Screw Compressors- Mathematical Modelling And Performance Calculation May 2026

Initialize rotor position θ = 0°
For each rotor chamber:
    Set initial m = m_suc, T = T_suc, p = p_suc
For θ = 0 to 360° step Δθ:
    Update V(θ) from geometry lookup table
    Calculate mass inflow from suction port (if open)
    Calculate leakage mass flows (blow-hole, radial, axial)
    Apply mass balance: m_new = m_old + (Σṁ_in - Σṁ_out)*Δt
    Calculate heat transfer to walls (using Nusselt correlation)
    Solve energy eq for u_new → T_new
    Solve real gas EOS for p_new
    If θ corresponds to discharge port opening:
        Allow mass outflow to discharge
    Store p(θ), T(θ)
End loop
Compute P_ind, P_shaft, efficiencies

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.

Leakage is the primary source of inefficiency in screw compressors. Gas flows from high-pressure chambers to low-pressure chambers through gaps (clearances). Initialize rotor position θ = 0° For each

Flow Equation: Flow is typically modelled using compressible flow through an orifice/nozzle equation: $$ \dotm_leak = C_d A \sqrt\frac2kk-1 P_1 \rho_1 \left[ \left(\fracP_2P_1\right)^\frac2k - \left(\fracP_2P_1\right)^\frack+1k \right] $$ Where $C_d$ is the discharge coefficient and $A$ is the clearance area.