Rankine Cycle – Processes with h-s Diagram

Rankine cycle is an ideal vapour cycle. It plays a major role in steam power plants. This cycle is mainly based on the conversion of input heat energy into output power, using turbine. The working fluid at the inlet repeatedly undergoes change of phase and in successive operations, energy is transmitted and output power is produced. Simple Rankine cycle consists of the following processes:

1. Process 1-2: Adiabatic expansion of steam (in turbine)
2. Process 2-3: Constant pressure heat rejection (in condenser) and
3. Process 3-4: Isentropic compression (in pump)
4. Process 4-1: Heating at constant pressure (in boiler)

All the above processes are reversible in nature.

Simple Rankine cycle can be easily understood if we understand its h-s Diagram. h-s diagram and block diagram of simple Rankine cycle are provided below:

h-s Diagram of Simple Rankine Cycle:

Block Diagram of Simple Rankine Cycle:

Processes in Simple Rankine Cycle:

Process 1-2 (turbine):

Here, dry saturated steam from the boiler is allowed to expand in a turbine isentropically (i.e., entropy remains constant).

Let h1 be the enthalpy of steam entering the turbine

Let h2 be the enthalpy of steam leaving the turbine

Work done by the turbine is given by

WT = h1 − h2

Process 2-3 (condenser):

Wet steam from the turbine is fed into a condenser, to perform condensation (wet steam is converted to water). As it is a heat rejection process , heat from the steam is rejected into atmosphere.

Let h2 be the enthalpy of steam entering the condenser.

Let h3 be the enthalpy of water leaving the condenser.

Heat rejected from condenser

QR = h2 − h3 W or

QR = h2 − hf2 W

Since, hf2 = h3 (the output from condenser is a fluid and graphically, the enthalpy at point 2 and point 3 are same.)

Process 3-4 (pump):

Water from the condenser is pumped into the boiler using an external pump. During this process, pressure increases P3 to P4 isentropically.

The enthalpy and temperature of water also increase due to pump work.

Let P3 ,h3 be the pressure and enthalpy at stage 3 respectively.

Let P4  and h4 be the corresponding values at stage 4.

Work done by the pump is given by

Wp = h4 − h3 = Vf3 (P4 − P3) W

where,

Vf3 → Specific volume of saturated water at pressure P3 (condenser pressure)

Note :

All the values of pressure here are substituted in N/m2. All values of enthalpy are substituted in J/kg.

Process 4-1 (boiler):

Here the saturated water from the pump is heated using a constant heat source (like furnace). The input saturated water is heated till it reaches super-heated condition. The temperature and enthalpy raises to a great extent, but the pressure is kept constant. The change of phase from liquid to vapour occurs in boiler.

Let h4 be the enthalpy of saturated water entering the boiler.

Let h1 be the enthalpy of super-heated steam coming out of the boiler.

The heat supplied is given by

QS = h1 − h4

See h-s diagram above for better understanding of all the above processes.

Efficiency of Simple Rankine Cycle:

As we know, efficiency is the ratio between output and input. Here the output is work done and input is heat energy.

Net work done = work done in turbine + work done in pump

Net heat transfer = heat produced in boiler + heat rejected in condenser