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 ]

The indicated power is the work done on the gas:

[ P_ind = \frac\omega2\pi \oint p \fracdVd\theta d\theta ]

Where ( \omega ) = angular speed (rad/s). The integration is over one full revolution.

Indicated efficiency (adiabatic efficiency):

[ \eta_ad = \frac\dotmactual \cdot (hdis,ad - h_suc)P_ind ]

Where ( h_dis,ad ) is the discharge enthalpy after isentropic compression.

Due to stiffness (rapid pressure changes), explicit solvers require very small ( \Delta\theta ). Implicit methods or adaptive step size are recommended. Typical run time for one operating point: 0.5–2 seconds on a modern CPU for a chamber model; full 3D CFD models may take hours.

Once a forward model is built, it can be coupled with optimization algorithms to maximize efficiency by varying:

Before any performance calculation begins, one must accurately define the rotor geometry. A twin-screw compressor consists of a male rotor (convex lobes) and a female rotor (concave flutes). The meshing of these rotors creates moving chambers that trap, reduce in volume, and discharge gas.