Question 9.8: Actual Gas-Turbine Cycle with Regeneration Determine the the...

The gas turbine discussed in Example 9–7 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. 9–42. We first determine the enthalpy of the air at the exit of the regenerator, using the definition of effectiveness:

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

Thus,

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

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

Thus,

\eta_{\mathrm{th}}=\frac{w_{\mathrm{net}}}{q_{\mathrm{in}}}=\frac{210.41  \mathrm{~kJ} / \mathrm{kg}}{570.60  \mathrm{~kJ} / \mathrm{kg}}=0.369 \quad \text { or } \quad 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 recover some of the thermal energy of the exhaust gases.