Gas turbine with reheat and 90% regenerator

Assumptions: air-standard ideal cycle; compression in one stage (100 to 1000 kPa) and two-stage expansion are isentropic; no pressure losses; $c_p = 1.005$ kJ/kg K, $\gamma = 1.4$, so $\frac{\gamma-1}{\gamma} = 0.2857$.

 1 ->[ C ]-2->[ Regen ]-x->[ CC ]-3->[ T1 ]-4
                 ^   |
                 |   v y (to exhaust)
 4 ->[ Reheater ]-5->[ T2 ]-6 -> hot side of Regen

States: 1 (100 kPa, 300 K) - compressor - 2 (1000 kPa) - regenerator - x - combustor - 3 (1400 K) - HP turbine - 4 (300 kPa) - reheater - 5 (1400 K) - LP turbine - 6 (100 kPa) - regenerator - y (exhaust).

1. Compressor exit temperature

$$\begin{aligned} T_2 &= T_1 \left(\frac{p_2}{p_1}\right)^{0.2857} = 300 \times 10^{0.2857} \\ &= 300 \times 1.9307 = 579.21\ \text{K} \end{aligned}$$

2. Turbine exit temperatures

First stage, 1000 kPa to 300 kPa:

$$T_4 = \frac{T_3}{(1000/300)^{0.2857}} = \frac{1400}{1.4106} = 992.51\ \text{K}$$

Second stage, 300 kPa to 100 kPa, after reheat to $T_5 = 1400$ K:

$$T_6 = \frac{T_5}{(300/100)^{0.2857}} = \frac{1400}{1.3687} = 1022.84\ \text{K}$$

3. Regenerator

Effectiveness $\varepsilon = \dfrac{T_x - T_2}{T_6 - T_2}$, so

$$\begin{aligned} T_x &= T_2 + 0.9(T_6 - T_2) \\ &= 579.21 + 0.9(1022.84 - 579.21) = 978.48\ \text{K} \end{aligned}$$

4. Work and heat (per kg of air)

$$\begin{aligned} W_C &= c_p (T_2 - T_1) = 1.005(579.21 - 300) = 280.61\ \text{kJ/kg} \\ W_{T1} &= c_p (T_3 - T_4) = 1.005(1400 - 992.51) = 409.53\ \text{kJ/kg} \\ W_{T2} &= c_p (T_5 - T_6) = 1.005(1400 - 1022.84) = 379.05\ \text{kJ/kg} \\ W_{net} &= 409.53 + 379.05 - 280.61 = 507.97\ \text{kJ/kg} \end{aligned}$$

Heat supplied in the combustor (x to 3) and reheater (4 to 5):

$$\begin{aligned} Q_s &= c_p (T_3 - T_x) + c_p (T_5 - T_4) \\ &= 1.005(1400 - 978.48) + 1.005(1400 - 992.51) \\ &= 423.63 + 409.53 = 833.16\ \text{kJ/kg} \end{aligned}$$

5. Thermal efficiency

$$\eta_{th} = \frac{W_{net}}{Q_s} = \frac{507.97}{833.16} = 0.6097$$

Answer: thermal efficiency $\eta_{th} \approx 61.0\%$ (0.6097).

The high value comes from the 90% regenerator: the hot turbine exhaust (1022.84 K) preheats the compressed air from 579.21 K to 978.48 K, so the fuel only has to supply the remaining heat. Reheat raises the work output, and the regenerator recovers most of the extra exhaust heat that reheat produces.