Rankine Cycle Calculator
Estimate ideal Rankine cycle performance for steam power plants: thermal efficiency, specific work, heat input and rejection, plus state properties at each point in the cycle.
Cycle Inputs
Typical boiler pressures: 3–18 MPa.
Typical condenser pressures: 0.005–0.015 MPa.
Superheated steam: 400–600 °C.
Set to 100% for an ideal Rankine cycle.
Pump losses are usually small; 80–90% is typical.
Used to compute total power and heat rates.
Key Results
Performance
- Thermal efficiency \(\eta_{th}\): – %
- Back work ratio \(w_p / w_t\): –
- Specific turbine work \(w_t\): – kJ/kg
- Specific pump work \(w_p\): – kJ/kg
- Specific net work \(w_{net}\): – kJ/kg
- Specific heat input \(q_{in}\): – kJ/kg
- Specific heat rejection \(q_{out}\): – kJ/kg
Power & Heat Rates
- Net power output \(\dot{W}_{net}\): – MW
- Turbine power \(\dot{W}_t\): – MW
- Pump power \(\dot{W}_p\): – MW
- Boiler heat rate \(\dot{Q}_{in}\): – MW
- Condenser heat rate \(\dot{Q}_{out}\): – MW
Cycle State Points (Approximate)
Properties are estimated using simple correlations (constant specific heats, saturated liquid at condenser, superheated vapor at turbine inlet). For design work, always verify with real steam tables or software.
| State | Description | p (MPa) | T (°C) | h (kJ/kg) | s (kJ/kg·K) |
|---|---|---|---|---|---|
| 1 | Saturated liquid at condenser outlet | – | – | – | – |
| 2 | Compressed liquid at pump outlet | – | – | – | – |
| 3 | Superheated vapor at turbine inlet | – | – | – | – |
| 4 | Turbine exhaust (wet vapor) | – | – | – | – |
What is the Rankine cycle?
The Rankine cycle is the idealized thermodynamic cycle used to model steam power plants. Water is pumped to high pressure, heated in a boiler to produce high-pressure steam, expanded through a turbine to produce work, and then condensed back to liquid in a condenser.
Four basic processes
- 1 → 2: Pump (liquid compression) – Increases pressure from condenser to boiler pressure. Work input \(w_p\).
- 2 → 3: Boiler (heat addition) – Adds heat at (approximately) constant pressure. Heat input \(q_{in}\).
- 3 → 4: Turbine (expansion) – Steam expands, producing shaft work \(w_t\).
- 4 → 1: Condenser (heat rejection) – Rejects heat to the environment at low temperature \(q_{out}\).
Key performance equations
Specific turbine work
\[ w_t = h_3 - h_4 \]
Specific pump work (approximate, incompressible liquid)
\[ w_p \approx v_f (p_2 - p_1) \]
Specific net work
\[ w_{net} = w_t - w_p \]
Heat input in boiler
\[ q_{in} = h_3 - h_2 \]
Heat rejection in condenser
\[ q_{out} = h_4 - h_1 \]
Thermal efficiency
\[ \eta_{th} = \frac{w_{net}}{q_{in}} = 1 - \frac{q_{out}}{q_{in}} \]
How this calculator approximates steam properties
Exact Rankine cycle analysis requires steam tables or an equation of state. To keep this tool fully client-side and fast, we use simplified correlations that are accurate enough for teaching, quick checks, and order-of-magnitude design:
- State 1 is assumed to be saturated liquid at condenser pressure. We approximate \(T_{sat}(p)\), \(h_f(p)\), and \(s_f(p)\) with smooth curves fitted to typical steam-table values.
- State 2 is a compressed liquid at boiler pressure. We use \(w_p \approx v_f (p_2 - p_1)\) with \(v_f \approx 0.001\ \text{m}^3/\text{kg}\) and \(h_2 \approx h_1 + w_p / \eta_P\).
- State 3 is superheated vapor at boiler pressure and specified temperature. We approximate enthalpy and entropy using constant specific heats: \(h_3 \approx h_{g,ref} + c_{p,g}(T_3 - T_{ref})\).
- State 4 is found from an isentropic expansion (with turbine efficiency) to condenser pressure, then mixing saturated liquid and vapor to match the entropy.
These approximations reproduce the qualitative behavior and typical efficiencies of Rankine cycles, but they are not a substitute for detailed design. For engineering decisions, always confirm with full steam-table software (e.g., IAPWS-IF97, NIST REFPROP, EES, or similar).
Improving efficiency
Real power plants use several modifications to improve Rankine cycle efficiency:
- Reheat – Steam is expanded in a high-pressure turbine, reheated, then expanded again.
- Regeneration – Feedwater heaters use extracted steam to preheat the condensate.
- Higher boiler pressure and temperature – Within material limits, this increases efficiency.
- Lower condenser pressure – Reduces exhaust temperature and increases turbine work.