Large Eddy Simulation Subgrid Model Research Articles

Experimental and LES study of unconfined jet impingement on a smooth flat heated plate with slots of different widths

ABSTRACT The present work focuses on the experimental and large-eddy simulation (LES) investigation of fluid flow and heat transfer due to the impingement of an unconfined turbulent slot jet on a smooth flat plate. Three LES sub-grid scale models are validated with the experimental observations for first time in terms effect of slot widths. A detailed parametric study is conducted considering nozzle to plate spacing ratio from 4 to 12, non-dimensional slot width from 0.015 to 0.035, and Reynolds number range from 4000 to 12000. The results show an appreciable change in the stagnation point and along the wall jet Nusselt numbers with the change in Reynolds number, nozzle-to-plate spacing and non-dimensional slot width. No significant effect of nozzle to plate spacing is observed along the wall jet Nusselt number beyond the streamwise location at 0.2. The local Nusselt number increases with an increase in Reynolds number while it decreases with an increase in nondimensional slot width. Comparison of various LES sub-grid models with RANS (k-ω SST) turbulence model is performed. The results show that turbulent kinetic energy plays a major role in enhancing the heat transfer rate. Dissipation of the turbulent kinetic energy increases with an increase in nozzle to plate spacing and non-dimensional slot width. Further, a correlation is proposed for the stagnation point and wall jet region Nusselt numbers in terms of effect of slots width, Reynolds number and non-dimensional nozzle to plate spacing.

Large-eddy simulation of Rayleigh–Bénard convection at extreme Rayleigh numbers

We adopt the stretched spiral vortex sub-grid model for large-eddy simulation (LES) of turbulent convection at extreme Rayleigh numbers. We simulate Rayleigh–Bénard convection (RBC) for Rayleigh numbers ranging from 106 to 1015 and for Prandtl numbers 0.768 and 1. We choose a box of dimensions 1:1:10 to reduce computational cost. Our LES yields Nusselt and Reynolds numbers that are in good agreement with the direct-numerical simulation (DNS) results of Iyer et al. [“Classical 1/3 scaling of convection holds up to Ra=1015,” Proc. Natl. Acad. Sci. U. S. A. 117, 7594–7598 (2020)] albeit with a smaller grid size and at significantly reduced computational expense. For example, in our simulations at Ra=1013, we use grids that are 1/120 times the grid resolution as that of the DNS [Iyer et al., “Classical 1/3 scaling of convection holds up to Ra=1015,” Proc. Natl. Acad. Sci. U. S. A. 117, 7594–7598 (2020)]. The Reynolds numbers in our simulations span 3 orders of magnitude from 1000 to 1 700 000. Consistent with the literature, we obtain scaling relations for Nusselt and Reynolds numbers as Nu∼Ra0.321 and Re∼Ra0.495. We also perform LES of RBC with periodic side walls, for which we obtain the corresponding scaling exponents as 0.343 and 0.477, respectively. Our LES is a promising tool to push simulations of thermal convection to extreme Rayleigh numbers and, hence, enable us to test the transition to the ultimate convection regime.

Scale-Resolving Simulations of a Statistically Targeted Forcing Method for Synthetic Turbulence Generation in a Freestream Turbulence

Abstract Computational fluid dynamics results for synthetic turbulence generation of freestream turbulence by a proposed statistically targeted forcing (STF) method are presented. The STF method has been previously documented for homogeneous isotropic and anisotropic turbulence and formulated to introduce a fluctuating velocity field with a distribution of first and second moments that match a user-specified target mean velocity and Reynolds stress tensor, by incorporating deterministic time-dependent forcing terms into the momentum equation for the resolved flow. This study extends its applicability to generation of freestream turbulence in scale-resolving simulations in which flow is spatially developing. The method provides flexibility in regions where synthetic turbulence needs to be generated or damped, for use in engineering level scale-resolving simulations such as large eddy simulation (LES), and hybrid Reynolds-averaged Navier–Stokes (RANS)-LES. The objective of this study is to evaluate the performance of the proposed STF method in simulations that incorporate monotonically integrated LES (MILES), Smagorinsky (SMAG) LES subgrid stress model, and dynamic hybrid RANS-LES (DHRL) model in reproducing inflow freestream turbulent flow, and the capability of each model to reproduce proper energy decay characteristics downstream of forcing. Results are inter-rogated and compared to target statistical velocity and turbulent stress distributions for inflow turbulence and evaluated in terms of energy spectra. Analysis of the influence of STF model parameters, mesh resolution, and LES subgrid stress model on the results is investigated. Results show that the STF method can successfully reproduce desired statistical distributions in a nearly isotropic freestream turbulent flow.

Evaluation of a Statistically Targeted Forcing Method for Synthetic Turbulence Generation in Scale-Resolving Simulations

Abstract Computational fluid dynamics (CFD) results are presented for synthetic turbulence generation by a proposed statistically targeted forcing (STF) method. The new method seeks to introduce a fluctuating velocity field with a distribution of first and second moments that approximate a user-specified target mean velocity and Reynolds stress tensor, by incorporating deterministic time-dependent forcing terms into the momentum equation for the resolved flow. The STF method is formulated to extend the applicability of previously documented methods and provide flexibility in regions where synthetic turbulence needs to be generated or sustained, for use in engineering level large eddy and hybrid large eddy/Reynolds-averaged Navier–Stokes CFD simulations. The objective of this study is to evaluate the performance of the proposed STF method in large-eddy simulation (LES) simulations of isotropic and anisotropic homogeneous turbulent flow test cases. Results are interrogated and compared to target statistical velocity and turbulent stress distributions and evaluated in terms of energy spectra. Analysis of the influence of STF model parameters, mesh resolution, and LES subgrid stress model on the results is investigated. Results show that the new method can successfully reproduce desired statistical distributions in a homogeneous turbulent flow.

A data-driven subgrid scale model in Large Eddy Simulation of turbulent premixed combustion

We derive a data-driven model of a subgrid scale (SGS) closure for turbulent premixed combustion in the context of Large Eddy Simulation (LES) using deep learning. We validate the model through LES of the direct numerical simulation (DNS) flame configuration and compare it to other subgrid models from the literature. The filtered DNS used as training data was provided by Lapeyre et al. (2019). The neural network developed in this study was designed to estimate the SGS flame surface density, using only local progress variable values as a basis. A priori tests show that the results inferred from the frozen neural network were comparable to results obtained from the convolutional neural networks (CNNs) using the full nonlocal set of variables, and were in good agreement with the filtered DNS. A model-agnostic method for interpreting machine learning was employed to investigate the behavior of the trained neural network. A posteriori evaluation using the network as an LES subgrid model demonstrates that the proposed data-driven modeling is more accurate than classical algebraic models in terms of the integrated flame area in the axial direction. This illustrates that the proposed data-driven subgrid model to represent the non-linear unresolved terms is a successful approximation from both an a priori and an a posteriori perspective and that only fully local values in the filtered domain suffice to yield good agreement with DNS results. This is in contrast to earlier attempts, which use the full LES domain dataset as input to the network.

Large-eddy simulation of wall-bounded turbulent flow with high-order discrete unified gas-kinetic scheme

In this paper, we introduce the discrete Maxwellian equilibrium distribution function for incompressible flow and force term into the two-stage third-order Discrete Unified Gas-Kinetic Scheme (DUGKS) for simulating low-speed turbulent flows. The Wall-Adapting Local Eddy-viscosity (WALE) and Vreman sub-grid models for Large-Eddy Simulations (LES) of turbulent flows are coupled within the present framework. Meanwhile, the implicit LES are also presented to verify the effect of LES models. A parallel implementation strategy for the present framework is developed, and three canonical wall-bounded turbulent flow cases are investigated, including the fully developed turbulent channel flow at a friction Reynolds number (Re) about 180, the turbulent plane Couette flow at a friction Re number about 93 and lid-driven cubical cavity flow at a Re number of 12000. The turbulence statistics, including mean velocity, the r.m.s. fluctuations velocity, Reynolds stress, etc. are computed by the present approach. Their predictions match precisely with each other, and they are both in reasonable agreement with the benchmark data of DNS. Especially, the predicted flow physics of three-dimensional lid-driven cavity flow are consistent with the description from abundant literature. The present numerical results verify that the present two-stage third-order DUGKS-based LES method is capable for simulating inhomogeneous wall-bounded turbulent flows and getting reliable results with relatively coarse grids.

Dynamic one-equation-based subgrid model for large-eddy simulation of stratified turbulent flows

The locally dynamic one-equation based subgrid-scale is extended for large-eddy simulation of stably stratified turbulent flows. It is comprehensively assessed by simulating turbulent channel flow for a range of Reynolds and Richardson numbers. It captures all the key flow features, such as suppression of vertical turbulent transport, presence of internal waves and pycnocline, and decrease of the friction coefficient and Nusselt number. The turbulence statistics show good agreement with the reference results thus demonstrating its applicability to stratified flows with variable mean shear.

Resolution-induced anisotropy in large-eddy simulations

Large eddy simulation (LES) of turbulence in complex geometries and domains is often conducted with high aspect ratio resolution cells of varying shapes and orientations. The effects of such anisotropic resolution are often simplified or neglected in subgrid model formulation. Here, we examine resolution induced anisotropy and demonstrate that, even for isotropic turbulence, anisotropic resolution induces mild resolved Reynolds stress anisotropy and significant anisotropy in second-order resolved velocity gradient statistics. In large eddy simulations of homogeneous isotropic turbulence with anisotropic resolution, it is shown that commonly used subgrid models, including those that consider resolution anisotropy in their formulation, perform poorly. The one exception is the anisotropic minimum dissipation model proposed by Rozema et al. (Phys. of Fluids 27, 085107, 2015). A simple new model is presented here that is formulated with an anisotropic eddy diffusivity that depends explicitly on the anisotropy of the resolution. It also performs well, and is remarkable because unlike other LES subgrid models, the eddy diffusivity only depends on statistical characteristics of the turbulence (in this case the dissipation rate), not on fluctuating quantities. In other subgrid modeling formulations, such as the dynamic procedure, limiting flow dependence to statistical quantities in this way could have advantages.

Numerical study of the effect of inlet geometry on combustion instabilities in a lean premixed swirl combustor

The effects of flow structure and flame dynamics on combustion instabilities in a lean premixed swirl combustor were numerically investigated using Large eddy simulation (LES) by varying the inlet geometry of combustor. The dynamic ksgs-equation and G-equation flamelet models were respectively employed as the LES subgrid models of turbulence and combustion. The divergent half angle (α) in the combustor inlet was varied systematically from 30° to 90° to quantify the effect of inlet geometry on the combustion instabilities. This variation caused considerable deformation in recirculation zones in terms of their size and location, leading to significant changes in flame dynamics. Analysis of unsteady pressure distributions in the combustor showed that the largest damping caused by combustion instabilities takes place at α = 45°, and the amplitude of acoustic pressure oscillation is largest at α = 30°. Examination of local Rayleigh parameters indicated that controlling flame-vortex interactions by modifying inlet geometry can change the local characteristics of combustion instabilities in terms of their amplification and suppression, and thus serve as a useful approach to reduce the instabilities in a lean premixed swirl combustor. These phenomena were studied in detail through unsteady analysis associated with flow and flame dynamics.

Numerical simulation of turbulent combustion: Scientific challenges

Predictive simulation of engine combustion is key to understanding the underlying complicated physicochemical processes, improving engine performance, and reducing pollutant emissions. Critical issues as turbulence modeling, turbulence-chemistry interaction, and accommodation of detailed chemical kinetics in complex flows remain challenging and essential for high-fidelity combustion simulation. This paper reviews the current status of the state-of-the-art large eddy simulation (LES)/prob-ability density function (PDF)/detailed chemistry approach that can address the three challenging modelling issues. PDF as a subgrid model for LES is formulated and the hybrid mesh-particle method for LES/PDF simulations is described. Then the development need in micro-mixing models for the PDF simulations of turbulent premixed combustion is identified. Finally the different acceleration methods for detailed chemistry are reviewed and a combined strategy is proposed for further development.

Multiscale three-point velocity increment correlation in turbulent flows

The three-point velocity increment correlation function is proposed to represent the multiscale correlations in turbulent flows. The inertial-inertial correlation and the inertial-dissipative correlation are discussed due to their endogenetic properties in turbulence and their roles in large-eddy simulation. The zero-correlation points are then emphasized as equilibrium points between them. The credibility of this theoretical result is numerically verified in both isotropic and anisotropic flows. Results imply the universality of this zero-correlation scaling in different turbulent flows. This work is expected to be a dependable theoretical base for creating multiscale subgrid models in large-eddy simulation. (C) 2014 Elsevier B.V. All rights reserved.

Mixing, intermittency and large eddy simulation of a turbulent round jet

Large Eddy Simulation (LES) is a promising technique for accurate prediction of turbulent free shear flows in a wide range of applications. Here the LES technique has been applied to study the intermittency in a high Reynolds number turbulent round jet in a co-flow environment. The objective of this work is to study the external intermittency of velocity and scalar fields. LES based time averaged statistics show good agreement with the experimental measurements. The calculated probability density distributions show a Gaussian shape near the centreline region and a delta function at the furthest radial locations. The agreement between LES results and experimental data are good for the external intermittency indicating that the dynamic LES subgrid model accurately predicts the external intermittency.

Time reversibility of Navier–Stokes turbulence and its implication for subgrid scale models

Among existing subgrid scale (SGS) models for large-eddy simulation (LES), some are time reversible in the sense that the dynamics evolve backward in time after a transformation at every point in space. In practice, reversible subgrid models reduce the numerical stability of the simulations since the effect of the subgrid scales is no longer strictly dissipative. This lack of stability constitutes often a criterion to reject this kind of models. The aim of this paper is to examine whether time-reversibility can constitute a criterion that a subgrid model has to fulfill, or has not to. Thereto, we investigate by direct numerical simulation (DNS) the time dependence of the kinetic energy of the resolved scales when the velocity is reversed in all or part of the length scales of the turbulent flow. These results are compared with results from existing LES subgrid models. It is argued that the criterion of time reversibility to assess subgrid models is incompatible with the main underlying assumption of LES.

Large Eddy Simulation and the effect of the turbulent inlet conditions in the mixing Tee

Abstract Thermal fatigue in Pressurized Water Reactor plants has been found to be very acute in some hot/cold Tee junction mixing zones. Large Eddy Simulation (LES) can be used to capture the unsteadiness which is responsible for the large mechanical stresses associated with thermal fatigue. Here one LES subgrid model is studied, namely the Dynamic Smagorinsky model. This paper has two goals. The first is to demonstrate some results obtained using the EDF R&D Code Saturne applied to the Vattenfall Tee junction benchmark (version 2006) and the second is to look at the effect of including synthetic turbulence at the Tee junction pipe inlets. The last goal is the main topic of this paper. The Synthetic Eddy Method is used to create the turbulent inlet conditions and is applied to two kinds of grids. One contains six million cells and the other ten million. The addition of turbulence at the inlet does not seem to have much effect on the bulk flow and all computations are in good agreement with the experimental data. However, the inlet turbulence does have an effect on the near wall flow. All cases show that the wall temperature fluctuation and the wall temperature/velocity correlation are not the same when a turbulent inlet condition is used. Inclusion of the turbulent inlet condition moves the downstream location of the maximum temperature/velocity correlation by 1 cm and reduces its magnitude by 10%. This result is very important because the temperature/velocity correlation is closely related to the turbulent heat transfer in the flow, which is in turn responsible for the mechanical stresses on the structure. Finally we have studied in detail the influence of the turbulent inlet condition just downstream of the mixing zone. We show the influence of including turbulent inlet condition on the structure of the flow Walker et al. (2009).

Toward advanced subgrid models for Lattice-Boltzmann-based Large-eddy simulation: Theoretical formulations

This paper addresses the issue of developing advanced subgrid model for large-eddy simulations (LES) of turbulent flows based on Lattice Boltzmann methods (LBM). Most of already existing subgrid closures used in LES-LBM are straightforward extensions of the most crude model developed within the Navier–Stokes equations, namely the Smagorinsky eddy-viscosity model. In a first part, it is shown how to obtain an improved eddy-viscosity subgrid model for LBM. The original implementation of the Inertial-Range Consistent Smagorinsky model proposed by Dong and Sagaut for the D3Q19 scheme is used as an illustration. In a second step, an original extension of the Approximate Deconvolution Method proposed by Adams and Stolz for Navier–Stokes simulation is proposed. This new LBM-LES approach does not rely on the eddy-viscosity concept and is written directly within the LBM framework. It is shown that it can be implemented thanks to a trivial modification of the existing LBM solvers for Direct Numerical Simulation.

Inertial consistent subgrid model for large-eddy simulation based on the lattice Boltzmann method

The recently introduced inertial-range (IR) consistent Smagorinsky model and the classical Smagorinsky model are applied to the large-eddy simulation (LES) of decaying homogeneous isotropic turbulence based on the lattice Boltzmann method (LBM), which is implemented using the 19-velocity D3Q19 lattice model. The objectives of this study are to examine the effectiveness of the LES-LBM technique for study of turbulence and to extend and validate the efficiency of the inertial-range consistent Smagorinsky model for lattice Boltzmann fluid dynamics. The LES-LBM results are compared with the direct numerical simulation data as well as experimental data. The time evolution of the kinetic energy and the decay exponents of the dissipation rate, the velocity derivative skewness, and instantaneous energy spectra are analyzed. The dependency of behavior of the model coefficients on the ratio of grid width Δ and the Kolmogorov scale η is examined numerically. The results demonstrate that the LES-LBM in conjunction with the IR consistent Smagorinsky model can be used to simulate turbulence more satisfactorily than the standard Smagorinsky model.

Optimal estimation for large-eddy simulation of turbulence and application to the analysis of subgrid models

The tools of optimal estimation are applied to the study of subgrid models for large-eddy simulation of turbulence. The concept of optimal estimator is introduced and its properties are analyzed in the context of applications to a priori tests of subgrid models. Attention is focused on the Cook and Riley model in the case of a scalar field in isotropic turbulence. Using DNS data, the relevance of the β assumption is estimated by computing (i) generalized optimal estimators and (ii) the error brought by this assumption alone. Optimal estimators are computed for the subgrid variance using various sets of variables and various techniques (histograms and neural networks). It is shown that optimal estimators allow a thorough exploration of models. Neural networks are proved to be relevant and very efficient in this framework, and further usages are suggested.

Subgrid models for large-eddy simulation using unstructured grids in a stabilized finite element framework

We present subgrid closures for large-eddy Simulation (LES) likely to be implemented in stabilized finite element methods. Selection criterion, dynamic procedure and multiscale approach are compared within simulations of freely decaying isotropic turbulence. In all cases, the numerical dissipation coming from the least-squares stabilization dominates the subgrid model. Despite this large numerical dissipation, the LES model, whichever it is, provides a sufficient physical dissipation to have a clear and major effect on the results. In particular the dynamic procedures and the multiscale models turn out to be very efficient, high-lighting a self-adaptive behaviour of the turbulent viscosity and consequently predict the correct energy transfer mechanisms, by accounting for the numerical part of the total dissipation.

LES of atomizing spray with stochastic modeling of secondary breakup

A stochastic subgrid model for large-eddy simulation of atomizing spray is developed. Following Kolmogorov’s concept of viewing solid particle-breakup as a discrete random process, atomization of liquid blobs at high relative liquid-to-gas velocity is considered in the framework of uncorrelated breakup events, independent of the initial droplet size. Kolmogorov’s discrete model of breakup is rewritten in the form of differential Fokker–Planck equation for the PDF of droplet radii. Along with the Lagrangian tracking of spray dynamics, the size and number density of the newly produced droplets is governed by the evolution of this PDF in the space of droplet-radius. The parameters of the model are obtained dynamically by relating them to the local Weber number with two-way coupling between the gas and liquid phases. Computations of spray are performed for the representative conditions encountered in idealized diesel and gas-turbine engine configurations. A broad spectrum of droplet sizes is obtained at each location with co-existence of large and small droplets. A novel numerical algorithm capable of simultaneously simulating individual droplets as well as a group of droplets with similar properties commonly known as parcels is proposed and compared with standard parcels-approach usually employed in the computations of multiphase flows. The present approach is shown to be computationally efficient and captures the complex fragmentary process of liquid atomization.

Large-Eddy Simulations: Where Are We and What Can We Expect?

Recent subgrid models for large-eddy simulations of turbulent flows are evaluated, particularly the dynamic-Smagorinsky combination, with emphasis on identifying the reasons for their success and the limits of their applicability. The argument is made that they reproduce the turbulent dissipation relatively well, but their main advantage is that they are robust to errors in that they have a built-in mechanism to adjust the dissipation without substantially modifying the larger scales. The question of the stresses is considered next. It is found that it is an intrinsic property of subgrid models that the stresses are essentially unpredictable, and the models considered are indeed found not to reproduce them correctly, even on the average. In particular, the stress-strain correlation is low in real turbulence, and because eddy viscosity models assume that both are proportional, they always result in either the wrong energy spectrum or the wrong stresses. This is confirmed by simulations of shear flows, where it is shown that the error of the mean flow can only be made small if the subgrid stresses are negligible. Stresses are however large-scale quantities that are carried by the resolved scales if the resolution is fine enough