exergy_energy analysis refrigeration cascade_Nasruddin.pdf

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol: 10 No: 06

105306-0808 IJMME-IJENS December 2010 IJENS I J E N S

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AbstractThis article presents a thermodynamic energy and

exergy analysis to optimize a cascade refrigeration system to be used for biomedical cold-storage application. An azeotrope mixture carbon dioxide and ethanepropane (R744+R170R290) cascade system has been promoted as a prospective alternative solution to the use of HFC refrigerants. A novel multilinear regression analysis was employed to develop mathematical expressions for maximum COP, optimum evaporating temperatures of the R290 cycle, and an optimum mass flow ratio in terms of evaporating temperature, condensing temperature and temperature differences in the systems cascade condenser. Index Terms Refrigeration, Exergy, Mixture, Carbon dioxide, Ethane, Optimize.

I. INTRODUCTION iomedical preservation requires storing biological specimens like stem cells, sperm, blood and organs, at a

storage temperature of around -80oC. For long-term storage of biological materials, temperatures below -120oC are generally considered to safeguard against the effects of devitrification and Crystallization [1]. The use of a single-cycle vapour compression refrigeration system can only achieve effective cooling of about -40oC, and the efficiency begins to deteriorate under -35oC due to the vast difference between the evaporating and condensing temperatures. Thus, in order to reach a lower temperature, a cascade refrigeration system is utilized [2]. Cascade refrigeration systems consist of at least two refrigeration systems that work independently. The two refrigeration systems are connected by a cascade heat exchanger where heat is released in the condenser low-temperature circuit (LTC) and is absorbed from the evaporator high-temperature circuit (HTC) [1]. Carbon Dioxide is emerging as the most popular and efficient working fluid in the low temperature circuit of these systems.

Manuscript received November 9, 2010. This work was supported in part

by Hibah Riset Pascasarjana 2010 University of Indonesia. M. Idrus Alhamid from Refrigeration and Air-Conditioning Laboratory,

Mechanical Engineering Department - Faculty of Engineering - University of Indonesia, Kampus UI Depok, 16424, Indonesia (corresponding author, e-mail: mamak@ eng.ui.ac.id).

Darwin R.B Syaka is a PhD student in Mechanical Engineering Department - Faculty of Engineering - University of Indonesia, Kampus UI Depok, 16424, Indonesia.

Nasruddin from Refrigeration and Air-Conditioning Laboratory, Mechanical Engineering Department - Faculty of Engineering - University of Indonesia, Kampus UI Depok, 16424, Indonesia.

Nomenclature COP [-] coefficient of performance

DT [oC] temperature difference in the cascade-condenser h [kJ/kg] specific enthalpy

hs [kJ/kg] specific enthalpy calculated at suction entropy

m& [kg/s] mass flow rate

LH mm && [-] ratio of high-temperature circuit mass flow rate to low-temperature circuit mass flow rate

P [kPa] pressure Q& [kW] heat transfer rate RC [-] Compressor pressure ratio S [kJ/kg.K] specific entropy T [oC] temperature W& [kW] work x [-] quality

desX& [kW] rate of exergy destruction Special characters [-] Efficiency [-] Exergetic efficiency [kJ/kg] Stream exergy Subscripts cas Cascade E Evaporator F Cooling space C Condenser H High-Temperature circuit isent Isentropic max maximum opt optimum L Low-Temperature circuit 0 ambient s Isentropic

Carbon dioxide offers many advantages, as it is non-toxic, non-flammable, readily available, inexpensive, and environmentally friendly (i.e. does not damage the ozone layer and has very low global warming potential [3]. However, since the triple point of CO2 is about -56C, it has to be mixed with other refrigerants (e.g. a hydrocarbon) for it to work at required temperatures as low as -85C. Although hydrocarbon refrigerants have good thermo physical properties and are environmentally friendly [4], they can be rendered less flammable if mixed with CO2.

Exergy and Energy Analysis of a Cascade Refrigeration System Using R744+R170 for

Low Temperature Applications M. Idrus Alhamid, Darwin R.B Syaka, and Nasruddin

B



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The experimental study of Niu and Zhang using a mixture of propane and carbon dioxide at low temperatures found the energy efficiency and cooling capacity of this mixture to be higher than R13 [5]. However, this mixture barely reached a minimum temperature of -72oC and the azeotrope mixture of carbon dioxide and propane produces a temperature glide [6]. Therefore an azeotrope mixture produces more efficient results an azeotrope mixture of ethane and carbon dioxide for low temperature applications [7], appears to offer better efficiency (COP) than a mixture of carbon dioxide and propane [8].

Several researchers have evaluated the thermodynamic performance of the two-stage cascade refrigeration systems. Bhattacharyya et al. [9] studied a carbon dioxidepropane (R744R290) optimum cascade evaporating system to define an evaporating temperature of R744 for application in heating circuits. Lee et al. [3] analyzed a carbon dioxideammonia (R744R717) cascade system thermodynamically to determine the optimum condensing temperature of R744 in the low-temperature circuit. Getu and Bansal [10] analyzed a carbon dioxideammonia (R744R717) cascade system thermodynamically to determine the optimum condensing temperature of R744 in the low-temperature circuit and mass flow ratio, to give the system maximum COP in terms of sub-cooling, superheating, evaporating temperature, condensing temperature and temperature difference in the systems cascade condenser. The thermodynamic analysis of the carbon dioxideammonia (R744R717) cascade system by Alberto Dopazo et al. [11] employed both exergy analysis and energy optimization, to determine the optimum condensing temperature of R744 in the low-temperature circuit. However, the aforementioned studies lacked a cascade system thermodynamic analysis of a carbon dioxide and ethanepropane (R744+R170R290) mixture.

Hence, the main aim of the current research is to conduct a thermodynamic energy and exergy analysis to determine the optimum condensing temperature of a carbon dioxide and ethane mixture (R744+R170) in the low-temperature circuit and mass flow ratio, which can optimize the systems COP in several areas, such as for various values of the condensing temperature, the evaporating temperature, and the temperature difference in cascade condenser of the system. The isentropic efficiency is regarded herein as a function of the pressure ratio of the compressor. This study also quantifies the exergy destruction of each component, to determine the contribution of each component to the overall efficiency of the system. A novel multilinear regression analysis was employed to develop mathematical expressions for maximum COP, optimum evaporating and condensing temperatures of the R290 cycle, and an optimum mass flow ratio in terms of evaporating temperature, condensing temperature and temperature difference in the systems cascade condenser.

II. THERMODYNAMIC ANALYSIS OF A CASCADE REFRIGERATION SYSTEM

The thermodynamic analysis of a two-stage cascade refrigeration system was conducted based on the following general assumptions.

1. Non-isentropic compression is expressed as a function of the pressure ratio. The combined motor and mechanical efficiency of each compressor is assumed to be 0.93 [3].

2. Negligible pressure and heat losses/gains in the pipe networks or system components.

3. Isenthalpic expansion across expansion valves. 4. Negligible changes in kinetic and potential energy. 5. The dead state conditions are 25oC and 101.3 kPa. 6. Difference between the refrigerated space

temperature (TF) and the evaporating temperature (TE) is 5oC.

7. System cooling capacity is 0.5 kW. Based on the above assumptions, balance equations are

applied to find the mass flow rate of each cycle, the work input to the compressor, the heat transfer rates of the condenser and the cascade-condenser, the entropy generation rate and the exergy destruction rate as follows:

Mass balance

=outin

mm && (1) Energy balance

=inout

hmhmWQ .. &&&& (2)

Exergy balance

+

=

outinoutj

jdes mmWQT

TX ...1 0 &&&&& (3)

Fig. 1 Schematic diagram of the cascade refrigeration system

CO2+C2H6-C3H8



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Fig. 2 Log P-h diagram of the cascade refrigeration system

CO2+C2H6-C3H8 Specific equations for each systems components are

summarized in table 1. The systems Coefficient of Performance (COP) has been

calculated by the following equation:

LH

E

WWQ

COP &&&+= (4)

The COP of the high temperature circuit has been calculated by the following equation:

H

ECasH W

QCOP &

&,= (5)

and for the low-temperature circuit

L

EL W

QCOP &&= (6)

The second-law efficiency of the whole system is defined as the ratio of the actual COP to the ideal COPcarnot, which is

carnotCOPCOP= (7)

Where:

EC

Ecarnot TT

TCOP =

(8)

The rate of heat transfer in the cascade heat exchanger is determined by:

)()( 3285 hhmhhmQ LHcas == &&& (9) The mass flow ratio can be derived from eq. (9) as

85

32/hhhh

mm LH =&& (10)

The equations of the mathematical model reveal that both the systems COP and its energetic efficiency can be expressed as a function of six design/operating parameters, as shown in the equation:

(COP,) = f (TE , TC , Tcas,E , DT, s) (11) The thermodynamic state points of the cascade refrigeration

system are presented in Table 2. In this analysis the parameter variations, include the cascade evaporating temperature (Tcas,E), varying from 0oC to -42oC, the temperature of the condenser varying from 30oC to 40oC, the evaporating temperature from -80oC to -90oC, and the temperature difference in the cascade heat exchanger from 0oC to 10oC. The impact of these parameters on the refrigeration system performance as the COP and exergy efficiency was analyzed.

The isentropic efficiency of each compressor is considered to be equal to the volumetric efficiency and it is estimated following the equation [11]

s = 1 0.04.RC (12) All refrigerant thermophysical properties were obtained

from the REFPROP 8 [12], for several state points as shown in Fig. 1 and 2, and are directly calculated for the system analysis main program with FORTRAN language.

Table 1 Balance equations for each system component Component mass energy exergy

High-temperature circuit

Compressor 56 mm && = Hm

sH

hhmW,

565 )(

= && )( 565 = mWX Hdes &&& Condenser 67 mm && = )( 677 hhmQC = && )( 767 = mX des &&Expansion device 78 mm && = 78 hh = )( 878 = mX des &&Cascade condenser 2385

, mmmm &&&& == )()( 233855 hhmhhmQcas == &&& )()( 233585 = mmX des&&&

High-temperature circuit

Compressor 12 mm && = Lm

sL

hhmW,

121 )(

= && )( 121 = mWX Ldes &&& Expansion device 34 mm && = 34 hh = )( 434 = mX des && evaporator 41 mm && = )( 411 hhmQE = && )(1 1410 +

= mQ

TTX E

Fdes &&&



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III. RESULTS AND DISCUSSION

A. Carbon Dioxide and Ethane Composition Selection Figure 3 shows the effect of a carbon dioxide (CO2) and

ethane (C2H6) composition in mole fraction at a condensing temperature (TC) = of 35oC, a temperature in the cascade evaporator heat exchanger (Tcas,E) = of -35oC, a temperature difference between the high temperature circuit evaporator and the low-temperature circuit condenser in the cascade heat exchanger (DT) = of 5oC and an evaporating temperature (TE) = of -85oC.

Fig. 3 Effect of CO2 composition on COP

Figure 3 shows that increasing the CO2 composition will generally decrease the COP of the system, whereas the highest COP value is obtained with 100% ethane. This can be explained by the fact that ethane has the high refrigeration effect and excellent performance in the low temperature circuit of a cascade refrigeration system [7]. A composition of less than 8% ethane (92% CO2) can not be used if the evaporator temperature (TE) is lower than -85oC, in order to prevent CO2 from reaching a solid vapour phase. Also, the ethane composition must be kept as low as possible to reduce ethane flammability.

Therefore, the composition that produces the best COP at mole fraction of carbon dioxide ethane is at 0.54 and 0.46 and is chosen as the optimum composition for an evaporator temperature of -85oC at its azeotrope point. Based on the above data, the cascade refrigeration system was analyzed for the mole fraction composition of 54% carbon dioxide and 46% ethane.

Since an azeotrope mixture of carbon dioxide and ethane is being promoted as a prospective alternative solution to HFC refrigerants, it is compared with R23 and R508b. It can be seen from Figure 4 that when the refrigerant propane is used in a high-temperature circuit, the COP value of the azeotrope mixture carbon dioxide + ethane functioning in the cascade condensing temperature is more effective than the COP of R508b and R23. Figure 4 shows that the relationship of Tcas,E with COP is not linear.

Fig, 4 Effect of Tcas,E on COP of some selection refrigerants

B. Exergy Destruction Figure 5 plots the curves of COP versus Tcas,E at TC = 35oC,

TE = -85oC and DT = 5oC. These plots are of the Tcas,E on the COP of the High-Temperature Circuit and the Low-Temperature Circuit, as determined by Eqs. (5) and (6). The COP of the High-Temperature Circuit increases with increasing Tcas,E, whereas the COP of the Low-Temperature Circuit decreases as Tcas,E increases is apparent in a carbon dioxide and ethane mixture (54+46). As shown in figure 4 it represents a balance between COPL and COPH. It can be seen that the intersection of COPL and COPH in figure 5.

Tabel 2 Calculation of thermodynamic state points of cascade system using REFPROP 8

Evaporator outlet Compressor outlet Condenser outlet Exspansion device outlet High-temperature circuit P5 = f (Tcas,E, x=1) P6=P7 P7=f(TC, x=0) P8=P5 T5= Tcas,E T6=f(P6, S5) T7=TC T8= Tcas,E h5 = f (T5, P5) h6s = f (P6, S5) h7= f (T7, P7) h8=h7 S5 = f (T5, P5) h6 = (h6s h5)/isent+ h5 S7= f (T7, P7) S8= f (P5, h8) Low-temperature circuit P1 = f (TE, x=1) P2=P3 P3=f(Tcas,C, x=0) P4=P4 T1= TE T2=f(P6, S1) T3= T5 DT=Tcas,C T4= TE h1 = f (T1, P1) h2s = f (P2, S1) h3= f (T3, P3) h4=h3 S1 = f (T1, P1) h2 = (h2s h1)/isent+ h1 S3= f (T3, P3) S4= f (P1, h4)



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Fig. 5 Effect of Tcas,E on COPL and COPH

The Maximum COP usually indicates minimum exergy destruction. It is shown by Fig 4 where the maximum COP for the refrigerant azeotrope mixture of carbon dioxide and ethane occurs in Tcas,E is equal by minimum exergy destruction system as shown in Fig 6. Fig. 6 shows the effect of Tcas,E on the exergy destruction of each component at the specified conditions, with a condensing temperature (TC) of 35oC, an evaporating temperature (TE) of -85oC and a temperature difference in the cascade-condenser (DT) of 5oC. Table 1 presents the details of the exergy analysis. The overall system efficiency is derived from the exergy destruction of each component. Therefore, focusing on exergy and its destruction for each component is a more direct way of analyzing the potential for enhancing the energy efficiency of the cascade refrigeration system.

Fig. 6 Effect of Tcas,E on exergy destruction rates of each

component and the whole system

Fig. 6 indicates that the exergy destruction rates of the components in the high-temperature (C3H8) circuit, except the cascade-condenser, decrease as Tcas,E increases. The exergy destruction rates of the compressor and the expansion valve in the low-temperature (CO2+C2H6) increases with increasing Tcas,E, while The exergy destruction rates of the evaporator is not affected by an increased Tcas.E. When Tcas,E = -40oC, the C3H8 compressor has the largest exergy destruction, followed in order by the CO2+C2H6 compressor, the C3H8 expansion valve, the condenser, the cascade-condenser, the CO2+C2H6 expansion valve and the evaporator. When Tcas,E is shifted to -20oC, however, the CO2+C2H6 compressor has the largest exergy destruction, followed by the C3H8 compressor, the cascade-condenser, the CO2+C2H6 expansion valve, C3H8 expansion valve, the condenser and the evaporator.

Notably, the amount of exergy destruction of some components increased as Tcas,E increased, but the others decreased. Accordingly, the total exergy destruction rate of the system is minimum at a certain Tcas,E, as shown in Fig. 6 where it is strongly influenced by compressor. This means that the largest irreversibilities occurring in a compressor are associated the largest irreversibilities occur in compressor is associated with the electrical, mechanical and isentropic efficiencies which are low because of the relatively small size of system considerably here. These large losses emphasize the need to pay close attention to the selection of this type of equipment, since components of inferior performance can considerably reduce the overall performance of the system.

C. Parameters Effect on COP and Exergetic Efficiency To evaluate the effect of the operating parameters on both

the systems COP and exergetic efficiency, a statistical procedure was used to analyze the parametric study results using the range of values indicated in the previous section. This statistical procedure is called the Bivariate Correlations. In Table 3, the results of the Pearson correlations can be observed. All of the evaluated parameters are statistically significant at the 0.001 level (2-tailed). Therefore, all the parameters considered in Eq. (13) should be included in the analysis and none should be discarded.

As seen in Table 3, the COP system is heavily affected by the compressor isentropic efficiency (sL and sH), LH mm && , TE, Tcas,E opt, DT and TC.

Table 3 Bivariate Correlation results of COP and exergetic efficiency TC TE DT sH sL Tcas,E opt COPmax II lh mm &&COPmax Pearson Correlation -0.420** 0.732** -0.534** 0.970** 0.974** 0.631** 1 0.975*

* -0.948**

Sig. (2-tailed) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 N 1331 1331 1331 1331 1331 1331 1331 1331 1331

II Pearson Correlation -0.343** 0.622** -0.703** 0.945** 0.942** 0.658** 0.975** 1 -0.875** Sig. (2-tailed) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 N 1331 1331 1331 1331 1331 1331 1331 1331 1331

**. Correlation is significant at the 0.01 level (2-tailed).



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Fig. 7 The COP system and exergetic efficiency as a function of (a) TE, (b)

DT and (c) TC Also, the compressor isentropic efficiency, LH mm && and TE

have a greater effect than Tcas,E opt and DT on the system COP; while the influence of TC is relatively small. Increases in the compressor isentropic efficiency and TE add to the COP system; however increases in DT and TC diminish the COP system.

The exergetic efficiency is clearly affected by the compressor isentropic efficiency (sH and sL), LH mm && , DT, Tcas,E opt, TE and TC. Just as was seen in the COP system, an increase in the compressor isentropic efficiency and TE results in an increase in the exergetic efficiency, and an increased DT and TC decreased exergetic efficiency.

In fig. 7, the COP system and the exergetic efficiency trends with TE (a), DT (b) and TC(c) are shown reveals as a linear relationship.

For all the cases previously studied, the compressor isentropic efficiency was considered as a function of the compression ratio using Eq. (12). Varying isentropic efficiencies in high-temperature and low-temperature circuits are shown in fig. 8 and show that the relationship between the compressor isentropic efficiency and the COP is not linear. It can be seen that the sL and sH cross at certain conditions.

Fig. 8 The COP system and exergetic efficiency as function of

the isentropic efficiency of compressor

Fig. 9 The COP system and exergetic efficiency as function of

LH mm && The mass flow rates ratio indicates the requirements for

compressor power consumption. A large ratio of the mass flow rate is also an indicator of the amount of power consumed by the compressor system. Fig. 9 shows that the COP trend is not a linear relationship. These results indicate that a maximum COP exists that corresponds to an LH mm && optimal value.

Fig. 10 shows the behavior of both the COP and the exergetic efficiency versus Tcas,E opt variations. These results indicate that there is a Tcas,E optimal value. Consequently, a maximum COP exists that corresponds to the Tcas,E opt optimal value. This optimal value also corresponds to the minimum for the exergy loss rate of the whole system, as can be seen in Fig.6.



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Fig. 10 The COP system and exergetic efficiency as a function

of Tcas,E

D. Optimization Fig. 11a shows the effect of the evaporating temperature TE

on the corresponding COPmax at various condensing temperatures TC and various temperature differences in the cascade-condenser DT. The figure shows that decreasing TE reduces COPmax. Fig. 11a reveals the linear relationships between COPmax and the parameters of TE, TC and DT.

Figs. 11b shows the influence of the evaporating temperature TE on the corresponding LH mm && opt at various condensing temperatures TC and various temperature differences in the cascade-condenser DT. The figure shows that decreasing TE increases LH mm && OPT. Fig. 11b also reveals the linear relationships between LH mm && OPT and the parameters of TE, TC and DT.

Fig. 11c presents the effect of the evaporating temperature TE on the corresponding Tcas,E opt at various condensing temperatures TC and various temperature differences in cascade-condenser DT. The figure shows that increasing TE will increases Tcas,E opt. Fig. 11c again reveals a linear relationship.

The effects of various parameters on the performance of the azeotrope mixture of carbon dioxide and ethanepropane cascade system have been observed. It is therefore imperative to develop mathematical equations as a guide for setting optimum thermodynamic design parameters.

Fig. 11 The influence of TE on (a) the COPmax, (b) on the

LH mm && opt and (c) the Tcas,E opt of a CO2+C2H6-C3H8 cascade refrigeration system .

Table 4 Summary of statistical information for eq. (15)-(17)

Predictor COPmax LH mm && OPT TCAS,E,OPT

Standard Error Coefficient

Probability Standard Error Coefficient

Probability

Standard Error Coefficient

Probability

Constant 0.0034400 0.000 0.0155400 0.000 0.2349000 0.00 TE 0.0000374 0.000 0.0001687 0.000 0.0025500 0.00 DT 0.0000374 0.000 0.0001687 0.000 0.0025500 0.00 TC 0.0000374 0.000 0.0001687 0.000 0.0025500 0.00

Number of points (n) = 1330 Number of points (n) = 1330 Number of points (n) = 1330 rms = 0.00431239 rms = 0.0194632 rms = 0.294205 Adjusted R2 = 99.8% Adjusted R2 = 98.2% Adjusted R2 = 98.8%



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With a multilinear method, the maximum coefficient of performance (COPmax), the optimum mass flow ratio of high-

temperature circuit to that of low-temperature circuit LH mm && opt and the optimum evaporating temperature of high-temperature circuit (Tcas,E,opt) of the cascade system were charted as a function of the input predictor variable data, such as evaporating (TE), condensing (TC), and difference in cascade heat exchanger temperatures (DT). The development of the regressed equations included the calculation of 1330 data sets.

The resulting equations for the maximum COP, the optimum mass ratio and the optimum cascade evaporating temperature are, respectively, given by:

COPmax = 2.78 + 0.0206 TE - 0.0150 DT - 0.0118 TC (13)

LH mm && opt = -2.17 - 0.0365TE + 0.0133DT + 0.0241TC (14)

Tcas,E opt = 11.5 + 0.664 TE - 0.397 DT + 0.368 TC (15) The unit used in Eqs. (13) to (15) is Celsius (oC). A

summary of statistical information is shown in table 4. The standard error coefficient is the standard error of the curve fit parameters, defined as the square root of the estimated variance of the parameter. The smaller the standard error the more precise the estimator. The probability value in table 4, indicates that the relationship between the predictor and the response variable is statistically significant at an a-level of .05 (2-tailed). This is also shown by the fact that the probability value for the estimated coefficient of the predictor variable is 0.000, which means that the predictor variable was significantly affected by the response variable.

The root mean square error is a frequently-used measure of the differences between values predicted by a model. An adjusted R2 that adjusts for the number of explanatory terms in a model can be interpreted as the portion of the total variation that is accounted for by the predictor variable. An adjusted R2 value of 98.2% of LH mm && opt means that 98.2% is due to the predictors variables while the remaining 1.8% is caused by something else.

IV. CONCLUSION This work studies the maximum coefficient of performance

COPmax for CO2+C2H6-C3H8 cascade refrigeration systems in reference to three design parameters: condensing temperature TC, evaporating temperature TE, and the temperature difference in the cascade-condenser DT. The following conclusions are drawn from the analytical results for a CO2+C2H6-C3H8 cascade refrigeration system.

1. For a specific system and operating conditions, results show that following both, exergy and energy optimization methods, an optimal condensing temperature of a cascade-condenser can be obtained.

2. An increase in the evaporating temperature increases the COP of the system and decreases the mass flow ratios. An increase in the temperature difference in the cascade condenser reduces both the COP and mass flow ratios.

An increase in the condensing temperature results in a decrease in the COP and an increase in refrigerant mass flow ratios

3. Using a multilinear regression method, the maximum coefficient of performance (COPmax), the optimum mass flow ratio of high-temperature circuit to that of low-temperature circuit,

LH mm && Opt, and the optimum evaporating temperature of high-temperature circuit (Tcas,E,opt) of the cascade system, can be obtained from Eqs. (13) (15).

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