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 the 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 modeling.

Turbomachinery flow modeling lives in a constant a compromise between accuracy and computational costs of numerical simulations. One of the key factors of that 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 physics of boundary layers where grid resolution does not suffice. Widespread wall functions were derived by the observation of few canonical flows, further expressed as 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, as rotating passages or swirled flows. In those flows, the mathematical formulations of wall functions do not account the distortion on the boundary layer due to the combined action of centrifugal and Coriolis forces.

Here we derive a wall function for rotating passages, through means of machine-learning. Multi-layer neural networks are suitable for this application, thanks to their non-linearity and high accuracy. LES simulations of rotating ducts at different Rossby number constitute a statistically significant training database.  A single axis of rotation is here considered.  Rossby numbers are selected to match with common reported values for fan applications. Input features are selected by locally normalizing combinations of raw flow fields.  Exploratory data analysis assures quality of data and leads the process of feature selection/combination.

The algorithm is training and optimized using Keras library. The derived predictor is embedded in runtime computations of OpenFoam v.18. Interface between C^++^ and Python 3.6 relies on the C_api library. Advanced solutions are here applied to fasten training time and to prevent overfitting. Model is validated through a steady simulation of a rotating duct at an intermediate Rossby number. Turbulence closure is performed using the k-epsilon model. Test data is not included in the original dataset to better understand generality of the model. We report a toe to toe comparison between the derived predictor and the standard OpenFoam’s *kWallFunction*. Results from machine-learning wall function show a better prediction of the friction coefficient and a slight better match with the log-law. Analysis of k^+^ as a function of y^+^ shows that the model is able to partially correct the overprediction of the turbulent kinetic energy given by the standard form. Computational time remains the same between the two SimpleFoam solvers.


A Machine-Learnt Wall Function for Rotating Diffusers

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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