Data-Driven Turbulence Modeling for Correcting Unsteady Transonic Predictions

Abstract

Numerical simulations with high accuracy are a fundamental part of modern aircraft design. The current industry standard for the simulation of aerodynamic flows are RANS simulations that require modeling of unresolved turbulence. The underlying assumptions of RANS equations and the corresponding turbulence models exhibit inadequacies that lead to errors. Field inversion and machine learning (FIML) is a data-driven turbulence modeling approach that introduces a spatially varying correction term in the turbulence model by using high-fidelity numerical or experimental reference data. Within this thesis the production term of the negative Spalart-Allmaras (SA) model is corrected. Using the RAE 2822 two-dimensional airfoil two test cases, one with numerical and one with experimental reference data, are designed to incorporate transonic flow effects such as shocks. The FIML approach is trained and applied on multiple steady cases with varying angles of attack, aiming to yield good corrections for steady transonic simulations and implicitly learning the change of the correction field with the angle of attack. In a second step, the trained model is applied to unsteady dual-time stepping simulations with a pitching airfoil at varying reduced frequencies and excitation amplitudes. The field inversion approach delivers good corrections of the reference quantity and related quantities for inadequacies caused by the SA turbulence model in transonic flow fields including shocks using a realistic number of reference points. Therefore, investigations regarding the number of reference points, the correction of non-reference variables, and varying free-stream conditions are conducted. Applying a fully-connected neural network with selected locally available flow features to a limited area of the flow field yields good results for the correction of steady simulations. For the application to unsteady simulations, the ML correction model shows ambiguous results regarding the accuracy and convergence issues for flow conditions including strong nonlinear effects. Applying a steady correction field which is the result of the field inversion or a corrected steady simulation yields improved convergence and promising correction results at excitation amplitudes smaller than one degree. Testing the ML approach on the second test case with experimental reference data shows issues regarding generalizability. Finally, multiple ideas regarding further work and improvements are presented.