32-design optimization of the flat plate collector a.pdf

11
Pergamon Solar Energy Vol. 60, No. 2, pp. llT87. 1997 0 1997 Elsevier Science Ltd PII: SOO38-092X(96)00142-9 All rights reserved. Printed in Great Britain 0038-092X/97 $17.00+0.00 DESIGN OPTIMIZATION OF THE FLAT PLATE COLLECTOR FOR A SOLID ABSORPTION SOLAR REFRIGERATOR S. 0. ENIBE$t and 0. C. ILOEJE$ National Centre for Energy Research and Development and Department of Mechanical Engineering. University of Nigeria, Nsukka, Nigeria (Received 17 May 1995; revised version accepted 8 October 1996) (Communicated by Volker Wittwer) Abstract-A study of the effects of various collector design parameters on the performance of a solar powered solid absorption refrigerator is presented. The refrigerator uses specially treated CaCI, as absor- bent and NH, as refrigerant and operates intermittently in a diurnal cycle. The study is undertaken using version 4.0 of a simulation programme, COSSOR, developed from a transient analysis of the system. A large number of simulations was undertaken to test the performance of the refrigerator for various choices of the collector design parameters. The latter include the plate emissivity and material; absorbent pellet diameter, thermal conductivity and packing density; collector tube size, spacing and material; and number of glazing. The refrigerator performance indicators, namely total condensate yield, mass of ice produced, coefficient of performance and effective cooling, are presented for the range of values of the collector parameters of interest. Using a multiple linear regression technique, the performance indicators are c’orrelated with the collector parameters by simple linear polynomial expressions. An objective function, suitable for selecting optimal values of the parameters, is defined, subject to specified constraints. Optimization was then carried out for the objective function. For the collector with steel tubes and steel plate, the refrigerator coefficient of performance obtained with optimal choices of tube size, spacing and plate emissivity is 0.073, representing an improvement of at least 30% with respect to the reference collector. A similar level of improvement was obtained for a collector with aluminium tubes and plate.0 1997 Elsevier Science Ltd. 1. INTRODUCTION A number of studies has been reported on the optimization of solar flat plate collectors. These include the work of Alizadeh et al. (1979) on a solar refrigerator, Willmott (1982) on the collec- tor orientation, and Chang and Minardi (1980) and Barley (1978) on the area of collection. Hollands and Stedman (1992) recently pre- sented an analysis for an optimum absorber plate fin thickness. These studies reveal that, in general, the optimization of a flat plate collector is strongly application specific. (1985, 1988). Relevant details of the collector assembly are shown in Fig. I, while the key dimensions are given in Table 1. The total absorber area is 1.41 m2, while the total mass of the absorbent and the total mass of the collector assembly (excluding the glazing) for the collector is, respectively, 7.5 and 52.5 kg. With a non-selective absorber in a double- glazed flat plate collector, the peak overall coefficient of performance was 0.053, but theo- retical estimates by several investigators (Stanish and Perlmutter, 198 1; Ezeilo, 1982; The refrigerator considered is a solar powered solid absorption system using stabilized calcium chloride pellets as absorbent and ammonia as refrigerant. The absorbent is prepared as pre- sented by lloeje ( 1986), and packed in the annular space between two coaxial tubes in a combined collector/generator/absorber. Other components of the refrigerator include a stag- nant water evaporative condenser, a receiver and an evaporator. The refrigerator operates intermittently in a diurnal cycle in the genera- tion, cool down and evaporation modes. Details of the design, construction and test performance of the refrigerator have been presented by Iloeje Ammonia / Back lnsula:lon 1 tAuthor to whom all correspondence should be addressed. Fig. 1. Cross-section of collector showing absorber/ $ISES member. generator tube. 77

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DESIGN OPTIMIZATION OF THE FLAT PLATE COLLECTOR

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Page 1: 32-DESIGN OPTIMIZATION OF THE FLAT PLATE COLLECTOR  A.pdf

Pergamon Solar Energy Vol. 60, No. 2, pp. llT87. 1997

0 1997 Elsevier Science Ltd PII: SOO38-092X(96)00142-9 All rights reserved. Printed in Great Britain

0038-092X/97 $17.00+0.00

DESIGN OPTIMIZATION OF THE FLAT PLATE COLLECTOR FOR A SOLID ABSORPTION SOLAR REFRIGERATOR

S. 0. ENIBE$t and 0. C. ILOEJE$ National Centre for Energy Research and Development and Department of Mechanical Engineering.

University of Nigeria, Nsukka, Nigeria

(Received 17 May 1995; revised version accepted 8 October 1996) (Communicated by Volker Wittwer)

Abstract-A study of the effects of various collector design parameters on the performance of a solar powered solid absorption refrigerator is presented. The refrigerator uses specially treated CaCI, as absor- bent and NH, as refrigerant and operates intermittently in a diurnal cycle. The study is undertaken using version 4.0 of a simulation programme, COSSOR, developed from a transient analysis of the system. A large number of simulations was undertaken to test the performance of the refrigerator for various choices of the collector design parameters. The latter include the plate emissivity and material; absorbent pellet diameter, thermal conductivity and packing density; collector tube size, spacing and material; and number of glazing. The refrigerator performance indicators, namely total condensate yield, mass of ice produced, coefficient of performance and effective cooling, are presented for the range of values of the collector parameters of interest. Using a multiple linear regression technique, the performance indicators are c’orrelated with the collector parameters by simple linear polynomial expressions. An objective function, suitable for selecting optimal values of the parameters, is defined, subject to specified constraints. Optimization was then carried out for the objective function. For the collector with steel tubes and steel plate, the refrigerator coefficient of performance obtained with optimal choices of tube size, spacing and plate emissivity is 0.073, representing an improvement of at least 30% with respect to the reference collector. A similar level of improvement was obtained for a collector with aluminium tubes and plate.0 1997 Elsevier Science Ltd.

1. INTRODUCTION

A number of studies has been reported on the optimization of solar flat plate collectors. These include the work of Alizadeh et al. (1979) on a solar refrigerator, Willmott (1982) on the collec- tor orientation, and Chang and Minardi (1980) and Barley (1978) on the area of collection. Hollands and Stedman (1992) recently pre- sented an analysis for an optimum absorber plate fin thickness. These studies reveal that, in general, the optimization of a flat plate collector is strongly application specific.

(1985, 1988). Relevant details of the collector assembly are shown in Fig. I, while the key dimensions are given in Table 1. The total absorber area is 1.41 m2, while the total mass of the absorbent and the total mass of the collector assembly (excluding the glazing) for the collector is, respectively, 7.5 and 52.5 kg. With a non-selective absorber in a double- glazed flat plate collector, the peak overall coefficient of performance was 0.053, but theo- retical estimates by several investigators (Stanish and Perlmutter, 198 1; Ezeilo, 1982;

The refrigerator considered is a solar powered solid absorption system using stabilized calcium chloride pellets as absorbent and ammonia as refrigerant. The absorbent is prepared as pre- sented by lloeje ( 1986), and packed in the annular space between two coaxial tubes in a combined collector/generator/absorber. Other components of the refrigerator include a stag- nant water evaporative condenser, a receiver and an evaporator. The refrigerator operates intermittently in a diurnal cycle in the genera- tion, cool down and evaporation modes. Details of the design, construction and test performance of the refrigerator have been presented by Iloeje

Ammonia

/ Back lnsula:lon 1

tAuthor to whom all correspondence should be addressed. Fig. 1. Cross-section of collector showing absorber/ $ISES member. generator tube.

77

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78 S. 0. Enibe and 0. C. Iloeje

Table 1. Reference design parameters of the refrigerator

Units Length, Width, Thickness, Inside diameter, Outside diameter,

mm mm mm mm mm

Collector plate Collector tube Collector air gap Glazing Back insulation Ammonia distribution tube Headers Condenser coil Receiver Evaporator coil Evaporator jacket Bond

1567 1330

1567 1567 1330 912

900 1 - - 54 59

70 900 4 - 900 109

18 21 - 18 21

18 21 88.25 94.25 18 21

- 200 203 59

Worsoe-Schmidt, 1983) indicate that COPS of the order of 0.1 are obtainable. In order to determine the collector design specifications which improve the refrigerator performance, a transient analysis of the system was developed (Iloeje et al., 1995) and was extended recently to cover the full refrigerator operating cycle (Enibe and Iloeje, 1997). The analysis led to the development of a computer programme, COSSOR, for its performance simulation.

A parametric study of the collector under consideration was reported by Iloeje et al. (1995). However, this covered the generation mode only because the refrigerator heat and mass transfer transients for the cool down and evaporation modes were not included. In this article, the results of a parametric study for the effects of various collector design specifications on the performance of the complete refrigera- tion system are presented. The latest version of COSSOR, version 4.0, is used for the study. Optimization results are also presented.

2. PARAMETRIC EFFECTS

A large number of parameters determine the behaviour of a flat plate solar collector for any application. This includes environmental vari- ables (ambient temperature, solar radiation characteristics, latitude and altitude of location, wind speed, time of year, etc.) as well as design variables (such as dimensions, material and radiation characteristics of the collector). For application in solar refrigeration, the heat transfer and thermal inertia of the condenser, receiver and evaporator are also important. It is clearly a cumbersome task to perform a realis- tic optimization with respect to all of these variables. We shall therefore limit them to the barest minimum.

Of the environmental variables, the most important in a solar refrigeration application are the solar radiation intensity, ambient tem- perature and wind speed, which, in themselves, have diurnal variations and are also affected by the latitude and the time of year. The variables are also strongly site-specific.

In a recent study (Iloeje and Enibe, 1995), the monthly mean daily radiation for many African cities was found to lie in the range of 8-32 MJ mm2 day-‘, with the annual mean value lying in the range 14-23 MJ m-‘day-‘. These data are comparable to the range of lo-22 MJ m-’ day-’ reported for several major world cities (Duffie and Beckman, 1980). An actual daily radiation value of 15.13 MJ me2 day-’ at Nsukka, Nigeria (lati- tude 7” north), on 14 January was selected for the study. The variation of the radiation inten- sity and ambient temperature with time for the test site and date are shown in Fig. 2.

The solar collector design parameters of inter- est are the collector plate material and emissiv- ity; material, diameter and spacing of the tubes housing the absorbent; number of glazing; and the thermal conductivity, mean diameter and packing density of the absorbent granules. Each

120 ,200

100 -

b 80 ; 3 a BO-

i

5 40-

20 -

01 5

Fig. 2. Transient performance of reference collector.

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Flat plate collector for a solar refrigerator 79

Table 2. Range of values of the collector parameters

Parameter

Absorber plate emissivity Collector tube spacing, m Collector tube OD, m Ammonia distribution tube OD, m Absorbent packing density, kg mm3 Pellet thermal conductivity, W m- ’ K ’ Absorbent pellet mean diameter, m Number of glazing

Reference Minimum Maximum value value value

0.9 0.152

0.059 0.021

483 0.23 0.0075 II

0.1 0.06 0.034 0.015

360 0.05 0.003

0.9 0.210 0.098 0.041

700 1.00 0.020 8

parameter is varied over the range of values specified in Table 2.

The most important performance indicators for the refrigerator are the total condensate yield per unit collector area, MnhJ, the total mass of ice produced per unit area, Mi,e, the total useful cooling obtained per unit area, Q, and the useful coefficient of performance, COP. The latter is defined as the total useful cooling divided by the total incident radiation during the generation mode. For an intermittent absorption system, the refrigerant condensed during the generation mode is usually fully evaporated during the reabsorption mode, the useful cooling being stored as ice. In this way, the refrigerator is prepared for the next day’s operation. The time available for reabsorption is therefore limited. The upper limit for the latter is taken as 11 h, based on observations of Iloeje (1985).

2.1. General test conditions

In order to ensure the consistency of the simulation conditions while reflecting the expected behaviour of a real system, the following conditions were imposed. (1)

(2)

(3) (4)

The generation and reabsorption (evapora- tion) modes start respectively at 8.5 and 21.0 h from midnight of the previous day. The refrigerator is fitted with a condensate level monitoring and control mechanism which monitors the mass of refrigerant con- densed during the generation mode. The mechanism switches the refrigerator to the cool down operating mode whenever the condensate mass decreases continuously over a fixed duration after 16.0 h. A fixed duration of 10 min was used for the test. All insulation is done with glass wool. The evaporating pressure is 3 bar, while the system pressure at the start of the genera- tion mode is 4.95 bar.

The refrigerator under the above conditions, together with specifications in Tables 1 and 2, is called the reference refrigerator, and its tran- sient performance is given in Fig. 2. The genera- tion mode occurs during the period 8.5-16.5 h from midnight, during which time the total insolation received is 15.13 MJ m-‘. The peak solar intensity, mean daytime ambient temper- ature, and daily average wind speed are 800 Wme2, 28.5”C and 1.09m s-r, respec- tively. The collector peak tube surface temper- ature, mass of refrigerant condensed and mass of ice produced are 104”C, 1.066 kg mm2 and 1.627 kg rne2, respectively. The useful overall coefficient of performance COP’ = 0.0559, while the useful cooling Q’= 0.8504 MJ m-2. The time fc : complete reabsorption is 7.51 h.

2.2. Efect ofpellet thermal conductivity and diameter

The thermal conductivity of the absorbent is low, and this has been recognized as a limiting factor to the refrigerator performance. Values of 0.087 W m-l K-r (Buffington, 1933) and 0.12-0.23 W m-l K-’ (Nielson and Worsoe- Schmidt, 1977) have been reported for pow- dered CaCl,, while an effective value of 0.105 W m-l K-’ was obtained for the treated granular absorbent at a packing density of 621 kgmm3 with air as the interstitial fluid (Iloeje, 1989). The low thermal conductivity is, in part, caused by the absorbent porosity. It may be improved through a more careful con- trol of the intra-pellet porosity and its distribu- tion, or by the use of special additives.

The effect of the pellet thermal conductivity on the refrigerator performance is shown in Fig. 3 for the collector with steel tubes and steel plate. As the thermal conductivity is increased in the range 0.05 < k8,< 1 ,O, the condensate yield, mass of ice produced, useful cooling and the useful COP increase steadily. At k,, = 1, representing a 20-fold increase over the mini-

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80 S. 0. Enibe and 0. C. Iloeje

“062 -

: 2 006 -

3 g 0 058 -

a 2 0056 -

$ 5 0054 -

Fig. 3. Effect of pellet conductivity on refrigerator performance.

mum value of 0.05, the COP increases by only 20% from 0.052 to 0.062. This improvement in performance may not justify the effort that may be required to improve the absorbent thermal conductivity.

The effect of the pellet mean diameter was also tested. As the diameter was varied from 0.005 to 0.02 m, no significant changes in the refrigerator performance were observed. For example, the COP increased by only 1.5% between the two pellet diameter limits. The refrigerator performance is therefore not sensi- tive to the pellet diameter. This is not surprising, since, as shown by Enibe (1995), the salt absorption/generation characteristics are not sensitive to the pellet diameter for D,, I 0.02 m and egr 20.12. The analysis assumed that the expansion, disintegration and compacting of the absorbent is negligible.

2.3. EfSect of absorbent packing density The packing density affects the mass of the

absorbent in the absorber/generator tube and hence its thermal capacity and maximum con- densate yield. It may be varied in practice by varying the range of pellet diameters and their fractional distribution. The density is related to the packing porosity through the expression

e, = 1 - PSI&. (1)

In turn, the bed porosity determines the effective thermal conductivity of the packing,

as described elsewhere (Enibe and Iloeje, 1997). The density of the pellet, estimated as 730 kg rnm3, serves as the upper limit of pS, while the lower limit is chosen as 365 kg rne3, corresponding to a packing porosity of 0.5.

The variation of the refrigerator performance with the packing density is shown in Fig. 4. A doubling of the density increases the COP and other performance indicators by no more than 13%. This performance improvement is consid- ered negligible, since, in any case, the collector mass per unit area is also increased.

2.4. Eflect of number of glazing As the number of glazing in a solar collector

system is increased, the overall top heat loss coefficient decreases. But this is accompanied by a loss in the solar transmittance (Duffie and Beckman, 1980; Norton, 1992) and an increase in the total mass of the collector assembly. The optimum number of glazing therefore depends very much on the mean operating temperature of the system under consideration. For the solar collector under study, which used a non-selec- tive absorber, the increase in performance with double glazing compared with single glazing is about 30%, while the best performances are achieved for 4 and 5 glazing (see Fig. 5). The performance decreases above 5 glazing because of the predominant effect of the decreased solar transmittance and increased collector thermal capacity. It is common practice, however, to

2 2

08 OR 350 400 450 500 550 600 650 700 750

0061

0063 -

: 0.062 - 9 E 0.061 - P L 006 -

B 0059 - 6 2 0058 -

z 0057 -

0.056 -

0.056 1 I 350 400 450 500 550 600 650 100 750

Absorbent packing densely, hq ITI-'

Fig. 4. Effect of absorbent packing density on refrigerator performance.

Page 5: 32-DESIGN OPTIMIZATION OF THE FLAT PLATE COLLECTOR  A.pdf

Flat plate collector for a solar refrigerator 81

Fig. 5. Effect of number of glazing on refrigerator performance.

use no more than 2 or 3 glazing. Since significant improvements in the collector performance may be achieved through other means (as will be shown later), it is preferable to utilise these alternatives.

2.5. Eflect of tube andplate material

The choice of the material for the collector plate is essentially limited to steel, aluminium, copper and their alloys. For the absorber/ generator tube, only steel or aluminium and their alloys may be used, copper and its alloys being excluded as copper reacts chemically with ammonia.

The reference refrigerator uses steel as the tube and plate material. The effect of alternate materials on the refrigerator performance is shown in Table 3. With steel tubes, the perfor- mance is improved by 13.2 and 16.6%, respec- tively, as the plate material is changed to

aluminium or copper. This improvement is caused by the higher thermal conductivity of these materials. In addition, aluminium has a lower thermal capacity. However, with alumin- ium tubes, the improvement in performance compared with the reference collector is 6.6, 16.3 and 19.7%, respectively, with steel, alumin- ium or copper as plate material. Thus, the choice of plate material alone has a more sig- nificant effect on performance than the choice of tube material alone.

Let the collector with steel plates and steel tubes be referred to as the type A collector. As Table 3 shows, the lightest collector is that with aluminium tubes and aluminium plate, the absorber/generator assembly mass being roughly 53% of that of the type A collector. For simplicity, we refer to the collector with aluminium tubes and aluminium plate as type B collector.

The best performance is obtained for the collector with aluminium tubes and copper plate, followed closely by the type B collector, its COP being approximately 97% that of the former. Since the type B collector is lighter and cheaper, it seems an obvious choice.

2.6. EfSect of tube size

The absorbent is packed in the annular space between two coaxial tubes, usually of the same materials. If all other parameters remain con- stant, the size of the inner and outer tubes determines the cross-sectional area, and hence the total mass of the absorbent in the bed, the annular gap for heat transfer across the bed, and the total thermal capacity of the absorber/generator tube. The thermal capacity of the latter includes contributions from the absorbent and the tube materials.

The inside and outside diameters of standard weight welded and seamless steel pipes (schedule 40), taken from Doolittle and Hale (1984) for 3-152 mm nominal diameters, are used.

Table 3. Effect of pipe/plate material combination

Type of material ($/$jj, Condensate mass, Mass of ice produced, Effective Evaporation

Tubes Plate kg m-* kJ me2 cooling COP time, h

Steel Steel 1.0 1.0653 1.6270 0.8334 0.0560 7.51 Steel Aluminium 0.9586 1.2044 1.9527 0.9423 0.0634 7.86 Steel Copper 1 SO083 1.2491 2.0204 0.9690 0.0652 8.04 Aluminium Steel 0.5685 1.1300 1.7848 0.8862 0.0596 7.87 Aluminium Aluminium 0.5274 1.2467 2.0095 0.9652 0.0651 8.14 Aluminium Copper 0.5772 1.2925 2.0926 0.9933 0.0670 8.38

Key: M, = mass of absorber/generator assembly (excluding glazing); MA = mass of absorber/generator assembly (excluding glazing) for collector with steel tubes and steel plate.

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82 S. 0. Enibe and 0. C. Iloeje

The size of the inner (ammonia distribution) tube of the absorber/generator was varied from Dd =0.015 to 0.042 m, the dimensions of the outer tube remaining constant. The results are shown in Fig. 6. For both the type A (steel tubes and steel plate) and type B (aluminium tubes and aluminium plate) collectors, only very slight changes in performance are observed. For example, for the type A collector, the useful cooling per unit area varies from a minimum of about 0.8 MJ mm2 at D, = 0.015 m to a maxi- mum of about 0.9 MJ rne2, an increase of only 12% [Fig. 6(a)]. The percentage increase for the type B collector is even much lower, as Fig. 6(b) shows. The best values of Dd occur around 0.030 m, for both collector types [Fig. 6(c)]. The corresponding refrigerator performance indicators are given in Table 4. In general, the performance of the type B collector is about 25% better than that of type A.

The effect of the outer tube size is shown in Fig. 7, where D,, varies from 0.034 to 0.098 m,

Fig. 6. Effect of ammonia distribution tube diameter on refrigerator performance: (a) collector type- A (with steel tubes and steel plate); (b) collector type B (with aluminium tubes and aluminium plate); (c) collector types A and B.

the size of the ammonia distribution tube remaining constant. For both collector types, the refrigerator performance varies somewhat parabolically with the size of the outer tube, the peak performance occurring at about D,,=O.O55 m. The corresponding values of the COP and other indicators are shown in Table 4. The two collector types have virtually the same performance at low tube sizes (Dpp ~0.04 m), because of thermal capacity effects. However, at larger tube sizes, the type B collector has up to 23% better performance.

2.7. Effect of collector tube spacing

The test collector uses six absorber/generator tubes bonded to the absorber plate at a pitch of 0.152 m. The tube spacing, IV,,, determines the fin efficiency, qr, defined as the ratio of the actual heat flow rate at the base of the fin to that which would occur if the entire fin were at the base temperature at steady state. The fin efficiency is given by Duffie and Beckman (1980) as

where

rlr = tanh@,)/&, (2)

Qf=W/(Q$d1°~5W’p -Dp& (3)

In turn, ylf influences the collector efficiency and hence the refrigerator coefficient of perfor- mance. Hollands and Stedman (1992) showed that by using an absorber fin with a step change in local thickness, up to 25% savings in material could be achieved with only a 5% loss in fin efficiency. However, the majority of solar collec- tors still use rectangular fins with uniform thick- ness because of ease of manufacture. The rectangular shape of the absorber plate used in the experimental collector was therefore not changed.

The effect of tube spacing on the refriger- ator performance is shown in Fig. 8, where the tube spacing is varied in the range 0.06 I IV, I 0.21 m, all other parameters not dependent on WP remaining constant at their reference values. As W, increases, the perfor- mance parameters Mnh3, Mice, Q and COP all increase up to their respective maximum values, and thereafter decrease. Since the amount of absorbent is fixed, increasing W,, increases the exposed collector area, leading to higher total incident radiation per unit mass of absorbent, higher condensate yields, and hence higher cool- ing capacity. With increasing W,, however, the mean plate temperature increases and the fin

Page 7: 32-DESIGN OPTIMIZATION OF THE FLAT PLATE COLLECTOR  A.pdf

Flat plate collector for a solar refrigerator

Table 4. Optimal values of the collector specifications for single parameter variation

83

Refrigerator performance at optimal value

Condensate mass, Single parameter varied Optimal value kg m-*

(a) Collector with steel tubes and steel absorber plate Plate emissivity” 0.3 1.4435 Tube spacing, m 0.08 1.223 Collector tube OD, m 0.055 1.0228 NH, distribution tube OD, m 0.033 1.0735

(b) Collector with aluminium tubes and aluminium absorber plate Plate emissivitp 0.26 1.8435 Tube spacing, m 0.09 1.5196 Collector tube OD, m 0.055 1.1779 NH, distribution tube OD, m 0.033 1.369

Mass of ice, Useful cooling, kg me2 MJ mm2

2.5008 1.250 0.0746 1.408 1.0257 0.0679 1.5665 0.8134 0.0545 1.7178 0.6669 0.0613

2.7928 1.25 0.08478 2.0836 1.2532 0.08431 1.9147 0.9291 0.06403 2.2888 1.0570 0.07169

COP

“This is the minimum plate emissivity with a reabsorption time 5 11 h.

Fig. 7. Effect of collector tube diameter on refrigerator per- formance: (a) collector type A (with steel tubes and steel plate); (b) collector type B (with aluminium tubes and alu-

minium plate); (c) collector types A and B.

efficiency falls, leading to an overall lowering of the collector efficiency as the heat loss rate rises. This causes the observed reduction in the refrigerator performance after a certain value of W,. Optimal spacings occur at 0.08 and

tors, respectively. The corresponding values for the condensate yield, mass of ice produced, useful cooling and COP are given in Table 4.

2.8. Efect of absorber plate emissivity The efficiency of solar energy collection can

0.09 m for the all-steel and all-aluminium collec- be improved considerably by the use of selective

0 \ ,

0

Fig. 8. Effect of collector tube spacing on refrigerator perfor- mance: (a) collector type A (with steel tubes and steel plate); (b) collector type B (with aluminium tubes and aluminium

plate); (c) collector types A and B.

Page 8: 32-DESIGN OPTIMIZATION OF THE FLAT PLATE COLLECTOR  A.pdf

84 S. 0. Enibe an d 0. C. Iloeje

coatings on the absorber surface. Consider the radiative heat exchange between a flat plate absorber at Tp and a glass cover at Tg. If aP is the solar absorbance of the plate and z the transmittance of the glass cover, then the rate of energy absorption per unit area is given by

qabs = @p zz~ (4)

where I is the incident solar radiation intensity. The radiative heat loss from the plate to the glazing, assuming infinite parallel plates, is given by

q1oss = a(T; -T;)

l/Ep+l/Eg-l. (5)

The above relations are incorporated in the collector heat balance equation used in develop- ing COSSOR. Selective surfaces which have high solar absorbance (~~20.9) and low ther- mal emittance (0.1 I cp 50.3) are commercially available (Norton, 1992).

The effect of collector plate emissivity on the refrigerator performance is shown in Fig. 9 for 0.1 se, 10.9, with aP kept constant at 0.9. As the plate emissivity is reduced, reduced heat losses [see eqn (5)] cause the mean plate and absorbent temperatures to rise, leading to increased condensate yields. Consequently, the mass of ice produced, the useful coefficient of performance and useful cooling increase. The refrigerator with aluminium tubes and plate performs much better than that with steel at ep > 0.2, but less at lower emissivity values. This is because of thermal capacity effects. If weight considerations are not critical, the all-steel col- lector may be used in place of the aluminium collector if a good selective absorber is utilized, especially in view of its lower cost.

As a result of the greater mass of refrigerant to be reabsorbed and the reduced collector heat loss rate, the reabsorption time increases with decreasing ep. The minimum values of cp which gave the highest COP with the absorption time remaining less than 11 h is taken as optimal and these are 0.34 and 0.26 for the refrigerator with all-steel and all-aluminium collectors, respectively. At these values, the condensate yield, mass of ice produced, coefficient of performance and effective cooling are show in Table 4. If lower values of emissivity are required, additional collector cooling strategies will have to be adopted, especially for the evaporation mode.

01 02 03 0.4 05 06 0, 0.s 09 3 , ( 3

1 I - 0, 0.2 03 04 05 0.6 0.7 08 0.0

“1 I

004 1 I 01 02 03 04 05 0.6 07 08 09

Absorber plate emmlssm,ty

Fig. 9. Effect of absorber plate emissivity on refrigerator performance: (a) collector type A (with steel tubes and steel plate); (b) collector type B (with aluminium tubes and

aluminium plate); (c) collector types A and B.

3. COLLECTOR OPTIMIZATION

The goal of optimization, in general, is to select the best set of several independent vari- ables in order to maximize or minimize a given performance criterion (or objective function). This is best carried out when the objective function can be expressed as an explicit function of the independent variables.

From the parametric studies presented in Section 2, it may be observed that of all the collector parameters considered, the most sig- nificant effects on the refrigerator performance result from the absorber plate emissivity and material, the size of the outer collector tube and its spacing on the absorber plate, as well as the number of glazing. The latter is usually limited to 2, while the choice of material is represented in the two collector types identified previously as types A and B. Letting the other parameters remain constant at their reference values, we seek to optimize the refrigerator performance

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Flat plate collector for a solar refrigerator 85

by adjusting the values of the three remaining parameters (outer collector tube size and spac- ing, and plate emissivity) for collector types A and B. Using the performance data presented in Figs 7-9, as well as further data generated for several randomly selected sets of collector parameters, together with other relevant data for the refrigerator system, any of the perfor- mance criteria may be correlated with an equa- tion of the form

where

Z,=(l-Xi)/(l-X,), for k=1,2,3, (7)

z, =X, +X* +X,, (8)

xl = LDpp -Dpp,minIl[Dpp,max -Dpp,minl~ (9)

x3 =Ep, (11) Wp.min = Dpp,min = Dd + Dgr Y (12)

and the exponent b is given in Table 5. In this way, the dimensionless parameters

Xi, X, and X, are within the range of O-l. The refrigerator useful coefficient of performance, COP, and the time for complete reabsorption, t evap, are correlated in this way using the linear regression algorithm described by Kuester and Mize (1973). The coefficients ai,j are given in Table 5. It should be noted that the dependence

of the coefficients on the environmental vari- ables is yet to be determined. They are therefore strictly applicable to conditions near those of Section 2.1, but may be used, with caution, for quick estimates at other conditions.

For a solar refrigerator, the most important performance criterion is the useful coefficient of performance, COP, which is to be maximized. The solar collector mass per unit area, MJA,, should be minimized. An objective function which combines these criteria may be given as

COP P-=/i,

WA:. -+A,---- COP WA, ’

(13)

where 1, and 1, are weighting factors which are assigned based on pragmatic considerations. We take A1 =0.8 and i, =0.2. The mathematical accent, ‘, refers to the reference collector.

In order to obtain the values for Xi, X, and X, which optimize the refrigerator performance, the regression equations are employed in the constrained Rosenbrock sequential search opti- mization procedure adapted from Kuester and Mize (1973). The objective function 9, defined in eqn (13), is utilized, subject to the following constraints:

OlXi < 1, for i= 1,2,4, ( 14) 0.1 IX, 50.9. (15)

The implicit variable, X, = tevap/l 1, is utilized to take advantage of the fact that the time available for nighttime reabsorption may be no more than about 11 h in a tropical environment (Iloeje, 1985).

Having obtained the best values for X1, X, and X, in this way, they are substituted in the COSSOR programme and used to determine

Table 5. Correlation coefficients and exponent for use with eqn (6)

Collector with steel tubes and steel plate Collector with aluminium tubes and aluminium plate

NH, Useful Evaporation NH3 Useful Evaporation i COP yield cooling time COP yield cooling time

0 1 2 3 4 5 6 7 8 9 R2 b

-4.2265 -24.641 - 17.792 -5.1506 6.4078 36.234 23.093 7.3136

-2.7436 - 13.523 -8.4631 -2.1276 3.4431 22.035 13.907 4.2669

- 1.5442 -9.7893 - 5.4962 - 1.6891 - 2.4483 - 17.685 -9.5242 - 3.8929

1.1028 7.4702 4.0438 1.4000 0.0059 -0.1421 0.1685 -0.4957 0.0312 1.4098 0.5064 0.8296

-0.0417 - 1.2445 -0.9187 -0.5309 0.936 0.774 0.7755 0.6711 1.3 1.6 1.7 2.0

-5.7189 - 35.790 - 33.079 -21.475 9.8337 65.158 52.258 24.131

-4.3593 -27.120 -21.798 - 9.9098 3.0241 23.033 16.725 11.569

- 1.3780 - 10.759 - 7.4870 -4.8261 -2.8045 - 24.479 - 13.525 0.2219

1.3733 10.619 6.7296 0.2151 0.0680 1.1138 1.0356 0.2396 0.0350 1.1650 0.6656 0.4364

-0.0836 - 1.5090 - 1.3234 - 0.4492 0.908 1 0.9252 0.9029 0.9001 1.3 1.3 1.3 1.5

RZ = regression coefficient; b = exponent in eqn (7); NH, = refrigerant condensed.

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86 S. 0. Enibe and 0. C. Iloeje

the optimum refrigerator performance. For the collector with steel tubes and steel plate, the maximum value of the objective function was obtained for X1 = 0.3381, X2 = 0.7827 and X, = plate emissivity = 0.1. In terms of the physi- cal dimensions, this implies D,,= 0.057 m and W, = 0.172 m. The refrigerator coefficient of performance obtained with these data using the COSSOR programme is 0.0731, corresponding to a useful cooling of 1.12 MJ rn-’ and an ice production rate of 2.51 kg mP2. Direct compu- tation of the data from eqn (6) gave similar results. At the optimum value, the COP is about 31% better than that of the reference collector.

Similarly, for the collector with aluminium tubes and aluminium plate, the maximum value of the objective function was obtained for X1 = 0.3869, X2 = 0.3968 and X, = 0.6345 (equal to plate emissivity). Hence, the optimum choices of D,, and W, are 0.06 and 0.104 m, respec- tively. The resulting refrigerator coefficient of performance is 0.0726, corresponding to a useful cooling of 1.1 MJ me2 and an ice production rate of 2.03 kg mP2. The improvement in perfor- mance compared with the reference collector is about 30%. It is interesting to note that the aluminium collector requires only a modest level of plate selectivity to achieve the same high performance compared with the steel collector.

It should be pointed out that these optimal data are indicative, as cost considerations were not included. Further, different climatic condi- tions from those used in the test would result in different optimal values.

For both collector types, it may be seen that at least a 30% increase in the coefficient of performance can be achieved by optimizing the choice of parameters. The limit of the coefficient of performance appears to be 0.08 under the conditions of the test. For higher performances, additional arrangements for cooling of the col- lector plate during the reabsorption mode would have to be devised. Currently, the collector cooling during this mode is enhanced by the flow of ambient air through the inner air layer shown in Fig. 1 because of natural convection. Further improvements in the COP may also be achieved by modifying the design of the evaporator coil.

4. CONCLUSIONS

The following conclusions may be drawn from the foregoing parametric and optimiza- tion studies.

(1)

(2)

(3)

Significant improvements in the refrigerator performance may be obtained through a careful choice of a number of collector parameters, especially the plate emissivity, spacing/size of the collector tube, and mate- rial of the collector tube and absorber plate. An increase of up to 25% in the coefficient of performance is possible by varying only a single parameter, notably the plate emis- sivity or tube spacing. A multivariable optimization of the collec- tor has been demonstrated. For the particu- lar conditions tested, the optimum choice of parameters for the all-steel collector is D,,=O.O57 m, W,=O.17 m and c,=O.l. A COP of 0.0731 is obtained with this collec- tor. For the all-aluminium collector, D,,=O.O6m, W,=O.l04m and ~~=0.63 gave optimum performance. The COP for the refrigerator with this collector is 0.0726. An improvement of at least 30% in the performance of the refrigerator is thus pos- sible by optimal choice of parameters with- out the need for additional collector cooling arrangements. The limit of the COP for the conditions of the test is about 0.08. To achieve perfor- mances higher than this, enhancements in the collector cooling during the reabsorp- tion mode and the evaporator coil heat transfer characteristics will be required.

NOMENCLATURE

A area (m’) a correlation coefficient

COP useful coefficient of performance D outside diameter (m) d inside diameter (m)

S objective function Z incident solar radiation intensity (W mSZ)

ID inside diameter (m) k thermal conductivity ( W m- 1 K)

A4 mass (kg) OD outside diameter (m)

Q useful cooling per unit area (J rnm2) q,,; absorbed solar-radiation intensity (W m-‘) qt.,.. radiative heat loss rate (W m-‘)

T temperature (K) t cvap time for complete evaporation (h)

U, collector heat loss coefficient (W m-* K-‘) W, collector tube spacing (m)

X dimensionless parameter defined in eqns (9)-( 11)

Greek letters clp plate solar absorbance e emissivity 6 porosity p density (kg m-“)

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Flat plate collector for a solar refrigerator 87

qr fin efficiency (%) $r fin efficiency parameter defined in eqn (3) 6 thickness (m) 5 solar transmittance i, weighting factor

Subscripts c collector/absorber/generator assembly d ammonia distribution tube g glass cover

gr absorbent pellet or granule ice ice

max maximum min minimum nh3 ammonia

s packed absorbent salt p collector plate

pp outer collector tube

Ackno&dgemenfs-The authors wish to acknowledge the support of the International Foundation for Science, Stockholm, Sweden, through grant G/1503-1 and the National Centre for Energy Research and Development, University of Nigeria, Nsukka, Nigeria. Improvements to the analysis, the COSSOR programme and this paper were undertaken while the first author was on study leave at the Italian Agency for New Technologies, Energy and the Environment (ENEA) in Rome, Italy, under the joint sponsorship of ENEA and the TRIL Programme of the International Centre for Theoretical Physics (ICTP), Trieste, Italy, for which we are grateful. The comments of three anonymous reviewers were found invaluable, and are hereby acknowledged.

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