Question

A vapor-compression refrigeration system which operates on the cascade cycle arrangement shown below is used to obtain refrigeration at a low temperature. Refrigerant-12 is the working fluid in the high-temperature cycle and Refrigerant-13 is used in the low-temperature cycle. For the Refrigerant 13 cycle, the working fluid enters the compressor as saturated vapor at -30°F and is compressed isentropically to 250 lbf/in2. Saturated liquid leaves the intermediate heat exchanger at 250 lbf/in2 and enters the expansion valve. For the Refrigerant 12 cycle, the working luid enters the compressor as saturated vapor at 20°F and is compressed isentropically to 160 lbf/in?. Saturated liquid enters the expansion valve at 160 lbf/in2. The refrigerating capacity of the cascade system is 20 tons. The tables shown below list property data for both Refrigerants. Determine: a) the power input to each compressor, in Btu/min, b the rate of heat transfer from the Refrigerant 12 passing through the high temperature condenser, in Btu/min, c) e oeral coefficient of performance of the cascade cycle, and d) the irreversibility rate of the intermediate heat exchanger, in Btu/min. Use To 90F, p 14.7 Ibl/in 586.3 Bin, 772 Bn m 57637 2268 d)2.24 Data for Refrigerant 13 P (psia) T(F h (Btu/lb) 106.3 30 2.46 s (Btu/lb/R) 54.4 40 h60.0 0.1265 0.1265 se 0.0352 250.0 250.0 40 h 16.2 Cycle B ata for Refrigerant heat eachang P (psia) T(F h (Btu/lb) 35.736 20 12.86 160.0 114.3 h 34.59 160.0 120h89.283 s0.1 s (Btu/IbR) 0.0285 he 79.38 0.1672 S0.0693 h, 88.18 0.1626 Cycle A Cos- -temperature 160.0 140 h93.059 0.1709

Answer 1

Given Data:

Qin 20 tons 4000 Btu/min

T, = 90°F-550° R

For Low-Temperature cycle properties of R-13 at various states

State 1 : Sat. vapor and -30°F

$h_1 =54.4\, \, Btu/lb\, \, \textup{and } s_1=0.1265\, \, Btu/lb^{\circ}R$

$\textup{State 2 : P = 250}\, \, lbf/in^ 2\textup{ and } s_2=s_1$

h2- 60 Btu/lb

State 3 Sat. Liquid and P 250 Ibf /in2

$h_3 = 16.2\, Btu/lb \textup{ and }s_3 = 0.0352\, \, Btu/lb^{\circ} R$

$\textup{State 4: } h_4 = h_3$

14 162 Btu/lb

$\textup{For High-Temperature cycle properties of R-12 at various states :}$

$\textup{State 5 : Sat. Vapor and T = 20}^{\circ}F$

$h_5 =79.38\, Btu/lb\, \,\textup{ and } s_5 = 0.1672\, \, Btu/lb^{\circ}R$

$\textup{State 6 : P = 160 } \, lbf/in^2 and \, \, s_6=s_5$

$h_6 = 90.876\, \, Btu/lb\, \, \, \, \, \, \, \textup{(On interpolation)}$

$\textup{State : 7 Sat. Liquid and P = 160\, }lbf/in^2$

$h_7 = 34.59\, Btu/lb \, \,\textup{ and } \, \, s_7 = 0.0285 \, Btu/lb^{\circ}R$

$\textup{State : 8 }h_8 =h_7$

$h_8 = 34.59\, Btu/lb\textup{ and }s_8=0.0738\, \, Btu/lb^{\circ}R$

$\textup{The Mass Flow rate for cycle A can be determined as : }(R-13)$

$\dot{m_A}=\frac{Q_{in}}{h_1-h_4}=\frac{4000}{54.4-16.2}=104.712\, \, \, lb/min$

$\textup{Using energy balance in heat exchanger to find flow rate in cycle B : }$

$\therefore \dot{m_A}(h_2-h_3)=\dot{m}_B(h_5-h_8)$

$\therefore 104.712(60-16.2)=\dot{m_B}(79.38-34.59)\, \Rightarrow \, \dot{m}_B=102.398\, \, lb/min$

$\textup{a)The power input to each compressor :}$

$W_A =\dot{m}_A(h_2-h_1)=104.712(60-54.4)$

${\color{DarkBlue} \therefore W_A=586.38\, \, Btu/min}$

$W_B= \dot{m_B}(h_6-h_5)=102.398(90.876-79.38)$

${\color{DarkBlue} \therefore W_B =1177.2\, \, Btu/min}$

$\textup{b)The rate of heat transfer in High Temperature Condenser : }Q_{out}$

$Q_{out}= \dot{m}_B(h_6-h_7)=102.398(90.876-34.59)$

${\color{DarkBlue} \therefore Q_{out}= 5763.6\, \, Btu/min}$

$\textup{c) The overall coefficient of performance of the cascade cycle : }(\beta)$

$(\beta )=\frac{Q_{in}}{W_A+W_B}=\frac{4000}{(586.38+1177.2)}$

${\color{DarkBlue} \therefore \beta =2.2681}$

$\textup{d) The irreversibility rate of the intermediate heat exchanger : } (I)$

$I =T_0[\dot{m}_A(s_3-s_2)+\dot{m}_B(s_5-s_8)]$

${\color{DarkBlue} \therefore I =2.2\, \, Btu/min}$