Screw Compressors- Mathematical Modelling: And Performance Calculation

[ \eta_ad = \frac\dotm actual \cdot (h dis,ad - h_suc)P_ind ]

[ \eta_m = \fracP_indP_shaft ] [ \eta_total = \eta_v \cdot \eta_ad \cdot \eta_m ] 4.5 Discharge Temperature Prediction From the first law and real gas properties:

Where ( h ) = clearance height, ( w ) = width, ( \mu ) = viscosity, ( L_path ) = leakage path length. Total leakage is summed over all paths and subtracted from the theoretical displacement to get actual mass flow rate : [ \eta_ad = \frac\dotm actual \cdot (h dis,ad

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

If ( \fracp_dp_u > \left(\frac2\kappa+1\right)^\frac\kappa\kappa-1 ) (subsonic): ( w ) = width

[ R_v = \fracV_sucV_dis ]

Where ( h_dis,ad ) is the discharge enthalpy after isentropic compression. Friction losses (bearings, oil shear, rotor meshing) are modelled as torque losses ( T_loss ): ( \mu ) = viscosity

If chocked (sonic flow at throat), the pressure ratio is replaced by the critical pressure ratio.