Machine Learning for Turbulence Modeling and Predictions

Abstract

A stand-alone machine learned turbulence model is applied for the solution of integral boundary layer equations, and issues and constraints associated with the model are discussed. The results demonstrate that grouping flow variables into a problem relevant parameter for input during machine learning is desirable to improve accuracy of the model. Further, the accuracy of the model can be improved significantly by incorporation of physics-based constraints during training. Data driven machine learning training requires trial-and-error approach, shows oscillations in a posteriori predictions, and shows unphysical results when used with arbitrary initial condition, as the query is essentially extrapolations. Physics informed machine learning addresses the above limitations, and is identified to be a viable approach for development of machine learned turbulence model.

Predictions of Steady and Unsteady Flows using Machine-learned Surrogate Models

“…The machine learning approach uses a solution database to generate a response surface of desired turbulent feature as a function of input features. A review of the literature shows that the machine learning tools have been used for turbulence modeling for: (1) direct field estimation, wherein the entire flow field is predicted [3,4]; (2) modeling uncertainty estimation, wherein model coefficients are calibrated to minimize modeling errors [5,6]; (3) turbulence model augmentation [7][8][9][10]. Turbulence model augumentation is the most common approach used in the literature, and has been applied for unsteady Reynolds Averaged Navier-Stokes (URANS) models either to adjust turbulence production or adjust turbulent stresses or introduce nonlinear stress components; and (4) to obtain a standalone turbulence model, wherein the desired turbulent features are the turbulent stresses.…”

“…For the latter, machine learning is used to infer lift and drag expected from the rotor blade profile at any radial location as a function of local inflow condition, such that they can used within actuator-line modeling framework to develop a mid-fidelity rotor model, which can account for inflow unsteadiness. This research builds on the authors' previous research [1] focusing on development of stand-alone machine-learned (ML) turbulence model for steady boundary layer flow. The key results from the previous research are summarized in the following section.…”

“…Precursor study [1] focused on development and validation of standalone ML turbulence models for steady boundary layer flow, including assessment of key issues associated with neural network training. To achieve the objectives, two different models were developed: (1) data-driven and ( 2) physics informed machine-learned (PIML) [14,15].…”

“…In the context of turbulent flows, which involves a wide range of length and time scales and remains a challenge for modelers, the development of low-fidelity models have stalled, and it seems highly improbable that low-fidelity models can be developed without introducing additional complexity (or computational cost). Machine learning (ML) is emerging as a powerful tool that can provide an alternative path to the traditional modeling approach, wherein neural networks can help identify the correlation between input and output flow variables [1].…”

Neural Ordinary Differential Equations for rotorcraft aerodynamics

“…In addition, traditional ML approaches are not suitable for physics-based applications because they do not satisfy physical conditions. As a result of this limitation, much effort has been dedicated to exploring physics-informed machine learning (PIML) methods that combine neural networks (NNs) with physics-based constraints (Dutta et al 2022;Bhushan et al 2021;Mao et al 2020;Rivera-Casillas et al 2020;Bhushan, Burgreen, Martinez, et al 2020;Raissi et al 2019;Raissi et al 2018).…”