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69th ASME Turbomachinery Technical Conference and Exposition (ASME Turbo Expo) (GT)

作者： Zhang, Zhen Zhang, Weiran Su, Xinrong Yuan, Xin Tsinghua Univ Dept Energy & Power Engn Beijing Peoples R China Univ Shanghai Sci & Technol Shanghai Peoples R China

ISBN: (纸本)9780791887998

In film cooling problems, the turbulent heat transport and the resultant cooling effectiveness distribution are difficult to predict for traditional Reynolds-averaged Navier-Stokes (RANS) methods. In this paper, a data-driven model of the turbulent Prandtl number is built based on the Physics Informed Neural Network (PINN), which trains the turbulence model based on flow data from RANS and temperature data from Large Eddy Simulation (LES). PINN is used as an efficient inverse solver to get turbulence information from the mean flow data such as velocity and temperature and also as a model trainer to train the algebraic turbulence model at the same time. Accelerated by modern GPUs, the PINN method has been a powerful competitor to the adjoint method and the ensemble Kalman filter to solve inverse problems. The obtained data-driven model can adjust the intensity of turbulent heat transport and thus reduce the error of the traditional RANS method. After validation, the model shows good generalization ability when the hole geometry and the blowing ratio vary.

关键词： Film cooling data-driven turbulence modeling turbulent heat transport PINN inverse problem

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On frozen-RANS approaches in data-driven turbulence modeling: Practical relevance of turbulent scale consistency during closure inference and application

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INTERNATIONAL JOURNAL OF HEAT AND FLUID FLOW 2022年 97卷

作者： Mandler, Hannes Weigand, Bernhard Inst Thermodynam Luft & Raumfahrt Pfaffenwaldring 31 D-70569 Stuttgart Germany

This paper addresses a consistency problem in data-driven turbulence modeling, which arises as the hypotheses are inferred from high-fidelity data but evaluated within a low-fidelity RANS solver. After elaborating on its origin, which is the systematic difference of the turbulent scales predicted by a low- and a high-fidelity solver, the frozen-RANS concept is thoroughly discussed as one possible mitigation strategy. Different variations of this concept are proposed varying in the way to incorporate the turbulent kinetic energy correction in the RANS solver and also in their degree to which they fulfill scale consistency. Applying these concepts to the neuralSST model, which is introduced in the companion paper (Mandler and Weigand, 2022), confirms the importance of scale consistency for an improved mean flow field prediction and that the latter can be achieved by a..-correction. This becomes particularly evident as the complexity of the test cases, which are different types of separated channel flows, increases. However, which particular strategy is employed to augment the low-fidelity prediction of the turbulent kinetic energy is of minor importance and the decision is mainly driven by the trade-off between the flexibility of the solver to modify the scale equations and the numerical stability of the resulting model.

关键词： data-driven turbulence modeling Scale equations Turbulent scale consistency Frozen-RANS k-correction

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data-driven augmentation of a RANS turbulence model for transonic flow prediction

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INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW 2023年第4期33卷 1544-1561页

作者： Grabe, Cornelia Jaeckel, Florian Khurana, Parv Dwight, Richard P. German Aerosp Ctr DLR Inst Aerodynam & Flow Technol Gottingen Germany Delft Univ Technol Fac Aerosp Engn Delft Netherlands

Purpose This paper aims to improve Reynolds-averaged Navier Stokes (RANS) turbulence models using a data-driven approach based on machine learning (ML). A special focus is put on determining the optimal input features used for the ML ***/methodology/approach The field inversion and machine learning (FIML) approach is applied to the negative Spalart-Allmaras turbulence model for transonic flows over an airfoil where shock-induced separation *** Optimal input features and an ML model are developed, which improve the existing negative Spalart-Allmaras turbulence model with respect to shock-induced flow ***/value A comprehensive workflow is demonstrated that yields insights on which input features and which ML model should be used in the context of the FIML approach

关键词： RANS data-driven turbulence modeling Machine learning Feature selection flower separation transonic flows

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Generalization Limits of data-driven turbulence Models

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FLOW turbulence AND COMBUSTION 2024年 1-36页

作者： Mandler, Hannes Weigand, Bernhard Univ Stuttgart Inst Aerosp Thermodynam Pfaffenwaldring 31 D-70569 Stuttgart Germany

Many industrial applications require turbulent closure models that yield accurate predictions across a wide spectrum of flow regimes. In this study, we investigate how data-driven augmentations of popular eddy viscosity models affect their generalization properties. We perform a systematic generalization study with a particular closure model that was trained for a single flow regime. We systematically increase the complexity of the test cases up to an industrial application governed by a multitude of flow patterns and thereby demonstrate that tailoring a model to a specific flow phenomenon decreases its generalization capability. In fact, the accuracy gain in regions that the model was explicitly calibrated for is smaller than the loss elsewhere. We furthermore show that extrapolation or, generally, a lack of training samples with a similar feature vector is not the main reason for generalization errors. There is actually only a weak correlation. Accordingly, generalization errors are probably due to a data-mismatch, i.e., a systematic difference in the mappings from the model inputs to the required responses. More diverse training sets unlikely provide a remedy due to the strict stability requirements emerging from the ill-conditioned RANS equations. The universality of data-driven eddy viscosity models with variable coefficients is, therefore, inherently limited.

关键词： data-driven turbulence modeling Machine learning Extrapolation Generalizability NeuralSST Ribbed two-pass cooling channel

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Feature importance in neural networks as a means of interpretation for data-driven turbulence models

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COMPUTERS & FLUIDS 2023年第1期265卷

作者： Mandler, Hannes Weigand, Bernhard Univ Stuttgart Inst Aerosp Thermodynam Pfaffenwaldring 31 D-70569 Stuttgart Germany

This work aims at making the prediction process of neural network-based turbulence models more transparent. Due to its black-box ingredients, the model's predictions cannot be anticipated. Therefore, this paper is concerned with the quantification of each feature's importance for the prediction of trained and fixed NNs, which is one possible type of explanation for opaque models. Two conceptually different attribution methods, namely permutation feature importance and DeepSHAP, are chosen in order to assess global, regional and local feature importance. The neuralSST turbulence model, which serves as an example, will be investigated in greater detail. While the global importance scores provide a quick and reliable way to detect irrelevant features and may thus be used for feature selection, only the (semi-)local analysis provides meaningful and trustworthy interpretations of the model. In fact, the local importance scores suggest that hypotheses with a common high-level influence on the turbulence model, e.g. adjusting the net production of turbulent kinetic energy or the Reynolds stress anisotropy, are similarly affected by local mean flow structures such as attached boundary layers, free shear layers or recirculation zones.

关键词： data-driven turbulence modeling NeuralSST Explainable AI (XAI) Interpretable machine learning Attribution method Feature importance

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A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty

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JOURNAL OF COMPUTATIONAL PHYSICS 2024年 508卷

作者： Agrawal, Atul Koutsourelakis, Phaedon-Stelios Tech Univ Munich Professorship Data Driven Mat Modeling Sch Engn & Design Boltzmannstr 15 D-85748 Garching Germany Munich Data Sci Inst MDSI Coremember Garching Germany

We propose a data -driven, closure model for Reynolds -averaged Navier-Stokes (RANS) simulations that incorporates aleatoric, model uncertainty. The proposed closure consists of two parts. A parametric one, which utilizes previously proposed, neural -network -based tensor basis functions dependent on the rate of strain and rotation tensor invariants. This is complemented by latent, random variables which account for aleatoric model errors. A fully Bayesian formulation is proposed, combined with a sparsity -inducing prior in order to identify regions in the problem domain where the parametric closure is insufficient and where stochastic corrections to the Reynolds stress tensor are needed. Training is performed using sparse, indirect data, such as mean velocities and pressures, in contrast to the majority of alternatives that require direct Reynolds stress data. For inference and learning, a Stochastic Variational Inference scheme is employed, which is based on Monte Carlo estimates of the pertinent objective in conjunction with the reparametrization trick. This necessitates derivatives of the output of the RANS solver, for which we developed an adjoint-based formulation. In this manner, the parametric sensitivities from the differentiable solver can be combined with the built-in, automatic differentiation capability of the neural network library in order to enable an end -to -end differentiable framework. We demonstrate the capability of the proposed model to produce accurate, probabilistic, predictive estimates for all flow quantities, even in regions where model errors are present, on a separated flow in the backward -facing step benchmark problem.

关键词： data-driven turbulence modeling Reynolds-averaged Navier-Stokes Uncertainty quantification Deep neural networks Differentiable solver

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Invariant data-driven subgrid stress modeling on anisotropic grids for large eddy simulation

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2024年 422卷

作者： Prakash, Aviral Jansen, Kenneth E. Evans, John A. Univ Colorado Boulder Boulder CO 80309 USA

We present a new approach for constructing data -driven subgrid stress models for large eddy simulation of turbulent flows using anisotropic grids. The key to our approach is a Galilean, rotationally, reflectionally and unit invariant model form that also embeds filter anisotropy in such a way that an important subgrid stress identity is satisfied. We use this model form to train a data -driven subgrid stress model using only a small amount of anisotropically filtered DNS data and a simple and inexpensive neural network architecture. A priori and a posteriori tests indicate that the trained data -driven model generalizes well to filter anisotropy ratios, Reynolds numbers and flow physics outside the training dataset.

关键词： Large eddy simulation data-driven turbulence modeling Galilean invariance Rotational and reflectional invariance Unit invariance Filter anisotropy

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Reynolds-Averaged turbulence modeling Using Deep Learning with Local Flow Features: An Empirical Approach

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NUCLEAR SCIENCE AND ENGINEERING 2020年第8-9期194卷 650-664页

作者： Chang, Chih-Wei Fang, Jun Dinh, Nam T. Emory Univ Div Radiat Oncol Atlanta GA 30322 USA Argonne Natl Lab Nucl Sci & Engn Div 9700 S Cass Ave Argonne IL 60439 USA North Carolina State Univ Dept Nucl Engn Raleigh NC 27607 USA

Reynolds-Averaged Navier-Stoke (RANS) models offer an alternative avenue in predicting flow characteristics when the corresponding experiments are difficult to achieve due to geometry complexity, limited budget, or knowledge. RANS models require the knowledge of subgrid scale physics to solve conservation equations for mass, energy, and momentum. Mechanistic turbulence models, such as k-epsilon, are generally evaluated and calibrated for specific flow conditions with various degrees of uncertainty. These models have limited capability to assimilate a substantial amount of data due to model form constraints. Meanwhile, deep learning (DL) has been proven to be universal approximators with the potential to assimilate available, relevant, and adequately evaluated data. Moreover, deep neural networks (DNNs) can create surrogate models without knowing function forms. Such a data-driven approach can be used in updating fluid models based on observations as opposed to hard-wiring models with precalibrated correlations. The paper presents progress in applying DNNs to model Reynolds stress using two machine learning (ML) frameworks. A novel flow feature coverage mapping is proposed to quantify the physics coverage of DL-based closures. It can be used to examine the sufficiency of training data and input flow features for data-driven turbulence models. The case of a backward-facing step is formulated to demonstrate that not only can DNNs discover underlying correlation behind fluid data but also they can be implemented in RANS to predict flow characteristics without numerical stability issues. The presented research is a crucial stepping-stone toward the data-driven turbulence modeling, which potentially benefits the design of data-driven experiments that can be used to validate fluid models with ML-based fluid closures.

关键词： data-driven turbulence modeling deep learning flow feature coverage mapping machine learning RANS

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Generalized Non-Linear Eddy Viscosity Models for data-Assisted Reynolds Stress Closure

Generalized Non-Linear Eddy Viscosity Models for Data-Assist...

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AIAA Science and Technology Forum and Exposition (AIAA SciTech)

作者： Parmar, Basu Peters, Eric Jansen, Kenneth E. Doosta, Alireza Evans, John A. Univ Colorado Boulder CO 80309 USA Ball Aerosp Boulder CO 80301 USA

ISBN: (数字)9781624105951

ISBN: (纸本)9781624105951

Reynolds Averaged Navier Stokes (RANS) models are the most popular tool for modeling turbulent flow. RANS models require modeling of an unclosed term called the Reynolds stress tensor, but state-of-the-art Reynolds stress closures such as Linear Eddy Viscosity and Non-Linear Eddy Viscosity models are inadequate for many complex flows of industrial interest, especially those exhibiting flow separation. In this article, we introduce Generalized Non-Linear Eddy Viscosity models as a candidate for Reynolds stress closure. The model form error in the conventional Linear Eddy Viscosity models and Non-Linear Eddy Viscosity models is mitigated by introducing a dependence on additional flow variables, in particular the mean pressure gradient. A frame invariant tensor basis formulation is used to arrive at the general model form. A dense feed-forward neural network is used as a surrogate model for the functional mapping in the model. The proposed model also ensures frame invariance and Galilean invariance in the model form. Numerical results for various flow configurations are presented to demonstrate the effectiveness of data-driven Generalized Non-Linear Eddy Viscosity models. We also discuss challenges to completely couple data-driven models and traditional RANS models.

关键词： RANS: Reynolds Averaged Navier Stokes data-driven turbulence modeling Neural Networks

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Invariant data-driven subgrid stress modeling in the strain-rate eigenframe for large eddy simulation

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2022年 399卷 1页

作者： Prakash, Aviral Jansen, Kenneth E. Evans, John A. Univ Colorado Boulder Boulder CO 80309 USA

We present a new approach for constructing data-driven subgrid stress models for large eddy simulation of turbulent flows. The key to our approach is representation of model input and output tensors in the filtered strain rate eigenframe. Provided inputs and outputs are selected and non-dimensionalized in a suitable manner, this yields a model form that is symmetric, Galilean invariant, rotationally invariant, reflectionally invariant, and unit invariant. We use this model form to train a simple and efficient neural network model using only one time step of filtered direct numerical simulation data from a forced homogeneous isotropic turbulence simulation. We demonstrate the accuracy of this model as well as the model's ability to generalize to previously unseen filter widths, Reynolds numbers, and flow physics using a priori and a posteriori tests. (c) 2022 Elsevier B.V. All rights reserved.

关键词： Large eddy simulation data-driven turbulence modeling Galilean invariance Rotational invariance Reflectional invariance Unit invariance

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