Spline-Based Parameterization Techniques for Twin-Screw Machine Geometries

The fully automated generation of computational meshes for twin-screw machine geometries constitutes a mandatory aspect for the numerical simulation (and shape-optimization) of these devices but proves to be a challenging task in practice. Therefore, the successful generation of computational meshes requires sophisticated mathematical tools. Commercially available classical mesh generators can produce high quality meshes from no more than a description of the rotor contours. However, since we are particularly interested in numerical simulations using the principles of Isogeometric Analysis, a spline-based geometry description rather than a classical mesh is needed.

In this paper, we propose a practical approach for the automated generation of spline-based twin-screw machine geometry parameterizations in two dimensions. For this purpose, we adopt the principles of Elliptic Grid Generation and present a parameterization algorithm that is compatible with an automated simulation pipeline based on the principles of isogeometric analysis.

To demonstrate the proposed techniques, we apply them to an example geometry and present the resulting parameterizations. Finally, we give a qualitative explanation of how the discussed techniques can be utilized to generate geometry parameterizations in three dimensions and their applications to shape-optimization on a variable rotor-pitch.