Consider the idealized four-steady-state-process cycle in which state 1 is saturated liquid and state 3 is either saturated vapor or superheated vapor. This system is termed the Rankine cycle and is the model for the simple steam power plant. It is convenient to show the states and processes on a T–s diagram, as given in Figure 1.
Principle components of Rankine cycle:
The four basic components of Rankine cycle are shown in figure 1 each component in the cycle is regarded as control volume, operating at steady state.
Pump: The liquid condensate leaving the condenser at the state 1 is pumped to the operating pressure of the boiler. The pump operation is considered isentropic.
Boiler: The heat is supplied in the working fluid (feed water) in the boiler and thus vapor is generated. The vapor leaving the boiler is either at saturated at the state 3 or superheated at the state 3||, depending upon the amount of heat supplied by the boiler.
Turbine: The vapor leaving the boiler enters the turbine, where it expands isentropically to the condenser pressure at the state 4. The work produced by the turbine is rotary (shaft) work and is used to drive an electric generator or machine.
Condenser: The condenser is attached at the exit of the turbine. The vapor leaving the turbine is wet vapor and it is condensed completely in the condenser to the state 1, by giving its latest heat to some other cooling fluid like water.
The various processes in simple Rankine cycle are:
1–2: Reversible adiabatic pumping process in the pump,
2–3: Constant-pressure transfer of heat in the boiler,
3–4: Reversible adiabatic expansion in the turbine (or other prime movers such as a steam engine),
4–1: Constant-pressure transfer of heat in the condenser.
The Rankine cycle also includes the possibility of superheating the vapor, as cycle 1–2–3|–4|–1.
If kinetic and potential energy changes are neglected, heat transfer and work may be represented by various areas on the T–s diagram. The heat transferred to the working fluid is represented by area a–2–2|–3–b–a and the heat transferred from the working fluid by area a–1–4–b–a. From the first law of thermodynamics we can conclude that the area representing the work is the difference between these two areas—area 1–2–2|–3–4–1. The thermal efficiency is defined by the relation
For analyzing the Rankine cycle, it is helpful to think of efficiency as depending on the average temperature at which heat is supplied and the average temperature at which heat is rejected. Any changes that increase the average temperature at which heat is supplied or decrease the average temperature heat is rejected will increase the Rankine-cycle efficiency.
In analyzing the ideal cycles in this chapter, the changes in kinetic and potential energies from one point in the cycle to another are neglected. In general, this is a reasonable assumption for the actual cycles.
The Rankine cycle has lower thermal efficiency than a Carnot cycle thermal efficiency with the same maximum and minimum temperatures as a Rankine cycle because of the average temperature between 2 and 2| is less than the temperature during evaporation.
- The first reason concerns the pumping process. State 1| is a mixture of liquid and vapor. Great difficulties are encountered in building a pump that will handle the mixture of liquid and vapor at 1| and deliver saturated liquid at 2|. It is much easier to condense the vapor completely and handle only liquid in the pump: The Rankine cycle is based on this fact.
- The second reason concerns superheating the vapor. In the Rankine cycle the vapor is superheated at constant pressure, process 3–3|. In the Carnot cycle all the heat transfer is at a constant temperature, and therefore the vapor is superheated in process 3–3||. Note, however, that during this process the pressure is dropping, which means that the heat must be transferred to the vapor as it undergoes an expansion process in which work is done. This heat transfer is also very difficult to achieve in practice.
Thus, the Rankine cycle is the ideal cycle that can be approximated in practice.