Reheat cycle at 14 bar: ideal efficiency

Assumptions: ideal cycle, isentropic expansion, feed pump work included ($W_p = v_f \Delta p$). Values from steam tables (IAPWS-IF97).

States: 1 = 14 bar, 300 C; 2 = 5 bar after HP turbine; 3 = 5 bar, 300 C (after reheat); 4 = 0.2 bar exhaust; 5 = saturated water at 0.2 bar.

Steam table data

(h in kJ/kg, s in kJ/kg K)

State 2: $s_2 = 6.9553 > s_g$ at 5 bar, so steam is slightly superheated (about 177.6 C). From the superheated table, $h_2 = 2807.1$ kJ/kg.

State 4:

$$\begin{aligned} x_4 &= \frac{7.4614 - 0.8320}{7.0753} = 0.9370 \\ h_4 &= 251.40 + 0.9370 \times 2357.55 = 2460.4\ \text{kJ/kg} \end{aligned}$$

Pump work: $W_p = 0.001017 (1400 - 20) = 1.40$ kJ/kg

(a) With reheating

$$\begin{aligned} W_T &= (h_1 - h_2) + (h_3 - h_4) \\ &= (3041.0 - 2807.1) + (3064.6 - 2460.4) \\ &= 233.9 + 604.2 = 838.1\ \text{kJ/kg} \\ W_{net} &= 838.1 - 1.4 = 836.7\ \text{kJ/kg} \\ Q_s &= (h_1 - h_5 - W_p) + (h_3 - h_2) \\ &= (3041.0 - 251.40 - 1.40) + (3064.6 - 2807.1) \\ &= 2788.2 + 257.5 = 3045.7\ \text{kJ/kg} \\ \eta &= \frac{836.7}{3045.7} = 0.2747 \end{aligned}$$

Answer (a): work done $\approx 836.7$ kJ/kg (838.1 kJ/kg turbine work), ideal efficiency $\approx 27.5\%$

(b) Without reheating

Steam expands directly from 14 bar, 300 C to 0.2 bar with $s = 6.9553$:

$$\begin{aligned} x &= \frac{6.9553 - 0.8320}{7.0753} = 0.8655 \\ h &= 251.40 + 0.8655 \times 2357.55 = 2291.8\ \text{kJ/kg} \\ W_T &= 3041.0 - 2291.8 = 749.2\ \text{kJ/kg} \\ W_{net} &= 749.2 - 1.4 = 747.8\ \text{kJ/kg} \\ Q_s &= 3041.0 - 251.40 - 1.40 = 2788.2\ \text{kJ/kg} \\ \eta &= \frac{747.8}{2788.2} = 0.2682 \end{aligned}$$

Answer (b): work done $\approx 747.8$ kJ/kg (749.2 kJ/kg turbine work), ideal efficiency $\approx 26.8\%$

If pump work is neglected, the efficiencies are 27.5% and 26.9%. Reheat increases work by about 12%, efficiency slightly, and makes the exhaust much drier.