Abstract
The solution of Reynolds-averaged Navier–Stokes equations employs an appropriate set of equations for the turbulence modelling. The closure coefficients of the turbulence model were calibrated using empiricism and arguments of dimensional analysis. These coefficients are considered universal, but there is no guarantee this property applies to test cases other than those used in the calibration process. This work aims at revisiting the calibration of the closure coefficients of the original Spalart–Allmaras turbulence model using machine learning, adaptive design of experiments and accessing a high-performance computing facility. The automated calibration procedure is carried out once for a transonic, wall-bounded flow around the RAE 2822 aerofoil. It was found that: (a) an optimal set of closure coefficients exists that minimises numerical deviations from experimental data; (b) the improved prediction accuracy of the calibrated turbulence model is consistent across different flow solvers; and (c) the calibrated turbulence model outperforms slightly the standard model in analysing complex flow features around additional test cases (ONERA M6 wing, axisymmetric transonic bump, forced sinusoidal motion of NACA 0012 aerofoil). A by-product of this study is a fully calibrated turbulence model that leverages on current state-of-the-art computational techniques, overcoming inherent limitations of the manual fine-tuning process.
Highlights
A deterministic computational fluid dynamics (CFD) analysis gives a single solution for a certain set of input parameters, e.g. geometry, free-stream flow conditions, etc
Uncertainty in the closure coefficients of a turbulence model is an important source of error in Reynolds-averaged Navier–Stokes (RANS) analyses, but no reliable estimator for this error component exists
The work detailed in this study addressed these aspects using state-of-the-art computational techniques, including a machine-learning software platform with an adaptive design of experiments algorithm, a modern flow solver, and a high-performance computing facility
Summary
A deterministic computational fluid dynamics (CFD) analysis gives a single solution for a certain set of input parameters, e.g. geometry, free-stream flow conditions, etc. These parameters may be uncertain and the associated. It is apparent that CFD workflows contain considerable uncertainty, often not quantified [18]. Numerical uncertainties in the results come from: (a) physical modelling errors and uncertainties, for example, in accurate predictions of turbulent flows; (b) numerical errors arising from mesh and discretisation inadequacies; and (c) aleatory uncertainties derived from natural variability, and epistemic uncertainties due to the lack of knowledge in the parameters of a specific fluid problem. The work presented in the current paper addresses the last type of uncertainty
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