Thermal performance testing of flat-plate collectors

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Solar Energy 82 (2008) 746–757 www.elsevier.com/locate/solener

Thermal performance testing of flat-plate collectors D. Rojas, J. Beermann, S.A. Klein *, D.T. Reindl Solar Energy Laboratory, University of Wisconsin – Madison, Madison, WI, United States Received 22 August 2007; received in revised form 3 January 2008; accepted 4 February 2008 Available online 3 March 2008 Communicated by: Associate Editor B. Norton

Abstract Existing standards for testing the performance of flat-plate solar collectors are documented in ASHRAE 93 [ANSI/ASHRAE Standard 93-2003, 2003. Methods of Testing to Determine Thermal Performance of Solar Collectors, ISSN: 1041-2336, ASHRAE, Inc., 1791 Tullie Circle, Ne, Atlanta, GA30329], ISO 9806-1 [ISO Standard 9806-1:1994(E), 1994. Test Methods for Solar Collectors – Part 1: Thermal Performance of Glazed Liquid Heating Collectors Including Pressure Drop, ISO, Case Postale 56, CH-1211 Geneve 20, Switzerland] and EN12975-2 [European Standard EN12975-2:2001, 2001. Thermal Solar Systems and Components – Solar Collectors – Part 2: Test Methods, CEN, Rue de Stasart, 36, B-1050, Brussels]. The ASHRAE 93 standard requires an experimental determination of the steadystate collector efficiency under prescribed environmental conditions for a range of collector fluid temperatures. Each test requires a minimum of 20 min and 22 tests are required to fully characterize a collector’s thermal performance. The ASHRAE 93 testing procedure is further complicated by the fact that the prescribed weather conditions do not often occur in some locations, which prolongs the time required to conduct the performance tests for a given collector. The EN12975-2 collector test procedure provides an alternative transient test method that can be conducted over a larger range of environmental conditions. This paper compares the results obtained by applying the EN12975-2 standard with results obtained from the ASHRAE 93 steady-state tests for a well-designed single-glazed selective surface flat-plate collector. The collector thermal parameters, FR(sa)e and FRUL obtained by the two test methods show good agreement. The incident angle modifier coefficient determined in the ASHRAE method, which uses a separate test for this purpose, was found to be more accurate than that determined in the transient method according to the EN12975-2 standard, which obtains this value and all other collector parameters in the same step. This transient method, however, uses a refined collector model that includes specific terms for the wind speed dependence and the collector thermal capacitance, which are absent in the ASHRAE model. The long-term collector thermal performance as a part of a water heating system was simulated using the efficiency curves derived from each of the test methods. The solar fractions obtained by simulation are within 7% for both cases. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Collector; Transient test; Simulation; ASHRAE 93; EN12975-2

1. Introduction Solar thermal collector performance tests provide collector parameters that are needed to predict the long-term performance of solar thermal systems. In some locations, collector tests using standards such as ASHRAE 93 are also required for certification and for rebates. The current out-

*

Corresponding author. E-mail address: [email protected] (S.A. Klein).

0038-092X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.02.001

door steady-state thermal performance test method documented in the ASHRAE 93 standard is resource-intensive and can only be conducted when the ambient weather conditions are suitable. In this paper, the quasi-dynamic testing procedure for glazed solar collectors defined in section 6.3 of the European Standard EN12975-2 is explored to determine whether it can yield thermal performance parameter estimates comparative with the ASHRAE 93 standard with less testing effort due to its less restrictive requirements on weather conditions. The results of the quasi-dynamic tests are compared with those of the traditional steady-state tests

D. Rojas et al. / Solar Energy 82 (2008) 746–757

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Nomenclature (sa)en

transmittance–absorptance product at normal incidence (–) AI average interval (s) b0 incident angle modifier coefficient (–) C heat capacity (kJ/kg K) c1 heat loss coefficient (W/m2 K) c2 temperature dependence of heat loss coefficient (W/m2 K2) c3 wind speed dependence of heat loss coefficient (J/m3 K) c4 sky temperature dependence of the heat loss coefficient (W/m2 K) c5 effective thermal capacity (J/m2 K) c6 wind speed dependence in the zero loss coefficient (s/m) DF diffuse fraction (%) dTm/dt mean plate temperature derivative (C/s) EL longwave irradiance (W/m2) 0 F collector efficiency factor (–) FRUL collector overall heat loss parameter (W/m2 K)

directly and based on annual simulations of collector thermal performance. 2. Steady-state solar thermal collectors tests The three most widely used standards for steady-state testing of glazed solar thermal collectors are ASHRAE 93, ISO 9806-1 and EN12975-2 (section 6.1). All three Standards require a collector time constant test, an instantaneous thermal efficiency test, and an incident angle modifier test. Despite some minor differences in their requirements, all of these standards will yield collector performance parameters that can then be used for estimating the long-term performance of an installed system. The following sections summarize the tests required to estimate a collector’s thermal performance parameters according to the ASHRAE 93 test standard. 2.1. Time constant test – s The time constant test consists of two steps. First, the collector is exposed to the sun and its inlet water temperature is temperature-controlled to match the prevailing outdoor air ambient dry bulb temperature. After steady-state conditions are achieved, as described in Table 2 for the ASHRAE Standard, the collector is abruptly shielded from receiving insolation by covering the collector with an opaque surface. Immediately thereafter, the collector inlet (controlled) and outlet (uncontrolled) temperatures are continuously observed. The decrease in collector outlet temperature over time provides information needed to esti-

FR(sa)e collector optical efficiency parameter (–) G* hemispherical solar irradiance (W/m2) Gb direct solar irradiance (W/m2) Gd diffuse solar irradiance (W/m2) Khb incidence angle modifier for direct radiation (–) Khd incidence angle modifier for diffuse radiation (–) mflow mass flowrate (kg/s) mflow dev mass flowrate deviation (%) Q useful energy gain (kJ) ST solar time (s) Ta ambient temperature (C) Tin inlet temperature (C) Tm mean fluid temperature (C) Tout outlet temperature (C) U wind speed (m/s) g collector efficiency (%) h incident angle (deg) r Stefan–Boltzmann constant (W/m2 K4)

mate the collector’s thermal time constant. The collector time constant represents the time needed for the temperature difference between outlet and inlet to decrease to 0.368 (1/e) of its initial value. The ISO and EN Standards use basically the same test procedure except that the difference between collector outlet and ambient temperatures is measured instead of difference between the outlet and inlet temperatures. First, the collector is shielded from the sun until steady-state conditions are achieved. Then the shield is removed abruptly and measurements are taken until the second steady-state is reached. The collector time constant is determined as the time, s, needed for the temperature difference between the collector outlet and the ambient to increase to the initial value plus a fraction of 0.632 of the difference between initial and final value. Steady-state conditions are defined to be achieved as soon as the outlet temperature of the collector does not vary more than ±0.05 °C per minute. In the EN Standard 12975-2 the determination of the time constant is optional. To perform this test, a minimum solar irradiance of 790, 800 and 700 (W/m2) are required by the ASHRAE, ISO and EN Standards, respectively. 2.2. Thermal efficiency test – gg The instantaneous thermal efficiency of a collector, gg, is calculated as the ratio between the useful energy gain and the solar irradiance, Gt, as shown in Eq. (1) Aa Ti Ta Q_ u gg ¼ ¼ F R ðsaÞe F R U L ð1Þ Ag G t A g Gt

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If the thermal efficiency test is performed at near normal incidence conditions so that (sa)e is constant and both FR and UL are constant within the range of tested temperatures, a straight line will result when gg is plotted against x, where x = [(Ti Ta]/Gt]. The measured value pair for gg and x is referred to as a ‘‘data point”. All of the steady-state test standards require a minimum of 16 data points at four different inlet temperatures to obtain the efficiency curve for a fixed-mount collector. The efficiency curve is produced using a leastsquares linear fit of the 16 data points. A graphical representation of the efficiency curve is presented in Fig. 1. The specific environmental conditions required by the ASHRAE 93 in performing the thermal efficiency test are presented in Table 1. The application of Eq. (1) requires that steady-state conditions be maintained during the testing period. Table 2 shows the allowed maximum variation of key variables that define a steady-state condition in accordance to ASHRAE 93. The ISO and EN standards for the steady-state thermal efficiency test have slightly different requirements, but tend to be equally restrictive in limiting the allowable variation of these key variables during the test. 2.3. Incidence angle modifier test – Khb(h) The actual thermal efficiency of a collector depends on the angle of incidence of the solar irradiance. The incidence angle modifier, Khb(h), is used to account for this angular dependence. The incidence angle modifier test consists of

measuring the collector efficiency at a fixed inlet temperature at steady-state conditions with different incidence angles. The different incidence angles are obtained by varying the azimuthal angle of the collector. The angular dependence of the incidence angle modifier is given (approximately) by 1 1 ð2Þ Khb ðhÞ ¼ 1 b0 cosðhÞ The parameter b0, assumed constant, is called the incidence angle modifier coefficient and is generally a positive number. According to both the ASHRAE and the ISO Standards, four efficiency measurements at 0°, 30°, 45° and 60° are needed to perform the test. The steady-state EN Standard prescribes only one efficiency measurement at 50° for flat-plate collectors. 2.4. Inlet temperature distribution for thermal efficiency tests ASHRAE 93 efficiency tests are conducted for four distinctly different collector inlet temperatures. ASHRAE 93 specifies two methods to determine these temperatures. The lowest inlet temperature is set equal to the ambient temperature at the test site in both methods, which can be problematic when ambient conditions are below 0 °C. The highest inlet temperature is defined based either on the manufacturer’s recommended maximum operating temperature or on specified efficiencies achieved during the tests. For both methods, the inlet temperature distributions can require temperatures above 130 °C for typical flat-plate or tubular collectors. This temperature is impractical when testing with water and far higher than the temperatures obtained in normal operation. When water is used as a heat transfer fluid, the ISO 9806-1 and EN12975-2 test standards recommend the maximum inlet temperature to be at least 70 °C and 80 °C, respectively. In contrast, the transient test method in the European Standard EN12975-2 distinguishes the types of collectors by their application and defines the maximum inlet temperature to be based on the collector type. In Section 6.3.4.4, EN12975-2 requires selection of the highest inlet temperatures so that the maximum fluid outlet temperatures are achieved. 2.5. Time effort

Fig. 1. Efficiency curve and data points.

Table 1 Required environmental conditions (ASHRAE 93) Variable

Absolute limits

Total solar irradiance normal to sun (W/m2) Diffuse fraction (%) Wind speed, u (m/s) Incidence angle modifier

790 (minimum) 20 (maximum) 2.2 < u < 4.5 98% < normal incidence value < 102%

A complete set of thermal efficiency tests requires 16 data points to fully characterize the thermal performance for a flat-plate collector. The efficiency for one data point is calculated from measurements taken over a data period during which steady-state conditions (as defined in Table 2) are maintained. Only data taken during the data period are used to calculate the efficiency for any given data point. In addition to maintaining steady-state conditions during the data period, steady-state conditions must also be maintained during a defined time interval prior to the data period, here called the pre-data period. A test period, as defined in


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constant likely do not increase the quality of the test results.

Table 2 Maximum variation of key variables (ASHRAE 93) Variable

Maximum variation

Total solar irradiance normal to surface (W/m2) Ambient temperature (K) Volume flow rate

±32

2.6. Available testing days

±1.5 The greater of ±2% or ±0.005 (gpm) The greater of ±2% or 1 (K)

In considering alternative geographic locations to conduct outdoor tests in accordance with ASHRAE 93, it is of interest to estimate the effect of uncontrolled climatic weather conditions on the ability to meet the criteria listed in Tables 1 and 2. ISIS irradiance data (ISIS) for solar zenith angle, beam and diffuse radiation, are available at 3 min intervals for several locations within the United States. For the following analysis 1 min data are generated by interpolation from the provided 3 min data. To evaluate the number of days suitable for outdoor testing during a certain time period, a suitable test day must be first defined. It is desirable to conduct more than one test per day. A day is considered to be a suitable test day if tests could have been performed for 3 h in total. For both types of outdoor test mounts, a test condition check is sequentially performed for the total irradiance normal to sun, diffuse fraction, and variation of irradiance upon the collector plane. First, the average value of the total irradiance normal to sun during the data period must be greater than 790 W/m2. Next, the diffuse fraction must be less than 20%. These two conditions are checked throughout the test period. The difference between the maximum and minimum solar irradiance upon the collector plane must be less than 64 W/m2 during any 10 min interval within the test period. These test condition checks have been conducted for the years 2003 through 2005 for four locations within the United States using the ISIS data. A ground reflectance value of 0.5 and a collector facing south tilted 50.5 (deg) have been considered for all calculations with the resulting average number of suitable days for outdoor testing shown in Table 4. Clearly, there are more opportunities to test solar collectors in locations such as Albuquerque and Salt Lake City than in other locations like Madison and Sterling. The presented numbers represent an upper limit for the number of days available for testing. The number of test days per year is further restricted by weekends, and variation in other uncontrolled parameters such as wind speed and ambient temperature. The fact that for the fixed test mount measurements must be taken symmetric to solar noon according to ASHRAE 93 further reduces the number of test days for this mount significantly.

Inlet temperature

ASHRAE 93, contains both the pre-data and the data periods. The situation is illustrated in Fig. 2. The required duration of the pre-data period depends on the test mount used. For outdoor tests with a fixed test mount, the pre-data period is 15 min (independent of the required collector time constant measurement); and for outdoor tests with an altazimuth mount, the pre-data period is reduced to 5 min or half of the collector time constant, whichever is larger. The length of the data period is independent of the test mount and specified to be the greater of a 5 min interval or an interval equal to the collector time constant. Pre-data periods have a large influence on the overall time required for a collector test. In fact, the pre-data period dominates the total time consumed for conducting a single outdoor fixed-mount test. Assuming a collector time constant less than 5 min (typical for flat-plate collectors), the data period during which the efficiency measurements are recorded would be 5 min while the pre-data period is 15 min. So 75% of the minimum time required for the test is used for the pre-data period alone with the measurements taken during this period not directly contributing to the archived test results. It is important to note that pre-data periods that are substantially longer than the collector time

Fig. 2. Data and pre-data period for the efficiency tests (s = collector time constant).

Table 3 Highest fluid outlet temperature as a function of collector type

Table 4 Number of test days per year

Collector type

Thot (°C)

Location

Latitude

Longitude

Fixed

Altazimuth

Domestic hot water preparation District heating Swimming pools Process heating

Ta + 60 Ta + 70 Ta + 15 Ta + 90

Sterling, VA Madison, WI Salt Lake City, UT Albuquerque, NM

39.0 43.1 40.8 35.0

77.4 89.3 112.0 106.6

75 87 148 198

95 115 181 228

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The EN12975-2 Standard provides an alternative collector thermal performance test method. This alternate method utilizes a quasi-dynamic collector model that is capable of accounting for transient effects. In addition, the specific data collection requirements in the EN129752 standard are less restrictive than the steady-state methods. The use of a dynamic collector model is presented and discussed in the next section with the intent of evaluating its potential as an alternative to present steady-state methods in order to improve the cost-effectiveness of thermal collector tests. 3. Quasi-dynamic test in standard EN12975-2:2001 The quasi-dynamic test method documented in section 6.3 of the EN12975-2 test standard is applicable to both glazed and unglazed solar collectors that operate with liquid transfer fluids. It is based on the outdoor steadystate test documented in sections 6.1 and 6.2 of the EN12975-2 test standard that uses a second-order dependence of efficiency with temperature difference. The major difference from the steady-state test method is that the collector useful energy gain is measured over small time intervals (5–10 min) while the solar irradiance and ambient temperature are allowed to vary. All the remaining operation parameters are controlled to within a specified range. The specified ranges for the dynamic test conditions are listed in Table 5. The recommended test sequence consists of data collection over 4–5 days, but the actual duration of the test will depend on the weather conditions during testing. Test ‘‘Day Types” (DT) are defined as different combinations of mean plate temperature and weather conditions. The EN12975 Standard requires that the inlet temperature be fixed for each day type to satisfy the mean fluid temperature requirements defined in Table 6. The tests for Day Types 1 and 2 could be completed in less than one day, however, those for Day Type 3 normally require two days. The choice of the hottest temperature (Thot) is provided in Table 3. 3.1. Measurements and data collection The Standard requires the measurements identified in Table 7 to be made during testing. The time-dependent measurements in the lower section of Table 7 must be collected using a sampling interval of 1–6 s, and later averaged over an interval of 5–10 min. Table 5 Test conditions Collector orientation (°) Tilt angle (°) Solar radiation (W/m2) Wind speed (m/s) Mass flow rate (kg/s m2)

Facing south ± 5 45 ± 5 >300 1–4 0.02 ± 1%

Table 6 Mean fluid temperature and weather conditions per Day Type Mean fluid temperature

Clear sky

Ta ± 3 K (Ta + Thot)/3 2 (Ta + Thot)/3 Thot (see Table 3)

Day Day Day Day

Type Type Type Type

Partly cloudy 1 3 3 4

Day Day Day Day

Type Type Type Type

2 3 3 4

Table 7 Required variable measurements Aperture, absorber and gross collector area Fluid capacity Azimuth and tilt angle Global and diffuse irradiance at collector aperture Incident long wave radiation at collector aperture Incident angle of direct solar radiation Surrounding air speed Surrounding air temperature Inlet and outlet temperature of the heat transfer fluid Flow rate of the heat transfer fluid

The collected data must be evaluated before the collector parameter identification process is initiated to ensure its variability and dynamic range meet the requirements to obtain the collector parameters in a statistically unbiased manner. The evaluation procedure consists of providing plots that show expected relations while demonstrating sufficient range of the measured variables. Those plots must be included in the final results of the test. 3.2. Collector parameters identification The model adds correction terms to the steady-state model given in Eq. (1) to account for unsteady-state conditions and other effects. Eq. (3) shows the governing equation for the unsteady-state tests including the dependence of direct and diffuse radiation, wind speed, sky temperature, incidence angle effects and effective thermal capacitance Q_ ¼ F 0 ðsaÞen Khb ðhÞGb þ F 0 ðsaÞen Khd Gd c6 uG A c1 ðtm ta Þ c2 ðtm ta Þ2 c3 uðtm ta Þ dtm þ c4 ðEL rT 4a Þ c5 dt

ð3Þ

A multiple linear regression is applied to the collector data that meet the test specifications in order to simultaneously identify the collector parameters. After all the parameters are identified, the parameters c3, c4 and c6 must be evaluated for statistical significance. In order to be included in the test results the t-ratio, defined in Eq. (4), of each coefficient should be greater than 2. If this is not the case, the regression should be repeated after setting the parameter to 0


tRATIO ¼

average parameter value standard deviation

ð4Þ

4. Experimental data collection A facility capable of performing thermal performance testing of collectors has been developed (Klein et al., 2007; Beermann, 2007). A schematic of the open loop setup used for data collection is shown in Fig. 3. This setup is used for both the steady-state and the quasi-dynamic test measurements. The design includes three electrical heaters to control the inlet temperature. Water was selected as the heat transfer fluid. Not shown in Fig. 3 is the weather station used to measure ambient temperature, relative humidity and wind speed. All variables described in Table 7 were measured at a sampling rate of 1 s, except the long wave irradiance, which was not measured. The uncertainty values for the measured variables are shown in Table 8. As a result of a testing day an input file is generated that contains all the measured variables integrated in periods of 10 s. The data collection process was then applied in accordance with the ASHRAE 93 and the EN12975-2 Standards. The experimental measurements were collected in Madison, WI for 18 different days between November 2006 and May 2007, with an average of 5 h of data collection per day. The experimental facility was designed to collect data according to the ASHRAE 93 Standard. Therefore, the control system used to regulate the inlet temperature was set to follow ambient temperatures variation, in order to maintain a constant temperature difference during testing. The highest inlet temperature used during data collection was 50 °C above ambient. This temperature level was judged to be sufficient even though ASHRAE 93 can

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Table 8 Uncertainty of measurements Variable

Uncertainty

Solar irradiance Inlet, outlet, ambient temperatures Temperature differences, inlet–outlet, inlet–ambient Mass flow rate

±2.9% ±0.54 (K) ±0.15 (K) ±1%

require higher maximum inlet temperatures depending on the collector specifications. 5. Experimental data processing The structure of the data processing method is the same for both the ASHRAE 93 and EN12975 Standards and it consists of two steps. First a file of short-term measurements that satisfy the requirements of the method must be selected from the available measurements. Next a regression technique is applied to identify the collector parameters. The first step requires that the experimental data be filtered in order to provide a set of points that meet the standard requirements. The main difference between the ASHRAE and the EN12975 Standards is that the first requires steady-state conditions for solar irradiance and the second does not. Therefore, different filter procedures are needed for each method. A program has been developed in MATLAB (2006) for the data filtering process and the regression step. The code is provided with an input file containing 10 s integrated values of the measured variables. 5.1. ASHRAE 93 method 5.1.1. File generation for regression The objective of this step is to provide a set of data points that meet the Standard requirements, in order to

Fig. 3. Test setup at Madison Area Technical College, Madison, WI (Klein et al., 2007; Beermann, 2007).

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apply the linear regression to them using the model described in Eq. (1). For this purpose the test data has been filtered using the requirements defined in Tables 1 and 2. 5.1.2. Output file Only 16 data points that meet the ASHRAE standard requirements were found in the input file as shown in Table 9. These data points were collected over 10 different days. The experimental data collection process was performed for a total of 18 days; however, the ASHRAE standard requirements to select a valid data point were difficult to meet during the testing period, precluding the selection of more points. The ASHRAE Standard prescribes 16 symmetric data points to perform the thermal efficiency test. Of the 16 selected data points in Table 9 only 10 are symmetric and one violates the requirements for wind speed. Therefore, the set of data presented in Table 9 does not strictly meet the ASHRAE 93 standard requirements. 5.2. EN12975 method 5.2.1. File generation for multiple linear regression The EN12975 Standard permits the selection of the time period, between 5 and 10 min, in which a data point is collected. To maximize the number of data points, an integration time of 5 min was selected. The objective of the file generation step is to provide a file that contains 5 min averages of the measured parameters during periods in which all other standard requirements are met. The data in this file are used in multiple linear regression (MLR) step in order to obtain the final collector parameters. Several filters were performed to each input file. Table 10 shows the operations done at each filter stage. Using the new file created after the filtering steps, the consecutive 10 s measurements for calculating 5 min averTable 9 Data points selected for the application of the ASHRAE 93 standard Day of year

G averagea (W/m2)

Ta average (°C)

Tin Ta (°C)

Solar noon deviation (min)

(Tin Ta)/ G (°C/(W/ m2))

g (–)

309 324 309 324 353 353 307 309 353 307 353 353 323 353 353 309

891 941 917 936 907 890 1000 928 897 1002 865 824 849 753 740 745

10.3 4.4 11.5 4.9 5.4 5.0 0.4 13.0 6.1 1.9 6.7 2.6 4.2 1.3 7.1 14.0

0.9 0.0 0.0 0.0 0.0 0.0 11.9 13.9 16.7 29.6 33.2 33.3 33.5 49.5 50.0 50.9

57 2 30 20 10 10 52 11 38 11 66 89 87 115 118 120

0.001 0.000 0.000 0.000 0.000 0.000 0.012 0.015 0.019 0.030 0.038 0.040 0.039 0.066 0.068 0.068

0.6744 0.6713 0.6655 0.6657 0.6661 0.6589 0.6241 0.6025 0.5767 0.5497 0.4796 0.4825 0.4722 0.3912 0.3468 0.3497

a

Solar irradiance measured on collector plane.

ages were selected (30 consecutive measurements), considering a reference value of approximately 0.02 (kg/s m2) for the collector mass flow rate. Two conditions are applied to select a set of 30 consecutive measurements for averaging in each time sequence: (1) the maximum allowed inlet temperature difference should be less than 1 (K); and (2) the average mass flow should not differ more than 1% to the reference value. The general approach was to select the maximum possible number of data 32 points in each time sequence. First, the computer code selects the 5 min averages with an average collector mass flow rate closest to the reference value. Then, it checks the deviation from the reference flow rate to ensure it is within the 1% limit followed by verifying that there are enough rows remaining to create a new data point. Then it selects the next 5 min average with the second closest average mass flow rate to the reference value, and then checks the deviation condition. This process is repeated until there are not enough measurements to create a new data point in the time sequence. At the end of this process the averages are calculated and stored in the output file. The output file contains 5 min averages of the experimental data as displayed in Table 11.

5.2.2. Long wave irradiance estimation The quasi-dynamic collector model requires the long wave irradiance. This quantity was not directly measured during collector testing. In order to consider this parameter in the model, the long wave irradiance is estimated based on collected information about the relative humidity and the ambient temperature. The expression for the heat flux on the collector provided by the sky thermal irradiance is shown in Eq. (5) Q_ ¼ c4 ðrT 4sky rT 4a Þ

ð5Þ

The sky temperature, Eq. (6), can be estimated considering the time of the day, and the ambient and dew point temperatures (Duffie and Beckman, 2006) T sky ¼ T a ð0:711 þ 0:0056 T dp þ 0:000073T 2dp 1

þ 0:013 cosð15tÞÞ4

ð6Þ

Table 10 Filter stages applied to input files Filter stage

Operation

1

– Selects rows with G > 300 (W/m2) – Selects rows with mflow > 0 (kg/s) – Selects rows with Qu > 0 (kJ)

2

– Cuts transitions in Tin – Selects time sequences with more than 5 min

3

– Calculates Tm and dTm/dt – Removes first row at beginning of time sequences – Selects rows with 1 (m/s) < u < 4 (m/s)

D. Rojas et al. / Solar Energy 82 (2008) 746–757 Table 11 Output file content

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Table 12 Day Type distribution of data points

Column

Variable

Name

Units

Day Type

18 Day data set

5 Day data set

1 2 3 4 5 6 7 8 9 10 11 12 13 15 15

Date Average interval Solar time Inlet temperature Outlet temperature Ambient temperature Mean plate temperature Mean plate temperature derivative Total solar irradiance Diffuse fraction Collector efficiency Incident angle Wind speed Mass flow rate Mass flow rate deviation

Date AI ST Tin Tout Ta Tm dTm/dt G* DF g h U mflow mflow dev

(ymmdd) (s) (s) (C) (C) (C) (C) (C/s) (W/m2) (%) (%) (deg) (m/s) (kg/s) (%)

1 2 3 4

15 31 278 51

8 25 125 19

Total

375

177

where Tsky and Ta are in (K) and Tdp (dew point temperature) is in (C), and the parameter t represents the hour from midnight.

Table 13 Data point distribution of Day Type 3 Tm Ta (C)

18 Day data set

5 Day data set

Sunny

Cloudy

Sunny

Cloudy

5–18 19–30 31–45

14 73 40

19 41 91

0 6 9

9 40 61

ð7Þ

The residuals are correlated and have variances that depend on the time sequence of the data points. It is a common practice to scale a t-student distribution (Box et al., 2005) to the residuals so they all have the same variance. A hypothesis test for outliers involves comparing ti with the critical values of the t-distribution. If ti is large, it casts doubt on the assumption that this residual has the same variance as the others. Confidence intervals that do not include zero are equivalent to rejecting the hypothesis (at a significance probability of 95%) that the residual mean is zero. Such confidence intervals provide evidence that the observation is an outlier for the given model. This knowledge was applied for detecting outliers in the output file. The 95% confidence interval for the residuals was calculated. The data points for which the confidence interval included zero were removed from the output file, and then the regression routine was applied again to the new output file. The application of this filter to the experimental data is not prescribed in the EN12975 Standard. However, the quantity and distribution of data points permits this additional filtering stage, in order to choose the best data to get the most accurate estimation of the collector parameters.

The method estimates the coefficients for the linear collector model in Eq. (3). The model for the transient collector test procedure is then applied to the output file and to the predicted collector parameters. Also calculated are the 95% confidence interval for the parameters and the residuals ri (Eq. (8)) defined as the difference between the measured energy gain per unit area and the same quantity predicted by the model for data point i _ _ Q Q ð8Þ ri ¼ A measured A predicted

5.2.5. t-ratio evaluation for c3, c4 and c6 According to the EN12975 Standard the t-ratio (Eq. (4)) of the coefficients c3, c4 and c6 should be greater than 2 for those parameters presented in the results. If the t-ratio is less than 2, the coefficient shall be set to zero and the parameter identification should be repeated with the adjusted collector model. In order to calculate the t-ratio of the three coefficients, the standard deviation is needed. This value was obtained using the 95% confidence interval information and assuming a normal distribution of all parameters.

5.2.3. Output file for multiple linear regression Two data sets were obtained from the input file. The complete information contained in the input file provided a total of 375 data points after the filtering process described in 5.2.1. This set of information corresponds to a total of 18 days of testing. In addition, data collected during a selection of 5 days were used to create another data set. Table 12 shows the distribution of the data points per Day Type in both data sets. Day Type 3 considers a range of Tm Ta for both cloudy and sunny days. Table 13 provides the distribution of the data points included in Day Type 3. 5.2.4. Multiple linear regression (MLR) The multiple linear regression (MLR) step identifies the collector parameters. The process is a regression using the collector model described in Eq. (3). Using Eq. (2) to expand the first term in the collector model expression, Eq. (7) is obtained F 0 ðsaÞen Khb ðhÞGb ¼ F 0 ðsaÞen Gb b0 F 0 ðsaÞen Gb

1 1 cosðhÞ

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6. Results

Table 15 Data point distribution of Day Type 3

6.1. ASHRAE 93 test

Tm Ta (C)

18 Day data set

5 Day data set

Sunny

Cloudy

Sunny

Cloudy

5–18 19–30 31–45

14 56 13

15 31 74

0 3 2

8 24 54

The incidence angle modifier coefficient (b0) obtained by applying the ASHRAE 93 Standard is estimated to be 0.1792. The collector parameters were obtained applying a linear regression to the data set showed in Table 9. Considering the uncertainty propagation from the measurements, the collector parameters were found to be 0.667 ± 0.0090 (–) for F0 (sa)en and 4.574 ± 0.234 (W/ m2K) for FRUL.

6.2. EN12975 test The transient model was applied to the sets of data described in 5.2.3, considering all terms in Eq. (3). The tratio of coefficient c6 was found to be below 2 in both sets of data; therefore, this coefficient was omitted from further consideration in the model as prescribed by Standard EN12975. In evaluating a revised model without coefficient c6, it was determined that the t-ratio for coefficient c4 was also below 2. As in the former case the model was revised to omit both coefficients c4 and c6. The final collector parameters were obtained in the third run of the model for both sets of data. The outlier filtering process described in Section 5.2.4 removed some of the experimental data points used in the models. From an initial set of 375 5min average data points in the 18 days data set and 177 5-min average in the 5 days set, only 269 and 123 data points, respectively, were used in the estimation of the collector parameters. Table 14 shows the distribution of these data points. Day Types 1 and 2 are relevant in the estimation of F0 (sa)en and the incidence angle modifier for direct and diffuse radiation. The number of data points considered in the estimation of these parameters is sufficient for an accurate representation, considering that the ASHRAE 93 only requires eight data points for their estimation. Most of the data points are concentrated in Day Type 3, the type with more combinations of different conditions, as shown in Table 15. Table 16 shows the predicted collector coefficients after the application of the transient model. The upper and lower bounds of the confidence intervals for the parameters are also displayed. The correlation coefficient (R2) obtained Table 14 Day Type distribution of data points Day Type

18 Day data set

5 Day data set

1 2 3 4

12 20 203 34

7 22 91 3

Total

269

123

Table 16 Predicted collector coefficients Predicted coefficients

18 Day data set Value ± 95% CI bounds

tRATIO

5 Day data set Value ± 95% CI bounds

tRATIO

F0 (sa)en c6 (s/m) c1 (W/m2 K) c2 (W/m2 K2) c3 (J/m3 K) c4 (W/m2 K) c5 (J/m2 K) b0 Khd

0.6422 ± 0.0030 – 5.3642 ± 0.2816 -0.0235 ± 0.0040 0.1804 ± 0.0796 – 9044.0 ± 519.9 0.1066 ± 0.0190 0.9789 ± 0.0067

428.1 – 37.4 11.8 4.44 – 34.1 n.a. n.a.

0.6397 ± 0.0026 – 5.1014 ± 0.2383 -0.0114 ± 0.0035 0.1759 ± 0.0936 – 10022.0 ± 435.4 0.1146 ± 0.0264 0.9892 ± 0.0062

457.0 – 42.0 6.36 3.68 – 45.1 n.a. n.a.

for the revised models was 99.7% and 99.9% for the 18 and 5 days sets of data, respectively. The parameter c2 was found to be negative. There is no specific indication in the Standard about the expected sign of this coefficient. It is clear from Eq. (3) that parameters c1 and c2 model the conduction and part of the convection heat losses of the collector. The wind speed and the long wave irradiance terms take into account the other parts of the heat losses. 7. ASHRAE 93 v/s EN12975-2 results 7.1. Incidence angle modifier test The incidence angle modifiers identified according to the EN12975 and ASHRAE 93 standards are shown as a function of incidence angle in Fig. 4. Differences between the EN12975 and ASHRAE 93 results are apparent for incidence angles greater than 40 deg with both EN12975 results indicating better collector performance at high incidence angles. The ASHRAE 93 curve coincides closely with literature predicted values for a single-glazed 1 cover collector (with no surface treatment) presented in Duffie and Beckman (2006). The difference in the incidence angle modifiers identified by the two test standards is not surprising. While the ASHRAE 93 standard prescribes four different measurements at incidence angles of 0°, 30°, 45° and 60°, the EN12975 standard test has no specific measurement requirements for the incidence angle modifier. This parameter is estimated at the same time as the other collector parameters in the linear regression. Fig. 5 shows the incidence angle distribution of the 269 data points that were in the 18 days data set.


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Fig. 4. Incidence angle modifiers.

model in Eq. (3), with both 18 and 5 days data sets. In the ASHRAE 93 test, the efficiency curve was also corrected by the ratio between the gross and effective areas (Ag/Aa). The curves show no differences in the y-intercept value, related to the optical efficiency. In addition, the slopes of the efficiency curves, related to the thermal loss coefficient, are similar but slightly steeper in the EN12975 curves. The EN12975 curves have curvature, which results from the quadratic term, c2, in the collector model used (Eq. (3)). The largest difference between the three curves is less than 5% in the efficiency estimation. However, as noted in the next section, it is the long-term performance estimates based on the collector test parameters, rather the efficiency curve itself that indicates the difference between the collector test results. Fig. 5. Incidence angle distribution in EN12975-2 18 days data set.

The data points included in the set by application of the EN12975 standard are concentrated at incidence angles between 0° and 40°. In this range, the incidence angle modifier, Khb, is very close to 1 as seen in Fig. 3. Data points for which the incidence angle is less that 40° are not useful in determining b0, so it is likely that the value determined from this data set is imprecise. 7.2. Thermal efficiency test Fig. 6 shows the efficiency curves for both Standards, plotted considering the following steady-state conditions: Gb = 680 (W/m2), Gd = 120 (W/m2), h = 15° and u = 3 (m/s). In order to plot the EN12975 test results as a function of Tin instead of Tm, a new set of parameters (not those in Table 14) was obtained from applying the multiple linear regression using Tin instead of Tm in the collector

7.3. Long-term performance A set of simulations were conducted with TRNSYS (Klein et al., 2004) to evaluate the effect of the differences in the efficiency curves, shown in Fig. 6, on the long-term performance of a typical solar domestic water heating system for three separate locations. A standard solar system is considered with the 7.8 m2 of the test collector, 75 l of water storage per m2 of collector and a maximum hot water load of 30 kg/h. This load was assumed constant between 9 a.m. and 11 p.m., and zero for the remaining time. The tank was modeled as a three node stratified tank. The collector water pump was set to work from 8 a.m. to 6 p.m. at a constant flowrate of 420 kg/h. Four different combinations of area/load were selected. The TRNSYS collector model used either Eq. (1) for the ASHRAE 93 test or the Eq. (3) for the EN12975 quasi-dynamic model. As the linear collector efficiency determined by the ASHRAE 93 standard does not consider wind speed, wind speed was

756


Fig. 6. Efficiency curves.

Table 17 Results of annual solar fraction simulations Area/load (m2 year/MJ)

Test type

Albuquerque NM (%)

Madison WI (%)

San Francisco CA (%)

7.7 103

ASHRAE 93 EN12975 – 18 d EN12975 – 18 d, u fixed EN12975 – 5d

53.4 52.5

34.9 33.6

44.7 43.3

52.2

33.6

43.6

52.5

33.7

43.4


66.4 64.5

43.5 41.3

55.6 52.9

64.0

41.3

53.4

64.4

41.4

53.1


87.2 83.1

57.4 53.4

73.0 67.7

82.2

53.4

68.5

82.8

53.5

67.9


100.0 97.0

68.0 62.4

86.0 78.6

95.6

62.5

79.7

96.5

62.5

78.8

4.0

4.2

4.5

1.5 104

3.1 104

4.6 10

4

uaverage (m/s)

ent cases. The first case uses the hourly wind speed directly from the weather database, and in the second case fixes this variable at a constant 5 (m/s). The solar fraction estimated for the systems using the EN12975-derived model are systematically lower than the solar fraction estimated from the ASHRAE 93-derived model due to the increased collector losses for the former case. For low values of area/load, the solar fractions predicted with the ASHRAE 93-derived model are slightly higher than those using the EN12975-derived models, but the differences are below 2.5% in all cases (see Table 17). Higher values of area/load result in increased differences between the ASHRAE 93 and the EN12975 models, yielding a maximum value of 7%. For the simulations conducted using the EN12975 data, the comparison of the performance with actual wind data vs. the constant 5 m/s wind speed, shows no significant differences in the predicted solar fractions. The fact that the EN12975 test method directly considers the effect of wind speed on collector performance may be an advantage of the EN12975 method over the ASHRAE method. 8. Conclusions

not used in the long-term performance simulation with the ASHRAE 93 test results. Wind speed was considered in the EN12975 standard performance estimation with two differ-

Steady-state collector Standards ASHRAE 93, ISO9806-1 and EN12975-2 (Sections 6.1 and 6.2) have been studied and compared, with particular interest in the ASHRAE 93 test method. The results of the comparison (not presented in this paper) have shown that all three standards provide similar results for the collector parameters. The feasibility of conducting solar thermal collector tests in accordance with ASHRAE 93, as related to the number of suitable days available for testing, depends strongly on the climatic conditions of the test site. Variation in wind speed and ambient temperature and the requirement of symmetric measurements additionally reduce the number


of test days calculated here. Northern climates are less suitable for solar collector tests, even though solar systems can be operated effectively in northern climates. As a result, the application of alternative test methods with higher feasibility and lower costs is desirable. EN12975-2 additionally offers a transient test method, with less restrictive solar radiation requirements and increased accuracy for estimating collector performance parameters. Both the steady-state ASHRAE 93 and the transient EN1297-2 Standards have been applied to a well-designed single-cover flat-plate collector. Experimental data were collected during winter and spring months in Madison, Wisconsin, during a period of 18 days for an average of 5 h per day. Over this period, only 10 data points that strictly meet the ASHRAE 93 Standard requirements have been collected. In the same period, 375 data points meet the required conditions in the EN12975-2 transient method. In addition, a subset of 177 data points that meet transient EN12975-2 were found considering 5 of the total 18 days data collection period. The reasons for the differences in the number of data points between both methods, are the less restrictive solar irradiance requirements and the shorter period to collect a data point (4 times shorter) in the case of the transient EN12975-2 Standard. The requirement of measurements symmetric to solar noon for a fixed test mount also significantly reduces the number of data points obtained in accordance with ASHRAE 93. The ASHRAE Standard conducts a separate test for the incidence angle modifier coefficient, with measurements at four different incident angles. The result with this method coincides with literature predicted values. The transient EN12975-2 Standard calculates this value in the same regression used to identify all of the collector parameters. Since the incident angles for most of the data are concentrated between 0° and 40°, and in this range the incident angle modifier is very close to 1, the regressed value of the incident angle modifier was judged to be inaccurate. The collector parameters obtained by both methods are very similar. No differences were detected in the y-intercept between both Standards. The transient method obtains a slightly steeper heat loss coefficient, but differences in the efficiency curve are always below 5%. The model used in this method allows the determination of the collector thermal capacitance, and utilizes a specific term for the wind

757

speed dependence. The fact that the transient EN12975 test method directly considers the effect of wind speed on collector performance is an advantage of this method over the ASHRAE 93. Long-term performance simulations were conducted with both sets of collector parameters for regular house water heating system. The results show differences smaller than 7% in all simulated locations and conditions. Acknowledgements The assistance of Tom Kaminski at Madison Area Technical College in Madison, WI was invaluable to the preparation of this paper. The financial assistance from Focus on Energy in Wisconsin, the Eduardo Neale Silva Scholarship (for D. Rojas) and the German Academic Exchange Service (DAAD) and Dr. Ju¨rgen-Ulderup-Stiftung, Germany (for J. Beermann) was appreciated. References ANSI/ASHRAE Standard 93-2003, 2003. Methods of Testing to Determine Thermal Performance of Solar Collectors, ISSN: 1041-2336, ASHRAE, Inc., 1791 Tullie Circle, Ne, Atlanta, GA30329. Beermann, J., 2007. Performance Testing of Solar Thermal Collectors, Final Project Report, Solar Energy Laboratory, University of Wisconsin – Madison. The test facility was constructed by Tom Kaminski at Madison Area Technical College, Madison, WI. Box, G.E.P., Hunter, J.S., Hunter, W.G., 2005. Statistics for Engineers, second ed. Wiley. Duffie, J.A., Beckman, W.A., 2006. Solar Engineering of Thermal Processes, third ed. Wiley. European Standard EN12975-2:2001. 2001. Thermal Solar Systems and Components – Solar Collectors – Part 2: Test Methods, CEN, Rue de Stasart, 36, B-1050, Brussels. Integrated Surface Irradiance Study (ISIS) Network, . ISO Standard 9806-1:1994(E), 1994. Test Methods for Solar Collectors – Part 1: Thermal Performance of Glazed Liquid Heating Collectors Including Pressure Drop, ISO, Case Postale 56, CH-1211 Geneve 20, Switzerland. Klein, S.A. et al., 2004. TRNSYS – Transient System Simulation Program, Version 16. Solar Energy Laboratory, University of Wisconsin, Madison. Klein, S.A., Reindl, D.T., Beermann, J., 2007. Alternative Methods for Performance Testing of Solar Thermal Collectors, American Solar Energy Society 2007 conference, paper 011A, Cleveland, OH, 2007. MATLAB, 2006. Release 14, MathWorks.