Rankine power cycle

Organic Rankine power cycle is the simplest and most efficient steam power plant cycles for power generation. This power plant steam cycle is named after William Rankine a Trained civil engineer who developed the theory. It was later elaborated by James clerk Maxwell. Almost all the power plants employ steam cycles which are variants of Rankine cycle.

Organic Rankine cycle is one of the most fundamental practically feasible vapour power cycles. In a power cycle heat energy (released by the burning of fuel in case of thermal plants, nuclear fission heat in case of nuclear plants) is converted into work (shaft work) and subsequently into electrical energy. The working fluid repeatedly performs a predefined succession of processes completing a cycle. Specifically in a vapour power cycle, the working fluid is water, which undergoes a change of phase in to steam.

Rankine cycle Process Diagram:

### Rankine cycle Pressure v/s Volume (PV diagram):

#### The Organic Rankine power cycle consists of the following processes

- Process 1-2: Reversible adiabatic expansion in the turbine
- Process 2-3: constant pressure transfer of heat in the condenser
- Process 3-4: Reversible adiabatic pumping process in the feed pump
- Process 4-1: constant pressure transfer of heat in the boiler

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The plots are shown for the different conditions of working fluid entering the turbine which are wet steam, dry saturated steam, and superheated steam. During the process1-2 the steam adiabatically expands in the turbine. The entropy of the working fluid remains constant during this process. In process 2-3 the heat energy left out in the working fluid is rejected to the cooling water in the condensers. The process of heat transfer is a isobaric process. The left out steam in the process 1-2 is dumped in the condenser and gets condensed. The condensate from the condenser is pumped into the steam generator or boiler by a feed water pump during the process 3-4. The feed water pumped into the steam generator based on heat input provided to it will be converted into wet steam or Dry saturated steam, or superheated steam thus completing the cycle.

### Rankine Temperature v/s entropy (s) (Ts) diagram

### Rankine enthalpy v/s entropy (hs) diagram

## Organic Rankine cycle equations

Applying steady flow energy equation to each of the processes on the basis of unit mass of fluid and assuming that the changes in kinetic and potential energy are negligible we have

For process 4-1 i.e regarding the boiler, we get

Q_{in} +h_{4} = h_{1}

h=enthalpy of steam at predefined pressure and temperature

h_{1} = h_{f} (specific enthalpy) for hot water at pressure p

h_{1} = h_{f} +h_{fg} for dry saturated steam at pressure p

h_{1} = h_{f} +x*h_{fg} for steam with dryness fraction x at pressure p

X is known as steam quality or equivalent evaporation

h_{1}= h_{f} + h_{fg} + c_{p}*(T_{sup }– T_{s}) for superheated steam at pressure p and temperature Tsup and T_{s} is the saturation temperature corresponding to the pressure at the outlet of boiler or steam generator.

For process 1-2 regarding the turbine we have

h_{1} = W_{T}+h_{2} where W_{T} is the turbine work

W_{T} = h_{1} – h_{2}

For process 2-3 regarding the condenser we have

h_{2} = Q_{2} +h_{3}

Where Q2 is the heat rejected by the turbine outlet steam to the cooling water.

Q_{2} = h_{2} – h_{3}

For process 3-4 regarding the feed water pump we have

h_{4} = W_{p} +h_{3}

Where Wp is the pump work.

W_{p} = h_{4} – h_{3}

Since the feed water pump handles water which is incompressible there occurs little change in the density of water as the pressure and temperature of feed water varies. Also the feed water pump generates heat energy which will increase the temperature of the feed water slightly. This temperature increase is assumed to be negligible in the following analysis. For reversible adiabatic compression using the relation

T*ds = dh – v*dp (dv = 0, ds = 0)

Where T is the temperature of feed water

ds is the change in the entropy of feed water = 0 as the process is adiabatic

v is the inverse of density or specific volume in m3/kg

dp is the change in the pressure = Pump discharge pressure – pump suction pressure = net head developed by the pump

dh = change in enthalpy of feed water due to work done by the pump.

Substituting ds = 0 in the above equation we get

dh = v*dp

dh = h_{4}-h_{3}, p = p_{1}-p_{2}. Hence h_{4}-h_{3} = v_{3}* p_{1}-p_{2}.

The table given below summarizes the Rankine cycle

## Rankine cycle efficiency

The cycle efficiency of defined as the ratio of net work output to the heat supplied to the steam generator. The net work is done on the turbine of which the power fed to pump to increase the head of feed water has to be subtracted as it constitutes an external source of energy given to the system(work done on the fluid) .The Rankine cycle efficiency is given as

η = net work output/ heat energy supplied to the steam generator

η = WT-Wp/Qin

η = (h1 – h2) – (hf4 – hf3)/ (h1 – hf4)

The feed water pump term (hf4 – hf3) can be neglected when the boiler pressures are low compared to the work done by the turbine and hence can be neglected. Thus the efficiency of Rankine cycle reduces to

η = (h1 – h2) / (h1 – hf4)

The overall efficiencies of Rankine cycle are of the order of 15-30%. The efficiency of Rankine cycle is directly proportional to the

η α 1-(TL/TH)

The efficiency of Rankine cycle can be improved by making some modifications in the processes such as increasing the average temperature at which heat is supplied(TH), decreasing the temperature at which the heat is rejected(TL). TL can be reduced by reducing the pressure in the condenser. Higher efficiencies can be achieved by increasing the boiler pressure, superheating the steam before it is allowed to expand in the turbine.

## Advantages of Rankine cycle

- The main advantage of Rankine cycle with reheaters is it prevents vapour condensation which damages turbine blades.
- The Rankine cycle is a practically feasible steam cycle in which the heat exchange at almost constant pressure is very much achievable compared to isothermal heat exchange in Carnot cycle.
- High turbine efficiencies can be achieved by using super heated steam.
- Long plant lives are achieved due to reduction in turbine erosion And low mechanical stresses.

## Disadvantages of Rankine cycle

The main disadvantage to the Rankine Cycle is the expansion process in the turbine usually leaves the working fluid in two phase condition. This will result in the formation of liquid droplets that may damage the turbine blades.