#### 3.1.2 The Rankine cycle

Having presented a modern practical steam power cycle, attention will now be given to the development of such a cycle from a basic vapour power cycle — the Rankine cycle.

For the purpose of illustrating the various power cycles, the Temperature-Entropy (T-S) and Enthalpy-Entropy (H-S) diagrams will be used. An understanding of thermodynamic properties — Entropy and Enthalpy is assumed. However, in the context of the following description of steam cycles, a review of Entropy will be beneficial.

Entropy is an abstract property of steam which increases when heat is added and decreases when heat is rejected. Its magnitude is such that if the temperature at which heat is transferred is multiplied by the change in entropy that results in the process, then that product equals the amount of heat transferred.

Now consider the simple Rankine cycle for steam, shown schematically in Fig 1.22 and on the T-S diagram in Fig 1.23.

Water is pumped into the boiler by the feed pump (process A-B). In the ideal Rankine cycle, there is no temperature rise across the pump and points A-B are coincident. The water is then heated to produce dry saturated steam (process B-C). The dry saturated steam is expanded through the turbine isentropically, i.e., without loss. This process (C-D) produces work along the turbine shaft. Finally the wet steam issuing from the turbine gives up its heat in the condenser and returns to water (process O-A).

The heat input to the boiler or 'the energy paid for' is represented by the area EABCDF on the T-S diagram. The work done by the cycle is represented by the area within the polygon ABCD. The heat rejected to the condenser is represented by the rectangle ADFE. In the context of power generation, Thermal Efficiency 17 is defined as:

Work done - (Energy for generation)/Heat input (i.e., energy paid for). Hence the Thermal Efficiency of the Rankine cycle, based upon Fig 1.23, 1.23 is 17 (Rankine) = Area ABCD/Area EABCDF.

The economic implication of cycle efficiency is a major factor behind the development of the cycle, whilst maintaining or reducing capital cost per electrical unit supplied. The other major consideration in the choice of cycle, is the engineering feasibility of various terminal conditions. The effect of changing terminal conditions is dealt with thoroughly in Section 3.3 of this chapter. However, it is useful to consider the following criteria when attempting to change cycle terminal conditions:

- No saturated steam must enter the condenser, i.e., point D must be within the vapour boundary (Fig 1.23).
- The exhaust wetness in the last turbine stage must not exceed 12%, i.e., DD' must be less than 12<7o of AD'.
- Material properties limit the maximum temperature within the cycle.