Professional steam turbine analysis: shaft power, electrical output, condenser heat duty, cooling water flow for all 4 turbine types. Powered by pyXSteam (±0.01 kJ/kg) with instant NIST table fallback.
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Rankine cycle theory · IAPWS-IF97 formulations · Turbine types · Worked examples · FAQ · Glossary
A steam turbine converts thermal energy in high-pressure steam into mechanical shaft work, driving a generator to produce electricity. The theoretical cycle is the Rankine cycle — four processes:
1→2 Isentropic Expansion (Turbine): Steam expands through nozzles and blades, converting enthalpy into shaft work. Entropy is constant in the ideal case; blade losses, tip leakage, and friction reduce real output below the isentropic ideal.
2→3 Isobaric Heat Rejection (Condenser/Exhaust): Exhaust steam condenses in a surface condenser (condensing turbine) or discharges to a lower-pressure process header (back-pressure turbine).
3→4 Isentropic Compression (Feed Pump): Condensate is pumped back to boiler pressure. Pump work is small (<2% of cycle work), often neglected in first-pass calculations.
4→1 Isobaric Heat Addition (Boiler/Superheater): Feed water is heated, boiled, and superheated at constant pressure. This is the largest heat input and determines fuel consumption.
Mollier (h–s) diagram: isentropic expansion is a vertical line; real expansion slopes right due to irreversibilities. Back-pressure (2ᵦₚ) has a small Δh; condensing (2c) uses the full pressure ratio for maximum power output.
Back-Pressure
Exhausts to a process steam header above atmospheric (1–20 bar abs). No condenser needed. Exhaust steam is fully available for process heating — true CHP with overall efficiencies of 70–85%.
Condensing
Exhausts to a sub-atmospheric condenser (0.04–0.10 bar abs). Maximum enthalpy drop = maximum power. Requires cooling water. Used in power stations (30–48% electrical efficiency).
Extraction (Pass-Out) — A controlled bleed at intermediate pressure for process use; remainder expands to final exhaust. Total power = Stage 1 + Stage 2:
Case A — Superheated exhaust (s₁ < sg at P₂)
Case B — Wet steam exhaust (sf₂ < s₁ < sg₂)
Common inlet conditions (IAPWS-IF97):
| P₁ (bar) | T₁ (°C) | h₁ (kJ/kg) | s₁ (kJ/kg·K) | Application |
|---|---|---|---|---|
| 10 | 180 | 2778 | 6.587 | Small industrial back-pressure turbine |
| 20 | 250 | 2903 | 6.545 | Medium CHP / district heating |
| 40 | 400 | 3214 | 6.958 | Industrial power station |
| 60 | 450 | 3302 | 6.719 | Combined cycle HRSG turbine |
| 100 | 500 | 3374 | 6.599 | Subcritical utility turbine |
| 250 | 600 | 3336 | 6.177 | Ultra-supercritical plant |
| Turbine Type | η_cycle | Heat Rate (kJ/kWh) | SSR (kg/kWh) | CHP η |
|---|---|---|---|---|
| Back-pressure (CHP) | 15–25% | 14 400–24 000 | 8–16 | 70–85% |
| Condensing (utility) | 30–38% | 9 470–12 000 | 4–7 | 30–38% |
| Supercritical condensing | 42–48% | 7 500–8 570 | 3.5–4.5 | 42–48% |
| Extraction CHP | 20–35% | 10 300–18 000 | 5–10 | 60–80% |
This calculator uses pyXSteam (IAPWS-IF97 via Pyodide) for maximum accuracy, with a built-in NIST saturation table fallback. Follow the steps below for any turbine type.
Click one of the four type buttons at the top of the calculator. Input fields and result labels update automatically:
| Type | Exhaust Goes To | Extra Inputs | Key Output |
|---|---|---|---|
| Back-Pressure | Process header (>1 bar) | P₂ header pressure | Process heat duty |
| Condensing | Surface condenser | Condenser pressure | Condenser duty, quality x |
| Extraction | Process bleed + exhaust | P_ext, bleed fraction | Stage 1 & 2 power split |
Toggle SI / Imperial. Enter absolute pressure P₁ and temperature T₁. The calculator auto-fills h₁ and s₁ from IAPWS-IF97. T_sat is shown so you can verify degree of superheat (T₁ − T_sat ≥ 10°C recommended).
For back-pressure: enter the process header pressure. For condensing: enter condenser pressure (0.04–0.10 bar abs). If you don't have cooling water data, use 0.07 bar abs (39°C, typical for temperate climates) as a conservative starting point.
Enter ṁ (kg/h), isentropic η_t, mechanical η_m and generator η_g. Defaults in the calculator (η_t=0.85, η_m=0.98, η_g=0.97) are reasonable for an industrial multi-stage turbine. For small single-stage units use η_t=0.65–0.72.
Scenario: 40 bar abs / 400°C steam at 60 000 kg/h, exhaust to 4 bar abs. η_t=0.80, η_m=0.98, η_g=0.97.
Isentropic efficiency η_t is the ratio of actual turbine work to the theoretical work if expansion were perfectly isentropic (reversible and adiabatic). On the Mollier diagram, isentropic expansion is a vertical line; real expansion slopes right because irreversibilities generate entropy.
Real losses arise from: (1) blade profile losses — boundary layer separation, trailing-edge wakes; (2) tip clearance leakage — steam bypasses blade tips without doing work; (3) disc windage and friction; (4) partial admission losses in small impulse turbines; (5) last-stage moisture losses in condensing turbines. Practical ranges: single-stage BP (≤500 kW): 62–75%; multi-stage industrial (0.5–50 MW): 78–86%; large utility (>100 MW): 87–92%.
Steam quality x < 0.88 means >12% liquid droplets in exhaust — these erode last-stage blades by high-velocity impact (Baumann: each 1% moisture reduces stage efficiency ~1%).
Solutions: (1) Raise inlet superheat — increase T₁ at fixed P₁; (2) Raise inlet pressure at fixed T₁; (3) Add interstage reheating — extract, reheat, re-admit; (4) Fit moisture separators between stages; (5) Apply stellite erosion shields on blade tips as a materials fix. Options 1–3 are thermodynamic fixes; options 4–5 are mitigations.
Rearrange the power equation: ṁ = W_target / [(h₁−h₂s) × η_t × η_m × η_gen] in kg/s.
Quick method: enter ṁ = 3600 kg/h (1 kg/s) and note the power. Then scale: ṁ_required = 3600 × (target_kW / calculated_kW) kg/h. Cross-check against your boiler's rated evaporation capacity. Always add 10–15% margin for startup, fouling, and part-load operation.
A pressure reducing valve (PRV) throttles steam in an isenthalpic process — no work is extracted, all pressure energy is destroyed as heat. A back-pressure turbine performing the same pressure reduction extracts shaft work first; exhaust steam arrives at the same condition and is equally useful for process heating.
Example: a 10 bar → 3 bar letdown at 10 t/h wastes ~350 kW of shaft work potential. A turbine-generator recovering this is worth ~£245 000/year at £80/MWh. Capital cost £300 000–500 000 → simple payback 1.2–2 years. Most industrial CHP schemes also qualify for government incentives.
Lower condenser pressure P₂ = lower T_sat = lower h₂ = larger Δh = more power. Each 0.01 bar reduction in P₂ below 0.07 bar abs adds ~5–15 kJ/kg to the enthalpy drop (~0.5–1% efficiency gain). Minimum P₂ is set by cooling water temperature (condenser T_sat must exceed CW inlet by ≥5–8°C), air ingress risk, last-stage blade annular area, and the x ≥ 0.87 erosion limit. Typical values: Northern Europe ≈ 0.030–0.045 bar; Middle East ≈ 0.060–0.090 bar.
Geothermal / HRSG: Yes — any steam turbine using water/steam as the working fluid is fully supported. IAPWS-IF97 covers 0–2000°C and 0–100 MPa.
Organic Rankine Cycle (ORC): No — ORC uses organic fluids (pentane, R245fa, toluene) with completely different thermodynamic properties. IAPWS-IF97 does not apply. Use CoolProp or REFPROP for ORC calculations — results from this calculator for ORC conditions will be completely incorrect.
Reheat extracts partially expanded steam from an intermediate stage, reheats it to near-inlet temperature in the boiler reheater, then re-admits it for further expansion. Benefits: ~4–6% efficiency gain; dryer exhaust (higher x); more specific work per kg steam.
To model with this calculator: Run Case 1 for HP turbine (P₁, T₁ → P_reheat). Note h_reheat_out. Run Case 2 for LP turbine using P_reheat and T_reheat as the "inlet" → P₂. Sum both shaft powers. This gives accurate results if reheat temperature is known.