Compressors, Gas Turbines and Jet Engines
Axial flow compressor has the following advantage over centrifugal compressor

Larger air handling ability per unit frontal area
Higher pressure ratio per stage
Aerofoil blades are used
Higher average velocities

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Compressors, Gas Turbines and Jet Engines
The assumption made in two stage compression with inter-cooler is that

There is no pressure drop in the inter-cooler
The suction and delivery of air takes place at constant pressure
The compression in both the cylinders is polytropic
All of the listed here

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