Rankine Cycle

The Rankine cycle is the cycle upon which most vapor power plants are based. The Rankine cycle was exists largely as a substitute for the Carnot cycle which has the highest thermal efficiency of any cycle (Carnot's theorem) but happens to be extremely difficult to execute in practice. The ideal Rankine cycle consists of 4 processes:

1-2 Isobaric heat rejection

2-3 Isentropic compression

3-4 Isobaric (constant pressure) heat addition

4-1 Isentropic expansion

For a real vapor power plant, isentropic processes can only be approximated (since irreversibilities are ever-present). Process 1-2 is generally executed under the vapor dome at constant pressure so that constant temperature is inevitable, the process going from high to low quality. However in reality some pressure is generally lost in the condenser so the process may not actually be isobaric or isothermal. Pressures in process 3-4 are generally controlled by the boiler where once again some pressure losses are inevitable.

A quick analysis of the ideal Rankine cycle assuming no work done in process 2-3 and 4-1 and processes 1-2 and 3-4 to be adiabatic gives:

q_in = h₃ - h₂

q_out = h₄ - h₁

w_in = h₂ - h₁

w_out = h₃-h₄

η_th = w_net/q_in = {(h₃-h₄) - (h₂ - h₁)}/{h₃ - h₂}

Like the Carnot cycle, the thermal efficiency of the Rankine cycle can be expressed: η_th = 1 - T*_in/T_out (where T*_in represents the average temperature of heat addition).

Thus increasing the efficiency of a Rankine cycle can be done by increasing the average temperature of heat addition or decreasing the average temperature of heat rejection.

In practice this is done in several ways:

Increasing boiler pressure

Increasing feedwater temperature through regeneration

Decreasing condenser pressure

In practice many of these techniques are used. However altering the boiler and condenser pressure can lead to unacceptable decreases in the steam quality at the turbine exit. Applying reheat is a common technique used to increase both the efficiency of the cycle as well as ensuring that the quality at the turbine exit is high (qualities less that 90% are usually not tolerable as excessive moisture will damage the turbine blades). In an ideal reheat Rankine cycle steam (or the working fluid) expands isentropically in a high pressure turbine, exiting as superheated steam. It is then reheated in the boiler to the inlet temperature to expand isentropically in a low pressure turbine. While a plant may use a number of reheat processes, the marginal increase in efficiency from each diminishes over time. Usually no more than 3 reheat processes are utilized.

More recently, vapor power plants have begun operating at supercritical pressures as a means of improving efficiency. There is however a limit to the temperature of heat addition since the machinery itself must be capable of withstanding such temperatures without failure.