Multi-fidelity optimization methods promise a high-fidelity optimum at a cost only slightly greater than a low-fidelity optimization. This promise is seldom achieved in practice, due to the requirement that low- and high-fidelity models correlate well. In this article, we propose an efficient bi-fidelity shape optimization method for turbulent fluid-flow applications with Large-Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) as the high- and low-fidelity models within a hierarchical-Kriging surrogate modelling framework. Since the LES-RANS correlation is often poor, we use the full LES flow-field at a single point in the design space to derive a custom-tailored RANS closure model that reproduces the LES at that point. This is achieved with machine-learning techniques, specifically sparse regression to obtain high corrections of the turbulence anisotropy tensor and the production of turbulence kinetic energy as functions of the RANS mean-flow. The LES-RANS correlation is dramatically improved throughout the design-space. We demonstrate the effectiveness and efficiency of our method in a proof-of-concept shape optimization of the well-known periodic-hill case. Standard RANS models perform poorly in this case, whereas our method converges to the LES-optimum with only two LES samples.
The volume of fluid (VOF) method is increasingly used in computational fluid dynamics (CFD) simulations of turbulent two-phase flows. The Reynolds-Averaged Navier-Stokes (RANS) approach is an economic and practical way for turbulent VOF simulations. Even though RANS-VOF simulations are widely conducted, the underlying physics is barely discussed. This study reveals the very basic closure requirement for RANS-VOF simulations.
In this short note we apply the recently proposed data-driven RANS closure modelling framework of Schmelzer et al. (2020) to fully three-dimensional, high Reynolds number flows: namely wall-mounted cubes and cuboids at Re=40,000, and a cylinder at Re=140,000. For each flow, a new RANS closure is generated using sparse symbolic regression based on LES or DES reference data. This new model is implemented in a CFD solver, and subsequently applied to prediction of the other flows. We see consistent improvements compared to the baseline $k-ω$ SST model in predictions of mean-velocity in the complet…
Despite their well-known limitations, RANS models remain the most commonly employed tool for modeling turbulent flows in engineering practice. RANS models are predicated on the solution of the RANS equations, but these equations involve an unclosed term, the Reynolds stress tensor, which must be modeled. The Reynolds stress tensor is often modeled as an algebraic function of mean flow field variables and turbulence variables. This introduces a discrepancy between the Reynolds stress tensor predicted by the model and the exact Reynolds stress tensor. This discrepancy can result in inaccurate me…
Turbulent problems in industrial applications are predominantly solved using Reynolds Averaged Navier Stokes (RANS) turbulence models. The accuracy of the RANS models is limited due to closure assumptions that induce uncertainty into the RANS modeling. We propose the use of deep learning algorithms via convolution neural networks along with data from direct numerical simulations to extract the optimal set of features that explain the evolution of turbulent flow statistics. Statistical tests are used to determine the correlation of these features with the variation in the quantities of interest…
Deep learning (DL)-based Reynolds stress with its capability to leverage values of large data can be used to close Reynolds-averaged Navier-Stoke (RANS) equations. Type I and Type II machine learning (ML) frameworks are studied to investigate data and flow feature requirements while training DL-based Reynolds stress. The paper presents a method, flow features coverage mapping (FFCM), to quantify the physics coverage of DL-based closures that can be used to examine the sufficiency of training data points as well as input flow features for data-driven turbulence models. Three case studies are fo…
In this paper, we propose normalizing flows (NF) as a novel probability density function (PDF) turbulence model (NF-PDF model) for the Reynolds-averaged Navier-Stokes (RANS) equations. We propose to use normalizing flows in two different ways: firstly, as a direct model for the Reynolds stress tensor, and secondly as a second-moment closure model, i.e. for modeling the pressure-strain and dissipation tensor in the Reynolds stress transport equation. In classical PDF closure models, a stochastic differential equation has to be modeled and solved to obtain samples of turbulent quantities. The NF…
The recent surge in machine learning augmented turbulence modelling is a promising approach for addressing the limitations of Reynolds-averaged Navier-Stokes (RANS) models. This work presents the development of the first open-source dataset, curated and structured for immediate use in machine learning augmented turbulence closure modelling. The dataset features a variety of RANS simulations with matching direct numerical simulation (DNS) and large-eddy simulation (LES) data. Four turbulence models are selected to form the initial dataset: $k$-$\varepsilon$, $k$-$\varepsilon$-$ϕ_t$-$f$, $k$-$ω$…
Generalizability of machine-learning (ML) based turbulence closures to accurately predict unseen practical flows remains an important challenge. At the Reynolds-averaged Navier-Stokes (RANS) level, NN-based turbulence closure modeling is rendered difficult due to two important reasons: inherent complexity of the constitutive relation arising from flow-dependent non-linearity and bifurcations; and, inordinate difficulty in obtaining high-fidelity data covering the entire parameter space of interest. In this context, the objective of the work is to investigate the approximation capabilities of s…
A novel machine learning algorithm is presented, serving as a data-driven turbulence modeling tool for Reynolds Averaged Navier-Stokes (RANS) simulations. This machine learning algorithm, called the Tensor Basis Random Forest (TBRF), is used to predict the Reynolds-stress anisotropy tensor, while guaranteeing Galilean invariance by making use of a tensor basis. By modifying a random forest algorithm to accept such a tensor basis, a robust, easy to implement, and easy to train algorithm is created. The algorithm is trained on several flow cases using DNS/LES data, and used to predict the Reynol…
** This article is published (open-access). ** A novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) is introduced to infer algebraic stress models for the closure of RANS equations directly from high-fidelity LES or DNS data. The models are written as tensor polynomials and are built from a library of candidate functions. The machine-learning method is based on elastic net regularisation which promotes sparsity of the inferred models. By being data-driven the method relaxes assumptions commonly made in the process of model development. Mode…
Transferable inference of turbulence models for urban flows with the Parameter-Regularised Ensemble Kalman Filter
Université Libre de Bruxelles（布鲁塞尔自由大学）；Aero-Thermo-Mechanics Laboratory（气动热力学实验室）；Brussels Institute for Thermal-Fluid Systems and Clean Energy (BRITE)（布鲁塞尔热流体系统与清洁能源研究所）；Department of Aeronautics, Imperial College London（帝国理工学院航空系）；I-X, Imperial College London（帝国理工学院I-X）；DIMEAS, Politecnico di Torino（都灵理工大学）；Brussels Institute for Advanced Studies (BrIAS)（布鲁塞尔高等研究院）；WEL Research Institute（WEL研究所）
Université Paris-Saclay, CNRS（巴黎萨克雷大学，法国国家科学研究中心）；Technical University of Munich（慕尼黑工业大学）；Sorbonne Université（索邦大学）
Recent works have explored the potential of machine learning as data-driven turbulence closures for RANS and LES techniques. Beyond these advances, the high expressivity and agility of physics-informed neural networks (PINNs) make them promising candidates for full fluid flow PDE modeling. An important question is whether this new paradigm, exempt from the traditional notion of discretization of the underlying operators very much connected to the flow scales resolution, is capable of sustaining high levels of turbulence characterized by multi-scale features? We investigate the use of PINNs sur…
