Assessment of a machine-learnt adaptive wall-function in a compressor cascade with sinusoidal leading edge

Near-wall modelling is one of the most challenging aspects of CFD 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, especially in RANS computations, which normally require that the first cell of the grid to fall inside the log-layer (50 < y+ < 200) [1]. This approach can be generally considered as robust, however the derivation of wall functions from attached flow boundary layers can mislead to non-physical results in presence of specific flow topologies, e.g. recirculation, or whenever a detailed boundary layer representation is required (e.g. aeroacoustics studies) [2]. 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 non-linear problems [3]. The learner that is derived from the multi-layer 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 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 [4][5]. The derived wall function is implemented in OpenFOAM v-17.12 [6], 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.