Mathematical simulation of a solar ejector-compression refrigeration system

Applied Thermal Engineering Vol. 16, Nos 819, pp. 669475, 1996 Copyright 0 1996Elsevier Science Ltd 1359-4311(95)00079-8 Printed in Great Britain. All rights reserved 1359-4311/96 $15.00 + 0.00

Pergamon

MATHEMATICAL SIMULATION OF A SOLAR EJECTOR-COMPRESSION REFRIGERATION SYSTEM R. Dorantes,* *Departamento

C. A. Estradat

and I. Pilatowskyt

de Energia, UAM-A, Av. San Pablo, No. 180, 02200, Mexico; and TLaboratorio de Energia Solar, IIM-UNAM, Ap. 34, 62580 Temixco, Morelos, Mexico (Received 7 November 1995)

Abstract-This paper presents a mathematical simulation for the dynamic thermal behavior of a solar ejector-compression refrigeration system with a capacity production of 100 kg of ice per day. It consists of an evacuated tube solar collector array, a thermal storage unit and an ejector-compression refrigeration unit. Due to the change in climate, the collector efficiency varies and, therefore, so does the system efficiency. This fact makes it necessary to evaluate the design of the system not just for a whole day but also for a whole year. The ejector-compression refrigeration system was designed to work with Freon Rl42b as the working fluid at condenser temperature (Z) of 3O”C,generation temperature (TG) of 105°C evaporator temperature (2-r) of - 10°C with a required generator heat load (Qo) of 5.6 kW and an obtained evaporator heat load (QE) of 2 kW, the corresponding COP was 34%. With these conditions, the ejector geometry was fixed and curves for Qo, QE and COP as a function of TCand TGwere obtained. A plot of the daily history of system storage tank temperature for two days of the year (one in January and one in June) is presented. Also graphs for the monthly average ice production, COP, collectors and system efficiencies are presented. The annual average values for COP, collector efficiency and system efficiency were 0.21, 0.52 and 0.11, respectively. Copyright 0 1996 Elsevier Science Ltd Keywords-Refrigeration;

solar collectors; ejector-compression

cycle; simulation.

NOMENCLATURE AC

CP FR G, h

m’ m”

PI&

I UL

solar collector array area, m* storage fluid heat capacity, J/kg-C collector heat removal factor, dimensionless solar radiation, W/m* enthalpy primary mass flow rate, kg/s secondary mass flow rate, kg/s heat flow rate that is lost from the storage unit to the surroundings, heat flow rate that comes from the solar collector array, Watts heat flow rate that goes to drive the refrigeration unit, Watts temperature, “C collector overall loss coeflicient, W/m*-K

Greek letters effective transmittance W)

Watts

absortance product, dimensionless

Subscripts

: f” G S

ambient condenser evaporator freon generator storage

INTRODUCTION

Solar-powered refrigeration systems based on the use of ejectors have been proposed and shown to be competitive with absorption- and Rankine-cycle-powered vapor-compression systems. An ejector refrigeration cycle is schematically shown in Fig. 1. The cycle consists of two sub-cycles. The power sub-cycle (6)-(l)-(3)-(4)-(6), defined by the part of the flow through the generator, operates between the thermodynamic states of the generator and condenser and generates the motive stream for compression. The refrigeration sub-cycle (5)-(2)-(3)-(4)-(5), defined by the flow through the evaporator, operates between the evaporator and the condenser. The pump is the only 669

R. Dorantes

670

et al.

CONDENSER

Fig. 1. Block diagram

of the ejector-compression

refrigeration

cycle.

component in the cycle which has moving parts and requires mechanical energy [l]. These two sub-cycles work as follows. Heat exchanged between the refrigerant and the external heat source (QG) causes high-pressure liquid evaporation in the vapor generator. The vapors (1) with a mass flow rate of m’ are allowed to expand through a converging-diverging nozzle in the ejector. The low pressure (2) produced by this expansion causes suction of vapors from the evaporator (2). The two streams mix in the ejector and leave after a recovery of pressure (3) in the diffuser part of the ejector. The emerging stream from the ejector is connected to the condenser. At the condenser, the heat is rejected (Qc) from the refrigerant to the surroundings, resulting in a condensed liquid refrigerant at the exit of the condenser (4). The liquid is then divided into two streams: one enters the evaporator after a pressure (5) reduction in the expansion valve and the other enters the generator after undergoing a pressure increase (6) by the pump. At the evaporator the fluid evaporates due to the heat gain (QE) from the cold source and leaves the evaporator with a mass flow rate of m”. The coefficient of performance (COP) of any refrigeration cycle is defined as the ratio between the produced refrigeration to the energy input into the cycle. If QG, Qc and QE are the heat-exchange flow rates in the generator, condenser and evaporator, respectively, and Wp is the mechanical energy to pump, then the COP is given by

‘Op=Qo$j'p

hz- hs

= ‘A,-h,’

where U = m”/m’ is the mass flow rate and h is the specific enthalpy. thermodynamic behavior of the cycle depend on the ejector characteristics.

The COP and the Figure 2 shows the

0.6 0.5

.

I

:

.

~:

75 80 Tg, "C

85

90

Te=14”C

0.4 4 0.3 0.2 0.1 0 60

65

70

95

Fig. 2. Influences of the generator temperature (TG) on the COP for a given ejector geometry and for several evaporator temperatures of the fluid Rl 1 with TC = 27.7”C and 4 = 5.76 [7].

Simulation

of a solar ejector-compression

refrigeration

system

671

influence of the generator temperature ( TG) on the COP for a given ejector geometry [7]. Each curve of that graph at constant evaporator temperature (TE) shows the three regimen behaviors of the ejector: mixing, transition and supersonic. The optimum value of COP in each curve is reached always at the transition regime. However, this transition regime is unstable and a small variation of T, produces a significant reduction of COP. This makes it necessary to have a good control of TG. Also, even though the COP values are small for TE close to 0°C the selection of the working fluid is very important for the cycle efficiency. The production of ice requires evaporator temperatures of at least - 10°C. For this temperature the cycle is impractical, because it needs a compression ratio greater than 4, this value is out of the range for the ejector-compressor operation. To solve this problem Sokolov [l-3] introduced a hybrid cycle for the ejector-compressor using a booster (Fig. 3). In this way, the vapor coming from the evaporator is compressed in two steps: the first one from PE to PE. is made by the booster of low compression ratio, and the second one from PE’to PC is made by the ejector. For the new cycle the COP is given by

U(h, - he,)

(2)

hz - hs + U(hj - h,) .

Sokolov [l] showed that this efficiency is much higher than that given by equation (1) and from a practical point of view the introduction of the booster is simple and realizable. Despite the fact that there are good experimental results reported with this system, few papers using solar energy as a source energy for the system exist. Kakababaev [5] and Holmes [6] presented experimental results obtained with CFC 12 as a refrigerant and for an air-conditioning system. However, their results were just for a specific condition of the system and did not show the dynamic behavior of the unit. In many solar systems, due to the change in climate, the collector efficiency varies and, therefore, so do the system efficiencies. This fact makes it necessary to evaluate the design of the systems, not just for a whole day, but for a whole year. The purpose of this paper is to present a mathematical simulation of the dynamic thermal behavior of a solar ejector-compression refrigeration system with a capacity production of 100 kg of ice per day that will be located in the city of Temixco, Morelos, Mexico. SYSTEM DESCRIPTION Figure 3 shows a diagram of the solar ejector-compression refrigeration system. It consists of an evacuated-tube solar-collector array, a thermal storage unit and an ejector-compression refrigeration unit. The storage unit is coupled to the solar-collector array, forming a closed loop

Storage Tank

Expansion Valve

&rnps Fig. 3. Block diagram

of the solar-hybrid-powered

ejector-compression

refrigeration

system.

R. Dorantes et al.

672

Fig. 4. Energy balance at the storage unit.

for the thermal fluid. The vapor generator is a heat exchanger connected to the storage unit. The whole system operates depending on the values of storage and ambient temperatures (T,, T,), keeping the evaporator temperature constant. An energy balance at the storage unit allows one to analyze the influence of the T, variations on the dynamic thermal behavior of the system. The purpose of this analysis is to design the best system that will be adequate for the weather conditions of Temixco. SYSTEM EQUATION Figure 4 shows schematically the heat balance at the storage unit. Applying the first law of thermodynamics, the following equation results:

dT,

(mc,)s dt

=

Qu -

Q~oss -

&ad,

where Q, Qlossand Qloadare the heat that comes from the solar-collector array, the heat that is lost from the storage unit to the surroundings and the heat that goes to drive the refrigeration unit, respectively. If Q”, Qlou and Qloadare known as a function of T, and time, equation (3), which is the system equation, can be solved for T,. Qu is given by Qu = Ac[&(tcr)Gt

- &U,_(Ts - 7-J

(4)

and Qlossby Q~oss = (UAW

- Ta),

(5)

where G,, the solar radiation, and T,, the ambient temperature, are functions of time, and the other factors are assumed constant [8]. Calculation

of Qload

An energy balance at the generator (Fig. 5) gives

(6) where QG is the generation heat which is a function of the condenser temperature, Tc, and the refrigerant temperature, Tn, at the outlet of the generator; QG is calculated following the methodology developed by Dorantes [4] for the analysis of a compression-ejector cycle. The system operation can be satisfied if

Fig. 5. Energy balance at the vapor generator.

Simulationof a solar ejector-compression refrigerationsystem Table

I. Parameters

used in the mathematical

Solar collector

Storage

tank

Organic

fluid for the refrigeration

cycle

673

simulation

FR (m) = 0.87 Fn Vr = 2.4 W/m’ AC = 18 ml Thermal fluid: Calorie HT43 Boiling point: 3 I I ‘C Freezing point: -9YC k = 0.13 W/m-“C cp = 2. I kJ/kg-“C p = 800 kg/m’ at IOO’C U = 0.40 W/mf-‘C V, = 1.1 m’ R142b

Also, it is known that Tfl = T,, - T, and

Tc = T, + TB,

(8)

where T, and TB are known constant temperatures. To produce 100 kg of ice, the operating conditions are established and for those conditions QG is known, AT, is fixed and (ml c&l is calculated by equation (7) and then fixed. Now, if Trl ,,,,”= T,I min- T, and Trl = T,I max- T, then three cases will happen: If Ts 5 T,, mm, the system does not operate. If TsI minI K I T,I maxyQload= Qc(Tc, T,,). If T, > T,, max,the system does not operate. Conditions 1, 2 and 3 are based on the operating curves of the ejector-compressor cycle where for the transition regime the limits are obtained to have the optimum efficiency. Outside of this interval, the system efficiency drops significantly. RESULTS In order to do the mathematical simulation R142b was chosen as the working fluid for the ejector-compression refrigeration system. This fluid has the thermodynamic properties adequate to the imposed system operation conditions. Even though the working fluid is a freon, it is not very aggressive against the atmospheric ozone. The refrigeration cycle was designed to work with the Freon Rl42b at a condenser temperature (Tc) of 30°C a generation temperature (TG) of 105°C an evaporator temperature (TE) of - 10°C with a required generator heat (QG) of 5.6 kW and an obtained evaporator heat (QE) of 2 kW, the corresponding COP was 34%. With these conditions, the ejector geometry was fixed and curves for QG, QE and COP as a function of Tc and TG were obtained. This information was used, along with the equations in the previous section, to simulate the thermal behavior of the whole system as a function of time during a day and thus during a year. Table 1 shows the relevant parameters used in the simulation. With a storage volume-collector area ratio of 0.06 m3/m2 and moderate weather conditions corresponding to the city of Temixco in the State of Morelos in Mexico (ambient temperature (T,) between 19 and 33°C and daily solar radiation (H) between 15 and 25 MJ/m2-day), the simulation was performed for different collector areas (A=). The value of Ac = 18 m’ (storage unit volume V, = 1.1 m3) was chosen. Figure 6 shows the daily history of system storage temperature for two days of the year: 17 and 162, which correspond to the months of January and June. Also, the Qu and Qload= QG(Tc. 7b) heats are plotted for the same days. As expected, in both cases, temperatures and heats are higher in June than in January. Figure 7 shows the monthly average COP, collector and system efficiencies. Also, the monthly average ice production is plotted. It can be seen from this figure that the lower efficiencies were obtained in summer, due mainly to the increment of the ambient temperature, T,, and thus the increment of the condensation temperature, Tc. In contrast, during the winter, the ice production increases up to its maximum value. Despite the climatic variations, the annual average value for COP was 21%. The annual average collector efficiency and system efficiency were 52 and 1 1%, respectively. For the collector area chosen, an annual average ice production of 104 kg/day was computed.

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140

50

Ts(Jan)

40

Ts(Jun) %

30

d

Qu(Jan) _

tI I

Qu(Jun)

20

Qload(Jan) Qload(Jun)

28

0

0 4

0

8

12

16

24

20

Time, Hrs. Fig. 6. Daily history

of system storage temperature for two days of the year: 17 and 162. The Q. and Qlond= Qo(Tc, T,I) heats are also plotted for the same days.

CONCLUSIONS The good efficiency obtained with the mathematical simulation of the ejector-compression refrigeration cycle assisted with the booster and using R142b as the working fluid suggests that this system is adequate as an icemaker. The model allows one to establish the limits for the systems optimum performance under the weather variations of the chosen city and shows the importance of the use of the storage tank as a unit to diminish the influence of those weather variations on the system. 1.00

180

0.90

160

0.80

140

2 J? 5 0.70

120

‘D c 0.80

y” 100

“E z 0.50

Collector

Efficiency

BO

2 ‘J 0.40 s ‘9 0.30

30

z

40

g ._ ‘ii 2 2 n .a

0.20

20

0.10

System

Efficiency

. 3

0.00 JAN Fig. 7. Monthly

m” 2

FEB MAR APR MAY JUN

average

COP, collector

JUL AGO SEP OCT NOV DEC

and system efficiencies for the 12 months.

I

and the monthly

average

ice production

Simulation

of a solar ejector-compression

refrigeration

system

675

Finally, this system, with the values found, competes theoretically with other solar absorption refrigeration systems with similar capacities of ice production. For example, the ISAAC system from Energy Concepts, Inc. (a U.S. company) gives daily 75 kg of ice using a solar collector area of 11.8 m’. The system analyzed gave an annual average ice production of 104 kg/day with a solar collector area of 18 ml. REFERENCES 1. M. Sokolov and D. Hershagal, Enhanced ejector refrigeration cycles powered by low-grade heat. Part 1. System characterization. Int. J. Refrig. 13, 351-356 (1990). 2. M. Sokolov and D. Hershagal, Enhanced ejector refrigeration cycles powered by low-grade heat. Part 2. Design procedures. Int. J. Refrig. 13, 357-363 (1990). 3. M. Sokolov and D. Hershagal, Enhanced ejector refrigeration cycles powered by low-grade heat. Part 3. Experimental results. Inr. J. R&g. 14, 24-31 (1991). 4. R. Dorantes, Performances theoriques et experimentales d’une machine frigorifique tritherme a ejecto-compression. Influence de la nature du fluide de travail. Analyses energetique et exergetique. Doctoral Dissertation, INSA of Lyon, France (1992). 5. A. Kakababaev and A. Dartelov, A freon ejector solar cooler. Ge1iofeknika 2, 4248 (1966). 6. R. Holmes and F. Zeren, Development of jet pump solar cooling system. Dept of Mech. Engng, Texas University, Report TENRAC/EDF-088 (1983). 7. L. T. Lu, Theoretical and experimental study of refrigeration by freon jet pump systems. Doctoral Dissertation, INPG/INSA, France (1986). 8. J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes. John Wiley and Sons, New York (1991).