What is the difference between isentropic and polytropic efficiency

The isentropic efficiency of the whole compression process can be written as. If an independent isentropic assessment is carried out for the small compression stages, then the isentropic efficienies of each of the stage can be written as. Or by using 4 and 5 , we get.

In case you can not make out, pay attention to the shaded grey area which is a quadrilateral. The length of the right edge is greater than the length of the left edge. This is because the top edge has a greater slope than the bottom edge. This also applies to the other two quadrilaterals underneath.

This difference is due to the fanning effect divergence of the isobars on the h-s diagram. How do we explain these diverging isobars?? Now, as per the second Tds relationship which was derived in Chapter 05 For an ideal gas enthalpy is a function of temperature, higher temperature means more enthalpy and vice versa. Let us try to give a physical explanation to the above conclusion.

The amount of compression work done is less for a denser gas. As the gas heats up and occupies more volume, more work is required for compression. When a gas is compressed adiabatically and reversibly, it heats up due to thermodynamic effects without any change in entropy.

When the compression stage has irreversabilities, the gas heats up more with an increase in entropy level and requires even more work. As the pressure ratio keeps increasing, the difference between ideal isentropic work and actual work keeps amplifying.

Then they can comparatively evaluate the aerodynamic quality of different pressure ratio machines. If they use the isentropic efficiency in the cycle design, they need to adjust the efficiency value whenever they change the system overall pressure ratio, which they do not know how to.

Because theoretically compressors or turbines should have the same polytropic efficiency independent of overall pressure ratios, if they are well designed, the polytropic efficiency becomes a more convenient choice for them.

Compressor evaluation in gas compressor fields likes to use the polytropic efficiency. For example, in a chemical plant multistage gas compressor, if each stage has the same polytropic efficiency, it will be also the same polytropic efficiency of the total stage machine. Another convenience comes for them. Ironically a similar air compressor field has more often used the isentrpoic efficiency despite the same compressor group.

It looks that a preference of the polytropic efficiency in a gas compressor community originates from a historical background.

The use of the polytropic efficiency requires the specification of the polytropic exponent n which will change depending on the working real gas and even its operating conditions, which will be inconsistent with the original intent, thus falling back to uncertainties.

It is up to you which one to take as a reference between an isentropic purely ideal and a polytropic close to actual process in the efficiency definition. Yes, polytropic work will provide the actual discharge temperature, but the polytropic work is, like the isentropic work, not equal to the actual work. Fundamentally the only real value that polytropic efficiency provides is for the compressor designer.

Specifically, when quantitatively comparing the aerodynamic performance of multistage compressors it is nice to not have to normalize efficiencies back to an average stage performance or to actually have to compare stage-by-stage performance.

From a holistic compressor performance perspective, especially from the point of view of how much power a compressor driver needs to provide and how much energy will be expended compressing the gas, polytropic efficiency is mostly useless. So why do compressor designers prefer polytropic over isentropic? Polytropic efficiency is always higher than isentropic efficiency and makes their compressors look better. And, yes, it allows comparing the aerodynamic quality of a compressor that has a pressure ratio of 10 for some process,with another compressor, for another process with a pressure ratio of 4.

However, once I compare two compressors for the same process conditions, all I care about is how much power they consume. The higher the compression ratio the compressor has, the higher the difference between isentropic and polytropic efficiency, and polytropic will always be higher. And the definition of entropy is very hard to explain.

Here the term 'n' of is 1. Facebook Twitter LinkedIn Whatsapp. Best Career Options after B. Tech Mechanical Engineering?