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NBS TECHNICAL NOTE 975

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

'53

975

'8

m

Round-Robin Test Program

^

for Liquid-Heating

Flat-Plate Solar Collectors
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress 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 performed by the National Measurement Laboratory, the National Engineering Laboratory,

and the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

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physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

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calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities^ — Radiation Research — Thermodynamics and

Molecular Science — Analytical Chemistry — Materials Science.

THE NATIONAL ENGINEERING LABORATORY provides technology and technical

services to users in the public and private sectors to address national needs and to solve national problems in the public interest; conducts research in engineering and applied science

in support of objectives in these efforts; builds and maintains competence in the necessary

disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities; provides engineering measurement traceability services; develops test methods and proposes engineering standards and code changes; develops and

proposes new engineering practices; and develops and improves mechanisms to transfer

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Engineering and Process Technology' — Building Technology — Fire Research —

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THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal Agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

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'Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234. •Some divisions within the center are located at Boulder, Colorado, 80303.

The National Bureau of Standards was reorganized, effective April 9, 1978.
m STANDARDS

AUG 1 8 1978

Results and Analysis of a Round-Robin Test

Program for Liquid-Heating Flat-Plate Solar Collectors i^

T ^(L V\rN \ (La t '^ C3 -^ <^jN>- ^'^V^

E. R. Streedi, W. C. Thomas2, A. G. Dawson, III2,

B. D. Wood^, and J. E. Hilli

'Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

^Department of Mechanical Engineering

Virginia Polytechnic Institute and

State University

Blacksburg, VA 24060

^Department of Mechanical Engineering

Arizona State University

Tempe, Arizona 85281

Sponsored by the Department of Energy

20 Massachusetts Avenue, NW

Washington, DC 20545

^f-ATZS O* ^

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued August 1978
National Bureau of Standards Technical Note 975

Nat. Bur. Stand. (U.S.). Tech. Note 975, 1 19 pages (Aug. 1978) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1978

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

Price $3 Stock No. 003-003-01959-3 (Add 25 percent additional for other than U.S. mailing)..
Preface

In discussing this round robin testing program, certain commercial

components were used and are identified in order to provide a descriptive

characterization of their features. Inclusion of a given component in

this report in no case implies a recommendation or endorsement by the

National Bureau of Standards, and the presentation should not be construed

as a certification that any component would provide the indicated performance.

Similarly, the omission of a component does not imply that its capabilities

are less than those of the included components. This report is intended

to be informative and instructive and not an evaluation of any commercially

available components.

Ill
Table of Contents

Abstract v

1. Introduction 1

2. Collector Performance 1

3. Collector Test Procedure 3

4. Round Robin Program Description 6

5. Results and Statistical Analysis of Data 7

6. Analysis of the Effect of Environmental Conditions 9

7. Analysis of the Effect of Random and Systematic Errors 15

8. Implication of Collector Performance Uncertainty on 20

System Performance

9. Conclusions 21

10. References 23

Appendix A - List of Round Robin Participants 79

Appendix B - Data Used in Analyzing the Effect of Environmental 81

Conditions

Appendix C- Analytical Relationships Used in the Collector

Model for Analyzing the Effect of Environmental

Conditions 104

IV
Results and Analysis of a Round Robin

Test Program for Liquid-Heating

Flat-Plate Solar Collectors

By

Elmer R. Streed, William C. Thomas, Aaron G. Dawson, III

Byard D. Wood, and James E. Hill

Abstract

A round robin test program was conducted at 21 United States test facilities, using a common test procedure, to determine the intercomparability of

theinnal performance data pertaining to two liquid-heating flat-plate solar

collectors.

The statistical analysis of the data revealed a relatively large spread

in the measured values of collector efficiency. Data from approximately

half the facilities were then selected for detailed analysis. A collector

analytical model was used to show that less than one-third of the mean-square

distance could be attributed to different environmental conditions from

facility to facility. It was found that the data showed less scatter for one of the two collectors than for the other. In general, the data were

consistent for any single facility; most of the scatter was therefore

attributed to systematic uncertainties from facility to facility. When the

data from six participants reportedly adhering to the requirements of ASHRAE

Standard 93-77 were analyzed, the scatter was found to be within normal

limits expected for the test procedure.

Key Words: Measurement; modelling; solar; standards; testing

1. Introduction

A proposed procedure for testing and rating solar collectors based on thermal performance was first published by the National Bureau of Standards

(NBS) in 1974 [1-3] . The procedure prescribed that a series of outdoor steadystate tests be conducted to determine the near-normal-incidence efficiency of

the collector over a range of collector operating temperature conditions.

The American Society of Heating, Refrigerating and Air-Conditioning Engineers

(ASHRAE) has recently adopted ASHRAE Standard 93-77 [4] , which is similar

to the original NBS procedure but calls for additional tests to determine

the collector time constant, as well as an incident angle correction factor

that can be applied to the near-normal-incidence efficiency to determine

collector performance as a function of incidence angle.

Since the publication of the NBS procedure [1] , several testing loops

have been built at the NBS site in Gaithersburg, Md. and experiments conducted

to verify the applicability of the test procedure to a variety of commerciallyavailable collectors. In addition, experiments have been conducted to support

the development of the new tests which have been included as part of ASHRAE

Standard 93-77. The results of these experiments will be forthcoming in a separate publication.

A second major part of the NBS solar collector test development work has

consisted of the round robin testing program described in this report. The

purpose of the program was to have a variety of testing laboratories across

the United States attempt to utilize the test procedure and then determine

the extent to which the results differed or were comparable.

2. Collector Performance

The performance of flat-plate collectors operating under steady-state condiItions can be described by the following relationship [5]:

-^ = I(Ta)e - U (t - t ) (1) A L p a

where q = useful heat output, W

2 A = cross-sectional area, m

I = total solar energy incident upon the plane of the

collector per unit time per unit area, W/m"^

(xa)^ = effective transmittance-absorptance product for

the cover plate-absorber combination

e
U^ = heat transfer loss coefficient for the solar

collector, W/(in^*°C)

t = average temperature of the absorber surface of

the solar collector, °C

t = ambient air temperature, °C

If one introduces the definition of either the collector efficiency factor

F' or the collector heat removal factor F [6] , equation (1) can be rewritten*

"^u . , , . ^f,i "^ ''f.e — , , = F'I(Ta) - F'U. ' —-^^ (2)

A

^ ^ 2 ^

or T= V(^°')e - W (tf,i - ta) (3)

where ^^ - temperature of the heat transfer fluid

leaving the collector, °C

tf = temperature of the heat transfer fluid

entering the collector, °C

If the solar collector efficiency is defined by

n =^

(4)

AI

then the efficiency can be written as

n = (Ta)3 - Ul ^P

, ^^

(5)

* Equation (2) is only approximately correct. The collector efficiency factor

F' is defined in terms of the local fluid temperature and since the fluid

temperature varies exponentially from inlet to exit, equation (2) is incorrect,

The error is insignificant for flat-plate collectors using a liquid heat

transfer fluid but can be significant for those using air.
or ^f,i^^f,e

-*^a

Ti = F'(Ta)g - F'U^ (6) or

n = FR(xa)e - Vl -^

(7)

f .1 a

Regardless of which form of the efficiency equation is used, equations

(5-7) indicate that if the efficiency is plotted against some appropriate

parameter (At/1), a straight line will result where the slope is some function

of Uj^ and the y intercept is some function of (Ta)g« In reality Ut is not

a constant but rather a function of the operating temperature of the collector

and of the ambient weather conditions such as air temperature, sky temperature,

and wind velocity and direction. In addition, (Ta)g varies with incident

angle to the collector and can vary to some extent as a function of the

spectral and spatial distribution of the incoming solar radiation.

3. Collector Test Procedure

The procedure proposed by NBS in references 1 and 2 is based on collectors

that can be isolated so that they have effectively one inlet and one outlet.

The energy of the fluid entering and leaving the collector can be determined

by making appropriate measurements. These quantities are then compared to

the energy incident upon the collector (also determined by measurement) in

order to calculate the collector efficiency. The fluid can be either a liquid

or a gas but not a combination of the two.

As part of the procedure, the apparatus to be used is specified when

the heat transfer fluid is a liquid (Figure 1) or air (Figure 2). The detailed

requirements of the apparatus are given along with specifications for instrumentation to be used in measuring incident solar radiation, temperature,

temperature difference, liquid flow rate, air flow rate, pressure, pressure

drop, time and weight. For the specification of instrumentation, emphasis

was placed on utilizing existing standards and other manuals of acceptable

' practice.

The series of tests consists of determining the average efficiency for

15-minute periods (integrating the energy quantities) over a range of temperature differences between the average fluid temperature and the ambient air.

The efficiency is then calculated by

jmcp (tf^^ - tf^i) dx

Tl =

(8)

A JI dx
where

m = mass flow rate of the heat transfer fluid, kg/s

c = specific heat of the heat transfer fluid, J/ (kg * C)

The flow rate is required to be steady and vary by less than + 1.0 percent

for the duration of each test. In addition, the heat transfer fluid shall

have a known specific heat which varies by less than 0.5 percent over the

temperature range of the fluid during a particular 15-minute test period.

Consequently, the efficiency can be determined by

r

1 = (9)

A J I dx

The test apparatuses specified in references 1 and 2 have been designed

so that the temperature of the fluid entering the collector can be controlled

to selected values. This feature is used to obtain the data over the temperature range desired. At least 16 data points are required for a complete

test series and they must be symmetrical with respect to solar noon (to

prevent biased results due to possible transient effects).

During each test period, the incident solar radiation must be "quasisteady" as indicated in Figure 3 (in contrast to days in which cloud cover can cause a time distribution such as shown in Figure 4) . Other requirements that must be satisfied for each data point are that the 15-minute average insolation be greater than 630 W/m and the incident angle between the

direct solar beam and the outward drawn normal from the collector be less

than 45°. In addition, the range of ambient temperatures for the entire test

series must be less than 30°C.

In developing the test procedure and writing the specific requirements,

one main area of concern was ensuring that the measurements made would be

sufficiently accurate so that the collector efficiency values would be meaningful.

It is recommended that the temperature rise in the heat transfer fluid

passing through the solar collector be measured with either a thermopile (air or liquid as the transfer fluid) or calibrated resistance thermometers (only

with a liquid). It is felt that an accuracy of ± 0.1°C is possible with such sensors and associated read-out devices. A variety of liquid flow meters

are available that will enable m to be determined to within + 1 percent of

the measured value. The measurement of the incident solar radiation using

pyranometers is perhaps the most critical and least accurate of all the measurements specified. As described in reference 2 typical accuracies of better
than 5 percent are difficult to attain. However, Latimer has shown [7]

that it is possible to obtain an accuracy of + 2.3 percent with the

better pyranometers provided they have been calibrated directly against

a primary or a working standard pyrhellometer using the sun as a source

and that they are properly installed and maintained. Based on this analysis,

the test procedure should result in efficiency values accurate to within + 4-5 percent.

As mentioned previously, ASHRAE has recently adopted Standard 93-77

which is similar to the NBS procedure. It was not adopted in time to be

specified in this round robin test program; however, its main features will

be described here for purposes of comparison.

The major changes in the conduct of the efficiency tests as specified

in Standard 93-77 compared to that specified in the NBS procedures

[1 and 2] are as follows:

/

1. The testing apparatus for water-cooled collectors has been

modified to include a storage tank for damping out thermal

transients and a by-pass for periodically calibrating the flow

meter in place.

2. The testing apparatus for air heaters has been rearranged so that air is "pulled" through the collector instead of being

blown through it (slight negative gage pressure in the collector).

3. More stringent requirements have been Included for the measurement of solar radiation. Only pyranometers which meet or ex- ceed the characteristics of a first class pyranometer as classified by the World Meteorological Organization [8] are allowed.

4. In conducting the test, data must be taken when the incident

angle is less than 30° (compared to 45° in [1, 2]).

5. The time period required for the integration of energy

quantities to compute one efficiency value has been decreased from 15 minutes to either 5 minutes or one time

constant, whichever is larger.

6. In computing efficiency, the gross frontal area of the

collector is used instead of aperture area.

7. The efficiency curve is drawn by plotting efficiency versus

the difference between inlet fluid temperature and ambient

temperature divided by the incident solar radiation. (Average fluid temperature is used in the NBS procedures [1, 2].)

Inlet fluid temperature was chosen to be used in the plot

primarily because the characteristics of the collector required

for the system design procedures as reported in references

9 and 10 can be determined directly from the curve.
The major new features of Standard ^Z-ll compared to the NBS procedures

[1, 2] are:

1. The collector is required to undergo a preconditioning test

prior to the start of the thermal tests. The collector

must be exposed for three cumulative days with no fluid passing through it and with the mean incident solar radiation

measured in the plane of the collector exceeding 17,000

kJ/(m^*day).

2. Prior to conducting the efficiency tests, a time constant test is done.

3. After completing the efficiency tests, a series of tests is

conducted to determine the collector's incident angle modifier.

4. The entire group of tests may be performed indoors using

a solar simulator if desired. The specifications for the

simulator are included and follow closely those of references

[11-13].

4, Round Robin Program Description

Participants in the program were obtained by soliciting interest with a Sources Sought Announcement in the May 15, 1975 Commerce Business Daily and

by individual letters to organizations known to be interested in solar

collector testing. The program was designed to provide experimental data

from various climatic regions and test facilities on two flat-plate liquidheating collectors with different heat transfer and optical properties.

Final selection of the organizations was made on the basis of test facility

experience, climatic and geographic regions, cost to modify facility and

labor to conduct the test, and willingness to conduct the test in accordance

with the NBS proposed procedure. A total of 21 organizations, including

three Government laboratories, as listed in Appendix A, participated in testing each collector. The distribution of participants with respect to geographical and climatic regions is shown in Figure 5.

Because of the large interest in the program, the relatively large

number of climatic regions, and the time required to perform the test, it was impractical to send the same two collectors to each participant. Therefore,

collectors were selected with sufficiently stable component properties and

from manufacturers with established quality assurance methods capable of keeping

thermal property variations to a minimum. One collector of each type was shipped to each participant for testing.

Collector No. 1 (PPG Industries) consisted of two 3.2 mm-thick tempered

glass cover-plates and an aluminum absorber plate with a flat-black coating

assembled into a sealed unit. The assembly was attached to a sheetmetal box

containing glass -fiber insulation as shown in Figure 6. Measurements made
at the manufacturer's plant of the absorber coating thickness on each of the

21 panels indicated variations from the center to the edge of about 0.0076 mm

in the range of 0.0127 to 0.0203 mm. The relationships between coating solar

absorptance (og), normal emittance (£„) and thickness are shown in Figure 7.

Independent measurement of Og and eTj (hemispherical emittance) using

actual coated samples resulted in values of 0.94 and 0.92, respectively.*

The solar transmittance of the glass used in the cover-plate assembly was determined to be 0.85 for an air mass 2 spectral distribution (measurements

were made on untempered glass). The glass normal emittance was measured to

be 0.85. While the collectors were carefully selected at the manufacturer's

plant, no other provisions were made to control the reproducibility of the

sample of collectors used in the program. Analysis of the known variations

in collector properties indicates that the efficiences should be reproducible

to within 1 or 2% if measured under identical conditions.

Collector No. 2 consisted of one 3.2 mm-thick tempered glass cover-plate

(Chamberlain Manufacturing Company (CMC)) with a seam-welded mild steel absorber

coated with a black chrome selective coating. The absorber was mounted on a thermal insulator and backed with glass-fiber insulation. The entire assembly

was mounted in a steel frame with a sheetmetal back and aluminum glazing frame

as shown in Figure 8. Spectral reflectance measurements made of six 30.48 cm

specimens coated at the same time as the absorber panels indicated a solar

absorptance of the black chrome coating of 0.95. The normal emittance

of the coatings was measured to be 0.14** The coating manufacturer***

also measured the solar absorptance and emittance of each panel using portable optical instrumentation. Those results are included in Table 1.

A list of the pertinent dimensions, optical properties, and materials

for each collector is presented in Table 1.

5. Results and Statistical Analysis

of Data

The primary result reported by each participant was a plot of collector

efficiency, r\, versus f , e f , i

7

1 along with the testing conditions for

2 7 each of the data points. A summary of the data is given in Table 2 and

Table 3 for collectors No. 1 and No. 2, respectively. The values of F'(xa)p

and F'U-r were determined by a first-order least-square-fit to all measured

data points. Mean and standard deviation values were calculated for these

two parameters for the group, using the following statistical equations:

* Lockheed Palo Alto Research Laboratory, Palo Alto, California.

** Gier-Dunkle Instrument Co., Emissometer Model DB-100, Santa Monica,

California

*** Olympic Plating Company, Canton, Ohio.
n

X . mean = *—' (iq) 1=1

and

n

n 2 E-H£-. (11)

standard = S = / ^-^ \ 1=1

deviation

n-1

The percent deviation from the mean for each set of data points is also shown

in the Tables.

An indication of the spread and distribution of F'(Ta) values for each

collector are shown in Figure 9. The greater frequency of values about the

mean for collector No. 2 is probably due to the fact that more of the data

were taken at smaller incidence angles for this collector than for collector

No. 1. An early version of ASHRAE Standard 93-77 was out for public review

before most participants started testing collector No. 2. Since it required

the incident angle to be less than 30° (compared to 45° in the [1, 2]), many

participants were undoubtedly influenced to test closer to solar noon.

The relatively large standard deviation of 7.7% for F'(Ta) for collector

No. 1 was not expected. It is felt that one major source of the deviation

was the use of a "black-and-white" pyranometer, model 8-48^ by eight participants. It has been reported [14] that the calibration factor (determined

originally with the instrument in the horizontal position) of a similarlydesigned instrument changed from 3 to 8% as the instrument was tilted up

from the horizontal to typical angles used for collector testing. The mean

value of the F'(Ta) values for those collectors (No. 1) where the "black

and white" pyranometer was used is 0.79 compared to a mean value of 0.725

for those collectors where an "all-black" (model PSP) pyranometer was used.

By arbitrarily reducing the measured F'(Ta) values in Group 1 by 0.065,

a new mean value for F'(Ta) for all 21 participants, of 0.73 would result

for collector No. 1. This correction would reduce the standard deviation

in F'(Ta)g to + 0.05 or + 6.8%.

Only five of the participants used the "black-and-white" pyranometer

for collector No. 2 and the standard deviation was only + 0.039 or + 4.64%

about the mean of 0.84. In addition, two participants apparently used the

gross area rather than the aperture area to calculate the efficiency, which

resulted in a 5% low value of F'(Ta) . Correction of these values would

reduce the standard deviation to ± 0.03 or + 3.6%.
A similar plot of the distribution of reported values for F'Uj for both

collectors is shown in Figure 10. As can be seen, the variation in reported

results is large. The standard deviation about the mean of 6.43 W/(m . c)

for the collector No. 1 is ± 1.01 W/(m . t) or ± 15.7%. For collector No. 2,

the mean is 4.37 W/(m - t) with a standard deviation of ± 1.20 W/Cm.t) or +27.7%. In order to explain the variation, a close examination was made of

the reported data.

As shown in Figure 6 for collector No. 1, the absorber plate is in thermal

contact with the outside mounting and cover-plate frame. Therefore, the edge

losses are dependent upon the collector array mounting configuration and can be particularly significant when an individual panel is exposed. The

influence of edge losses in F'Ut is shown in Figure 11. The variation, from

no edge loss to an edge loss of about 3 times the value of 0.5 W/(m. C) for

a typically insulated edge, results in a percentage difference of + 7% to -26%

from the mean value of F'Ut reported for the collector.

Each participant was requested to enclose the No. 1 collector in a 5 cm x

10 cm frame with a plywood backing to provide a more uniform test situation for

this collector. A review of the collector mounting procedures plus the description of the actual tests indicated that some unusual conditions did exist.

For example, extra insulation was used around the back and edges of some of the

collectors, mass flow rates different from the prescribed 0.02 kg/(s.m ) were

used, and incidence angles exceeded 45 degrees in some cases. By omitting these

data from the analysis, a new mean value of F'U-r of 6.56 W/(m. t) would result

with a standard deviation of ± 0.75 W/(m^. C) or ± 11.4%.

The influence of one extreme value for F'Ut for collector No. 2 had a large effect on the statistical analysis. By considering the value of 1.6

W/Cm"^*!;) to be an outlyer [15] and therefore omitted, the mean value of F'Ut

would become 4,58 W/(m . "c) and the standard deviation + 0.775 W/(m% *fc) or ± 16.8%.

The significantly lower overall loss coefficient for collector No. 2 is

due in part to better thermal insulation of the absorber plate from the

exterior environment and the use of a selective coating. However, the

single glazing makes the collector heat loss more susceptible to wind and

ambient temperature. The range in measured values of overall loss coefficient

for the five collectors that exhibited F'da) values of 0.85 (very close

to the corrected mean of 0.844) are + 20% and - 17% from the mean as illustrated in Figure 12.

6. Analysis of the Effect of Environmental

Conditions

It was felt that the range of environmental conditions existing during

the tests at the various facilities across the country undoubtedly caused

a portion of the data scatter. In order to determine the amount, one of

the round robin participants, W.C. Thomas and his graduate student A.G.

Dawson, III of Virginia Polytechnic Institute and State University undertook

a detailed analysis of the data. The results of that study are reported
in this Section [16] . The general approach used was to reference all measured

thermal efficiencies to a common set of environmental conditions by using

analytical models for the two flat-plate collectors tested.

Screening and Selection of Data

The data were examined for complete documentation and consistency with

respect to test conditions. The objective was to assemble at least ten complete sets of data. It should be noted that regional location, altitude,

and climatic conditions at the testing laboratories were not criteria for

screening the data. After the screening process, 12 sets were selected for

collector No. 1 (PPG) and 10 sets were selected for collector No. 2 (CMC).

Typically, test results were not included in the analysis because diffuse

fractions, wind speed, ambient temperature, incident angles, or type of test

fluid were not available. In some cases, the calculated results required

by [1, 2] were incomplete. Where possible, these were completed and the

results used. For example, incident angles were calculated provided the times

of testing and collector orientation were reported. Results for more than

the required 16 data points were given by some participants. For these cases,

the 16 points nearest solar noon were selected. The additional points were

not included to avoid weighting the particular facility more heavily than

the others.

The data corresponding to the figures to be shown in this Section are tabulated in Appendix B. Testing organizations are identified by the letter

designation of Tables 2 and 3. The solid curves shown are least-squares

second-order polynomials unless noted otherwise. Following reference [17],

the mean value of the square of the distance f rom_ the points to the curve

("mean square") is used to compare the closeness of correlations.

Figure 13 shows the efficiencies as reported by the 12 selected organizations for collector No. 1. The abscissa values were recalculated from the data

so that the efficiency curve could be drawn using inlet fluid temperature instead of average fluid temperature. This abscissa selection makes the plot

consistent with [4] . The points shown to the left of the ordinate axis are

for tests where the inlet temperature was less than the ambient temperature.

Participant K reported two measurements where the abscissa was outside the

range shown. While the results were included in the statistical analysis,

the points are not shown in the graphs. The second-order curve shows an increasing slope as f,i ~ a increases contrary to what would be expected

I if all data were taken at one laboratory.

Identification of the data points in Figure 13 with each participant

showed, generally, a small amount of scatter for individual organizations.

The spread, consequently, results from the differences in efficiency values,

at the same conditions, by the various organizations. The ordinate intercept

for the second-order curve shown is 0.731,

Figure 14 shows the results reported for collector No. 2 as reported by

the 10 selected participants. Generally, the efficiencies reported by the

different laboratories agree more closely than do those in Figure 13. Since

10
this was the second collector tested and since the collector was less sensitive to the method of mounting on the test frame, the trend is as expected.

The second-order curve has a continuously decreasing slope with an ordinate

intercept of 0.80.

Figures 15 and 16 show a subset of the above-selected test results where

each facility shown reportedly adhered to the more stringent requirements of

ASHRAE Standard 93-77 [4]. There were five organizations (A, G, H, J, N)

testing the collector No. 1 and seven organizations (G, H, J, N, 0, R, U)

testing collector No. 2 that reportedly met these requirements. Figures 15

and 16 show clearly that the differences are much more pronounced from

test facility to test facility compared to the scatter reported by a given

facility. There is much less scatter associated with test results shown

in Figure 15 and 16 than in Figures 13 and 14, respectively.

Analysis Approach

The principal task was to determine how much of the scatter about the

curves, as shown in Figures 13 through 16, could be attributed to the differences in environmental conditions under which the tests were conducted. The

analysis approach involved adjusting each of the efficiency values or data

points up or down depending on whether the combined effect of the actual

test environment would theoretically result in a higher or lower efficiency

if the same test were conducted at a "reference" set of conditions. The

criterion for evaluating the effect of the data adjustment was to compare

the before and after values of the mean square of the regression analysis.

Measured efficiencies as reported were adjusted to a common set of conditions by subtracting the theoretically-determined efficiency at actual (experimental) conditions from the theoretical efficiency at the common ("reference")

condition and adding the result algebraically to the experimentally-determined

efficiency. The expression for the corrected efficiency is

n (std. conditions, corrected) = n (actual conditions, measured) +

[ti (std. conditions, theoretical) -

n (actual conditions, theoretical)] (12)

Applying the correction required a theoretical thermal performance analytical

model and the configuration, dimensions, and heat transfer properties for each

collector. It should be noted, however, that the theory was used only to

determine an efficiency difference. Therefore small uncertainties in collector

properties and the analytical model would have had an even smaller effect

on the corrected efficiency values.

"Reference" conditions selected were generally the mean values of the

reported test conditions reported with round-off to convenient values. This

criterion for a set of "reference" conditions resulted in the minimum overall

adjustment of data. The "reference" environmental conditions selected are

shown in Table CI of Appendix C,

11
Description of Analytical Model

The collector model used was based on state-of-the-art collector theory

as siimmarized in reference [6]. Extensions have been made to account for

the effects of the scattered component of solar radiation and temperature

and composition of the heat transfer fluid. The presence of scattered radiation effectively changes the transmittance of the cover-plate assembly.

Scattered radiation is accounted for by considering two limiting cases. The

scattered radiation is assumed to be either completely diffuse or from an apparent origin near the sun.

All the test facilities which furnished the results under consideration

used either water or ethylene glycol-water mixtures as the transfer fluid.

The properties of glycol mixtures, as functions of temperature and concentration, were taken from reference [18] and programmed as an interpolation table.

The complete details of the model and equations and how they were solved

are given in Appendix C.

Use of the Analytical Model

After the data were compiled, a set of cards was prepared for each test

facility with operating conditions, environmental conditions, and measured

efficiencies encoded. The collector design parameters and "reference" conditions were, of course, the same for all test facilities. Corrections to

the measured efficiencies were then made progressively by accounting for one operating environmental variable at a time. Using the inlet fluid temperature in the abscissa rather than the mean fluid temperature resulted in a considerable simplification. Had the mean fluid temperature been used, it

would have been necessary to carry out a separate calculation to correct the

mean fluid temperature to "reference" conditions. As the corrections to

"reference" conditions were applied progressively, the mean squares were used

to evaluate the effectiveness of that particular correction. In addition,

the graphs were studied visually by superimposing them on previous graphs

to observe trends

.

A separate statistical analysis plot routine and package were used to

prepare the graphs. The graphs were drawn by a Calcomp plotter in conjunction

with Virginia Polytechnic Institute and State University's IBM 370/158 digital

computer. Second-order polynomial representations of collector efficiency

were used since the representation essentially duplicated the results of the

analytical model at "reference" conditions. (The mean squares of the fits

to the standard theoretical curves were less than 0.02), Other considerations that were taken into account in the decision to use the second-order

equation include the requirements of ASHRAE 93-77 [4] and the observation

that a linear fit gives somewhat higher than expected values of the ordinate

intercept Fj^(Ta)g.

Results

The results with all the environmental and operating conditions considered are shown graphically in this section and in tabular form in Appendix B.

12
In all the graphs that show discrete efficiency points, the solid lines

are least-squares curves rather than a comparison per se with the theoretical model.

Figures 17 through 20 show the theoretical effect on efficiency of

environmental conditions. The abscissas correspond approximately to the

ranges reported in the round robin program. The curves show the effect

of a single parameter with the others constant at "reference" values.

Note that (t^ . - t )/l is held constant for each plot. The effects

of parameters 'depend strongly on the inlet temperature. The two inlet

temperatures selected to depict the results are 10°C and 70°C above ambient

which brackets the recommended test range [1, 2, 4]. In view of Figures

17 through 20, the expected efficiency changes resulting from correcting

to "reference" conditions are generally not large, as will be shown below,

compared to the more extreme differences noted in Figures 13 through 16.

Figure 21 shows the theoretical efficiency values calculated for collector No. 1 for the actual conditions reported by the 12 selected participants. The curve has a slightly increasing slope. The shape indicates

that this combination of environmental conditions overshadows the increase

of Uj with temperature. The scatter about the curve is, of course, justified

in the absence of any experimental error. The efficiency spread at the

I abscissa value of 0.07 (°C.m )/W is pronounced but does not completely account

for the spread at the corresponding value in Figures 13 and 15. Figure 22

shows the calculated efficiency for collector No. 1 at "reference" conditions.

Figure 23 shows efficiencies corrected for all environmental and operating

conditions. The mean squares are reduced from 27.9 in Figure 13 to 20.6

(percentage points-squared) in Figure 23. It is significant to note that

II the increasing slope is essentially removed in Figure 23 as a result of the

il correction.

Figure 24 shows the theoretical efficiencies calculated for the collector No, 1 tests that reportedly met ASHRAE 93-77 requirements. The slightly

increasing slope observed in Figure 15 is suppressed and the scatter is not

as large. Figure 25 shows the corrected efficiencies. The mean square is reduced

from 23.2 in Figure 15 to 17.1 in Figure 25 as a result of accounting for the

differences in test conditions. The mean square of 17.1 in Figure 25 is

less than the value of 20.6 in Figure 23.

The theoretical efficiency values for the actual test conditions are shown for collector No. 2 in Figure 26, Here, as for all the collector

No. 2 curves, the combination of test conditions and collector performance

characteristics result in a second-order curve with a slightly decreasing

slope. The scatter resulting from different test environments is again substantial but does not fully account for the scatter observed in Figure 14.

The theoretical efficiency curve at "reference" conditions is shown in

Figure 27.

Applying the corrections to the efficiencies shown in Figure 14, the

result for collector No. 2 is shown in Figure 28. The mean square is reduced

from 17.5 to 13.5 in accounting for different environmental and test conditions. Many of the points that are farther away from the best-fit curve

13
still appear in Figure 28. Restricting the results to those tests which

reportedly met ASHRAE 93-11 conditions, Figure 29 shows the theoretically

justifiable scatter. Figure 30 shows the corresponding corrected results

from the seven organizations. Comparing Figure 28 with Figure 3-0, many,

but not all, of the larger differences are eliminated. The mean square

is reduced from 8.5 in Figure 16, to 7.2 in Figure 30. A large reduction

in scatter is observed in simply going from Figure 14, with a mean square

of 17.5, to Figure 16 with 8.5. On the other hand, the mean square for

the corrected results in Figure 28 is only about 23 percent lower than

for Figure 14.

Figures 16 and 30 show that the efficiencies reported by participant

are significantly lower than those reported by the other six participants.

Figures 31 through 33 show the consensus of the results from the other

six organizations. The mean square is substantially reduced. The correction process reduces the mean square from 4.6 in Figure 31 to 4.0 in

Figure 33. The best correlation obtained in the study, without arbitrarily

omitting results, is that shown in Figure 33.

Linear best-fit curves, corresponding to the four principal figures,

are shown in Figure 34-37. These curves are included so that the intercepts

and slopes can be compared with the results obtained from all 21 organizations.

Table 4 is a summary of the pertinent statistical information for linear

and second-order least-squares fits to the various sets of efficiencies.

In conducting this analysis, it could not be concluded which of the

two limiting cases that were considered best accounts for the effects

of scattered radiation. Assuming scattered radiation originates from a direction near the sun, the cover transmittance is the same for beam

and scattered radiation. In the other limiting case, scattered radiation

was considered completely diffuse and a correction was applied. However,

the overall effects on efficiencies resulting from these corrections were considerably less than the experimental uncertainties.

Attempts to investigate the sensitivity of the correlations to sky

temperatures were also inconclusive. Sky temperatures of ambient minus 6°C

for summer and ambient minus 20°C for winter [6] were used in place of

equation (6) of Appendix C. The mean squares changed by less than 1.0 when

compared to the corresponding plots using equation (6). Although sky temperatures may have a significant effect on measured efficiency, the effect

could not be identified from the information available.

An attempt was made to test the adequacy of the correlations for wind,

percent scattered, etc. It was not possible to evaluate the individual correlations because of the relatively large amount of scatter in the results

after all other corrections had been made.

The effect of different techniques for mounting collectors on test frames,

which would change the back and side insulation, was considered. Again, no general trends could be associated with the mounting- technique.

14
In general, the results from the collector No, 1 tests show more scatter

than the results from the later collector No. 2 tests. The correction procedure, however, reduced the amount of scatter more for the former test results.

Applying corrections progressively, each effect considered either reduced

the mean square or resulted in a change too small to determine a definite

trend. Individual large deviations from the best-fit curve were reduced

significantly. The many points clustered closer, however, were changed

with less consistent trends. The combined effect resulted in changes of

the mean square which were small. The scatter remaining after the corrections were applied is attributed primarily to experimental and data reduction errors and will be addressed in Section 7. However, the limitation

of the correction theory and the possibility of differences between the

12 collectors must be considered. It is also recognized that normal outdoor weather can have an adverse effect on measuring and recording apparatuses.

Figures 38 and 39 show, for the two collectors used in the round robin

program, theoretical curves for more favorable and less favorable combinations of environmental conditions. These hypothetical limiting-case combinations are based on conditions and ranges allowed by ASHRAE 93-77. The graphs

are included to show the importance of referencing efficiencies to a common environment. The approach developed herein could be extended and verified

to apply more generally to flat-plate collectors.

7. Analysis of The Effect of

Random and Systematic Errors

As shown in Section 6 of this report, there was considerable scatter

in the data when considered as a combined group (i.e.. Figures 13 and 14);

however, the data for an individual facility were generally consistent and

showed very little scatter. In addition, correcting the data for the different environmental conditions that existed from facility to facility was shown to reduce the scatter between facilities by less than 30%. Therefore,

one concludes that either the requirements of the test are not restrictive

enough or that there were systematic errors which were not accounted for

by the various participants. In order to examine those possibilities,

another round robin participant, B.D. Wood of Arizona State University,

conducted the analysis reported in this Section.

The data taken during a given test are recorded and reduced to a plot of

thermal efficiency, ri > versus the parameter (t^ ^ - t )/I, here called X. Each

measurement has associated with it a random or uncertainty error and a systematic error such that (the specific heat is assumed to be known exactly):

(m ± w. + Am) c [( At^^ ± w + A(Atf)]

n ± w ± An = 1 (13)

^ (I ± wj ± Al) (A ± w^ ± aA)

15"
X ± wx ± AX =

[(tf i + Wf^ • ± Atf .) - (t + w +

t,i - tfji - r,i a ta - At^)]

(I ± w-j- + AI)

(14)

where At^ = t^^^ - t^^.

w = random or uncertainty error which could be either positive or negative with the same probability. The sign of w is indeterminant

.

A = systematic error. The sign could be either positive or negative and will remain fixed for a given test apparatus (e.g.,

conduction errors for thermocouple measurement, calibration

error for pyranometer, or radiation error for ambient air

temperature measurement).

Random errors cause data scatter for a particular test facility. Systematic errors cause a disagreement between test facilities. Since there is

relatively small scatter (less than 4%) for a given test facility, it is

reasonable to assume that the discrepancies among the combined data are due

primarily to systematic errors at the facilities. However, if the test

specifications were not tight enough, similar discrepancies could occur.

First consider the scatter that could be attributed to the experimental

uncertainty in the specifications of the test in [1, 2] and [4]. The maximum

uncertainty or error allowable is

:

w, = ±

3n w. +

"g^ m

in

3At, w

Atf

ill w

yi 't + ^

3n w^ (15)

or. w ^ =

Tl + m ^ At

m Atf

Similarly J

^X_

X

+ ^t +^t

f ,i a (^£.i - 'a' +

^

+

^

w.

(16)

(17)

The allowable uncertainty or inaccuracy in the measurements as specified

in or estimated from [1, 2] and [4] are such that:

16
-^ = ± 0.01

m

''Atf = + 0.1°C

-^ = ± (0.03 + %t)

w,-^ = ± 0.01

A

""t^: . = + 0.5°C

''t^ = ± 0.5°C

Therefore

'S= ± (0.05 + °^+ Oil)

n Atj I ^=±(0.03+ —li^ + °il) (19)

f ,1 a From [1,2] and [4], I >^ 630 W/m , therefore equations (18) and (19) become:

W A , -Jl^ ± (0.0502 + ^^-^)

n At^

Ji:^ ± (0.0302 + —5i^^—

)

,(21) ^

^f,i ^a

Considering collector No. 2, the following typical test values are taken

from Tables 1 and CI:

A = 1.79 m^

m =0.0358 kg/s

Cp = 4187 J/(kg.°C)

I > 630 W/m^

t = 20°C

a Then, and noting that At^ can be calculated by:

Tl l_k

'P

Atf = -0—L^ (22) m c

17
Atj > 7.523T1

t. . > 20 + 630X

(23)

(24)

and

^ < + (0.0502 + 0.10 ) n 7.523T1

^ < + (0.0302 + 1.0 ) X 630X

(26)

Equations (25) and (26) can be used to define the "maximum error" band for

the test data for collector No. 2. For example, the data in Figure 37 can be correlated by:

n = 0.814 - 4.98X (27)

Then for each value of X and corresponding n , the maximum error band allowable from references [1, 2] and [4] can be calculated as follows:

0.01 0.05 0.10

nw

0.764 0.565 0.316

± 0.068 ± 0.074 ± 0.092

w,wX

+ 0.052 + 0.042 + 0.029

± 0.189 0.062 0.046

w. + 0.0019 + 0.0031 + 0.0046

Figure 40 is a replot of Figure 36 where all the uncorrected data for ^ collector No. 2 for the 10 selected participants is shown along with the maxi- mum error band defined above. Figure 41 is a similar plot but for only

those participants which reported adhering strictly to the requirements

of ASHRAE Standard 93-77. Figures 42 and 43 are corresponding plots after

the data have been corrected to "reference" conditions.

Since the data of Figures 41 and 43 all lie within the this error

band, one might conclude that the scatter was due entirely to allowable

uncertainty as specified in references [1, 2] and [4] and no systematic

error existed at the facilities shown in Figures 41 and 43. It can more

logically be assumed that the data scatter among the various test facilities

taken as a group would most probably follow some sort of randomness and be
considerably less than the maximum allowable error band. Therefore, a second analysis was done.

A numerical experiment was conducted to determine the "anticipated" data

scatter from 10 hypothetical test facilities, each claiming compliance

with ASHRAE 93-77. Table 5 is a matrix of possible errors associated with

each measurand. The probability of each error is the same (this is conservative

compared to a normal probability distribution about the mean). A UNIVAC library

program was used to generate a random number between and 1.0. This number

with a corresponding error selected from Table 5 for each measurand at the

ten hypothetical facilities was then used to select the appropriate error. Hence, 60 random numbers between and 1.0 were required to generate Table 6,

which is a tabulation of errors assigned with each measurement at each

of the 10 hypothetical test facilities. The collector computer model described

in Appendix C was used to obtain an efficiency curve for collector No. 2.

This curve was then used to calculate the temperature rise across the collector

for a given collector inlet temperature at the following conditions:

I = 1000 W/m^ or 630 W/m^

A = 1.79 m^

m = 0.0358 kg/s

t^ = 20°C

at^ . = 20, 30, 40, 50, ...°C

Then in order to calculate the supposedly measured efficiencies for each

collector at the 10 test facilities, the following relationships were used;

I. = 1000 + Ai or 630 + Ai (28)

A. = 1.79 + AA. (29)

m. = 0.0358 + Am (30)

t„. = 20 + At (31)

tf i. ^ = tf . + At (32)

^^j,k='tk+^^tj (33)

These supposedly measured efficiencies are shown in Figures 44 and 45 for an insolation of 630 W/m and 1000 W/m , respectively. As expected, the scatter

is considerably less than the "maximum" error band also shown in the Figures.

By comparing Figures 43 and 45, one concludes that the data scatter that

19
actually occurred (after the data were corrected for differences in operating

and environmental conditions) among those facilities that reportedly adhered

to ASHRAE Standard 93-77 was much larger than should be expected. Also

notice that the combined errors in the numerical experiment only shifted

the curve up or down without changing the slope. Therefore, systematic

facility errors undoubtedly existed. Unfortunately, an evaluation of the

experimental apparatuses and various experimental techniques of the various

participants was not performed.

Each participant was provided with a copy of the test procedure which

describes the accuracy, precision and calibration requirements for each

measurement. However, meeting these requirements does not preclude the

possibility of uncertainties arising from sensor installation, data acquisition, or data reduction.

Based on the data available, it is only possible to hypothesize that some combination of the following systematic errors caused a portion of the data

scatter:

Systematic Facility Errors ;

- heat transfer between the test apparatus and the collector (proximity

of heat sources to the collector)

- reduced heat losses to ambient due to shielding of collector

support stand

- test apparatus not at steady state or "quasi-steady-state" conditions during tests

- change in specific heat of the transfer fluid

- inexperienced technicians conducting the tests.

Systematic Instrumentation Errors :

- conduction errors in thermocouple installations

- pyranometer calibration error

- flow meter calibration error

8. Implication of Collector Performance Uncertainty

on System Performance

The significance of the variation in the reported performance for a particular collector can be illustrated by calculating the expected system performanct

for two sample solar systems.

20
For the first example, the performance was calculated for a typical com- bined solar domestic hot water and space heating system. A residence located

in Madison, Wisconsin with a design heat loss of 21 kW was selected, A hot

water demand of 0.32 m per day combined with the space heating load re- sulted in an average monthly energy requirement for the year of about

1.7 X 10 J. The solar energy system assumed consisted of 80 m of collector No. 1. Other system features included a heat exchanger between the

collector and storage, an insulated 3.8 m liquid storage tank, a domestic

hot water heat exchanger and preheat storage tank with suitable pumps and

controls. Auxiliary energy was supplied when sufficient energy was not

available from thermal storage.

The calculation of the fraction of the load supplied by solar energy was performed using the f-chart method [9]. The collector thermal performance

factors used for F'CTa)^ and F'tl^ are listed in Table 4 for the mean, "best"

and "worst" values as reported in Section 5 of this report. The results

show a deviation of + 10.3 and - 11.8 percentage points in yearly solar fraction from the mean value or a total spread of 22.1 percentage points.

A second sample problem was completed again using the f-chart technique.

A solar domestic hot water system was simulated in five different cities across the country. For this calculation, it was assumed that 5.37 m of

collector No. 2 without a heat exchanger were used. The relationship between

F' and ¥^ was taken from reference [6]. The collector was assumed tilted at an angle equal to the latitude and the system used a 0.45 m storage tank.

The system supplied hot water at a constant temperature of 60°C with a constant inlet temperature which varied from city to city as shown in Table 8

and 9, The system was simulated using the collector performance factors

from all 10 test facilities identified in Section 6 of this report. Table 8

shows the calculated yearly fraction of the hot water load supplied by solar

energy using data from the six facilities adhering to the requirements of

ASHRAE Standard 93-77. The maximum spread is 6.5 percentage points for

Washington, D.C. Table 9 shows the results using data from test facilities

reporting the five highest and the five lowest performance. Again the maximum

spread occurs in Washington, D.C, 17.8 percentage points.

9, Conclusions

The results of the analysis indicate that the majority of the reported

differences in measured collector efficiency in the round robin testing

program resulted from experimental error or systematic differences from

facility to facility rather than from differences in the outdoor test

environments.

The preparation and mounting of the collector for test appeared to cause

a large uncertainty in test results for collector No. 1.

The use of a pyranometer meeting the World Meteorological Organization

Class I requirements and a pyranometer calibrated for use at test tilt angles

was found to be of major importance.
The environment can have a significant effect on the measured collector

efficiency even when conditions prescribed by current standards are met.

Within the limitation of the accuracy of flat-plate collector performance

theory, it was found that test results could be referenced to a common

environment using a straightforward analytical procedure. The procedure

significantly reduced the differences in measured efficiencies reported by

the various participants.

Efficiency correlations from individual participants generally showed

small scatter. Larger differences were observed, however, between efficiencies

measured by various participants at approximately the same conditions. The

second series of tests (on collector No. 2) gave more consistent results than

the first.

Tests that reportedly met the more restrictive ASHRAE 93-77 requirements

showed much more consistency among participants. It was not apparent,

however, whether the improvement resulted from the additional restrictions

or better experimental procedures by those participants. By restricting

efficiency measurements for collector No. 2 to 6 of the 7 participants

reportedly meeting ASHRAE 93-7 7 requirements, highly consistent results

were observed.

It is felt that outdoor solar collector testing will continue to be performed at an ever increasing rate. The technique of correcting test results

to "reference" conditions is a potentially useful aid for the solar

collector industry. The technique should be validated and then packaged into

a useful tool that could easily be utilized within the industry. In addition, procedures need to be adopted to ensure facility-to-facility agreement.

Continuing experiments would be desirable where two or three "independent"

facilities would conduct a series of tests and insure intercomparability.

The facilities would be picked so that extremes in environmental conditions

could be studied. The tests might include:

- interchanging collectors

- determining the effect of environmental conditions on data

scatter and reproducibility (wind, sky temperatures, insolation level, percent diffuse, ambient temperature)

- intercomparison of pyranometers

- determining the spectral distribution of the radiation for

the three locations

- determining when steady conditions occur for thermal testing.

22
10. References

1. Hill, J.E., and T. Kusuda, "Methods of Testing for Rating Solar

Collectors Based on Thermal Performance", NBSIR 74-635 , December,

1974.

2. Hill, J.E., Streed, E.R., Kelly, G.E., Geist, J.C., and T. Kusuda,

"Development of Proposed Standards for Testing Solar Collectors and

Thermal Storage Devices", NBS Technical Note 899 , February, 1976.

3. Hill, J.E., and E.R. Streed, "A Method of Testing for Rating Solar

Collectors Based on Thermal Performance", Solar Energy , Vol. 18,

No. 5, 1976.

4. "Methods of Testing to Determine the Thermal Performance of Solar

Collectors", ASHRAE Standard 93-77, ASHRAE, 345 East 47th Street,

New York, New York 10017, 1977.

5. Hottel, H.C., and B.B. Woertz, "The Performance of Flat-Plate Solar

Heat Collectors", ASME Transactions , Vol. 64, p. 91, 1942.

6. Duffie, J.A. , and W.A. Beckman, Solar Energy Thermal Process , John

Wiley and Sons, New York, 1974.

7. Latimer, J.R., "Radiation Measurement", Technical Manual Series No. 2 , Canadian National Committee for the International Hydrological Decade,

Building No. 8, Carling Avenue, Ottawa, Canada, 1971.

8. Guide to Meteorological Instrumentation and Observing Practices , Secretariat of the World Meteorological Organization, Geneva, Switzerland, 4th Edition, 1971.

9. Klein, S.A., Beckman, W.A. , and J.A. Duffie, "A Design Procedure for

Solar Heating Systems", Solar Energy , Vol. 18, No. 2., 1976.

10. Klein, S.A., Beckman, W.A. , and J.A. Duffie, "A Design Procedure for

Solar Air Heating Systems", Solar Energy , Vol. 19, No. 5, 1977.

11. Yass, K. , and H.B. Curtis, "Low-Cost Air Mass 2 Solar Simulator",

NASA TM X-3509 , presented at the United States Section Meeting of

the International Solar Energy Society, held in Cleveland, Ohio,

October 3-4, 1973.

12. Simon, F.F., and P. Harlamert, "Flat-Plate Collector Performance

Evaluation, the Case for a Solar Simulator Approach", NASA TM X-71427 , presented at the United States Section Meeting of the International

Solar Energy Society, held in Cleveland, Ohio, October 3-4, 1973.

13. Ramsey, J.W., Borzoni, J.T. , and T.H. Holland, "Development of FlatPlate Collectors for Heating and Cooling of Buildings", NASA CR-134804 3 June, 1975.

23
14. Norrls, D.J., "Calibration of Pyranometers in Inclined and Inverted

Positions", Solar Energy , Vol. 16, No, 1, 1974,

15. ASTM E178-75, "Standard Recommended Practice for Dealing with Outlying Observations", Annual Book of ASTM Standards , Part 41, ASTM,

Philadelphia, Pa., 19103.

16. Thomas, W.C., and A.G. Dawson, III, "Analysis of Data and Results

for the Round Robin Flat-Plate Collector Test Program", VPI & SU

Report Eng. 7 7-23 , Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 1977. (NTIS PB-275-576, p. 86).

17. Ostle, B., Statistics in Research , Chapter 6, Iowa State College

Press, Ames, Iowa, 1954,

18. Glycols , Union Carbide Corporation, 270 Park Avenue, N.Y, 10017,

1971.

19. Kays, W.M., "Numerical Solutions for Laminar Flow in Circular Tubes",

ASME Transactions , Vol. 77, p. 1265, 1955.

20. Buchberg, H. , Catton, I., and D.K. Edwards, "Natural Convection in

Enclosed Spaces - A Review of Application to Solar Energy Collection , ASME Transactions , Vol. 98C, pp. 184-188, May, 1976.

21. Eckert, E.R.G., and R.M. Drake, Jr., Analysis of Heat and Mass Transfer , p. 65, McGraw-Hill, N.Y. , 1972.

22. Woodman, T.P., "The Effect of Design and Operating Parameters on the

Performance of Flat-Plate Solar Collectors-Calculation Method and

Detailed Appraisal," Solar Energy , Vol. 19, No. 3, pp. 263-270, 1977.

23. "Baseline Solar Collector," Glass Division, PPG Industries, Inc.,

One Gateway Center, Pittsburgh, Pa. 15222, 1974.

24. "Technical Data on the Chamberlain Manufacturing Corporation FlatPlate Solar Collector", Chamberlain Manufacturing Corporation, 845

Larch Ave., Elmhurst, Illinois 60126, February, 1976,

25. Bolz, R.E., and G.L. Tuve , Editors, Handbook of Tables for Applied

Engineering Science , pp. 441-457, The Chemical Rubber Company,

Cleveland, Ohio, 1970.

24
i Table 1.

Characteristics

Pertinent Collector Characteristics

(from the manufacturer's literature)

Collector

No. 1 Collector

No. 2

i Manufacturer

i

1

1 Gross dimensions (m)

PPG Industries

1.93 X 0.86

Chamberlain

Mfg. Co.

2.14 X 0.92

2 Gross area (m )

2 Effective aperture area (m )

Weight per gross area (kg/m )

j Volumetric capacity per gross area

(m^/m^)

Pressure drop across collector (Pa)

(at operating mass flow rate)

iCover plate assembly

Number of glass plates

Material

Dimensions (m)

Solar transmittance (single glass)

Hemispherical emittance

Coefficient of expansion (mm/mm/°C)

Specific heat J/(kg»°C)

sAbsorber Plate

1.74

1.60

31.8

0.72 X 10

0.83

-3

Herculite glass

1.90 X 0.84

0.85

0.84

Unknown

857.7

Unknown

1.6

1Four co-Clear temp

2.08 X 0.86

0.90

0.88

2.78 X 10'

Unknown

^-6

Material

Dimensions

Flow configuration

Coating

Solar absorptance

Hemispherical emittance

Aluminum Mild steel

1.90 X 0.84 2.09 X 0.86

13 parallel pass 19 parallel pass

Durachron 600 Black chrome

L/G flat black

0.94 0.94

0.92 0.12

jAir space(s)

Between covers (mm)

Between cover and absorber (mm)

Insulation

Material •3 Density (kg/m ) Thickness (mm)

Thermal conductivity (W/m'^'K)

9.53

12.7

Glass-fiber

48.1

76.2

0.035

19.0

Glass-fiber

^80

76.2

Unknown

25
o2OO

to

0)oc

COeuo

VM

»-i (U a.

COBH

-- CN _^ _H fn -- -^

— .^ rsi 3 ^O ^a £ • in o •

-o a> a* C (U CO o o

00 -H

r» ^ oo

^^ rsi

P-, (^

— in

-^ -- fO o —• ^ oo O O -^

A|

0) OD —I 00 0100

O)

^^

U 0) « C ^ 0) >, 0) oo tu p ^ ^ 00 CO C "O SDW (DO o ^

t- CO

M • CN ^ >O

QJ iH

XI

CO H ^ f- o — fNj O -* r^ sO r«. r-v

r^ in r*

—H in + 1 —t

(N

—<

Pn—«

^0

O

in li-i I +

r-* r^ -* + 1 + 1 + 1 + 1

IDO

s:8u

i-> d)6

•HUO

CO "-t o ^

to CO 'H 0) •H r-l &0 CO J3 c >

•H CO (J

CO •H 3 o

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27
Table 4. Summary of Ordinate-Intercepts , Slopes, and Mean Squares Values

for Efficiency Correlations

Efficiency No. of Linear Curve Second-Order

Set Values Intercept (-)Slope* Mean Sq. Intercept Mean Sq,

No. 1 Uncorrected 192 0.705 5.61 30.5 0.731 27.9

• Corrected 192 0.728 5.98 20.6 0.733 20.6

Theoretical 192 0.692 5.71 2.46 0.696 2.4

Uncorrected ASHRAE 80 0.707 6.30 23.2 0.722 23.2

Corrected ASHRAE 80 0.726 6.51 16.8 0.728 17.0

Theoretical ASHRAE 80 0.691 5.72 1.5 0.693 1.5

No. 2 Uncorrected 160 0.813 4.82 18.0 0.798 17.5

Corrected 160 0.816 5.11 13.8 0.806 13.5

Theoretical 160 0.814 4.98 4.0 0.802 3.7

Uncorrected ASHRAE 112 0.820 4.77 8.8 0.807 8.5

Corrected ASHRAE 112 0.824 5.08 7.5 0.811 7.1

Theoretical ASHRAE 112 0.814 4.99 3.8 0.806 3.7

Uncorrected ASHRAE 96 0.826 4.77 5.6 0.807 4.6

Corrected ASHRAE 96 0.829 5.09 4.8 0.812 4.0

Theoretical ASHRAl' 96 0.814 4.98 4.0 0.805 3.7

* W/(m2 . 'C)

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50
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50

Figure 19 Effect of Environmental Conditions on Efficiency for

Collector No. 2 at "Reference" Conditions with

52
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Figure 20 Effect of Environmental Conditions on Efficiency for

Collector No. 2 at "Reference" Conditions with

[tf^. - t^]/I = 0.07 (°C.m^)/W

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78
Appendix A

List of Round Robin Participants

Collector

#1 #2

Collector

#1 #2

Organization Organization

M^rthur D. Little, Inc.,

Cambridge, Massachusetts

,W. David Lee

Arizona State University

Tempe, Arizona

B.D. Wood

Chamberlain Manufacturing Co.

Waterloo, Iowa

i| J.D. Morris

Desert Sunshine Exposure

Tests, Inc.

S Phoenix, Arizona

G. Zerlaut

! Honeywell, Inc.

; Minneapolis, Minnesota

j J.D. Kopecki

Lennox Industries, Inc.

Marshalltown, Iowa

David C. Lee

Lockheed Palo Alto

Research Lab

Palo Alto, California

K.L. Marshall

Martin Marietta Corporation

Denver, Colorado

J. Kidd

New Mexico State University

Las Cruces, New Mexico

H.L. Connell

X X PPG Industries X

Pittsburgh, Pennsylvania

M. Barker

X X University of Dayton X X

Dayton, Ohio

H.E. Smith

X University of Florida X X

Gainsville, Florida

E.A. Farber

X X University of Tennessee X X

at Chattanooga

Chattanooga, Tennessee

L. Russell

X X University of Texas X X

at Arlington

Arlington, Texas

T.J. Lawley

X X University of Utah X X

Salt Lake City, Utah

R.E. Boehm

X X University of Tulsa X X

Tulsa, Oklahoma

B.V. Ketchum

X X University of Miami

Coral Gables, Florida

L.E. Poteat

X X University of California at Los Angeles

Los Angeles, California

H. Buchberg

79
Appendix A (cont.)

Collector

#1 #2

Organization

Virginia Polytechnic X X

Institute and State University

Blacksburg, Virginia

W.C. Thomas

Civil Engineering X

Laboratory/NCBC

Port Hueneme, California

E. Durlac

National Aeronautics X

and Space Administration

Lewis Research Center

Cleveland, Ohio

F

.

Simon

University of California X X

Los Alamos Scientific

Laboratory

Los Alamos, New Mexico

S.W. Moore

National Bureau of Standards X X

Washington, D.C.

J. Jenkins

80
Appendix B

Data Used in Analyzing the Effect

of Environmental Conditions

Data, measured results, and the theoretical analysis for each test facility are given in the following tabulations. "XPARM" is the abscissa of the

collector efficiency curve as reported in terms of mean fluid temperature.

The theoretically determined parameters are shown below the measured values.

"FARM" entrees are the corresponding abscissa values of the collector

efficiency curve in terms of the inlet fluid temperature.

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03
Appendix C

Analytical Relationships Used in the Collector

Model for Analyzing the Effect of Environmental Conditions

NOMENCLATURE

A = net collector area

Ag = edge area

c = specific heat

D = outside diameter

D = hydraulic diameter

F = fin efficiency

F' = collector efficiency factor

Ftj = flow factor

G = transfer fluid mass flow per unit collector area

h = film conductance

I = total solar radiation measured in the collector plane

k = thermal conductivity

K = length extinction coefficient

L = collector length, thickness

m = parameter (equation 34)

n = index of refraction

n^ = no. flow tubes

Nu = Nusselt No.

P^ = perimeter around fluid passageway

Pr = Prandtl No.

Q = useful energy

04
Ra = Raleigh No.

Re = Reynolds No., based on D

T = temperature

U = thermal conductance

V = wind speed

W = distance between flow tubes

a = absorptance

e = emittance

r\ = efficiency, diffuse fraction

9, Go = angle between surface normal and beam radiation

p = reflectance

a = Stefan-Boltzmann Constant

T = transmittance

Subscripts

a air, ambient

b back side, beam

c, cl, c2 cover, no. 1 = inside

ca cover to ambient

d diffuse

e effective, edge

f transfer fluid

fi fluid inlet

i long wavelength diffuse, back insulation

j cover no.

L overall loss

105
o fluid-to-ambient loss

p absorber plate

pc plate-to-cover 1

m mean

r radiation

s solar wavelength specular property, sky

T top loss

a considering absorptance only

12 cover 1 to cover 2

11,1 two components of polarization

The collector efficiency is given by

Q

n = -^— X 100% (1)

I A

c

where I is the total solar radiation on the (outer) surface of the cover as measured by a pyranometer in the same plane. The useful heat transfer is

given by

Qu = W ((-°)e ^ - UL^Tfi - T^))

(2)

A summary of the relationships which lead to expressions for U-r , (Ta)g and

Ft, follow. The developments are essentially from reference [61. Reference

[13] was used in developing the expressions for optical properties. Heat

transfer correlations for internal flow and natural convection are from

references [19] and [20] respectively. Expressions for the properties of

air were taken from reference [21].

The expressions are listed for analyzing the two-cover collector. A

brief discussion of the changes required to analyze the single cover system

follows the list of equations.

The expression for the loss coefficient is developed from

^i

Ub = r-

^^^ ^i

106
Ue=^^ (4)

e c

h^ = {5.7 + 3.8[V^,m/s]} W/(m2-°C) (5)

T = [0.0552 (Ta/°K)^*^]°K (6)

o[T^ + T^ 1 [T + T 1 .^.

, __ _ pm cl pm cl W;

'-VC - 1/ep + 1/c^, - 1

hp^ = Nu(Ra) [k^/LpJ (8)

Upc = \pc + V ^^^

a[T^ + T^ ] [T + T ] u cl c2 cl c2 /'1^^ ^-^" = 1/.,, ^ l/c,, - 1

<">

h3^2 = Nu(Ra) [^fiJ'L-^2^ (11)

Ul2 = h^l2 + ^12 (12)

Va = ^2^[T^2-^^/^^c2-Tal (13)

Tel = V " ^"T/Upcl t V " "^a^ (16)

Tc2 = V " Ultl/Upc + I/U12] t V - ^al (17)

107

iiiaii »i iii iinnifm i« i«n nin i»ii
Finally

Ul = Ub + U3 + Ut + TiiT .2epa[T^p^ - T^]/[Tp^ - Tj (18)

The effective transmittance-absorptance development is

e2^-j = arc sin (sin (e)/n^) ; j = 1,2 (19)

2 _ sin (9 2 - e) (20)

sin^(e + e)

2

tan (62 - 0) . (2i) Pl»J ~

^ tan^(0 + e)

Ml,j = H -PM,jj'/[l --aSjpfUjJ (22)

^as,j = ^^P (-Lc,jKj/cos 62) (24)

^s,j = -^as,: [^11, j +M,j]/2 (25)

- Ml,j^^ -"-^asjtl - 2pn^.]} (26)

llc,j ^ 2 2 ^ "^asJPlUj

Pl,j{l + -as,j[l - 2P1,J]} (27)

Picj 2 2

1 - T Q .

Pp.,ji = fp||c,j +Pic,jJ/2 (28)

rsl2 =

"^sl "^32/^1 " Pel Pc2^ (29)

Pcl2 = Pel + Pc2'^sl/tl " PclPc2^ (^°^

Tr/2

^sd = J

Tg (e) sin (29) d0 (31)

o 108
where t (0) is given by equation (25) or (29) for 1 or 2 covers, respectively,

xa) = % ^^^ " "^d^ ^sl2 + ^d ^sd.l2}

1 - [1 - ap]p^i2(60°) (32)

Finally,

(xa)^ = (xa) + X32[l " x^^^J [1 - Up^/UpJ +

tl - ^as,2Hl - Up3 [1/Up^ + 1/Ui2]}

(33)

The expression for F^ is developed from

m = (U^/lkL ])

1/2

F = sinh (m[W-D]/2)/{cosh (m[W-D] /2)m[W-D] /2}

(34)

(35)

0.0668 [RePrD /L]

Nuf(RePrDe/L) = 3.66 +

^

1 + 0.04 (RePrDg/L)^/^

hf = NUf[kf/Dg]

Uq = {W[1/{Ul[D + F(W - D)]} + l/[Pi hf]}"l

(37)

(38)

F' = U^/Ul (39)

^R " tG c /U^] {1 - exp (-F'Ul/[G c ])} (40)

Since the calculations proceed in an iterative fashion, the following

expressions are used to converge the plate and fluid temperatures.

Tpm = Tf^+ Q^Pihf/[Lnt]

(41)

(42)

109
For collector No. 2 with a single cover, equations (10-12) and (17) were not used. The subscript "c2" in equation (13) was replaced with

"cl", 1/Ut2 "^^ deleted in equation (15) and t^2 ^^s deleted from equation

(18). In a similar fashion, j = 1 in the (xa) development; equations (29)

and (30) were not used; the 2's were deleted from the subscripts in equation (32); the last term and Tg2 were deleted from equation (3); and, finally,

the fin efficiency, equation (35), was essentially unity.

The order of progression of computation using a digital computer for

this model is described. The environmental conditions, operating conditions,

collector dimensions, heat transfer properties, and other quantities shown

in Table Cl must be specified to calculate efficiency. The computational

procedure uses several iterative loops to handle the nonlinear dependence

of Ut on temperature. Equations (3-6) and (19-32) are solved. Equation

(31) is integrated numerically using a trapezoidal scheme. For a specified

inlet temperature, a trial value several degrees higher is assumed for the

mean plate temperature. The cover temperatures are calculated from equations

(16) and (17) for the assumed mean plate temperature until the former con- verge within 0.5 °C. A top-loss coefficient is determined from equation (15)

for the trial plate temperature. Equations (18) and (33-35) are next solved.

The mean fluid temperature is assumed initially as the plate temperature to

determine fluid properties and the convection heat transfer coefficient

using equations (36) and (37). The collector efficiency factor and heat

removal factor are calculated from equations (38-40). The useful heat transfer

is next determined from equation (2) and subsequently used in equation (41)

to check the assumed mean fluid temperatures. The calculations are repeated

using the updated fluid temperatures until convergence within 0.5 °C is obtained. The mean plate temperature is then calculated from equation (42)

and compared with the assumed value. The calculations starting with equation (16) are repeated until the plate mean temperature converges to within

0.5 °C. Finally, the collector efficiency is determined from equation (1).

The analytical model and computer code were verified by checking final

results with a desk calculator and by comparison with other theoretical results

in the literature. In particular, the result for the theoretical model agrees

with those shown in references [2] and [22].

The required dimensions were taken from the collector manufacturer's

literature [23, 24] and from the information in Table 1. The heat transfer

properties for the collector materials were generally those provided by the

manufacturers or from a handbook [25]. The dimensions and heat transfer

properties used for both collectors No. 1 and 2 are shown in Table Cl.

Since a considerable amount of uncertainty was associated with the effective

value of the edge-loss coefficient, it was selected primarily on the basis

of giving the best least squares fit of theoretical to experimentally determined

efficiencies. The experimental results also influenced the selection of

the "extinction coefficient" of the cover materials when used with the index

of refraction shown. With these two parameters specified, equations (19-29) can be used to calculate transmittance values in terms of the beam incident

angle

.

110
Table CI, Summary of Environmental and Operating Conditions and Collector

Properties for the Theoretical Performance Model

Environmental and Operating Conditions: "Standard" Values

2 T^ = 20°C

a

^d = 0-15

S = 45°

U = 1000 W/m' V„ = 3 m/s

15°

Ethylene Glycol Concentration =0.0

G = 0.02 kg/(s*m^)

w

9

Dimensions and Heat Transfer Properties

A. PPG Collector; A^ = 1.602 m^

L = 0.841 m

Dg = 1.2 cm

kp = 221 W/(m*°C)

L^ = 5.35 cm

Lp^ = 0.953 cm

n = 1.518

"t

= 13 D = 1.27 cm

Pi = 1.5 cm h

= 1.524 mm

e P = 0.92

»P = 0.95

H

= 0.045 W/(m* °C) «e= 1.50 W/Cm^- °C)

e c = 0.85 "ic

= 0.02

KL. = 0.04 Lt 9 = 0.953 cm

B. CMC Collector; A^ = 1.789 m'

L = 0.860 m

D^ = 0.5 cm

k = 47.6 W/(m-°C)

L- = 7.62 cm

L = 1.9 cm

pc n = 1.518

t =19 D = 4.07 cm

^ = 8.5 cm S

= 0.911 mm

e = 0.12

P

a

P = 0.96

^ = 0.045 W/(m* °C) Ue = 0.90 W/(m2- °C)

= 0.88 T.XC

= 0.02

L = 0.035

111
H;B$-1MA (REV. 11-77)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. TN 975

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Results and Analysis o£ a Round-Robin Test Program for

Liquid-Heating Flat-Plate Solar Collectors

5. Puhlication Date August 1978

6. Performing Organization Code

7 Author(s) K. R. Streed, W. C. Thdmas, A. G. Dawson, III,

B. D. Wood, ana J. E. Hill 8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract /Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Department of Energy

tesearch § Development Branch for Solar Heating and Cooling

Dffice of the Asst. Secretary for Conservation § Solar Applicatio

Washington, D.C. 20545

13. Type of Report & Period Covered

W. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less tactual summary of most sigfiificant information. If document includes a significant

bibliography or literature survey, mention it here.)

A round robin test program was conducted at 21 United States test facilities, using a common test procedure, to determine the intercomparability of thermal performance data

pertaining to two liquid-heating flat-plate solar collectors.

The statistical analysis of the data revealed a relatively large spread in the measured

values of collector efficiency. Data from approximately half the facilities were then

selected for detailed analysis. A collector analytical model was used to show that

less than one-third of the mean-square distance could be attributed to different environmental conditions from facility to facility. It was found that the data showed less

scatter for one of the two collectors than for the other. In general, the data were

consistent for any single facility; most of the scatter was therefore attributed to

systematic uncertainties from facility to facility. When the data from six participants

reportedly adhering to the requirements of ASHRAE Standard 93-77 were analyzed, the

scatter was found to be within normal limits expected for the test procedure.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only tfie first letter of tfie first key word unless a proper name; separated by semicolons)

Measurement; modelling; solar; standards; testing.

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