Large-eddy simulations of incompressible Newtonian fluid flows with approximate deconvolution models based on the van Cittert method are reported. The Legendre spectral element method is used for the spatial discretization to solve the filtered Navier--Stokes equations. A novel variant of approximate deconvolution models blended with a mixed scale model using a dynamic evaluation of the subgrid-viscosity constant is proposed. This model is validated by comparing the large-eddy simulation with the direct numerical simulation of the flow in a lid-driven cubical cavity, performed at a Reynolds number of 12'000. Subgrid modeling in the case of a flow with coexisting laminar, transitional and turbulent zones such as the lid-driven cubical cavity flow represents a challenging problem. Moreover, the coupling with the spectral element method having very low numerical dissipation and dispersion builds a well suited framework to analyze the efficiency of a subgrid model. First- and second-order statistics obtained using this new model are showing very good agreement with the direct numerical simulation. Filtering operations rely on an invertible filter applied in a modal basis and preserving the C0-continuity across elements. No clipping on dynamic parameters was needed to preserve numerical stability.
We put forth a dynamic modeling framework for sub-grid parametrization of large eddy simulation of turbulent flows based upon the use of the approximate deconvolution procedure to compute the Smagorinsky constant self-adaptively from the resolved flow quantities. Our numerical assessments for solving the Burgers turbulence problem shows that the proposed approach could be used as a viable tool to address the turbulence closure problem due to its flexibility.
In this article, we demonstrate the use of artificial neural networks as optimal maps which are utilized for convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects. We demonstrate that an effective eddy-viscosity is predicted by our purely data-driven large eddy simulation framework without explicit utilization of phenomenological arguments. In addition, our data-driven framework precludes the knowledge of true sub-grid stress information during the training phase due to its focus on estimating an effective filter and its inverse so that grid-re…
This paper puts forth a new large eddy simulation closure modeling strategy for two-dimensional turbulent geophysical flows. This closure modeling approach utilizes approximate deconvolution, which is based solely on mathematical approximations and does not employ additional phenomenological arguments to the model. The new approximate deconvolution model is tested in the numerical simulation of the wind-driven circulation in a shallow ocean basin, a standard prototype of more realistic ocean dynamics. The model employs the barotropic vorticity equation driven by a symmetric double-gyre wind fo…
Deconvolutional artificial neural network (DANN) models are developed for subgrid-scale (SGS) stress in large eddy simulation (LES) of turbulence. The filtered velocities at different spatial points are used as input features of the DANN models to reconstruct the unfiltered velocity. The grid width of the DANN models is chosen to be smaller than the filter width, in order to accurately model the effects of SGS dynamics. The DANN models can predict the SGS stress more accurately than the conventional approximate deconvolution method (ADM) and velocity gradient model (VGM) in a prior study: the …
We present an approximate deconvolution (AD) large eddy simulation (LES) model for the two-layer quasigeostrophic equations. We applied the AD-LES model to mid-latitude two-layer square oceanic basins, which are standard prototypes of more realistic stratified ocean dynamics models. Two spatial filters were investigated in the AD-LES model: a tridiagonal filter and an elliptic differential filter. A sensitivity analysis of the AD-LES results with respect to changes in modeling parameters was performed. The results demonstrate that the AD-LES model used in conjunction with the tridiagonal or di…
A novel approach for modeling the progress variable reaction rate in Large Eddy Simulations of turbulent and reacting flows is proposed. This is done in the context of two popular flamelet models which require the progress variable variance as input. The approach is based on using a recently proposed deconvolution method for modeling the variance. The deconvolution-modeled variance, is used as an input in the flamelet models for modeling the filtered progress variable rate. The assessment of the proposed approach is conducted a priori using direct numerical simulation data of turbulent premixe…
The goal of this paper is twofold: first, it investigates the effect of low-pass spatial filters for approximate deconvolution large eddy simulation (AD-LES) of turbulent incompressible flows. Second, it proposes the hyper-differential filter as a means of increasing the accuracy of the AD-LES model without increasing the computational cost. Box filters, Padé filters, and differential filters with a wide range of parameters are studied in the AD-LES framework. The AD-LES model, in conjunction with these spatial filters, is tested in the numerical simulation of the three-dimensional Taylor-Gree…
A Novel Explicit Filter for the Approximate Deconvolution in Large-Eddy Simulation on General Unstructured Grids: A posteriori tests on highly stretched grids
This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution(AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient(10^{-3})
We present a single-layer feedforward artificial neural network architecture trained through a supervised learning approach for the deconvolution of flow variables from their coarse grained computations such as those encountered in large eddy simulations. We stress that the deconvolution procedure proposed in this investigation is blind, i.e. the deconvolved field is computed without any pre-existing information about the filtering procedure or kernel. This may be conceptually contrasted to the celebrated approximate deconvolution approaches where a filter shape is predefined for an iterative …
Predicting the behavior of turbulent flows using large-eddy simulation requires modeling of the subgrid-scale stress tensor. This tensor can be approximated using mixed models, which combine the dissipative nature of functional models with the capability of structural models to approximate out-of-equilibrium effects. We propose a mathematical basis to mix (functional) eddy-viscosity models with the (structural) Bardina model. By taking an anisotropic minimum-dissipation (AMD) model for the eddy viscosity, we obtain the (single-layer) AMD-Bardina model. In order to also obtain a physics-conform…
In large-eddy simulations, subgrid-scale (SGS) processes are parameterized as a function of filtered grid-scale variables. First-order, algebraic SGS models are based on the eddy-viscosity assumption, which does not always hold for turbulence. Here we apply supervised deep neural networks (DNNs) to learn SGS stresses from a set of neighboring coarse-grained velocity from direct numerical simulations (DNSs) of the atmospheric boundary layer at friction Reynolds numbers Re_τ up to 1243 without invoking the eddy-viscosity assumption. The DNN model was found to produce higher correlation of SGS st…
Large-eddy simulations of the turbulent flow in a lid-driven cubical cavity have been carried out at a Reynolds number of 12000 using spectral element methods. Two distinct subgrid-scales models, namely a dynamic Smagorinsky model and a dynamic mixed model, have been both implemented and used to perform long-lasting simulations required by the relevant time scales of the flow. All filtering levels make use of explicit filters applied in the physical space (on an element-by-element approach) and spectral (modal) spaces. The two subgrid-scales models are validated and compared to available exper…
In Large-Eddy simulation of particle-laden flow, the effect of the unresolved scales on the particles needs to be modelled. In this work we analyse three very promising models, namely the approximate deconvolution method (ADM) which was proposed for particle-laden flow independently by Kuerten (Phys. Fluids 18, 2006) and Shotorban and Mashayek (Phys. Fluids 17, 2005) and two stochastic models, proposed by Shotorban and Mashayek (J. Turbul. 7, 2006) and Simonin et al. (Appl. Sci. Res. 51, 1993). We present results from a priori and a posteriori analysis of these models in isotropic turbulence a…
Explicit filtering in large eddy simulation (LES) of a turbulent barotropic flow on the sphere in spectral space is studied and compared to implicit filtering. Here, a smooth filter is applied to the nondivergent barotropic vorticity equation (BVE) on the rotating sphere to divide the flow field into resolved scale (RS) and subfilter scale (SFS) motions. A portion of the SFS motions are reconstructed theoretically using the approximate deconvolution model (ADM). While the unreconstructed portion consists of the subgrid scale (SGS) motions and needs to be modeled separately. In order to investi…
The Navier-Stokes equations describe the motion of viscous fluids. In order to predict turbulent flows with reasonable computational time and accuracy, these equations are spatially filtered according to the large-eddy simulation (LES) approach. The current work applies a volume filtering procedure according to Schumann (1975). To demonstrate the procedure the Schumann filter is first applied to a convection-diffusion equation. The Schumann filter results in volume-averaged equations, which are not closed. To close these equations a model is introduced, which represents the interaction between…
In isotropic helical turbulence, a new single helical model is suggested for large eddy simulation. Based on the Kolmogrov's hypotheses, the helical model is proposed according to the balance of helicity dissipation and the average of helicity flux across the inertial range, and the helical model is a kind of eddy viscosity model. The coefficient of the helical model is constant and can be also determined dynamically. Numerical simulations of forced and decaying isotropic helical turbulence demonstrate that the helical model predicts the energy and helicity evolution well. The statistical char…
A non-intrusive data assimilation methodology is developed to improve the statistical predictions of large-eddy simulations (LES). The ensemble-variational (EnVar) approach aims to minimize a cost function that is defined as the discrepancy between LES predictions and reference statistics from experiments or, in the present demonstration, independent direct numerical simulations (DNS). This methodology is applied to adjust the Smagorinsky subgrid model and obtain data assimilated LES (DA-LES) which accurately estimate the statistics of turbulent channel flow. To separately control the mean and…
Accurate simulations of high-pressure transcritical fuel sprays are essential for the design and optimization of next-generation gas turbines, internal combustion engines, and liquid propellant rocket engines. Most important and challenging is the accurate modelling of complex real-gas effects in high-pressure environments, especially the hybrid subcritical-to-supercritical mode of evaporation during the mixing of fuel and oxidizer. In this paper, we present a novel modeling framework for high-fidelity simulations of reacting and non-reacting transcritical fuel sprays. In this method, the high…
Traditional large eddy simulation is based on Kolmogrov's hypothesis, and done in the inertial range. In inertial range the LES model coefficient is scale-invariant. In many cases, such as computing in the boundary layer, the filter scale is not in the inertial range, and the model coefficient changes drastically with the filter scale, thus the assumption of scale-invariance is not proper. In this paper, we propose a general principle of constraint, and then we deduce two concrete constraints based on the existing spectrum theory and priori data. The constrained dynamic Smogorinsky model can p…
We assess the ability of three different approaches based on high-order discontinuous Galerkin methods to simulate under-resolved turbulent flows. The capabilities of the mass conserving mixed stress method as structure resolving large eddy simulation solver are examined. A comparison of a variational multiscale model to no-model or an implicit model approach is presented via numerical results. In addition, we present a novel approach for turbulent modeling in wall-bounded flows. This new technique provides a more accurate representation of the actual subgrid scales in the near wall region and…
Structural subgrid stress models for large eddy simulation often allow for backscatter of energy from unresolved to resolved turbulent scales, but excessive model backscatter can eventually result in numerical instability. A commonly employed strategy to overcome this issue is to set predicted subgrid stresses to zero in regions of model backscatter. This clipping procedure improves the stability of structural models, however, at the cost of reduced correlation between the predicted subgrid stresses and the exact subgrid stresses. In this article, we propose an alternative strategy that remove…
A posteriori study of Thermal-Large Eddy Simulation in solar receiver operating conditions
PROMES-CNRS, UPR 8521, Université de Perpignan Via Domitia（普罗梅斯-法国国家科学研究中心联合研究组，UPR 8521，佩皮尼昂维达米蒂亚大学）；LISN–CNRS, UMR 9015, Université Paris-Saclay（利萨恩-法国国家科学研究中心联合研究组，UMR 9015，巴黎萨克雷大学）
Temperature fluctuations in an atmospheric convective boundary layer are investigated by means of Large Eddy Simulations (LES). A statistical characterization for both weak temperature fluctuations and strong temperature fluctuations has been found. Despite the nontriviality of the dynamics of temperature fluctuations, our data support the idea that the most relevant statistical properties can be captured solely in terms of two scaling exponents, characterizing the entire mixed layer. Such exponents control asymptotic (i.e. core and tails) rescaling properties of the probability density functi…
Wall-modelled large-eddy simulation of turbulent channel flow with unstable stratification
Institute of Extreme Mechanics, School of Aeronautics, Northwestern Polytechnical University（西北工业大学航空学院极端力学研究所）；National Key Laboratory of Aircraft Configuration Design, Key Laboratory for Extreme Mechanics of Aircraft of Ministry of Industry and Information Technology（飞机总体设计全国重点实验室、工业和信息化部飞机极端力学重点实验室）
This paper studies the large-eddy simulation (LES) of isothermal turbulent channel flows. We investigate zero-equation algebraic models without wall function or wall model: functional models, structural models and mixed models. In addition to models from the literature, new models are proposed and their relevance is examined. Dynamic versions of each type of model are also analysed. The performance of the subgrid-scale models is assessed using the same finite difference numerical method and physical configuration. The friction Reynolds number of the simulations is 180. Three different mesh res…
The effects of passive scalar anisotropy on subgrid-scale (SGS) physics and modeling for Large-Eddy Simulations are studied experimentally. Measurements are performed across a moderate Reynolds number wake flow generated by a heated cylinder, using an array of four X-wire and four cold-wire probes. By varying the separation distance among probes in the array, we obtain filtered and subgrid quantities at three different filter sizes. We compute several terms that comprise the subgrid dissipation tensor of kinetic energy and scalar-variance and test for isotropic behavior, as a function of filte…
Large Eddy Simulation is based on decomposition of turbulent flow structures to large energy containing scales and small subgrid scales. The present study captures all flow low energy modes of a sample shear layer using the proper orthogonal decomposition (POD) method. In order to analyze the role of flow low energy modes on subgrid scale parameter prediction, the a-priori approach is chosen on a stereoscopic particle image velocimetry (SPIV) data that its missing/erroneous data is reconstructed using the gappy POD method. Particularly, similarity and mixed models are used to evaluate the SGS …
The mixing effectiveness, i.e., the enhancement of molecular diffusion, of a flow can be quantified in terms of the suppression of concentration variance of a passive scalar sustained by steady sources and sinks. The mixing enhancement defined this way is the ratio of the RMS fluctuations of the scalar mixed by molecular diffusion alone to the (statistically steady-state) RMS fluctuations of the scalar density in the presence of stirring. This measure of the effectiveness of the stirring is naturally related to the enhancement factor of the equivalent eddy diffusivity over molecular diffusion,…
Artificial neural network (ANN) is tested as a tool for finding a new subgrid model of the subgrid-scale (SGS) stress in large-eddy simulation. ANN is used to establish a functional relation between the grid-scale (GS) flow field and the SGS stress without any assumption of the form of function. Data required for training and test of ANN are provided by direct numerical simulation (DNS) of a turbulent channel flow. It is shown that ANN can establish a model similar to the gradient model. The correlation coefficients between the real SGS stress and the output of ANN are comparable to or larger …
We consider the induction of magnetic field in flows of electrically conducting fluid at low magnetic Prandtl number and large kinetic Reynolds number. Using the separation between the magnetic and kinetic diffusive lengthscales, we propose a new numerical approach. The coupled magnetic and fluid equations are solved using a mixed scheme, where the magnetic field fluctuations are fully resolved and the velocity fluctuations at small scale are modelled using a Large Eddy Simulation (LES) scheme. We study the response of a forced Taylor-Green flow to an externally applied field: tology of the me…
Dynamic mixed turbulence modeling using a super-resolution generative adversarial approach
RWTH Aachen University（亚琛工业大学）；University of Cambridge（剑桥大学）；University of Southampton（南安普顿大学）；University of Notre Dame（圣母大学）；University of Edinburgh（爱丁堡大学）
The behaviour of the turbulent Prandtl number ($Pr_t$) for buoyancy-affected flows near a vertical surface is investigated as an extension study of {Gibson \& Leslie, \emph{Int. Comm. Heat Mass Transfer}, Vol. 11, pp. 73-84 (1984)}. By analysing the location of mean velocity maxima in a differentially heated vertical planar channel, we {identify an} {infinity anomaly} for the eddy viscosity $ν_t$ and the turbulent Prandtl number $Pr_t$, as both terms are divided by the mean velocity gradient according to the standard definition, in vertical buoyant flow. To predict the quantities of interest, …
Accurate subgrid-scale turbulence models are needed to perform realistic numerical magnetohydrodynamic (MHD) simulations of the subsurface flows of the Sun. To perform large-eddy simulations (LES) of turbulent MHD flows, three unknown terms have to be modeled. As a first step, this work proposes to use a priori tests to measure the accuracy of various models proposed to predict the SGS term appearing in the transport equation of the filtered magnetic field. It is proposed to evaluate the SGS model accuracy in term of "structural" and "functional" performance, i.e. the model capacity to locally…
This work is dedicated to providing a detailed account of the flow dynamics in the closure region of an internal ship air cavity. A geometrically simple multiwave test cavity is considered, and a simulation of the flow is conducted using large-eddy simulation coupled with an algebraic Volume of Fluid interface capturing method. Results reveal that the flow in the closure region is highly unsteady and turbulent. The main cause of this is established to be the pressure gradient occurring due to the stagnation of the flow on the beach wall of the cavity. The pressure gradient leads to a steep inc…
