Scale separation for implicit large eddy simulation

With implicit large eddy simulation (ILES) the truncation error of the discretization scheme acts as subgrid-scale (SGS) model for the computation of turbulent flows. Although ILES is comparably simple, numerically robust and easy to implement, a considerable challenge is the design of numerical discretization schemes resulting in a physically consistent SGS model. In this work, we consider the implicit SGS modeling capacity of the adaptive central-upwind weighted-essentially-non-oscillatory scheme (WENO-CU6) [X.Y. Hu, Q. Wang, N.A. Adams, An adaptive central-upwind weighted essentially non-oscillatory scheme, J. Comput. Phys. 229 (2010) 8952–8965] by incorporating a physically-motivated scale-separation formulation. Scale separation is accomplished by a simple modification of the WENO weights. The resulting modified scheme maintains the shock-capturing capabilities of the original WENO-CU6 scheme while it is also able to reproduce the Kolmogorov range of the kinetic-energy spectrum for turbulence at the limit of infinite Reynolds number independently of grid resolution. For isentropic compressible turbulence the pseudo-sound regime of the dilatational kinetic-energy spectrum and the non-Gaussian probability-density function of the longitudinal velocity derivative are reproduced.     

Finite element-based large eddy simulation using a combination of the variational multiscale method and the dynamic Smagorinsky model

A finite element-based large eddy simulation (LES) is proposed using a combination of the residual-based variational multiscale (RBVMS) approach and the dynamic Smagorinsky eddy-viscosity model. In this combined model, the cross-stress terms are modelled using the RBVMS approach while the eddy-viscosity model is used to represent the Reynolds stresses. The eddy-viscosity is computed dynamically in a local fashion for which a localized version of the variational Germano identity is developed. To improve the robustness of the local dynamic procedure, two types of averaging schemes are considered. The first type employs spatial averaging over homogeneous direction(s) which is only applicable to turbulent flows with statistical homogeneity in at least one direction. The second type is based on Lagrangian averaging over fluid pathtubes, which is applicable to inhomogeneous turbulent flows. The predictions from the combined model are compared to the direct numerical simulation or experimental data and also to the predictions from the RBVMS model. This is done for two cases: turbulent flow in a channel (Re_τ = 590) and flow over a cylinder (Re_D = 3, 900). For the turbulent channel flow, predictions are similar between the RBVMS model and the combined model. For flow over a cylinder, the combined model provides better predictions, specifically for fluctuations in the streamwise velocity and lift.     

A fractal flame-wrinkling large eddy simulation model for premixed turbulent combustion

Combustion plays an important role in a wide variety of industrial applications, such as gas-turbines, furnaces, spark-ignition engines, and various air-breathing engines. The ability to predict and understand the behavior of reacting flows in practical devices is fundamental to improved combustors with higher efficiency and reduced levels of emissions. At present, large eddy simulation is considered the most promising approach for premixed combustion modeling since the large-scale energy containing flow structures are resolved on the grid. However, the typically thin reaction zone cannot be resolved. To overcome this difficulty flamelet models, in which the reaction is assumed to take place in thin layers, wrinkled by the turbulence can sometimes be used. In these models, the turbulent flame speed can be represented as the product of the laminar flame speed, S_u, corrected for the effects of stretch (strain and curvature) and the flame-wrinkling, Ξ. In this study, we propose to model Ξ using fractal theory. This model requires sub-models for the fractal dimension, and the inner and outer cut-offs—the latter being set by the grid. A model is proposed for the inner cut-off, whereas an empirical parameterization is used to provide the fractal dimension. The proposed model is applied to flame kernel growth in homogeneous isotropic turbulence in a fan-stirred bomb and to a lean premixed flame in a plane symmetric dump combustor. Good qualitative and quantitative agreement with experimental data were obtained for the proposed model in both cases. Comparison with other well-known turbulent flame speed closure models shows that the proposed model behaves at least as good, or even better, than the reference models.     

On discretization errors and subgrid scale model implementations in large eddy simulations

We analyze the impact of discretization errors on the performance of the Smagorinsky model in large eddy simulations (LES). To avoid difficulties related to solid boundaries, we focus on decaying homogeneous turbulence. It is shown that two numerical implementations of the model in the same finite volume code lead to significantly different results in terms of kinetic energy decay, time evolutions of the viscous dissipation and kinetic energy spectra. In comparison with spectral LES results, excellent predictions are however obtained with a novel formulation of the model derived from the discrete Navier–Stokes equations. We also highlight the effect of discretization errors on the measurement of physical quantities that involve scales close to the grid resolution.     

A restricted nonlinear large eddy simulation model for high Reynolds number flows

Recent numerical studies of the restricted nonlinear (RNL) model have demonstrated its ability to reproduce important features of wall turbulence despite a severe reduction in the number of degrees of freedom. In these prior studies, the RNL model included full resolution of the viscous term. In this work, we extend the RNL model to arbitrarily high Reynolds numbers by developing a RNL large eddy simulation (LES) framework along with a method to systematically identify an appropriate streamwise wavenumber support based on spectral properties of wall turbulence. This method leads to a band-limited RNL–LES system which is successful in reproducing some of the most important statistical features captured in previous low to moderate Reynolds number simulations, e.g. the mean velocity and second-order moment profiles. The RNL–LES framework offers a new approach to understanding the connection between coherent structures and the momentum transfer mechanisms of wall turbulence at arbitrarily high Reynolds numbers, where resolution of the viscous terms can become computationally expensive even with the relatively low computational complexity afforded through the dynamical restriction of the RNL model.     

Modeling of filtered heat release for large eddy simulation of compressible infinitely fast reacting flows

A priori and a posteriori studies for large eddy simulation of the compressible turbulent infinitely fast reacting shear layer are presented. The filtered heat release appearing in the energy equation is unclosed and the accuracy of different models for the filtered scalar dissipation rate and the conditional filtered scalar dissipation rate of the mixture fraction in closing this term is analyzed. The effect of different closures of the subgrid transport of momentum, energy and scalars on the modeling of the filtered heat release via the resolved fields is also considered. Three explicit models of these subgrid fluxes are explored, each with an increasing level of reconstruction and all of them regularized by a Smagorinsky-type term. It is observed that a major part of the error in the prediction of the conditional filtered scalar dissipation comes from the unsatisfactory modeling of the filtered dissipation itself. The error can be substantial in the turbulent fluctuation (rms) of the dissipation fields. It is encouraging that all models give good predictions of the mean and rms density in a posteriori LES of this flow with realistic heat release corresponding to large density change. Although a posteriori results show a small sensitivity to subgrid modeling errors in the current problem, extinction–reignition phenomena involving finite-rate chemistry would demand more accurate modeling of the dissipation rates. A posteriori results also show that the resolved fields obtained with the approximate reconstruction using moments (ARM) agree better with the filtered direct numerical simulation since the level of reconstruction in the modeled subfilter fluxes is increased.     

An improved dynamic subgrid-scale model and its application to large eddy simulation of rotating channel flows

Rotating turbulence occurs extensively in nature and engineering circumstances. Meanwhile, understanding physical mechanisms of the rotating turbulence is important to the fundamental research of turbulence. The turbulent flow in rotating frames undergoes two kinds of Coriolis force effects. First, a secondary flow is induced in the case that there is a mean vorticity component perpendicular to the rotating axis. Second, there are augmenting or suppressing effects on the turbulence if there i…     

Relevance of the subgrid-scales for large eddy simulations of turbulence-radiation interactions in a turbulent plane jet

An a priori study based on direct numerical simulation (DNS) of a non-isothermal turbulent plane jet has been carried out in order to analyse the role of the small-scales of turbulence on thermal radiation. Filtered DNS and large eddy simulation (LES) without subgrid-scale (SGS) model have been estimated for the radiative heat transfer. The comparison of the results highlights the subgrid-scale influence over the filtered radiation quantities, such as the radiative intensity and the radiative emission. The influence of the optical thickness is also studied. It is shown that the subgrid-scales are not significant near the centerline of the jet, where the radiative heat transfer is more important, and therefore that the SGS can be neglected in this configuration. However, when the optical thickness increases, the SGS become relevant and SGS modeling may be needed.     

Modelling of the subgrid scale wrinkling factor for large eddy simulation of turbulent premixed combustion

We propose a model for assessing the unresolved wrinkling factor in the large eddy simulation of turbulent premixed combustion. It relies essentially on a power-law dependence of the wrinkling factor on the filter size and an original expression for the ‘active’ corrugating strain rate. The latter is written as the turbulent strain multiplied by an efficiency function that accounts for viscous effects and the kinematic constraint of Peters. This yields functional expressions for the fractal dimension and the inner cut-off length scale, the latter being (i) filter-size independent and (ii) consistent with the Damköhler asymptotic behaviours at both large and small Karlovitz numbers. A new expression for the wrinkling factor that incorporates finite Reynolds number effects is further proposed. Finally, the model is successfully assessed on an experimental filtered database.     

Filter size definition in anisotropic subgrid models for large eddy simulation on irregular grids

The definition of the characteristic filter size to be used for subgrid scales models in large eddy simulation using irregular grids is still an unclosed problem. We investigate some different approaches to the definition of the filter length for anisotropic subgrid scale models and we propose a tensorial formulation based on the inertial ellipsoid of the grid element. The results demonstrate an improvement in the prediction of several key features of the flow when the anisotropicity of the grid is explicitly taken into account with the tensorial filter size.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

On the use of spires for generating inflow conditions with energetic coherent structures in large eddy simulation

While it has long been a practice to place spires near the inlet of a wind tunnel to quickly develop a turbulent boundary layer with similarities to an atmospheric boundary layer, this has not been the case for creating turbulent boundary layer inflow in large eddy simulations (LESs) of turbulent flows. We carry out LES with the curvilinear immersed boundary method to simulate the flow in a wind tunnel with a series of spires in order to investigate the feasibility of numerically developing inflow conditions from a precursory spire LES and assessing the similarities of the turbulence statistics to those of an atmospheric boundary layer. The simulated mean velocity field demonstrates that a turbulent boundary layer with height equal to the spire height develops very quickly, within five spire heights downstream. The major attribute of using spires for precursory simulations is the spatially evolving coherent structures that form downstream of the spires offering a range of length scales at both the vertical and streamwise directions allowing multiple turbulent inflow conditions to be extracted from a single simulation. While the distribution of length scales far from the spires resembles an atmospheric boundary layer, some turbulence statistics have some significant differences.     

A mixing controlled direct chemistry (MCDC) model for diesel engine combustion modelling using large eddy simulation

A mixing controlled direct chemistry (MCDC) combustion model with sub-grid scale (SGS) mixing effects and chemical kinetics has been evaluated for Large Eddy Simulation (LES) of diesel engine combustion. The mixing effect is modelled by a mixing timescale based on mixture fraction variance and sub-grid scalar dissipation rate. The SGS scalar dissipation rate is modelled using a similarity term and a scaling factor from the analysis of Direct Numerical Simulation (DNS) data. The chemical reaction progress is estimated from a kinetic timescale based on local internal energy change rate and equilibrium state internal energy. An optical research engine operating at conventional operating conditions and Low Temperature Combustion (LTC) conditions was used for evaluation of the combustion model. From the simulation results, the effect of SGS scalar mixing is evaluated at different stages of combustion. In the context of LES, the new approach provides improved engine modelling results compared to the Direct Chemistry Solver (DCS) combustion model.     

Dynamic gradient models for the sub-grid scale stress tensor and scalar flux vector in large eddy simulation

A number of dynamic variants of the modulated gradient model (MGM) for the sub-grid scale (SGS) stress tensor and the SGS scalar flux vector are developed and evaluated a posteriori in large eddy simulations of neutral and stably stratified turbulent channel flow. Two dynamic procedures are evaluated: one based on the local equilibrium hypothesis (called local-dynamic models) and one based on the global equilibrium and steady state hypotheses (global-dynamic models). These local-dynamic (LD) and global-dynamic (GD) versions of MGM are found to be much more accurate than the constant coefficient MGM in neutral turbulent channel flow at friction Reynolds numbers of 180 and 590. The constant coefficient MGM and GD-MGM are also found to yield the correct asymptotic behaviour close to the wall, which indicates the suitability of coupling the MGM kernel with the GD procedure. For the SGS scalar flux vector, LD and GD versions of the MGM are evaluated along with LD and GD versions of the recently proposed Smagorinsky-gradient (SGM) and Vreman-gradient (VGM) models. Tests in neutral and stably stratified channel flow at friction Reynolds number of 180 and friction Richardson numbers of 0 and 18 reveal that all six dynamic SGS scalar flux vector models are able to reproduce first-order and second-order turbulent statistics accurately. The simulations help further establish the stability and accuracy of SGM and VGM, which have not been tested previously. None of the dynamic gradient-based SGS scalar flux vector models are found to yield the correct asymptotic behaviour, however, and this issue needs further investigation.     

大孔径静态干涉成像光谱仪径向畸变导致的谱线偏移误差的校正

为提高大孔径静态干涉成像光谱仪在视场增大时的光谱定标精度,减小径向畸变对光谱精度的影响,本文提出一种基于光谱——畸变关联模型的光谱定标系数修正方法,给出了波数和波长修正公式.采用594.1?nm和632.8?nm气体激光器对成像光谱仪进行了光谱成像实验,并对数据进行了处理和分析.结果表明,当存在0.3％的桶形畸变时,边...     

Analysis of a dynamic model for subfilter scalar dissipation rate in large eddy simulation based on the subfilter scalar variance transport equation

Accurate prediction of non-premixed turbulent combustion using large eddy simulation (LES) requires detailed modelling of the mixing between fuel and oxidizer that occurs at scales smaller than the LES filterwidth. The small-scale mixing process can be quantitatively characterized by two related variables, the subfilter scalar variance and the subfilter scalar dissipation rate. A recently proposed alternative dynamic modelling procedure for the subfilter scale dissipation rate, designed for use with transport equation based models for subfilter scalar variance, is analysed in this work. This new dynamic non-equilibrium modelling approach produces a nonlinear interaction between variance and dissipation rate predictions that makes it difficult to isolate the performance of any single modelling component in a conventional LES simulation. To gain a better understanding of the new model, a three-part study is undertaken here. The first part of the study uses a priori analysis to examine some novel aspects of the model’s computation and guide its practical implementation. In the second part of the study, detailed a posteriori analysis of the model is performed. This analysis suggests that the dynamic estimate of the dissipation rate model coefficient helps to compensate for over-prediction of variance production rates and improves the accuracy of variance prediction. However, improved modelling of the variance production term, which in turn depends on the accuracy of models for the subfilter scalar flux, is necessary to allow both the scalar variance and dissipation rate to be predicted accurately. Therefore, the third part of the study examines the effect of the scalar flux model on the predictions of the dynamic non-equilibrium model. Use of a mixed model for the fluxes, rather than a gradient-diffusion-only model, is found to improve variance predictions in some cases.     

An energy-consistency-preserving large eddy simulation-scalar filtered mass density function (LES-SFMDF) method for high-speed flows

An energy-consistency-preserving large eddy simulation-scalar filtered mass density function (LES-SFMDF) method is developed to improve the existing LES-SFMDF method in high-speed flows, especially supersonic flows. The high-speed source term in the SFMDF transport equation is analysed theoretically from a new point of view, and then several primary principles are proposed for the LES-SFMDF to achieve a good consistency even along discontinuities. Based on these principles and further theoretical analysis, the high-speed source term of the enthalpy in the SFMDF is modelled and computed from both MC and LES variables rather than the usually used solely LES variables. This new LES-SFMDF method is used for simulating the flows in a shock tube and in a subsonic temporally developing mixing layer. This method shows a better particle energy consistency than the existing method when applied across discontinuities in supersonic laminar flows. Unlike the existing method, with this energy-consistency-preserving LES-SFMDF method, particle energy consistency is consistent with particle mass consistency so that particle energy consistency can benefit from particle velocity correction. This method also demonstrates robustness for various numbers of particles.