A Framework for Characterizing Structural Uncertainty in Large-Eddy Simulation Closures

Motivated by the sizable increase of available computing resources, large-eddy simulation of complex turbulent flow is becoming increasingly popular. The underlying filtering operation of this approach enables to represent only large-scale motions. However, the small-scale fluctuations and their effects on the resolved flow field require additional modeling. As a consequence, the assumptions made in the closure formulations become potential sources of incertitude that can impact the quantities of interest. The objective of this work is to introduce a framework for the systematic estimation of structural uncertainty in large-eddy simulation closures. In particular, the methodology proposed is independent of the initial model form, computationally efficient, and suitable to general flow solvers. The approach is based on introducing controlled perturbations to the turbulent stress tensor in terms of magnitude, shape and orientation, such that propagation of their effects can be assessed. The framework is rigorously described, and physically plausible bounds for the perturbations are proposed. As a means to test its performance, a comprehensive set of numerical experiments are reported for which physical interpretation of the deviations in the quantities of interest are discussed.     

A dynamic global-coefficient mixed subgrid-scale model for large-eddy simulation of turbulent flows

A dynamic global-coefficient mixed subgrid-scale eddy-viscosity model for large-eddy simulation of turbulent flows in complex geometries is developed. In the present model, the subgrid-scale stress is decomposed into the modified Leonard stress, cross stress, and subgrid-scale Reynolds stress. The modified Leonard stress is explicitly computed assuming a scale similarity, while the cross stress and the subgrid-scale Reynolds stress are modeled using the global-coefficient eddy-viscosity model. The model coefficient is determined by a dynamic procedure based on the global-equilibrium between the subgrid-scale dissipation and the viscous dissipation. The new model relieves some of the difficulties associated with an eddy-viscosity closure, such as the nonalignment of the principal axes of the subgrid-scale stress tensor and the strain rate tensor and the anisotropy of turbulent flow fields, while, like other dynamic global-coefficient models, it does not require averaging or clipping of the model coefficient for numerical stabilization. The combination of the global-coefficient eddy-viscosity model and a scale-similarity model is demonstrated to produce improved predictions in a number of turbulent flow simulations.     

Subgrid continuum modeling of particle motion in a turbulent flow

An Eulerian continuum approach to modeling the motion of dispersed particles within the framework of the large-eddy simulation method is developed. The approach is based on a kinetic equation for the filtered probability density function for the particle velocity in a turbulent flow. Models for the subgrid turbulent stresses of the dispersed phase are presented.     

Large Eddy Simulations Using the Subgrid-Scale Estimation Model and Truncated Navier–Stokes Dynamics

We describe a procedure for large eddy simulations of turbulence which uses the subgrid-scale estimation model and truncated Navier–Stokes dynamics. In the procedure the large eddy simulation equations are advanced in time with the subgrid-scale stress tensor calculated from the parallel solution of the truncated Navier–Stokes equations on a mesh two times smaller in each Cartesian direction than the mesh employed for a discretization of the resolved quantities. The truncated Navier–Stokes equations are solved through a sequence of runs, each initialized using the subgrid-scale estimation model. The modeling procedure is evaluated by comparing results of large eddy simulations for isotropic turbulence and turbulent channel flow with the corresponding results of experiments, theory, direct numerical simulations, and other large eddy simulations. Subsequently, simplifications of the general procedure are discussed and evaluated. In particular, it is possible to formulate the procedure entirely in terms of the truncated Navier–Stokes equation and a periodic processing of the small-scale component of its solution. Received 27 April 2001 and accepted 16 December 2001     

Backscatter Models for Large-Eddy Simulations

Using previously established properties of nonlinear subgrid-scale interactions we derive deterministic models of backscatter for large-eddy simulations. The models provide approximately equal amounts of forward and inverse transfer and consequently affect only weakly the total kinetic energy of turbulence. The modeling procedures are tested on a simple case of forced isotropic turbulence with the inertial range and in turbulent channel flow. The presence of backscatter increases the physical realism of large-eddy simulations. Received: 24 January 1997 and accepted 20 March 1997     

A Bayesian Calibration–Prediction Method for Reducing Model-Form Uncertainties with Application in RANS Simulations

Model-form uncertainties in complex mechanics systems are a major obstacle for predictive simulations. Reducing these uncertainties is critical for stake-holders to make risk-informed decisions based on numerical simulations. For example, Reynolds-Averaged Navier-Stokes (RANS) simulations are increasingly used in the design, analysis, and safety assessment of mission-critical systems involving turbulent flows. However, for many practical flows the RANS predictions have large model-form uncertainties originating from the uncertainty in the modeled Reynolds stresses. Recently, a physics-informed Bayesian framework has been proposed to quantify and reduce model-form uncertainties in RANS simulations for flows by utilizing sparse observation data. However, in the design stage of engineering systems, when the system or device has not been built yet, measurement data are usually not available. In the present work we extend the original framework to scenarios where there are no available data on the flow to be predicted. In the proposed method, we first calibrate the model discrepancy on a related flow with available data, leading to a statistical model for the uncertainty distribution of the Reynolds stress discrepancy. The obtained distribution is then sampled to correct the RANS-modeled Reynolds stresses for the flow to be predicted. The extended framework is a Bayesian calibration–prediction method for reducing model-form uncertainties. The merits of the proposed method are demonstrated on two flows that are challenging to standard RANS models. By not requiring observation data on the flow to be predicted, the present calibration–prediction method will gain wider acceptance in practical engineering design and analysis compared to the original framework. While RANS modeling is chosen to demonstrate the merits of the proposed framework, the methodology is generally applicable to other complex mechanics models involving solids, fluids flows, or the coupling between the two (e.g., mechanics models for the cardiovascular systems), where model-form uncertainties are present in the constitutive relations.     

低密度流体界面不稳定性大涡模拟

采用拉伸涡亚格子尺度应力模型对湍流输运中的亚格子作用项进行模式化处理,发展了适用于可压多介质黏性流动和湍流的大涡模拟方法和代码MVFT（multi-viscous flow and turbulence）。利用MVFT代码对低密度流体界面不稳定性及其诱发的湍流混合问题进行了数值模拟。详细分析了扰动界面的发展,流场中冲击波的传播、相互作用、湍流混合区边界的演化规律,以及流场瞬时密度和湍动能的分布和发展。数值模拟获得的界面演化图像和流场中波系结构与实验结果吻合较好。三维和二维模拟结果的比较显示,两者得到的扰动界面位置、波系及湍流混合区边界基本一致,只是后期的界面构型有所不同,这也正说明湍流具有强三维效应。     

Large-eddy simulation of turbulent buoyancy-driven flow in a rectangular cavity

Turbulent buoyancy-driven flow in a rectangular cavity with two differentially heated opposite walls is investigated numerically by means of large-eddy simulation (LES). Different dynamic global-coefficient subgrid-scale models for weakly compressible flows are applied to simulate the natural convective flow. It is shown that transition of the boundary layer is delayed in cases where the model coefficients are fixed or changing dynamically according to the Germano identity. On the contrary, in the ‘global equilibrium’ approach, the result shows an earlier change in flow regime due to lower subgrid-scale viscosity. Further, it is also demonstrated that three-dimensional effects of the natural convective flow may be significant due to the presence of adiabatic side walls.     

Large-eddy simulation of turbulent channel flow at transcritical states

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. A physically consistent subgrid-scale turbulence model is incorporated, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum and thermal boundary layer thicknesses. Different turbulent Prandtl number formulations and their components are discussed in context of strong property variations.     

Subgrid-scale modelling at low mesh reynolds number

Subgrid-scale models are derived for large-eddy simulations in the limit of low mesh Reynolds number, or, equivalently, resolution approaching that required for full resolution of the simulated turbulent flow. The models are constructed from standard forms of the dissipation spectrum in a manner analogous to that used to derive the classical Smagorinsky-Lilly model from the inertial range spectrum. Practical methods for computing the subgrid-scale eddy viscosity are described, together with examples of the effects of using such models in a real simulation.     

LES/RANS方法混合函数特性研究

将两方程k-ω SST湍流模型和Sagaut的混合尺度亚格子模型通过一个混合函数相结合, 构造出一种混合大涡/雷诺平均N-S方程模拟方法(hybird large eddy simulation/reynolds-averaged navier-stokes, Hybrid LES/RANS), 采用这种混合模拟方法结合5阶WENO格式对Ma=2.8平板湍流边界层进行了数值模拟, 并在计算区域上游入口处采用“回收/调节”方法生成湍流脉动边界条件, 通过考查RANS区域向LES区域的过渡参数及网格分辨率对这种混合模拟方法进行了评价. 计算结果表明: 该文采用的混合模拟方法可以捕捉到湍流边界层中的大尺度结构且入口边界层平均参数不会发生漂移, 混合函数应当将RANS区域和LES区域的过渡点设置在对数律层和尾迹律层的交界处, 而过渡应当迅速以获得正确的雷诺剪切应力分布, 在该文采用的模型及数值方法的条件下, 流向及展向的网格小至与Escudier混合长相当时, 能够获得可以接受的脉动速度的单点-二阶统计值.     

Features of a Turbulent Jet at High Supersonic Velocities

The results of modeling a turbulent supersonic jet at M = 5 using large-eddy simulation (LES) are presented. The structural features of turbulence formed in this flow are analyzed. The possibilities of the large-eddy simulation method and the complexities of simulation of the compressibility effects in jet flows at high Mach numbers are considered. Such features of the supersonic jet as the local turbulent shocklets and Mach waves are reproduced numerically. It is shown that in the neighborhood of the jet the trajectories of ejection flow are located along the front of Mach waves. Anisotropic turbulent structures whose longitudinal scale is greater than the transverse scale by an order of magnitude are revealed in the jet. An estimate of the baroclinic effects shows their weak influence on the vorticity generation in the jet flow considered.     

Wall modeling for implicit large-eddy simulation and immersed-interface methods

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re _τ  = 395 up to Re _τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re _h = 5,000 and the periodic hill at Re _H = 10,595 and Re _H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.     

Assessment of the modulated gradient model in decaying isotropic turbulence

A recently introduced nonlinear model undergoes evaluations based on two isotropic turbulent cases: a University of Wiscosion-Madison case at a moderate Reynolds number and a Johns Hopkins University case at a high Reynolds number. The model uses an estimation of the subgrid-scale (SGS) kinetic energy to model the magnitude of the SGS stress tensor, and uses the normalized velocity gradient tensor to model the structure of the SGS stress tensor. Testing is performed for the first case through a comparison between direct numerical simulation (DNS) results and large eddy simulation (LES) results regarding resolved kinetic energy and energy spectrum. In the second case, we examine the resolved kinetic energy, the energy spectrum, as well as other key statistics including the probability density functions of velocities and velocity gradients, the skewness factors, and the flatness factors. Simulations using the model are numerically stable, and results are satisfactorily compared with DNS results and consistent with statistical theories of turbulence.     

A von Neumann–Smagorinsky turbulent transport model for stratified shear flows

A simple subgrid turbulent diffusion model based on an analogy to the von Neumann–Richtmyer artificial viscosity is explored for use in modelling mixing in turbulent stratified shear flow. The model may be more generally applicable to multicomponent turbulent hydrodynamics and to subgrid turbulent transport of momentum, composition and energy. As in the case of the von Neumann artificial viscosity and many subgrid-scale models for large-eddy simulation, the turbulent diffusivity explicitly depends on the grid size and is not based on a quantitative model of the unresolved turbulence. In order to address the issue that it is often not known a priori when and where a flow will become turbulent, the turbulent diffusivity is set to zero when the flow is expected to be stable on the basis of a Richardson/Rayleigh–Taylor stability criterion, in analogy to setting the von Neumann artificial viscosity to zero in expanding flows. One-dimensional predictions of this model applied to a simple shear flow configuration are compared to those obtained using a K–ε model. The density and velocity profiles predicted by both models are shown to be very similar.     

COMPARISION OF NUMERICAL SCHEMES IN LARGE-EDDY SIMULATION OF THE TEMPORAL MIXING LAYER

A posteriori tests of large-eddy simulations for the temporal mixing layer are performed using a variety of numerical methods in conjunction with the dynamic mixed subgrid model for the turbulent stress tensor. The results of the large-eddy simulations are compared with filtered direct numerical simulation (DNS) results. Five numerical methods are considered. The cell vertex scheme (A) is a weighted second-order central difference. The transverse weighting is shown to be necessary, since the standard second-order central difference (A′) gives rise to instabilities. By analogy, a new weighted fourth-order central difference (B) is constructed in order to overcome the instability in simulations with the standard fourth-order central method (B′). Furthermore, a spectral scheme (C) is tested. Simulations using these schemes have been performed for the case where the filter width equals the grid size (I) and the case where the filter width equals twice the grid size (II). The filtered DNS results are best approximated in case II for each of the numerical methods A, B and C. The deviations from the filtered DNS data are decomposed into modelling error effects and discretization error effects. In case I the absolute modelling error effects are smaller than in case II owing to the smaller filter width, whereas the discretization error effects are larger, since the flow field contains more small-scale contributions. In case I scheme A is preferred over scheme B, whereas in case II the situation is the reverse. In both cases the spectral scheme C provides the most accurate results but at the expense of a considerably increased computational cost. For the prediction of some quantities the discretization errors are observed to eliminate the modelling errors to some extent and give rise to reduced total errors.     

Confined and Agitated Swirling Flows with Applications in Chemical Engineering

Turbulent, swirling flows are encountered frequently in chemical engineering practice. In this article, experiments and simulations on two classes of swirling flows, viz. agitated flows (stirred tanks), and confined swirling flows are discussed. Results of large-eddy simulations of stirred tank flow are compared with experimental data, mainly phase-resolved LDA data of the flow in the vicinity of the impeller. Next to the average velocity field, also the turbulent kinetic energy, and the anisotropy of the Reynolds stress tensor have been assessed. An important application of confined swirling flow is the cyclone separator (hydrocyclones for the separation of liquids, gas cyclones for gas-solid separation). The flow in a swirl tube geometry exhibiting many of the typical features of swirl flows (e.g. vortex breakdown) is discussed. Furthermore, a large-eddy simulation of the gas flow in a high-efficiency Stairmand cyclone separator is presented. Two examples of process modeling based on flow simulations are briefly treated: orthokinetic agglomeration of crystals in a stirred tank, and particle separation in a cyclone. This revised version was published online in July 2006 with corrections to the Cover Date.     

Approximate Wall Boundary Conditions in the Large-Eddy Simulation of High Reynolds Number Flow

The near-wall regions of high Reynolds numbers turbulent flows must be modelled to treat many practical engineering and aeronautical applications. In this review we examine results from simulations of both attached and separated flows on coarse grids in which the near-wall regions are not resolved and are instead represented by approximate wall boundary conditions. The simulations use the dynamic Smagorinsky subgrid-scale model and a second-order finite-difference method. Typical results are found to be mixed, with acceptable results found in many cases in the core of the flow far from the walls, provided there is adequate numerical resolution, but with poorer results generally found near the wall. Deficiencies in this approach are caused in part by both inaccuracies in subgrid-scale modelling and numerical errors in the low-order finite-difference method on coarse near-wall grids, which should be taken into account when constructing models and performing large-eddy simulation on coarse grids. A promising new method for developing wall models from optimal control theory is also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.