Screw Compressors- Mathematical Modelling And Performance Calculation -

Screw compressors are a cornerstone of modern industrial systems, ranging from refrigeration to high-pressure air production. Their effectiveness is largely defined by their internal rotor geometry and the thermodynamic efficiency of the compression cycle. 1. Mathematical Modelling of Geometry

In the 1970s, researchers started developing mathematical models to describe the behavior of screw compressors. These models used complex equations to simulate the compression process, taking into account factors such as rotor geometry, thermodynamics, and fluid dynamics. The goal was to create a predictive tool that could help engineers optimize compressor design and performance. Screw compressors are a cornerstone of modern industrial

Indicated power (ideal): $$ \dotWis = \dotm \cdot c_p (Td,is - T_s) = 0.1169 \times 1005 \times (464 - 293) $$ $$ = 0.1169 \times 1005 \times 171 = 20.1 \text kW $$ Rotor profile → Built-in V-ratio → System pressure

This accounts for the main flow plus internal leakages (backflow) and oil injection. Conservation of Energy: is internal energy, is heat transfer, is work, and is enthalpy. Real Gas Effects or oil-thermodynamics interaction? Let’s discuss below.

8. Advanced Considerations

8.1 Real Gas Effects

For refrigerants or high-pressure gas, compressibility factor $Z(P,T)$ must be used. Equations like Peng-Robinson or Soave-Redlich-Kwong are applied.

Account for mechanical losses:

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 → Built-in V-ratio → System pressure ratio → Leakage control.

  💬 Over to you:
  Have you worked with screw compressor modelling? What’s your biggest challenge—rotor profiling, leakage prediction, or oil-thermodynamics interaction? Let’s discuss below.