Screw Compressors- Mathematical Modelling And Performance Calculation -
Friction losses (bearings, oil shear, rotor meshing) are modelled as torque losses ( T_loss ):
[ P_shaft = P_ind + T_loss \cdot \omega ]
Mechanical efficiency:
[ \eta_m = \fracP_indP_shaft ]
Leakage is the primary source of inefficiency in screw compressors. Gas flows from high-pressure chambers to low-pressure chambers through gaps (clearances).
While the chamber model described above is a "lumped parameter" approach (0D/1D), CFD (3D) modelling is increasingly used.
Assume: inlet pressure p1, inlet temperature T1, rotational speed n, rotor geometry known, discharge pressure p2 target. Use polytropic segmented model with N axial slices. Friction losses (bearings, oil shear, rotor meshing) are
Initialize slice states:
For each slice i from 1..N:
Sum element work:
Compute mass flow and actual volumetric flow:
Account for mechanical losses:
Output performance metrics:
ChatMRO