Screw Compressors- Mathematical Modelling And Performance Calculation ✦ Fast

The Story of Screw Compressors: Unveiling the Secrets of Mathematical Modelling and Performance Calculation

Indicated power: $$ \dotWind = \fracn \cdot z_160 \cdot Wind $$ The Story of Screw Compressors: Unveiling the Secrets

3. Volumetric Performance & Leakage

3.1 Theoretical displacement and volumetric efficiency

• Theoretical displacement per revolution (V_th) determined from rotor geometry and axial length: V_th = A_g × axial_length_per_rev (m^3/rev), where A_g is geometric trapped cross-sectional area.
• Volumetric efficiency η_v = Q_actual / Q_theoretical = (1 − φ_leak − φ_reexp − φ_filling)

  Rotor Profile Generation: Contemporary designs often utilize asymmetric rotor profiles, which can reduce the "blow-hole" area (a major source of internal leakage) by up to 90% compared to older designs. The Story of Screw Compressors: Unveiling the Secrets

  Output performance metrics:

  Leakage flow equation (compressible flow, orifice model): $$ \dotmleak = C_d \cdot Agap \cdot \sqrt \frac2R T_up \cdot \frac\kappa\kappa-1 \left[ \left( \fracP_downP_up \right)^\frac2\kappa - \left( \fracP_downP_up \right)^\frac\kappa+1\kappa \right] $$ The Story of Screw Compressors: Unveiling the Secrets

  5.1 Indicated Diagram (P-V Diagram)

  The integration yields the pressure-volume relationship.