Rankine Cycle | How to Calculate the Efficiency of the Rankine Cycle?

Steam turbines are used all over the world in different power plants. These types of turbines are most commonly used in coal power plants and hydroelectric power plants. A boiler uses to convert water into steam. This produced steam is sent to a steam turbine for electricity production. A steam turbine works on the Rankine cycle. Therefore, rankine cycle is also known as a steam cycle. In the previous article, we discussed the working and types of steam turbines. Therefore, this article mainly describes the Rankine cycle, its types, working, and efficiency.

What is a Rankine Cycle?

A Rankine Cycle is a most widely used thermodynamic cycle in various power plants such as nuclear power plants or coal-fired power plants. The Rankine cycle describes the procedure through that a reciprocating steam engine or a steam turbine extracts mechanical energy from the working medium when it flows between a heat reservoir and heat source

In simple words, a Rankine cycle describes how a heat engine such as a steam engine extracts thermal energy from a heat source and uses this energy to produce electricity. These heat sources may have combustion of ethanol, biomass, oil, natural gas, coal or nuclear fission process etc.

In the 19th century, William John Macquorn Rankine designed the Rankine cycle.

Rankine cycle

The thermal energy extraction capacity of the Rankin engine varies according to the heat sink temperature and heat source temperature. 

According to Carnot’s theorem, the higher the temperature difference, the engine can extract more mechanical energy from thermal energy.

Ideal Rankine Cycle

In the case of the vapour cycle, if the working medium moves over the different parts of a powerplant without any friction pressure and irreversibility loss, the cycle is referred to as the ideal Rankine cycle.

The Rankine cycle is a major working cycle of all power plants in which operating liquid changes continuously from liquid to vapour and vapour to liquid. It is a theoretical cycle in which thermal energy transforms into useful work.

A T-s diagram of the Rankine cycle is given below, which will be helpful to understand the Rankine cycle working.

Rankine cycle T-s diagram
Rankine Cycle T-s diagram

The stages of completing a Rankine cycle are given below:

  1. Isentropic Compression (1 to 2): In this stage, a pump uses to transfer the water or other working medium from the water body (canal or tank etc.) into the boiler. The pump requires a small amount of energy for initial pumping. It pumps the fluid by increasing the pressure of the fluid, but fluid entropy remains the same. For initial pumping, the work done on the pump is given below:
  2. Constant Pressure Heat Addition Process (2 to 3): As the water is delivered into the boiler, an external heat source provides heat to the boiler. The boiler heated the water at constant pressure and converts it into dry saturated vapour (steam). During this process, the enthalpy of the liquid changes, and pressure remains constant.
  3. Isentropic Expansion (3 to 4): After the constant pressure heat addition process, the steam enters into the turbine area, where it expands. As the steam expands, it strikes with the turbine blades, which convert the thermal energy of the steam into rotational energy (mechanical work). As the turbine blades are rotated, they also rotate a crankshaft that further rotates the coil of the generator. As the coil rotates in a magnetic field, it produces electricity. During this whole process, the pressure and temperature of the steam decrease; due to that, some condensation can happen.  
  4. Constant Pressure Heat Rejection Process (4 to 1): The vapour or steam enters the condensate tank after the expansion process. In this condensation process, the vapour is condensed to convert it into saturated liquid.  During this process, the vapour rejects heat, but its liquid pressure remains the same.

In an ideal Rankine cycle, the turbine and pump work under isentropic conditions. It means the turbine and pump don’t generate entropy; they just increase the performance of the cycle.

The Rankine cycle (shown in the above diagram) avoids the working medium to end up in the superheated vapour area after expanding in the turbine, which decreases the energy dissipated by the condenser.

Read More: Working of Carnot Cycle

Actual Rankine Cycle (non-ideal)

In an actual Rankine cycle (or practical power plant), the expansion process in the turbine and compression process in the pump can’t happen under isentropic conditions. In simple words, these are non-reversible processes, and fluid’s internal energy (entropy) increases during these processes.

This cycle raises the required power by the pump to some extent and decreases the turbine’s produced output power.

The formation of water droplets controls the efficiency of steam turbines. When the water droplets condense, they strike the blades of the turbine at high speed; due to that, erosion and pitting occur on the turbine blades. This erosion and pitting gradually reduce the life and productivity of the turbine blades. The simplest method to solve this issue is to superheat the steam.

Actual Rankine cycle T-s diagram

In the above given T-s diagram of the Rankine cycle, state 3 is at the boundary of the two-phase range of water and steam. After expanding, the steam will convert into a very wet form. When steam is superheated, state 3 moves to the right (and up) in the above figure and generates dry steam after expansion.

Thermal Efficiency of Rankine Cycle

The work performed by the turbine, which is decreased by the pump divided by the heat energy received by the boiler is known as the Rankine cycle thermal efficiency.

Efficiency of the Rankine Cycle

The water vapor absorbs a calorific value that can calculate by the below-given equation:calorific heat

The boiler converts the water into superheated steam. This steam is delivered to the turbine. Then, as the line F-G in the above figure shows, the water vapor thermal energy converts into kinetic energy. The decrease in enthalpy uses to compute the amount of kinetic energy produced by a steam turbine. It can calculate by using the below-given equation:output power of the Rankine cycle

As the turbine exits the steam, it goes in the condenser. The condenser condenses it into a liquid form. In this case, thermal energy uses to change water into steam (latent heat). The thermal energy of the condensed water can be calculated from the enthalpy reduction (line G-C) using the following equation:output heat

After the condensation process, the condensed water is pumped again into the boiler by increasing the water pressure. As shown in the above diagram (line C to D), the enthalpy of the water has not increased much. It means that the energy released into the air is less important. You can calculate the input energy value using the below-given formula:Incoming energy

Now finally, the Rankine cycle efficiency can be calculated by the following formula:

Thermal Efficiency = [(Work Output — Work input)/Heat entered into the system]

  • The overall thermal efficiency of the latest nuclear power plant having a Rankine cycle is about 33%. So, 3000 MWth of fission reaction heat is required to make 1000 MWe of electricity.
  • Supercritical fossil fuel power plant operating at supercritical pressures (such as higher than 22.1 MPa) has an efficiency of up to 43 percent.
  • Subcritical fossil fuel power plants operating at critical pressures (less than 22.1 MPa) may accomplish efficiency between 36% to 40%.

Read More: Working of Brayton Cycle

How to increase the efficiency of the Rankine Cycle?

The efficiency of the Rankine cycle can be improved through following way:

  1. Reduce the average temperature
  2. Superheat the steam
  3. Increase boiler pressure
  4. Decrease the condenser pressure

1) Basic Idea

The first method to increase the efficiency of the Rankine cycle is to reduce the average temperate at which heat releases from the working medium as it is in the condenser.

The other method is to raise the average heat transfer temperature of the working medium as it is in the boiler.

2) Increase the Boiler Pressure

As you increase the boiler’s working pressure, the boiler temperature will also increase at which the boiling process occurs.

This process increases the average temperature at which heat transfers into the working medium, which improves the cycle’s thermal efficiency.

3) Superheating the Steam

By superheating the steam to a high temperature, the average heating temperature of the steam may increase without raising the pressure of the boiler.

Superheating the steam to a higher temperature has very pleasant effects. This reduces the moisture contents of the steam at the outlet of the steam turbine.

4) Decrease the Condenser Pressure

The other method is to reduce the working pressure of the condenser. As you lower the working pressure, the heat dissipation temperature will also be reduced.

The general effect of reducing the pressure in the condenser increases the thermal efficiency of the Rankine engine.

Rankine Cycle Components

The main parts of the Rankine cycle are:

  1. Boiler
  2. Condensate tank
  3. Boiler pump
  4. Steam turbine

1) Boiler

The Rankine cycle uses a boiler to convert the water into steam according to the turbine’s desired temperature and pressure. 

Read Also: Different types of Boilers

2) Pump

It is a device which uses to transfers the water from one area to another high area. The main objective of the pump is to transfer the water from the reservoir or other water source into the boiler.

Read More: Different types of Pumps

3) Steam Turbine

The main purpose of the steam turbine is to rotate the shaft of the generator to produce electricity. The turbine extracts the mechanical power from the steam and sends it into the condensate.

Read Also: Working of Steam Turbine

4) Condenser

It cools the steam, converts it into liquid form, and sends this water back into the boiler.

What is the difference between an actual cycle and an ideal rankine cycle?

An ideal cycle has the following process:

  • Reversible process
  • Isothermal heat addition
  • Constant pressure (isobaric)
  • No interaction with surrounding/environment

But in a practical power plant, such processes can’t achieve.  The ideal Rankine cycle is just a theoretical cycle while an actual Rankine cycle is a practical cycle that uses in different power plants.

The ideal Rankine cycle has 100% efficiency, which is higher than an actual cycle. The Carnot cycle has a very nearly efficiency to the ideal Rankine cycle efficiency.

The below-given diagram shows the T-s and P-v diagram of the Rankine cycle.

rankine cycle PV diagram, rankine cycle T-s diagram

The above given T-s and P-v figure represents the actual and ideal Rankine cycle as follows:

Actual Rankine Cycle1-2-b-3-4-1
Ideal Rankine Cycle1-2′-b-3′-4′-1

FAQ Section

What is Reheat Rankine Cycle?

A reheat Rankine cycle is a process through which the efficiency of the cycle improves. It has an inter-phase of inflating steam.  

Generally, after the 1st phase of expansion, which decreases the initial pressure of the steam, the steam is heated to (or near) the extreme temperature of the heat source.

Why is reheating done in Rankine Cycle?

A reheating process in a Rankine cycle is done because:

  • Heat supply increases.
  • The service life of the turbine increases
  • Turbine blades erosion process reduces
  • The dryness fraction of the turbine outlet rises, and moisture reduces
  • Thermal efficiency increases or decreases according to the temperature source of heat addition.

What is the Rankine cycle used for?

A Rankine cycle uses to calculate the functionality of the steam turbine system. It is also depleted to study piston steam engine performance.

What pump is used in the Rankine cycle?

  1. Hydraulic diaphragm metering pump
  2. Centrifugal Pump
  3. Roto-jet pump.

A rankine cycle comprises of?

Rankine cycle is a reversible process that consists of two constant temperature and two constant pressure processes.

Read More
  1. What the different types of heat engines?
  2. How does a Carnot cycle work?
  3. How does a Stirling cycle work?
  4. Working of Otto Cycle

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