Air enters the compressor of a gas turbine at 100 kPa and 25°C. For a pressure ratio of 5 and a maximum temperature of 850°C determine the back work ratio and the thermal efficiency using the Brayton
cycle.
Given information
Initial pressure, "p_1=100kPa"
Initial temperature, "T_1=25^0 C"
Compression ratio, r =5
Turbine inlet temperature, "T_3=850^0 C"
At temperature "T_1=25^0 C=298 K" and the pressure "p_1=100 kPa"
"h_1=295.17+{(298-295)\/(300-295)}*(300.9-295.17)=298.608 kJ\/kg"
"(p_r)_1=1.3068+{(298-295)\/(300-295)}*(1.386-1.3068)=1.35432"
"(p_r)_2=(p_2\/p_1)((p_r)_1= 5 *1.35432=6.7716"
At "(p_r)_2=6.7716"
By interpolating
"h_2=472.24+{(6.7716-6.742)\/(7.268-6.742)}*(482.49-472.24)=472.8168 kJ\/kg"
At temperature "T_3=850^0 C=1123 K"
"h_3=1184.28+{(1123-1120)\/(1140-1120)}*(1207.57-1184.28)=1187.77 kJ\/kg"
"(p_r)_3=179.7+{(1123-1120)\/(1140-1120)}*(193.1-179.7)=181.71"
"(p_r)_4=(p_4\/p_3)((p_r)_3= 1\/5 *181.71=36.342"
At "(p_r)_4" =36.342
By interpolation
"h_4=756.44+{(36.342-35.5)\/(37.35-35.5)}*(767.29-756.44)=767.38 kJ\/kg"
We know the thermal efficiency of the cycle
"\u03b7={(1187.77-767.38)-(472.8168-298.608)}\/1187.77-472.8168"
"\u03b7=0.344"
The back work ratio
"bwr = W_c\/W_t=(h_2-h_1)\/(h_3-h_4)"
"bwr =(472.8168-298.608)\/(1187.77-767.38)"
"bwr =0.4144"
bwr = 41.44 %
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