Evaluations of SGS Combustion,Scalar Flux and Stress Models in a Turbulent Jet Premixed Flame

A newly developed fractal dynamic SGS (FDSGS) combustion model and a scale self-recognition mixed (SSRM) SGS stress model are evaluated along with other SGS combustion, scalar flux and stress models in a priori and a posteriori manners using DNS data of a hydrogen-air turbulent plane jet premixed flame. A posteriori tests reveal that the LES using the FDSGS combustion model can predict the combustion field well in terms of mean temperature distributions and peak positions in the transverse distributions of filtered reaction progress variable fluctuations. A priori and a posteriori tests of the scalar flux models show that a model proposed by Clark et al. accurately predicts the counter-gradient transport as well as the gradient diffusion, and introduction of the model of Clark et al. into the LES yields slightly better predictions of the filtered progress variable fluctuations than that of a gradient diffusion model. Evaluations of the stress models reveal that the LES with the SSRM model predicts the velocity fluctuations well compared to that with the Smagorinsky model.     

Fourier neural operator approach to large eddy simulation of three-dimensional turbulence

Fourier neural operator (FNO) model is developed for large eddy simulation (LES) of three-dimensional (3D) turbulence. Velocity fields of isotropic turbulence generated by direct numerical simulation (DNS) are used for training the FNO model to predict the filtered velocity field at a given time. The input of the FNO model is the filtered velocity fields at the previous several time-nodes with large time lag. In the a posteriori study of LES, the FNO model performs better than the dynamic Smagorinsky model (DSM) and the dynamic mixed model (DMM) in the prediction of the velocity spectrum, probability density functions (PDFs) of vorticity and velocity increments, and the instantaneous flow structures. Moreover, the proposed model can significantly reduce the computational cost, and can be well generalized to LES of turbulence at higher Taylor-Reynolds numbers.     

Large eddy simulations of a turbulent thermal plume

Large eddy simulations of a three-dimensional turbulent thermal plume in an open environment have been carried out using a self-developed parallel computational fluid dynamics code SMAFS (smoke movement and flame spread) to study the thermal plume’s dynamics including its puffing, self-preserving and air entrainment. In the simulation, the sub-grid stress was modeled using both the standard Smagorinsky and the buoyancy modified Smagorinsky models, which were compared. The sub-grid scale (SGS) scalar flux in the filtered enthalpy transport equation was modeled based on a simple gradient transport hypothesis with constant SGS Prandtl number. The effect of the Smagorinsky model constant and the SGS Prandtl number were examined. The computation results were compared with experimental measurements, thermal plume theory and empirical correlations, showing good agreement. It is found that both the buoyancy modification and the SGS turbulent Prandtl number have little influence on simulation. However, the SGS model constant C _s has a significant effect on the prediction of plume spreading, although it does not affect much the prediction of puffing.     

Development of Gas-Particle Euler-Euler LES Approach: A Priori Analysis of Particle Sub-Grid Models in Homogeneous Isotropic Turbulence

A new large eddy simulation (LES) approach for particle-laden turbulent flows in the framework of the Eulerian formalism for inertial particle statistical modelling is developed. Local instantaneous Eulerian equations for the particle cloud are first written using the mesoscopic Eulerian formalism (MEF) proposed by Février et al. (J Fluid Mech 533:1–46, 2005), which accounts for the contribution of an uncorrelated velocity component for inertial particles with relaxation time larger than the Kolmogorov time scale. Second, particle LES equations are obtained by volume filtering the mesoscopic Eulerian ones. In such an approach, the particulate flow at larger scales than the filter width is recovered while sub-grid effects need to be modelled. Particle eddy-viscosity, scale similarity and mixed sub-grid stress (SGS) models derived from fluid compressible turbulence SGS models are presented. Evaluation of such models is performed using three sets of particle Lagrangian results computed from discrete particle simulation (DPS) coupled with fluid direct numerical simulation (DNS) of homogeneous isotropic decaying turbulence. The two phase flow regime corresponds to the dilute one where two-way coupling and inter-particle collisions are not considered. The different particle Stokes number (based on Kolmogorov time scale) are initially equal to 1, 2.2 and 5.1. The mesoscopic field properties are analysed in detail by considering the particle velocity probability function (PDF), correlated velocity power spectra and random uncorrelated velocity moments. The mesoscopic fields measured from DPS+DNS are then filtered to obtain large scale fields. A priori evaluation of particle sub-grid stress models gives comparable agreement than for fluid compressible turbulence models. It has been found that the standard Smagorinsky eddy-viscosity model exhibits the smaller correlation coefficients, the scale similarity model shows very good correlation coefficient but strongly underestimates the sub-grid dissipation and the mixed model is on the whole superior to pure eddy-viscosity model.     

Large-eddy simulation study of an air flow past a heated square cylinder

A large-eddy simulation (LES) technique has been used for the calculation of an air flow past a heated square cylinder. The LES method is a conventional one with the Smagorinsky eddy-viscosity model, and the computational grid is small enough to be handled by workstations. The computed turbulent flow field quantities agree well with the experimental results reported by Lyn et al. (J Fluid Mech 304:285–319, 1995). Particular attention has been spent to the convective heat transfer and the prediction of the thermal fluctuations in case of a fluid with Pr = 0.71. The LES results agree well with the empirical correlations proposed by Hilpert and Sparrow et al. for the average Nusselt number.     

An improved anisotropy-resolving subgrid-scale model for flows in laminar–turbulent transition region

Some types of mixed subgrid-scale (SGS) models combining an isotropic eddy-viscosity model and a scale-similarity model can be used to effectively improve the accuracy of large eddy simulation (LES) in predicting wall turbulence. Abe (2013) has recently proposed a stabilized mixed model that maintains its computational stability through a unique procedure that prevents the energy transfer between the grid-scale (GS) and SGS components induced by the scale-similarity term. At the same time, since this model can successfully predict the anisotropy of the SGS stress, the predictive performance, particularly at coarse grid resolutions, is remarkably improved in comparison with other mixed models. However, since the stabilized anisotropy-resolving SGS model includes a transport equation of the SGS turbulence energy, k_SGS, containing a production term proportional to the square root of k_SGS, its applicability to flows with both laminar and turbulent regions is not so high. This is because such a production term causes k_SGS to self-reproduce. Consequently, the laminar–turbulent transition region predicted by this model depends on the inflow or initial condition of k_SGS. To resolve these issues, in the present study, the mixed-timescale (MTS) SGS model proposed by Inagaki et al. (2005) is introduced into the stabilized mixed model as the isotropic eddy-viscosity part and the production term in the k_SGS transport equation. In the MTS model, the SGS turbulence energy, k_es, estimated by filtering the instantaneous flow field is used. Since the k_es approaches zero by itself in the laminar flow region, the self-reproduction property brought about by using the conventional k_SGS transport equation model is eliminated in this modified model. Therefore, this modification is expected to enhance the applicability of the model to flows with both laminar and turbulent regions. The model performance is tested in plane channel flows with different Reynolds numbers and in a backward-facing step flow. The results demonstrate that the proposed model successfully predicts a parabolic velocity profile under laminar flow conditions and reduces the dependence on the grid resolution to the same degree as the unmodified model by Abe (2013) for turbulent flow conditions. Moreover, it is shown that the present model is effective at transitional Reynolds numbers. Furthermore, the present model successfully provides accurate results for the backward-facing step flow with various grid resolutions. Thus, the proposed model is considered to be a refined anisotropy-resolving SGS model applicable to laminar, transitional, and turbulent flows.     

A-priori testing of an eddy viscosity model for the density-weighted subgrid scale stress tensor in turbulent premixed flames

In this study, we report on the direct measurement of the density-weighted subgrid scale (SGS) stress tensor in turbulent premixed flames. In large-eddy simulations (LES), this unresolved tensor is typically modelled using eddy viscosity approaches. Additionally to the direct measurement, we provide a pure experimentally based a-priori test of the commonly used eddy viscosity model suggested by Smagorinsky. For two turbulent premixed V-shaped methane–air flames, a statistical analysis is presented where the correlation between the directly measured SGS stress tensor and the eddy viscosity model following Smagorinsky is tested. The measurement strategy is based on the application of a dual-plane stereo-PIV technique which enables the measurement of the 3D flow field in two parallel planes. This allows the determination of velocities as well as velocity gradients in all three directions. Here, a vector resolution of 118 μm was achieved. For a priori testing, the data are subjected to a spatial filtering procedure that reproduces the application of the filter function in LES. The calculation of velocity gradients is performed after the application of this spatial averaging. Additionally to the velocity field, the flame front position is deduced from the clearly observable step in the tracer particle number density between burnt and unburnt regions of the flame. This facilitates the direct single-shot-based evaluation of all components of the density-weighted SGS stress tensor. Additionally, the model expressions related to these terms can be determined, which is done in this first study for the static Smagorinsky model. With that, the instantaneous local comparison between directly measured stress terms and modelled terms is possible, based on the instantaneous local evaluation procedure. The measurement procedure is described, and first results are presented and discussed. They show a rather poor performance of the static form of the Smagorinsky model (with fixed Smagorinsky constant). Our future aims are to use the directly measured SGS data for the a-priori comparison with more advanced models.     

Balance equation of the generalised sub-grid scale (SGS) turbulent kinetic energy in a new tensorial dynamic mixed SGS model

A new dynamic model is proposed in which the eddy viscosity is defined as a symmetric second rank tensor, proportional to the product of a turbulent length scale with an ellipsoid of turbulent velocity scales. The employed definition of the eddy viscosity allows to remove the local balance assumption of the SGS turbulent kinetic energy formulated in all the dynamic Smagorinsky-type SGS models. Furthermore, because of the tensorial structure of the eddy viscosity the alignment assumption between the principal axes of the SGS turbulent stress tensor and the resolved strain-rate tensor is equally removed, an assumption which is employed in the scalar eddy viscosity SGS models. The proposed model is tested for a turbulent channel flow. Comparison with the results obtained with other dynamic SGS models (Dynamic Smagorinsky Model, Dynamic Mixed Model and Dynamic K-equation Model) shows that the tensorial definition of the eddy viscosity and the removal of the local balance assumption of the SGS turbulent kinetic energy considerably improves the agreement between results obtained with Large Eddy simulation (LES) and Direct Numerical Simulations (DNS), respectevely. Received August 26, 1999     

Comparative study of implicit and subgrid‐scale model large‐eddy simulation techniques for low‐Reynolds number airfoil applications

A computational study of a high‐fidelity, implicit large‐eddy simulation (ILES) technique with and without the use of the dynamic Smagorinsky subgrid‐scale (SGS) model is conducted to examine the contributions of the SGS model on solutions of transitional flow over the SD7003 airfoil section. ILES without an SGS model has been shown in the past to produce comparable and sometimes favorable results to traditional SGS‐based large‐eddy simulation (LES) when applied to canonical turbulent flows. This paper evaluates the necessity of the SGS model for low‐Reynolds number airfoil applications to affirm the use of ILES without SGS‐modeling for a broader class of problems such as those pertaining to micro air vehicles and low‐pressure turbines. It is determined that the addition of the dynamic Smagorinsky model does not significantly affect the time‐mean flow or statistical quantities measured around the airfoil section for the spatial resolutions and Reynolds numbers examined in this study. Additionally, the robustness and reduced computational cost of ILES without the SGS model demonstrates the attractiveness of ILES as an alternative to traditional LES. Published 2012. This article is a US Government work and is in the public domain in the USA.     

Large Eddy Simulation of Scalar Mixing in a Coaxial Confined Jet

The highly turbulent flow occurring inside gas-turbine combustors requires accurate simulation of scalar mixing if CFD methods are to be used with confidence in design. This has motivated the present paper, which describes the implementation of a passive scalar transport equation into an LES code, including assessment/testing of alternative discretisation schemes to avoid over/undershoots and excessive smoothing. Both second order accurate TVD and higher order accurate DRP schemes are assessed. The best performance is displayed by a DRP method, but this is only true on fine meshes; it produces similar (or larger) errors to a TVD scheme on coarser meshes, and the TVD approach has been retained for LES applications. The unsteady scalar mixing performance of the LES code is validated against published DNS data for a slightly heated channel flow. Excellent agreement between the current LES predictions and DNS data is obtained, for both velocity and scalar statistics. Finally, the developed methodology is applied to scalar transport in a confined co-axial jet mixing flow, for which experimental data are available. Agreement with statistically averaged fields for both velocity and scalar, is demonstrated to be very good, and a considerable improvement over the standard eddy viscosity RANS approach. Illustrations are presented of predicted time-resolved information e.g. time histories, and scalar pdf predictions. The LES results are shown, even using a simple Smagorinsky SGS model, to predict (correctly) lower values of the turbulent Prandtl number in the free shear regions of the flow, compared to higher values in the wall-affected regions. The ability to predict turbulent Prandtl number variations (rather than input these as in combustor RANS CFD models) is an important and promising feature of the LES approach for combustor flow simulation since it is known to be important in determining combustor exit temperature traverse.     

CFD ANALYSIS OF TURBULENT FLOW PAST SQUARE CYLINDER USING DYNAMIC LES

Computational fluid dynamics (CFD) analysis of turbulent flow past a square cylinder is conducted using large eddy simulation (LES). In the first part of the paper, the implementation of the three-dimensional (3-D) LES computation based on the conventional standard Smagorinsky model (S model) shows a good prediction capability compared with that of turbulence models based on Reynolds-averaged Navier-Stokes equations (RANS models). Next, the computation using the dynamic Smagorinsky model (DS model) is carried out, and the improvement by the use of DS model is described. Lastly, the Lagrangian dynamic Smagorinsky model (LDS model) is introduced to overcome the disadvantages of DS model, e.g., calculation instability. Results obtained from the various SGS models are compared with those from experiments.     

Non-Equilibrium Mixing of Turbulence Scales Using a Continuous Hybrid RANS/LES Approach: Application to the Shearless Mixing Layer

A new subgrid-scale (SGS) model based on partially integrated transport method (PITM) is applied to the case of a turbulent spectral non-equilibrium flow created by the mixing of two turbulence fields of differing scales: the shearless mixing layer. The method can be viewed as a continuous hybrid RANS/LES approach. In this model the SGS length scale is no longer given by the size of the discretization step, but is dynamically estimated using an additional transport equation for the dissipation rate. The results are compared to those corresponding to the classical model of Smagorinsky and to the experimental data of Veeravalli and Warhaft. A method for creating an anisotropic analytical pseudo-random field for inflow conditions is also proposed. This approach based on subgrid-scale transport modelling combined with anisotropic inlet conditions gives better results for the prediction of the shearless mixing layer.     

Large Eddy Simulations Using an Unstructured Grid Compressible Navier - Stokes Algorithm

Large Eddy Simulation (LES) of the decay of isotropic turbulence and of channel flow has been performed using an explicit second-order unstructured grid algorithm for tetrahedral cells. The algorithm solves for cell-averaged values using the finite volume form of the unsteady compressible Jittered Navier-Stokes equations. The inviscid fluxes are obtained from Godunov's exact Riemann solver. Reconstruction of the flow variables to the left and right sides of each face is performed using least squares or Frink's method. The viscous fluxes and heat transfer are obtained by application of Gauss' theorem. LES of the decay of nearly incompressible isotropic turbulence has been performed using two models for the SGS stresses: the Monotone Integrated Large Eddy Simulation (MILES) approach, wherein the inherent numerical dissipation models the sub-grid scale (SGS) dissipation, and the Smagorinsky SGS model. The results using the MILES approach with least squares reconstruction show good agreement with incompressible experimental data. The contribution of the Smagorinsky SGS model is negligible. LES of turbulent channel flow was performed at a Reynolds number (based on channel height and bulk velocity) of 5600 and Mach number of 0.5 (at which compressibility effects are minimal) using Smagorinsky's SGS model with van Driest damping. The results show good agreement with experimental data and direct numerical simulations for incompressible channel flow. The SGS eddy viscosity is less than 10% of the molecular viscosity, and therefore the LES is effectively MILES with molecular viscosity.     

基于人工神经网络的亚格子应力建模

亚格子(SGS)应力建模在湍流大涡模拟(LES)中有着极为重要的作用. 传统亚格子应力模型存在相对误差较大、耗散过强等问题. 近年来, 计算机技术的发展使得人工神经网络(ANN)等机器学习方法逐渐成为亚格子应力建模型的新研究范式. 本文着重考虑滤波宽度及雷诺数影响, 在不可压缩槽道湍流中建立了亚格子应力的ANN模型. 该模型以滤波后的直接数值模拟(fDNS)流场物理量及滤波尺度为输入信息, 相应滤波尺度下的亚格子应力为输出量. 通过对不同滤波尺度及不同雷诺数数据的训练, ANN模型能够给出与直接数值模拟(DNS)高度吻合的亚格子应力. 此外, 模型在亚格子耗散等非ANN建模量上也有着优异的预测性能, 与基于DNS获得的对应物理量的相关系数大都在0.9以上, 较梯度模型及Smagorinsky模型有明显提升. 在后验测试中, ANN模型对流向平均速度剖面的预测同样优于梯度模型、Smagorinsky模型及隐式大涡模拟(ILES)等传统LES模型. 在脉动速度均方根预测方面, 除了某些法向位置外ANN模型的性能整体上相对其他3个模型有所提升. 然而, 随着网格尺度的增大ANN模型预测的结果与fDNS结果的偏差逐渐增大. 总之, ANN方法在发展高精度亚格子应力模型上具有很大的潜力.      

Effects of the Similarity Model in Finite-Difference LES of Isotropic Turbulence Using a Lagrangian Dynamic Mixed Model

A Lagrangian dynamic formulation of the mixed similarity subgrid (SGS) model for large-eddy simulation (LES) of turbulence is proposed. In this model, averaging is performed over fluid trajectories, which makes the model applicable to complex flows without directions of statistical homogeneity. An alternative version based on a Taylor series expansion (nonlinear mixed model) is also examined. The Lagrangian models are implemented in a finite difference code and tested in forced and decaying isotropic turbulence. As comparison, the dynamic Smagorinsky model and volume-averaged formulations of the mixed models are also tested. Good results are obtained, except in the case of low-resolution LES (32³) of decaying turbulence, where the similarity coefficient becomes negative due to the fact that the test-filter scale exceeds the integral scale of turbulence. At a higher resolution (64³), the dynamic similarity coefficient is positive and good agreement is found between predicted and measured kinetic energy evolution. Compared to the eddy viscosity term, the similarity or the nonlinear terms contribute significantly to both SGS dissipation of kinetic energy and SGS force. In order to dynamically test the accuracy of the modeling, the error incurred in satisfying the Germano identity is evaluated. It is found that the dynamic Smagorinksy model generates a very large error, only 3% lower than the worst-case scenario without model. Addition of the similarity or nonlinear term decreases the error by up to about 50%, confirming that it represents a more realistic parameterization than the Smagorinsky model alone.     

Validation of large eddy simulation method for study of flatness and skewness of decaying compressible magnetohydrodynamic turbulence

In the present work we study potential applicability of large eddy simulation (LES) method for prediction of flatness and skewness of compressible magnetohydrodynamic (MHD) turbulence. The knowledge of these quantities characterizes non-Gaussian properties of turbulence and can be used for verification of hypothesis on Gaussianity for the turbulent flow under consideration. Prediction accuracy of these quantities by means of LES method directly determines efficiency of reconstruction of probability density function (PDF) that depends on used subgrid-scale (SGS) parameterizations. Applicability of LES approach for studying of PDF properties of turbulent compressible magnetic fluid flow is investigated and potential feasibilities of five SGS parameterizations by means of comparison with direct numerical simulation results are explored. The skewness and the flatness of the velocity and the magnetic field components under various hydrodynamic Reynolds numbers, sonic Mach numbers, and magnetic Reynolds numbers are studied. It is shown that various SGS closures demonstrate the best results depending on change of similarity numbers of turbulent MHD flow. The case without any subgrid modeling yields sufficiently good results as well. This indicates that the energy pile-up at the small scales that is characteristic for the model without any subgrid closure, does not significantly influence on determination of PDF. It is shown that, among the subgrid models, the best results for studying of the flatness and the skewness of velocity and magnetic field components are demonstrated by the Smagorinsky model for MHD turbulence and the model based on cross-helicity for MHD case. It is visible from the numerical results that the influence of a choice subgrid parametrization for the flatness and the skewness of velocity is more essential than for the same characteristics of magnetic field.     

A general optimal formulation for the dynamic Smagorinsky subgrid‐scale stress model

In this paper, a general optimal formulation for the dynamic Smagorinsky subgrid‐scale (SGS) stress model is reported. The Smagorinsky constitutive relation has been revisited from the perspective of functional variation and optimization. The local error density of the dynamic Smagorinsky SGS model has been minimized directly to determine the model coefficient C_S. A sufficient and necessary condition for optimizing the SGS model is obtained and an orthogonal condition (OC), which governs the instantaneous spatial distribution of the optimal dynamic model coefficient, is formulated. The OC is a useful general optimization condition, which unifies several classical dynamic SGS modelling formulations reported in the literature. In addition, the OC also results in a new dynamic model in the form of a Picard's integral equation. The approximation tensorial space for the projected Leonard stress is identified and the physical meaning for several basic grid and test‐grid level tensors is systematically discussed. Numerical simulations of turbulent Couette flow are used to validate the new model formulation as represented by the Picard's integral equation for Reynolds numbers ranging from 1500 to 7050 (based on one half of the velocity difference of the two plates and the channel height). The relative magnitudes of the Smagorinsky constitutive parameters have been investigated, including the model coefficient, SGS viscosity and filtered strain rate tensor. In general, this paper focuses on investigation of fundamental mathematical and physical properties of the popular Smagorinsky constitutive relation and its related dynamic modelling optimization procedure. Copyright © 2005 John Wiley & Sons Ltd.     

On the influences of key modelling constants of large eddy simulations for large-scale compartment fires predictions

An in-house large eddy simulation (LES) based fire field model has been developed for large-scale compartment fire simulations. The model incorporates four major components, including subgrid-scale turbulence, combustion, soot and radiation models which are fully coupled. It is designed to simulate the temporal and fluid dynamical effects of turbulent reaction flow for non-premixed diffusion flame. Parametric studies were performed based on a large-scale fire experiment carried out in a 39-m long test hall facility. Several turbulent Prandtl and Schmidt numbers ranging from 0.2 to 0.5, and Smagorinsky constants ranging from 0.18 to 0.23 were investigated. It was found that the temperature and flow field predictions were most accurate with turbulent Prandtl and Schmidt numbers of 0.3, respectively, and a Smagorinsky constant of 0.2 applied. In addition, by utilising a set of numerically verified key modelling parameters, the smoke filling process was successfully captured by the present LES model.     

Rotation characteristic and granular temperature analysis in a bubbling fluidized bed of binary particles

In this work,a discrete particle model(DPM) was applied to investigate the dynamic characteristics in a gas-solid bubbling fluidized bed of binary solid particles.The solid phase was simulated by the hardsphere discrete particle model.The large eddy simulation(LES) method was used to simulate the gas phase.To improve the accuracy of the simulation,an improved sub-grid scale(SGS) model in the LES method was also applied.The mutative Smagorinsky constant case was compared with the previously published experimental data.The simulation by the mutative Smagorinsky constant model exhibited better agreement with the experimental data than that by the common invariant Smagorinsky constant model.Various restitution coefficients and different compositions of binary solids were investigated to determine their influences on the rotation characteristics and granular temperatures of the particles.The particle translational and rotational characteristic distributions were related to certain simulation parameters.     

基于人工神经网络的湍流大涡模拟方法

大涡模拟方法(LES)是研究复杂湍流问题的重要工具,在航空航天、湍流燃烧、气动声学、大气边界层等众多工程领域中具有广泛的应用前景.大涡模拟方法采用粗网格计算大尺度上的湍流结构,并用亚格子(SGS)模型近似表达滤波尺度以下的流动结构对大尺度流场的作用.传统的亚格子模型由于只利用了单点流场信息和简单的函数关系,在先验验证中相对误差较大, 在后验验证中耗散过强. 近几年来,机器学习方法在湍流建模问题中得到了越来越多的应用.本文介绍了基于人工神经网络(ANN)的湍流亚格子模型的最新进展.详细地讨论了人工神经网络混合模型、空间人工神经网络模型和反卷积人工神经网络模型的构造方法.借助于人工神经网络强大的数据插值能力,新的亚格子模型的先验精度和后验精度均有显著提升. 在先验验证中,新模型所预测的亚格子应力的相关系数超过了0.99,在预测精度上远高于传统的大涡模拟模型. 在后验验证中,新模型对各类湍流统计量和瞬态流动结构的预测都优于隐式大涡模拟方法、动态Smagorinsky模型、动态混合模型等传统模型.因此, 人工神经网络方法在发展复杂湍流的先进大涡模拟模型中具有很大的潜力.