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Thermodynamic Calculations of Cascade Vapor Compression Refrigeration Cycle

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Thermodynamic Calculations of Cascade Vapor Compression Refrigeration Cycle

Introduction

In the event that a high COP of a refrigeration cycle is of greater importance compared to other factors, it is possible to significantly increase the COP of a basic cycle through the use of a multistage vapor compression cycle. This is especially true when the pressure ratio between the heat rejection and heat absorption pressures is large 5 or more.
Multistaging involves one or more intermediate pressures between the heat rejection and heat absorption pressures, and a series of compressors operating between successive pressure intervals.
Cascade cycle is simply a chain of single stage vapor compression cycles operating in series, such that the condenser of a lower temperature cycle provides the heat input to the evaporator of the higher temperature cycle.

Creation functions on properties and processes of working fluids

with(ThermophysicalData):

Pressure in the saturated region as a function of temperature, quality and working fluid

Temperature in the saturated region as a function of pressure, quality and working fluid

Specific enthalpy in the saturated region as a function of temperature, quality and working fluid

Specific enthalpy in the saturated region as a function of pressure, quality and working fluid

Specific entropy in the saturated region as a function of temperature, quality and working fluid

Specific entropy in the saturated region as a function of pressure, quality and working fluid

Density in the saturated region as a function of temperature, quality and working fluid

Density in the saturated region as a function of pressure, quality and working fluid

Temperature as a function of pressure, specific entropy and working fluid

Temperature as a function of pressure, specific enthalpy and working fluid

Specific enthalpy as a function of pressure, temperature and working fluid

Specific entropy as a function of pressure, temperature and working fluid

Density as a function of pressure, temperature and working fluid

Specific entropy as function of pressure and specific enthalpy and working fluid

Density as function of pressure and specific enthalpy and working fluid

ScompPTPEFFwf := proc (p1, T1, p2, eff, wf) local h2, T2; h2 := HcompPTPEFFwf(p1, T1, p2, eff, wf); T2 := TPHwf(p2, h2, wf); return SPTwf(p2, T2, wf) end proc:

TcompPTPEFFwf := proc (p1, T1, p2, eff, wf) local h2; h2 := HcompPTPEFFwf(p1, T1, p2, eff, wf); return TPHwf(p2, h2, wf) end proc:

DcompPTPEFFwf := proc (p1, T1, p2, eff, wf) local h2, T2; h2 := HcompPTPEFFwf(p1, T1, p2, eff, wf); T2 := TPHwf(p2, h2, wf); return DPTwf(p2, T2, wf) end proc:

Critical temperature as a function of working fluid

Critical pressure as a function of working fluid

Input Data

Temperature of heat source

(3.1)

Temperature of heat consumption

(3.2)

Temperature difference in the evaporator

(3.3)

Temperature difference in the condenser

(3.4)

Temperature difference between working fluids in low pressure and high pressure circuits

(3.5)

Isentropic efficiency of the compressor

(3.6)

Pressure increase in compressor 1

(3.7)

Working fluid in low pressure circuit

(3.8)

Working fluid in high pressure circuit

(3.9)

Calculations

Temperature of the working fluid at the evaporator outlet

(4.1)

Pressure of the working fluid at the evaporator outlet

(4.2)

Specific enthalpy of the working fluid at the evaporator outlet

(4.3)

Specific entropy of the working fluid at the evaporator outlet

(4.4)

Specific volume of the working fluid at the evaporator outlet

0.4881666858e-1*Units:-Unit(m^3/kg)

(4.5)

Pressure of the working fluid at the compressor 1 outlet

(4.6)

Pressure of the working fluid at the condenser outlet

(4.7)

Temperature of the working fluid at the condenser outlet

(4.8)

Specific enthalpy of the working fluid at the condenser outlet

(4.9)

Specific enthalpy of the working fluid at the condenser outlet

(4.10)

Specific volume of the working fluid at the condenser outlet

0.9388227496e-3*Units:-Unit(m^3/kg)

(4.11)

Pressure of the working fluid at the evaporator intlet

(4.12)

Specific enthalpy of the working fluid at the evaporator intlet

(4.13)

Temperature of the working fluid at the evaporator intlet

(4.14)

Specific enthalpy of saturated liquid of the working fluid at the evaporator inlet

(4.15)

Quality of the working fluid at the evaporator intlet

x[4, L] := Units:-Standard:-`*`(Units:-Standard:-`+`(h[4, L], Units:-Standard:-`-`(h[sl, 4, L])), Units:-Standard:-`/`(Units:-Standard:-`+`(h[1, L], Units:-Standard:-`-`(h[sl, 4, L]))))

(4.16)

Specific entropy of saturated liquid of the working fluid at the evaporator inlet

(4.17)

Specific volume of saturated liquid of the working fluid at the evaporator inlet

0.8220990714e-3*Units:-Unit(m^3/kg)

(4.18)

Specific entropy of the working fluid at the evaporator inlet

(4.19)

Specific volume of the working fluid at the evaporator inlet

0.1219334720e-1*Units:-Unit(m^3/kg)

(4.20)

Specific entropy of the working fluid at the compressor 1 outlet after isentropic compression

(4.21)

Temperature of the working fluid at the compressor 1 outlet after isentropic compression

(4.22)

Specific enthalpy of the working fluid at the compressor 1 outlet after isentropic compression

(4.23)

Enhtalpy change in the compressor after isentropic compression

(4.24)

Enhtalpy change in the compressor 1 after actual compression

l[c1] := Units:-Standard:-`*`(Units:-Standard:-`+`(h[2, L, is], Units:-Standard:-`-`(h[1, L])), Units:-Standard:-`/`(eta[comp]))

(4.25)

Specific enthalpy of the working fluid at the compressor 1 outlet after actual compression

(4.26)

Specific enthalpy of the working fluid at the compressor 1 outlet after actual compression

(4.27)

Specific entropy of the working fluid at the compressor 1 outlet after actual compression

(4.28)

Specific volume of the working fluid at the compressor 1 outlet after actual compression

0.1878649972e-1*Units:-Unit(m^3/kg)

(4.29)

Temperature of the working fluid at the compressor 2 intlet

(4.30)

Pressure of the working fluid at the compressor 2 intlet

(4.31)

Specific enthalpy of the working fluid at the compressor 2 intlet

(4.32)

Specific entropy of the working fluid at the compressor 2 intlet

(4.33)

Specific volume of the working fluid at the compressor 2 intlet

0.3400315959e-1*Units:-Unit(m^3/kg)

(4.34)

Temperature of the working fluid at the condenser outlet

(4.35)

Pressure of the working fluid at the condenser outlet

(4.36)

Specific enthalpy of the working fluid at the condenser outlet

(4.37)

Specific entropy of the working fluid at the condenser outlet

(4.38)

Specific volume of the working fluid at the condenser outlet

0.1016510305e-2*Units:-Unit(m^3/kg)

(4.39)

Pressure of the working fluid at the compressor 2 outlet

(4.40)

Pressure increase in the compressor 2

pi__2 := Units:-Standard:-`*`(p[2, H], Units:-Standard:-`/`(p[1, H]))

(4.41)

Pressure of the working fluid at the expansion valve 2 outlet

(4.42)

Specific enthalpy of the working fluid at the expansion valve 2 outlet

(4.43)

Temperature of the working fluid at the expansion valve 2 outlet

(4.44)

Specific enthalpy of saturated liquid of the working fluid at the expansion valve 2 outlet

(4.45)

Quality of the working fluid at the expansion valve 2 outlet

x[4, H] := Units:-Standard:-`*`(Units:-Standard:-`+`(h[4, H], Units:-Standard:-`-`(h[sl, 4, H])), Units:-Standard:-`/`(Units:-Standard:-`+`(h[1, H], Units:-Standard:-`-`(h[sl, 4, H]))))

(4.46)

Specific entropy of saturated liquid of the working fluid at the expansion valve 2 outlet

(4.47)

Specific volume of saturated liquid of the working fluid at the expansion valve 2 outlet

0.8206876245e-3*Units:-Unit(m^3/kg)

(4.48)

Specific entropy of the working fluid at the expansion valve 2 outlet

(4.49)

Specific volume of the working fluid at the expansion valve 2 outlet

0.1509289005e-1*Units:-Unit(m^3/kg)

(4.50)

Specific entropy of the working fluid at the compressor 2 outlet after isentropic compression

(4.51)

Temperature of the working fluid at the compressor 2 outlet after isentropic compression

(4.52)

Specific enthalpy of the working fluid at the compressor 2 outlet after isentropic compression

(4.53)

Enhtalpy change in the compressor 2 after isentropic compression

(4.54)

Enhtalpy change in the compressor 2 after actual compression

l[c2] := Units:-Standard:-`*`(Units:-Standard:-`+`(h[2, H, is], Units:-Standard:-`-`(h[1, H])), Units:-Standard:-`/`(eta[comp]))

(4.55)

Specific enthalpy of the working fluid at the compressor 2 outlet after actual compression

(4.56)

Specific enthalpy of the working fluid at the compressor 2 outlet after actual compression

(4.57)

Specific entropy of the working fluid at the compressor 2 outlet after actual compression

(4.58)

Specific volume of the working fluid at the compressor 2 outlet after actual compression

0.9158027894e-2*Units:-Unit(m^3/kg)

(4.59)

Ratio of mass flow rates between the high pressure circuit and that of the low pressure circuit

phi := Units:-Standard:-`*`(Units:-Standard:-`+`(h[2, L], Units:-Standard:-`-`(h[3, L])), Units:-Standard:-`/`(Units:-Standard:-`+`(h[1, H], Units:-Standard:-`-`(h[4, H]))))