Description

Adiabatic expansion of steam in a turbine, characterized by its isentropic efficiency. Water and steam properties are evaluated with the IAPWS Industrial Formulation 1997 (IAPWS-IF97).

Steam turbine

Calculation methods

• Shaft power: power, outlet temperature, outlet quality and specific steam consumption for a given steam flow, inlet state, outlet pressure and isentropic efficiency.
• Isentropic efficiency from the outlet temperature: efficiency and power of an operating turbine from the measured inlet and outlet conditions. Applicable while the outlet steam is superheated.
• Steam flow for a required power: steam mass flow and specific steam consumption needed to deliver a given shaft power.

Model

State 1 is the inlet ($P_{in}$, $\dot{m}_{in}$ in the figure) and state 2 the outlet ($P_{out}$). The isentropic outlet state $2s$ is found at $P_2$ with the inlet entropy; the real outlet enthalpy follows from the isentropic efficiency:

$s_{2s} = s_1 \qquad \eta_{iso} = \frac{h_1 - h_2}{h_1 - h_{2s}} \qquad h_2 = h_1 - \eta_{iso} (h_1 - h_{2s})$

$\dot{W} = \dot{m} (h_1 - h_2) \qquad SSC = \frac{3600}{h_1 - h_2}$

where $h$ is the specific enthalpy (kJ/kg), $s$ the specific entropy, $\dot{m}$ the steam mass flow, $\dot{W}$ the shaft power (kW) and $SSC$ the specific steam consumption (kg/kWh). The outlet temperature and quality $x_v$ follow from $P_2$ and $h_2$. The mass flow is the same at inlet and outlet.

Range of application

• The inlet steam must be superheated or supercritical. Properties are valid up to 800 °C at pressures up to 100 MPa.
• Adiabatic expansion: heat losses, leakage, extraction and the generator efficiency are not included; the power is the shaft power.
• An outlet quality below about 0.88 indicates moisture levels that cause erosion of the last-stage blades.
• The efficiency from the outlet temperature requires a superheated outlet: for wet steam, the temperature equals the saturation temperature and does not determine the enthalpy.