Pergamon Solar Energy Vol. 60, No. I, pp. 49-59, 1997

0 1997 Elsevier Science Ltd PII: S0038492X(%)001314 All rights reserved. Printed in Great Britain

0038-092X/97 $17.00+0.00

MODELLING, OPTIMISATION AND PERFORMANCE EVALUATION OF A PARABOLIC TROUGH SOLAR COLLECTOR STEAM GENERATION

SYSTEM

SOTERIS KALOGIROU,*f* STEPHEN LLOYD ** and JOHN WARD ** * Higher Technical Institute, Department of Mechanical Engineering, P.O. Box 423, Nicosia, Cyprus, and

** University of Glamorgan, Department of Mechanical Engineering, Pontypridd, Mid Glamorgan, CF37 1DL. UK

(Received 1 April 1996; accepted for publication 12 October 1996) (Communicated by Doug Hittle)

Abstract-A parabolic trough collector (PTC) system used for steam generation is presented in this paper. PTCs are the preferred type of collectors used for steam generation due to their ability to work at high temperatures with a good efficiency. The modelling program developed called PTCDES is used to predict the quantity of steam produced by the system. The flash vessel size, capacity and inventory determines how much energy is used at the beginning of the day for raising the temperature of the circulating water to saturation temperature before effective steam production begins. Optimisation of the flash vessel pre- sented here uses a simplified version of the program PTCDES. System performance tests indicate that the modelling program is accurate to within 1.2% which is considered very adequate. Finally, the theoreti- cal system energy analysis is presented in the form of a Sankey diagram. The analysis shows that only 48.9% of the available solar radiation is used for steam generation. The rest is lost either as collector or thermal losses. 0 1997 Elsevier Science Ltd.

1. INTRODUCTION

Parabolic trough collectors (PTCs) are fre- quently employed for solar steam generation because temperatures of about 300°C can be obtained without any serious degradation in the collector efficiency. A typical application of this type of system is the Southern California power plants known as Solar Electric Generating Systems (SEGS) which have a total installed capacity to date of 354 MWe (Kearney and Price, 1992).

Three methods have been employed to gener- ate steam using parabolic trough collectors (Murphy and May, 1982):

(1)

(2)

(3)

the steam-flash concept, in which pressur- ised water is heated in the collector and then flashed to steam in a separate vessel; the direct or in situ concept, in which two- phase flow is allowed in the collector receiver so that steam is generated directly; the unfired-boiler concept, in which a heat-transfer fluid is circulated through the collector and steam is generated via heat exchange in an unfired boiler.

The flash steam generation concept has

+Author to whom all correspondence should be addressed. $ISES Member.

advantages with respect to other systems due to the superiority of water as a heat transfer fluid compared to heat transfer oils used in unfired boilers, the relatively low capital cost of the system as no heat exchanger is required, and the avoidance of any flow stability problems demonstrated in the in situ systems.

The system presented here consists of a para- bolic trough collector, a flash vessel, a high- pressure circulating pump, and associated pumps and pipework (see Fig. 1). The solar collector system works by drawing water from the flash vessel, which is circulated through the receiver of the solar collector at high pressure to inhibit evaporation into the receiver and hence prevent flow stability problems. The high- temperature, high-pressure water is flashed into steam at atmospheric pressure in the flash vessel which acts as a steam separator. The specifica- tions of the solar collector system are tabulated in Table 1.

The flash vessel is a vertical vessel (as shown in Fig. l), with the inlet for the water located about one-third of the way up its side. The standard design of flash vessels requires that the diameter of the vessel is chosen so that the steam flows towards the top outlet connection at no more than about 3 m s-l, This should ensure that any water droplets can fall through the steam in contra-flow, to the bottom of the vessel. Adequate height above the inlet is

49

50 S. Kalogirou et al.

Thermocouple number

Temperature measurement point

Collector outlet Collector inlet Flash vessel bottom Flash vessel top Ambient

STEAM OUTLET

SPRING LOADED FLASH VESSEL

FLASH VALVE

Fig. 1. The complete steam generation system.

Table 1. PTC system specifications

Item Value/type

Collector aperture area 3.5 mz Collector aperture 1.46 m Rim angle 90” Glass-to-receiver ratio 2.17 Receiver diameter 22mm Concentration ratio 21.2 Tracking mechanism type Electronic Mode of tracking Collector axis: N-S horizontal

E-W tracking Mass flow rate 0.012 kg s-r rn-’

necessary to ensure separation and this is also facilitated by having the inlet projecting down- wards into the vessel. The diameter and height of the flash vessel to ensure separation were determined as 65 and 600 mm, respectively.

The objective of this paper is to present the modelling, optimisation and system perfor- mance evaluation. The system optimisation aims to minimise the system start-up energy requirement.

2. SYSTEM MODELLING

A modelling program called PTCDES is writ- ten in BASIC language. The program is used to determine the quantity of the steam produced by the steam generation system, i.e., the collec- tor and the flash vessel. The principle of opera- tion of the program is that it employs the values of the solar beam radiation on a horizontal

surface and ambient air temperature from a reference year for Nicosia, Cyprus, developed previously ( Kalogirou, 1991). The beam radia- tion values are corrected hourly for the collector inclination.

In this analysis a representative day for each month is taken as shown in Table 2. These are chosen because the value of extraterrestrial solar radiation is closest to the month’s average at that day (Duffie and Beckman, 1991).

In the program the actual measured collector performance parameters of test slope and intercept are required. These were obtained by testing the collector according to the procedures specified by ASHRAE Standard 93 (1986). The program takes into account, in addition to the sensible heat and the thermal capacity of all the system components, all the heat losses from

Table 2. Average day of each month

Month Day

January 17 February 16 March 16 April 15 May 15 June 11 July 17 August 16 September 15 October 15 November 14 December 10

Modelling, optimisation and performance of a PTC steam generation system 51

the system, i.e., the flash vessel body, pipes and pump body. After all these losses are estimated, the flash vessel inlet water temperature is deter- mined. From the difference in enthalpy of this hot water to the water contained in the flash vessel, the steam production is calculated.

The program also considers the losses during the overnight cooling period which were calcu- lated assuming that the temperature of the water in the vessel at the beginning of this period is equal to the flash vessel bottom temperature. Thus, the effect of using the flash vessel for thermal storage was investigated. After the night losses were calculated, the initial flash vessel water temperature for the succeeding day was determined. The daytime input energy is then determined by using the collector performance equation, with the appropriate optical losses estimated by using the incidence angle modifier, also determined according to ASHRAE Standard 93 (1986). From the input energy, the thermal losses are subtracted and the remaining energy is used either to pre-heat or, once the pre-heat cycle is complete, to produce steam. The program can thus be used to model the behaviour of the system during pre-heat and predict the daily steam production of the system. The program “PTCDES” flow chart is shown in Fig. 2.

For the heat loss from the cylindrical flash vessel the following relation was used:

QFS= l-1,

ln(t + Di) Do Di ln(Di+t) 1

-I- A

27ckH ’ 27rkiH ’ 0.25

(1) The third term of the denominator of eqn ( 1) estimates the free convection from the external flash vessel walls (insulation) to the environment (Holman, 1989).

The flash vessel outer wall temperature is determined from:

START

Rf4D WEAlHER DATA Es WPulcouEcTDR&m PARANEIERSDATAPRDNAFILE

NDDIPY OATA IF RfoulRED

” ‘OR I

AT THE REoINNINo OF MN NONTH KsntuTE NIQNY LOSSES AND INllUL FIASH

VESSEL WATER 1EUPERAlURE

EsllNAlE n (THERNAL)

1

nNDPRoDwTouANnrf

I ADD TO PREVIOUSLY PRDDIJCED PRDDucl

I

ADD HOURLY PRODUCT TO OlUNfHY PKODUCEDWPREWDUSNDUR

I

DClERMHE NDURLY YM EFFICIENCY

I DCKRUINE Ou

I PRINT RESULTS

Fig. 2. Program “PTCDES” flow chart.

DT is equated to T, - T.. This iteration process

T,= T-[ QFsrg ;&)I continues until DT - (T, - T,) is less than 1 “C. For the heat loss from the pipes, the UA

(2) value approach, followed by many solar energy simulation programs like TRNSYS (Klein et al., 1990) and F-Chart (Klein and Beckman,

The difference between wall temperature and 1983), is used. The heat loss from the pipes is

ambient temperature is checked against the DT then’ value. If the difference is more than l”C, then Qpipes = UAV’- Ta) (3)

52 S. Kalogirou et al.

The pump employed was of cylindrical form and positioned vertically. Therefore, the heat loss from the pump body is calculated by the relations applied to vertical cylinders, i.e. :

Q p_p = 1.42/$,&T- T,) (4)

The accuracy of the simulation depends to a great extent on the validity of the reference year. This was investigated when modelling the performance of hot water production from (PTCs) (Kalogirou et al., 1993). Although the variation reported was 7%, this cannot be gener- alised as an expected variation.

The input data to the program PTCDES is shown in Table 3, whereas a typical output for the 3.5 m* collector model for the months July-September is shown in Fig. 3. The monthly total useful energy and the mean daily steam production for the whole year are shown in Table 4.

3. SYSTEM OPTIMISATION

A system optimisation was undertaken to determine the capacity (size) and inventory (content) of the flash vessel. This would affect the start-up or pre-heat energy requirements of the system as the greater the water quantity the bigger the requirement. However, the system performance will reduce (in terms of steam production) if the thermal mass of the system is reduced too much. This is because the addi-

Table 3. Program “PTCDES” input data

Parameter Value

Solar radiation* Ambient temperature* Aperture width Aperture area Collector optical efficiency

(test intercept) Slope of collector performance graph

(test slope) Flash vessel water content Flash vessel outside diameter Flash vessel inside diameter

1.46m 3.5 m2 0.638

0.387 W mm2 K-r

0.7 kg 105 mm 65 mm

Flash vessel wall thickness Flash vessel height

2mm 0.6 m

UA value of the pipes Pump body area Insulation conductivity Mass flow rate Mass of circulated water

0.93 W K-r 0.12 mz 0.035 W m-r K-r 0.042 kg s-r 4kg

*Values normally taken from reference year. For the simpli- fied version of the program, single constant values are used as indicated.

tion of make-up water would then “dilute” the system temperature and possibly result in the performance and hence production of steam becoming unstable.

The system refinement could be readily achieved by optimising the flash vessel water capacity and inventory and also by optimising the flash vessel dimensions and construction in order to lower the system thermal capacity and losses. One constraint on the optimisation which should be noted, however, is that there is a minimum water mass of circulating water, con- tained in the pipes, which is fixed and cannot be changed.

Another possibility which should be consid- ered as a system refinement is the use of the flash vessel as a storage vessel. This will be done by oversizing the flash vessel and would have the advantage of starting the system in the morning with the water at a higher temperature but has the disadvantage of a greater water mass to heat up.

A simplified version of the simulation pro- gram PTCDES was used for the system optimi- sation. In this version of the program, a constant radiation input and ambient temper- ature throughout the day is used so that the system performance can be investigated theoretically independently of the weather conditions.

The modelled performance of the system, for constant values of solar radiation and ambient air temperature equal to 500 W m-* and 30°C respectively, is shown in Fig. 4, where the daily production of steam is plotted against the flash vessel capacity and content. The vertical lines represent the different flash vessels simulated in this investigation. The table incorporated in Fig. 4 shows the dimensions of the various flash vessels considered in this simulation.

As the energy input is the same for all cases, increased steam production means that less energy is used in the pre-heat cycle. It can be seen from Fig. 4 that the highest predicted steam production is for vessel #l with a water content of 0.6 1. Although a system with flash vessel #l provides the maximum steam production, its operation is not very stable as a possible drop of its water capacity would lower its perfor- mance drastically. A more sensible selection is flash vessel #2 with 0.7-l capacity. This system presents only a 0.8% reduction in steam pro- duction when compared with vessel #l but is more stable.

It should be stressed that because of the

Modelling, optimisation and performance of a PTC steam generation system 53

IuNTil = JULY

TIME COLLECTOR HOURLY CUMULATIVR USEFUL EFFICIENCY PRODUCTION' PRODUCTION' ENER&

6.00 0.51 0.00 0.00 137.21 7.00 0.54 0.36 0.36 485.02 8.00 0.58 1.46 1.82 9.00 0.58 1.88 3.69

10.00 0.57 2.05 5.75 11.00 0.56 2.15 7.90 12.00 0.56 2.20 10.10 13.00 0.56 2.23 12.32 14.00 0.58 2.30 14.62 15.00 0.59 2.17 16.79 16.00 0.59 1.84 18.64 17.00 0.55 1.38 20.02 864.08 18.00 0.50 1.07 21.09 666.40 19.00 0.17 0.00 21.09 0.00

Month average production = 6.024 kg&day Month Total USEFUL ENERGY 3: 13572.8 Wh

TIME

7.00 8.00 9.00

10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00

COLLECTOR HOURLY CUMULATIVE USEFUL ENERGY EFFICIENCY PRODUCTION' PRODUCTION' ENERGY= LOSS2

0.57 0.00 0.00 372.65 68.56 0.56 1.13 1.13 721.24 128.00 0.55 1.52 2.65 950.49 124.12 0.53 1.71 4.36 1066.24 120.23 0.51 1.77 6.12 1103.25 117.34 0.51 1.83 7.95 1140.50 115.02 0.52 1.86 9.80 1159.06 114.25 0.54 1.93 11.73 1203.24 113.68 0.56 1.90 13.63 1189.18 115.98 0.59 1.85 15.48 1156.74 118.10 0.58 1.52 17.00 948.31 121.21 0.54 1.23 18.23 770.25 125.29

Month average production = 5.209 kg/m'-day Month Total USEFUL ENERGY = 11781.1 Wh

nGNTH=s-Ei?

TIME

7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00

COLLECTOR HOURLY CUMULATIVE EFFICIENCY PRODUCTION' PRODUCTION'

0.54 0.00 0.00 0.50 0.60 0.60 0.47 1.18 1.78 0.44 1.23 3.02 0.42 1.26 4.28 0.42 1.31 5.59 0.44 1.40 6.99 0.47 1.47 8.46 0.51 1.55 10.01 0.55 1.71 11.72 0.58 1.84 13.56 0.26 0.00 13.56

910.33 1173.76 1282.06 1343.00 1374.49 1392.46 1435.45 1357.79 1150.75

USEFUL ENERGY'

234.14 549.31 736.92 770.77 788.09 819.57 875.48 916.67 968.75 1070.32 1149.06

0.00

ENERGY LOSSZ 25.56

108.81 125.87 122.16 118.87 116.16 114.04 113.28 112.70 114.62 116.56 119.48 123.16 108.29

ENERGY LOSS2 42.85

124.64 128.79 125.09 122.38 120.25 119.47 119.28 121.59 124.10 126.42 112.33

Month average production = 3.873 kg/m'-day Month Total USEFUL ENERGY = 8879.1 Wh

Notes : 1. Steam production in kg 2. Useful energy and energy loss in Wh

Fig. 3. Simulation program “FTCDES” typical output.

complexity and inter-relationship of the 4. STEAM GENERATION SYSTEM parameters, the analysis undertaken here cannot PERFORMANCE EVALUATION be generalised and should be applied to indivi- First, the transient system performance is dual cases to determine the optimal design for evaluated to investigate the energy required to a particular collector system. pre-heat the system followed by the model

54 S. Kalogirou et al.

Table 4. Predicted monthly energy collection and steam production

PTCDES results

Useful Mean steam Daily energy production clearness

Month (kWh) (kg m -‘day-‘) index KT

January 0.759 0.116 0.47 February 1.226 0.320 0.51 March 4.187 1.640 0.54 April 6.270 2.654 0.56 May 8.450 3.665 0.56 June 12.597 5.572 0.62 JOY 13.573 6.024 0.64 August 11.781 5.209 0.62 September 8.879 3.873 0.59 October 4.532 1.876 0.58 November 1.851 0.632 0.51 December 0.880 0.175 0.47 Annual 2249.5 kWh 952.7 kg mm2

validation. The model is validated by comparing the experimental daily steam production with predicted results under steady-state conditions. It is also validated under transient conditions when the collector is shaded.

13

12

11

10

9

6

vessel #l

1 I I I I I I I I I I

0.3 1 0.5 1 0.4 0.6 0.8 I 1.3 1.7 2 4 6 8 12.5 0.4 0.6 0.5 0.7 0.9 1.1 1.5 2 3 5 6 10 I5

Flash vessel water capacity (kg)

4.1. Pre-heat energy evaluation For a cold start the amount of energy required

to pre-heat the system depends on the thermal capacity of the various system components, on the total water quantity and on the thermal losses.

The pre-heat energy can be measured by recording the temperatures at various points in the system together with the solar radiation falling on the collector aperture area. For this purpose a computer data acquisition system was set up utilising K-type thermocouples for temperature measurement and an Eppley radio- meter for recording the solar radiation. The measurement position of each thermocouple is shown in Fig. 1.

The measured temperatures during a cold start of the system equipped with flash vessel #2, together with the corresponding solar radia- tion, are shown in Fig. 5. The system is at the end of the pre-heat cycle when the temperature at T4 (flash vessel top) reaches the temperature T3 (flash vessel bottom). This indicates that steam is now being produced at a steady rate and that the flash vessel has approximately

vessel #2 vessel #3 vessel #4 vessel #5

Fig. 4. Predicted steam production for various size flash vessels.

Modelling, optimisation and performance of a PTC steam generation system 55

Thermocouple number

Tl T2 T3 T4 TS

Tempcraturc measuremenl poiut

Collector oullci Collector inlet Flash vessel bollom Flash vessel top Ambient

Note: Effective aperture area=3 m*

0 I I I I I I I I

10 20 30 40

Time (minutes)

Fig. 5. Pre-heat cycle graph.

reached the steady-state temperature. From the data shown in Fig. 5, this is achieved after approximately 35 min. During this time period the insolation was approximately 690 W m-‘, which represents the total energy available to the collector of 4.3 MJ. It can be seen from Fig. 5 that the temperature at the top of the flash vessel (T4), slowly increases by conduction from the bottom of the vessel until the collector outlet temperature reaches 100°C. When this happens the temperature increases more rapidly but more energy is still needed (about 0.25 MJ) to pre-heat this part of the vessel. The steam produced during this period is condensed on the relatively cold vessel walls until their temper- ature reaches the value of T3 at which point the pre-heat cycle is completed and the system starts producing useful steam.

4.2. Validation of the model This was investigated by performing all day

experiments during which both the steam pro- duction and the weather conditions were recorded. The measured weather data were then used in the simulation programs “PTCDES”, the output of which were compared with the actual performance data. The experiments were

performed for two days, one sunny summer day with high ambient temperature (hot) and one sunny winter day with a low value (cold). For these experiments a flash vessel #l, of 54 mm diameter, 600 mm height with a 0.6 1 water content was used.

The program was modified slightly by delet- ing the statements converting the horizontal beam radiation into radiation falling on the collector surface as the latter was measured during the experiment directly.

Comparisons between the predicted and actual performance are shown in Figs 6 and 7 where the cumulative steam production is plot- ted for both cases. It can be seen from the figures that the program is accurate for the hot sunny summer day, whereas the difference is greater for the cold sunny winter day. The total system production together with the percentage differences between the actual and the predicted system performance are shown in Table 5. The small percentage difference shown in the last column of Table 5 clearly indicates that the model gives good predictions, which are accu- rate to within 1.2%.

An additional verification of the accuracy of the modelling was carried out by fitting flash

56 S. Kalogirou et al.

6.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00

limp of day

0 Actual 0 PTCOES Rdlctlon

Fig. 6. Comparison between predicted and actual system performance (summer day, hot)

2.0

2.6

2.4

2.2

2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Tim of QY

0 ActLmt 0 PTCDES PrOdIction

Fig. 7. Comparison between predicted and actual system performance (winter day, cold).

vessels #l and #3 (detailed in the table included from where it can be seen that there is a good in Fig. 4) on the collector and testing the system agreement between the actual and predicted with different water capacities. The daily steam results. The maximum difference (8%) is for production was compared to the predicted per- flash vessel #l with a water capacity of 0.3 1. formance. For this purpose, actual hourly values This can be attributed to the fact that the of solar radiation and ambient air temperature make-up water was manually added at different were used. The results are shown in Table 6 occasions as needed and not constantly as

Modelling, optimisation and performance of a PTC steam generation system 57

Table 5. Cumulative summary between actual and predicted system performances

Total system production (kg) Percentage

difference PTCDES with respect

Item Actual prediction to actual

Hot sunny day 11.72 11.68 -0.3 Cold sunny day 2.57 2.54 -1.2

assumed by the program. This has a greater effect on the system with flash vessel #l which is more sensitive to water capacity.

In addition to the above testing procedure, the performance of the system was also exam- ined under transient conditions. This was achieved by shading the collector whilst keeping the system pump operating. The shading was removed after 1 h. In this way the cooling and the heating of the system could be investigated.

In Fig. 8 the actual and the predicted collector inlet and outlet temperatures are plotted. In this case the collector inlet temperature is equivalent, to a good approximation, to the temperature 73 (flash vessel bottom). The agreement between the experimental and modelled plots is very good, both with respect to time and tem- perature profiles and to the minimum water temperature reached at the end of the l-h period. It can be seen from Fig. 8 that initially the collector outlet temperature is greater than the inlet. This happens until the energy stored in the collector receiver is given up to the circulating fluid. After 2-3 min, the situation is

reversed and the collector inlet temperature is greater than the outlet temperature. This is because the losses from the collector receiver are responsible for cooling down the system. The receiver together with the pump are rela- tively poorly insulated parts of the system. It can also be seen from Fig. 8 that only 13 min ( 1.6 MJ) are required for the system to recover and return to steady-state condition after the shading is removed.

4.3. Theoretical system energy analysis

The results from the model simulation can be used to produce theoretically the system Sankey diagram. Such an analysis for a day with con- stant radiation of 500 W m-‘, ambient air tem- perature of 30°C and all other parameters as shown in Table 3 is presented in Fig. 9. The analysis is performed for the 3.5 m2 aperture area model with flash vessel #l and 0.6 1 water capacity. The analysis shown graphically in Fig. 9, in the form of a Sankey diagram, indi- cates the magnitude of the various losses of the system.

From Fig. 9 it can be seen that only 48.9% of the solar energy falling on the collector is utilised for steam generation. A large percentage of the losses is due to collection losses, 41.5%, and the rest, 6.9%, is made up of thermal losses. Energy losses due to raising the water temper- ature from ambient to 100°C is 2.2% and for the rig is 0.5%.

A better representation of the thermal losses is shown in Fig. 10, where it can be seen that

Table 6. Comparison between actual and predicted system performance for different flash vessels and capacities

Actual Predicted Percentage difference steam steam between actual

Flash Capacity production production and predicted vessel (1) (kg) (kg) production

#1 0.3 8.38 7.76 8 0.5 12.46 11.87 5 0.6 13.87 13.47 3

#3 1.1 12.88 12.51 3 1.5 12.58 12.34 2 2.0 12.73 12.36 3

Table 7. Percentage system losses and percentage useful energy for higher operating temperatures

Collector operating Collector Thermal temperature (“C) losses (%I,) losses (%)

100 41.5 6.9 150 44.7 11.7 175 46.5 14.4 200 48.1 17.1

Sensible heat and thermal capacity

losses (%)

2.7 5.0 6.0 7.1

Useful energy (8)

48.9 38.6 33.1 27.7

58 S. Kalogirou et al.

99 ‘iaullff

98

97

96

95 STEADY STATE

94 REGION

93 92

91

90

89 88 87

86

85

84

83 -10

Radialion= 0 W/m’

I I I I I

10 30 50

Time (minutes) Cl Tl (actual) + T2 (actual) 0 Tl (modelled)

CDLLECI’DR SHADED

STEADY STATE REGION

Radiation 690 W/n?

A T2 (modelled)

Fig. 8. Comparison of actual and predicted transient response.

COLLEXTOR LOSSES 23.5 MJ

41.5% THERMAL LOSSES 3.9 Ma SENSIBLE HEAT (1.25 MJ) +

& THERMAL CAF’ACM’Y (0.28 MI) e

6.9% 2.7%

SOLAR

EEY

Z% yJ ZGY INPUT USEFUL 33.2 MJ ENJZRGY 58.S % 27.8 MJ

48.9%

Fig. 9. System Sankey diagram.

losses from the pipes amount to 52.6%, losses from the pump body amount to 37.5% and the rest (9.9%) is due to flash vessel body losses.

The same analysis can be performed for the system operating at higher temperatures. This is shown in Table 7, where the percentage losses and the percentage useful energy for various operating temperatures are tabulated. The same input parameters, as described above, are used in this analysis for comparison purposes. It can be seen from Table 7 that the higher operating

temperature affects mainly the thermal losses, the sensible heat losses and the thermal capacity losses, whereas the collector losses are not greatly affected.

5. CONCLUSIONS

A parabolic trough solar energy collector system for steam generation is presented in this paper together with the system modelling and optimisation. The modelling was used for the

Modelling, optimisation and performance of a PTC steam generation system 59

LOSSES FROM PIPES (37.6%)

SENSIBLE HEAT (23.6%)

NP BODY LOSSES (26.9%)

FLASH VESSEL LOSSES (7.

CAPACITANCE LOSSES (5.2%)

Fig. 10. Theoretical thermal losses from the system.

prediction of the daily steam production and the system start-up energy requirements. Energy invested in the pre-heating of the flash vessel is inevitably lost due to the diurnal cycle. The losses during the long overnight shutdown return the vessel to near ambient conditions each morning. Therefore, the optimisation is focused on the selection of the flash vessel

I dimensions and capacity which minimise the system start-up energy requirement and thus maximise system output. The optimum flash vessel diameter and inventory obtained from this analysis are 65 mm and 0.7 1, respectively. From the results presented, 4.3 MJ are required for pre-heating the system. When shading is introduced for 1 h, 1.6 MJ are required for the system to recover and return to the steady-state condition. From the results presented, which include testing of the system under both steady- state and transient conditions, it can be con- cluded that the modelling program developed is accurate to within 1.2%. From a theoretical system energy analysis, it was shown that only about 49% of the incident radiation falling on the collector is utilised for steam generation. The rest are thermal and collection losses. Operation of the system at higher temperatures affects mostly the system thermal losses.

A PUP Di D0

NOMENCLATURE

pump body area (m*) internal flash vessel diameter (m) external flash vessel diameter including insulation (m)

temperature difference (K) flash vessel height (m) pump height (m) flash vessel wall thermal conductivity (Wm )

-1 K-i

insulation thermal conductivity (W m-i K-l) heat loss from flash vessel (W) heat loss from pipes (W) heat loss from pump body ( W) water temperature (K) flash vessel wall thickness (m) ambient temperature (K) flash vessel outer wall temperature (K)

REFERENCES

ASHRAE Standard 93 (1986) Method for Testinn to Deter- mine the Thermal Performance of Solar Collectors.

Duffie J. A. and Beckman W. A. (1991) Solar Enaineerinp of Thermal Processes, 2nd Edn. Jo’hn Wiley-& Sons, New York.

Holman J. P. (1989) Heat Transfer. McGraw-Hill, New York.

Kalogirou S. (1991) Solar energy utilisation using parabolic trough collectors in Cyprus. M. Phil. Thesis, The Poly- technic of Wales.

Kalogirou S., Lloyd S. and Ward J. (1993) Modelling of a parabolic trough collector system for hot water pro- duction. In Proceedings of ISES World Congress, Buda- pest, Hungary, Kaboldy E. (Ed.), Vol. 5, pp. 145-150.

Kearney D. W. and Price H. W. (1992) Solar thermal plants- LUZ concept (current status of the SEGS plants). Pro- ceedings of the Second Renewable Energy Congress, Reading, UK, Sayigh A. A. M. (Ed.), Vol. 2, pp. 582-588.

Klein S. A. and Beckman W. A. (1983) F-CHART, F-Chart Software, Middleton, WI.

Klein S. A. et al. (1990) TRNSYS, A Transient Simulation Program, Solar Energv Laboratorv. Universitv of Wis- consin, Madison, WIT*

I

Murnhv L. M. and Mav E. K. (1982) Steam Generation in .&e-Focus Solar Cdrrectors: ‘a Co’mparatioe Assessment of Thermal Performance, Operating Stability, and Cost Issues. SERI/TR- 13 11.