Higher inlet temperature means higher head for same pressure ratio and gas. If we assume massflow and efficiency unchanged it means absorbed power goes up.
Practically if the inlet conditions change, for instance depart from design, then efficiency would also change. And again if this is departing from design then you would expect lower efficiency. So absorbed power would even further increase then.
Change in inlet temperature on a multistage machine -due to volume ratio effect - would also affect the shape of surge line and it also affects which impeller initiates surge for a given rotative speed.
Generally speaking, at constant massflow, head increase gets you closer to surge but volume flow increase gets you farther
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My response was based on the compressor running at fixed speed.
If the compressor is on VSD, and speed control is by pressure control on stage 1S, then the compressor will speed up when stage 1S temp is high to keep mass flow constant. And compressor power will go up - same reply as @rotw. At higher speed and higher head due to higher suction temp, the new operating point will be closer to surge.
Assume, a compressor has already been designed for the maximum volume flowrate conditions. Thus, physical volume of the gas occupied and subsequently the flowrate is fixed. Now, as inlet gas temperature increases, gas becomes lighter, although the physical volume of the gas occupied is fixed. Lighter gas density implies lighter mass flowrate. Power consumed by the compressor is proportional to mass flowrate. Hence, power consumption would fall.
Few comments on the last post when applied to real world:
1- Seems a valid reasonining at constant efficiency. But absorbed power is function of polytropic efficiency. So, if the operation at higher inlet temperature result on the one hand in operating the compressor in the low efficiency region and on the other it occurs that the base case (low temperature) is selected for optimal efficiency then - all other things being equal - it is possible that power could increase.
2 - Compressor maximum volumetric flowrate conditions is not necessarily the limiting factor for compressor capacity. For example you could be compliant in terms of maximum volume flow but because inlet temperature has increased, tip speed also need to increase and it could eventually exceed the maximum allowed impeller tip speed; this scenario would require to revisit the original assumption of flowrate maintained fixed. I suggest as reference: K. Ludtke book 'Process Centrifugal Compressors' @ page 104/328 for further considerations about maximum volume flow for a compressor frame.
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