Thanks PingPong,
My intention is figure out how compressor (designed yet) could be work when it is operating in a off design point, like for instance, when the MW increase suddenly in the system.
In such condition, if the MW varies, the flow rate will change also, since density is affected. But the compressor does not follow the same performance curve. My understanding is that such curve is for a certain compressor at certain speed working with a certain gas at certain inlet conditions. Any changes in those will lead a new performance curve (Hp vs Qv)
I am trying to find out and explain why the curve (Hp vs Qv) with higher density is shifted up.
Considering now a compressor, designed for operating at certain conditions.
Assumptions:
Mass flow constant
Suction pressure constant
Suction pressure constant
Z constant (in reality, does not)
k constant (the same, with changes in gas composition it will change)
Fixed speed
Given curve for initial inlet conditions with a initial gas composition.
Suddenly the MW increases. What would it happen?
System curve
==========
Increase in MW, increase in density
Density = MW P / R T Z
Increase in density, increase the fricction coeficient since Re is proportional to density, and this is proportional to friction factor.
Therefore, the slope of the resistance curve of the system becomes steeper, and the intersection with the compressor curve will be at lower flow rate and higher polytropic head.
Compressor curve
=============
Buuuuut, the compressor does not follow the same curve than the initial one. As consequence of the MW increase, density increases, and frictional internal looses are higher now for any flow rate. Therefore, the compressor shall offer higher power, thus higher polytropic head (mass flow constant). Considering, just the compressor behaivour (no the system), we could say that for the same Qv, the politropic head will be higher because more power comes from fixed rpm driver (it fits its torque to the resistance torque, giving a new operation torque. At fixed rpm, the power then will increase). Therefore, the curve (Hp vs Qv) is shifted up for higher density as it is reflected in the attached figure. (Source: "Centrifugal Compressors. Principles of operation and control." - A. Eli Nisenfeld)
Take into account that the discharge pressure will increase also. Higer politropic heand and constant and higher density, higher differential pressure. Because of inlet pressure remains fixed, discharge pressure will increase.
Operation point
===========
Considering this new compressor curve and the new system curve, the interaction will light the new operation point.
Please, correct me if I am wrong. I am so interested in this analysis
Regards,
RML
Edited by rmarzo, 15 August 2014 - 05:15 PM.