Screw Compressors- Mathematical Modelling And Performance Calculation [2021] Jun 2026

Mathematical models must account for several distinct leakage paths:

Screw compressors are positive displacement compressors that use two intermeshing screws to compress fluids. The screws are designed to rotate in a way that creates a continuous series of small pockets, which capture and compress the fluid. The compression process involves a combination of adiabatic and isothermal processes, making it complex to model and analyze.

To accurately simulate a screw compressor, engineers treat the moving inter-lobe space as a transient control volume. The governing physics rely on the simultaneous solution of conservation laws and fluid property relationships. The Control Volume Approach

Unlike dynamic compressors (e.g., centrifugal), screw compressors trap a fixed volume of gas and reduce that volume to increase pressure. The performance of a screw compressor is dictated by the precision of its rotor profiles (male and female), the clearance between them, and the thermodynamic properties of the working fluid. To accurately simulate a screw compressor, engineers treat

Minor clearances along the sealing lines. Flow Equations

Screw compressors have established themselves as vital components in refrigeration, air conditioning, and process gas industries, favored for their reliability and ability to handle high-pressure ratios efficiently. As demand for higher efficiency and lower operating costs grows, and performance calculation have become essential for optimizing screw compressor design, moving beyond traditional experimental methods to advanced computer-aided simulations .

Several modelling approaches have been developed for screw compressors, including: The performance of a screw compressor is dictated

Historically, early screw machines suffered from poor volumetric efficiencies due to large symmetric profile clearings. However, pioneering advancements spearheaded by researchers like , Ian K. Smith , and Ahmed Kovacevic established a rigorous thermodynamic foundation. Their seminal work, crystallized in the core reference monograph Screw Compressors: Mathematical Modelling and Performance Calculation , revolutionized how asymmetric rotor profiles are developed and optimized.

Where:

In oil-injected screw compressors, lubricating oil is sprayed directly into the working chamber during the compression process. This alters the mathematical model significantly due to multi-phase interactions. performance indicators are calculated.

represent mass flows through the suction and discharge ports.

The contact ratio ensures no leakage between lobes. Mathematically, the sealing line length is minimized to reduce blow-hole leakage.

Actual mass flow: m_dot = η_v × m_dot_th

Between the high-pressure rotor end-faces and the discharge casing wall.

Once the geometric and thermodynamic models are solved (typically via numerical integration like Runge-Kutta), performance indicators are calculated.