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# Discharge gas Temperature for Poly-tropic Process and Adiabatic Process2

## Discharge gas Temperature for Poly-tropic Process and Adiabatic Process

(OP)
In a Centrifugal Compressor, Can anyone explain why the discharge gas temperature(T2) in polytropic process is higher than discharge gas temperature (T2) calculated in Adiabatic process? I understand that discharge gas temperature (T2) in adiabatic shall be higher than T2 in Polytropic process. This is due to the fact that in adiabatic process there will not be any heat exchange from/to the system and surroundings. Heat generated within the compressor should increase the discharge gas temperature where as in Polytropic process heat will be dissipated to surroundings from casing, bearings, etc. Any help please.

Sonu Dandala
Rotating Equipment Engineer

### RE: Discharge gas Temperature for Poly-tropic Process and Adiabatic Process

are you comparing isentropic vs. polytropic ?
"http://en.wikipedia.org/wiki/Gas_compressor"
consider the equations for ideal gases,
for real gases things are a bit more complex.

### RE: Discharge gas Temperature for Poly-tropic Process and Adiabatic Process

(OP)
Any help?

Sonu Dandala
Rotating Equipment Engineer

### RE: Discharge gas Temperature for Poly-tropic Process and Adiabatic Process

souravasnu,
You posted a horribly worded question/lecture on Monday at 3:00 am EST in the U.S., the majority of people who might help are in the U.S. You didn't get a response in 3 hours so you start fussing at people for not yet providing you free expert advice quickly enough. I saw your first post before I had breakfast, and decided to think about it while I ate and get ready for my day. I get back to my office and find your second post. That very much disinclines me from wanting to help. I'll assume that any information I might have provided is too late to help, so I'll not bother.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. —Galileo Galilei, Italian Physicist

### RE: Discharge gas Temperature for Poly-tropic Process and Adiabatic Process

A compressor is a compressor is a compressor...

Both "polytropic" and "adiabatic" are calculation methods - there are no physical polytrpic or adiabatic compressors. Having said that:

Polytropic (calculation): A polytropic process is one in which changes in gas characteristics during compression are considered. The polytropic exponent n is experimentally determined for a given type of machine and may be lower or higher than the adiabatic exponent k. Because the value of n changes during the compression process, an average value is used.

Adiabatic (calculation): An adiabatic (isentropic) process is one in which no heat is added or removed from the systemAdiabatic efficiency is defined as the ratio of work output for an ideal isentropic compression process to the work input to develop the required head.

### RE: Discharge gas Temperature for Poly-tropic Process and Adiabatic Process

To me it is as follows;

Polytropic compression is an isentropic compression assuming an infinite or small number of compression steps; reason is that the isobaric curves in a enthalpy vs entropy diagram are not parallel.

As consequence; at low pressures isentropic and polytropic are very close. It is even more true when efficiencies are approaching 1. The distorsion between polytropic and isentropic increases at low efficiencies.

Isentropic is adiabatic + reversible. Not agree with above post which also does not answer to the OP question.
So isentropic is defined as an ideal case where there is no heat exchange with surroundings (this increases the compression work) + no friction losses ; isentropic head is determine accordingly and is fixed / known for a given pressure ratio, defined gas properties (via equation of state) and known inlet temperature.

In reality if you know the (real) discharge temperature of machine, say via measurement, you can calculate the effective or actual head (total actual enthalpy difference) so you could know the polytropic efficiency which is the inverse ratio of actual head respective to polytropic head ; the latter itself is derived from isentropic head by using integration and concept of limit (whereby small compression steps tend to zero). The other way around, if you know the polytropic efficiency you determine the discharge temperature and so forth.

Adiabatic should be an intermediate case between isentropic path and actual polytropic path in a Molier diagram, therefore adiabatic discharge temperature should be somewhere in between isentropic and polytropic case as far as I am correct.

"If you want to acquire a knowledge or skill, read a book and practice the skill".

### RE: Discharge gas Temperature for Poly-tropic Process and Adiabatic Process

Another way to say that is:
• All gas compression varies from ideal adiabatic processes
• Positive displacement compressor variance from ideal is acceptably small and using the adiabatic constant yields useful answers
• Dynamic compressor variance from ideal is too great for an adiabatic assumption to provide useful answers
The key is "useful answers". The reason we do any of this arithmetic is to attempt to predict performance. Any answer that results in a decision that leads to a successful design is "useful".

When people have tried to use an adiabatic assumption with centrifugal or axial compressors have had field temperatures and pressures that required different materials than were installed--not a good outcome. So we've evolved to polytropic calculations that (when you get the polytropic exponent right) adequately match computed values with measured values.

I'm not sure of the basis for

#### Quote:

I understand that discharge gas temperature (T2) in adiabatic shall be higher than T2 in Polytropic process.
. That does not jibe with my experience. I've seen polytropic exponents that were higher than adiabatic exponents and some that were lower.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. —Galileo Galilei, Italian Physicist

### RE: Discharge gas Temperature for Poly-tropic Process and Adiabatic Process

That does not jibe with my experience. I've seen polytropic exponents that were higher than adiabatic exponents and some that were lower.

Zdas,

To me, at least for centrifugals, I thought it should be the case that adiabatic is somewhere between isentropic and polytropic.
But now that you wrote this, I have to think about it again...

What comes in mind is centrifugals for very high pressure application which would typically result in very low volume flow.
In that case it could be that more heat (adibatic case) is beneficial in the sense that it increases quickly the volume flow and thus the polytropic efficiencies. If polytropic efficiencies increase very fast (again I suspect this is the case at very low flow) it might provide benefit on the overall whereby the extra compression work due to the heat (adiabatic case) was compensated and balance was positive.

Apart from this, I would be curious to know from a theretical view point, how Zdas observation translates in a Mollier diagram whereby possibly the adiabatic head can be higher than polytropic head. I am not saying it does not happen, just to educate myself.
Thanks

"If you want to acquire a knowledge or skill, read a book and practice the skill".

### RE: Discharge gas Temperature for Poly-tropic Process and Adiabatic Process

I can't help with that. Every attempt to link polytropic processes with thermodynamic theory that I've ever read has ended up reverting to empirical results. The polytropic assumption seems to be a fairly big bucket of "that is just how things work". I'm fine with that from a practical viewpoint, but the scientist in me wants there to be a pretty relationship that I can follow back to first principles. Best I can tell, that path has to jump a couple of sharks that no one has been able to get over yet.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. —Galileo Galilei, Italian Physicist

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