Rankine Cycle Steam Solver
This tool solves the Rankine steam power cycle using the IAPWS-IF97 formulation for water and steam
properties. Enter any two independent properties at each state point and it fills in the rest,
exactly the way you would by hand. Energy balances around the boiler, turbine, condenser, and pump
then link the four states into a complete cycle, including thermal efficiency, back-work ratio,
and net work output.
Works for ideal isentropic cycles and actual cycles with pump and turbine isentropic efficiencies.
Flags over-specified or conflicting states so you know immediately if the inputs are inconsistent.
Runs entirely in the browser. No account required.
How to use the Rankine cycle solver
- Set pressure and temperature units using the segmented controls in the left sidebar. Options are kPa, MPa, bar, or psi for pressure; C or K for temperature.
- Toggle assumptions to match your problem. Isobaric boiler and condenser are on by default, which links P across each component. Enabling sat. liquid at pump inlet fixes x = 0 at State 1 automatically.
- Enter any two properties at each state. The green dots on the schematic indicate solved states. Teal fields are filled in by the solver; you can override any of them by typing a value directly.
- Read cycle performance in the right panel. Net work, heat input, heat rejected, thermal efficiency, and back-work ratio update instantly.
- Enter a mass flow rate (optional) to convert specific work and heat quantities into power and heat rates (kW).
- Export the full cycle summary using Copy (PNG to clipboard), PNG (download), or PDF. The T-s and P-v diagrams can be exported separately from their own buttons.
The Rankine cycle: a quick review
The ideal Rankine cycle is the standard model for steam power plants. It consists of four processes:
- 1 to 2: Pump (isentropic compression). Sat. liquid from the condenser is pumped to boiler pressure. The pump work is small relative to turbine work, giving a low back-work ratio.
- 2 to 3: Boiler (isobaric heat addition). Water is heated, boiled, and typically superheated at constant pressure. This is where the bulk of heat input occurs.
- 3 to 4: Turbine (isentropic expansion). Superheated steam expands through the turbine, producing work. The turbine exit may be wet (two-phase) or superheated depending on inlet conditions and condenser pressure.
- 4 to 1: Condenser (isobaric heat rejection). Wet or superheated steam at low pressure condenses to sat. liquid, rejecting heat to the cooling medium.
Worked example: ideal Rankine cycle
Problem: Boiler at 8 MPa / 480 C, condenser at 8 kPa. Ideal isentropic cycle. Find thermal efficiency.
State 3 (turbine inlet): P = 8 MPa, T = 480 C. IAPWS-IF97 gives h3 = 3349.5 kJ/kg, s3 = 6.661 kJ/kg·K.
State 1 (pump inlet): sat. liquid at 8 kPa. h1 = 173.9 kJ/kg, s1 = 0.593 kJ/kg·K.
State 4 (turbine exit): s4 = s3 at 8 kPa gives x4 = 0.795, h4 = 2083.4 kJ/kg.
State 2 (pump exit): s2 = s1 at 8 MPa gives h2 = 181.9 kJ/kg.
Result: w_net = (h3 - h4) - (h2 - h1) = 1258.1 kJ/kg; q_in = 3167.6 kJ/kg; thermal efficiency = 39.7%.
Key cycle quantities
| Quantity | Expression | Notes |
|---|
| Turbine work | w_t = h3 - h4 | Per unit mass flow |
| Pump work | w_p = h2 - h1 | Small for liquids |
| Heat input | q_in = h3 - h2 | Boiler |
| Heat rejected | q_out = h4 - h1 | Condenser |
| Thermal efficiency | eta = w_net / q_in | First law |
| Back-work ratio | bwr = w_p / w_t | Typically 0.5-2% |
Ways to improve Rankine cycle efficiency
- Increase boiler pressure. Higher boiler pressure raises the mean temperature of heat addition, improving efficiency. Wet turbine exit quality decreases, which is the main constraint.
- Superheat the steam. Superheating increases h3 and usually raises turbine exit quality, allowing higher boiler pressures in practice.
- Decrease condenser pressure. Lower condenser pressure lowers the temperature of heat rejection. Condenser pressure is limited by the available cooling medium temperature.
- Reheat cycle. Steam is expanded partway in the turbine, reheated in the boiler, then expanded again. Reduces moisture at exit while maintaining efficiency gains from high pressure.
- Regenerative feedwater heating. Extracted steam from the turbine heats the feedwater, reducing boiler heat input and improving cycle efficiency.
Frequently asked questions
What is IAPWS-IF97?
IAPWS-IF97 is the International Association for the Properties of Water and Steam industrial
formulation from 1997. It covers water and steam from 0 to 800 C and up to 100 MPa using
region-based equations for enthalpy, entropy, and specific volume. This solver implements
Regions 1 (compressed liquid) and 2 (superheated steam) along with the saturation curve (Region 4).
What does "two independent properties fix a state" mean?
For a pure substance with one phase (liquid or vapor), specifying any two intensive properties
(P, T, h, s, v) fully determines the thermodynamic state. In the two-phase region, P and T
are no longer independent, so you need quality x as one of the two inputs instead.
The solver detects which region a state is in and uses the appropriate equations.
Why is my turbine exit quality below 0.85?
Low exit quality means a large fraction of the steam is liquid droplets at the turbine exit,
which erodes turbine blades. The practical lower limit is usually around x = 0.85. To increase
exit quality, superheat the steam further, raise the boiler pressure (counterintuitively, higher
pressure with sufficient superheat gives higher exit quality), or use a reheat stage.
Can I use this for refrigeration cycles?
Not directly. This solver is specific to water/steam via IAPWS-IF97. Vapor-compression
refrigeration cycles use different working fluids (R-134a, R-410A, etc.) with their own
property tables. A refrigerant property solver is on the roadmap for Resultant.
Part of Resultant,
a free suite of browser-based tools for undergraduate engineering coursework.
No backend, no account, no paywall.