# Compressor Isentropic Efficiency: What, How, Several Types, Examples

Compressor isentropic efficiency is a measure of degradation of energy efficiency while doing actual compression compared to ideal case, where the energy efficiency is maximum.

Ideal processes are reversible and hence an ideal device that shows reversibility is efficient. The work done in an ideal process is maximum possible work output. However, all the actual processes and devices are irreversible to some extent and hence inefficient.

## What is compressor isentropic efficiency?

Isentropic Efficiency of compressor is defined as the efficiency of the compressor when compared to an ideal isentropic process.

To define isentropic efficiency we must first understand an isentropic process. An isentropic process is an ideal process which is both adiabatic as well as reversible. In real world such an idealistic process is not possible. Thus a work done by a compressor in an isentropic process is thus an idealistic case when there is no change in entropy taking place.

Isentropic efficiency of a compressor is defined as the ratio of work done while the compression is carried out without any change in entropy vs actual work done.

## How to calculate compressor isentropic efficiency?

The calculation of isentropic efficiency requires calculation of isentropic and actual work done

Isentropic efficiency of a gas compressor can be calculated, if the inlet and exit temperatures of the compressors ae given.

Let’s Consider,

T2ideal = ideal stagnation temperature at compressor outlet

T1 = stagnation temperature at compressor inlet

T2 = actual stagnation temperature at compressor outlet

Then,

Isentropic efficiency can be calculated as nc = (T2ideal -T1 )/ (T2  T1 )

## What is isentropic efficiency?

Isentropic efficiency is the measure of deviation from ideal behavior for steady state flow devices.

Isentropic efficiency measures the loss of energy in an actual steady-state process such as that of a turbine, a pump or compressor and a flow nozzle when compared to that of the process, if it is carried out isentropically.

The work done is calculated for actual process and compared with that of isentropic process keeping the same inlet and exit conditions. The ratio of both these work done provides the isentropic efficiency.

## Compressor isentropic efficiency formula

Isentropic Efficiency of Compressor formula is denoted by the ratio of ideal or isentropic work done to actual work done.

Here, T2’ denotes the exit temperature for ideal or isentropic case.

T1 denotes the temperature at inlet

T2 denotes the temperature at outlet for actual case

Cp is the specific heat, which is considered constant. In terms of compression pressure ratio, the above formula is denoted by:-

Where,

Where Pr is compression pressure ratio, γ is the ratio of specific heats Cp/Cv.

Form above, the Actual exit temperature T2 can be calculated by

## Typical Isentropic Efficiencyof Compressor

Isentropic compression is carried out with minimum work done to carry out a step change. Actual work done is always higher than isentropic work and hence isentropic efficiency is lower than 100.

Consider the h-s diagram below for work done by isentropic compression ( ws) vs actual work done (wa). P1 and P2 are the inlet and exit pressure respectively. For same inlet and outlet pressures, the actual work done is always higher than isentropic work done.

The compressor efficiency generally decreases if the internal leakages are high leading to recycling of gas being compressed and mechanical and frictional losses.

Typically, for a compressor which is designed efficiently, the isentropic efficiency ranges from 75 to 85%.

## Scroll Compressor Isentropic Efficiency

Like other compressor types, scroll compressor isentropic efficiency also depends upon construction and design.

Efficiency losses in a scroll compressor includes mechanical losses, losses of energy due to internal leakages, loses due to heat transfer and deviation from isothermal operation, losses due to pressure drop in piping and losses that occur when converting from electrical to mechanical energy in the motor.

The Mechanical efficiency is around 90%, the pressure drop and internal leakages efficiency is around 90% and the motor efficiency is around 90%. These losses sum up to have a practical scroll compressor of around 70% efficiency. For a scroll compressor fitted with a speed controller additional 5% loses are incurred.

When compared to rotary compressors, it is found that scroll compressors have slightly lower efficiencies for same pressure ratios.

## Reciprocating Compressor Isentropic Efficiency

For reciprocating compressors, the isentropic efficiency depends largely on size of compressors.

Normally, larger the size more is its efficiency. Reciprocating compressors utilized for home appliances have efficiencies of 40-60%. Medium size (semi-) hermatic compressors have efficiencies between 50-70%. Large size open compressors have efficiencies of 60-80% at full load.

Higher speed reciprocating compressors generally have higher efficiencies compared to low speed reciprocating compressors.

## Centrifugal Compressor Isentropic Efficiency

Lower size centrifugal compressors have lower isentropic efficiency than compared to higher size machines.

All the factors such as mechanical losses, flow losses, motor losses are applicable for other types of compressors are true for centrifugal compressors as well.

Since in centrifugal compressors the rotating speed of a centrifugal compressor is an inverse function of diameter to maintain a desired peripheral speed at the outer diameters of the impellers, very large compressors may operate at low speeds(say, 3000 rpm)  and very small compressors may operate at very high speeds ( say, 30000 rpm).

As the compressor size decreases, the passage for gas to flow becomes narrow. This leads to higher frictional losses and hence lowers the isentropic efficiency.

## Refrigeration Compressor Isentropic Efficiency

Isentropic efficiency of a refrigeration compressor is affected by superheat of the refrigerant along with other factors.

The efficiency of a compressor employed in refrigeration service is impacted by the design of the refrigeration circuit. If the evaporator, throttling device and suction line is not properly designed it can lead to higher superheat of the refrigerant leading to lower gas densities leading to compressor operating at a point from its best efficiency.

## Compressor Isentropic Efficiency Values

Compressor isentropic efficiencies values depend upon type of compressor, capacity, speed, design and construction.

Isentropic efficiency of centrifugal compressor varies from 70-85%. Efficiency of reciprocating compressors vary from 40 % to 80 % depending upon capacity and compression ratios. Efficiency of Screw compressors vary from 65% to 75%.

## Isentropic Efficiency Compressor Example

Example: Air enters an adiabatic compressor at 300 K, 1 atm pressure. The work input to the compressor is 350 kJ per kg of air flowing through the compressor. Given that the compressor has an isentropic efficiency of 0.85, calculate the actual exit temperature and pressure of the compressor. Use the constant specific heat relations for this problem.

Solution:

with CP = 1.01 kJ/kg K and k = 1.4 for air.

Solve to get T2s= 595 K.

Since 1 − 2s is isentropic;

## Heat Pump Compressor Isentropic Efficiency

Similar to refrigeration compressor among other factors the efficiency of heat pump compressor is also impacted by degree of superheat of the refrigerant.

A heat pump is a device used to heat a space by taking heat from outside ambient air. A heat pump works in a reverse way in comparison to a refrigeration cycle. Performance of a heat pump is defined by:[l

Where, |Q| is the useful heat supplied by the heat pump

W is the net work input to the system

A heat pump compressor efficiency is also influenced by the degree of superheat of the refrigerant irrespective of compressor type. Modern heat pump systems use scroll compressors which have higher isentropic efficiencies compared to other compressor types.

## Gas Turbine Isentropic Efficiency

Gas turbine isentropic efficiency is defined as the ratio of real work done for expansion of gas to ideal work done.

A gas turbine system can be defined in a h-s diagram as below:

The isentropic efficiency for a gas turbine is defined by following expression:

ηT=Real Turbine Work/ Isentropic Turbine Work

## Air Compressor Isentropic Efficiency

To calculate isentropic efficiency of an air compressor, we need to know the properties of air, which can be incorporated into the expession for calculating the efficiency of a compressor in general.

This can be explained by an example:

Consider air of 100 cum/min at 20°C (density ρ at these conditions is equal to 1.2 kg/m3) and initial pressure of 0.1 Mpa.The compressor compresses it to a pressure of 0.25 Mpa.  The power consumtion of the motor is 200 KW.

The isentropic efficiency of compressor is given by:-

nis = (isentropic work done),nw/(Actual work done), na

Here, the actual work done is known as the compressor power consumption is known. The isentropic work done can be calculated as follows:

nw= V · ρ · z · R · (273+t) · γ/(γ-1) · [(P2/P1)(γ-1)/γ-1]

Where,

V= volume in cum/m

z= Compresibility facotor, 1 for air

ρ= density of air

R= universal gas constant,  286 J/(kg*К) for air

γ = ratio of specific heat, 1.4 for air

Calculating, by putting the above values we get

nw = 175.5 KW

Thus, the isentropic efficiency of compression is nw/na = 17.5./200 = 0.88 or 88%

## Screw Compressor Isentropic Efficiency

A screw compressor operating efficiency depends largely upon its size and the compression ratio.

A screw compressor once designed has a fixed volume ratio unlike the reciprocating or centrifugal compressors. The isoentropic efficiency in the designed volumetric ratio is maximum. However, if the compressor is operated beyond the specified volume or compression ratio, there is a sharp drop in its isentropic efficiency.

Other than that, the isentropic efficiencies of small srew compressors are considerably lower than large screw compressors. This is because of increased frictional loss due to smaller flow path available.

## Isentropic Efficiency of Axial Flow Compressor

Isentropic efficiency for an axial flow compressor is best among all the compressor types.

Comparing the efficiencies of reciprocating compressors, centrifugal compressors and axial flow compressors, the later has the best efficiencies and ranges above 90%. This is mostly because of of minimum mechanical and aerodynamic losses it encounters as the gas traverses the path thoruch the compressing device.

A typical axial compressor is shown below. it has got alternate rotaing vanes and static airfoils, which converts the kinetic energy to pressure. An animated simulation of an axial compressor; Image credit: Wikipedia

Axial flow compressors are generally employed for high flow rates primarily in jet engines, as turbines and some process apllications. For a given flow however, compared to a centrifugal machine which has a raidal flow componet, the axial flow compressors have lower wetted area and loe sealing requriement contributing to its higher isentropic efficiency.

## Compressor Polytropic Efficiency vs Isentropic Efficiency

When comparing the work done by a compressor in theorotical terms, polytropic efficiency is always higher than than the isentropic efficiency.

Polytropic compression and isentropic compression both are ideal cases and do not convey the actual process. Polytropic efficiency is the theoritical efficiency calculated for a infinitely small change in pressure over the range of pressure change in a compression process.

If the pressure change approches zero the polytropic efficiency is equivlnet to isentropic efficiency. If the pressure change is large, the polytropic efficiency is significnatly more than the isoentropic efficiency. In other words, polytropic efficiency sets the limit for maximum isentropic efficiency.

Sangeeta Das

I am Sangeeta Das. I have completed my Masters in Mechanical Engineering with specialization in I.C Engine and Automobiles. I have around ten years of experience encompassing industry and academia. My area of interest includes I.C. Engines, Aerodynamics and Fluid Mechanics. You can reach me at https://www.linkedin.com/in/sangeeta-das-57233a203/