Screw Compressors- Mathematical Modelling And Performance Calculation

Using the caloric equation of state, this transforms into an explicit differential equation for temperature ( ), which is solved simultaneously with pressure ( 4. Fluid Flow and Leakage Modelling

GT‑SCORG also supports advanced features such as refrigerant drop‑in studies, optimisation of rotor geometry and port timing, and the development of digital twins for condition monitoring and fault detection. When paired with GT‑Automation, engineers can perform rotor optimisation by varying geometry parameters while using the built‑in optimiser of GT‑SUITE.

Q̇oil=hoilAdroplet(Tgas−Toil)cap Q dot sub o i l end-sub equals h sub o i l end-sub cap A sub d r o p l e t end-sub open paren cap T sub g a s end-sub minus cap T sub o i l end-sub close paren Using the caloric equation of state, this transforms

[ \dotQ oil = h oil-gas \cdot a_oil \cdot (T_gas - T_oil) \cdot V_chamber ]

The performance of a screw compressor is fundamentally determined by the geometry of its rotors. The male and female rotors, with their helical lobes and grooves, form the working chambers where the fluid is trapped and compressed. The is the primary mathematical approach for designing these rotor profiles. This method uses the theory of gearing to define the surfaces of the rotors, ensuring correct meshing and continuous contact between the male and female rotors. By specifying the profile of the gate rotor (or a cutting tool), the mating screw rotor's profile is generated as the envelope to the family of the gate rotor's surfaces across the rotation. This mathematical model allows engineers to calculate all necessary geometric parameters, such as the rotor's cross-sectional profile, the volume of the working chambers, and the areas of suction and discharge ports as functions of the rotation angle. Q̇oil=hoilAdroplet(Tgas−Toil)cap Q dot sub o i l end-sub

Theoretical mass flow (no leakage): Q_th = V_d × n (m^3/s at suction conditions) m_dot_th = Q_th × ρ_suction = Q_th × p1/(R T1)

. This analytical approach is essential for optimizing complex rotor profiles and predicting performance across varying operating conditions. Springer Nature Link 1. Geometric Modelling This method uses the theory of gearing to

. This volume decreases as the rotors mesh, leading to compression. 2. Thermodynamic Modelling of the Compression Process