# Turbine Isentropic Efficiency: 9 Interesting Facts To Know

Before discussing about turbine isentropic efficiency, we shall understand the meaning of “isentropic”. The term isentropic means “constant entropy”.

Efficiency of a turbine, in simple words is, output divided by input. Isentropic efficiency refers to the efficiency achieved in isentropic conditions. Isentropic conditions, however are difficult to achieve so isentropic efficiency is the maximum achievable efficiency of a turbine for given temperature and pressure conditions. This article discusses about isentropic efficiency of turbine in detail.

## Turbine isentropic efficiency definition

As discussed earlier, isentropic efficiency is the efficiency achieved by the turbine in isentropic (entropy doesn’t change) conditions. Isentropic conditions are difficult to achieve hence, isentropic efficiency is the maximum possible efficiency that can be achieved by the turbine in given pressure and temperature conditions.

Due to irreversiblities and friction losses, the turbine produces slightly lesser output than theoretical value. Hence, actual efficiency is calculated. Figure below shows isentropic curve and actual curve of a typical turbine working on Brayton cycle.

## How do you calculate isentropic efficiency of turbine?

Isentropic efficiency of a turbine is calculated using values of inlet and outlet enthalpies and ideal inlet enthalpy of turbine.

Mathematically, the isentropic efficiency can be found using the formula given below-

$\eta&space;_{Iso}=&space;\frac{h_{in}-h_{out}}{h_{in}-h_{outideal}}$

Where,

h represents specific enthalpy

## Isentropic efficiency turbine example

Consider an isentropic expansion of Helium in a gas turbine. Turbine receives gas at high pressure (point 3) of 6.7 Mpa with a temperature of 1190 K. The gas exits at low pressure of 2.78 Mpa (shown in point 4) Temperature of gas at turbine exit is 839K.

Calculate: The actual work done by turbine during this process when isentropic efficiency of turbine is 91%.

Work done by the turbine can be calculated by following equation-

$W_{T}=&space;h_{3}-h_{3s}=&space;C_{p}(T_{3}-T_{4s})$

For monoatomic gas, values for molar specific heats are-

$C_{v}=12.5&space;\frac{J}{molK}$ $C_{p}=20.8&space;\frac{J}{molK}$

Converting the units of Cp we get,

$C_{p}=5200&space;\frac{J}{KgK}$

Work done is then,

5200 x (1190-839)= 1.825 MJ/kg

Real work done is,

$W_{real}=\eta&space;_{T}.W_{T}=1.661&space;\frac{MJ}{Kg}$

## Is higher isentropic efficiency better?

Efficiency means net output delivered using a certain amount of input. If the output delivered is more then the efficiency achieved is also more.

Higher isentropic efficiency means higher output achieved. It is always desirable that a turbine produces more work or output. Hence, it is better when isentropic efficiency is higher. Also, with increase in isentropic efficiency of turbine, the irreversibilities in the turbine decrease which directly increases the desired work output.

## Is a turbine adiabatic?

Adiabatic means no heat transfer takes place I.e. Qin – Qout is zero.

Turbines are adiabatic devices. While designing turbines, following points can be taken into consideration-

• Turbine is adiabatic and reversible.
• Kinetic and potential energies are negligible.
• Only shaft work is done.
• Enthalpy is changed hence it is NOT an isenthalpic process.

Above points when written mathematically, a special equation called as steady state energy equation (SFEE) can be introduced.

SFEE can be written as-

$Q-W=(h_{2}-h_{1})+\frac{(V_{2}^{2}-V_{1}^{2})}{2000}+\frac{g(Z_{2}-Z_{1})}{1000}$

## What is a nozzle?

Nozzles increase the kinetic energy of fluid at expanse of pressure energy. Nozzles have their applications in both subsonic and supersonic flows.

Nozzles are used in hose pipes to increase the velocity of flow of water, they are also used in rocket engines to produce high amount thrust, used in Pelton turbine to increase the flow velocity of water that strikes the runner.

Image credits: RaketendüseCC BY-SA 3.0

## Types of nozzles

Nozzle follows continuity equation. Nozzles are classified on the basis of required velocity of the fluid and mach number of the working fluid.

According to mach number and desired velocity, nozzles can be classified as-

• Convergent nozzle- It has larger area at the entry and smaller area at the exit. The fluid particles rush through the exit with a higher velocity to maintain flow continuity.
• Divergent nozzle- It has smaller area at the entry and larger area at the exit. The fluid particles exit at a lower velocity.
• Convergent- divergent nozzle- This type of nozzle is mixture of both convergent and divergent nozzles. These nozzles are used for supersonic flow in compressible fluids. The mach number is always greater than 1 while using this nozzle.

## SFEE for nozzle

There are some assumptions that are followed while writing SFEE for a nozzle. These assumptions depend on the application of the device, these assumptions may not be same while writing SFEE for a turbine.

Assumptions for writing SFEE for a nozzle are-

• Nozzle walls are adiabatic.
• There is no work interaction.
• Negligible potential energy difference.
• Inlet kinetic energy is negligible compared to outlet kinetic energy.

Following above assumptions, SFEE for a nozzle can be written as-

$h_{1}=h_{2}+\frac{mV_{2}^{2}}{2}$

## Parts of convergent divergent nozzle

Convergent divergent nozzle is used when the mach number of fluid flow is greater than 1. The C/D nozzle has three main regions. Every region has its own flow characteristics.

The three main regions of C/D nozzle are-

• Inlet- The fluid enters at a lower velocity through inlet.
• Throat- The fluid velocity equals to the local speed of sound I.e. mach number is equal to 1. The pressure at this region is called as critical pressure and velocity is called as critical velocity.
• Exit- The fluid exits through this region.

## Isentropic efficiency of nozzle

Nozzles increase the kinetic energy of fluid at expanse of pressure energy. Nozzles are used in subsonic, sonic as well as supersonic flows.

The ratio of actual exit kinetic energy to isentropic exit kinetic energy is called as isentropic efficiency of nozzle.

Isentropic efficiency of nozzle can be written as-

$\eta&space;_{Niso}=&space;\frac{V_{2}^{2}}{V_{2iso}^{2}}$

Abhishek

Hi ....I am Abhishek Khambhata, have pursued B. Tech in Mechanical Engineering. Throughout four years of my engineering, I have designed and flown unmanned aerial vehicles. My forte is fluid mechanics and thermal engineering. My fourth-year project was based on the performance enhancement of unmanned aerial vehicles using solar technology. I would like to connect with like-minded people.