Polytropic Head of the compressor

[planck121]

Hi,
Many compressor design books suggest that the polytropic head is governed by the impeller gemorty and speed. To which I agree because the vector velocity diagram on the impeller is what determines the head the system along with the angular speed.

However, I have been recently involved in trending some compressor performace through our online PI systems where I am observing something quite contrary. I see a variation in the polytropic head (green line on attached sheet) being directly proportional to the variation in the p2/p1 pressure ratios (yellow trend)...The speed for the system during this time is fairly constant.....

If we go by the first princples the polytropic head (green line) should be fairly stable with changing p2/p1. I also understand that if the gas weight mw changes it should be reflected in the output pressure p2 and not the poly head which should only be dependent on the geometry and speed at the impeller. But this does not seem to be the case in the trends.

Could someone please shed some light on this. Would be much appreciated.

Thanks

 

[zdas04]

I spend a lot more time with PD compressors where I can use adiabatic assumptions than with dynamic compressors where you have to use polytropic stuff, but as I recall several of the adiabatic equations can be used for dynamic machines if you replace the adiabatic constant with a polytropic constant (e.g., temperature change across the stage is a simple substitution). The adiabatic constant is absolutely dependent upon gas content. My limited understanding says that the polytropic constant must be at least partially a function of composition. I don't have anything to base that assumption on since in my experience the polytropic constants are experimentally derived so there is obviously more to it than gas composition.

David

 

[pmover]

assuming you are referencing centrifugal compressors . . .

However, I have been recently involved in trending some compressor performace through our online PI systems where I am observing something quite contrary. I see a variation in the polytropic head (green line on attached sheet) being directly proportional to the variation in the p2/p1 pressure ratios (yellow trend)...The speed for the system during this time is fairly constant.....
the poly head value will change with varying pressure ratio, even if speed is relatively constant. examine the compressor curves.

If we go by the first princples the polytropic head (green line) should be fairly stable with changing p2/p1.
not true. examine the compressor curves and be sure the mfg is basing head on poly eqn and not otherwise. can have a constant speed with varying head and Rc.

I also understand that if the gas weight mw changes it should be reflected in the output pressure p2 and not the poly head which should only be dependent on the geometry and speed at the impeller. But this does not seem to be the case in the trends.
if MW changes from original design, for a given set of inlet conditions, the outlet conditions (namely P, Z & T) will change at a given speed; yet poly head will remain the same. examine the poly head equation and the compressor curves.

hope this helps.
-pmover

 

[CaracasEC]

Thorough understanding of the concepts of head required by the process and head produced by the compressor is absolutely essential if dynamic compressor operation is to be understood. Note that the head required by the process is inversely proportional to the gas density. If the gas density decreases, the head required by the process will increase. Gas density will decrease if gas temperature increases, inlet pressure decreases or molecular weight decreases. If the head required by the process increases, the flow rate of any dynamic compressor will decrease. If the gas density increases, the head required by the process will decrease and dynamic compressor flow rate will increase. Simply stated, for a given impeller vane shape, head produced by a dynamic compressor is a function of impeller diameter and impeller speed. Once the impeller is designed, it will produce only one value of head for a given shaft speed and flow rate. The head produced by a dynamic compressor is not significantly affected by gas density. However compression ratio and discharge pressure curves are invalid if the inlet gas temperature, inlet pressure or molecular weight changes. This may be confusing at first but always remember how head is produced by a dynamic compressor. Gas density influences the head required by the process...