Anand Pratap Singh

New approaches in turbulence and transition modeling using data-driven techniques

A data-driven approach to the modeling of turbulent and transitional flows is proposed in this work, with the goal of developing more robust and accurate closure models. The key idea is to (i) infer the functional form of deficiencies in known closure models by applying inverse problems to computational and experimental data, (ii) use machine learning to reconstruct the improved functional forms, and (iii) to inject the improved functional forms in simulations to obtain more accurate predictions. The inverse modeling step, on its own, can yield valuable insight to the modeler, essentially converting data to information. The machine learning step is a tool to convert information into modeling knowledge. Representative examples are used to describe the methodology and to demonstrate its viability. The first example investigates the modeling of a non-equilibrium turbulent boundary layer, and the second involves the modeling of bypass transition to turbulence. Evidence from these problems emphasizes the utility of the proposed approach in offering new routes to closure modeling in general computational physics disciplines.

Using field inversion to quantify functional errors in turbulence closures

A data–informed approach is presented with the objective of quantifying errors and uncertainties in the functional forms of turbulence closure models. The approach creates modeling information from higher-fidelity simulations and experimental data. Specifically, a Bayesian formalism is adopted to infer discrepancies in the source terms of transport equations. A key enabling idea is the transformation of the functional inversion procedure (which is inherently infinite-dimensional) into a finite-dimensional problem in which the distribution of the unknown function is estimated at discrete mesh locations in the computational domain. This allows for the use of an efficient adjoint-driven inversion procedure. The output of the inversion is a full-field of discrepancy that provides hitherto inaccessible modeling information. The utility of the approach is demonstrated by applying it to a number of problems including channel flow, shock-boundary layer interactions, and flows with curvature and separation. In all these cases, the posterior model correlates well with the data. Furthermore, it is shown that even if limited data (such as surface pressures) are used, the accuracy of the inferred solution is improved over the entire computational domain. The results suggest that, by directly addressing the connection between physical data and model discrepancies, the field inversion approach materially enhances the value of computational and experimental data for model improvement. The resulting information can be used by the modeler as a guiding tool to design more accurate model forms, or serve as input to machine learning algorithms to directly replace deficient modeling terms.

Machine-Learning-Augmented Predictive Modeling of Turbulent Separated Flows over Airfoils

A modeling paradigm is developed to augment predictive models of turbulence by effectively utilizing limited data generated from physical experiments. The key components of our approach involve inverse modeling to infer the spatial distribution of model discrepancies, and, machine learning to reconstruct discrepancy information from a large number of inverse problems into corrective model forms. We apply the methodology to turbulent flows over airfoils involving flow separation. Model augmentations are developed for the Spalart Allmaras (SA) model using adjoint-based full field inference on experimentally measured lift coefficient data. When these model forms are reconstructed using neural networks (NN) and embedded within a standard solver, we show that much improved predictions in lift can be obtained for geometries and flow conditions that were not used to train the model. The NN-augmented SA model also predicts surface pressures extremely well. Portability of this approach is demonstrated by confirming that predictive improvements are preserved when the augmentation is embedded in a different commercial finite-element solver. The broader vision is that by incorporating data that can reveal the form of the innate model discrepancy, the applicability of data-driven turbulence models can be extended to more general flows.

Characterizing and Improving Predictive Accuracy in Shock-Turbulent Boundary Layer Interactions Using Data-driven Models

A data-driven framework is applied to enhance Reynolds-averaged Navier-Stokes (RANS) predictions of flows involving shock-boundary layer interactions. The methodology involves solving inverse problems to infer spatial discrepancies in the Spalart Allmaras (SA) model and projecting these discrepancies to locally non-dimensional flow features using machine learning. The machine-learned reconstruction of the discrepancy is then used within the RANS partial differential equation solver for predictions. The methodology is applied to problems involving transonic flow over an axisymmetric bump, oblique shock-boundary layer interactions and shock train flows. The ability of the model to assimilate data (surface pressure and field velocities) while predicting other quantities (Reynolds stresses) is studied. Different approaches to infer discrepancies are compared, including a form that preserves a log-layer constraint in the SA model.