The Rankine Cycle in Steam Power Plants

The fluid conditions and energy input and output at each part of the Rankine Cycle are illustrated in the T-s and h-s diagrams, where T represents absolute temperature, h represents enthalpy, and s represents entropy. The following sequence describes the fluid conditions at each point:

1. Superheated steam at the outlet of the boiler’s superheater (steam turbine inlet).
   1-2. Adiabatic expansion in the steam turbine (ideal conditions) from the turbine inlet to the turbine outlet (condenser inlet).
2. Wet steam at the outlet of the steam turbine (condenser inlet).
   2-3. Condensation process in the condenser.
3. Condenser outlet (boiler feed pump inlet).
   3-4. Adiabatic pressure increase to boiler pressure in the boiler feedwater pump.
4. Compressed water at the outlet of the feedwater pump (boiler inlet).
   4-5. Heating process at constant pressure to the saturated water condition in the boiler.
5. Point at the saturated water condition in the boiler.
   5-6. Evaporation process at constant pressure in the boiler’s evaporator.
6. Saturated steam at the outlet of the boiler’s evaporator (superheater inlet).
   6-1. Heating process at constant pressure in the boiler’s superheater.

This sequence describes the thermodynamic states and processes the fluid undergoes as it moves through the cycle, from the superheated steam entering the turbine to the condensed and pressurized water re-entering the boiler.

Thermal Efficiency of the Rankine Cycle

The thermal efficiency of the Rankine cycle is determined by the ratio of net work output to the heat input in the boiler. Mathematically, it is expressed as:

η = (W_turbine – W_pump) / Q_in

Where η is the thermal efficiency, W_turbine is the work done by the turbine, W_pump is the work consumed by the pump, and Q_in is the heat added in the boiler. Enhancing the cycle’s efficiency can be achieved by increasing the steam inlet pressure and temperature, reducing the condenser pressure, or implementing regenerative feedwater heating.

IMPACT OF DESIGN PARAMETERS ON THERMAL EFFICIENCY

Steam Inlet Pressure
The thermal efficiency of the Rankine cycle can be improved by increasing the steam inlet pressure. However, if the steam pressure is increased without raising the inlet temperature, the moisture fraction in the low-pressure (LP) turbine rises, resulting in increased moisture-related losses in the LP turbine. When the moisture fraction in the LP turbine reaches 8–12%, measures to mitigate erosion on the long turbine blades in the final stages of the LP turbine become necessary. In such cases, it is more effective to simultaneously increase the inlet temperature along with the inlet pressure increase. The critical pressure and steam temperature are 22.12 MPa and 374.2°C, respectively. In large-scale power plants, the supercritical inlet pressure generally exceeds the critical pressure.

Exhaust Pressure
A lower exhaust pressure contributes to improved thermal efficiency. The improvement in thermal efficiency is due to the lower exhaust pressure. Since the exhaust steam from the condensing turbine is saturated and wet, the exhaust pressure depends on the cooling water temperature in the condenser. In practice, the exhaust pressure is determined by considering the following factors:

• The condenser cooling water temperature and the cost of condenser equipment, circulation pipes, related pumps, etc.
• The moisture fraction in the final stage of the LP turbine.
• The volumetric flow rate of the steam and the length of the LP turbine’s final stage blades.

By managing these parameters carefully, the Rankine cycle can achieve higher efficiency, with optimized performance in both the turbine and the condenser stages.