Gas turbine 800 kW with regenerator

Cycle: 1–2 compressor, 2–x regenerator (air side), x–3 combustion chamber, 3–4 turbine, 4–y regenerator (gas side) to exhaust.

Data: $p_1 = 100$ kPa, $T_1 = 288$ K, $\dot m = 6$ kg/s, $r_p = 6$, $T_3 = 900$ K, $\varepsilon = 0.8$, $\eta_c = \eta_t = 0.85$, $c_p = 1.005$ kJ/kg K, $\gamma = 1.4$, so $\frac{\gamma-1}{\gamma} = 0.2857$ and $r_p^{0.2857} = 6^{0.2857} = 1.6685$.

     +----------- Regenerator ---------+
     |  x (hot air)        y (exhaust) |
 1   |2                     4          |
 -> [C] ------> [CC] -3-> [T] ---------+
      \=========shaft=====/  ==> Gen

Compressor

$$\begin{aligned} T_{2s} &= T_1 r_p^{0.2857} = 288 \times 1.6685 = 480.53\ \text{K} \\ T_2 &= T_1 + \frac{T_{2s}-T_1}{\eta_c} = 288 + \frac{192.53}{0.85} = 514.51\ \text{K} \\ W_c &= c_p (T_2 - T_1) = 1.005 \times 226.51 = 227.64\ \text{kJ/kg} \end{aligned}$$

Turbine

$$\begin{aligned} T_{4s} &= \frac{T_3}{r_p^{0.2857}} = \frac{900}{1.6685} = 539.40\ \text{K} \\ T_4 &= T_3 - \eta_t (T_3 - T_{4s}) = 900 - 0.85 \times 360.60 = 593.49\ \text{K} \\ W_t &= c_p (T_3 - T_4) = 1.005 \times 306.51 = 308.04\ \text{kJ/kg} \end{aligned}$$

Regenerator and heat supplied

Since $T_4 > T_2$, regeneration is possible:

$$\begin{aligned} T_x &= T_2 + \varepsilon (T_4 - T_2) = 514.51 + 0.8(593.49 - 514.51) = 577.70\ \text{K} \\ Q_s &= c_p (T_3 - T_x) = 1.005(900 - 577.70) = 323.92\ \text{kJ/kg} \end{aligned}$$

Efficiency and power

$$\begin{aligned} W_{net} &= W_t - W_c = 308.04 - 227.64 = 80.40\ \text{kJ/kg} \\ \eta_{th} &= \frac{W_{net}}{Q_s} = \frac{80.40}{323.92} = 0.2482 = 24.82\% \\ P_{net} &= \dot m W_{net} = 6 \times 80.40 = 482.4\ \text{kW} \end{aligned}$$

For comparison, without the regenerator $Q_s = 1.005(900 - 514.51) = 387.42$ kJ/kg and $\eta = 20.75\%$, so the regenerator raises efficiency by about 4.1 percentage points.

Answer: Plant thermal efficiency = 24.82 %, net power developed = 482.4 kW (with the given data the plant cannot actually deliver its rated 800 kW at 6 kg/s).