Steam turbine simulation

1 inlet -> [extraction, exhaust] (extraction / back-pressure staging)

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Governing equations

The exact equations the solver works for a steam turbine — the same math shown in the app's "Theory" panel, not a black box.

S(T_{2s}, P_2) = S(T_1, P_1),\qquad T_2 = T_1 + \eta\,(T_{2s}-T_1)\quad(\text{each section: real-gas isentropic expansion})

\text{HP: } P_1 \to P_{ext},\quad h_{ext} = H(T_{ext}, P_{ext})\quad(\text{full flow } F \text{ expands to the extraction pressure})

\dot m_{ext} = f\,F \ \text{drawn at } P_{ext};\qquad \text{LP: } P_{ext} \to P_{exh}\ \text{on the un-extracted } (1-f)F

W_{shaft} = F\,(h_{in} - h_{ext}) + (1-f)\,F\,(h_{ext} - h_{exh})

T: temperature [K]
P_1: inlet (throttle) pressure [Pa]
P_{ext}: extraction (intermediate draw) pressure [Pa]
P_{exh}: exhaust (back-pressure header / condenser) pressure [Pa]
T_{2s}: isentropic outlet temperature of a section [K]
\eta: per-section isentropic efficiency
F: inlet molar flow [mol/s]
f: extraction fraction (share drawn off at P_ext) [-]
\dot m_{ext}: extraction draw = f·F [mol/s]
h_{in}: inlet molar enthalpy [J/mol]
h_{ext}: molar enthalpy after the HP section (at P_ext) [J/mol]
h_{exh}: exhaust molar enthalpy (after the LP section) [J/mol]
W_{shaft}: total shaft power: HP (full flow) + LP (un-extracted flow) sections [W]

Parameters

outlet_pressure [Pa, exhaust]; optional extraction_pressure [Pa, between exhaust and inlet] + extraction_fraction [0-1] for an extraction draw; efficiency [default 0.80] — multi-section steam expander (extraction / back-pressure), power [W] = sum of both sections; on the steam-tables (IAPWS) package a wet exhaust is tracked (phase 'mixed', exhaust_quality reported) with a Baumann wetness efficiency correction

Steam turbine simulation

Governing equations

Parameters

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