Question

a)        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.

Answer 1

Given information;

Initial pressure, $p_1=100kPa$

Initial temperature, $T_1=25° C$

Compression ratio, r =5

Turbine inlet temperature, $T_3=850°C$

At temperature $T_1=25°C=298 K$

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 $T_3=850° C=1123 K$

$h_3=1184.28+{(1123-1120)/(1140-1120)}×(1207.57-1184.28)=1187.77 kJ/kg$

$(p_r)_3=179.7+{(1123-1120)/(1140-1120)}×(193.1-179.7)=181.71$

$(p_r)_4=(p_4/p_3)((p_r)_3= 1/5 ×181.71=36.342$

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

$η=\dfrac{(1187.77-767.38)-(472.8168-298.608)}{1187.77-472.8168}$

$η=0.344\\ η=34.4 \%$

The back work ratio

$bwr = W_c/W_t=(h_2-h_1)/(h_3-h_4)$

$bwr =\dfrac{(472.8168-298.608)}{(1187.77-767.38)}$

$bwr =0.4144\\ bwr = 41.44 \%$