Answer to Question #170739 in Mechanical Engineering for PULI Gayathridevi

Question

An ideal Brayton-cycle gas turbine with regeneration but no reheat or intercoolingoperates at full load with an inlet temperature to the compressor of 60oF and an inlet temperature to the turbine of 1540oF. The cycle is also to be operated at part load at a pressure ratio of 3.0 with a turbine inlet temperature of 1100o F. Compare the thermal efficiency and network output per lbm flow for the two operating points if the working fluid (air) is treated as a perfect gas and the maximum possible regeneration is obtained.

Answer 1

Full Load

$1. T_1=520R, P_1=1atm$

$1 \to 2$ isentropic compressor

$T_2=T_1(\frac{P_2}{P_1})^{\frac{k-1}{k}}=540 R(6)^{\frac{1.4-1}{1.4}}=867.6R$

$4 \to 5$ isentropic turbine

$T_5=T_4(\frac{P_5}{P_4})^{\frac{k-1}{k}}=2000 R(\frac{1}{6})^{\frac{1.4-1}{1.4}}=1199R$

$\eta_t=\frac{W_t-W_c}{Q_{in}}$

$\frac{W_t}{m}=(h_4-h_5)=c_p(T_4-T_5)=0.24(2000-1199)=192 Btu/lbm$

$\frac{W_c}{m}=(h_2-h_1)=c_p(T_2-T_1)=0.24(867.6-520)=83.4Btu/lbm$

$\frac{Q_{in}}{m}=(h_4-h_3)=c_p(T_4-T_3)=\frac{W_t}{m}=192 Btu/lbm$

$\eta_t=\frac{192-83.4}{192}=56.2$ %

$\frac{W_{net}}{m}=\frac{W_t-W_c}{m}=109 Btu/lbm$

Part Load

$1 \to 2$ isentropic compressor

$T_2=T_1(\frac{P_2}{P_1})^{\frac{k-1}{k}}=711.7R$

$4 \to 5$ isentropic turbine

$T_5=T_4(\frac{P_5}{P_4})^{\frac{k-1}{k}}=1139.8R$

$\frac{W_t}{m}=c_p(T_4-T_5)=0.24(1560-1140)=101 Btu/lbm$

$\frac{W_c}{m}=c_p(T_2-T_1)=0.24(711.7-520)=46Btu/lbm$

$\frac{Q_{in}}{m}=\frac{W_t}{m}=101 Btu/lbm$

$\eta_t=\frac{101-46}{101}=54.4$ %

$\frac{W_{net}}{m}=101-46=55 Btu/lbm$