Screw Compressors- Mathematical Modelling And Performance Calculation

Mathematical modeling of screw compressors is a complex process that bridges geometry, thermodynamics, and fluid dynamics. Most modern performance calculations rely on Lumped Parameter Models (LPM) or Computational Fluid Dynamics (CFD) to predict efficiency, power consumption, and mass flow.  1. Geometric Fundamentals 

• Suction Phase: Pressure remains approximately constant as volume increases.
• Compression Phase: Volume decreases, pressure rises.
• Discharge Phase: Gas is pushed out at constant pressure.

• Screw compressor: A type of compressor that uses two intermeshing screws to compress a fluid.
• Mathematical modeling: The process of developing mathematical equations to describe the behavior of a system.
• Performance calculation: The process of evaluating the performance characteristics of a compressor.
• Computational fluid dynamics (CFD): A numerical method used to simulate fluid flow and thermodynamic processes.
• Finite element method (FEM): A numerical method used to discretize and solve equations.
• Finite difference method (FDM): A numerical method used to discretize and solve equations.

1. The Integral Method: This method involves integrating the equations of motion and energy over the entire compressor to obtain the performance characteristics.
2. The Zone Method: This method divides the compressor into several zones, each representing a specific thermodynamic process, and solves the equations for each zone.
3. The CFD Method: This method uses computational fluid dynamics to simulate the fluid flow and thermodynamic processes within the compressor.

1. Experimental Testing: Experimental testing of screw compressors is performed to validate the mathematical models and performance calculations.
2. Comparison with Measured Data: The calculated performance characteristics are compared with measured data to verify their accuracy.

• Add frictional and parasitic power: P_drive = W × n + P_fric(n) + P_parasitic.

8.2 Oil-Injection Modelling

Oil-injection improves sealing and cooling. Additional terms in energy equation: $$ \fracdUd\theta = \dotQgas + \dotQoil - \dotW + \dotmin hin - \dotmout hout + \dotmoil cp,oil (T_oil - T_gas) $$ Mathematical modeling of screw compressors is a complex