Assessment of a Machine-Learnt Adaptive Wall-Function in a Compressor Cascade With Sinusoidal Leading Edge
Authors: Tieghi Lorenzo , Corsini Alessandro , Delibra Giovanni , Angelini Gino 
Published: September 2020

Abstract
Near-wall modeling is one of the most challenging aspects of computational fluid dynamic computations. In fact, integration-to-the-wall with low-Reynolds approach strongly affects accuracy of results, but strongly increases the computational resources required by the simulation. A compromise between accuracy and speed to solution is usually obtained through the use of wall functions (WFs), especially in Reynolds averaged Navier–Stokes computations, which normally require that the first cell of the grid to fall inside the log-layer (50 &lt; y+ &lt; 200) (Wilcox, D. C., 1998, Turbulence Modeling for CFD, Vol. 2, DCW Industries, La Cañada, CA). This approach can be generally considered as robust, however the derivation of wall functions from attached flow boundary layers can mislead to nonphysical results in presence of specific flow topologies, e.g., recirculation, or whenever a detailed boundary layer representation is required (e.g., aeroacoustics studies) (Craft, T., Gant, S., Gerasimov, A., Lacovides, H., and Launder, B., 2002, “Wall – Function Strategies for Use in Turbulent Flow CFD,” Proceedings to 12th International Heat Transfer Conference, Grenoble, France, Aug. 18–23). In this work, a preliminary attempt to create an alternative data-driven wall function is performed, exploiting artificial neural networks (ANNs). Whenever enough training examples are provided, ANNs have proven to be extremely powerful in solving complex nonlinear problems (Goodfellow, I., Bengio, Y., Courville, A., and Bengio, Y., 2016, Deep Learning, Vol. 1, MIT Press, Cambridge, MA). The learner that is derived from the multilayer perceptron ANN, is here used to obtain two-dimensional, turbulent production and dissipation values near the walls. Training examples of the dataset have been initially collected either from large eddy simulation (LES) simulations of significant 2D test cases or have been found in open databases. Assessments on the morphology and the ANN training can be found in the paper. The ANN has been implemented in a Python environment, using scikit-learn and tensorflow libraries (Scikit-Learn Developers, 2019, “Scikit-learn v0.20.0 User Guide,” Software, Scikit-Learn Developers; Abadi, M., Barham, P., Chen, J., Chen, Z., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., Isard, M., Kudlur, M., Levenberg, J., Monga, R., Moore, S., Murray, D. G., Steiner, B., Tucker, P., Vasudevan, V., Warden, P., Wicke, M., Yu, Y., and Zheng, X., 2016, “TensorFlow: A System for Large-Scale Machine Learning,” 12th Symposium on Operating Systems Design and Implementation, Savannah, GA, Nov. 2–4, pp. 265–283). The derived wall function is implemented in openfoam v-17.12 (CFD Direct, 2020, “OpenFoam User Guide v5,” CFD Direct, Caversham, UK), embedding the forwarding algorithm in run-time computations exploiting Python3.6m C_Api library. The data-driven wall function is here applied to k-epsilon simulations of a 2D periodic hill with different computational grids and to a modified compressor cascade NACA aerofoil with sinusoidal leading edge. A comparison between ANN enhanced simulations, available data and standard modelization is here performed and reported.