Testing procedures for solar air heaters: A review

Energy Convers. Mgmt Vol. 32, No. 1, pp. 11-33, 1991 0196-8904/91 $3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright © 1991 Pergamon Press plc

TESTING P R O C E D U R E S FOR SOLAR AIR HEATERS: A REVIEW

RAM CHANDRA and M. S. SODHA Centre of Energy Studies and Research, Devi Ahilya Vishwavidyalaya, Khandwa Road Campus,

Indore~,52 001, India

(Received 28 December 1988; received for publication 20 April 1990)

Abstract--There are numerous designs of solar air heaters available in the literature IN. K. Bansal, R. Chandra and M. A. S. Malik, Solar air heaters. In Reviews of Renewable Resources of Energy (Edited by M. S. Sodha, S. S. Mathur and M. A. S. Malik). Wiley Eastern, New Delhi 0984) (Ref. [1]); M. S. Sodha, N. K. Bansal, A. Kumar, P. K. Bansal and M. A. S. Malik, Solar Crop Drying. CRC Press, Cleveland, Ohio (1987) (Ref. [2]). Therefore, there is a need for a repeatable test method independent of outdoor environmental conditions and test location. Various experimental techniques have been described so as to allow the net thermal output of an irradiated solar air heater array to be reproduced indoors. The effect of air leaks has been incorporated into the performance equations. The other well known testing procedures have also been described. A method for generating design data for solar air heaters is described.

A a

A¢ Ae Ag

Ag

A~ FR UL A~

a

N O M E N C L A T U R E

= Collector aperture area (m 2) = Cross-sectional areas of duct (m 2) = Collector edge area (m 2) = Collector gross area (m 2)

= Intercept of collector efficiency curve determined in accordance with ASHRAE 93-97 (dimensionless)

Cf --- D e E~l=

4 = F" ~-

FR= b=

F~L -=

F~L = FRL = G,I=

d= h c =

k e =

k i = kp=

L = t ¢ =

L i - -

r n = r h c

t h L =

~ S A ~

Slope of collector efficiency curve determined in accordance with ASHRAE 93-97 (W/m z °C)

Width of flow channel (m) Specific heat of air (J/kg °C) Equivalent diameter (m) Emissive power of cover 1 (W/m 2) Emissive power of absorber plate (W/m 2) Emissive power of sky (W/m:) Collector efficiency factor (dimensionless) Collector heat removal factor (dimensionless) Flow channel depth (m) Collector heat removal factor when air leaks in Collector heat removal factor when air leaks out Collector heat removal factor for two collectors connected in series (dimensionless) Total global irradiance incident upon aperture plane of collector (W/m 2) Fluid mass flow rate per unit collector aperture area (kg/m z s) Convective heat transfer coefficient in duct wall (W/m2°C) Thermal conductivity, edge insulation (W/m°C) Thermal conductivity, back insulation (W/re°C) Thermal conductivity, absorber plate (W/re°C) Incident angle modifier (dimensionless) Length of collector (m) Thickness of edge insulation (m) Thickness of back insulation (m) Mass flow rate (kg/s) Mass flow rate of transfer fluid through collector during ASHRAE Standard 93-97 tests (kg/s) Air mass flow rate at collector inlet (kg/s) Leakage air mass flow rate (kg/s) Thermal output of conventional heat source (W) Thermal output of conventional heat source when located up-stream of non-irradiated array (W) Daily thermal output of irradiated collector array (k J)

Qsh = Thermal output of electric strip heaters (W) Qs~ = Heat loss from section of pipe located in laboratory which supplies collector array (W) 0u = Net thermal output of collector array (W) Re = Reynolds number (dimensionless)

11

12 CHANDRA and SODHA: TESTING PROCEDURES FOR SOLAR AIR HEATERS

S ~

l =

/co

/al =

lfi = t~'=

If =

I H =

/hi

lho =

l L =

I m

Tsky

A t m = tYb= uL=

Zw= ~n

0= 6 rl

r/hS # p 2" n

(r~)o At

Tc

Quantity of solar irradiance absorbed by absorber plate of single collector (W) Time (s) Ambient temperature (°C) Fluid temperature leaving collector array (°C) Laboratory ambient temperature (°C) Fluid temperature entering collector array (°C) Fluid temperature entering non-irradiated collector array with upstream heat source (°C) Mean fluid temperature (°C) Upper temperature limit for heating element thermostat (°C) Average fluid temperature within heat source (°C) Fluid temperature entering heat sources (°C) Fluid temperature leaving heat source (°C) Lower temperature limit for heating element thermostat (°C) (Tn+ Tfo)/2 (°C) Effective sky temperature (K) Log-mean temperature difference (°C) Collector back and edge loss coefficient (W/m2°C) Collector overall loss coefficient (W/m 2 °C) Collector top loss coefficient (W/m 2 °C) Wind velocity (m/s) Absorptance of collector absorber coating to solar spectrum at normal incidence (dimensionless) Absorptance of plate (dimensionless) Angle of incidence between direct solar beam and normal to collector aperture (deg)

= Absorber plate thickness (m) = Collector efficiency based on net area (dimensionless) = Heat source efficiency (dimensionless) = Air viscosity (kg/m s) = Air density (kg/m 3) = Effective transmittance at normal incidence (dimensionless) = Effective transmittance-absorptance product for collector at normal incidence (dimensionless) = Length of time step (s) = Theoretical time period in each cycle (min) = Collector time constant (min)

1. I N T R O D U C T I O N

When there are a large number o f solar air heating systems available in the market , the designer and potential user o f these systems must consider a number o f factors when compar ing their merits. These can mainly categorized as: (1) thermal performance, (2) cost and (3) lifetime, durability, maintenance and ease o f installation. The thermal performance o f collectors is compared by using the concept o f thermal efficiency. It is generally believed that the thermal efficiency of a solar collector is the major requirement for prediction o f the thermal performance of the complete solar system of which the solar air collector is a part. It is, therefore, impor tant that this thermal efficiency information be in a form which is useful for existing and projected future solar energy system design methods.

The instantaneous efficiency o f a solar collector can be characterized by two parameters, rl0 (collector zero loss efficiency) and U (collector loss coefficient), at any operat ing point T* [ = ( T m - Ta)/G] by the Hottel-Whil l ier equat ion

r / = r/0 - U T*. (1)

However, the two parameters r/0 and U do not permit a decisive compar ison between two collectors unless the average operat ing point T* is known. This, in turn, depends strongly on t/0, U, collector area, energy demand and location. Consequently, the consumer is unable to evaluate the merits of a given collector without extensive knowledge of how a solar heating system performs. Further, the manufac turer cannot adequately specify the merits o f his collector in sales literature.

There are three major requirements for the thermal testing o f solar collectors. These are:

(1) To assist the collector designer in evaluating the thermal performance of a collector. In this way, the thermal test can be used as a quantitative developmental test.

(2) To provide a rational basis for compar ing the thermal performance o f different solar collectors.

(3) To enable the collector absolute thermal performance to be predicted under a given set o f conditions which are different f rom the test.

CHANDRA and SODHA: TESTING PROCEDURES FOR SOLAR AIR HEATERS 13

While some of the above information can be obtained from individual component testing, the collector overall thermal performance can only be determined with certainty from a collector thermal efficiency test.

The thermal performance of solar collectors can be established via two possible experimental approaches.

(i) The comparative test. A test collector is evaluated against a standard collector to give a relative measure of one thermal performance to another. The test requires that the two collectors be of a similar size and type, but this is not always convenient. To assess the long term thermal performance of the test collector, the absolute thermal performance of the standard collector must be known.

(2) The absolute thermal performance test. A collector is tested to determine its thermal efficiency over a range of operating conditions. The thermal performance characteristics of the test collector can then be used in calculation procedures to compare collectors, and if the collector has been tested several times after ageing treatments, to assess their long term thermal performance.

The two test approaches have sometimes been combined such that the collectors to be compared are tested simultaneously to determine their absolute thermal performance characteristics. This approach does not improve the experimental accuracy, but it does provide identical climatic conditions in the comparison of collector performances.

In designing a test procedure, the same variables must be measured for either a comparative or absolute test, except that measurement of the solar radiation flux could be avoided for the comparative method. To offset this minor advantage, the absolute thermal performance of the standard collector must be known and assumed invariant between each test. Then, the long term thermal performance of the test collector can be predicted.

The thermal performance of solar collectors can be rated according to the normalized loss coefficient U/rlo [3]. The collector rating can then be used in conjunction with system performance prediction methods and economic and durability factors to decide which is the better collector for a given application.

The purpose of this article is to review the testing procedures for solar air heaters. A solar air heat unit can be tested outdoors as well as indoors. However, any testing procedure should be repeatable, i.e. independent of outdoor environmental conditions of a testing place. One can use a solar simulator to irradiate solar panels. However, the high cost of solar simulators, their limited availability and the physical constraint that most solar simulators are designed to irradiate a single panel rather than a collector array consisting of several panels rules out their use.

The other attractive option which can be adopted is the replacement of the energy normally furnished by an outdoor irradiated solar collector by an equivalent amount of energy supplied by a conventional energy source [4]. This can be attempted by any one of the following three ways:

(1) The first option is the use of a conventional heat source such as in-line electrical resistance heaters as a heat source to supply the net thermal output of an irradiated array. It has, however, some limitations, namely (i) outdoor stagnant conditions can not be duplicated, (ii) the power input is localized rather than distributed along the length of the absorber plate of a collector panel. In addition to this, the use of in-line electrical resistance heaters may not receive adequate support from the solar community because the collector array is not part of the experimental set up.

(2) The second option may be the use of a conventional heat source in series with a non-irradiated collector array and a storage by-pass. The heat source may be located upstream or downstream of the non-irradiated array. The outdoor stagnant conditions can be easily simulated.

(3) The third option is the attachment of electric strip heaters to the rear of non-irradiated solar absorber plates. It eliminates the problem of the localized heat source and also allows the outdoor stagnant conditions to be duplicated in the laboratory.

All these possibilities have been analysed in this article. Analytical models have been presented. The ASHRAE, NBS, BSE and other relevant testing procedures have also been discussed.


2. P E R F O R M A N C E EQUATIONS

An analytical model is developed to simulate the performance of the solar air heating unit. All the three methods which allowed the net thermal output of an irradiated collector array to be duplicated under non-irradiated conditions, as discussed earlier, are investigated. The model presented takes into account various important factors, such as the effect of leakage in the solar air heater, the effect of recirculation of air, the conditions of intermittent and constant temperature output, etc.

2.1. Irradiated collectors arrays 2.1.1. With no air leak. When no air leaks occur, then under steady-state conditions, the useful

energy from a single irradiated solar collector can be expressed in accordance with the Hottel- Whillier-Bliss (H-W-B) analysis

(2t: = Ag [K..(A.IAg) FR(z~).G - (AalAg) FR UL (tn -- ta) ]. (2)

The useful energy output of an array consisting of M collectors connected in parallel is

GuM = M Qu (3)

The useful energy output of an array which includes collectors connected in series can be represented similarly, by modifying the heat removal factor, FR accordingly. For a single solar collector module

m C p [ l _ f AaF' UL'~-] F.= ULAaL exp~ ~--~;-)j (4>

where F ' is the collector efficiency factor. The values of F ' for a number of solar air heaters, shown in Fig. 1, are given in Bansal et al. [1]. Even though F' and UL are temperature dependent, in this analysis, both of them are assumed constant. Equation (4) for the case where two collectors are connected in series, becomes

FR2=UL2A ~ ~ /j (5)

which can be rewritten as

FR2 =FR[1

Thus. for two collectors in series

(FR UL)2 = (FR UL) I1

and similarly

[FR (Z~).]2 = [FR (z~)d F 1 L

2 mcp J" (6)

(FR UL) A. 1 ~-~ j (7)

(FR UL) A a] j. (8)

Equations (7) and (8) can be generalized to any number. N. of identical collectors in series in the following way

(FR UL)N = - 1-- 1

and

FR(~)"mCpfI(FR-U-L)A~.IN~I-- 1 (10) [FR(Za)"IN=(FRUL)NA . rhCp J J"

Thus. for N irradiated collectors connected in series, the useful energy output. Quu. is

~uN = NA, [K~ -~g (FR (ZOt)n)N G -- -~g (FR UL)N (t~ -- t.) 1. (11)

Air in

CHANDRA and SODHA:

To

TESTING PROCEDURES FOR SOLAR AIR HEATERS

Ut

( " ~ hi hz ._) T,

t o ) FLow over absorber

Us

(1)

(2)

To Ut

-~ - - (1)

k~ / '~ '~ h I h z ~ hr' zl • j ,

(2) /"'-"~ h 2 , . ~ h 5 l hr'23

(b) FLow both sides of the absorber

15

To U t

(1)

(C) FLOW into the plane of paper

(2)

T, U~

h2 --"~% I h,, 23

(d) FLow under the absorber

(1)

(2)

To Ut Ut

. . . . . . . ~ - - I I1 ~ (21

(3)

U~ Ub

t o ) FLow under t r iangular duct ( f ) Absorber with s'(raight fins

Ut

to) Matrix solar air heater

Fig. I. Designs of solar air heaters.

Finally, the useful energy output of a solar collector array consisting of M rows of N collectors connected in series is given by

QUMN=MNAg[K~(FR(~),)~G--~g(FRUL)N(t~--ta) 1. (12)

2.1.2. With air leaking in. The construction of conventional solar air heaters, and the fact that they will operate with a significant pressure difference between the heated air stream and ambient,


suggests that a significant amount of air may leak into or out of them. Close and Yusoff [5] have analysed the effects of air leaks on solar air heaters. Consider the case where air is leaking into the collector as shown in Fig. 2. Equation (12) for the useful energy output of a solar collector array is modified because of incorporating the leakage effect.

For a constant leakage rate along the length of a solar air collector, the Hottel-Whillier-Bliss equation modifies to

where the heat removal factor F~L is given by

" #/'hi C'\ I( (l "I-~LX)...._miC, mi/'l I [( Fm_~..AL cUL.) I n (~)]} I -'~/ 1 - e x p 1-~ . (14)

For two collectors connected in series, equation (14) is modified to

(r~L u,) A, (1 -~ F~L 2 = F~L 1 #/L (15)

2rhiC p 1 +-~'i

Alternatively,

and

(F~L Ut)2 = (F~L UL) UOA.(I + A, ULF',/ l - Cp-I 2 l~ i l~L

(F~L (zm).)2 = (F~L (Z~).) [l A {1 rhiC o ~l

(16)

(17)

[ mic iN} (FRL (Z00") m' CP (I + ~iL) I (FRLUL)A"(I+A-'-U-L--F;)] (19) (F~L eL) A. UL F'] m i Cp (1 + -~i

Thus, for N irradiated collectors connected in series, the useful energy output, ~u~¢, is

~.uN=NA.{K~_~s(F~L(TGt)n)NG__~s(F~LUL)NI1 rhLC,// I +-~-, t,.~r (F~/UO.)] (t~ - t,) t (20)

and

Equations (16) and (17) can be generalized to any number, N, of identical collectors in series as

1 - 1 __ ,, _ . _ ~ , ~ L / | ( F ~L VL ) ,, = (I _m~ C, "i " '+" .A. + A. ~:L F'/ miC0(l +~) J (.S)


rhl ~ CoLLector ] ~° rhl q CoLLector I rh*- t,i I tio ~- tt' I tfo- / ",,.

13'1 k r6 u t, to

Fig. 2. Schematic diagram showing air leaking in. Fig. 3. Schematic diagram showing air leaking out.

The useful energy output of a solar collector array consisting of M rows of N collectors in series is given by

(~uuu=MNAi{K,,-~(F~L(x~)n)u G - - ~ ( F ~ L UL)N [1 t h L C p [ 1

(21)

2.1.3. With air leaking out. Consider the case where air is leaking out from the collector as shown in Fig. 3. The useful energy from such a single irradiated solar air collector can be

a a (2u =A,[K~,-~sF,i ('co~).G -~F,i. UL(t~- t.)] expressed as

where

m' CP (1- iL] { 1 FAaF'ULIn(I_riIL For two collectors connected in series, equation (23) is modified to

F~ U~. _A_, .l ( ".0] 2 t/li Cp 1 - - ~ i i

F~L 2 = Ft~L[1

Alternatively,

and

[F~L (~m).12=[F~L(~).]I1 - F~L Ut___A, 1 . tilL "

(22)

(23)

(24)

(25)

(26)

Equation (25) and (26) can again be generalized to any number, N, of identical collectors in series as

and

_- _ F~,_v_~.A. 1 } . (2s) . rhL

ECM 32 I--B


The useful energy output for N irradiated solar collectors connected in series, QuN, and that of a solar collector array consisting of M rows of N identical collectors connected in series, QUMN, are then given by

(2vN=NA~{K,,-~g[F~L (z~),]u G--~gg(F~LUL)N(t~--ta)} (29)

and

;a 1 (2uMu = MNAg K,, (F~e(rCt),)u G -- ~gg (FaL UL)N (t, -- ta) . (30)

2.1.4. With specified temperature output. The flat plate solar air collector efficiency, Q.,/Ag G, is usually defined for a given heat transfer fluid flow rate. The fluid output temperature depends on the fluid flow rate. In many applications using solar air heaters, such as constant drying, it is desirable to adjust the fluid flow rate to maintain a constant output temperature. In such cases, one needs an expression for the useful energy, as well as for the efficiency in terms of the input and output fluid temperatures.

The useful energy for a single irradiated solar air collector can be expressed as

Qu = rh Cp (tfo - tn). (31)

Equating equations (31) and (2), one can arrive at the following expression

(tfo__ta)=_~pK,_~gFa(zCt)nG+(tn__ta)[l__ rhCp._~gFRA, Aa UL]. (32)

It may be remarked that, instead of making tfo alone as a constant by adjusting rh, it is better to make tro - ta = Tfo as a constant. Equation (32) can easily be generalized for the case of a solar collector array of M rows of N collectors connected in series by the procedure adopted in the previous sections. The result is

Tfo,M N = MN K,~ [Fa (Z~)n]U 6 + Tn 1 rh Cp Ag

where [FR(z~),]N and (FR UL)N are given, respectively, by equations (10) and (9). Equation (31) gives the desired expression for the constant outlet temperature. Although an

accurate flow-control system for equation (33) is difficult to advise at this stage, even then a simple system, as shown in Fig. 4, can be considered. The output temperature Tro ( = tfo - ta) from this collector is controlled by a solenoidal valve which is installed at the inlet of the collector. The

^ S - _.o,'t. "-. / / \

\ " , , J " ® \ \

Fig. 4. Schematic diagram of flow control system.


thermal switch, with a sensor immersed inside the thermopile box measuring temperature difference across the collector, controls On and Off of the solenoidal valve. When Tfo drops down from a specific constant temperature, the solenoidal valve opens and the flow rate inside the collector is reduced until Tro reaches the specified value. The moment it so happens, the solenoidal valve is closed down. This concept has been a success in the case of liquid heating collectors. One can easily derive the time period z between each ouput pulse.

The energy balance to the collector as a whole gives

(MC)s ~t = Aa G ( z ~ )e - UL Aa ( t s - - t a ) - (MC)f ~tt f (34)

where (MC)s and (MC)f are the total thermal capacities of the solid and the fluid elements of the collector, respectively. The solid and fluid elements are assumed to be at mean temperature t s and If, respectively.

The rate of energy stored in the fluid mass element can be assumed to be proportional to that in the solid element due to the heat transfer resistance between them, therefore,

dtf _ K dts (35) dt dt

where K is a constant related to the thermal capacities of the fluid and the solid element and the heat transfer characteristics between them. Equation (34) can be solved in conjunction with equation (35) to give

E - ( t f - t a)/G = exp( - tire) (36)

E - (t~ - ta)/G

where

and

E = (z~)~K/UL (37)

Zc = [(MC)s + K(MC)f]/ULAa. (38)

Equation (36) describes the transient heat transfer behaviour of the collector. If tro is the preset temperature in the thermal switch, i.e. the desired output fluid temperature, then the time period z between each output pulse is given by

z - - In I E - (tfo - t.)/G 7 = - E

z/z = _ ln[E- rf°/G] o r

(39)

(40)

2.2. Replacement of the irradiated array with a conventional heat source

A conventional heat source, such as an in-line electrical resistance heater, is used to replace the irradiated solar collector array. The solar collector should be tested according to ASHRAE standard 93-77 (described later in Section 3.1.2) and the values of FR UL, FR(XCt),, and K,, should be determined. The inlet fluid temperature to the heat source, tn, ambient temperature, t,, and global solar radiation incident upon the aperture plane of the collector are measured. The required thermal ouptut of the heat source is then calculated using equation (12).

2.3. Replacement o f the irradiated array with a conventional heat source in series with a non- &radiated array

2.3.1. Heat source located downstream of a collector: with no air leak. Figure 5 shows a non-irradiated solar collector with a downstream conventional energy source. The useful energy output of a single collector may be expressed as

Q__.~u = K~v(zct) n G - - UL( t p - - t~), (41) A~


t 1,

Fig. 5. Non-irradiated solar collector with downstream conventional energy source

Equating equations (41) and (2) and solving for t,, one obtains

(42)

For a non-irradiated solar collector (G = 0), equation (42) reduces to

t pn = fiki - 4,) + f,l (43)

where t,, is the mean plate temperature of a non-irradiated collector. The net thermal output of a non-irradiated solar collector and heat source, &c.,, can be expressed as

Q NCH =g- UL(t,,-fa,). W) a

One requires that &a must be equivalent to the output of an irradiated solar collector given by equation (2) and, therefore,

(45)

For an arrangement shown in Fig. 5, the inlet fluid temperature to the non-irradiated array is identical to the inlet fluid temperature for the corresponding irradiated array. Consequently, equations (44) and (43) can be combined to give

(46)

Generalizing to the case where the heat source is located downstream of M rows of N collectors connected in series, one obtains

(47)


2.3.2. Heat source located downstream o f collector and air leaking in. Using the procedure outlined in the previous section with the help of equations developed in Section 2.1.2, one can easily arrive at the following expression for 0h,,Mu

(~hs, M N = M N ( K ~ g [ F ~ L (Z°t),]NG A~

where (F[L UL)s and [F~L (Te),lu are given by equations (18) and (19), respectively. 2.3.3. Heat source located downstream o f collector and air leaking out. With the help of equations

developed in Section (2.1.3), one can obtain the following expression for ~)hs, MU

(~hs'Mu=MN{K=~g [F~L(zct)"]uGA g --Aa(FRLUL)N(ta'--ta)G}Ag (49)

where (FgL UL)U and [F~L(T~t),]u are given by equations (27) and (28), respectively. 2.3.4. Heat source located upstream o f a collector: with no air leak. Figure 6 shows a

non-irradiated solar collector with an upstream conventional energy source. Equating the net energy output from the non-irradiated collector with an upstream heat source to that of an irradiated collector yields

Q*, Aa VL(t*, -- tai) = K= r,(zct), G - V , VL(tfi -- ta)- (50)

The inlet fluid temperature to the non-irradiated collector array is different from the previous case because of the heat source location. Equation (43), therefore, modifies to

tp* = FR(t~ -- t ,) + ta,. (51)

An energy balance on the heat source results in the following expression for t*

Q*s t~' = t. + th C--~" (52)

4

Non-irradiated solar coLLector

Q~s

Conventional heat source

Fig. 6. Non-irradiated solar collector with upstream conventional energy source.


Equation (50), (51) and (52) can be solved to give

Q~s=Ka~'~ggFR(TO~)nGAg - (FRUL)(ta'--ta)Ag Aa (53)

which, for the case of the heat source located upstream of M rows of N collectors connected in series, generalizes to

MN{K, , A, "~g [FR (z~,]N G Ag -- -~g (FR UL )u (tal - ta) Ag}

Qh*.MN = (54) [ ~ (FR UL)NAg]

I- L J

2.3.5. Heat source located upstream of a collector with air leaking in. Using the procedure outlined in Section (2.3.4) with the help of equations developed in Section (2.1.2), one can derive the following expression for "* Q hs, MN

" , Ohs, MN =

Mg(g~gg[g+L('COt)n]sGhg---'~g(g~tL -I---~-a [F,1-UL (F~LUL)N]}(t~, -ta)

( UL)NAa {1 ..1L FnLCp F ~ 1 1t}

(55)

A a A~ t Qhs. MN * MN k,, ~g [FRL (zc(),]NG A g - ~gg (FRL eL)N(tal -- ta) (56)

Therefore, the proper quantity of energy to be supplied to a conventional heat source in series with a non-irradiated array may be computed using either of equations (47), (48), (49), (54), (55) or (56) as appropriate.

2. 4. Replacement of the irradiated array with strip heaters attached to non-irradiated solar collectors

This method replaces the solar energy absorbed by an irradiated collector array by energy supplied by electric strip heaters attached to the rear of non-irradiated absorber plates.

The quantity of solar energy absorbed by the absorber plate of a single collector is

S = A~ K~, (rot), G. (57)

For a collector array consisting of M parallel rows of N collectors connected in series, equation (57) is modified to

Qsh = MN Aa K~, (z~t ). G. (58)

where (F+L UL) N and [F~L (Z~t)n]N are given by equations (18) and (19), respectively. 2.3.6. Heat source located upstream of a collector with air leaking out. For this case, equation

(54) is modified into the following equation


Once K,~ and (z~t), are known (by using ASHRAE 93-77 test [6]), Q~h can be determined.

2.5. A lgor i thm f o r collector per formance

An analytical model for evaluating the thermal efficiency of a solar air heater is presented. The analysis presented is for a single cover flat-plate collector.

2.5.1. Solar air collector. The collector efficiency is given by

Qu x 100%. (59) )1 = G A a

Qu = AaFR [K=~(T~), G - U t ( t ~ - ta) ] (60)

when there is no leak, and

Q . u = A a F ~ t L { K a ~ ( , O t ) n G _ U L [ 1 rhLGp t/ 1

when air is leaking in, and

Ou = Aa FRL [K,,(z~),G - UL(t fi -- t,)] (62)

when air is leaking out. The loss coefficient, UL is the sum of the top loss coefficient Ut and the back (and edge) loss

coefficient Ub. Since Ut depends on the mean absorber plate temperature, the following expression is used in

an iterative approach

tp = V R [t n - t a q- K,,(zct) ,G/UL] + t, - K , , ( z ~ ) , G/UL. (63)

When air is leaking in or out, FR is replaced by FffL or F~L, respectively. The leakage flow rate is determined by measuring the air flow rate upstream as well as downstream of the collector.

The heat transfer coefficient hr depends on the mean fluid temperature trm given by

/fm = ~ [tn - ta "t- Xa, ('c~)n G/UL] + K,¢(z~t), G / U L . (64)

The value of F ' for the appropriate collector being analysed is given in Bansal et al. [1]. The procedure for evaluating the convective heat transfer coefficient is given in Duffle and Beckman [7].

The basic algorithm for calculating the thermal performance of a collector is as follows:

Step 1. The operating conditions, design parameters heat transfer properties and fluid inlet temperature are specified. The collector and material parameters independent of temperature are calculated.

Step 2. An initial estimate of tp, in terms of tn, is made using equation (62). Step 3. With the current estimate of tp, Ut, Ub and UL are calculated in a separate subroutine.

Next, FR(or F~L or FRL ) is calculated. An estimate of trm, in terms of tp, is made. Step 4. With the current estimate of trm, hf is calculated in a separate subroutine. F ' and FR are

calculated to obtain an improved estimate of trm- Step 4 is repeated until trm converges. Step 5. Equation (62) is again used to improve the estimate of tp. Steps 3, 4 and 5 are repeated

in an iterative procedure until tp converges. Step 6. The outputs Qu are calculated from the appropriate equations (60), (61) or (62) and the

efficiency from equation (59).

2.5.2. Hea t source. This section gives the analytical model for the heat source which has been used in replacing the irradiated solar collector array.

The energy supplied to a conventional heat source used in series with non-irradiated collectors is computed by using appropriate equations (47), (48), (49), (54), (55) or (56). An energy balance for the heat source under steady-state conditions yields

Qhs = rhCp (tho - thi) + (UA)hs (/'h - t~l) (65)

An expression for Qu is


where

~h = /hi q- tho 2

The efficiency of a heat source, qh,, is defined as

/~ Cp( lho - - /hi) ~hs = ~hs

which gives

(66)

(67)

~hs ~hs lho = ~ "]- /hi" (68)

rh Cp

Equation (68) is used in the simulation model for tho.

3. TEST P R O C E D U R E S FOR S O L A R AIR H E A T I N G C O L L E C T O R S

Optimized collector parameters are very important for any application. For ensuring generality, two main classes of parameters have to be taken into account:

(1) Environmental parameters: ambient air temperature, incident solar radiation intensity and wind velocity.

(2) Operating parameters: inlet and outlet air temperatures and air flow rates.

Testing and presentation of results is done in the form of r/vs At/G curves. At is different in different testing procedures, e.g. in the ASHRAE standard, At = (t~ - ta) and recommends the use of FR, whereas in the NBS standard, At = ( ip - q) and recommends the use of F ' . It may be mentioned that ASHRAE recommends testing of air heaters for two flow rates per unit area, namely 10 and 30 l/s-m 2, which may be satisfactory for comparing several air heaters, but it does not give an elaborate picture of how the air heater will perform under flow rates widely different from the ones above. Reddy and Gupta [8] have given a methodology to overcome this problem, and it will be described later.

In the absence of air leaks, the efficiency of a solar air heater may be described by any one of

q = K,, (z~t), UL(~ -- ta) (69) G

UL (t~ + fro

q -- F ' K , , ( ~ ) . \ 2

the following equations:

G (70)

)1 = FRIK,,(~ct), - UL(~- - t , l . (71)

Regardless of the form of the efficiency equation, equations (69)-(71) indicate that, if )/is plotted against some appropriate At/G, a straight line will result, where the slope is some function of UL and the q intercept is some function of (T~t),[ = K,,(~at),].

It is, however, possible to correlate the collector parameters obtained from various temperature bases to each other. The conversion factors are given in Table 1.

3.1. NBS test procedure

A proposed procedure for testing and rating the thermal performance of solar collectors was published by NBS in 1974 [9]. The procedure prescribed that a series of outdoor steady-state tests be conducted to determine the near normal incidence efficiency of the collector over a range of temperature conditions. The test configuration for the solar collector employing air as the transfer fluid is shown in Fig. 7.

C H A N D R A and SODHA: TESTING PROCEDURES FOR SOLAR AIR HEATERS 25

Table I. Conversion factors for the collector efi$ciency to various temperature bases (after Ref. [11])

F R U L F ' U L F" U L To by Multiply or or or

obtain $ ~ FR (~)e F ' (z~t), F" (zct)~

FR UL 1 l 1 or F ' U L 1 F" U L

Fa(z~) * 1 + 2rh C O +

1 1 F ' U L 1 or FR UL F" U L

F'('cot)< 1 - 2mC~-~ 1 +. 2mC~--:

F" U L 1 1 1

or FR UL F ' UL F" (~r,)c l - rh-~-p 1 - 2mC-- p

For mounting the collector and other measuring instruments, certain precautions are taken. These have been discussed as follows:

(a) Solar collector

The solar collector is mounted in its rigid frame at the predetermined tilt angle (for stationary collectors) or movable frame (for movable collectors) and anchored rigidly enough to a foundation so that the collector can hold its selected angular position against a strong gust of wind.

(b) Ambient temperature

The ambient temperature sensor is housed in a well-ventilated instrumentation shelter with its base 1.25 m (4.1 it) above the ground and with its door facing north, so that the sun's direct beam cannot fall upon the sensor when the door is opened. The outside of the instrument shelter is painted white. Usually, care is taken to keep away any obstruction at a distance less then twice the height of the obstruction itself (i.e. trees, fences, buildings, etc.).

(c) Pyranometer

The pyranometer is mounted on a surface parallel to the collector surface in such a manner that it does not cast a shadow on the collector plate. Precautions are always taken to avoid subjecting

Ambient Cross- sectional area

temperature Pyronometer of duct = o' x b~7 sensor ~ , .... ~,,J...

A % I c

E

if)

~ Air f low ~ . . ,_ 16 measuring ~ . ~ . ~ a p p a r a t u s , . .

Cross-sect ionat area of

duct = a x b

To e lec t ron ic integrator - ' I~ or strip chart recorder

._c

i S ^ < ~ ' ~ ~,/~-~;b, I Mixing

. . ! . . . . i f ~ ° ~ - ' / - ~ ' ~ I device " l / I ,s • , . . . . . . l i i needed

\ h-:-o'o'o"'o J InsuLation

Manometer

ThermopiLe Junctions at center of segments of

e q u a l cross s e c t i o n a l a r e a s )

Air r econd i t ion ing

a p p a r a t u s "I" C a l i b r a t e d dry b u l b t e m p e r a t u r e

m e a s u r i n g device

Fig. 7. NBS testing configurations for the solar collector when the transfer fluid is air (after Ref. [9]).

ECM 32 I--C


the instrument to mechanical shocks or vibration during the installation, and it is oriented so that the emerging leads or the connector are located north of the receiving surface (in the Northern Hemisphere) or are kept shaded in some other manner. This minimizes heating of the electrical connections by the sun. Care is also taken to minimize the reflected and reradiated energy from the solar collector reaching the pyranometer. Pyranometers, supplied with shields, are so adjusted that the shield lies parallel to and just below the plane of the thermopile. Pyranometers not supplied with a shield may be susceptible to an error due to reflections of radiation. Precautions can be taken by constructing a cylindrical shield, the top of which is kept coplanar with the thermopile.

(d) Reconditioning apparatus

For the reconditioning apparatus shown in Fig. 7, a heat exchanger is used to cool the transfer fluid for simulating the building lead and an electric resistance heater is used to control the inlet temperature to the prescribed test value. This combination of equipment of an equivalent system should control the temperature of the fluid entering the solar collector to within ___ 0.5°C of the prescribed inlet during the complete test period.

(e) Test ducts

The air inlet duct, between the air flow measuring apparatus and the solar collector, should have the same cross-sectional dimensions as the inlet manifold to the solar collector. The air outlet duct, between the solar collector and the reconditioning apparatus, shall have the same cross-sectional dimensions as the outlet manifold from the solar collector.

( f) Air leakage

Air leakage through the air flow measuring apparatus, air inlet test duct, the solar collector and the air test duct should not exceed ___ 1.0% of the measured air flow. The air leakage rate can be determined by measuring the air flow rate at the outlet as well as the inlet of the collector. Any difference between the two measurements gives the air leakage.

The performance of a solar collector is determined by obtaining the values of the instantaneous efficiency for a large combination of values of incident insolation, ambient temperature and inlet fluid temperature. This requires experimentally measuring the rate of incident solar radiation on the solar collector as well as the rate of energy addition to the transfer fluid as it passes through the collector (all under quasi-steady-state conditions).

3. l.l. Testing procedure. The tests should be performed at a constant air inlet temperature. Recommended inlet temperatures are 10, 30, 50 and 70°C; however, the values that can realistically be used will depend upon the particular collector design and the environmental conditions at the location and time of the year when the collector is being tested. Equation (70) may be used to obtain the efficiency curve according to this method. At least four data points should be taken for each value of t~, two during the time period before solar noon and two in the period following solar noon so that the data points are symmetrical with respect to solar noon and any transient effects that may be present do not bias the test results. It is desirable that, in addition to the fitted curve, all the measurement data is reported so that any difference in efficiency solely due to operating temperature level of the collector can be discerned in the test report. Usually, the measurements are averaged over a time interval of 15 rain; care is, however, taken to ensure that the solar insolation is steady for each 15 min segment during which an efficiency value is determined. Either electronic integrators or continuous pen strip chart recorders may be used to determine the integrated values of incident solar radiation and temperature rise across the collector. However, a strip chart recorder with a recommended chart speed of 30 cm/h must always be used to monitor the output of the pyranometer to ensure that the incident radiation has remained steady during the 15 min segment. Prior to measurements, the pyranometer should be checked to make sure that there is no accumulation of water vapour enclosed within the glass cover; the use of wet pyranometers is not allowed for measurements.

To obtain a sufficiently good quasi-steady state, the collector is first allowed to stand in the sun under stagnant (no fluid flow) conditions. The transfer fluid is then circulated through the collector for at least 30 min prior to the period in which the data is recorded; during this period, a check


is made to ensure that the flow rate of the transfer fluid does not vary by more than +_ 1% and that the incident solar radiation remains steady.

The air flow rate is kept at a constant value of 0.01 m/s per m 2 of collector area in this test procedure. If the collector has been designed for a different flow rate, the design flow rate is used for the measurements.

To determine the diffuse part of the total radiation and report it for the test, the sensing element of the pyranometer is shaded from the direct beam of the sun just before and just after each 15 min testing periods and the value of the radiation determined. This is usually accomplished by using a small disc attached to a slender rod on a direct line between the pyranometer and the sun; the disc has to be of a proper size to shade the sensing element alone.

For each 15 min segment, the efficiency is determined, by using the equation

(72) 1/=

f ~t2 G dt

The quantities m and Cp have been taken out of the integration sign in the numerator, since they remain essentially constant during the measurements. Ae in the above equation is not the absorber area but the transparental aperture area.

3.1.2. Calculation of theoretical power requirements. In order to calculate the theoretical power required to move the transfer fluid through the solar collector, the following equation is used:

rn AP Pth - (73)

P

3.1.3. Time constant. If transient conditions are present during the test, the steady-state equation (72) is not valid because a part of the absorbed energy is utilized for heating the collector and its components. The corresponding relationship for transient conditions is

the rate of the rate of the rate of change of energy absorbed energy loss energy of = in the collector - from the the collector by the collector by and its absorber conduction, components convection and

radiation

The above conditions can also be expressed as [7, 10]:

C___~_A d T__ f rhCp T - = FR[(t~) e -- Ue(tn -- t,)] - - - -7 - - ( re tn)

Aa dt A a

the rate of energy carried

- away by the transfer fluid

(74)

(75)

where

K = F ' UL A~d -- 1 . (77)

dTr = K dTre (76) dt dt

(1) The exit temperature of the transfer fluid is related to the average temperature by

where Tf is the average temperature of the collector and C A is the heat capacity of the collector. Equation (75) can be solved for the exit temperature of the transfer fluid, Tre, as a function of

time, t, after making the following assumptions [11]:

28 C H A N D R A and SODHA: TESTING PROCEDURES FOR SOLAR AIR HEATERS

(2) L (z~)~, UL, T,, rh, Cp and t~ are all constant for the period covered by the transient solution. The solution to equation (75) is then given by the following expression

rhCp T, FRI(Z~t)e--FRUL(tf--ta)----~-a( fe- - tn) / m C. t' ~ = e x p ~ - ~ - ~ a )" (78)

n~ Cp FRI (zo~)~- fR UL (tn -- ta)--~-(Tr~i.i,,~,- t.)

3.2. A S H R A E Standard 93-77

The NBS procedure prescribed that a series of outdoor steady-state tests be conducted to determine the near-normal-incidence efficiency of the collector over a range of temperature conditions. The American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) has recently adopted ASHRAE Standard 93-77 [6]. It is similar to the original NBS procedure but calls for additional tests to determine the collector time constant as well as its incident angle modifier.

The test procedure specified in ASHRAE Standard 93-77 is limited to 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 used in conjunction with the energy incident upon the collector (also determined by measurement) to calculate the pertinent performance factors for the collector. The fluid can be either a liquid or gas but not a combination of the two.

A part of the procedure and the apparatus is specified in Fig. 8. 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 test procedure is carried out in four steps:

(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 aperature exceeding 17,000 kJ/m 2. d (1500 Btu/ft 2. d).

(2) The time constant test is made. (3) The efficiency tests are conducted. (4) A series of tests are conducted to determine the collector incident angle modifier.

5 4a x b min

Ammb; . _ PyranometerJ Cross-sectionaL area

: 'ture .9o,,0uc,=a, b sensor " " ~ .~.. .... ~ .... I I

L~E ~'E v W i o n ~ t ? ~ ' ! i : x ! n ' i " "" / ~ ~ sensor j . ~ u - ~ l M i g /

,_ ~ . . . . . . ~ ^ ~ . ~ j ,-,-u__x_u I dev ices / ........ ;~..,,-..-~.[ ~ mm [nee~ecl Air rate measuring

~" "ll'U " "" I ,~ I apparatus

[ ' ~ Differential pressure measuring d e v i c e

. .i Air [ reconditioning ~ Air fLow

I

Fig. 8. Testing configuration for the solar collector when the heat transfer fluid is air, ASHRAE Standard 93-77 (after Rcf. [6]).


3.2. I. Time constant test. The time constant for a collector could be theoretically calculated using equation (78). However, there is a large uncertainty in knowing the value of the effective heat capacity CA. Duffle and Beckman [7] have shown that the upper limit for this heat capacity is the sum of the mass times the specific heat for each of the components that make up the collector (absorber, glass, insulation, etc.), plus that of the heat-transfer fluid required to fill the collector. However, if this were used for CA, the time constant would be overestimated, because the temperature of some materials in the collector changes by only a fraction of the amount that the fluid temperature changes in such a transient process. Consequently, the time constant is required to be determined experimentally in ASHRAE Standard 93-77.

The actual test can be carried out in one of two ways. The most straightforward technique is to expose the collector to the solar radiation and after the entering and existing fluid temperatures have stabilized, suddenly shield the collector from the sun and monitor the exit fluid temperature on a strip-chart recorder. The incident radiation must initially be above 790 W/m 2 (250 Btu/ft z. h). The entering fluid should be within + 1 °C ( + 2°F) of the ambient temperature, if possible, for the duration of the test. This latter requirement simplifies the data-reduction process using the left-hand side of equation (78).

A second technique that can be used is to shield the collector from the sun altogether (conduct the test inside, for example). The inlet fluid temperature is adjusted to 30°C (54°F) above the ambient, and after the exit temperature has stabilized, the inlet temperature is suddenly decreased to within + I°C ( + 2°F) of the ambient.

3.2.2. Efficiency tests. The effÉciency test series consists of determining the average efficiency (integrating the energy quantities) over a range of temperature differences between the average fluid temperature and the ambient air. The efficiency is calculated by using equation (69). The time period r z - r~ to be used for the integration of the energy quantities is either 5 min, or one time constant, whichever is larger. The efficiency is computed on the basis of gross collector area. The flow rate is required to be steady and should not vary more than ___ 1.0°% for the duration of each test. In addition, the heat transfer fluid shall have a known specific heat which varies by < 0.5% over the temperature range of the fluid during a particular test period.

The test apparatus specified in ASHRAE 93-77, has 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 temperatures range desired. At least 16 "data points" are required for a complete test series, and they must be taken symmetrically with respect to solar noon (to prevent biased results due to possible transient effects).

During each test period, the incident solar radiation must be "quasi-steady". Other requirements that must be satisfied for each "data point" are that the average irradiance be > 630W/m 3 (200 Btu/ft 2 h) and the incident angle between the sun and the outward drawn normal from the collector be < 30 °. In addition, the range of ambient temperatures for the entire test series must be < 30°C (54°F). This condition may not be fulfilled in countries where ambient temperature during summer touches 45°C.

The measurements made and the calculated efficiency for each "data point" are reported in tabular form and also in graphical form. The ordinate is the efficiency and the abscissa is the measured temperature difference (between fluid inlet and ambient) divided by the irradiance.

3.2.3. Incident angle modifier. As with the time constant test, there are two ways in which the incident angle modifier test can be done. The first technique is applicable when the incident angle can have any arbitary value, as with a solar simulator or with an outdoor movable test rock. In this case, a thermal efficiency test is conducted in accordance with all the requirements of the procedure used to get the near-solar-noon efficiency curve except that:

(1) The inlet fluid temperature is held within +_ I°C ( +_ 2~F) of the ambient temperature, and (2) The test is made for incident angles of 0, 30, 45 and 60 °.

By comparing these test results here with those obtained in establishing the efficiency curve at incident angles of < 30 °, values of K,* can be computed as a function of incidence angle (up to


60°). Simon and Buyco [12] have shown that the effective transmittance-absorptance product (z~)¢ of a solar collector can be satisfactorily described by

( ~ ) e = (g~)o,n

where K~ is the incident angle modifier and (z~)¢., is the effective transmittivity-absorptance product for normal incidence.

The second technique is applicable for outside testing with a permanent test rack where the collector orientation cannot be arbitrarily adjusted with respect to the direction of the incident solar radiation (except for perhaps adjustments in tilt). The collector is tested for a complete day with the inlet fluid temperature held constant as above. The efficiency values are computed continuously and "pairs" of values are selected, one from the morning and one from the afternoon, which correspond to values of 30, 45 and 60 ° in incident angle. The two efficiency values in each pair are averaged to compensate for transient effects and then used as above to compute the incident angle modifier.

3.2.4. Calculation of all day solar efficiency from the test data of ASHRAE Standard 93-77. As explained in the previous sections, the series of solar collector tests conducted according to ASHRAE Standard 93-77 results in a determination of the thermal efficiency of the collector at near-normal-incidence conditions as a function of the difference between the inlet fluid temperature to the collector and the ambient temperature as well as the incident solar radiation normal to the collector plane. In addition, the parameter incident angle modifier is determined. From these two performance factors, it is possible to predict the all-day collector efficiency. In order to complete the calculation for a given day, the following steps are required:

Step 1. Step 2. Step 3.

Step 4.

Step 5.

Step 6.

Step 7.

Step 8. Step 9.

Inlet fluid temperature to the collector, tfi(°C). Ambient air temperature, t a ( °C) .

Incident solar radiation upon the plane of the collector, I (W/mE). If the radiation on the horizontal surface is known, then it can be multiplied by the ratio of total radiation on the tilted surface (normal to the collector plane) to that on a horizontal surface, to calculate L Collector thermal efficiency at normal incidence, determined in accordance with AHSRAE Standard 93-77, and using data from Steps l, 2 and 3. Incident angle between the direct solar beam and outward drawn normal to the collector plane. Incident angle modifier, determined in accordance with ASHRAE Standard 93-77, and using the value of 0 from Step 5. [Aa/As] F R ('~t)e, n, Y intercept from the collector thermal efficiency at normal incidence curve determined in accordance with ASHRAE Standard 93-77. Energy output of the collector (W/m2). Collector thermal efficiency, Step 8/Step 3.

The calculation procedure is carried out using Table 2.

Table 2. Computation of all day solar collector efficiency

Hour of the day (solar time)t Calculation Daily steps l 2 3 4 5 6 7 8 9 I0 total Step I Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9

tHour 1 may be 6-7 or 7-8 and so on,


3.3. B S E a n d o ther p r o c e d u r e s

The BSE procedure prescribes that the optical efficiency and thermal loss characteristics of a solar collector be determined independently through a series of outdoor and indoor tests. There are other methods also, such as the Israeli procedure, Australian procedure, etc. which have been described in detail by Sodha et aL [2], and the generalized method discussed by Proctor [13].

4. GENERATING DESIGN D A T A

A method proposed by Reddy and Gupta [8] for generating design data for solar air heaters is very useful.

The performance of a solar air heater depends on the following parameters:

(i) Choice of construction materials, i.e. r, ct and c. (ii) Ambient conditions, i.e. Ta, Vw and I.

(iii) Geometry, i.e. L, a and b. (iv) Inlet temperature of the air, T~. (v) Air properties, Cf, k, #, p.

(vi) Flow rate rn.

For a given flow rate, the instantaneous collector efficiency can be expressed as

r/ = F ' [(T0~)e - - U L (A tm/G)] .

In terms of temperature difference across, the collector,

rh Cp (tro - tn) q - G

The basic algorithm is developed in the following manner.

Step 1.

Step 2.

(79)

(8O)

Test data are obtained for various values of A/m and G and a curve r/ vs ( A t m / G ) is obtained. Equations (79) and (80) are written in the following form:

r /= F ' { ( T 0 ~ ) e - - U L [(/fo --/a) -b (tfi -- ta)]/2G } (81)

and

~/= 2rnCp [(tfo - t~) - (t~ - ta)]/2G. (82)

Another set of curves is obtained by plotting ~ vs the difference of (tro- ta ) /2G and (t~ - q ) / 2 G . Step 3. Curves obtained in Steps 1 and 2 are superimposed, and the resultant curve can be used

to compute the collector parameters.

It should be mentioned that equations (81) and (82) are valid when air is recycling in the collector, i.e. tn > t~. In the absence of air recycling, i.e. (tn = ta), equations (81) and (82) are further simplified.

Air heater test data are generally obtained from rather smaller installations. To use this data for a large heating installation made up of several parallel and series combination of solar air heaters is likely to give erroneous results. This is because air heaters of the same configuration but different physical dimensions do not yield similar performance curves for the same t~, since performance curves are not dependent on (~ alone but one air stream velocity V and the equivalent diameter, D e .

If the performance curves of a particular air heater are available for different t~, these can be used to predict the performance of another air heater of the same configuration but of difference physical dimensions by the procedure outlined by Reddy and Gupta [8]. The required equation is


where subscripts 1 and 2 are for two air collectors and

d = r h / a . l . M

and

61 = V . a . b . M . p .

Thus, two air heaters of different physical dimensions but of similar configuration will have similar performance curves for d s which satisfy equation (83).

Biondi et al. [14], while analysing the technical performances of several solar air heaters, pointed out that solar air heaters can be characterized by means of two coefficients.

(i) Air mass flow rate per unit collector area (G). (ii) Collector geometric coefficient K.

The convective heat transfer coefficient in solar air heaters is calculated by using the following well known Charter's relations

Nu = 0.0158 (Re) °s . (84)

Biondi et al. [14] introduced a "geometric coefficient K " defined by

L K = h 0 0.2--------/. (85)

v ~ e

The coefficient Khas the unit m -°':5. By using the definitions G = rh/A and rh = p VA¢, one obtains V = GL/bp and by using equation (85), it modifies to

V = dKD°25/p. (86)

Equation (84) then becomes

Nu = 0.0158 De (87)

which gives the convective heat transfer coefficient he, as follows.

he = 0.0158 k ( d K / # ) °s. (88)

If k (thermal conductivity of air) and # (air dynamic viscosity) are considered as constant, hc depends only on the product dK. The performances, working efficiency and temperature gain, again depend on (~ (the temperature gain, directly and the efficiency, by means of FR); therefore, one can say that the performances of solar air collectors under the same conditions for other parameters depend only on d and K.

5. N O R M A L I Z E D LOSS COEFFICIENT

The thermal performance of solar collectors can also be rated by the normalized loss coefficient U/~lo [3]. It is a measure of the quality of energy that a collector can provide. A collector classification based on this parameter would not be a measure of how efficiently a collector works. This would be given by the second parameter iT0. Thus, a comparison of collectors should be made on two complementary levels:

(I) Compare normalized loss coefficient. (2) Compare ~70, cost and durability.

Thus, the collector test results should be given in the form

r /= r/0 (1 - U ' T* ). (89)

When the collector parameters are specified as ~/0 and U' they are directly related to the system design methods: U ' relates to the quality of energy to be collected and r/0 A relates to the quantity of energy to be collected.


Further, it should be stressed that no classification used on thermal performance alone will be adequate to compare collectors. Two parameters are required to characterise a solar collectors, and it is advantageous if one of these can be linked with the economic comparison. Consequently, the normalized loss coefficient can be used to categorize solar collectors but not to compare them absolutely.

6. C O N C L U S I O N

The various testing procedures for solar air heaters have been discussed. These collectors can be well tested indoors by allowing the net thermal output of an irradiated solar air heater array to be reproduced indoors under different leaking conditions. The rating of solar air heaters can also be done by the normalized loss coefficient along with the collector zero loss efficiency. A method has also been described which, by using the performance curves of a solar air heater for different (~, can predict the thermal performance of a solar air heater of the same configuration but of different physical dimensions.

Acknowledgements--The authors are grateful to Lata Mathur and K. Giri for their expert typing of the manuscript.

R E F E R E N C E S

1. N. K. Bansal, R. Chandra and M. A. S. Malik, Solar air heaters. In Reviews of Renewable Resources of Energy (Edited by M. S. Sodha, S. S. Mathur and M. A. S. Malik). Wiley Eastern, New Delhi (1984).

2. M. S. Sodha, N. K. Bansal, A. Kumar, P. K. Bansal and M. A. S. Malik, Solar Crop Drying. CRC Press, Cleveland, Ohio (1987).

3. J. P. Kenna, Sol. Energy 29, 431 (1982). 4. A. F. Fanny, W. C. Thomas, C. A. Scarbrough and C. P. Terlizzi, Analytical and experimental analysis of procedures

for testing solar domestic hot water systems. MBS Building Science Series 140 (1982). 5. D. J. Close and M. B. Yusouff, Sol. Energy 20, 459 (1978). 6. ASHRAE, Method of testing to determine the thermal performance of solar collector, ASHRAE Standard 93-77 (1977). 7. J. A. Duffle and W. A. Beckman, Solar Engineering of Thermal Processes. Wiley, New York (1980). 8. T. A. Reddy and C. L. Gupta, Sol. Energy 25, 527 (1980). 9. J. E. Hill and T. Kusuda, Method of testing for rating solar collectors based on thermal performance. NBS Report

NBSIR 74-635 (December 1974). 10. S. A. Klein, J. A. Dut~e and W. A. Beckman, ASME J. Engng Power 96A, 109 (1974). I 1. G. O. C. Lof, Flat plate and non-concentrating collectors. In Solar Energy Technology Handbook (Edited by W. C.

Dickinson and P. N. Cheremisinoff). Marcel Dekker, New York. 12. F. F. Simon and E. H. Buyco, Outdoor flat plate collector performance prediction from solar simulator test data. NASA

TM-71707, presented at the 10th AIAA Thermal Physics Conference, Denver, Colo. (27-29 May 1976). 13. D. Proctor, Sol. Energy 32, 377 (1984). 14. P. Biondi, L. Cicala and G. Farina, Sol. Energy 41, 101 (1988).

Documents

Testing procedures for solar air heaters: A review