EngineerHub.orgLiquid pressurization
Saturated condensate enters the feed pump and is raised from condenser pressure to boiler pressure. The fluid remains liquid; shaft work causes only a small rise in enthalpy and temperature.
Work input: wp = h2 − h1Drawing No. EH–PG–004 // Power Generation & Grid
Rankine Cycle Simulator & Calculator
Reviewed August 2026
Calculate and learn a simple, reheated, regenerative, or combined reheat-and-regeneration Rankine steam cycle. Follow each process from condensate pumping through boiler heat addition, turbine expansion and condensation, then inspect efficiency, heat rate, power, steam quality, state points, and live T–s and h–s diagrams.
Industrial steam properties: water and steam states are evaluated with an in-page implementation of IAPWS-IF97 Regions 1, 2, 3 and 4. The model runs entirely in your browser and checks 12 official IF97 benchmark states when the page loads.
Cycle performance
Thermal efficiency
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thermodynamic cycle
Heat rate
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kJ/kWh
Net power
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at entered steam flow
Net specific work—
Gross turbine work—
Pump work—
Total heat input—
Condenser heat rejection—
Final turbine-exit condition—
Extraction / bleed fraction—
First-law residual—
Thermodynamic state points
| State | Pressure | T (°C) | h (kJ/kg) | s (kJ/kg·K) | x | Phase |
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Simple Rankine cycle: state-by-state process guide
The four cards correspond to the simple-cycle state numbers. Reheat and regenerative options add intermediate states, which are explained below and reflected automatically in the table and diagrams.
Boiler heat addition
High-pressure water is heated in the economizer, evaporated at saturation, and normally superheated before the turbine. This is the principal external heat input to the cycle.
Heat input: qin = h3 − h2Turbine expansion
Steam expands to condenser pressure and produces shaft work. A real turbine generates entropy, so its enthalpy drop is smaller than for an ideal isentropic expansion.
Work output: wt = h3 − h4Condensation
Exhaust steam rejects heat at nearly constant condenser pressure until it becomes saturated liquid again. The pump can then repeat the cycle.
Heat rejected: qout = h4 − h1When advanced options are enabled: reheat divides turbine expansion into high- and low-pressure sections with a reheater between them. Regeneration diverts a calculated steam fraction to an open feedwater heater, creating two pump processes and a direct-contact mixing state. State numbers therefore change with the selected arrangement; use the active state table as the definitive sequence.
Background
Engineering basis, governing equations, assumptions, diagrams and validation of the Rankine-cycle model.
The model applies steady-flow mass and energy balances to the pump, boiler, turbine, reheater, open feedwater heater and condenser. It supports four arrangements: a simple cycle, reheat only, one ideal open feedwater heater only, and reheat combined with one open heater.
All specific energies are calculated per kilogram of main steam entering the high-pressure turbine. When extraction is enabled, only the remaining fraction continues through the final turbine section and condenser. The entered steam mass flow scales specific net work into thermodynamic net power.
State 1 is saturated liquid leaving the condenser at the selected condenser pressure. The pump raises this liquid to the pressure required by the boiler or, in a regenerative cycle, first to the open-feedwater-heater pressure.
Because liquid water has a small specific volume, a large pressure increase requires comparatively little specific work. The ideal pump process is isentropic; the actual outlet enthalpy is corrected by pump isentropic efficiency:
h2 = h1 + (h2s − h1)/ηpThe pressure rises sharply, but temperature, entropy and enthalpy rise only slightly. That is why states 1 and 2 nearly overlap on a full-cycle T–s or h–s diagram. The magnified pump inset preserves the actual calculated Δh, Δs and ΔT without falsely enlarging the main-cycle path.
Physical interpretation
- Energy crosses the boundary as shaft work into the fluid.
- No external heat transfer is assumed.
- The fluid remains a compressed liquid; no boiling occurs in the pump.
- Higher boiler pressure increases pump work, but pump work normally remains much smaller than turbine work.
The boiler-side process is modelled as heat addition at the selected boiler pressure. It represents several physical heat-transfer zones that may be separate pieces of equipment in a real plant.
Economizer: compressed feedwater is heated toward the saturation temperature. Evaporator: latent heat converts saturated liquid into saturated vapor at nearly constant temperature and pressure. Superheater: additional heat raises the vapor temperature above saturation before turbine admission.
qboiler = h3 − h2Increasing main-steam temperature generally raises the average temperature of heat addition and can improve both cycle efficiency and turbine-exit dryness. Raising boiler pressure can improve ideal-cycle efficiency, but without sufficient superheat or reheat it may also make the turbine exhaust wetter.
At the turbine inlet, high-pressure steam expands and transfers energy to the rotor as shaft work. The ideal reference process keeps entropy constant. A real turbine has aerodynamic losses, leakage and other irreversibilities, so its actual enthalpy drop is reduced by the entered isentropic efficiency.
h4 = h3 − ηt(h3 − h4s)The actual path therefore moves to the right on a T–s or h–s diagram because entropy increases. If the outlet enters the saturation dome, steam quality x is the vapor mass fraction. Lower quality means more liquid moisture. The page reports quality as an educational screening indicator; actual permissible moisture is turbine-specific.
With reheat enabled, this expansion is divided into HP and LP sections. Steam first expands to reheat pressure, receives additional heat, and then expands to condenser pressure from a hotter and usually drier starting state.
The condenser removes the exhaust enthalpy that was not converted into work and returns the working fluid to liquid. In the idealized model, heat rejection occurs at the selected condenser pressure until saturated liquid is reached.
qout = h4 − h1Condenser pressure is linked to the saturation temperature at which heat can be transferred to the cooling system. Lower pressure increases the available turbine enthalpy drop and usually improves efficiency, but it also increases equipment size, air-ingress sensitivity and the risk of wet turbine exhaust. Real condensers may produce slightly subcooled condensate and experience pressure losses; those effects are outside this model.
The simple-cycle shorthand is 1 pump inlet → 2 pump outlet → 3 turbine inlet → 4 turbine outlet → 1. Extra equipment creates extra thermodynamic states, so the numbering must expand.
Reheat: pump outlet, main-steam inlet, HP-turbine outlet, reheater outlet and LP-turbine outlet are all separate states. Regeneration: the condensate pump, open-heater outlet, boiler-feed pump and extraction point are separate states. Combined mode: both sets are present.
The state table and plotted labels always use the active sequence generated by the solver. Do not assume that “state 3” means the same physical location in every preset; follow the state name as well as its number.
For an adiabatic turbine section with isentropic efficiency ηt:
hout = hin − ηt(hin − hout,s)For a pump:
hout = hin + (hout,s − hin)/ηpThe model solves the isentropic outlet state from pressure and inlet entropy using the same IF97 property engine; it does not rely on a fixed vΔP approximation.
ηth = wnet/qin HR = 3600/ηthFor the ideal open feedwater heater, the bleed fraction is obtained from the mixing balance:
y hbleed + (1−y)hcondensate = hsat.liq, FWHThe page implements IAPWS-IF97 Region 1 for compressed liquid, Region 2 for superheated steam, Region 3 for dense fluid near the critical region, and Region 4 for saturation. Region selection is automatic.
At startup, the code checks nine Region 1–3 property points and three Region 4 saturation points against official IF97 verification tables. A failed self-test blocks calculation and displays an error rather than silently returning suspect results.
The interface is restricted to subcritical boiler pressure below 22.064 MPa and temperatures no higher than 650 °C. It does not use Region 5.
Superheat raises the average temperature of external heat addition and often improves both efficiency and turbine-exit dryness. Reheat interrupts expansion, returns steam to a high temperature, and normally produces a much drier final exhaust. Regeneration sacrifices some turbine flow to preheat feedwater, thereby reducing low-temperature boiler heat addition.
These improvements do not guarantee the same ranking for every input set. Extraction pressure, reheat pressure, component efficiencies and condenser conditions all matter, which is why the simulator performs a complete state-by-state balance.
The saturation dome separates compressed liquid, two-phase mixture and superheated vapor. Boiler and reheater paths are sampled at constant pressure using the property engine, while turbine and pump paths connect their calculated inlet and outlet states. A dashed extraction line denotes bleed flow to the open heater rather than a full-main-flow process.
Pump work is included in every balance. On a full Rankine-cycle T–s or h–s plot, the pump temperature and enthalpy rise is only a few pixels compared with the boiler and turbine ranges, so states 1 and 2 can appear almost coincident. The diagram therefore includes a locally magnified pump inset; the inset uses the same calculated state values and reports the actual Δh, Δs and, on the T–s view, ΔT.
The plant schematic emphasizes mass-flow routing. The Sankey is a first-law energy view: total external heat input divides into net cycle work and condenser heat rejection. Band thicknesses are proportional to the calculated specific-energy flows.
The cycle is steady-state and neglects kinetic and potential energy, piping pressure drops, boiler and condenser pressure losses, heat leakage, turbine gland leakage, generator losses and mechanical losses. Turbine and pump isentropic efficiencies are constant. The open feedwater heater is ideal and leaves as saturated liquid at extraction pressure.
The SI/US switch changes only input and display units; the property and cycle calculations remain in SI internally. Real plants commonly use multiple heaters, drain cascades, moisture separation, reheating pressure losses, non-uniform turbine efficiencies, auxiliary loads and condenser subcooling. Consequently, use this page for education, sensitivity studies and preliminary thermodynamic screening—not equipment guarantees, acceptance tests or final plant design.
With 10 MPa boiler pressure, 10 kPa condenser pressure, 500 °C main steam, 85% turbine efficiency and 80% pump efficiency, the simple superheated preset gives approximately 34.06% thermal efficiency, 10,569 kJ/kWh heat rate and 1,080 kJ/kg net work. At 100 kg/s this corresponds to about 108 MW of thermodynamic net power.
The final calculated quality is about 0.874, so the page raises a moisture-screening notice. Reheat at the same main-steam conditions substantially improves exit dryness, illustrating why reheat is valuable even when the efficiency increase is modest.
Frequently Asked Questions
Common questions about the model and its results.
A Rankine cycle is a closed steam-power cycle in which liquid water is pumped, heated and vaporized, expanded through a turbine, and condensed back to liquid. It is the thermodynamic basis of most steam power plants.
Reheat raises steam temperature between turbine sections. The subsequent low-pressure expansion starts from a higher-entropy superheated state, so the final exhaust normally contains less moisture.
Extraction steam preheats feedwater before the boiler. This reduces low-temperature external heat addition and raises the average temperature at which the remaining external heat is supplied.
The page implements IAPWS-IF97 Regions 1, 2, 3 and 4 and automatically selects the appropriate formulation. Official verification points are checked in the browser at startup.
No. The 0.88 value is only an educational screening threshold. Actual allowable moisture depends on blade design, stage location, erosion criteria and the turbine supplier's limits.
No. It is appropriate for learning, sensitivity studies and preliminary screening. Detailed design requires plant-specific pressure losses, turbine maps, heater trains, auxiliary loads, mechanical and electrical losses, and verified design data.
Liquid condensate enters the pump and is pressurized from condenser pressure to boiler pressure, or first to feedwater-heater pressure in a regenerative cycle. Because liquid water has a small specific volume, the enthalpy and temperature increase is small compared with boiler and turbine changes.
Reheat and regeneration add equipment and therefore add thermodynamic states. The active state table and diagrams always show the correct numbering for the selected arrangement; follow both the number and the state name.