National Bureau of Stamiards

Library, E-01 Admin. BJdg.

OCT 6 1981

lOO

NBS TECHNICAL NOTE 1140

U.S. DEPARTMENT OF COMMERCE/ National Bureau of Standards

Uncertainty in Determining Thermal

Performance of Liquid-Heating

Flat-Plate Solar Collectors

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NATIONAL BUREAU OF STANDARDS

/ The National Bureau of Standards' was established by an act of Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

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Uncertainty in Determining Thermal Performance

of Liquid-Heating Flat-Plate Solar Collectors

Elmer Streed

David Waksman

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

MATKUIAL BUBSAU

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Prepared for:

U.S. Department of Energy

Office of Solar Applications for Buildings

Office of the Assistant Secretary Conservation and Solar Applications

Washington, D C 20585

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f:cJi.Mj(LClA riotU.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued April 1981
National Bureau of Standards Technical Note 1140

Nat. Bur. Stand. (U.S.), Tech. Note 1140, 97 pages (April 1981) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1981

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Price $4.00

(Add 25 percent for other than U.S. mailing)
UNCERTAINTY IN DETERMINING THERMAL PERFORMANCE OF LIQUID-HEATING FLAT-PLATE SOLAR COLLECTORS

By

E.R. Streed and D. Waksman

ABSTRACT

Thermal performance measurements of eight liquid-heating flat-plate solar collectors were

conducted with two to four collectors of each type at four outdoor test sites. Tests were

performed in accordance with the procedure prescribed by ASHRAE Standard 93-77. Statistical

analysis of data sets for each collector type within test sites and between test sites was

done using ASTM recommended methods to evaluate test method measurement uncertainty.

Illustrations of the influence of thermal performance data uncertainty are presented for

collector material degradation, collector rating and calculated system performance.

KEY WORDS: Collector rating; measurement; solar collector; standards; thermal

performance; uncertainty.

ili
PREFACE

/ The Department of Energy (DoE) is conducting an Interim Solar Collector Testing Program to stimulate the establishment of a permanent collector testing/certification program.

Elements of the program are related to the verification of test procedures, evaluation and

improvement of test laboratory capabilities, and the measurement and distribution of

reliable performance data for solar collectors. This study of collector thermal performance

data uncertainty was conducted by the National Bureau of Standards (NBS) in support of this

DoE test program.

This report is Intended to be informative and instructive; it is not meant to be an evaluation of products or facilities. In no case does such identification imply

recommendation or endorsement by the National Bureau of Standards, nor does it imply

that the products are necessarily the best available for the purpose.

The cooperation of the following people is greatly appreciated: Richard D. Whitaker and

William Dokos, DSET Laboratories, Inc. ; Ross McCluny, James Huggins and James Rowland,

Florida Solar Energy Center; Roger Wedell and Ronald Dammann, Lockheed Palo Alto Research

Laboratory; Ken Shih and Mark Rallas, Wyle Laboratories; and Aaron Dawson, Virginia

Polytechnic Institute and State University. The devoted effort of Dr. John Mandel in performing the statistical analysis, instrument calibration by John Jenkins, data collection

by Cathy Scarbrough and Patricia Christopher, and computerized calculations by William May,

all at NBS, contributed significantly to the evaluation and presentation of the data.

iv
TABLE OF CONTENTS

Page

ABSTRACT iii

PREFACE iv

LIST OF TABLES AND FIGURES vi

SI CONVERSION UNITS vii

1. INTRODUCTION 1 1.1 Background 1 1.2 Current Studies 1 1.3 Report Purpose 2

2. THERMAL PERFORMANCE TEST METHOD 3 2.1 General 3 2.2 Efficiency 3 2.3 Incident Angle Modifier. 4

3. THERMAL PERFORMANCE DATA UNCERTAINTY 8 3.1 General 8 3.2 Measurement Uncertainties 8 3.3 Meteorological Uncertainty 9

4. BASELINE DATA 11

4.1 Collector Description 11

4.2 Test Sites 11

4.3 Measured Data 13

5. DATA ANALYSIS 17 5.1 General 17 5.2 Thermal Efficiency 17 5.3 Incident Angle Modifier 21

6. IMPACT OF DATA UNCERTAINTY 23

6.1 General 23

6.2 Collector Degradation 23 6.3 Collector Rating 23

6.4 System Performance 26

7. CONCLUSIONS ' 30

8. RECOMMENDATIONS 31

I 9. REFERENCES 32

APPENDIX A. Data Statistical Analysis 34

A-1 General 34

A-2 Residual Standard Deviation 34

APPENDIX B. Detailed Collector Description Data 38

APPENDIX C. Thermal Performance Data 41

APPENDIX D. Solar Heating and DHW System Description 90
Page

LIST OF TABLES

Table 1. Environmental Test Conditions Allowed by ASHRAE Standard 93-77 10

Table 2. Test Collector Specimen Description 12

Table 3. Baseline Collector Intercept and Slope Data for All Collectors 14

Table 4. Incident Angle Modifier Baseline Data 16

Table 5. Standard Deviation and Coefficient of Variation of Intercept

Within and Between Test Sites 19

Table 6. Standard Deviation and Coefficient of Variation of Slope

Within and Between Test Sites 20

Table 7. Incident Angle Modifier Standard Deviation Values Within and

Between Test Sites 22

Table 8. Thermal Performance Properties of Four Typical Flat Plate

Collectors and Associated Data Uncertainties 25

Table 9. Measurement Uncertainty Influence on Rating 27

Table 10. Collector Measurement Uncertainty Influence on System Prediction 28

Table A-1. Data Point Residual Standard Deviations for All Measurements 36

Table B-1. Collector Material Properties and Pertinent Dimensions 39

Table B-2. Individual Collector Area Measurements by Test Site No. 1 40

Table B-3. Collector Area Measurements for Each Test Site 40

LIST OF FIGURES

Figure 1. Typical solar collector thermal performance plot and data points 5 Figure 2. Typical solar collector incident angle modifier plot and data points. • . 7 Figure 3. Uncertainty associated with the ASHRAE 93-77 efficiency measurements

for a single-glazed selective absorber type collector 9 Figure 4a. Comparison of data point spread for double covered selective

absorber type collector with uncertainty band 18

Figure 4b. Comparison of data point spread for double covered nonselective

absorber type collector with uncertainty band 18

Figure 5. Sensitivity of a single glazed selective absorber type collector

to changes in transmittance 24

Figure 6. The relationship between solar fraction and incident angle modifier

slope for December and annual performance 29

Figure A-L Illustrations of the calculation and significance of standard

deviation 35

Figure A-2a Comparison of first and second order curve fits for FRP covered

nonselective absorber type collector 37

Figure A-2b Comparison of first and second order curve fits for one cover, heat trap, nonselective absorber type collector 37
SI CONVERSION UNITS

In view of the present accepted practice in this country for building technology, common

U.S. units of measurement have been used in the data appendix. In recognition of the

position of the United States as a signatory to the General Conference of Weights and

Measures, which gave official status to the metric SI system of units in 1960, assistance

is given to the reader interested in making use of the coherent system of SI units by giving

conversion factors applicable to U.S. units used in this document.

Length

1 in = 0.0254 meter (exactly)

1 ft = 0.3048 meter (exactly)

Area

1 in^ = 6.45 X lO"** meter^

1 ft^ = 0.09290 meter2

Volume

1 in = 1.639 X 10~^ meter^

1 gal (U.S. liquid) = 3.785 x lO'^ meter^

Mass

1 ounce-mass (avoirdupois) = 2.834 x 10~^ kilogram

1 pound-mass (avoirdupois) = 0.4536 kilogram

Pressure or Stress (Force/Area)

1 inch of mercury (60°F) = 3.377 x 10^ pascal

1 pound-force/inch^ (psi) = 6.895 x 10^ pascal

Energy

1 foot-pound-force (ft-lbf) = 1.356 joule

1 Btu (International Table) = 1.055 x 10^ joule

1 kilowatt-hour = 3.600 x 10^ joule = 3.412 x 10^ Btu

Power

1 watt = 1 X 10 erg/second

1 Btu/hr = 0.2929 watt

Temperature

to^ = 5/9 (top - 32)

Heat

1 Btu-in/h'ft2.°F = 1.442 x 10"^ W/m-K (thermal conductivity)

1 Btu/lbm-°F = 4.184 x 10^ J/kg-K (specific heat)

1 langley = 4.184 x lO"" J/m2 = 1 cal/cm^ = 3.69 Btu/ft^

1 . INTRODUCTION

1.1 Background

The Department of Energy (DoE) and the Department of Housing and Urban Development

(HUD) are committed to the demonstration of building solar heating and cooling

applications in the United States. One of the objectives of the demonstration

program involves the development of standardized procedures and methods for testing

and evaluating solar collectors. As stated in the "National Program for Solar

Heating and Cooling of Buildings" [1] , the National Bureau of Standards (NBS) is

working with industry and professional organizations to develop nationally recognized consensus test procedures.

The ASHRAE Standard 93-77 [2] has been adopted in the United States (U.S.) as a consensus test method for determining the thermal performance of solar collectors

and is generally recognized as an adequate procedure. Initial development of the test procedure [3] and experimental evaluation for selected flat-plate, evacuated

tubular and low concentrating collectors [4] have been reported by NBS. A round

robin type study of the basic test procedure was conducted utilizing 21 test facilities with two types of flat-plate collectors during 1976 and 1977. Analysis

of these results [5] showed that correction for the influence of the environment

and test conditions to a set of reference conditions for incidence angle, diffuse

fraction, wind, irradiance and ambient temperature resulted in only a minor reduction in data spread. It was concluded that systematic type measurement problems

resulting from instrument calibration, sensor installation and procedural variations are probably more significant contributors to the data uncertainty.

1.2 Current Studies

In order to stimulate the establishment of an industry operated collector testing and

certification program, DoE organized an Interim Collector Testing Program in 1978.

The program had three major objectives as follows:

1. Provide state-of-the-art thermal performance data for designer,

manufacturer and consumer use on a large number of collectors

2. Provide a technical base for the establishment of a collector

certification and rating program

3. Evaluate and modify (if necessary) collector performance test methods

The thermal performance measurements portion of the program has been completed and

the data are being compiled for publication. Only a limited number of tests were

conducted for comparability purposes.

The primary factors that need to be determined are a measure of the repeatability

and reproducibility of ASHRAE Standard 93-77. Repeatability is related to the

variability in replicate results obtained on the same product within a single test facility. Reproducibility is related to the variability in results obtained on

the same product between test sites.

As part of the overall DoE Solar Energy Program, a project was initiated in 1978 by

NBS [6] to investigate accelerated and "real time" test methods for predicting

collector durability and reliability. Representative commercially available flatplate solar collectors and their materials are being exposed outdoors in four

different U.S. climatic regions and with two types of solar simulators. As part

of the characterization of the collectors, initial thermal performance measurements

were made on multiple samples of each collector at each test site prior to commencing the exposure tests. These baseline data consisting of measurements

made on eight collector types at each of four sites, with two to four collector

replicates at each site, provide an appropriate data set which is used in this

study to evaluate collector thermal performance measurement capabilities.
II

The NBS test programwas primarily designed for durability/reliability considerations,

and does not include some features desirable for identifying individual factors

contributing to the measurement uncertainty, such as product variability, specific environmental conditions, and test apparatus. Additional investigations to evaluate

and improve the ASHRAE test method are currently being conducted under the direction

of an ASHRAE 93R (Revision) Committee.

1.3 Report Purpose

It is the intent of this study to show the following: (1) overall uncertainty

in collector thermal performance data as reported by commercial test facilities

on commercially available solar collectors (individual error sources will not be

identified except for some cursory observations of possible causes) , and

(2) illustrations of how the uncertainty in individual collector test results affects

the rating and selection of collectors for system design and for determining degradation with exposure or operating time.
THERMAL PERFORMANCE TEST METHOD

2.1 General

The thermal performance tests used to obtain the instantaneous efficiency were

specified to be performed in general accordance with ASHRAE Standard 93-77. This consensus test method for both air and liquid heat transfer fluids includes guidelines for the test apparatus configuration, instrumentation accuracy, and precision

tolerances. The measurements needed to determine the instantaneous efficiency are temperature, fluid mass flow, solar irradiance, and collector area, as expressed by

the following equation:

n = m c (t - t .)/!> (1) p f,o f,i t g

where n = collector efficiency

2 m = fluid mass flow rate (kg/s-m ) c = fluid specific heat (J/kg-°C)

P

tj. . = transfer fluid inlet temperature (°C) t- = transfer fluid exit temperature (°C)

t , o „ A = collector gross area (m ) g

2 I = solar irradiance (W/m )

.

These measurements must be performed precisely with calibrated instruments capable of

achieving the prescribed accuracy and also must be performed within a limited range

of weather ana test conditions. During testing, the solar irradiance, inlet

temperature, and fluid flow rate must be maintained within close tolerances for time

periods in excess of the collector time constant to insure that a quasi-steady state

thermodynamic condition prevails in the collector with respect to the gain and loss

of energy. Climatic factors such as ambient temperature and wind have relatively

wide allowable ranges and they must be measured and reported as well as the solar

diffuse fraction and relative humidity. Other test parameters which may Influence

the thermal performance but are not specifically restricted are tilt angle, sky

temperature and solar spectral distribution.

The test procedure specifies that at least four inlet temperatures shall be used to obtain near normal incidence efficiency values over a range of operating conditions.

At least four data points shall be taken at each inlet temperature. When measurements

are made outdoors on a non-tracking mount, two data points should be taken before

solar noon and two after solar noon to cancel out heat capacity effects. Measurements

made using a solar simulator or an altazimuth mount are conducted with the sun normal to the collector during the test period. Each data point is obtained by

integrating the measured parameters over a five-minute period (longer for collectors

with time constants in excess of five minutes) and calculating the efficiency as indicated in equation 1.

2.

2

Efficiency

ASHRAE Standard 93-77 is based upon the Hottel-Whlllier-Bliss analytical model which

assumes that the efficiency of a flat-plate solar collector operating under steadystate conditions and normal incidence can be described by:

n = F^(Ta)^-F^Uj(t^^^- t^)/lj (2)
where F = collector heat removal factor

R

(xa) = effective transmittance-absorptance product

s

2 o U = heat transfer loss coefficient [W/ (m -"C)]

The concept of the collector heat removal factor, Fr, was introduced in the testing

of thermal collectors to preclude the necessity for determining the mean temperature

of the absorber plate. The parameter Fj^ is defined as:

actual useful energy collected by a flat-plate collector

R

~ useful energy collected if the entire flat-plate collector

surface were at the inlet fluid temperature

The quantity Fj^ may be expressed in exponential form as follows:

ll - e -<W'^ %) I (3)

R U^A

L a

2 where A = collector aperture area (m )

.

a

The collector efficiency factor F' is made up of a series of heat path resistances

dependent upon the absorber physical construction (materials and configuration) and

the heat transfer coefficient from absorber surface-to-heat transfer fluid. Thus,

the effects of collector physical design, mass flow rate, and fluid thermophysical

properties are manifested in the collector's measured efficiency, assuming that the

external boundary conditions of total incident radiation flux (I^-), ambient

temperature (t ), sky temperature, wind velocity, etc., are relatively constant.

3. A plot of the collector efficiency versus the AT/I^ parameter for the range of

inlet temperatures can result in a linear relationship. The intercept on the "y"

axis is equal to Aa/Ag FR(Ta)g* and the slope is equal to Aa/Ag Fj^Uj^*. Because

of non-linearity in the loss coefficient with temperature, Ul is not always constant, and the test method provides for presenting the data by either a first-order

or a second-order polynomial fit to the data points.

A typical plot of the efficiency curves for a collector with a double cover and a flat black absorber and for one with a single cover and a selective absorber are shown in Figure 1. Examples of variation in wind and diffuse fraction are shown

for individual data points obtained on different measurement days. The influence

of environmental conditions on individual data points is smoothed out by fitting a curve to all 16 of the measured data points.

2.3 Incident Angle Modifier

ASHRAE Standard 93-77 also provides for measurements of the influence of solar

incidence angle on the collector efficiency. The incident angle modifier, Kc(-,is

used in this method as a coefficient of the transmittance-absorptance product,

(Ta)g = K^j (xa) , to describe non-tracking collector performance when irradiated

off-normal. The coefficient is used in calculating collector all-day performance.

The value of K^x fo^ many flat-plate collectors can be plotted as a function of

*The reported values are based upon calculations using collector gross area. Each term

should be multiplied by the ratio of the gross area-to-aperture area (Ag/A^) to conform

to the definition of the heat removal factor expressed in equation 3, which is based upon

aperture area.
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THERMAL PERFORMANCE DATA UNCERTAINTY

3.1 General

The evaluation of a test method involves an analysis of the total measurement

process including:

o measurement personnel expertise

o test facility quality

o local environmental factors

o test specimen characteristics

.

The identification of individual sources of uncertainties would require the use of

well characterized reference samples for measurement under identical environmental

conditions or the exchange of the same specimen for measurements by each test facility. The conduct of this durability program did not permit sample control to this extent. The evaluation was conducted in a manner similar to the procedures

employed by industry in a certification program. Collectors are typically randomly

selected from production lots, sent to a qualified laboratory and tested under the

prevailing environmental conditions within the prescribed test limitations.

Therefore, typical variations in collector production, pre-test collector handling,

test apparatus calibration, test procedure, and data reduction are aggregated in the

data.

Some factors which contribute to the uncertainty can be determined from analysis

of the information obtained as part of the test procedure. For example, the

collector gross area must be measured for use in calculating the efficiency as expressed by equation 1. Analysis of the reported area data for Test Site No. 1 indicates a coefficient of variation cvj- of 0.33 percent for "within" a test site.

Similar analysis for the four test sites indicates a coefficient of variation cvr

of 0.94 percent for "between" test sites. Assuming that the "within" value reflects

the average variation in manufacturing tolerances for these collectors and that the

larger "between" value is more indicative of measurement uncertainties, then the area determination becomes a significant part of the coefficient of variation for

intercepts calculated in Section 5.2.

The area, standard deviation, and coefficient of variation data are tabulated in

Tables B-2 and B-3 of Appendix B.

3.2 Measurement Uncertainties

The influence of individual and cumulative instrumentation calibration and operational errors has been calculated [7] using propagated measurement uncertainty

functions. Uncertainty functions were determined for the allowable accuracies

specified in the test procedure (assuming 2- a instrumentation errors) for

individual measurements of solar irradiance, fluid flow rate, temperature and working

fluid thermophysical properties plus a 1 percent uncertainty associated with the

data acquisition. The magnitude of the calculated measurement uncertainty asso- ciated with parameters comprising the x and y axes is illustrated in Figure 3 by

the rectangles superimposed on the solid lines. Uncertainties of about +4

percentage points are indicated for typical flat-plate collectors. The largest

assumed individual contributing parameter is the uncertainty of +3 percent related

to the measurement of solar irradiance.
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3. 3 Meteorological Uncertainty

Additional variability in efficiency will result from the meteorological variations

allowed in the test method. The range of allowable test conditions for solar

irradiance, incidence angle, ambient temperature and wind speed specified in the test

method are shown in Table 1.

Table 1. Environmental Test Conditions Allowed by ASHRAE Standard 93-77

Environmental Parameter

Ambient air temperature range < 30''C Wind speed across collector should be <_ 4.5 m/s

Total solar irradiance within collector plane > 630 W/m2

Beam solar irradiance incident angle < 30°

Reflected solar irradiation < 0.20

The difference in calculated thermal performance for a single glass cover, selective absorber type collector exposed to these extreme conditions is represented

by the solid curves shown in Figure 3. Calculations were made using an analytical

model [5] based upon traditional heat transfer relationships for flat-plate

collectors. It should be noted that the simultaneous occurrence of these extreme

"high" or "low" meteorological conditions is extremely unlikely.

Experimental verification of the calculated meteorological extremes was performed

in a solar simulator to the extent that the conditions could be achieved. The solid

black squares represent data points taken using the extreme exposure conditions

listed under "simulator tests" in Figure 3. The experimental data points are bracketed around the solid curve labeled "average outdoor" which represents the mean

value reported for round-robin type tests [5] on a similar collector. The experimental data were obtained with a xenon type solar simulator [8].

10
4. BASELINE DATA

4.1 Collector Description

Liquid-heating flat-plate type collectors were selected for use in the test program.

The designs chosen were representative of commonly used materials and types of

construction. All collectors from each manufacturer were from the same production

lot. The cover and absorber materials, their pertinent optical properties and

average areas (gross and aperture) are shown for the respective collectors in

Table 2. The absorber material optical property data are based upon measurements

of at least ten samples taken from the actual absorber of each collector type. The

solar transmittance of the glass materials was obtained using the full cover and a pyranometer (ASTM Standard E424 Method B [9]). The solar transmittance of non-glass

cover materials and the solar absorptance values were obtained from spectral measure- ments with an integrating sphere (ASTM Standard E424 Method A [9]). Emittance was measured using a portable-type instrument employing a thermopile and infrared

reflectance technique, in accordance with ASTM Standard E408, Method A [10].

Detailed descriptions of each collector's construction dimensions and pertinent

material properties useful for thermal analytical modeling are listed in Table B-1,

Appendix B.

4.2 Test Sites

One of the major objectives of the durability program is to determine the influence

of environmental exposure conditions on collector degradation. The same type of

information is required for evaluation of thermal performance testing.

Four exposure test sites were selected which represent both the median and extreme

United States climatological conditions. These test sites can be briefly described

as follows

Climatological Extremes

Site 1. hot, dry

high solar radiation

(high UV radiation would accompany these conditions)

The hot, dry condition can be found in south-western states

(i.e. Arizona, Nevada and New Mexico). DSET Laboratories, Inc.,

located in Phoenix, Arizona was selected as this test site.

Site 2. hot, humid

high solar radiation

(low to moderate UV radiation would accompany these conditions)

The hot, humid condition can be found either in Florida or along the

Gulf Coast in the states of Alabama, Mississippi, Louisiana or Texas.

The Florida Solar Energy Center, located in Cape Canaveral, Florida was

selected as this test site.

Median Climatological Conditions

Site 3. moderate temperature

dry

high solar radiation

moderate UV radiation

The moderate, dry condition can be found primarily in California. The

Lockheed Research Laboratory, located in Palo Alto, California, was

selected as this test site.

11
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O o> 00 iH * 4JCSI CO O CN o CM v£) 00 -a- cd v a 00 VO o\ <f r^ r-^ rH VD

a) (U -^ • • • « < ^

tH iH rH rH rH rH CM CN

cu

(JO

tfl n to

O CM 0^ in CM CM

n

O dj CO ^v LO cn 00 m a\ CM VD rH ^

oog 1-H r^ in vO 00 C7^ LO C3^ <: 1-1 e • • • CJ3 ^—

fsl <-\ CN iH iH iH CM CN

(Uostfl CO VO CM 1^ I^ u-i

O CJN 4J tH C3^ cyv o 00 r^ 00 00

4-1 • • • • a 1 O O o o o O

d o

iH 0) rt o N •H c

V-i ;-! (fl (U Cfl 4J r^ r^ 00 r^ u-1 VD rr» in

4J ^ a. 00 C3^ <3N C3^ cy. a\ C3> C3^ c a o u • • « , o S CO o

CO o O o O

d o O

d

4-1 ^ U2 a (U <:

•H ^ u M

QJ o

CD

m

0) ,Q ^ O <: (U

r-i 4J 4J CU s CU c iH (U CU CU 6 •H TJ TD

(U cfl ^ > > u •H CU e •H a I—1

iH

u fu >< c N ;-i •H J-l •H 0) CU J= o •H 'H 0) O 0) s > > u u CO 3 4-1 0) 4-» CO -i^ •^ tl ^ 4-1 ^

013 CU <U (U

O CO

w

O CU 4J IS o a fi o c o cr a U B •H >^ 3 CO CCJ -H CO -H CO o & U CO rH iH -H

J-i iH iH CO .H CO iH CO o o c •H

O CO o M m Ph m fL, m hJ CJ PL, W W PL, PL, o

0) iH

i-l (U o o u

CO CO CO •M H 4J CU (U

tn CO jj ^*^

0)

H -H

H e o 00 \0 VD LO o <} o in vo C/1 COc

<3S 00 00 C^ 00 C3^ 00 <y\ 00 CJ^ CM o CD o o d d o d d d

(1)

H

I—1 ^ iH

to (0 H •H

(-1 e a 0) c i-l CO P Vj •H ^j 5 CD 1 u fe H •a 1 1 s c 1 M CO CU CO c 1 CO C 4-1 JZ CO [ 1 P4.a E

PM rH

(U

1—1 ? CO •H CO

O CO

O

M 4= <U 4-1 rH fd •<->

W -H

fa fa >o

i-J o H !D

W CJ> fe Pn

u

(1) CO 0)

4-1 CO

u

u

•H o

CO rH

M

•H

M

^-1 CU

4-1 4-1 (-1 •a CO 3 !-l CO M en CU (U en CU !-i CO 0) O CU

(1) CO CO 4J rC en a. (U CO CU rH rH O -H

4J nj

Cfl rH 5 10 nH

CO

r-l

O CO

4-1 tH

Ph >,

Pi

H

4-1 CO CO iH S ^ |3 O hJ O tl4 w o fc ^ :3 O fa ^ fc fa ^ouu (u H O

<C pq

u

Q

w fe CJ !B ^ u ou

,Q

-O

0) 4JMO

CO

CU3

iH

Cd>

MHo

(U00

Cdu

0) K

12
I

Site 4. moderate temperature

humid

moderate solar radiation

moderate to low UV radiation

The moderate, humid condition can be found in the Pacific Northwest,

Mid-Atlantic and Mid-South regions of the United States. The NBS test facility, located in Gaithersburg, Maryland will serve as this test site.

Each of the commercial sites was determined by an industry inspection team to be

capable of conducting tests in accordance with ASHRAE Standard 93-77 [11]. In addition, on-site checks of the instrumentation used by these laboratories were

made by the Solar Energy Research and Education Foundation (SEREF) with their

Laboratory Intercorrelation Test Equipment (LITE) apparatus as part of the DoE

Collector Testing Program. In general, they were found to meet the required

ASHRAE measurement specifications. Since the main concern of this study was in

establishing the precision of the test method, detailed study of the type and

accuracy of the individual sensors and apparatus used at each test facility was

not considered necessary.

4.3 Measured Data

Four test series, each having a sample of the eight collector types, were measured

at Sites 1 and 2, and two test series at Sites 3 and 4. The thermal performance of

all collectors in Series 1, 3 and 4 was measured prior to outdoor stagnation

testing. Collectors in Series 2 were exposed for three days to a minimum daily

solar radiation of 17,100 KJ/m^ (1500 Btu/ft^) prior to the initial thermal performance measurements. Series 2 is intended to determine the significance of the

three-day preconditioning exposure specified in ASHRAE Standard 93-77. The complete

set of baseline data is tabulated in Appendix C. All the measured data required to calculate and generate the efficiency curves are recorded for each data point. In addition, the time, wind, diffuse fraction, collector orientation and tilt are listed.

Baseline data for all collectors measured are listed in Table 3 by intercept

[optical efficiency, FR(Ta)g] and slope (heat loss coefficient, FrUl) . The curve

fits and resultant values reported by the test sites were verified using the data

points supplied by each test facility.

The baseline data for the incident angle modifier consists of measurements made on

most of the collectors at Sites 1, 2 and 3. Measurements were made on Collectors C and G along each of two orthogonal axes, i.e. parallel and perpendicular to the

fluid-flow axis of the collector, because of special cover configurations causing

non-symmetrical incident angle effects. The other collectors were not measured in

the parallel direction. The test procedure describes two methods for incident angle

modifier measurement. Test facilities No. 1 and No. 2 used a tracking mount and

maintained a constant incident angle for each data point. Test facility No. 3 held

the collector at a fixed tilt and orientation, and measured the efficiency when the sun

was at the desired incident angle. The incident angle modifier can be expressed as:

K = 1 + B (-^ - 1) (4) ai o cos9

where B = slope of the curve connecting data points plotted for ¥^j versus (-^ - 1) and

cos

= the incident angle

.

13
ouo

14-1 O

(UP.o

T3

P-ou

(Uoo

(Uc

•HrH

(U

COn) pa

J2

to H o in 0^ CM CJV vO

O 00 CO o <!• o

hJ 00 00 VD o H

O

H CN cn r^ o- CN

C) r~. <f r~ in

O r^ rH 0^ vO in rH CO

Pi • • • • • • • • • • {^ m in in in VO in vO m m in in in

£33 ^-Na vo i-i cn cn vD 0^ cn r^ 00 r~ o CO H CO <r cn <t CN CN CN o cn Csl vi- in ^ vO VD VO VO VO vO VD VO VD vo vO o o O O o o O o o o o o m 00 0^ CN CN in O i-H CN 00 r^ o

fj o es) r-. VO <f OS

O r- cn <f 00 CS) c^ •* -* * in r-( -d- cn cn in in 00 m m in in in in in in in -* in in

CI

/^Ns eg r~. CO cn Ov cn vO as vD o 00 as H r-. vO m vO •vi- cn <r CN 00 in 00 00

oi in in

m in in

m in in

mmmm o o c o o o o o o o o c

r~- 00 Ov CN CN r^ in OS as 00 ON r^

hJ

O ts 00 as

Om r~ <f <t vO o <l-

[4

u-l r^ vO o 00 CN o r-i cn as 00

m

vO VO in vO vO VD VO vD

m <r in in

p4

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Pi vO vO vO vO vD vD vO vD vO vD vD vO o o o o o O o o o o o o

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r~- VO VO vO vD vD r^ vO vO in vO vO

W

^^3 CO 00 C?v o 00 CJS (M CN tH

m c:s -*

t- iH a\ CJV o> 00 i-H

O o CN as

M as

s--' vD in in in LO vO vO vO vO in vO in

PS • • • • • • • • • • fi< d o o o o o O o o o o o

o\ -* cn r^ CN (3^ 00 <f in CO

m * J vO r^ cn CJ^ i-H O in 00 in o in 00

-a- .-( 00 rH oO -d- cn in CN o CO

cnn CSl cn cn cn cn cn CN CN CO CO

Q ^^a 00 <n vO

O o 00 in vD r-~ in vO o H -d- ro (N -* <f in m cn o- CO CO r^

^-^ vO vO vO vO VD vD VD vD vO vD vO vO

P(i fn ° d

ddd o dddddd

00 CT\ vO cn <f vO rH <r o CO iH o

hJ 1^ vD o vO CN r~~ ~a- o CO <r

m vO ^.^

fe

ro OV c^ om CN r-~ CO CN o i-H

O

<f CO cn <j- -d- ^ <f -a- -* <f •vf <r

U

/—

N a in o 00 o <r iH r-~ .—1 C3N r^ CSI CSS

I- * CN cn <f CSJ 1-Hm <r <!• iH

m <f

in in in in in in in in

m inm

m o o o o o o o o o o o o

0-) 00 as r-- 00 iH cr> in rH 00 CS) o

hJ vO CSI r-> in 00 o cr> cn CTi r~. 1-H o

^.^

fe

<!• <r <r <t cn r^ in r~~ •<r rH CN CN in in in m in in in in in m in vO

PQ ^a <f o CSI vO <f

O 00 00 Cvl vD CN o H in -* in vO m cn -* -a- m CO r- 00

Pi vO VO VO vD VD vO vO vO vO vD vO vD O o o o o o o o o O o o

as o 00 t3> CN CN .H as Csl CN CO r~. hJ m -* -* CSI in o- C3> CN iH VD ON t^ ^PS

fe

in vf in o- CN in <f <f as VO CSl CO

v3- -vT <r <r in o- <f * cn CO <f in

<:

^^^a CSI vO CN r-t 00 vO CN rH r-~ CO r~~ o H O o\ <SJ o o O rH 00 CN iH O m vO in VO VO VD VD vO m vO vO vO VO O o o o O O O o o O o o M cn O 0) JJ •H O 1-1 rH CN cn <r r-H CN CO o- rH CN iH CN

(U (U rH w Oo •U Q)

Cfl 4-1 EH cn

T-{ CN CO >aM-lO

1^O

J-l u

cd MH

CD>. ,Q

•a

<u •HrHa

•H

4J

I-Hs

(U ^

4-1 D)aB

>N

(U Xi

4-1»

(Uuo

14H(Uu

0) J3H

cfl . (U CO u

CO

ao u •H o M u ca o 3

<u cr

7-t <u

I-Ho >> o rQ

CO •a

cn (U o 4-1 ^1 n) OD C

60

W) •H c to •H 0)

tf) T1 3

cn -o (U

cu 3 u iH a Cd iH > 3o 0) iH 3

CO

U o 4-1 c <u

<D

X

m

U

XI

4-1 <u 3 > (U a tn J= <uu m ex

cu 0) 3 u

rH

ca o > 4J

(U cd

03 <;

<u x:

M

H <:

,,

0) uoz

14
For the flat-plate collectors evaluated in this program, the incident angle modifier

was essentially a linear function when plotted versus ( ^ - 1) • The baseline ' cosO

values of B for all measured collectors are shown in Table 4. Because of the

sparsity of suitable clear days, no incident angle measurements were made at test

facility No. 4.

I

15
CO u

cB P

<Uc

•H

iH

0)CO

C

n)m

pq ^

^1 (U (U p. •H o

IH I—1

•H

m

13

/-*s s; ^

(U l-l rH ^—

00e pi <! oH

4-1

a c w

(U ij T3 hj •H o O o cH

<r

0) i-H

,J2to H

in

O VD CM a^ o 00 o>

sd od1 1 1 11 11 O1 ^ ^-s M ,-^ M /^ M l-H M

0^ CN r^ ^ >w/ \^y ^w' 00 o 00 rH O 00 in rH rH v£> CM CVJ iH rH iH CM rH rH d ' ' 1 1 1 1 '

iH 00 VO o rH o\ * <y\ r-i r^ 00

pen oo1 OO1 o1

rH o1 1

00 00 CT\ r^

CN ro CO in

W CMd

iH iH 11 1 rH1

r^ r^ 00

O •<r r^ Csl O r—1

vO o O d1 1

CM1

rH1

,-t CN

•K * * * * *

/-% ,—s M /-N M ^-v M M

0^ <r (M

N

N

— *--• o U o\ o <! 00 <3N c^ in 00

CM CM CM r-H CM rH CM (N O1 1 1 1 1 1 1 '

CM vO iH

m

O

O rH <f

m

O

1—11

rH1 11 11

<-t

r-~ <r o o o CM

iH o- o rH cr\ <f < Od o o1

rH

O1 w

a) •Hn fH CM <!• rH sf ,-{ <u

C/3

(U u

•HM

.-1 CM CO

4-1 03

(U H I

>s

COS

eu >% 60

CO CO 3 to

cu to M CO CO p.

to

to o

to 4-1 a u o CO

4-1 T-ip

r-{ o

(U •rl

r-t T) ^ C

CO (U U & CO u

D. OJa.

CO 4J CO c 4J

(U c e 0)

0) e u <u 3 (-< CO 3

CO to

eu CO B (UH

16
DATA ANALYSIS

5.1 General

The data analysis was performed using the concepts and terminology recommended by

ASTM Standard Recommended Practice E177 [12], where appropriate. A brief description

of frequency, distribution, normal distribution, and the role of standard deviation

is given in Appendix A.

The test sites supplied linear and polynomial equations representing first and

second order curve fits to the data points. The linear equations were used for the

analysis used in this report to expedite the calculations and simplify the presentation of heat loss coefficient data. Technical justification for the use of linear

coefficients is provided in Section A-2, Appendix A.

5.2 Thermal Efficiency

The intercept and slope values listed in Table 3 are subject to two sources of

variability: the random variability between individual collectors of the same type

measured at the same site and the additional variability resulting from different

sites. Each source is characterized by a standard deviation. The former is called

the "within" (sites) standard deviation (sr)* The standard deviation encompassing

both "within" sites variability and variability among sites is referred to as "between" sites standard deviation (sr). Detailed descriptions of the statistical

analysis methods are given in References 13, 14, and 15.

It is also possible to calculate the uncertainty, determined as a standard deviation,

of the grand average thermal performance for each type of collector. Such a standard

deviation, pertaining to an average, is generally called a standard error. Tables 5 and 6 list the mean, standard error and the standard deviation "within" and "between"

sites for intercepts and slopes, respectively. The standard deviations are listed

both in their original form and as relative percentage values of the overall mean.

There appears to be no relation between the standard deviations for any particular

type of collector and the corresponding mean values. The variability exhibited by

the standard deviations in a particular column of Table 5 and 6 is within the

expected sampling errors of standard deviations based on the number of samples

involved

.

As might be expected, the "between" standard deviations that include site-to-site

variability are somewhat larger than those measured for within-site variability. For

intercepts, the coefficient of variation (standard deviation expressed as relative

percent of the mean value) is about 2.1 percent for "within", cvj-,and 2.4 percent for

"between", cvj^. The corresponding values for the slope are approximately 5.9 percent

and 8.4 percent.

Graphical depiction of the spread of individual data points from each test site and

a comparison with the +4 percent to +5 percent random error band associated by Jenkins

and Hill [7] with the instrumentation and represented by the dashed lines is shown

in Figures 4a and 4b for Collectors D and B, respectively. It should be noted that no data were rejected on the basis of being an "outlier." The data points include

variations in factors such as the measurement and calculation of collector area, flow rate, tilt angle, and orientation (tracking or fixed)

.

17
I.U COLLECTOR D

RESIDUAL STD. DEV. = 0.0202 0.8 -

1

o

Ik

UJ

0.6

0.4

'^'^^'^^'^^^..^^^

0.2

1 1 1 1 1 1 1 i

.01 .02 .03 .04 .05 .06 .07 .08

tf,i-ta °Cm2

I

" W

Figure 4a. Comparison of data point spread for double covered selective

absorber type collector with uncertainty band

1.0

0.8

^ 0.6 UJu

£ 0.4

0.2

COLLECTOR B

RESIDUAL STD. DEV. = 0.0184

'^\^^^^

-1 1 1 1 1 1 1 1 .01 .02 .03 .04

tf,i-ta

.05 .06

'Cm2

.07 .08

I W

Figure 4b. Comparison of data point spread for double covered nonselective

absorber type collector with uncertainty band

18
u

(0

(U HG

0)>

0) «c

(0a

•H

,C

4J •H

:s

4JP.

(Uu

(U

Cio

•H

4J

CD •Ho

•HU

•H

•S

CO •H>

0) Pu

(0

IT)

0) co

•H CX5 vD iH < r^ CO 00 >a- ^ p:i 00 m t-~ 0^ C3^ r-~ 0^ 0^

CO • • • • •H U CM CNJ CNJ i-t iH csl CO rH H ^S

!2 §

14-1 (U3 O 4J u P9 C vO r>~ vO

m <J> I-t CN CO

0) r~. \0 •0- iH iH 00 CM <N

•H iH iH rH CM iH iH CM rH a OS o O O O O o O o •H to

4-1 o o U-l(U 5c

n)c M o o iH -* -d- r~> CO

m > vD VC r- 0^ <y> CO rH eg

•H o •

4-1 ^? CS i-t CM 1—1

1—1 CM CM <-^ CO •H C > •H

•H T3 3 M

CO C3\ u-i \0 in 00 in

O o o in O -* CSJ rH in CN 00 c M r-l iH r-l 1—1

.H rH r-^ o CO to o o o o o o o o u • • • • • W o c

CO 4-1 <U C S (U CJ^ r-\ 00 vO vO r-^ o CO o CJ^ iH r~- m m O 00 00

MH

M • • • • • • o ° 1-H o o o iH l-\

d

uoM

t-l U

TJ

Vj r-\ ro CN vO C3> vO r-\ CO

CO cu vD r~ -* cn CO sD

O in

T) 3 OO o o O

O T~\ o c iH o O O o o O O o CO CO • • 4J > o

OT

4JD.

(U o CN r~~ CO CO i-H o CN U C iH m CO <r O in »£> CO

l-i ct ^ vO U~l vD vO vD in vO

<ua • • • • • • • • •u S o o o o o o o o cMMo

4-1 o

(U < PQ o o w Fb o 33 iH

rHou

as

CO

u 1> > u o V?

B-s; ^w'c C CD •H <U x: >

4-1 4J •H (U :2 PQ c C o O

•H •rt

4-1 4J

CO CO •H •H M M

CO CO > >

14H HH o o p 4-1 § s

•H •H O CJ •H •H «H MH

MH 14-1 (U <U 8 5

0) <u bO on

<0 CO u u

0) (U > >

<c <

19
HC

0)

4-J MC

cd

•H

:3

P.o

4hO

•HO

•Hm

0)ouC

n)CoH

4J

n) •H>oU

n) co r~^ CSl VO o o r-^ -*

•H CT) 00 iH c^i 00 r^j r^

m 4-1 P< • • • • nj > Oi o- r^ in t-^ O VD in

•H

O <H

H <-i

U >5

n) > c

4-(

<1)

O

4-1 4J (U C M

CU vO r^ r-~ .H o CO CO CM

•H

U u-i VD o r^ o rH VD rH

O

•H

M in CM CO <r in VO CO CO o H-l0) 5

'ac

n)C (-1 CNI [^ 00 r-l 0^1 I^ VO

O o > CM 00 o- r-~ Csl O 1—1 r-~ H O . . • 4-1 fr^ 00 -a- u-1 r~- r-. vO m CM

cd •H> C3

d) •H a

4-1 x) •H M :2

to T3

m r^ CO 00 o CO 00 CO

C

M r~- VD CO CO >o vO r-~ in

n) to 0-) rv) og CM -tf CO (^g rH

4J • • • CO o C

to 4J

0) c s (U o 1—1

iH 00 0^ i-H o> vO o CM <r 00 tj> in in vD m

MH »-i • o in i-H CM vD CM <f CN CSJ ^o^

Vl w

13

!-i CO CU "X) 00

O ^ r^ <f in

m TS 3 en r^ C^J r-i o in <r <r d iH CN o rH CM iH CM 1—1 ^

CO CO • • a • • • • 4-1 > O

C/2

rsl <u e iH u-i t-~ in o\ vD

m rH

a c • CO CO 00 a\ CO CJ^ o vD O CO u Ul lO CM o <t- CT. o- vD

,H 0) o • c.S^ ^ U~l -* CO >^ in in in

>-l o

4-1 O

0) < PQ o o pa fX4 o w 1-H

T-\Oo

COu > > ^ u B-; s-s ^-^c c 0)

•iH CU ^ >

4-J 4-1 •H QJ :s pq c C o O

•H •H

4-1

U

CO CO •H •H U l-l CO CO > > C c

(U a) •H •H

CJ

O

H •H m UH

14H IH

01 (U 8 8

a) CU ao on

to CO M M

OJ d) > > < <

20
5.3 Incident Angle Modifier (lAM)

Although the total sample size for incident angle modifier (lAM) measurements is

only one-half that for thermal efficiency, these data are important because of the

lack of comparative lAM data and the interest in values for calculating all-day

performance. Analysis of the data listed in Table 4 was performed for two individual

test sites and combined for three test sites as shown in Table 7. The mean values

for Collectors A and G exhibited relatively large differences for "within" data.

The corrugated outer cover on Collector G probably influences the angular transmittance, and this combined with the difference in diffuse solar fraction between

test sites (about 10 percent at Site 1 and about 25 percent at Site 2) could con- tribute to the large differences found for this collector. There is no apparent

reason for the large difference for Collector A. The "within" test site standard

deviations do not exhibit a consistent trend with collector type.

Analysis of the lAM data to obtain "between" site standard deviation shows a large

variation with collector type but the average coefficient of variation (expressed

in percent) of 34 percent remains about the same with or without the extreme high

or low values shown for collectors A, C, E, and F. Variations in lAM of this

magnitude cannot be attriouted to product variability for the flat-plate collectors

used in this program.

21
03

<U

4-1 •H

•UM

(U Hc

0)

4J

(U PQ•ac

n)d

•H

x;

4J•H

cn

OJ

CO >CoH

4-1 CO •H>

OJ o

t3M

CO§

4-1 tnM

OJ •H

•r-l Uc

42

CO H

vO - a rH d St

60 ^ cn CN

m CO >

1-1 o II II II m ^s > »- , u Pi < > •1

r~ o iH 00

m

m

«N ro U1 iH CN <t

K

CD

OO

OO

cyi cn 1 11 1r 1 rHd o o 00

cn

nn iH o o 00 cn 00 cy> o m cr. m CN c<g r^ CN vo

O CM o o u-i i-H o o CM -HO o o t • • <f • • • CN • • * •<i- o o O

c» LO o o o 00

m CN r^

r^ 1-1 CN 0^ CN CN iH

m

m

Pn oo o o cn

cn

Od o o T—1 d o o iHm

00 o CN in iH

m

(U vD

m U-l VO CN <r

a.

w t—) O o iH 1 1 1 1 .-)

O o VD

!>^ • • • rn 1 1 1 1 • CM H o o uo

4-) o

OJ o <r I-I in in in

m r-~ o iH [^ CN * cn CN cn vO 1-1 <f

.H

Q iH o o -* rH o o vD 1—1 O o -d- o • • • CN • CN • CM u o o o

00 00 00 o o c» iH <t vD

-* CN <r r^ CN (N VO i-H cn

U

d o o cr> CNd o o Oi-H CNO o o

1-1 o

cno o CN

m

(N

CT\ iH CSI PQ d o o

<r 1 11 1 . 1 1

1-1 d

O o CM

CN o m Csj o o o- ~* <y\ CM

-4- i-i CN o !H iH a\ CN in < od o o in

lO o o o

iH oo o o

in

Vj c c c

(U T3 T)

O T3 T3

O TJ -n o 4-J M U -H u U -H M M -H s

CO CO 4J CO CO 4-1 CO CO 4-1 i

"2

u -a CO -o ^1 TJ CO T) !-l 13 CO CO d c O C -H M c c o C -r-l U C C O C -H « )-l CO CO U CO > > CO CO u CO > > CO CO U CO > >

CO CU 4-1

U 4-1 d) o <u 4-1

uU <UO cu 4J )-l 4-1 <U o

p4 2 cn

W C«

Q 6-S s CO

w

w

n ^S

X CO

W CO

Q B-S

(UO

m

u 0) cu cu 9 •u 4-1 4-1

m o •H •H •H t«

r-l c« CN

CO ^

CO 4J =!fe 4J 4-1 CM

4-1 to CO to

CO cu (U CU *• O H H H iH

22
6. IMPACT OF DATA UNCERTAINTY

6.1 General

The uncertainty associated with commercial collector performance data is seldom

published by the manufacturer and is not required to be reported by the test method.

Three applications for typical thermal performance data have been selected for

illustration of the impact of the data uncertainty discussed above, as follows:

o Evaluation of collector degradation

o Collector rating

o System performance prediction,

6.2 Collector Degradation

One method of quantitatively evaluating changes in the material properties or thermal

characteristics of a collector is to perform thermal efficiency tests before and

after non-operational exposure testing. Depending upon the data uncertainty, thermal

performance measurements could reveal incremental changes in the cover solar transmittance, plate solar absorptance or emittance, and changes in insulation thermal

conductivity. Analytical studies of probable error resulting from instrumentation

only [16] indicated that an uncertainty band of about 4 percent in the thermal perfor- mance could be obtained. This uncertainty in knowing the actual thermal performance

corresponds to changes in the solar transmittance, absorptance or emittance of about

0.10 and a change in back insulation thermal conductivity of about 50 percent for the

collectors studied in this program. Consequently, changes in material properties of

this magnitude would be required to clearly discern material property changes from

the measurement uncertainty band for many flat-plate collectors.

The influence of changes in the solar transmittance (t) of the cover material for

Collector A is illustrated in Figure 5. The dark curves represent the calculated

first order efficiency curve for x values of 0.90 and 0.82. The light curves represent the instrumentation uncertainty associated with this collector and indicates

that a change of 0.08 in x would be required to positively conclude that a material

property change had occurred. An uncertainty of 0.025 at a nominal intercept value

of 0.60 represents a 4 percent change in relative efficiency which is approximately

equal to the 2a "within" site coefficient of variation (4.1 percent) determined for

intercept measurements reported in this study. Therefore, thermal performance

measurements may not be sensitive to material degradation changes incurred during

short-term (30-day) durability tests.

6.

3

Collector Rating

Rating a solar collector on the basis of thermal performance is useful for several

purposes. Among the primary ones of interest to the consumer are:

o To rank collectors on the basis of all-day output

o To determine the relative difference (%) in energy output for a specific application.

One proposed rating method [17] for ranking collectors uses the ASHRAE Standard 93-77 curve (efficiency and incident angle modifier) to calculate the collector daily

thermal output for days with specified inlet temperature, solar radiation and

ambient temperature.

The influence of data uncertainty on all-day collector energy output was calculated

for four flat-plate collectors with the properties and data uncertainties shown in

Table 8. Calculations were made with a clear day solar radiation profile occurring

at 40°N latitude, 0°C ambient temperature and a 60°C (140 F) collector inlet

temperature. The data uncertainties used for the intercept, slope and incident

angle modifier slope were determined from the baseline data analysis. Computations

23
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to

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CO

(U3

bO

•H O) GO r^ CO lo CO cNi '-r

A3N3l3IJd3

24
I

(U 4J

CO rH

PL,

4-1

tfl to

i-H tu In •H

4J iH c

to •H O CO •H 4J P. U

>^ (U H oc M E3 DO CO t^ 4J

to

<4-(

Q

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(U 4-1 •H CO

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p. CO o to u <

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01 c u CO C

nt tn B )-i

(-1 o o 4-1 4-1 o

t-l CU

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n)B

V4

(U x:H

00

OJ tH^

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O lO

00 C3N ir\ r^ o o iH rH

H 1 o"1 o O1 O1

<N CN r~~ <Ti <r

J E ro

m iH r^

O iH CO

O tH

PiU • fn o ^ u^ \D en ^ 1 1 1 1

^-^a o in

O CM

H r^ (3> o <f ^— v£> ^ o vO

Pi

Pu o o d

d

4J 4J c c

1-1 •H tu •H CU

OJ to > to > ^ p^ •H Pm •H M 4-1 4-1 o ^ o ^ O

tn

u tu o (U Xi to tH to tH < iH (U tH (U PO w PQ CO u

•H

4-1 <U CO P- to ?^ iH H P4 M •a O (U

4-1

u

Ou V4

(U (U o H > M-l

T-l o c O u •H o <U

pt;

en tfl

u tn

M tfl CU to

CO to ^ to

I-l .H •H iH o o fn o

rH .H tH CM o iH CM CO -d- s

-a

<uSP

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tu •H

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25
were made for the nominal intercept and slope value, and the combination of uncertainties that would yield the lowest energy output, the greatest energy output, and

a mixture of high and low uncertainties to give an intermediate energy output as shown in Table 9. Rankings based upon the outputs for each calculation series are shown not to change for the collectors evaluated. However, when comparing the energy

output of a collector with a high combination of uncertainties to the energy output

of another collector with a low combination of uncertainties, a different ranking can be obtained.

6.4 System Performance

The prediction of a solar energy system's seasonal or annual performance with respect

to meeting the heating or domestic hot water load can be calculated using system

simulation programs. The f-chart method [18] is based upon a correlation technique

derived from detailed modeling of a typical solar heating and hot water system in

a number of U.S. cities with different combinations of component characteristics,

sizes and loads. The collector performance, characterized by the first-order

efficiency curve and the lAM slope, is used in conjunction with average local weather

conditions and the site dependent load to determine the contribution to the load

(fraction of the load) made by solar energy. F-chart calculations were made for a 152 m2 residence occupied by a family of four and located in Madison, Wisconsin and in

Washington, D.C. (see Appendix D for system description). The nominal collector area with a double cover selective absorber and a single cover flat black absorber, to provide 0.50 and 0.75 of the annual heating requirements for each location, were

calculated as shown in Table 10. The solar fractions for the same areas were also

calculated using the high and low values of collector uncertainty obtained from the

baseline analysis shown in Table 7. Differences of about +0.03 in solar fraction

are attributed to the efficiency uncertainty for Collector 4 and about +0.045 for

Collector 1. The 0.50 system fraction is somewhat more sensitive to the uncertainty

values than the 0.75 system fraction for Collector 1.

The influence of a +20 percent uncertainty in the lAM for either flat-plate collector is

shovm in Table 10 to have less than a +0.01 effect on the annual system solar fraction.

A sensitivity study of the relationship between the value of Bq and the normalized

solar fraction for the solar heating and domestic hot water system example is shown

for Collectors 1 and 4 in Figure 6. The solid curves are for the month of December

and the dashed curves are for the annual performance in Madison, Wisconsin. Changes

in the incident angle modifier slope of +0.05 or about +28 percent for a nominal

value of Bo = 0.175 would result in a relative percentage change in annual solar

fraction of about +3.0 percent for Collector 4 and +2.5 percent for Collector 1.

26
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28
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29
CONCLUSIONS ^

Statistical analysis of the thermal performance data sets obtained on eight liquidheating, flat-plate solar collectors at four test sites broadly dispersed in the

United States have confirmed that the total experimental uncertainty is about the same as the probable estimate of random error predicted for the use of ASHRAE

Standard 93-77. Measurement error is believed to be the major contributor to the

"within" test site variability (repeatability), and environmental effects a significant factor influencing the slope (loss coefficient) data obtained "between"

test sites (reproducibility) . No evidence of product variability was discerned for

the various collector types.

On the basis of first-order curve fits of the data points, an average "within" test

site coefficient of variation, %cvr, of 2.1 percent and "between" test site

coefficient of variation, ^Cvr, of 2.4 percent was calculated for the intercept

[Fr (Ta)e].

Similar data for the overall heat loss coefficient, FrU^, indicated "within" (^cvj.)

coefficient of variation value of 5.93 percent and "between" (Z^^^ of 8.37 percent.

The coefficient of variation (^cvr) for incident angle modifier data of 34 percent

was shown based upon measurements at three test sites. Application of these uncer- tainty values to three application areas where thermal performance data have

significant impact were shown as follows:

o Material degradation equivalent to about a 0.10 change in cover transmittance or absorber solar absorptance and emittance

o Variations in collector all-day thermal output of from +17 to +68 percent for specific winter operating conditions resulting

in significant ranking changes

o Variations in residential annual heating and domestic hot water

solar fraction of +6 to 7 percent.

I

30
RECOMMENDATIONS

The establishment of data uncertainty and measurement precision for commercial

products requires careful evaluation of test procedures and continued vigilance of

experimental facilities. It is recommended that a systematic evaluation of the test procedure be conducted within at least three test sites with replicate measurements

(using the same "standard" collector types at each site) . Collectors with stable but

different material configuration designs should be selected. Some of the factors that

should be considered are:

o Absorbers with serpentine flow, headers with parallel passage and

fully wetted

o Curved covers vs. flat

o Selective vs. non-selective coatings

o Relative high loss vs. low loss design (edge and back).

These measurements should be conducted with test apparatus that has been calibrated

to the same field reference using a reference heat source or equivalent procedure.

Measurements should be conducted under a range of local conditions as permitted by

the test procedure (ambient temperature, wind, irradiance, diffuse fraction).

Initial testing should be conducted on all collectors at one site using the same instrumentation. Series testing of groups of about four collectors utilizing

one collector as a reference in all tests would minimize instrumentation uncertainties

associated with the flow and solar irradiance measurements. The collectors would be

measured once per month at each site over a six-month period (to include summer and

winter) with the largest meteorological variations. At the conclusion of the program,

the collectors could be returned to the site of the initial testing to corroborate

the results if the uncertainties were larger than suspected from statistical principles

of the sampling number.

31
9 . REFERENCES

1. "National Program for Solar Heating and Cooling of Buildings," Report No. ERDA 76-6, Department of Energy, Washington, DC, November 1976,

2. "Methods of Testing to Determine the Thermal Performance of Solar Collectors,"

ASHRAE Standard 93-77, ASHRAE, 345 East 47th Street, New York, NY 10017,

Corrected Printing 1978.

3. Hill, J.E., Streed, E.R., Kelly, G.E., Geist, J.C. and Kusuda, T. , "Development

of Proposed Standards for Testing Solar Collectors and Thermal Storage Devices,"

NBS Technical Note 899, National Bureau of Standards, Washington, DC 20234,

February 1976.

4. Hill, J.E., Jenkins, J. P., and Jones, D.E., "Experimental Verification of a Standard Test Procedure for Solar Collectors," NBS BSS 117, NBS, Washington, DC

20234, January 1979.

5. Streed, E.R., Thomas, W.C, Dawson, A.G. , Wood, B.D., and Hill, J.E., "Results

and Analysis of a Round-Robin Test Program for Liquid-Heating Flat-Plate Solar

Collectors," NBS Technical Note 975, NBS, Washington, DC 20234, August 1978.

6. Waksman, D., Streed, E.R., and Seiler, J., "Solar Collector Durability/Reliability

Test Program Plan," NBS Technical Note 1136, NBS, Washington, DC 20234, January

1981.

7. Jenkins, J. P., and Hill, J.E. , "A Comparison of Test Results for Flat-Plate

Water-Heating Solar Collectors Using the BSE and ASHRAE Procedures," Presented

at Winter Annual Meeting, American Society of Mechanical Engineers, New York, NY,

December 1979 (Paper No. 79-WA/501-4)

.

8. Lunde, A.R., "Solar Collector Reliability Test Program-Baseline Thermal Performance Tests," Report No. TR2-5615-8000-004, The Boeing Company, Seattle, WA,

February 1, 1980.

9. ASTM Standard E424-71, "Standard Methods of Test for Solar Energy Transmittance

and Reflectance (Terrestrial) of Street Materials," ASTM, 1916 Race Street,

Philadelphia, PA 19103.

10. ASTM Standard E408-71, "Total Normal Emittance of Surfaces Using Inspection Meter

Techniques," ASTM 1916 Race Street, Philadelphia, PA 19103.

11. Niessing, W.J., "Laboratories Technically Qualified to Test Solar Collectors in

Accordance with ASHRAE Standard 93-77: A Summary Report," NBSIR 78-1535, NBS,

Washington, DC 20234, November 1978.

12. Duncan, A.J., "Views of the E-11 Task Group on Statements of the Precision and

Accuracy of a Test Method," ASTM Standardization News , December 1978, ASTM, 1916

Race Street, Philadelphia, PA 19103.

13. Mandel, J., "Repeatability and Reproducibility," Materials Research and Standards , Vol. II, No. 8, ASTM, 1916 Race Street, Philadelphia, PA 19103, pp. 8-16.

14. Mandel, J., "The Analysis of Interlaboratory Test Data," ASTM Standardization

News , ASTM, 1916 Race Street, Philadelphia, PA 19103, March 1977.

15. Mandel, J., and Paule, R. C. , "Interlaboratory Evaluation of a Material with

Unequal Numbers of Replicates," Analytical Chemistry , Vol. 42, p. 1194,

September 1970.

32
16. Thomas, W. C. , "Analysis of Solar Collector Reliability and Durability Test

Data," VPI&SU Progress Report, NBS, Washington, DC 20234, February 1980.

17. "Thermal Performance Rating Method for Solar Collectors," Document RMD-5,

SEREF Rating Method Committee, SEREF, Suite 800, 1001 Connecticut Avenue, NW,

Washington, DC 20036, November 14, 1978.

18. Beckman, W.A., Klein, S .A. , and Duf f ie, J. A., "Solar Heating Design by the

f-Chart Method," John Wiley and Sons, New York, NY, 1977.

33
APPENDIX A: DATA STATISTICAL ANALYSIS

A-1 General

The rectangles shown in Figure A-la constitute a histogram in which the base (A,B) of

the rectangle ABCD represents a small interval of possible results of the measuring

process. The area of the rectangle ABCD represents the relative frequency of values

lying in the interval AB. As larger and larger data samples become available, the

total range of values can be divided into smaller intervals. The histogram then

generally approaches a smooth curve called a frequency distribution such as illustrated in Figure A-lb.

A precise measuring process is represented by a narrow frequency distribution. The

smaller the precision, the wider the frequency distribution will be (see Figures

A-lc and A-ld) . The width of a distribution is measured by its "standard deviation,"

^- , which is a quantity expressed in the same units as the measured value. Thus, the

standard deviation is an inverse measure of the precision.

A type of frequency distribution that is of great theoretical and practical importance

is the "normal" (or "Gaussian") distribution. In a normal distribution, an interval

extending from a point located at one standard deviation below the mean to one located

at one standard deviation above the mean, will correspond to a relative frequency

(probability) of about 2/3 (68.27 percent). This is a +1 sigma interval. The

probability corresponding to a +2 sigma interval is approximately 95 percent and that

corresponding to a +3 sigma interval is about 99.7 percent, as illustrated in

Figure A-lc. The probabilities are measured by the area bounded by the curve on top

and by the lower and upper limits of the interval on both sides. These probabilities

pertain to the normal curve and one not necessarily correct for other types of distributions.

A measuring process generally contains more than one source of variation (imprecision)

.

Each source will have a frequency distribution with a definite sigma value. The joint

effect of the various sources of error is a frequency distribution resulting from the

superposition of the various individual curves. The standard deviation corresponding

to this overall curve is the square root of the sum of the squares of the individual

standard deviation. The square of the standard deviation is called the "variance."

The central value, or "mean," of a frequency distribution is not necessarily the "true

value" of the quantity measured. The distance between the "true value" and the mean

of the distribution is called the "bias" of the method. Often the true value is not

known and must be replaced by a "nominal" or "reference" value. A method with a large

bias is said to be inaccurate or of low accuracy (see Figure A-le)

.

A- 2 Residual Standard Deviation

When a curve (or straight line) is fitted to a set of data points, the vertical

distance between the observed points and the fitted curve can also be measured in

terms of a standard deviation. The smaller this "standard deviation of fit" (also

called standard deviation of residuals or residual standard deviation) , the better

the fit.

A comparison of the standard deviation of the residuals for the curve fits for each

data point for Collectors C and E are shown in Figures A-2a and A-2b. Collector C had the lowest residuals (least deviation from a linear fit) and Collector E had the

greatest deviation. Relatively little difference is indicated between the

first- and second-order curve fits; consequently, first order curves were used to represent the intercept and slope. Table A-1 lists the residual standard deviation

for curve fits to each collector data set.

34

I

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to

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I I I I SlN3M3)inSV3M JO dBSIMnN

35
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to 13

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to H

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13 C^J vO r~~ iH CM o vO o CO 00 rH 00

n 4-1 o en tJ^ 00 ON CM r^ 00 a> 00 00

m

en rH o rH

O o r-i T-{ o o <r o o O o O o o O O o o o o o

CO • • • • • • • • • (U Pi>p o> o <r o- CM r-~ o 00 a> r-. r^ in

"O en CO t^ 00 00 iH <f r-\ 00 vO VD o

(La 4J CSJ -* in CO o <f t^ CO o CO rH r-. en iH o o o ,-\ rH o o CM r^ <-i o O o o o o O o o o O O o

to • • • • • • • • • • • •

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en iH o o o o o c O o o rH rH O o o o o o o o o o O O

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en r-i o T-i

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(U p o CNI o <t CM ON <-t o CM CM CO C3^ tJ VD in rH t3^ o CJ^ r^ CM 00 O o CO

pq 4J o ^£) CO CO CM

O <r t^ in CO o v£> en rH o rH •H r-i r-f o o o rH rH rH o o o O O o o o o O o O CO • • • • • 0) PJ>

0) p CM CO ^ CM <-{ r~ in -* in CO 00

^3 <H vOm r-~ CJ^ C3> o o 00 vO in -*

<: 4-1 VO in r^ Csl (y\ CO CJ> i^ rH CO r^ r-~ en <-i rH o r^ o o o o rH o O rH o O o O o o o o O o O o CO • • • • • • • <u Pi

U30) •HH ,-\ CM CO <r rH CM CO ~d- ^ CM ^ CM

(U CO

4J (U

to 4J

<U -H rH CM CO <f H W

36
.03 .04 .05 .06

tfj-ta °Cm2

I W

Figure A-2a. Comparison of first and second order curve fits for FRP covered

nonselective absorber type collector

I.U

COLLECTOR C 0.8 _ 1st ORDER Sx = 0.0055 2nd ORDER Sx = 0.0036

EFFICIENCY o

o

:^

at -^^^_^

0.2

1 1 1 1 1 1 1

.01 .02 .03 .04 .05 .06

tf,i-ta °Cm2

.07 .08

I W

Figure A-2b. Comparison of first and second order curve fits for one cover, heat trap, nonselective absorber type collector

37
APPENDIX B: DETAILED COLLECTOR DESCRIPTION DATA

Table B-1 lists the important dimensions and material properties required for thermal

analytical modeling. Most information was obtained from the manufacturers

literature. When the literature was not available, dimensions were taken from one

collector. Handbook property values for thermal conductivity, refractive index and

extinction coefficient were used when not specified by the manufacturer.

Table B-2 lists collector area measurements made for each collector at Test Site 1. Calculations of the standard deviation and "within" test site coefficient of variation

are shown.

Table B-3 lists collector area measurements reported by each facility. Calculation

of the standard deviation and "between" test site coefficient of variation is shown.

38
•^ 00 CO 00 CO

in

CN en

in

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in

CN

a. rH vO CM p^ o m o >d- r-- cn rH (^^ r-- >* cn * O -* O ^ IS pe • • • • • • • • • • • • • • • • • r-i o o rH o Cvl o rH o in

CM

rH

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CM

CN i-{ in

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CN

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CN

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l-i c U o c O

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O 1 •H ^ B tu M l|H ^ M tu P. u >-l •H u o U •H o o 3 tu tu tu O 3 o o O u O •H U-t 4.1 to •I-t IH 4-1 to •rH (U o 14H ^ rO CO rH •H tu 14H H •H Pi U fi tu >< fX 4= tu X p. ^ X! r-i 14H 3 3 (X O ^ gS ^ J3

tuH pi2w

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tu o O 4-1 4J til H •H to

u to /-^ CU ) 4J 4J rH a M Vj rH rH c« to to P<

tu (U tu Ph 0) cr

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tu

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to rH•H

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39
Table B-2. Individual Collector Area Measurements by Test Site No. 1

^^'^-^„„^^^ Series

1 2 3 4 Mean

Std

Dev

Coeff. of

Var. (%)

Collector ^"''"~>--„^^^ (ft2) (ft2) (ft2) (ft2) (ft2) Sr

A 23.35 23.35 23.30 23.40 23.35 0.041 0.175

B 18.70 18.75 18.70 18.78 18.73 .039 .211

C 28.12 28.05 28.16 28.12 28.11 .046 .163

D 18.00 17.94 17.91 17.91 17.94 .042 .236 E 20.68 20.56 20.57 20.51 20.58 .072 .348 F 20.73 20.84 21.26 20.81 20.91 .238 1.14

G 27.80 27.88 27.88 27.81 27.84 .043 .156

H 31.50 31.61 31.50 31.60 31.55 ,061 .193

Average Coefficient of Variation, ZcVj. = .328%

(^cvj- = 0.212% without 1.14 outlier value)

Table B-3 • Collector Area Measurements for Each Test Site

^^^-^.TTest Site

1 2 3 4 Mean

Std

Dev

Coeff. of

Var, (%)

Collector ^"""^^.^.^ (ft2) (ft2) (ft2) (ft2) (ft2) Sr

A 23.35 23.19 22.81 23.16. 23.13 0.228 0.99

B 18.73 18.72 18.37 18.71 18.64 0.175 0.94

C 28.11 27.88 27.56 27.87 27.86 0.226 0.81

D 17.94 17.88 17.53 17.88 17.81 0.187 1.05

E 20.58 20.35 20.17 20.32 20.36 0.169 0,83

F 20.91 20.71 20.38 20.70 20.68 0,219 1.06

G 27.84 27.64 27.25 27.60 27.58 0.245 0.89

H 31.55 31.51 30.94 31.51 31.38 0.292 0.93

Average Coefficient of Variation, %cvR0.94%

40
APPENDIX C: THERMAL PERFORMANCE DATA

The test data and measured efficiencies are tabulated in the ASHRAE Standard 93

prescribed foirmat for all efficiency tests. The data are identified by collector type,

series number, and laboratory number (test site) . In view of the present accepted

practice in this country for building technology, common U.S. units of measurement

have been used for the data tables.

41
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89
APPENDIX D: DESCRIPTION OF SOLAR SPACE HEATING AND DOMESTIC WATER HEATING SYSTEM

SIMULATED USING F-CHART

Collector

o Area: Sized for each collector in each city to provide 50% and 75% of the

seasonal space heating and hot water load

o Orientation: Tilted equal to the latitude, 0°, azimuth (south facing)

Collector Type Fr(toc)^ (Btu/°F.ft2.h)

lAM

Bo

1 One glass cover Black paint absorber

0.670 -1.080 -0.08

2 Two glass cover Selective absorber

0.642 -0.56 -0.175

Collector Loop Heat Exchanger

o None

Main Storage Tank

o Capacity: 15 Btu/°F-ft2 (1.85 gal/ft^)

Space Heating Load Heat Exchanger

° ^L C^in

UA

= 2.0

Space Heating Load

o Building Effective UA: 12912 Btu/°F-day

(8 Btu/degree dayft^ for a residence having a floor area of 1614 ft^)

o Internal Heat Generation: None (Building Effective UA given above is assximed to be a net value including the effect of internal

heat generation)

Domestic Hot Water System

o Daily Draw: 70 gal/day

o Cold Water Temperature: 55 °F

o Hot Water Temperature: 140°F

90
^BS-114A (REV. 2-8C)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS TN 1140

2. Performing Organ. Report No. 3. Publication Date April 1981

4. TITLE AND SUBTITLE

Uncertainty in Determining Thermal Performance of Liquid-Heating

Flat-Plate Solar Collectors

5. AUTHOR(S)

Elmer S treed, David Waksman

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Department of Energy

Office of Solar Applications for Buildings

1000 Independence Avenue, SW

Washington, DC 20585

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

LI. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnificant

bibliography or literature survey, mention it here)

Thermal performance measurements of eight liquid-heating flat-plate solar

collectors were conducted with two to four collectors of each type at four

outdoor test sites. Tests were performed in accordance with the procedure

prescribed by ASHRAE Standard 93-77. Statistical analysis of data sets for

each collector type within test sites and between test sites was done using

ASTM recommended methods to evaluate test method measurement uncertainty.

Illustrations of the influence of thermal performance data uncertainty are presented for collector material degradation, collector rating and

calculated system performance.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

collector rating; measurement; solar collector; standards; thermal performance;

uncertainty

13. AVAILABILITY

[j^ Unl imited

I I For Official Distribution. Do Not Release to NTIS

[x] Order From Sup. of Doc, U.S. Government Printing Office, Washington, DC

20402. Q^ Order From National Technical Information Service (NTIS), Springfield, VA. 2216 I

14. NO. OF

PRINTED PAGES

97

15. Price

$4.00

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