A Machine-Learnt Wall Function for Rotating Diffusers

Data-driven tools and techniques have proved their effectiveness in many engineering applications. Machine-learning has gradually become a paradigm to explore innovative designs in turbomachinery. However, industrial Computational Fluid Dynamics (CFD) experts are still reluctant to embed similar approaches in standard practice and very few solutions have been proposed so far. The aim of the work is to prove that standard wall treatments can obtain serious benefits from machine-learning modelling. Turbomachinery flow modeling lives in a constant compromise between accuracy and the computational costs of numerical simulations. One of the key factors of process is defining a proper wall treatment. Many works point out how insufficient resolutions of boundary layers may lead to incorrect predictions of turbomachinery performances. Wall functions are universally exploited to replicate the physics of boundary layers where grid resolution does not suffice. Widespread wall functions were derived by the observation of a few canonical flows, further expressed as a simple polynomial of Reynolds number and turbulent kinetic energy. Despite their popularity, these functions are frequently applied in flows where the ground assumptions cease to be true, such as rotating passages or swirled flows. In these flows, the mathematical formulations of wall functions do not account for the distortion on the boundary layer due to the combined action of centrifugal and Coriolis forces. Here we will derive a wall function for rotating passages, through means of machine-learning. The algorithm is directly implemented in the N-S equations solver. Cross-validation results show that the machine-learnt wall treatment is able to effectively correct the turbulent kinetic energy field near the solid walls, without impairing the accuracy of the RANS turbulence model in any way.