Polytropic efficiency of turbomachinery 1

[ohm727]

Hi, members

Polytorpic efficiency or small-stage isentropic efficiency is easily found in any textbooks of turbomachinery introduction. Its definition and difference from the adiabatic or isentorpic efficiency are well understood. But I am eager to know why the polytropic efficiency is to be introduced there, and at what cases people use it rather than the isentropic efficiency.

Thanks.

 

[milltir]

In general, positive displacement compressors are calculated on the adiabatic cycle (see API 618 Reciprocating Compressors), and rotordynamic compressors on the polytropic cycle (see API 617 Centrifugal and Axial Compressors). As with everything there are exceptions, single stage or air compressors are often calculated on the isentropic cycle. Solar Turbines uses the isentropic cycle for their range of centrifugal compressors. Polytropic efficiency is always greater than adiabatic efficiency, how much greater being dependent on the process conditions (adiabatic exponent and pressure ratio).

 

[ohm727]

Thanks, milltir.

Could you explain more why the positive displacement compressors prefer the adiabatic (or isentropic) efficiency, and the centrifugal and axial compressors prefer the polytropic efficiency.

In a textbook by Dixon, it is said that the polytropic efficiency is useful when two compressors with different pressure ratios are to be compared. But I cannot fully figure it out.

 

[Montemayor]

ohm727:

Empirical field experience has demonstrated that compression in reciprocating compressors closely follows a reversible adiabatic process (constant entropy). I have seen this in such gases as CO2, air, Nitrogen, Methane, Nitrous Oxide, and the common refrigerants. The GPSA Engineering Databook also is in agreement with this experience and recommends this method above all others when dealing with reciprocating machines.

What does your second paragraph refer to? You don't mention whether the two compressors are the same type (nor which type) nor do you define what it is that you are comparing. Please be clear and specific in your questions in order to understand what you are asking. I'll await your reply. Are we supposed to know who "Dixon" is? Cite the book title, publisher, year and/or country of origin.

 

[ohm727]

Thanks, Montemayor

Sorry about my insufficient information about the second paragraph. Here is the whole title of the textbook.

Fluid Mechanics Thermodynamics of Turbomachinery
S.L.Dixon
Pergamon Press, 3rd edition 1978

On page 38, he said that "The adiabatic efficiency, although fundamentally valid, can be misleading if used for comparing the efficiencies of turbomachines of differing pressure ratios."

I cannot understand why in such a case the polytropic efficiency is better. I look forward to your another reply.

 

[rlewis]

For Centrifugal Compressors, the actual stage ratings are developed from test curves and converted to head and efficiency. On a Polytropic basis, the curves do not vary regardless of actual gas, whereas on an isentropic or adaibatic basis, the base rating curve would be invalid due to differences in cp and k of the actual vrs test gas. Since gas machines have impeller base ratings on a polytropic basis, it is simpler to state the performance on a polytropic basis rather than change it to an isentropic basis after it has been calculated. This is especially true when MW,K,Z type calculations are employed.

One exception is of course air comprssors which have historically often been stated on an isentropic basis, but of course always use the same gas (air).

Furher complicating, If a Mollier Chart (or Real gas equations) are used to calculate performance, the polytropic impeller ratings must be converted to adiabatic head and efficiency in order to compute delta H along constant entropy lines. Again, since historically gas compressors state performance as polytropic, the results are converted back to a polytropic basis once the overall calculation is done.

The conversion is pretty easy since Work = Polytropic Head/Polytropic eff and also = Adiabatic Head / Adiabatic eff.

As long as you aren't going to change the gas, performance can be stated on either an adiabatic or polytropic basis.

All of the above comments apply to how manufacturers use base ratings when calculation machine performance.

 

[gtsim]

Work transfer and thus power calculation is path dependent (i.e. work transfer is not a thermodynamic property). Polytropic process accounts for the path (small stages) where as isentropic only considers the start and end point. Using polytropic efficiency gives a more accurate calculation of power required.

 

[sailoday28]

I believe that the polytropic process is basically for non-flow type problems and where the mass does not change.
Ie. A compression or expansion process caused by movment of a piston in a cylinder.

 

[gtsim]

Polytropic and Isentropic analysis can be developed for both steady flow and non-steady fow processes. You can check this in Engineering Thermodynamics by Rogers and Mayhew.

 

[sailoday28]

gtsim and others: Please see my question on
Polytropic process
thread 391-131687