Screw Compressors- Mathematical Modelling And Performance Calculation (2026)

d(m⋅u)dt=Q̇−PdVdt+∑ṁinhin−∑ṁouthoutthe fraction with numerator d open paren m center dot u close paren and denominator d t end-fraction equals cap Q dot minus cap P the fraction with numerator d cap V and denominator d t end-fraction plus sum of m dot sub i n end-sub h sub i n end-sub minus sum of m dot sub o u t end-sub h sub o u t end-sub is the specific internal energy of the gas. Q̇cap Q dot

Once the differential equations are solved (usually via numerical methods like Runge-Kutta), we can calculate the key performance indicators (KPIs): Volumetric Efficiency ( ηveta sub v

to find the ideal rotor size, speed, and injection positions for specific duties. Key Strengths

The foundation of any screw compressor model is the geometric definition of the male and female rotors. The performance of the compressor—including its displacement, leakage rates, and efficiency—is directly dictated by the rotor profile. Rotor Kinematics

The work is structured into five distinct parts that bridge the gap between abstract mathematical theory and industrial application: Amazon.com Part 1: Historical and Technical Review

A triangular leakage path formed at the intersection of the rotor tips and the housing cusp. Leakage Flow Equations Because clearances are narrow (typically

The performance of a screw compressor is fundamentally dictated by its rotor profile. Mathematical modelling begins by defining the coordinate systems for the male (lobe) and female (groove) rotors.

Multi-arc asymmetric profiles reduce leakage while enhancing structural integrity.