Computerized economic optimization of refrigeration system design

Computerized economic optimization of refrigeration system design

Energy Conversion & Management 40 (1999) 1089±1109 Computerized economic optimization of refrigeration system design N. Usta*, 1, A. Ileri Middle Eas...

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Energy Conversion & Management 40 (1999) 1089±1109

Computerized economic optimization of refrigeration system design N. Usta*, 1, A. Ileri Middle East Technical University, Mechanical Engineering Department, Ankara, Turkey Received 2 December 1997; received in revised form 1 August 1998; accepted 10 December 1998

Abstract The purpose of this paper is to show the importance of economic optimization of large capacity or industrial refrigeration systems and to present the results and conclusions obtained by a computer software which was developed speci®cally to determine the economic optimum values of the design parameters of refrigeration systems. Both liquid chillers and groups of cold storage rooms operating at various levels of low temperatures are covered. Various case studies and sensitivity analyses have been performed to provide speci®c numerical examples and to determine the e€ects of certain parameters. It was found that condenser type, ambient temperature, yearly operating hours, electricity price, real interest rate and refrigerant are the most important parameters in the economic optimum design of refrigeration systems. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Refrigeration; Economic optimization; Computerized analysis

1. Introduction Determining the required cooling capacity based on load calculations and selection of the appropriate components are the most important design steps. Equipment selection a€ects both the initial (capital) and operational (electrical power) costs, so the opportunity for economic optimization exists. * Corresponding author. E-mail address: [email protected] (N. Usta) 1 Present address: The University of Leeds, Mechanical Engineering Department, Room 332a, Leeds, LS2 9JT, UK 0196-8904/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 1 9 6 - 8 9 0 4 ( 9 9 ) 0 0 0 0 4 - 7

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Nomenclature EV H i L N n P PRV r Sc Si COP

expansion valve high real interest rate low annual operating time (h) expected life (20 years [13]) electrical power consumption (kW) pressure reducing valve electricity cost ($/kWh) lifetime system cost ($) initial cost ($) Coecient of performance

The basic design variables of the system, such as temperature di€erences at the evaporator and condenser, compressor eciency, need of multipressure compression and insulation thickness, could not be decided convincingly without economic optimization, which balances the e€ects on initial and capital costs. However, due to the large amount of iterative calculations that are involved, in practice, this optimization is often done roughly, using rules of thumb engineering judgment and past experience. The authors recently computerized this optimization procedure, so that it could be easily applied in typical industrial design work [1]. Also, by applying the optimization program to a number of selected speci®c cases, numerical solutions were obtained as the examples. Further, the e€ects of the parameters involved on the results were examined with the aim of formulating useful generalizations. Actually, any refrigeration cycle operation involves a number of irreversibilities related to temperature di€erences and pressure losses at di€erent components forming the system. For this reason, it may be thought that the thermoeconomic optimization of the system should be based on exergy or other second law concepts rather than be limited to ®rst law basis calculations. Discussions and several examples of exergy based thermoeconmic optimization are available in the literature, for example, Ref. [2]. However, when the quality of the input (electricity in this study) and of the output (heat absorbed at a speci®ed temperature in this study) are ®xed, the ®rst law (energy) analysis is sucient for correctly judging the e€ects of certain variables or modi®cations on the system performance. Therefore, the analyses presented here are done by customary energy considerations, reducing the required e€ort considerably. The available ®rst law (COP) based optimization studies on refrigeration systems are related to particular equipment or optimization of a speci®c refrigeration system with limited variables. Dhar [3] studied the optimization of liquid chilling plant equipments and performed a simulation on a big liquid chilling plant in India. Granryd [4] studied the parameters in¯uencing energy demand in heat pumps and refrigerating systems. The economic temperature di€erences in evaporators and condensers were found for a single example system assuming that the cost function is linear, but this is not very realistic in practice. Cerepnalkovski [5]

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studied a proper choice of the type of condenser for a refrigeration system possibility for energy saving. He worked on a mechanical compression refrigeration system with R22. The result showed that a water-cooled condenser is more suitable than an air-cooled and evaporative condenser. Siddiqui [6,7] has performed economic analyses of absorption system components to optimize various operating parameters. Sun [8,9] has presented the detailed thermodynamic data and optimum design maps for absorption refrigeration systems. The maps can be used as guides in choosing operating conditions for designing such systems or for existing systems. Tan et al. [10] have developed a refrigeration simulation software package, REFAID, to optimize the design of a refrigeration system for teaching purposes. In this study, the optimization parameters, variables and the optimization technique are explained with some sensitivity analyses which are useful for optimum economic design of refrigeration systems. 2. Computerization Firstly, a program was prepared to perform the cooling load calculation of refrigeration systems in a short time and accurately in accordance with international ASHRAE standards [11,12]. All the tables which are needed in the calculations were formulated as a function of the input values. Secondly, the new equations of thermodynamic properties for common refrigerants (R12, R134A, R22, 502 and R717) were prepared [1], because algorithms available in the literature are found to be complex for this work, since they involve iterations. The cycle analysis can be performed quickly and accurately by these new equations without any iterations. Then, a computer software package was prepared for the optimization of the di€erent refrigeration systems. The output speci®es the optimum values of condenser and evaporator temperatures, condenser water inlet and outlet temperature for water-cooled systems, the insulation thickness for cold rooms, interstage pressure in multipressure applications and, ®nally, the initial and operational cost for the most economic design. In the economic analysis, life cycle costing was used to consider the investment and operating cost of the system over its life span [13]. The polynomials giving the equipment costs were obtained using the Unit Cost List of the Ministry of Public Works of Turkey [14], which is a main reference unit cost list in Turkey, and is based on international standards. The operating cost was calculated from the power requirements of compressors, fans and pumps in the system. The maintenance cost and salvage value were not taken into account, for simplicity. Hence, the overall cost expression is:   1 n : Sc ˆ Si ‡ N:P:r …1 ‡ i† ÿ i…1 ‡ i†n 3. Optimization programs For a refrigeration system, the object function refers to the lifetime system cost and should be minimized in the optimization. However, all parts of the systems need not be examined in

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the optimization, because the systems, even working at di€erent conditions, require some identical parts, such as sight-glasses, or the costs of some parts, such as expansion valves, do not change very much, and the total cost of these parts is a small part of the total system cost. The optimization program was developed for direct application to various common industrial cases which are classi®ed as shown below: AÐLiquid chiller system Case 1: With air-cooled condenser. Case 2: With water-cooled condenser. BÐCold storage rooms BÐ(i ) Temperatures of rooms are around 08C. Case 3: With air-cooled condenser. Case 4: With water-cooled condenser BÐ(ii ) Temperatures of rooms are around 08C, and there are ultralow (around ÿ408C ) temperature rooms. Case 5: With air-cooled condenser. Case 6: With water-cooled condenser. BÐ(iii ) There are ultralow temperature (around ÿ408C ) rooms. Case 7: With air-cooled condenser. Case 8: With water-cooled condenser. As seen, both liquid chillers and cold storage rooms are separately considered. Two cases (with air- and water-cooled condensers) are analysed for each of the basic application modes. Chiller systems operate with some subcooling (5 K) and superheating (5 K) (see Fig. l(a)). Almost all actual storage room operation conditions are covered by three basic possibilities: 1. All rooms operate at temperatures that are close to each other and around 08C. The evaporators are throttled to the lowest pressure, and a common compressor is used as shown in Fig. 1(b). 2. As above, but with an additional demand at a temperature signi®cantly lower than all the others. Then, a two-stage compression with intercooling and ¯ash gas removal at the common high temperature room pressure was assumed (see Fig. 1(c)). 3. All rooms at an ultralow temperature. Again, two-stage compression and with intercooling and ¯ash gas removal was assumed (Fig. 1(d)). However, this time, in contrast to the above case, this intermediate pressure could be optimized, since there were no high temperature evaporators to dictate this intermediate state. The investment cost of a system consists of the chiller or evaporator, compressor, air- or water-cooled condenser, and if used, the water cooling tower, intercooler and ¯ash tank and, ®nally, insulation costs. The operational cost consists of the electricity cost of the compressor motor, condenser fan motor or pump and evaporator fan motor. The electricity cost of the cooling tower fan motor and pump and the cost of make-up water are included when necessary. The variables are the evaporator, condenser and water cooling tower water inlet and outlet

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Fig. 1. (a) The view of Case 1 and Case 2. (b) The view of Case 3 and Case 4. (c) The view of Case 5 and Case 6. (d) The view of Case 7 and Case 8.

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Fig. 2. Variation of optimized temperature in chillers with water-cooled condenser (chiller Twater in = 158C, Twater out = 88C).

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temperatures, interstage pressure and insulation thickness of the storage room walls. It should be noted that the insulation thickness is optimized separately for each aspect. Since some of the variables are constrained, for example, the condenser temperature in an air-cooled condenser should be greater than the outside temperature, it was required to take such constraints into the consideration. The modi®ed Hooke and Jeeves method [15] was chosen for this constrained optimization study. The optimization procedure is given in the Appendix. 4. Sample case studies with generalized results The optimization programs formulated and developed as explained in the previous sections can be used to specify the values of operational variables and select appropriate equipment for real, speci®c commercial design jobs. These computer programs were run a number of times, and some of the basic results are presented in tables and ®gures to illustrate their usage and capabilities. 4.1. Optimum condenser and evaporator temperatures The condenser and evaporator temperatures for chillers and cold rooms with either water- or air-cooled condensers were investigated. The optimized evaporator temperature is higher, and the condenser temperature is lower, up to several degrees, for water chilling units, as well as cold storage rooms, when the yearly operating time is high or the e€ective interest is low. This is so no matter whether the condenser is cooled by tower water (Fig. 2) or ambient air (Fig. 3). Also, as expected, the condenser temperatures are signi®cantly lower (about 338C vs about 508C) if the unit is cooled by water rather than air. These results are generalized in Fig. 4 which presents the condenser temperature di€erence, de®ned as the condenser temperature minus the inlet temperature of outside air or water from the cooling tower. This temperature di€erence is much higher in air-cooled units (about 9 K±6 K for storage rooms and 12 K±7 K for chillers) and varies more with ambient conditions. As noted, the values for chillers are higher than those for storage rooms, irrespective of the condenser type. Although, not shown, it was also found that systems with lower capacities require slightly lower condenser temperature, while the evaporator is almost una€ected. 4.2. Optimum insulation thickness Fig. 5 shows that the optimum insulation to be used in storage rooms is a€ected both by real interest rate and yearly operation period of the system. For a temperature di€erence of 50 K and interest rate of 8%, the optimum insulation thickness changes from 17 cm for 5000 h to 14 cm for 3000 h and further to 9 cm for 1000 h of yearly operation. The in¯uence of the interest rate increases also with operation time and temperature di€erence. If the interest rate is 16% rather than 8%, the optimum insulation thickness would be 14 cm rather than 17 cm for 5000 h. The thickness increases with temperature di€erence as well; however, the increases are not linear. For example, for 3000 h and 8% interest rate, when the temperature di€erence

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Fig. 3. Variation of optimized temperatures in chillers and cold rooms with air-cooled condenser (chiller Twater in = 158C, Twater out = 88C).

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Fig. 4. Variation of optimized condenser temperature di€erences vs dry or wet bulb temperatures in air- and watercooled condenser systems (N = 4000 h, i = 8%).

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Fig. 5. Optimum insulation thickness in cold storage rooms (k = 0.0232 W/m2K, Toutside = 358C).

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increases from 10 K to 60 K, the optimum thickness increases from 6 cm to 15 cm, i.e. only by 2.5 (rather than 6) times. 4.3. Optimum interstage pressures The evaporator, optimum condenser and interstage pressures are shown in Fig. 6 as a function of the storage temperature of a multipressure application. As seen, although the optimum intermediate pressure follows the geometric mean pressure, it exceeds the mean by about 20%. 4.4. E€ect of electricity cost The e€ects of the change of electricity price, in percentage of the current value, on the condenser temperature di€erence are shown in Fig. 7 for air-cooled and for water-cooled condenser systems. It is clear that lower electrical costs permit up to several degrees higher condenser temperatures. The e€ect of electricity cost on insulation is higher, as illustrated in Fig. 8. The variation of electricity cost relative to the initial costs, as considered in Figs. 7 and 8, may be used to investigate not only di€erent periods in a country where prices vary at di€erent rates, but also to compare operations at di€erent cost structures at any given time. For example, the current electrical cost is relatively higher in Turkey in comparison to the USA which should cause changes in optimum operation, as implied on the above ®gures. 4.5. E€ects of the system life The system life does not a€ect the optimum condenser temperature signi®cantly as shown in Table 1 for air cooled and in Table 2 for water-cooled condenser systems. However, long system life increases the optimum insulation thickness as shown in Table 3. 4.6. E€ects of refrigerant As seen in Table 4, for the air-cooled condensers, the optimum condenser temperature di€erence is smallest for R12 and largest for R22 among the four refrigerants examined. For the water-cooled condensers (Table 5), however, the dependence on the refrigerant is less, and Table 1 The e€ect of system life on condenser temperature di€erence (K) and cost (1000 $) in a R22 system with air-cooled condenser Life (years)

Condenser temperature di€erence (K)

Yearly operating cost

Investment cost

Total life cost

10 15 20 25

8.74 8.49 8.37 8.30

8.578 8.411 8.322 8.270

29.28 30.28 31.114 31.646

86.59 102.292 112.821 119.927

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Fig. 6. Interstage and condenser pressure vs storage room air in multipressure applications in cold rooms with water-cooled condenser systems (Twb = 218C. Toutside = 358C, N = 4000 h, i = 8%).

now R22 has the lowest values, while R717 is highest. As noted before, as the ambient temperatures increase, the condenser temperatures increase and the condenser temperature di€erences decrease. Table 6 shows the COP values and costs with di€erent refrigerants. It is

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Fig. 7. The e€ect of change of electricity cost ($/kWh in %) on condenser temperature di€erence in air- and watercooled condenser systems.

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Fig. 8. The e€ect of change of electricity cost ($/kWh in %) on insulation thickness at di€erent temperature di€erences (TD) across a wall in water-cooled condenser systems.

seen that, while the COP and operational costs vary slightly, the investment cost depends more on the refrigerant. Ammonia has the best COP and lowest costs in all respects compared to the halogenated refrigerants.

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Table 2 The e€ect of system life on condenser temperature di€erence (K) and cost (1000 $) in a R22 system with watercooled condenser Life (years)

Condenser temperature di€erence (K)

Yearly operating cost

Investment cost

Total life cost

10 15 20 25

6.25 6.11 6.03 6.00

14.618 14.213 13.993 13.862

84.72 87.794 89.804 91.136

182.794 209.431 227.181 239.106

Table 3 The e€ect of system life on insulation thickness in a R22 system with water-cooled condenser with respect to temperature di€erence (TD) Life (years)

TD = 10 K

TD = 20 K

TD = 30 K

TD = 40 K

TD = 50 K

TD = 60 K

10 15 20 25

54 60 64 67

82 91 96 100

104 114 121 125

122 134 142 147

138 151 160 167

153 167 177 183

Table 4 The change of condenser temperature di€erence (K) with di€erent outside temperature in di€erent refrigerants in an air-cooled condenser system Condenser temperature di€erence (K) Outside Temperature (8C)

R12

R22

R502

R717

30 32 34 36 38 40

7.36 7.22 7.08 6.94 6.8 6.6

8.82 8.64 8.46 8.28 8.1 7.92

8.39 8.21 8.03 7.85 7.67 7.49

8.17 8.01 7.85 7.69 7.53 7.37

4.7. Use of a heat exchanger The use of a liquid suction heat exchanger was examined, and it is concluded that it does not a€ect the optimum operating conditions and the minimum cost considerably. However, such exchangers may be used for practical reasons. 4.8. A comparison of the optimized design with an existing design How much di€erence the optimization may make is illustrated in Table 7, which compares an arbitrarily selected existing design (A Cold Storage in Ankara) with the recommendations

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Table 5 The change of condenser temperature di€erence (K) with di€erent outside temperature in di€erent refrigerants in air-cooled condenser system Condenser temperature di€erence (K) Outside WB Temperature (8C)

R12

R22

R502

R717

20 22 24 26 28 30

6.2 6.11 6.02 5.93 5.83 5.73

6.08 5.99 5.89 5.8 5.7 5.6

6.15 6.06 5.96 5.86 5.76 5.66

6.66 6.65 6.64 6.63 6.62 6.61

Table 6 Change of COP and cost (1000 $) with di€erent refrigerants in a water-cooled condenser systems

COP Yearly operating cost Investment cost Total life cost

R12

R22

R502

R717

4.37 14.529 102.997 245.65

4.4 14.512 98.279 240.760

4.59 14.394 80.353 221.68

5.35 14.026 65.139 202.268

Table 7 Optimum and existing cases for a cold storage in Ankara

Average Insulation Thickness (mm) Twb (8C) Tcond. (8C) Twater in (8C) Twater out (8C) Costs (1000 $, in January 1995) Evaporator Compressor Condenser Cooling tower Insulation Annual operational Total investment Life cost

Existing

Optimum

Di€erence (%)

100 21 40 25 33

146 21 31 25 30

46.0 0.0 ÿ22.5 0.0 ÿ9.1

11.3 31.875 2.944 3.256 31.90 22.5 81.894 302.813

10.281 25.413 8.706 2.713 46.438 17.062 93.544 261.086

ÿ9.0 ÿ20.3 195.7 ÿ30.1 45.6 ÿ24.2 14.2 ÿ13.8

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found by the new program. Note that about 14% reduction in life cost is obtained by optimization in this example, even though the condenser size and insulation thickness were increased, and hence, their initial costs were increased. The saving in yearly operational cost (and, hence, in energy consumption) is more signi®cant at 24%, which is partly due to load reduction and partly due to improved COP. This saving in energy also implies a number of consequences, such as an identical reduction in environmental e€ects related to generation and distribution of electrical power.

5. Conclusions In this study, the life time system cost, which considers investment and operational costs of the system over its life span, was minimized as a generalized investigation on economic optimization of refrigeration systems. Evaporator temperature, condenser temperature, water inlet and outlet temperatures of cooling tower, interstage pressure and insulation thickness were chosen as the optimization variables. The e€ects of yearly operating hours, real interest rate, cooling capacity, outside design dry and wet bulb temperatures, system life and price of electricity on the optimization variables were examined. The conclusions can be summarized as follows: 1. Optimum condenser temperature di€erence changes between 8±14 K for an air-cooled condenser and 5.5±7 K for a water-cooled condenser, depending on ambient temperature and evaporator temperature. The optimum evaporator temperature di€erence in chiller systems is found as 10±11 K. Increasing of yearly operating hours and price of electricity decreases the condenser temperature di€erence and increases the evaporator temperature di€erence. A change of system life and capacity does not change the optimum temperatures signi®cantly. In addition, a change of refrigerant causes around 1 K change in the temperatures. The optimum water inlet temperature for water-cooled condensers, obtained from a cooling tower, was found as approximately 3 K higher than ambient wet bulb temperature, and the optimum di€erence between water inlet and water outlet temperatures in water cooling condensers is around 6 K. 2. Since insulation thickness fairly depends on the yearly operating hours, electricity price, real interest rate, system life and temperature di€erence across the building wall, it is not possible to state a simple and de®nite range of optimum insulation thickness. However, increasing of yearly operating hours, electricity price, the life and the temperature di€erence increases the optimum insulation thickness, and increasing in the real interest rate decreases the thickness. The change of the thickness with respect to these parameters was illustrated with the detailed ®gures. 3. The maximum COP and minimum life time cost can be satis®ed with R717 amongst the examined refrigerants (R12, 22, 502, 717). 4. The optimum interstage pressure in the multipressure systems was found as about 20% higher than the geometric mean of the evaporator and condenser pressures.

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5. The use of a liquid suction heat exchanger does not a€ect the optimum operating conditions and the minimum cost considerably. However, such exchangers may be used for practical reasons. Since many parameters a€ect the optimum design variables of refrigeration systems, dependable economic analyses can only be achieved by computerized optimum procedures. However, when such detailed analysis could not be done due to limited time and budget, the generalized results provided here could be useful guidelines for engineers in designing refrigeration systems.

Appendix .1. Optimization procedure The cost function, which consists of investment and operational cost, is considered as an objective function which is a function on n variables and should be minimized in the constrained region of the variables. The cost function is formulated as below:   1 n : Sc ˆ Si ‡ N:P:r …1 ‡ i† ÿ i…1 ‡ i†n The optimization procedure is as follows: 1. Choose an initial base point b1 and a step length hj for each variable xi, i = 1, 2, . . . , n. A ®xed step h is used for each variable at the beginning of the optimization. 2. Carry out an exploration about b1. The purpose of this is to acquire knowledge about the local behaviour of the function. This knowledge is used to ®nd a likely direction for the pattern move by which it is hoped to obtain an even greater reduction in the value of the function. The exploration about b1 proceeds as indicated. 2.1. Evaluate f(b1) 2.2. Each variable is now changed in turn, by adding the step length. Thus, f(b1 + h1e1) is evaluated, e1 is a unit vector in the direction of the x1-axis. If this reduces the function, replace b1 by (b1 + h1e1). If not, ®nd f(b1 ÿ h1e1) and replace b1 by (b1 ÿ h1e1) if the function is reduced. If neither step gives a reduction, leave b1 unchanged and consider changes in x2, i.e. ®nd f(b1 + h2e2), etc. When all n variables have been considered, a new base point b2 will be found. 2.3. If b2 = b1, i.e. no function reduction has been achieved, the exploration is repeated about the same point b1, but with a reduced step length. Reducing the step length(s) to one-tenth of its former value appears to be satisfactory in practice. 2.4. If b2 is not equal to b1, a pattern move is made. 3. The pattern move utilizes the information acquired by exploration and accomplishes the function minimization by moving in the direction of the established `pattern'. The procedure is as follows. 3.1. It seems sensible to move further from the base point b2 in the direction (b2 ÿ b1), since

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Fig. A1. Flow chart of the modi®ed Hooke and Jeeves method.

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Fig. A2. Flow chart of the exploration of the method.

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that move has already led to a reduction in the function value. So, the function is evaluated at the next pattern point. In general, Pi ˆ bi ‡ 2…bi‡1 ÿ bi †: 3.2. Then, continue with exploratory moves about P1, Pi. 3.3. If the lowest value at step 3.2 is less than the value at the base point b2(bi+1 in general), then a new base point b3(bi+2) has been reached. In this case, repeat 3.1. Otherwise, abandon the pattern move from b2(bi+1) and continue with an exploration about b2(bi+1). 4. Terminate the process when the step length(s) has been reduced to a predetermined small value. For each trial point, it is checked whether it lies within the constraint region. If so, the objective function is evaluated in the normal way. If not, the objective function is given a very large value. In this way, the search method will be directed back into the feasible region and, hence, towards the minimum point within the feasible region. The ¯ow charts of the method are given in Figs. A1 and Fig. A2. References [1] Usta N. Computerized Analysis and Economic Optimization of Refrigeration Systems. MS Thesis, Mechanical Engineering Department, METU, Ankara, 1993. [2] Wall G. I. J. of Refrigeration 1991;14:336. [3] Dhar P.L. Optimization in Refrigeration system. Ph.D. Thesis in Mechanical Engineering, Indian Institute of Technology, Delhi, 1974. [4] Granryd E. 1990. I.I.R/I.I.F Commission E2, Stockholm. [5] Cerepnalkovski I. 1990. I.I.R/I.I.F Commission E2, Stockholm. [6] Siddiqui MA. Energy Conversion and Management 1997;38(9):889. [7] Siddiqui MA. Energy Conversion and Management 1997;38(9):905. [8] Sun DW. Energy Sources 1997;19(7):677. [9] Sun DW. Applied Thermal Engineering 1997;17(3):211. [10] Tan FL, Ameen A, Fok SC. Computer Applications in Engineering Education 1997;5(2):115. [11] Dossat RJ. Principles of Refrigeration. London: John Wiley & Sons, 1981. [12] ASHRAE. Equipment Handbook, 1988 Chapter 20. [13] ASHRAE. Application Handbook, 1991 Chapter 33. [14] Birim Fiat and Tari¯eri, Bayindirlik ve Iskan Bakanligi, Ankara (in Turkish) Unit Cost List, Ministry of Public Works of Turkey, 1995. [15] Bunday BD. Basic Optimization Methods. Baltimore: Edward Arnold Ltd, 1984.