluid to the storage tank water. If and when the temperature difference between the collector and the storage tank falls below the set value, the differential controller switches OFF the pump circulator, thus circulation of fluid through the system stops. The temperature difference between the collector and the storage must be so adjusted that there will be no heat lost from the storage tank, via the collector, under any conditions. For the purpose of this work, DT settings of 2 or 4 K were employed in order to provide for more time of water circulation through the collectors, as compared to a real application where DT settings of 8–12 K are used taking into consideration the operation of the pump, the length of piping, the heat exchanger, etc. As described before, all relevant weather data along with the operational and output data of the system are registered during the experimental session at intervals of 30 s and are temporarily stored in an EXCEL file on the controlling PC and are available, on request at the end of the session, for downloading and subsequent calculations and/or documentation. The data includes solar radiation, ambient air temperature, wind speed, collector inlet and outlet temperatures, water flow rate through the collector, water flow rate to consumption, water temperatures in the storage tank, draw-off water temperature and cold feed water temperature.
4. Experimental investigation and measurements The particular performance tests of the solar collector have been carried, remotely, over the period of 2 years. The selected system has been tested under normal weather conditions and at no load. During the testing the periodic measurement of associated climatic and operating parameters such as solar radiation, and ambient temperature. has been made through a computer based data-acquisition system. Table 1 presents the technical details of instrumentation used in this study. 4.1. Statistical analysis Nhe testing of the solar collector produced a good amount of data, and a statistical analysis has been carried out to determine inconsistencies and analyze it in a statistical manner. Along with the statistical analysis of the experimental results, calculations of the absolute error in the measurements were also carried out, to evaluate the boundaries in the system performance. The following sub sections describe the procedures followed and the calculation results. 4.2. Methodology for instrumentation error analysis of a typical solar collector The possible errors in the determination of the energy collected, system behavior and temperature fluctuations due to instrumentation error, has been estimated. For the determination of overall error corresponding to the instruments used the root sum square formula has been used. According to root sum square method, a quantity R is computed
1005
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
which is a known function of n independent variables u1, u2, u3, . . . , un, such that
R ¼ f ðu1 ; u2 ; u3 . . . un Þ
ð1Þ
It is assumed that u0 s are the measured quantities and have associated errors as ±Du1, ±Du2, ±Du3, . . . , ±Dun, respectively; these errors will cause an error DR in the computed result R. If the Du0 s are considered as statistical bounds the probable errors uncertainties (TR) are determined by using the root sum square method. The possible error uncertainty, i.e., measure of overall errors can be expressed as:
" ER ¼
@R @u1 wu1
2
@R @u2 wu2
þ
2
þ ... þ
@R @un wun
2 #1=2 ð2Þ
where w(u1), w(u2), w(u3), . . . , w(un) are the associated errors in measurement of u1, u2, u3, . . . , un respectively. 4.2.1. Instantaneous efficiency Using Eq. (9) the absolute error in the determination of the instantaneous efficiency can be expressed as:
Eg ¼
"
@g wmw @mw
2
þ
@g wDT i @ DT i
2 þ
2 @g @g wA wi þ @I @Ac c
2 #1=2
ð3Þ where mw represents the mass of the water, DT the water temperature difference at the collector outlet and inlet, I the intensity of incident solar radiation and A the collector area. The above equation can be further simplified by multiplying and dividing by the instantaneous efficiency as:
Eg ¼
" 2 2 #1=2 wmw wAc þ ... þ mw Ac
ð4Þ
4.2.2. Energy collected Using Eq. (10) the absolute error in the determination of the collected energy can be expressed as:
EQ ¼
"
@Q wmw @mw
2
@Q þ wDT @ DT
2
2 #1=2 @Q þ wc @C
ð5Þ
where mw represents the mass of the water, DT the difference in the initial and final temperature of the water, and C the specific heat of water. The above equation can be further simplified by multiplying and dividing by the instantaneous efficiency as:
EQ ¼
" # 2 w 2 1=2 wmw c þ ... þ mw C
ð6Þ
Table 2 Results of the errors with 99% confidence limits. Flow (L/s)
Eg (%)
EQ (%)
0.07 0.18 0.25
34 22 20
14 14 14
6. Experimental results To achieve the most representative behavior, the system was monitored over a period of 2 years with continuous measurements taken every day. The results were then evaluated and only the ones with continuous sunshine and solar radiation over 800 W/m2 were used. The analysis and plots were statistically analyzed to find similarity in behaviors concerning thermal stratification in the storage tank, collector efficiency and energy stored in the storage tank, which constitute important parameters in a solar water heating system. 6.1. Thermal stratification Typical temperature curves were produced with the system under no load and varying solar radiation and different water flow rates through the collector and heat exchanger circuit. The typical behavior of the temperature profiles at the top, mid and lower tank sections is shown in Fig. 2. As it can be observed the mid and upper temperatures are very close, making the stratification clearly detectable only at the lowest part of the tank. Apparently the position of the heat exchanger in the tank had a major role on the temperature pattern in the tank. In an effort to examine the daily behavior of the system, its sensitivity to variable changes, its stability over time, and its possible degradation over time the temperature profiles of all seasons were collected, and the characteristics of those profiles were statistically analyzed. The data used for the statistical analysis included results with variations of hot water flow (0.07 and up to 0.25 L/s), variations of solar energy (over 800 W/m2), and variations over time. This statistical analyses yield an upper tank temperature profile of linear behavior with an average slope of 0.064 and a standard deviation of 0.008 (RSD value of 12.5%). The lower temperature profile yield a similar linear behavior with an average slope of 0.021 and a standard deviation of 0.004 (RSD of 17.6%). The above analysis gave a surprising result, pointing to the fact that the system is actually insensitive to typical variations of solar energy and thru flow. The temperature profiles at the top and the bottom of the storage tank can very well be predicted with high degree of accuracy, several hours after the system startup. This behavior is shown in Fig. 3, from which one may easily predict, with 95% confidence, that at any day the temperature rise of the water at the top and bottom of the tank, 2 h after the system has begun its operation will be 14 °C (±3 °C), and 5 °C (±1.5 °C) respectively.
5. Errors 6.2. Collector efficiency Using the above equations for the absolute error, the results were calculated as shown in Table 2. Some of the errors proved to contribute very little to the total error. An example of this was the error due to the area which was several orders of magnitude smaller than the rest of the errors. The most dominant errors were that of the water flow measuring devices and that of the solar intensity measuring devices. Even tough the values of the errors shown in Table 2, may seem high, they are of similar order of magnitude, when compared with similar analyses [25].
A measure of the collector performance is the collection efficiency, defined as the ratio of the useful gain over some specified time period to the incident solar energy over the same time period [24]:
R
Q dt g¼ Ru
ð7Þ
Q u ¼ McðT o T i Þ
ð8Þ
A Idt
1006
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
60.0
Temperature, deg C
50.0
y = 0.0963x + 38.665
40.0
y = 0.0269x + 25.908
30.0 20.0 10.0 0.0
0
15
30
45
60
Time (min) Fig. 2. Typical temperature profile in the storage tank.
Temperature Increase, deg C
12 10 y = 0.08x 8
y = 0.064x
6
y = 0.0479x
4
y = 0.0289x y = 0.0214x
2
y = 0.0138x 0
0
20
40
60
80
100
Time (min) Fig. 3. Top and bottom temperature profiles along with the 95% confidence boundaries.
The instantaneous thermal efficiency of the collector, g, defined as the ratio of the actual useful energy gain (Qu) over the product of the incident solar radiation (I) and the collector surface area (A) is:
g¼
Qu IA
ð9Þ
Substituting (2) into (3) gives:
g¼
McðT o T i Þ IA
ð10Þ
The above equation was used to calculate the instantaneous efficiencies of the collector using the data collected throughout the period of testing. The instantaneous thermal efficiency of the collector, g, is also expressed in terms of the collector thermal properties and temperatures by the following equation [24]:
g ¼ F R sa F R U L
Ti Ta I
ð11Þ
The collector efficiency g is plotted against (Ti Ta)/I, so that the resulting line has a slope of (FRUL), and when Ti = Ta the intercept is FR(sa), known as the ‘‘no loss efficiency’’. The resulting plot will be a straight line only if conditions are such that FR, UL and (sa) are
constants. In practice UL is not a constant as heat losses will increase as the temperature of the collector rises further above ambient temperature (thermal conductivity of materials varies with temperature). The calculated values of the instantaneous efficiency of the solar collector for the period under investigation were also grouped together and analyzed statistically to find out that the efficiencies under those real conditions can also be highly predictable. The same methodology as before was applied in order to examine the system efficiency and the effects of the time, hot water flow, and solar radiation to this important parameter. Fig. 4 shows the variation of the instantaneous efficiency of the solar collector with DN/I, as well as the efficiency variations with 95% confidence. According to this grouping and the subsequent statistical analysis, the average slope of the collector efficiency over the past 2 years is 7.498, i.e. the collector heat loss coefficient UL is 7.498 W/m2 °C (with a standard deviation of 1.01, RSD of 13.5%), while the average constant value corresponding to the ‘‘no loss efficiency’’ is 0.6155 with a standard deviation of 0.05 or RSD of 8%). This implies that the characteristic equation describing the collector thermal performance can be expressed by the following equation:
1007
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
DTa g ¼ 0:6155 7:498 I
ð12Þ
The above equation does not represent a high efficiency collector and there is space for improvement; it is evident that it can perform better if its optical characteristics, s and a, and the quality of its thermal insulation (thermal conductivity and thickness) are improved. The first one will result to an increase in the no loss efficiency, i.e. a figure higher than 0.6155, while a lower thermal conductivity or greater thickness will reduce the heat loss coefficient to a figure lower than 7.498 and consequently the heat losses from the collector. Figs. 6 and 7 show the experimental results along with their associated calculated errors shown as bands. The figures also show the average values of the respective parameters for both the no loss efficiency and the slope of the collector under investigation with 99% confidence boundaries.
6.3. Energy collected The average energy collected can subsequently be estimated from the tank storage temperatures. This estimation is also shown in Fig. 5, below: The above plot (Fig. 5) assumes 2/3 of the water at the upper temperature and the rest at the lower temperature. According to this assumption the system stores energy following a linear behavior and this can easily be predicted. Again, as before, the effects of time (aging of the system), hot water flow (0.07–0.25 L/s), solar radiation within the ranges used, and wind speed (0.0–0.7 m/s) played an insignificant role to the end result. For example, according to this behavior the energy that is stored by the system, 2 h after its initial daily operation, is 42 kJ/kg (±6 kJ/kg). As it was observed the solar energy fluctuations are important only when calculating the instantaneous efficiency and instantaneous energy absorbed by the hot water, but when it come to the average
1.0 0.9 0.8
Efficiency
0.7 0.6 0.5
y = -5.473x + 0.7139
0.4 y = -7.498x + 0.6155
0.3 y = -9.5231x + 0.5171
0.2 0.1 0.0 0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
2o
ΔΤ /Ι (m C/W) Fig. 4. Collector efficiency with 95% confidence limits.
Energy in kJ/kg
40.0
30.0 y = 0.2426x y = 0.2083x
20.0 y = 0.1741x 10.0
0.0
0
20
40
60
80
100
Time (min) Fig. 5. Energy stored as hot water in reservoir with 95% confidence limits.
120
1008
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
0.0
0
5
10
15
20
25
2o
System Slope (W/m C)
-2.0
-4.0
-6.0
-8.0
-10.0
-12.0
-14.0
Measuring Points Fig. 6. Slope of the system performance with 95% confidence limits.
0.80
Value of System Constant
0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00
0
5
10
15
20
25
30
Measuring Points Fig. 7. The experimental results of the system no loss efficiency.
efficiency and total energy stored in the tank, those fluctuations were not important for the end result. Apparently, this behavior has to do with the energy inertia of the system which is tied to its mass, temperature achieved at the collectors, system heat losses, system heat capacity, etc.
7. Conclusions There are some very notable results from the measurements taken over this 2 year period. The first is the fact that the system appears to be very predictable in spite of the fact that the thermal behavior of a solar water heating system constitutes a complex problem involving a number of interrelated parameters. The temperatures in the tank and the energy collected could be easily predicted within a few degrees (and kJ’s) over a long period of time (Table 3).
Table 3 Results of the system statistical analysis. Characteristic
Parameter
Statistical performance
Tank upper temperature Tank lower temperature Efficiency (g) Energy collected (q)
Tu = a(t)
Tu = (0.064 ± 0.008)t
TL = a(t)
TL = (0.021 ± 0.004)t
g = a(y) + b
g = [7.498(±1.01)]y + 0.6155(±0.050)]
q = at
q = (0.2083 ± 0.034)t
The second is the fact that the system is relatively insensitive to solar radiation fluctuations. Solar radiations of 800–1100 W/m2 gave exactly the same system behavior. Also the changes in hot water flow did not produce any significant energy changes. The flow ranges used were from 0.07 and up to 0.25 L/s. Again these
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
flow variations did not produce any noticeable result on the energy collected in the tank. The third major observation is the fact that the average efficiency of the solar collector is also predictable. The efficiency of this particular collector could easily be predicted with a relatively high degree of accuracy (within 0.2). Taking into account that this value corresponds to 2.7% error, and that from the basic error analysis (considering the error due to the mass, the temperature, the area and the intensity) of the collector efficiency results in an error of the order of 7.2%, this value looks very reasonable. Calculating the absolute error one obtains the value of 16% for the error in the solar collector efficiency. The measured variation of the same value over time yields to a value of 7.2% indicating that the solar collector performance is well within its calculated and expected performance. The above findings are very helpful in predicting the behavior of a particular solar water heating system of known configuration and thermal characteristics and properties characteristics, such as for example its efficiency characteristic graph. In particular, knowing the performance boundaries, one could use them as a tool to assess the performance degradation of the solar collector with time and make a qualitative comparison of the system performance. Furthermore, they can serve as a tool to find out malfunctions in the system, if for example the performance of the system declines from the investigated boundaries. Acknowledgements This work was compiled from experimental data recorded in the solar energy e-learning laboratory which was developed as part of the MARVEL Project of the European Leonardo da Vinci Programme. References [1] European Solar Thermal Energy Industry Federation (ESTIF), Solar Thermal Markets in Europe (Trends and Market Statistics 2006)., June 2007. [2] C. Carboni, R. Montanari, Solar thermal systems: advantages in domestic integration, Renewable Energy V33 (6) (2008) 1364–1373. [3] F. Ardente, G. Beccali, M. Cellura, V. Lo Brano, Life cycle assessment of a solar thermal collector, Renewable Energy V30 (7) (2005) 1031–1054. [4] I.M. Michaelides, W.C. Lee, D.R. Wilson, P.P. Votsis, An investigation into the performance and cost effectiveness of thermosyphon solar water heaters, Renewable Energy 2 (3) (1992) 219–225.
1009
[5] C.M. Kemp, US Patent No. 451384, 1891. [6] A.C. Arthur, A novel solar-savings fraction prediction methodology for integral passive solar water heaters, PhD Thesis, Cranfield Institute of Technology, UK, 1990. [7] R.C. Lindsay, W.C. Thomas, Experimental investigation of test procedures for thermal performance of integral collector/storage solar water system, in: Proceedings of the ASME Solar Energy Conference, Knoxville, Tennessee, USA, 1985, pp. 349–58. [8] Z. Lavan, J. Thompson, Experimental study of thermally stratified hot water storage tanks, Solar Energy 19 (1977) 519–524. [9] J. Reiss, D.A. Bainbridge, Breadbox designs, Alternative Sources of Energy 46 (1978) 16–21 (Part 47). [10] P.C. Eames, B. Norton, The effect of tank geometry on thermally stratified sensible heat storage subject to low Reynolds number flows, International Journal of Heat and Mass Transfer 41 (14) (1998) 2131–2142. [11] J.S. Tiller, V. Wochatz, Performance of integrated passive solar water heaters (Breadbox-type) under varying design conditions in the South-eastern US, in: Proceedings of the Seventh National Passive Solar Conference, Knoxville, Tennessee, USA, 1982, pp. 975–80. [12] S.L. Grassie, N.R. Sheridan, The use of planar reflectors for increasing the energy yield of flat-plate collectors, Solar Energy 19 (1977) 663–668. [13] D.P. Grimmer, K.G. Zinn, K.C. Herr, B.E. Wood, Augmented solar energy collection using various planar reflective surfaces: theoretical calculations and experimental results, Solar Energy 21 (1978) 497–501. [14] D.C. Larson, Concentration ratios for flat-plate solar collectors with adjustable mirrors, Journal of Energy 4 (4) (1980) 170–175. [15] H. Tabor, Stationary mirror systems for solar collectors, Solar Energy 2 (1958) 27–33. [16] I.S. Taha, S.M. Eldighidy, Effect of of-south orientation on optimum conditions for maximum solar energy absorbed by a flat-plate collector augmented by plane reflector, Solar Energy 25 (1980) 373. [17] M. Smyth, P.C. Eames, B. Norton, A comparative performance rating for an integrated solar collector/storage vessel with inner sleeves to increase heat retention, Solar Energy (1999) 291–303. [18] N.K. Ghaddar, Stratified storage tank influence on performance of solar water heating system tested in Beirut, Renewable Energy 4 (8) (1994) 911–925. [19] Z.F. Li, K. Sumathy, Performance study of a partitioned thermally stratified storage tank in a solar powered absorption air conditioning system, Applied Thermal Engineering 22 (11) (2002) 1207–1216. [20] A. Zachár, I. Farkas, F. Szlivka, Numerical analyses of the impact of plates for thermal stratification inside a storage tank with upper and lower inlet flows, Solar Energy 74 (4) (2003) 287–302. [21] A.A. Hegazy, M.R. Diab, Performance of an improved design for storage-type domestic electrical water-heaters, Applied Energy 71 (4) (2002) 287–306. [22] Jordan Ulrike, Furbo Simon, Thermal stratification in small solar domestic storage tanks caused by draw-offs, Solar Energy 78 (2) (2005) 291–300. [23] S. Knudsen, Consumers influence on the thermal performance of small SDHW systems – theoretical investigations, Solar Energy 73 (1) (2002) 33–42. [24] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, John Wiley, New York, 1991. [25] I. Purohit, P. Purohit, Instrumentation error analysis of a paraboloid concentrator type solar cooker, Energy for Sustainable Development 13 (2009) 255–264.
Contents lists available at ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
An experimental investigation of the performance boundaries of a solar water heating system I.M. Michaelides, P.C. Eleftheriou ⇑ Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, P.O. Box 50329, 3603 Lemesos, Cyprus
a r t i c l e
i n f o
Article history: Received 18 January 2010 Received in revised form 18 January 2011 Accepted 1 February 2011 Available online 5 February 2011 Keywords: Solar water heating Solar collector Collector efficiency Thermal energy storage Thermal stratification Solar system error analysis
a b s t r a c t This paper presents the performance characteristics of a solar water heating system consisting of a 3 m2 flat plate collector and a 68 L tank, from readings taken over a period of 2 years under real weather conditions. It focuses on the characteristics and the behavior of the system, its response to solar radiation and hot water flow rate through the collector under no load conditions and in the evaluation of the errors associated with the system performance measurements. The system behavior proved to be linear with small relative standard deviations (less than 15%) within the values of the calculated errors and also relatively insensitive to solar radiation fluctuations ranging from 800 to 1100 W/m2. Flow rate variations from 0.07 and up to 0.25 L/s did not produce any noticeable effects on the energy collected in the storage tank of the system under investigation. The calculated absolute errors in the system instantaneous efficiency ranged from 34% for low flow and up to 20% for the high flows. Ó 2011 Elsevier Inc. All rights reserved.
1. Introduction The use of solar energy for thermal applications constitutes today one of the most popular engineering applications in the world. According to the European Solar Thermal Energy Industry Federation [1], the average installed capacity in the EU27 and Switzerland in 2006 was 27 kWth per 1000 capita, showing a spectacular growth of 47%. Cyprus with more than 530 kWth per 1000 capita is the distant leader while Austria with 225 and Greece with 208 are in second and third place. Currently, the most widespread solar application is for residential water heating. Today, systems for hot water production in single-family houses are dominant as they are proving economically feasible and viable [2]. The thermal behavior of a solar water heating system, however, constitutes a complex problem involving a number of interrelated parameters such as the solar radiation and other weather conditions, the water flow rate through the collector, the storage tank configuration, the effectiveness of the heat exchanger, and the thermal load. Based on the great number of such systems in operation today a number of researchers have examined the environmental impact of such systems and life cycle assessments have been performed [3,4]. An integrated collector/storage solar water heater was first patented in 1891 [5]. Due to its rather simple and concise structure, this type of system offers a value for money approach to permit ⇑ Corresponding author. Tel.: +357 25002622; fax: +357 25002769. E-mail addresses: [email protected] (I.M. Michaelides), polyvios. [email protected] (P.C. Eleftheriou). 0894-1777/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2011.02.001
the wide scale domestic adoption of solar water heating. Arthur [6] illustrated that a simple cylindrical shape offers a practical solution to maximizing the storage volume to exposed surface area, while Lindsay and Thomas [7] demonstrated that it is necessary to maintain thermal stratification within the store system for an attractive system. Lavan and Thompson [8] indicated that vessels with low aspect ratios promote internal mixing and vessels with a north–south alignment have higher aspect ratios and thus maintaining higher levels of thermal stratification. Reiss and Bainbridge [9] suggested that ‘long thin vessels are more suitable than short squat vessels’ and simulations conducted by Eames and Norton [10] showed that an aspect ratio of 3:1 was a good value to use. Tiller and Wochatz [11] suggested that ‘storage volume/glazing ratio of 51–69 L/m2 operate better for systems in cooler climates’. Theoretical analyses of reflector/collector combinations [12–16] suggest that use of a concentrator improves significantly the system thermal efficiency. As suggested, concentrating reflector increases the solar energy collection of a cylindrical vessel, with a low surface area to volume ratio. The thermal stratification in the storage tank is also an important aspect that affects the system performance and is a desirable phenomenon that improves the collector efficiency since the collector inlet fluid temperature is lower than mixed mean storage temperature. Smyth et al. [17] dealt with the design of the storage itself by examining a number of sleeve design configurations, and proposing an optimized one, while Eames and Norton [10] undertook and experimental investigation of the thermal performance of
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
1003
Nomenclature A c FR I m mw Qu t Ti To Ta Tu TL
solar collector surface area, m2 specific heat of fluid, J/kg °C solar collector heat removal factor intensity of incident solar radiation, W/m2 mass flow rate of fluid through the collector, kg/s mass flow rate of water, kg/s useful energy gain, W time temperature of fluid at collector inlet, °C temperature of fluid at collector outlet, °C ambient air temperature, °C water temperature at the upper zone of the storage tank water temperature at the lower zone of the storage tank
stratified hot water storage and also the effect of inlet and outlet port locations on store performance. Ghaddar [18] observed a substantial increase of up to 20% in the energy delivered when stratification is employed in the storage tank, as compared with fully mixed tank model. A number of studies suggested different types of inserts to the tank for enhancing stratification [19,20] while others elaborate on cases of constant inlet water temperature without any inserts, which is the most usual and practical case [21]. Simulations conducted by Jordan and Furpo [22] showed that the difference between a permanent inlet into a relative storage height of 0.3 compared to a permanent inlet into the very bottom of the tank leads to a decrease of the solar fraction while the annual mean temperature of the lower 15% of the storage height increases by 2.5 K. Numerical simulations have been carried out to investigate how the thermal performance of the systems is influenced by the tank volume for different hot-water consumptions and by mixing in the solar tank during draw-offs [23]. In the present study, the behavior of the solar water heating system and the effect of temperature stratification in the storage tank under real weather conditions along with the effect of solar energy and hot water flow variations are investigated from data recorded over a period of 2 years. The results obtained throughout the test period were evaluated and statistically analyzed to find similarity in behaviors concerning thermal stratification in the storage tank and the collector efficiency, which constitute important parameters in a solar water heating system. 2. Description of the experimental setup The system concerned is a forced circulation solar system within the solar energy e-learning laboratory of the Higher Technical Institute in Nicosia, Cyprus. The schematic diagram of the system is illustrated in Fig. 1, while the system specifications are shown in Table 1. It comprises a pilot solar energy conversion plant which consists of two flat-plate solar collectors having a surface area of 3 m2 located on the flat roof of the laboratory at a slope of 42° from horizontal, an insulated cylindrical thermal storage tank located indoors and other auxiliary equipment and accessories. It is also equipped with all necessary instrumentation, control and communication devices (Table 1) which are needed for remote access, control, and data collection and processing. The storage tank has a capacity of 68 L; it is of the vertical type, made of copper, with an internal height of 600 mm. It is equipped with temperature sensors for the measurement of water temperature at three different levels, bottom (50 mm above bottom), mid-point (300 mm above bottom) and top (550 mm from bottom). The differential controller
UL
a DN DNa DNo
g s RSD
overall heat loss coefficient of the solar collector, W/m2 absorptance difference in the initial and final temperature of the water the temperature difference between the collector inlet temperature (Ti) and the ambient air temperature (Ta) the temperature difference between the collector water inlet temperature (Ti) and the collector water exit temperature (To) instantaneous efficiency of solar collector transmittance relative standard deviation
Fig. 1. System schematic diagram of the experimental setup: (1) Solar collector, (2) pyranometer, (3) pump, (4) storage tank, (5) expansion tank, (6) feed water, (7) and (17) check valves, (8) pressure relief valve, (9) motorised valve, (10) Differential Temperature controller, (11) and (13) water flow meters, (12) drain valve, (14) wind speed and ambient air temperature sensors, (15) and (16) temperature sensors, (18) heat exchanger.
was installed with one of the temperature sensors inserted at the outlet of the collector and the other sensor at the lower part of the storage tank. The installed hard- and software includes features for controlling external devices, responding to events, processing data, creating report files, and exchanging information with other applications. This configuration allows for continuous and remote data collection under any circumstances. The basic data-acquisition system consists of a PC equipped with a 12-bit, high speed, 16-channels multiplexer coupled with a 16-channel sub-multiplexer, which includes cold junction compensation capabilities. In addition to the above the system is connected to an external board which accepts TTL inputs for controlling the various operations of the mechanical system. The controlling PC is also connected to a dedicated server which runs php and a number of other programs such as office applica-
1004
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
Table 1 System specifications. Collector Type: Flat-plate Net surface area: 2.72 m2 (gross area 3 m2) Absorber plate: Copper tubes/plates with selective coating Tilt angle: 42° to horizontal N–S orientation Total system pressure: 2 bar Storage tank Material: Copper, 1 mm thick Height 600 mm Capacity: 68 L Insulation thickness (polyurethane): 50 mm Measuring instrumentation Data logger PC type 16-channel, 12-bit, high speed general board multiplexer 16-channel, 12-bit, temperature board (sub-multiplexer with cold junction compensation) Flow meter Placed at the tank inlet (for water consumption), accuracy: ±1% of reading Placed at pump inlet (for hot water circulation), accuracy: ±5% of reading Storage tank thermocouples T-type copper–constantan thermocouples Placed at 50 mm, 300 mm and 550 mm from bottom Accuracy: ±0.5 °C Resolution: 0.1 °C Radiation Pyranometer accuracy: ±7% of reading Pyranometer resolution: 0.1 W/m2 Fixed at the same inclination as the collector Ambient temperature thermocouple T-type, copper–constantan, air probe, placed at collector side Accuracy: ±0.5 °C Resolution: 0.1 °C Wind speed Accuracy: 3% Resolution: ±0.1 m/s
tions and databases, allowing this way secure communication with the system and offering internet connection. All relevant weather data as well as operational and output data of the system are registered during an experimental session at intervals of 30 s and are temporarily stored in an EXCEL file on the controlling PC and are available for downloading for subsequent calculations and/or documentation. The data includes solar radiation, ambient air temperature, collector inlet and outlet temperatures, water flow rate through the collector, water flow rate to consumption, water temperatures in the storage tank, draw-off water temperature and cold feed water temperature. 3. Experimental procedure The system is allowing the experimentation only within certain hours of the day, when the variables to be measured have reached a rather stable condition. The initialization procedure, which runs automatically checks for the weather and system data and automatically records them on the spreadsheet to be typed. The actual experimental procedure starts only after a number of selections are made by the user (such as temperature differential for the controller). After this initial selection, the system is turned into the acquisition mode and all the relevant variables are recorded in 30 s intervals. There is no need to adjust other system variables during the experimental procedure as those are set at the start. The Differential Temperature controller (DT) compares the temperature at the collector with the lowest storage tank temperature
and accordingly it controls the operation of the circulating pump. The latter is automatically switched on when the collector temperature is higher than the storage tank temperature by an amount equal to the temperature difference set on the controller through the software tool. The pump circulates the heating medium through the collector where it absorbs the incident solar radiation. The solar energy absorbed is converted into thermal energy which is then transferred by the heating fluid to the storage tank heat exchanger. Heat is transferred from the fluid to the storage tank water. If and when the temperature difference between the collector and the storage tank falls below the set value, the differential controller switches OFF the pump circulator, thus circulation of fluid through the system stops. The temperature difference between the collector and the storage must be so adjusted that there will be no heat lost from the storage tank, via the collector, under any conditions. For the purpose of this work, DT settings of 2 or 4 K were employed in order to provide for more time of water circulation through the collectors, as compared to a real application where DT settings of 8–12 K are used taking into consideration the operation of the pump, the length of piping, the heat exchanger, etc. As described before, all relevant weather data along with the operational and output data of the system are registered during the experimental session at intervals of 30 s and are temporarily stored in an EXCEL file on the controlling PC and are available, on request at the end of the session, for downloading and subsequent calculations and/or documentation. The data includes solar radiation, ambient air temperature, wind speed, collector inlet and outlet temperatures, water flow rate through the collector, water flow rate to consumption, water temperatures in the storage tank, draw-off water temperature and cold feed water temperature.
4. Experimental investigation and measurements The particular performance tests of the solar collector have been carried, remotely, over the period of 2 years. The selected system has been tested under normal weather conditions and at no load. During the testing the periodic measurement of associated climatic and operating parameters such as solar radiation, and ambient temperature. has been made through a computer based data-acquisition system. Table 1 presents the technical details of instrumentation used in this study. 4.1. Statistical analysis Nhe testing of the solar collector produced a good amount of data, and a statistical analysis has been carried out to determine inconsistencies and analyze it in a statistical manner. Along with the statistical analysis of the experimental results, calculations of the absolute error in the measurements were also carried out, to evaluate the boundaries in the system performance. The following sub sections describe the procedures followed and the calculation results. 4.2. Methodology for instrumentation error analysis of a typical solar collector The possible errors in the determination of the energy collected, system behavior and temperature fluctuations due to instrumentation error, has been estimated. For the determination of overall error corresponding to the instruments used the root sum square formula has been used. According to root sum square method, a quantity R is computed
1005
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
which is a known function of n independent variables u1, u2, u3, . . . , un, such that
R ¼ f ðu1 ; u2 ; u3 . . . un Þ
ð1Þ
It is assumed that u0 s are the measured quantities and have associated errors as ±Du1, ±Du2, ±Du3, . . . , ±Dun, respectively; these errors will cause an error DR in the computed result R. If the Du0 s are considered as statistical bounds the probable errors uncertainties (TR) are determined by using the root sum square method. The possible error uncertainty, i.e., measure of overall errors can be expressed as:
" ER ¼
@R @u1 wu1
2
@R @u2 wu2
þ
2
þ ... þ
@R @un wun
2 #1=2 ð2Þ
where w(u1), w(u2), w(u3), . . . , w(un) are the associated errors in measurement of u1, u2, u3, . . . , un respectively. 4.2.1. Instantaneous efficiency Using Eq. (9) the absolute error in the determination of the instantaneous efficiency can be expressed as:
Eg ¼
"
@g wmw @mw
2
þ
@g wDT i @ DT i
2 þ
2 @g @g wA wi þ @I @Ac c
2 #1=2
ð3Þ where mw represents the mass of the water, DT the water temperature difference at the collector outlet and inlet, I the intensity of incident solar radiation and A the collector area. The above equation can be further simplified by multiplying and dividing by the instantaneous efficiency as:
Eg ¼
" 2 2 #1=2 wmw wAc þ ... þ mw Ac
ð4Þ
4.2.2. Energy collected Using Eq. (10) the absolute error in the determination of the collected energy can be expressed as:
EQ ¼
"
@Q wmw @mw
2
@Q þ wDT @ DT
2
2 #1=2 @Q þ wc @C
ð5Þ
where mw represents the mass of the water, DT the difference in the initial and final temperature of the water, and C the specific heat of water. The above equation can be further simplified by multiplying and dividing by the instantaneous efficiency as:
EQ ¼
" # 2 w 2 1=2 wmw c þ ... þ mw C
ð6Þ
Table 2 Results of the errors with 99% confidence limits. Flow (L/s)
Eg (%)
EQ (%)
0.07 0.18 0.25
34 22 20
14 14 14
6. Experimental results To achieve the most representative behavior, the system was monitored over a period of 2 years with continuous measurements taken every day. The results were then evaluated and only the ones with continuous sunshine and solar radiation over 800 W/m2 were used. The analysis and plots were statistically analyzed to find similarity in behaviors concerning thermal stratification in the storage tank, collector efficiency and energy stored in the storage tank, which constitute important parameters in a solar water heating system. 6.1. Thermal stratification Typical temperature curves were produced with the system under no load and varying solar radiation and different water flow rates through the collector and heat exchanger circuit. The typical behavior of the temperature profiles at the top, mid and lower tank sections is shown in Fig. 2. As it can be observed the mid and upper temperatures are very close, making the stratification clearly detectable only at the lowest part of the tank. Apparently the position of the heat exchanger in the tank had a major role on the temperature pattern in the tank. In an effort to examine the daily behavior of the system, its sensitivity to variable changes, its stability over time, and its possible degradation over time the temperature profiles of all seasons were collected, and the characteristics of those profiles were statistically analyzed. The data used for the statistical analysis included results with variations of hot water flow (0.07 and up to 0.25 L/s), variations of solar energy (over 800 W/m2), and variations over time. This statistical analyses yield an upper tank temperature profile of linear behavior with an average slope of 0.064 and a standard deviation of 0.008 (RSD value of 12.5%). The lower temperature profile yield a similar linear behavior with an average slope of 0.021 and a standard deviation of 0.004 (RSD of 17.6%). The above analysis gave a surprising result, pointing to the fact that the system is actually insensitive to typical variations of solar energy and thru flow. The temperature profiles at the top and the bottom of the storage tank can very well be predicted with high degree of accuracy, several hours after the system startup. This behavior is shown in Fig. 3, from which one may easily predict, with 95% confidence, that at any day the temperature rise of the water at the top and bottom of the tank, 2 h after the system has begun its operation will be 14 °C (±3 °C), and 5 °C (±1.5 °C) respectively.
5. Errors 6.2. Collector efficiency Using the above equations for the absolute error, the results were calculated as shown in Table 2. Some of the errors proved to contribute very little to the total error. An example of this was the error due to the area which was several orders of magnitude smaller than the rest of the errors. The most dominant errors were that of the water flow measuring devices and that of the solar intensity measuring devices. Even tough the values of the errors shown in Table 2, may seem high, they are of similar order of magnitude, when compared with similar analyses [25].
A measure of the collector performance is the collection efficiency, defined as the ratio of the useful gain over some specified time period to the incident solar energy over the same time period [24]:
R
Q dt g¼ Ru
ð7Þ
Q u ¼ McðT o T i Þ
ð8Þ
A Idt
1006
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
60.0
Temperature, deg C
50.0
y = 0.0963x + 38.665
40.0
y = 0.0269x + 25.908
30.0 20.0 10.0 0.0
0
15
30
45
60
Time (min) Fig. 2. Typical temperature profile in the storage tank.
Temperature Increase, deg C
12 10 y = 0.08x 8
y = 0.064x
6
y = 0.0479x
4
y = 0.0289x y = 0.0214x
2
y = 0.0138x 0
0
20
40
60
80
100
Time (min) Fig. 3. Top and bottom temperature profiles along with the 95% confidence boundaries.
The instantaneous thermal efficiency of the collector, g, defined as the ratio of the actual useful energy gain (Qu) over the product of the incident solar radiation (I) and the collector surface area (A) is:
g¼
Qu IA
ð9Þ
Substituting (2) into (3) gives:
g¼
McðT o T i Þ IA
ð10Þ
The above equation was used to calculate the instantaneous efficiencies of the collector using the data collected throughout the period of testing. The instantaneous thermal efficiency of the collector, g, is also expressed in terms of the collector thermal properties and temperatures by the following equation [24]:
g ¼ F R sa F R U L
Ti Ta I
ð11Þ
The collector efficiency g is plotted against (Ti Ta)/I, so that the resulting line has a slope of (FRUL), and when Ti = Ta the intercept is FR(sa), known as the ‘‘no loss efficiency’’. The resulting plot will be a straight line only if conditions are such that FR, UL and (sa) are
constants. In practice UL is not a constant as heat losses will increase as the temperature of the collector rises further above ambient temperature (thermal conductivity of materials varies with temperature). The calculated values of the instantaneous efficiency of the solar collector for the period under investigation were also grouped together and analyzed statistically to find out that the efficiencies under those real conditions can also be highly predictable. The same methodology as before was applied in order to examine the system efficiency and the effects of the time, hot water flow, and solar radiation to this important parameter. Fig. 4 shows the variation of the instantaneous efficiency of the solar collector with DN/I, as well as the efficiency variations with 95% confidence. According to this grouping and the subsequent statistical analysis, the average slope of the collector efficiency over the past 2 years is 7.498, i.e. the collector heat loss coefficient UL is 7.498 W/m2 °C (with a standard deviation of 1.01, RSD of 13.5%), while the average constant value corresponding to the ‘‘no loss efficiency’’ is 0.6155 with a standard deviation of 0.05 or RSD of 8%). This implies that the characteristic equation describing the collector thermal performance can be expressed by the following equation:
1007
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
DTa g ¼ 0:6155 7:498 I
ð12Þ
The above equation does not represent a high efficiency collector and there is space for improvement; it is evident that it can perform better if its optical characteristics, s and a, and the quality of its thermal insulation (thermal conductivity and thickness) are improved. The first one will result to an increase in the no loss efficiency, i.e. a figure higher than 0.6155, while a lower thermal conductivity or greater thickness will reduce the heat loss coefficient to a figure lower than 7.498 and consequently the heat losses from the collector. Figs. 6 and 7 show the experimental results along with their associated calculated errors shown as bands. The figures also show the average values of the respective parameters for both the no loss efficiency and the slope of the collector under investigation with 99% confidence boundaries.
6.3. Energy collected The average energy collected can subsequently be estimated from the tank storage temperatures. This estimation is also shown in Fig. 5, below: The above plot (Fig. 5) assumes 2/3 of the water at the upper temperature and the rest at the lower temperature. According to this assumption the system stores energy following a linear behavior and this can easily be predicted. Again, as before, the effects of time (aging of the system), hot water flow (0.07–0.25 L/s), solar radiation within the ranges used, and wind speed (0.0–0.7 m/s) played an insignificant role to the end result. For example, according to this behavior the energy that is stored by the system, 2 h after its initial daily operation, is 42 kJ/kg (±6 kJ/kg). As it was observed the solar energy fluctuations are important only when calculating the instantaneous efficiency and instantaneous energy absorbed by the hot water, but when it come to the average
1.0 0.9 0.8
Efficiency
0.7 0.6 0.5
y = -5.473x + 0.7139
0.4 y = -7.498x + 0.6155
0.3 y = -9.5231x + 0.5171
0.2 0.1 0.0 0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
2o
ΔΤ /Ι (m C/W) Fig. 4. Collector efficiency with 95% confidence limits.
Energy in kJ/kg
40.0
30.0 y = 0.2426x y = 0.2083x
20.0 y = 0.1741x 10.0
0.0
0
20
40
60
80
100
Time (min) Fig. 5. Energy stored as hot water in reservoir with 95% confidence limits.
120
1008
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
0.0
0
5
10
15
20
25
2o
System Slope (W/m C)
-2.0
-4.0
-6.0
-8.0
-10.0
-12.0
-14.0
Measuring Points Fig. 6. Slope of the system performance with 95% confidence limits.
0.80
Value of System Constant
0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00
0
5
10
15
20
25
30
Measuring Points Fig. 7. The experimental results of the system no loss efficiency.
efficiency and total energy stored in the tank, those fluctuations were not important for the end result. Apparently, this behavior has to do with the energy inertia of the system which is tied to its mass, temperature achieved at the collectors, system heat losses, system heat capacity, etc.
7. Conclusions There are some very notable results from the measurements taken over this 2 year period. The first is the fact that the system appears to be very predictable in spite of the fact that the thermal behavior of a solar water heating system constitutes a complex problem involving a number of interrelated parameters. The temperatures in the tank and the energy collected could be easily predicted within a few degrees (and kJ’s) over a long period of time (Table 3).
Table 3 Results of the system statistical analysis. Characteristic
Parameter
Statistical performance
Tank upper temperature Tank lower temperature Efficiency (g) Energy collected (q)
Tu = a(t)
Tu = (0.064 ± 0.008)t
TL = a(t)
TL = (0.021 ± 0.004)t
g = a(y) + b
g = [7.498(±1.01)]y + 0.6155(±0.050)]
q = at
q = (0.2083 ± 0.034)t
The second is the fact that the system is relatively insensitive to solar radiation fluctuations. Solar radiations of 800–1100 W/m2 gave exactly the same system behavior. Also the changes in hot water flow did not produce any significant energy changes. The flow ranges used were from 0.07 and up to 0.25 L/s. Again these
I.M. Michaelides, P.C. Eleftheriou / Experimental Thermal and Fluid Science 35 (2011) 1002–1009
flow variations did not produce any noticeable result on the energy collected in the tank. The third major observation is the fact that the average efficiency of the solar collector is also predictable. The efficiency of this particular collector could easily be predicted with a relatively high degree of accuracy (within 0.2). Taking into account that this value corresponds to 2.7% error, and that from the basic error analysis (considering the error due to the mass, the temperature, the area and the intensity) of the collector efficiency results in an error of the order of 7.2%, this value looks very reasonable. Calculating the absolute error one obtains the value of 16% for the error in the solar collector efficiency. The measured variation of the same value over time yields to a value of 7.2% indicating that the solar collector performance is well within its calculated and expected performance. The above findings are very helpful in predicting the behavior of a particular solar water heating system of known configuration and thermal characteristics and properties characteristics, such as for example its efficiency characteristic graph. In particular, knowing the performance boundaries, one could use them as a tool to assess the performance degradation of the solar collector with time and make a qualitative comparison of the system performance. Furthermore, they can serve as a tool to find out malfunctions in the system, if for example the performance of the system declines from the investigated boundaries. Acknowledgements This work was compiled from experimental data recorded in the solar energy e-learning laboratory which was developed as part of the MARVEL Project of the European Leonardo da Vinci Programme. References [1] European Solar Thermal Energy Industry Federation (ESTIF), Solar Thermal Markets in Europe (Trends and Market Statistics 2006).
1009
[5] C.M. Kemp, US Patent No. 451384, 1891. [6] A.C. Arthur, A novel solar-savings fraction prediction methodology for integral passive solar water heaters, PhD Thesis, Cranfield Institute of Technology, UK, 1990. [7] R.C. Lindsay, W.C. Thomas, Experimental investigation of test procedures for thermal performance of integral collector/storage solar water system, in: Proceedings of the ASME Solar Energy Conference, Knoxville, Tennessee, USA, 1985, pp. 349–58. [8] Z. Lavan, J. Thompson, Experimental study of thermally stratified hot water storage tanks, Solar Energy 19 (1977) 519–524. [9] J. Reiss, D.A. Bainbridge, Breadbox designs, Alternative Sources of Energy 46 (1978) 16–21 (Part 47). [10] P.C. Eames, B. Norton, The effect of tank geometry on thermally stratified sensible heat storage subject to low Reynolds number flows, International Journal of Heat and Mass Transfer 41 (14) (1998) 2131–2142. [11] J.S. Tiller, V. Wochatz, Performance of integrated passive solar water heaters (Breadbox-type) under varying design conditions in the South-eastern US, in: Proceedings of the Seventh National Passive Solar Conference, Knoxville, Tennessee, USA, 1982, pp. 975–80. [12] S.L. Grassie, N.R. Sheridan, The use of planar reflectors for increasing the energy yield of flat-plate collectors, Solar Energy 19 (1977) 663–668. [13] D.P. Grimmer, K.G. Zinn, K.C. Herr, B.E. Wood, Augmented solar energy collection using various planar reflective surfaces: theoretical calculations and experimental results, Solar Energy 21 (1978) 497–501. [14] D.C. Larson, Concentration ratios for flat-plate solar collectors with adjustable mirrors, Journal of Energy 4 (4) (1980) 170–175. [15] H. Tabor, Stationary mirror systems for solar collectors, Solar Energy 2 (1958) 27–33. [16] I.S. Taha, S.M. Eldighidy, Effect of of-south orientation on optimum conditions for maximum solar energy absorbed by a flat-plate collector augmented by plane reflector, Solar Energy 25 (1980) 373. [17] M. Smyth, P.C. Eames, B. Norton, A comparative performance rating for an integrated solar collector/storage vessel with inner sleeves to increase heat retention, Solar Energy (1999) 291–303. [18] N.K. Ghaddar, Stratified storage tank influence on performance of solar water heating system tested in Beirut, Renewable Energy 4 (8) (1994) 911–925. [19] Z.F. Li, K. Sumathy, Performance study of a partitioned thermally stratified storage tank in a solar powered absorption air conditioning system, Applied Thermal Engineering 22 (11) (2002) 1207–1216. [20] A. Zachár, I. Farkas, F. Szlivka, Numerical analyses of the impact of plates for thermal stratification inside a storage tank with upper and lower inlet flows, Solar Energy 74 (4) (2003) 287–302. [21] A.A. Hegazy, M.R. Diab, Performance of an improved design for storage-type domestic electrical water-heaters, Applied Energy 71 (4) (2002) 287–306. [22] Jordan Ulrike, Furbo Simon, Thermal stratification in small solar domestic storage tanks caused by draw-offs, Solar Energy 78 (2) (2005) 291–300. [23] S. Knudsen, Consumers influence on the thermal performance of small SDHW systems – theoretical investigations, Solar Energy 73 (1) (2002) 33–42. [24] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes, John Wiley, New York, 1991. [25] I. Purohit, P. Purohit, Instrumentation error analysis of a paraboloid concentrator type solar cooker, Energy for Sustainable Development 13 (2009) 255–264.