Uncertainty Analysis and Data-Driven Model Advances for a Jet-in-Crossflow

Ling, Julia; Ruiz, Anthony; Lacaze, Guilhem; Oefelein, Joseph C.

doi:10.1115/1.4034556

Cited by 35 publications

(11 citation statements)

References 32 publications

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“…Ling and Templeton [120] developed a machine learning method to evaluate potential inadequacy of RANS models by using DNS databases. This approach has been recently applied to more complex flows (e.g., jet in crossflow [143]). The results include several fields of binary labels (whether the specified model assumption is violated), which could be further processed to obtain a variance of Reynolds stress discrepancy that can be incorporated into the covariance kernel field.…”

Section: Quantifying and Reducing Reynolds Stress Uncertainties With mentioning

confidence: 99%

Quantification of model uncertainty in RANS simulations: A review

Xiao

Cinnella

2019

Progress in Aerospace Sciences

307

131

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In computational fluid dynamics simulations of industrial flows, models based on the Reynoldsaveraged Navier-Stokes (RANS) equations are expected to play an important role in decades to come. However, model uncertainties are still a major obstacle for the predictive capability of RANS simulations. This review examines both the parametric and structural uncertainties in turbulence models. We review recent literature on data-free (uncertainty propagation) and data-driven (statistical inference) approaches for quantifying and reducing model uncertainties in RANS simulations. Moreover, the fundamentals of uncertainty propagation and Bayesian inference are introduced in the context of RANS model uncertainty quantification. Finally, the literature on uncertainties in scale-resolving simulations is briefly reviewed with particular emphasis on large eddy simulations.

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Section: Quantifying and Reducing Reynolds Stress Uncertainties With mentioning

confidence: 99%

Quantification of model uncertainty in RANS simulations: A review

Xiao

Cinnella

2019

Progress in Aerospace Sciences

307

131

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“…The physics can be incorporated into these learning algorithms by adding a regularization term (based on governing equations) in loss function or modifying the neural network architecture to enforce certain physical constraints.In addition to reduced order modeling and chaotic dynamical systems, the turbulence closure problem has also benefited from the application of ML algorithms and has led to reducing uncertainties in . Different machine learning algorithms like kernel regression, single hidden layer neural network, random forest [44][45][46] have been proposed for turbulence closure modeling. Sarghini et al [47] proposed the hybrid approach in which the neural network is used for learning Bardina's scale similar subgrid-scale model for turbulent channel flow.…”

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confidence: 99%

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

Pawar

San

Rasheed

et al. 2020

Theor. Comput. Fluid Dyn.

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In the present study, we investigate different data-driven parameterizations for large eddy simulation of two-dimensional turbulence in the a priori settings. These models utilize resolved flow field variables on the coarser grid to estimate the subgrid-scale stresses. We use data-driven closure models based on localized learning that employs multilayer feedforward artificial neural network (ANN) with point-to-point mapping and neighboring stencil data mapping, and convolutional neural network (CNN) fed by data snapshots of the whole domain. The performance of these data-driven closure models is measured through a probability density function and is compared with the dynamic Smagorinksy model (DSM). The quantitative performance is evaluated using the cross-correlation coefficient between the true and predicted stresses. We analyze different frameworks in terms of the amount of training data, selection of input and output features, their characteristics in modeling with accuracy, and training and deployment computational time. We also demonstrate computational gain that can be achieved using the intelligent eddy viscosity model that learns eddy viscosity computed by the DSM instead of subgrid-scale stresses. We detail the hyperparameters optimization of these models using the grid search algorithm.Keywords Turbulence closure · Deep learning · Neural networks · Subgrid scale modeling · Large eddy simulation 1 Introduction Direct numerical simulation (DNS) of complex fluid flows encountered in many engineering and geophysical applications is computationally unmanageable because of the need to resolve a wide range of spatiotemporal scales. Large eddy simulation (LES) and Reynolds Averaged Navier-Stokes (RANS) modeling are two most commonly used mathematical modeling frameworks that give accurate predictions by considering the interaction between the unresolved and grid-resolved scales. The development of these models is termed as the turbulence closure problem and has been a long-standing challenge in fluid mechanics community [1][2][3][4].In LES, we filter the Navier-Stokes equations using a low-pass filtering operator that separates the motion into small and large scales, and in turn, produces modified equations which are computationally faster to solve than actual Navier-Stokes equations [5][6][7]. The interaction between grid-resolved and unresolved scales is then taken into account by introducing subgrid-scale stress (SGS) term in the modified equation. The main task of the SGS model is to provide mean dissipation that corresponds to the transfer of energy from resolved scales to unresolved scales (the production of energy at large scales is balanced by the dissipation of energy at small scales based on Kolmogorov's theory of turbulence). The dissipation effect of unresolved scales can be included utilizing an eddy viscosity parameterization obtained through grid-resolved quantities. These approaches are called as functional approaches which assume isotropy of small scales to present the average dissipation of t...

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“…Duraisamy et al [3,4] have used Gaussian processes to predict the turbulence intermittency and correction terms for the turbulence transport equations. Ling and Templeton [5] trained random forest classifiers to predict when RANS assumptions would fail.Ling et al [6,7] further used random forest regressors and neural networks to predict the Reynolds stress anisotropy. Wang et al [8] have recently investigated the use of random forests to predict the discrepancies of RANS modeled Reynolds stresses in separated flows.…”

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confidence: 99%

“…Ling et al [6,7] further used random forest regressors and neural networks to predict the Reynolds stress anisotropy. Wang et al [8] have recently investigated the use of random forests to predict the discrepancies of RANS modeled Reynolds stresses in separated flows.…”

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A Priori Assessment of Prediction Confidence for Data-Driven Turbulence Modeling

Wang

Xiao

et al. 2017

Flow Turbulence Combust

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Although Reynolds-Averaged Navier-Stokes (RANS) equations are still the dominant tool for engineering design and analysis applications involving turbulent flows, standard RANS models are known to be unreliable in many flows of engineering relevance, including flows with separation, strong pressure gradients or mean flow curvature. With increasing amounts of 3-dimensional experimental data and high fidelity simulation data from Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), data-driven turbulence modeling has become a promising approach to increase the predictive capability of RANS simulations. However, the prediction performance of data-driven models inevitably depends on the choices of training flows. This work aims to identify a quantitative measure for a priori estimation of prediction confidence in data-driven turbulence modeling. This measure represents the distance in feature space between the training flows and the flow to be predicted. Specifically, the Mahalanobis distance and the kernel density estimation (KDE) technique are used as metrics to quantify the distance between flow data sets in feature space. To examine the relationship between these two extrapolation metrics and the machine learning model prediction performance, the flow over periodic hills at Re = 10595 is used as test set and seven flows with different configurations are individually used as training sets. The results show that the prediction error of the Reynolds stress anisotropy is positively correlated with Mahalanobis distance and KDE distance, demonstrating that both extrapolation metrics can be used to estimate the prediction confidence a priori. A quantitative comparison using correlation coefficients shows that the Mahalanobis distance is less accurate in estimating the prediction confidence than KDE distance. The extrapolation metrics introduced in this work and the corresponding analysis provide an approach to aid in the choice of data source and to assess the prediction performance for data-driven turbulence modeling.Even with the rapid growth of available computational resources, numerical models based on Reynolds-Averaged Navier-Stokes (RANS) equations are still the dominant tool for engineering design and analysis applications involving turbulent flows. However, the development of turbulence models has stagnated-the most widely used general-purpose turbulence models (e.g., k-ε models, k-ω models, and the S-A model) were all developed decades ago. These models are known to be unreliable in many flows of engineering relevance, including flows with three-dimensional structures, swirl, pressure gradients, or curvature [1]. This lack of accuracy in complex flows has diminished the utility of RANS as a predictive simulation tool for use in engineering design, analysis, optimization, and reliability assessments.Recently, data-driven turbulence modeling has emerged as a promising alternative to traditional modeling approaches. While data-driven methods come in many formulations and with different assumptions, t...

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Uncertainty Analysis and Data-Driven Model Advances for a Jet-in-Crossflow

Cited by 35 publications

References 32 publications

Quantification of model uncertainty in RANS simulations: A review

Quantification of model uncertainty in RANS simulations: A review

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

A Priori Assessment of Prediction Confidence for Data-Driven Turbulence Modeling

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