Question

A gas turbine power plant working on the Brayton cycle with regeneration of 80% effectiveness. The air at the inlet to the compressor is at 1 bar and 300 K the pressure ratio is 6 and maximum cycle temperature is 1200 K. The turbine and compressor each have an efficiency of 80%.
The efficiency of the cycle with the regeneration is_______%.

• A. 30.6

Answer 1

The correct option is A 30.6

Given, ${\eta }_{\text{egeneration}}=0.8$
${\eta }_T=0.8={\eta }_C$ $P_T=1bar$
$T_1=300K$
$T_3=1200$
$r_P=\frac{P_2}{P_1}=6$
$\Rightarrow P_2=6\times 1=6bar$
$\left(\frac{T_2}{T_1}\right)={\left(\frac{P_2}{P_1}\right)}^{\frac{\gamma -1}{\gamma }}=(6{)}^{\frac{0.4}{1.4}}$
$\Rightarrow T_2=500.55K$
$\frac{T_4}{T_3}={\left(\frac{P_4}{P_3}\right)}^{\frac{\gamma -1}{\gamma }}$
$\Rightarrow T_4=1200\times {\left(\frac{1}{6}\right)}^{\frac{0.4}{1.4}}=719.2k$
${\eta }_C=\frac{T_2-T_1}{T_2-T_1}$
$\Rightarrow 0.8=\frac{500.55-300}{T_2-300}$
$\Rightarrow T_2^{\prime }=550.68K$
${\eta }_r=\frac{T_4^{\prime }-T_3}{T_4-T_3}$
$\Rightarrow 0.8=\frac{T_4^{\prime }-1200}{719.2-1200}$
$\Rightarrow T_4^{\prime }=815.36K$
${\eta }_{reg}=\frac{T_b-T_2}{T_4^{\prime }-T_2^{\prime }}$ $\Rightarrow 0.8=\frac{T_5-550.68}{815.36-550.68}$ $T_s=762.42K$ $\eta =\frac{W_T-W_C}{Q_S}=\frac{c_p(T_3-T_4^{\prime })-c_p(T_2^{\prime }-T_1)}{c_p(T_3-T_5)}$ $=\frac{(1200-815.36)-(550.68-300)}{(1200-762.72)}=30.6\%$