Rankine Cycle: What is it? (Ideal vs. Actual + T-s Diagram)

What is the Rankine Cycle?

The Rankine Cycle is a vapor-power cycle used in steam power plants to convert heat into shaft work through steam turbines. Its four basic components are a boiler, turbine, condenser and feed pump.

The boiler adds heat at nearly constant pressure. It converts pressurized feedwater into steam at the pressure and temperature required for power generation.

Steam expands through the turbine and produces shaft work. The exhaust then enters a condenser, where heat rejection converts it to liquid water before the pump raises its pressure for the next cycle.

The following plant layout shows where the Rankine loop sits within a steam-electric generating station.

Typical Power Plant Cycle

Steam-electric plants convert turbine shaft work into Electrical power. The heat source may be combustion, nuclear fission, geothermal heat or another source suited to the working fluid.

The diagram divides this power plant into four sub-systems.

• Sub-system A: The Rankine loop, containing the turbine, condenser, pump and boiler.
• Sub-system B: The stack or chimney for exhausting combustion gases when the plant burns fuel.
• Sub-system C: An electric generator that converts turbine shaft work into electrical energy.
• Sub-system D: The cooling-water system that receives rejected heat from the condenser while the exhaust steam becomes condensate.

The analysis below follows sub-system A through one complete cycle.

The Rankine arrangement avoids compressing a wet vapor mixture, one practical problem in a vapor Carnot cycle. Its pump handles liquid water instead.

Ideal Rankine Cycle

An Ideal Rankine Cycle assumes isentropic pumping and turbine expansion, with constant-pressure heat addition in the boiler and constant-pressure heat rejection in the condenser.

It is the basic model for vapor-power plants in which a working fluid repeatedly changes between liquid and vapor.

The pressure-enthalpy (p-h) and temperature-entropy (T-s) diagrams track the state changes described below.

1-2-3 Isobaric Heat Transfer or Constant pressure heat addition in a boiler

The boiler is a heat exchanger that transfers energy from the plant’s heat source to water at nearly constant pressure. Compressed liquid enters at state 1 and is heated through saturation to the specified state 3 shown on the T-s diagram.

The energy balance in the boiler is or energy added in a steam generator,
q_in= h₃-h₁

3-4 Isentropic Expansion or Isentropic expansion in a turbine

Steam enters the turbine at state 3. In the ideal model it expands adiabatically and isentropically to state 4, turning the turbine shaft and generator.
Work delivered by the turbine when heat transfer to the surroundings is neglected:
W_{turbine out}= h₃-h₄

4-5 Isobaric Heat Rejection or Constant pressure heat rejection in a condenser

Vapor enters the condenser at state 4 and rejects heat to the cooling-water circuit. In the ideal model, condensation occurs at constant pressure and the working fluid leaves as liquid at state 5.
Energy rejected in the condenser, q_out= h₄-h₅

5-1 Isentropic Compression or Isentropic compression in a pump

Liquid leaves the condenser at state 5 and enters the feed pump. The pump supplies work to raise its pressure to the boiler pressure. Pump work is usually much smaller than turbine work because the liquid’s specific volume is low, but it remains part of net cycle work.
Work was done on the pump per kg of water, W₅₁= h₅-h_1.

The thermal efficiency of the Rankine cycle is given by:

OR

Difference Between Ideal and Actual Rankine Cycle

The ideal Rankine cycle is less efficient than a reversible Carnot Cycle operating between the same maximum and minimum temperatures because Rankine heat addition occurs over a temperature range.

Real Rankine cycle components have pressure drops, heat transfer and mechanical losses. Turbine and pump efficiencies are below 100%, so the actual Rankine cycle produces less net work for the same idealized state limits.

Figures 1-a and 1-b compare the ideal and actual Rankine cycles on P-v and T-s diagrams.

Rankine Cycle Representation is as follows on P-v and T-s diagrams:
Ideal Rankine Cycle	1-2‘-b-3‘-4‘-1
Actual Rankine Cycle	1-2-b-3-4-1

The Critical Point (CP) is at the top of the saturation dome in Figures 1-a and 1-b. The dome’s left boundary is the saturated-liquid line. The region to its left contains compressed, or subcooled, liquid.

The dome’s right boundary is the saturated-vapor line. The region to its right contains superheated vapor, while the area inside the dome is a liquid-vapor mixture.

Energy Analysis of Ideal Rankine Cycle

Each Rankine component is modelled as a steady-flow control volume: boiler, turbine, condenser and pump. The ideal-cycle energy balances are shown below.

Ideal Rankine Cycle Components	Heat	Work
Boiler feed Pump Wpump-in
Boiler
Turbine
Condenser

Thermal efficiency of Ideal Rankine cycle

Energy Analysis of Actual Rankine Cycle

The actual vapor cycle differs from the ideal Rankine Cycle because entropy is generated in real components. Pressure losses, non-isentropic turbine and pump operation, heat leakage and mechanical losses reduce net output.

Fluid Friction

Fluid friction causes pressure drops through the boiler, condenser and connecting pipes. The turbine therefore receives steam below the boiler discharge pressure unless the feed system provides extra pressure.

Long steam lines, fittings and valves add more pressure loss between the boiler and turbine.

The actual turbine-stop-valve condition is therefore shown as point 3’ in Figure 1-a, below the ideal boiler-outlet pressure at point 3.

Raising feed-pump discharge pressure can offset part of this pressure loss, but doing so increases pump work. Plant design balances that extra input against the required turbine inlet state.

Steam leaks and failed steam traps also waste mass and energy before the flow reaches the turbine.

Supplying the rated turbine output under these losses requires more heat input or a greater steam flow. Either change lowers overall efficiency compared with the ideal model.

Energy balance for the actual Rankine Cycle is as follows:

Actual Rankine Cycle Components	Heat	Work
Boiler feed Pump Wpump-in
Boiler
Turbine
Condenser

Thermal efficiency of Ideal Rankine cycle

Overall cycle efficiency must include turbine and pump irreversibilities. Pump work is often small relative to turbine output because the pump handles liquid, but the calculation should retain it unless a stated approximation permits omission.

The actual-cycle relations compare turbine and pump enthalpy changes with their isentropic reference states:

Where:

• h_2a Actual enthalpy at the pump exit
• h_4a Actual enthalpy at the turbine exit
• h_2s Ideal isentropic enthalpy at the pump exit
• h_4s Ideal isentropic enthalpy at the turbine exit

Other Factors of Irreversibility

Other factors responsible for the irreversibility of the actual vapor power cycle are:

• Sub-cooling of condensate in the condenser
• Losses associated with bearings
• Steam leakages
• Condenser air-leaks