We show that the discrepancies in Reynolds-averaged Navier-Stokes (RANS) modeled Reynolds stresses can be explained by mean flow features. A physics-informed machine learning framework is proposed to improve the predictive capabilities of RANS models by leveraging existing direct numerical simulations databases.

pdf/physics-informed-machine-learning-approach-for-4cxbkqbrf7.pdf

Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data

Recent advances on the numerical modelling of turbulent flows

Turbulence closure models are central to a good deal of applied computational fluid dynamical analysis. Closure modeling endures as a productive area of research. This review covers recent developments in elliptic relaxation and elliptic blending models, unified rotation and curvature corrections, transition prediction, hybrid simulation, and data-driven methods. The focus is on closure models in which transport equations are solved for scalar variables, such as the turbulent kinetic energy, a timescale, or a measure of anisotropy. Algebraic constitutive representations are reviewed for their role in relating scalar closures to the Reynolds stress tensor. Seamless and nonzonal methods, which invoke a single closure model, are reviewed, especially detached eddy simulation (DES) and adaptive DES. Other topics surveyed include data-driven modeling and intermittency and laminar fluctuation models for transition prediction. The review concludes with an outlook.

Some Recent Developments in Turbulence Closure Modeling

https://pure.tue.nl/ws/files/128418577/1_s2.0_S0360544219309168_main.pdf

On the accuracy of turbulence models for CFD simulations of vertical axis wind turbines

Turbulence modeling is a critical component in numerical simulations of industrial flows based on Reynolds-averaged Navier-Stokes (RANS) equations. However, after decades of efforts in the turbulence modeling community, universally applicable RANS models with predictive capabilities are still lacking. Recently, data-driven methods have been proposed as a promising alternative to the traditional approaches of turbulence model development. In this work we propose a data-driven, physics-informed machine learning approach for predicting discrepancies in RANS modeled Reynolds stresses. The discrepancies are formulated as functions of the mean flow features. By using a modern machine learning technique based on random forests, the discrepancy functions are first trained with benchmark flow data and then used to predict Reynolds stresses discrepancies in new flows. The method is used to predict the Reynolds stresses in the flow over periodic hills by using two training flow scenarios of increasing difficulties: (1) the flow in the same periodic hills geometry yet at a lower Reynolds number, and (2) the flow in a different hill geometry with a similar recirculation zone. Excellent predictive performances were observed in both scenarios, demonstrating the merits of the proposed method. Improvement of RANS modeled Reynolds stresses enabled by the proposed method is an important step towards predictive turbulence modeling, where the ultimate goal is to predict the quantities of interest (e.g., velocity field, drag, lift) more accurately by solving RANS equations with the Reynolds stresses obtained therefrom.

A Physics Informed Machine Learning Approach for Reconstructing Reynolds Stress Modeling Discrepancies Based on DNS Data

Coolant flows in the cores of current gas-cooled nuclear reactors consist of ascending vertical flows in a large number of parallel passages. Under post-trip conditions such heated turbulent flows may be significantly modified from the forced convection condition by the action of buoyancy, and the thermal-hydraulic regime is no longer one of pure forced convection. These modifications are primarily associated with changes to the turbulence structure, and indeed flow laminarization may occur. In the laminarization situation heat transfer rates may be as low as 40% of those in the corresponding forced convection case. The heat transfer performance of such ‘mixed’ convection flows is investigated here using a range of refined ReynoldsAveraged-Navier-Stokes (RANS) turbulence models. While all belong to the broad class of Eddy Viscosity Models (EVMs), the various RANS closures have different physical parameterizations and might therefore be expected to show different responses to externally-imposed conditions. Comparison is made against experimental and Direct Numerical Simulation (DNS) data. In addition, Large Eddy Simulation (LES) results have been generated as part of the study. Three different CFD codes have been employed in the work: ‘CONVERT’, ‘STAR-CD’, and ‘ Code_Saturne ’, which are respectively in-house, commercial, and industrial packages. It is found that the early EVM scheme of Launder and Sharma [1] is in the closest agreement with consistentlynormalized DNS results for the ratio of mixed-to-forced convection Nusselt number ( Nu/Nu 0). However, in relation to DNS and experimental data for forced convection Nusselt number, other models perform better than the LaunderSharma scheme. The present investigation has revealed discrepancies between direct-simulation, experimental, and the current LES studies.

/pdf/rans-and-les-investigations-of-vertical-flows-in-the-fuel-tabwsjbomn.pdf

RANS and LES Investigations of Vertical Flows in the Fuel Passages of Gas-Cooled Nuclear Reactors

The thesis introduces a new version of an elliptic-blending low-Reynolds-number eddy-viscosity Reynolds-averaged Navier Stokes model. It is a model intended to be implemented in an industrial solver. It will be argued that there is still room for such a simple model, though eddy-viscosity models must rely on developments specificallymade for higher order formulations. It is the aim of the v2 ? f model to integrate elements of Reynolds-stress modelling developments into a simpler formulation, but the former paradoxically suffers from numerical stiffness, which kept it out of reachof industry researchers everyday simulations. The v2 ? f formulation endeavours to reproduce the near-wall asymptotic behaviour of the turbulent quantities, as sounder alternative to empirical damping functions, and the required near-wall balance of small terms represents a numerical challenge.The present work first provides a comprehensive review of v2 ? f developments proposed over the past twenty years, and the different remedies for the numericalstiffness linked to the original formulation. The review focuses on ten v2 ?f variants, proposed between 1991 and 2006, whose behaviour is compared in some fundamental flows: the channel flow for five different Reynolds numbers, the asymptotic case of the logarithmic layer at infinite Reynolds number and the case of a flow with homogeneous sheared turbulence.Based on the conclusions of the review, the thesis proposes new developments. Firstly, the derivation of a new model, namely the ? ? ? model, is introduced. It relies on the resolution of two non-dimensional variables: ? represents the wall-normal anisotropy and ? is a wall-proximity sensor. It is argued that only this formulation can address the numerical problems already mentioned without altering the predictions. Secondly, additional upgrades of the ? ? ? model are proposed to correct the dissipation rate equation. The aim is to improve the model behaviour in some specific regions of a boundary layer, by isolating some viscous terms and by improving the representation of turbulent transport at the edge of a boundary layer. Final developments are combined in a new model, the BL-v2/k model.The ? ? ? and BL-v2/k models are then validated for a set of two pressure induced separated flows and two buoyant flows, and beneficial effects of the proposed developments on the predictions are demonstrated. The numerical properties of theconvergency of the BL-v2/k model are also reported at the end of this work.

Development of a robust elliptic-blending turbulence model for near-wall, separated and buoyant flows

The present work is concerned with the modelling of ascending turbulent ('mixed convection') flow in a vertical heated pipe. All fluid properties are assumed to be constant and buoyancy is accounted for within the Boussinesq approximation. Four Eddy Viscosity Models (EVMs) are examined against experimental measurements and the direct numerical simulation data of You et al. (2003). The EVMs embody distinct physical refinements with respect to the parent high-Reynolds-number k-e model. Large Eddy Simulations (LES) employing the classical Smagorinsky sub-grid-scale model are also presented. Three different CFD codes have been employed in the study: 'CONVERT', 'Code_Saturne', and 'STAR-CD', which are respectively in- house, industrial, and commercial packages. In relation to forced convection Nusselt number and local friction coefficient, discrepancies are identified between 'reference' data sources, namely earlier DNS and experimental results and the present LES computations. The Launder-Sharma closure (Launder and Sharma, 1974) is in the closest agreement with DNS results for levels of heat transfer impairment in ascending mixed convection flow, although again there is a lack of consensus between reference sources.

Refined eddy viscosity schemes and large eddy simulations for ascending mixed convection flows

! v 2 " f model that addresses numerical issues usually arising with such models without any loss in prediction accuracy. The model is based on elliptic blending, and unlike its “codefriendly” predecessors, it correctly predicts nearwall asymptotic behaviours without impairing its overall robustness, which brings it to the same level of stability as most standard eddy viscosity models used in industrial applications. The model is tested in cases featuring heat transfer when buoyant forces strongly influence the turbulence regime, and its anisotropy. The case of air flowing upwards inside a heated infinite pipe and a heated channel are studied. The different formulations of the

/pdf/a-new-formulation-of-the-v2f-model-using-elliptic-blending-4yljcwqypx.pdf

A New Formulation of the V2F Model using Elliptic Blending and its Application to Heat Transfer Prediction

Adaptive wall-functions are developed for the near-wall elliptic-blending eddy-viscosity model (Billard and Laurence, Int. J. Heat Fluid Flow 33(1), 45–58, 2012). The aim of the new methodology is to make the predictions of this turbulence model less dependent on the spatial resolution in the viscous, buffer and logarithmic layer of the near-wall flow. It can be used in meshes for which localized areas with fine resolution are embedded into the coarsely meshed full domain. This allows reducing the computational cost by focusing the grid points density in critical non-equilibrium flow regions. It is based on Kalitzin et al. (J. Comput. Phys. 204(1), 265–291, 2005) but unlike the latter the dimensionless quantities provided by the wall-functions are converted into physical values by means of a turbulence rather than a mean-flow velocity scale. To justify this choice, the wall-function correction of wall shear-stress and heat-flux is presented as a Nusselt number linearization. Two wall-treatments are proposed for use in unstructured mesh finite-volume schemes: 1/ the wall-function values are applied as boundary conditions or 2/ the wall-function profiles are applied over a cluster of cells in the wall vicinity. The latter also addresses the issue of inner cell-size jumps as often produced by automatic mesh generators. The method is validated on channel flows for several types of meshes and Reynolds numbers. Heat-transfer application on a ribbed wall duct test-case is presented. The grid consists in a very coarsely meshed region upstream of a localized focus zone with classical down-to-the-wall resolution, and the heat-transfer and velocity profile are still accurately predicted.

Adaptive Wall Functions for an Elliptic Blending Eddy Viscosity Model Applicable to Any Mesh Topology

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