Design, construction, performance evaluation and economic analysis of an integrated collector storage system

~

Pergamon

Renewable Eneryy, Vol. 12, No. 2, pp. 17%192, 1997 ~ 1997ElsevierScienceLtd All rights reserved.Printedin Great Britain PII : S0960-1481 (97)00029-3 0960-1481/97 $17.00+ 0.00

TECHNICAL NOTE Design, construction, performance evaluation and economic analysis of an integrated collector storage system SOTERIS K A L O G I R O U Mechanical Engineering Department, Higher Technical Institute, P.O. Box 423, Nicosia, Cyprus

(Received 20 February 1997; accepted 15 March 1997) Abstract--The design and construction of an Integrated Collector Storage (ICS) system is presented in this paper. The main advantage that such a collector system presents, with respect to conventional flat-plate collectors, is the fact that it is of a very low profile. The main disadvantage of these collectors comes from the design of the system, i.e. with the receiver of the collector being also the storage vessel, it is not possible to insulate it properly and there are significant heat losses during the night. System modelling and optimisation is carried out by the use of a computer code written for the purpose. Performance results presented are in good agreement with the predicted results, especially for the end-of-day storage temperature which is predicted to within 5.1%. The initial cost of the system presented here is 13% cheaper than the corresponding flat-plate (FP) collector of the same aperture area and storage volume. Additionally, the economic analysis of the two systems, performed with the F-Chart program, showed a yearly F-value of 0.85 for the ICS system compared to 0.83 for the FP system, a pay-back period of nine years for the ICS system, compared to 11 years for the FP system and a life cycle saving of C£330 for the ICS system compared to C£201 for the FP system. © 1997 Elsevier Science Ltd.

1. INTRODUCTION Low temperature water heating in Cyprus and in many parts of the world is usually satisfied by flat-plate thermosiphon solar collectors. The development of simpler and cheaper solar energy devices will help in the spread of solar energy as a means of producing hot water from renewable energy sources. Additionally, the main disadvantage of flat-plate collectors is the fact that they are comparatively tall units which makes them unattractive aesthetically. In Cyprus, as a result of the frequent short term cuts in water supply, a cold water storage tank is installed on top of the solar collector, supplying both the hot water cylinder and the cold water needs of the house, thus making the collector unit taller and even less attractive. The main disadvantage of the ICS systems is the high thermal loss from the storage tank to the surroundings, since most of the surface area of the storage tank cannot be thermally insulated as it is intentionally exposed for the absorption of solar radiation. In particular, the thermal losses are greatest during the night and overcast days with low ambient temperature. Due to these losses, the water temperature drops substantially during the night especially during the winter. In this paper, the design, modelling and optimisation of the system are presented. This is followed by a description of the method used to construct the collector. The performance of the system is evaluated and the computer model is validated. Finally, the economic justification of the system is presented. 179

180

Technical Note 2. DESIGN OF THE SYSTEM

The design of Integrated Collector Storage (ICS) units depends on the operational characteristics of each application in relation to the environmental conditions of the particular site. ICS collectors are primarily used for domestic hot water production and are generally suitable for small scale applications in the range of 100-200 l/day. As the area and range of application coincides with that of flat-plate collectors, it is necessary to investigate the possible advantages that ICS units present against the fiat-plate ones. For the construction of the ICS model presented here, the area to volume ratio of a flat-plate collector was used, i.e. 35 1/m2, for comparison purposes. The design of the ICS system has been carried out by considering a horizontal cylindrical tank which is at the time the absorber and hot water storage. Various types of ICS units are demonstrated by Tripanagnostopoulos and Yianoulis [1]. In this paper, a different shape of collector curve is proposed. It is desirable to have collectors that have a good overall efficiency with reduced heat losses. Concentrating collectors are of such a type and this makes them suitable for high temperature applications. But, it is also desirable to have concentrating collectors that can function satisfactorily with minimum requirements for tracking. One type of concentrator, which has the capability of reflecting all of the incident radiation to the absorber within wide limits, is the compound parabolic concentrator (CPC). Their potential as collectors of solar energy was pointed out by Winston [2]. These are more useful as linear or trough-type concentrators and any radiation entering the aperture within the collector acceptance angle, will be reflected to an absorber by specularly reflecting parabolic mirrors. The acceptance angle is defined as the angle through which a source of light can be moved and still converge at the absorber. The orientation of a CPC collector is related to its acceptance angle. A possible orientation for such a collector is along a horizontal east-west axis, sloped towards the equator at an angle equal to the local latitude. The minimum acceptance angle in this case should be equal to the maximum incidence angle projected in a north-south vertical plane during the times when output is needed from the collector. In practice, bigger angles are used to enable the collector to collect diffuse radiation at the expense of a lower concentration ratio. Smaller (less than 3) concentration ratio CPCs are of greatest practical interest. These are able to accept a large proportion of diffuse radiation incident on their apertures and concentrate it without the need of tracking the sun [3]. 2.1. Design of the collector shape From the many shapes of the nonimaging CPC collectors, the cusp type is chosen. A fully developed cusp concentrator for a cylindrical receiver is shown in Fig. 1. The particular curve illustrated has an acceptance half-angle, 0A, of 60 ° or a full acceptance angle, 20A, of 120°. Each side of the cusp has two mathematically distinct segments smoothly joined at a point P related to 0A. The first segment, from the bottom of the receiver to point P, is the involute of the receiver's circular cross section. The second segment is from point P to the top of the curve, where the curve becomes parallel to the yaxis [4].

Y

On + nl2

Fig. 1. Fully developed cusp.

Technical Note

181

Y T

X

Fig. 2. Mirror co-ordinates for ideal nonimaging cusp concentrator.

With reference to Fig. 2, for a cylindrical receiver the radius R and acceptance half-angle, 0A, the distance, p, along a tangent from the receiver to the curve, is related to the angle 0, between the radius to the bottom of the receiver and the radius to the point of tangency, 7", by the following expressions for the two sections of the curve [4] : p(O) = RO,

101 ~< 0A + n / 2

(the involute part of the curve)

nf{0+0A +~/2--COS (0-- 0A)}) p(0) = ~ -1+~nn (0--~A)A) ~,

0A+~/2 ~ 0 ~< 3~/2--0A.

(1)

The two expressions for p(O) are equivalent for the point P in Fig. 1, where 0 = 0A+~/2. The curve is generated by incrementing 0 in radians, calculating p and then calculating the co-ordinates, X and K by: X = RsinO-pcosO

Y = -- R cos 0 - p sin 0.

(2)

Figure 1 shows a full untruncated curve which is the mathematical solution for a reflector shape with the maximum possible concentration ratio. The reflector shape shown in Fig. 1 is not the most practical design for a cost-effective concentrator, because reflective material is not effectively used in the upper portion of the concentrator. As in the case of the compound parabolic collector, a theoretical cusp curve should be truncated to a lower height and slightly smaller concentration ratio. Graphically, this is done by drawing a horizontal line across the cusp at a selected height and discarding the part of the curve above the line. Mathematically, the curve is defined to a maximum angle 0 value less than 3~/2-0A. The shape of the curve below the cut-off line is not changed by truncation, so the acceptance angle used for the construction of the curve [using eq. (1)] of a truncated cusp is equal to the acceptance angle of the fully developed cusp from which it was truncated. A large acceptance angle of 70 ° is used in this design so that the collector is able to collect as much diffuse radiation as possible. The fully developed cusp together with the truncated one is shown in Fig. 3. The receiver radius considered in the construction of the cusp is 0.24 m. The actual cylinder is 0.20 m (Section 2.2). This is done in order to create a gap at the underside of the receiver and the

Truncation

=X Fig. 3. Truncation of a nonimaging concentrator.

182

Technical Note Glass cover

Fig. 4. The final collector.

edge of the cusp, in order to minimise the optical and conduction losses. The actual acceptance angle of the truncated cusp for a receiver diameter of 0.20 m is 75 ~'. The final design of the collector is shown in Fig. 4. The dimensions of the low iron glass (purchased by a local flat-plate collector manufacturer) are 1.95 x 0.95 m. The collector width finally used is 0.925 m, so that there is enough space at the collector edges for fixing the glass cover. The same is true for the two ends. Therefore, the final collector aperture is 1.77 m 2 which, in combination with the absorber diameter used, gives a concentration ratio of 1.47. 2.2. System modelling and optimisation The modelling program used for this optimisation is called ICS and is written in BASIC language. The program simulates the system during the energy collection period (day-time) and during the cooling-down period (night-time). It is used to determine the end-of-day storage temperature, the daily heat gain of the system and the next morning storage temperature. The principle of operation of the program is that it employs the value of beam and diffuse solar radiation on a horizontal surface and ambient air temperature from a reference year for Nicosi~Cyprus, developed previously [5]. The values are corrected hourly for the collector orientation. In the analysis, a representative day for each month is taken as shown in Table 1. These are chosen because the value of extraterrestrial solar radiation is closest to the month's average at that day [6]. The program flow chart is shown in Fig. 5. The model considers the sun's heat input to the collector from which the heat losses are subtracted, in order to estimate the useful energy stored in the collector absorber. The optical efficiency of the collector is calculated from the following relation : no = z~pN(1 - - A f ) cos (0).

(3)

The input energy is calculated from : (4)

Q = Ru~Aan o

where R~) is the solar radiation at the hour of estimation calculated from the direct and diffuse components according to the procedures outlined by Duffle and Beckman [6] for the collector inclination, and Aa is the collector aperture area. The heat balance of the system is shown graphically in Fig. 6. For simplicity, the temperature Ta~ shown in Fig. 6 is considered as the mean between the storage tank temperature (Ts) and the ambient temperature (Tq~) at the hour of calculation. The various heat losses from the system are estimated using the following relations :

Table 1. Average day of each month used in simulations Month January February March

Day 17 16 16

Month April May June

Day 15 15 11

Month July August September

Day 17 16 15

Month October November December

Day 15 14 10

Technical Note

183

8TART

R E A D W E A T H E R DATA F R O M P I L E

INPUT REQUIRED DATA

I

_1

I

I

G E T M O N T H L Y DATA F R O M

8UEROUTINE

v I

1 FOR EACH HOUR

II

I "T'"ATE'UN

ANOL"

I

I E$TIMATE RADIATION FALLING ON COLLECTOR APERTURE I

I

EETIMATE OPTICAL EFFICIENCY AND INCIDENT RADIATION

I

FOR EACH CALCUATION STEP

I "T "ATE NEAT LO""

I

I EETi"ATE U''FUL EHE"Y

I

t

@o I .T,.ATE

I .T,.ATE

.EW T. I + T.ER.AL EFF~,EHCY

I

@,...o

I

RINT END OF HOUR RESULT8

FOR EACH HOUR OF NIGHT-TIME

I .TI'ATEHEATLO"EE

I

I

I

.T,.ATENEWT.

I

() ;~-

NO

I

PRINT RESULTS

()

I

Fig. 5. Program ICS flow chart.

184

Technical Note T(j)

~Qg Qr

Glass cover ,~ Qe

Air

Absorber

Tal

TO)

k.._Insulation

~

Qi

Fig. 6. Graphical representation of the system's heat balance.

2.2.1. Convection heat losses from the absorber. Qc = (T~ - Tal)gDL(Nuk/D)

(5)

where N u is the Nusselt number for laminar flow for horizontal cylinders and is found from [7] : 0.518 (Gr/Pr) °25 N u = 0.36+ (1 + (0.559/Pr)0.5625) °444

(6)

2.2.2. Radiation heat losses from the absorber.

Qr = trnOL~(Ts + 273) 4 -- (T~ + 273) 4 .

(7)

2.2.3. Heat losses from the glass cover.

Qg = Nu(k/e)(Tal - To~)

(8)

where P is the perimeter of the glass. The value of N u applied is for inclined surfaces and can be obtained from [7]: N u = 0.14{(GrPr) I/3 - (108pr) ~/3} + 0 . 5 6 ( G r P r cos 0) TM.

(9)

2.2.4. Heat losses from the collector walls. Q, = g.4(Tal

-

-

T0~).

(10)

Finally the useful energy can be obtained from :

Qu = O - ( Q c +Qr+Og +Qi)

(11)

The new storage temperature Tsn is found from : Tsn = Ts+Qu/(419OM)

(12)

where M is the mass of the water in the absorber (kg). F o r the night-time heat losses the same relations as eqs (5)-(10) are used with the initial storage temperature being equal to the end-of-day storage temperature. The new storage tank temperature (T~n) is estimated from : Tsn = Ts -- QL/(4190 M)

(13)

where QL is the sum of all losses. The width-to-length ratio determines how much area is lost due to shading at off-normal conditions. For fixed volume to area ratios, the a m o u n t of heat losses from the tank is also affected as the diameter-to-length ratio of the tank changes accordingly. The objective is to find the size of a system

Technical N o t e

185

Table 2. Collector configurations simulated for system optimisation Configuration

Collector width (m)

Collector length (m)

Absorber diameter (m)

0.80 1.00 1.33

2.5 2.0 1.5

0.18 0.20 0.24

1 2 3

Notes : (1) Collector aperture = 2 m 2. (2) Absorber capacity = 65 1.

which collects the maximum possible amount of solar energy whilst at the same time keeping the thermal losses to a minimum. The optimisation was carried out by considering three different configurations as shown in Table 2. The results of the program are shown graphically in Fig. 7 where the end-of-day and next-morning storage temperatures are plotted for the various months of the year. It can be seen from Fig. 7 that configuration #1 gives the highest end-of-day storage temperature, but a low next-morning temperature. Configuration #3 gives lower values for both temperatures, whereas configuration #2 is a compromise between the two and it was therefore selected. 3. CONSTRUCTION OF THE SYSTEM The prototype collector model was constructed with medium density fibres ( M D F ) wood 18 m m in thickness. This is a synthetic type of w o o d which has good dimensional stability, is able to withstand fine cuts and exhibits very good resistance to humidity. The shape of the curve drawn on A u t o C A D and plotted accurately on a plotter, was glued on a piece of M D F , which was then crafted as accurately as possible to the line of the curve. This piece of M D F was used as a guide for the production of the other pieces required, on a vertical spindle moulder machine. The cusp forms constructed in this way were fastened perpendicularly, on another piece of M D F w o o d (Fig. 8). Care was taken to fix the cusp forms in line. On the inside of these forms 0.5 m m galvanised sheet metal was fixed with small screws. On the surface of this sheet a self-adhesive reflective material (scotchcal 5400) was fixed. Glasswool insulation was used on the outside surface of the collector space covered with pieces of galvanised sheet metal. A more permanent and practical model of the collector will be constructed with fibreglass using the method described by Kalogirou et al. [8]. In this case polyurethane insulation will be used, injected in the cavity of the collector wall created with fibreglass. This method of construction was considered in the economic analysis that follows (Section 5). The material was used for the construction of the collector absorber is copper painted with selective

90 80 End-of-day storage

. j . < ~ . . . . -o" " ' ~ - ~

70 60 50 40 30 20 10 0

Next day ~ o m g e

.........

case #2

temperature °C

.......

case #3

I

I

I

I

I

l

F

M

A

M

J

J

A

S

Month

Fig. 7. Output from the simulation program.

I

I

O

N

D

186

Technical Note

Fig. 8. Method of cusp concentrator construction.

paint with absorptance of 0.9 and emittance of 0.1. No special selective treatment of the absorber surface was used in an attempt to reduce cost. The side view of the collector which incorporates the cold-water tank is shown in Fig. 9. The total height of the complete set-up is 1.35 m. This height exhibits a significant reduction as compared to a height of about 3 m of the normal flat-plate collector system. A circular cold-water tank would reduce the overall height even more. 4. SYSTEM PERFORMANCE EVALUATION The system was setup as described in Section 3 and its performance was evaluated by measuring the end-of-day storage temperature, and the storage temperature at the morning of the next day. These two temperatures are used for validating the simulation program ICS and are considered as the most important parameters to the end user. In this way the effectiveness of the system during the solar energy collection period (day-time) and during the cooling-down period (night-time) can be evaluated. The results for one complete year are shown in Table 3, together with the corresponding values obtained from the simulation program ICS and the percentage differences between the two. The actual values of temperatures tabulated in Table 3 are the mean values of readings obtained over a number of days (five minimum) in which the day shown in Table 1 is included. It can be seen from Table 3 that the modelling program is fairly accurate for the estimation of the end-of-day storage temperature (maximum difference 5.1%), whereas the deviation for the next morning temperature is greater (11.3%). This is mainly attributed to the wind-transfer model for the heat losses from the glass used in the program and to the accuracy of the U-value considered for the collector wall. In any case the results quantify the magnitude of the expected disadvantage of this type of collector. It is believed by the author that this disadvantage will be greatly reduced by the use of polyurethane insulation for the collector walls and transparent insulation for the glass cover.

_

'"o

T

Cold water tank II e-

I

N~

City water supply

Fig. 9. The complete system.

Y~ [--

Technical Note

187

Table 3. Comparison of actual and predicted results End-of-day storage temperature (°C) Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

Next morning storage temperature ('~C)

Model

Actual

% Diff.

Model

Actual

% Diff.

41.2 51.3 63.1 70.5 70.1 75.9 82.3 86.2 83.4 71.5 51.9 44.2

40.2 49.6 59.9 68.3 66.6 73.2 81.5 82.9 79.3 68.2 50.5 42.6

2.4 3.3 5.1 3.1 5.0 3.6 1.0 3.8 4.9 4.6 2.7 3.6

16.5 21.0 26.6 30.6 32.5 37.2 41.1 43.1 40.2 34.3 23.7 18.4

15.2 18.9 24.2 28.0 29.0 33.0 39.9 41.2 37.1 32.6 22.3 17.1

7.9 10.0 9.0 8.5 10.8 11.3 2.9 4.4 7.7 5.0 5.9 7.1

5. ECONOMICS A cost comparison will be attempted here, to compare the initial cost of the system to that of a fiat-plate collector. A cost breakdown of the present system for the 1.77 m 2 aperture area is shown in Table 4. The cost breakdown for the complete system which includes two ICS panels, a cold water tank, framework, valves, piping and insulation, and labour, is shown in Table 5. It can be seen from Table 5 that the total cost of a complete ICS system is C£542. The corresponding fiat-plate collector of the same collector area, hot water storage and cold water tank size is C£610. Therefore, the proposed system exhibits a 13% reduction. The costing, however, should be investigated over the life of the system for which the performance characteristics of the system are required. For the economic analysis the F-Chart program developed by the University of Wisconsin [9] was used. The program runs through the values of mean monthly solar radiation and mean monthly air temperatures which are detailed in Ref. [10] and may not be repeated here. The program calculates the following :

Table 4. Cost breakdown of the ICS panel Item Cusp (made from fibreglass at C£14/m 2) Reflective material a t C £ 8 / m 2 Hot water cylinder/absorber Sheet metal for back cover Glassing complete with rubber seal Insulation Labour Sub-total Design, supervision, overheads and profit @ 30% of sub-total Total cost

Cost (C£) 45 25 30 7 8 10 30 155 47 202

Technical Note

188

Table 5. Cost breakdown of the complete system Item

Cost (C£)

2-ICS panels Framework Cold water tank Valves, piping and insulation Installation labour cost Total

(1) (2) (3) (4)

404 30 60 20 30 542

Amount of solar radiation falling on the collector surface [GJ]. Domestic hot water load [G J]. Auxiliary load required to cover the load [GJ]. F-value, i.e. the solar fraction (heat gain as a fraction of the total heat requirements).

The program requires two sets of parameters : (1) System parameters. (2) Economic parameters. The system parameters required by the program are shown in Fig. 10. The heat loss coefficient and net energy delivery, as obtained from the actual performance results, are 6.3 W/°C and 26370 k J/day,

City call number .............. 346 No. of u n i t s t e s t e d . . . . . . . . . . . 2 Glazing area per unit ......... 1.77 C o l l e c t o r h e a t l o s s c o e f f i c i e n t 6.3 Collector net energy delivery 26370 Collector slope ............... 35 Collector azimuth (South=0)... 0 Incidence angle mod type(9-11) 9 N u m b e r of g l a z i n g s . . . . . . . . . . 1 Inc angle modifier constant. 0 Inc angle modifier value(s). 1 .999 .998 .995 .981 .953 .882 .7 .35 0 Fuel (I=EL,2=NG,3=OIL, 4=OTHER) 1 E f f i c i e n c y o f f u e l u s a g e ...... 100 Daily hot water usage ......... i00 W a t e r set t e m p e r a t u r e . . . . . . . . . 60 ICS unit tank volume .......... 130 U A of a u x s t o r a g e t a n k . . . . . . . . 0 Aux environment temperature... 20 F i r s t m o n t h of u s e (1-12) ..... 1 Last m o n t h o f u s e (1-12) ..... 12

m2 W/°C KJ/DAY Deg. Deg.

% LITERS °C LITERS W/°C °C

Fig. 10. System parameters used in the F-Chart program.

Technical Note

189

respectively. The economic parameters required by the program are shown in Fig. 11. The system is analysed economically over a 15-year period. The alternative fuel considered in both cases is electricity, price 0.053 C£/kWh, which is used at 100% efficiency (immersion heater). The output of the program is shown in Fig. 12. Similar analysis is performed for the flat-plate collector system of the same size. A comparison of the parameters obtained from the economic analysis are shown in Table 6. It can be seen from Table 6 that the ICS system is better in all respects than the corresponding flatplate collector system. If the low profile advantage is also considered, the present system merits serious consideration for future solar energy applications. The life cycle savings shown in Table 6, are calculated by subtracting the present worth of the capital and operating costs from the present worth of the fuel savings, both calculated for the period of the life of the system. These savings represent the economic advantage of the solar system over a fuel-only system. In addition to the economic analysis, the program gives the two constant parameters of the standard collector performance equation i.e. optical efficiency = 0.57 and energy loss coefficient = 1.78 W / m > C (Fig. 12). Therefore, the collector performance equation can be written as : AT i / = 0.57-- 1 . 7 8 - - . I

(14)

The corresponding equation for the flat-plate collector system used in the analysis is : AT q = 0.77--6.78--. I

(15)

This equation applies to a well designed and produced flat-plate collector system manufactured locally. The advantage of the ICS system, during the collection period, can be seen from these

Econ analysis detail (0 T O 4). Cost per unit area ............ Area independent cost ......... Price of electricity ........... Annual % increase i n e l e c ..... Period of economic analysis... % down payment ................ Annual mortgage interest rate. Term of mortgage .............. Annual market discount rate... % extra insur & main in year 1 ANNUAL % INCREASE I N I & M .... % resale value ................

1 114 138 053 5 15 I00 9 15 8 1 2 i0

£/m a £ £/KWh % YEARS % % YEARS % % % %

Fig. 11. Economic parameters used in the F-Chart program.

Table 6. Comparison of economic parameters System FP ICS

Yearly F-value

Initial investment (C£)

Life cycle savings (C£)

Pay-back period (Years)

0.83 0.85

610 542

201 330

11 9

190

Technical Note

***

GJ JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC YR

ICS

SOLAR GJ 1.4

WATER

HEATING

LOAD GJ 0.5

LOSS GJ 0.0

1 .5

0.5

0 .0

2.0 2.2 2.2 2 .4 2.5 2.5

0.5 0.5 0.5 0.5 0.5 0.5

0.0 0.0 0.0 0 .0 0.0 0.0

2 .2

0 .5

0.0

2.0 i. 5 1 .3 23.6

0.5 0 .5 0.5 6.3

0.0 0.0 0 .0 0.0

OPTICAL EFFICIENCY ENERGY LOSS COEFF.

SYSTEM

= .57 --- 1 . 7 8

FIRST YEAR FUEL COST FIRST YEAR FUEL SAVINGS INITIAL INVESTMENT DOWN PAYMENT - TAX CREDIT 15 Y E A R M O R T G A G E PAYMENT RESALE VALUE ANNUALIZED PAYMENT LIFE CYCLE SAVINGS LIFE CYCLE COST

***

AUX

F

0.2 0.2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.2 0.2 1.0

0.55 0.69 0.83 0.94 0.99 1.00 1.00 1.00 1.00 0.93 0.69 0.54 0.85

W / m 2 °C £ £ £ £ £ £ £ £ £

14 79 542 542 0 54 87 330 742

Fig. 12. F-Chart program output.

equations; i.e. because the energy loss coefficient for the ICS system is about 1/4 that of the corresponding flat-plate collector, the ICS system works more efficiently at higher collector inlet temperature.

6. CONCLUSIONS The design, optimisation and construction of an ICS collector is presented. From the model validation it was proved that the program is in agreement with the experimental results, especially for the end-of-day storage temperature which is predicted to within 5.1%. The initial cost of the system is 13% lower than the corresponding flat-plate collector system of the same aperture area. The economic analysis gave results in favour of the ICS system when compared to a flat-plate system of the same size with values of solar contribution equal to 0.85 against 0.83, life cycle savings of C£330 against C£201 and pay-back period of nine years against 11 years. If the reduced height of the ICS system is also considered it can be concluded that the ICS system can be used effectively for domestic hot-water production.

Technical Note

191

NOMENCLATURE

A Aa Af D F Gr I k L M n 11o

N Nu P Pr

Q Qo Q~ Qg Qr

Qo QL R Ru~

Ts Ts. U

area [m 2] aperture area [m 2] geometric factor absorber diameter [m] solar fraction Grashof number solar radiation [W/m 2] thermal conductivity [J/kgK] collector length [m] mass of water in the absorber [kg] thermal efficiency optical efficiency average number of reflections Nusselt number perimeter of the glass cover [m] Prandtl number rate of input energy [W] conduction heat loss [W] heat losses through the collector walls [W] glass cover heat losses [W] radiation heat losses from the absorber [W] rate of useful energy [W] total heat losses [W] absorber radius [m] total solar radiation at the hour of estimation [W/m 2] intermediate temperature { = (Ts + Tq))/2} [K] storage tank temperature [K] new storage tank temperature [K] ambient temperature at the hour of calculation [K] Overall heat transfer coefficient [W/m 2 K]

Greek symbols AT P 0 OA o"

absorptance temperature difference { = Ti-- T.} [K] emittance distance shown in Fig. 2--reflectance incidence angle--angle shown in Fig. 2 [deg.] acceptance half-angle [deg.] Stefan Bolzmann constant { = 5.669 x 10 8 W/m 2 K} transmittance

Abbreviations CPC C£ FP ICS MDF

Compound Parabolic Collector Cyprus pounds Flat Plate Integrated Collector Storage Medium Density Fibres.

REFERENCES

1. T r i p a n a g n o s t o p o u i o s , Y. a n d Y i a n o u l i s , P., I n t e g r a t e d collector s t o r a g e systems with s u p p r e s s e d t h e r m a l losses. Solar Energy, 1992, 48, 31~43.

192

Technical Note

2. Winston, R., Solar concentrators of novel design. Solar Energy, 1974, 16, 89-95. 3. Pereira, M., Design and performance of a novel non-evacuated 1.2x CPC type concentrator, Proceedings of Intersol 85 Ninth Biennial, Congress of ISES, Montreal, Canada, 1985, Vol. 2, pp. 1199 1204. 4. McIntire, W. R., Truncation of nonimaging cusp concentrators. Solar Energy, 1979, 23, 351-355. 5. Kalogirou, S., Solar energy utilisation using parabolic trough collector in Cyprus. Masters thesis, The Polytechnic of Wales, 1991. 6. Duffle, J. A. and Beckman, W. A., Solar Engineering of Thermal Processes, 2nd Edn, John Wiley, 1991. 7. Holman, J. P., Heat Transfer, McGraw-Hill, 1989. 8. Kalogirou, S., Eleftheriou, P., Lloyd, S. and Ward, J., Low cost high accuracy parabolic troughs : construction and evaluation. Proceedings of the Third Worm Renewable Energy Congress, Reading, U.K., 1994, Vol. 1, pp. 384-386. 9. Klein, S. and Beckman, W., F-Chart, F-Chart Software. Middleton, Wisconsin, 1983. 10. Kalogirou, S. and Lloyd, S., Use of parabolic trough collectors for hot water production in Cyprus--a feasibility study. Renewable Energy, 1992, 2(2), 117-124.