Calculation — Screw Compressors- Mathematical Modelling And Performance

Mathematical modelling of screw compressors has evolved from simple "black box" calculations to sophisticated simulations that account for micron-level clearances and complex fluid-structure interactions. By mastering these models, manufacturers can push the boundaries of energy efficiency, making industrial processes more sustainable and cost-effective.

For each cavity (the space formed between the meshing rotors and the casing), mass and energy conservation laws are applied. For oil‑injected compressors, separate balances for the gas and oil phases are required, coupled through empirical heat transfer models. The energy equations for both phases are linked by an inter‑phase heat transfer correlation.

Mathematical modelling transforms twin-screw compressor design from empirical trial-and-error into a predictable science. By solving coupled geometric, thermodynamic, and fluid dynamic equations, engineers can pinpoint efficiency losses caused by specific leakage pathways or improper built-in volume ratios. This optimization leads to quieter, cooler, and significantly more energy-efficient compression systems.

Rotor profiles are engineered using rack-generation techniques or analytical meshing calculus. The curves must satisfy the law of gearing to minimize blow-hole areas and sealing line lengths. Chamber Volume Calculation The instantaneous displacement volume

$$ \dotW_ind \approx 20.1 / 0.85 = 23.65 \text kW $$ Mathematical modelling of screw compressors has evolved from

Several specialised software tools are available for screw compressor modelling and performance calculation.

There are five primary leakage paths in a twin-screw compressor:

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is established via transformation matrices using the center distance ( ) between the shafts: Share public link

One of the earliest and most influential models was developed by a team of researchers at the University of Michigan. They created a comprehensive model that accounted for the interactions between the rotors, the casing, and the working fluid. This model, known as the " Michigan Model," became the foundation for future research and development in the field.

The foundation of any screw compressor model is the accurate mathematical definition of the rotor profiles . : This involves defining the

is the heat transfer rate between the gas, rotors, casing, and injected oil. is the instantaneous pressure. is the specific enthalpy.

The development of digital twins – virtual replicas of physical compressors that continuously receive operational data – will enable condition monitoring, predictive maintenance and performance optimisation over the entire lifecycle of a compressor installation. and the working fluid. This model

Where:

Mathematical modelling and performance calculation of screw compressors involve a multi-layered approach that integrates complex rotor geometry with thermodynamic and fluid flow principles . The primary goal is to predict key performance characteristics—such as , power consumption , and discharge temperature —by simulating the compression cycle within the machine's changing control volumes . 1. Geometric Modelling

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