Question 9.7: Actual Gas-Turbine Cycle with Regeneration Determine the the...

The gas-turbine discussed in Example 9–6 is equipped with a regenerator. For a specified effectiveness, the thermal efficiency is to be
determined.
Analysis The T-s diagram of the cycle is shown in Fig. 9–41. We first determine the enthalpy of the air at the exit of the regenerator, using the definition of effectivenes

\begin{aligned}\epsilon &=\frac{h_{5}-h_{2 a}}{h_{4 a}-h_{2 a}} \\0.80 &=\frac{\left(h_{5}-605.39\right) kJ / kg }{(880.36-605.39) kJ / kg } \rightarrow h_{5}=825.37 kJ / kg\end{aligned}

Thus,

q_{ in }=h_{3}-h_{5}=(1395.97-825.37) kJ / kg =570.60 kJ / kg

This represents a savings of 220.0 kJ/kg from the heat input requirements. The addition of a regenerator (assumed to be frictionless) does not affect the net work output. Thus,

\eta_{\text {th }}=\frac{w_{\text {net }}}{q_{\text {in }}}=\frac{210.41 kJ / kg }{570.60 kJ / kg }=0.369 \text { or } 36.9 \%

Discussion Note that the thermal efficiency of the gas turbine has gone up from 26.6 to 36.9 percent as a result of installing a regenerator that helps to recuperate some of the thermal energy of the exhaust gases.