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.      

A large eddy simulation of the near wake of a circular cylinder

Viscous flow around a circular cylinder at a subcritical Reynolds number is investigated using a large eddy simulation (LES) coupled with the Smagorinsky subgrid-scale (SGS) model. A fractional-step method with a second-order in time and a combined finite-difference/spectral approximations are used to solve the filtered three-dimensional incompressible Navier-Stokes equations. Calculations have been performed with and without the SGS model. Turbulence statistical behaviors and flow structures in the near wake of the cylinder are studied. Some calculated results, including the lift and drag coefficients, shedding frequency, peak Reynolds stresses, and time-average velocity profile, are in good agreement with the experimental and computational data, which shows that the Smagorinsky model can reasonably predict the global features of the flow and some turbulent statistical behaviors. The project supported by the National Science Fund for Distinguished Scholars (10125210), the Special Funds for Major State Basic Research Project (G1999032801) and the National Natural Science Foundation of China (19772062)     

Shear‐improved Smagorinsky modeling of turbulent channel flow using generalized Lattice Boltzmann equation

Generalized Lattice Boltzmann equation (GLBE) was used for computation of turbulent channel flow for which large eddy simulation (LES) was employed as a turbulence model. The subgrid‐scale turbulence effects were simulated through a shear‐improved Smagorinsky model (SISM), which is capable of predicting turbulent near wall region accurately without any wall function. Computations were done for a relatively coarse grid with shear Reynolds number of 180 in a parallelized code. Good numerical stability was observed for this computational framework. The results of mean velocity distribution across the channel showed good correspondence with direct numerical simulation (DNS) data. Negligible discrepancies were observed between the present computations and those reported from DNS for the computed turbulent statistics. Three‐dimensional instantaneous vorticity contours showed complex vortical structures that appeared in such flow geometries. It was concluded that such a framework is capable of predicting accurate results for turbulent channel flow without adding significant complications and the computational cost to the standard Smagorinsky model. As this modeling was entirely local in space it was therefore adapted for parallelization. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical prediction of turbulent flows using Reynolds‐averaged Navier–Stokes and large‐eddy simulation with uncertain inflow conditions

Numerous comparisons between Reynolds‐averaged Navier–Stokes (RANS) and large‐eddy simulation (LES) modeling have already been performed for a large variety of turbulent flows in the context of fully deterministic flows, that is, with fixed flow and model parameters. More recently, RANS and LES have been separately assessed in conjunction with stochastic flow and/or model parameters. The present paper performs a comparison of the RANS k ? ε model and the LES dynamic Smagorinsky model for turbulent flow in a pipe geometry subject to uncertain inflow conditions. The influence of the experimental uncertainties on the computed flow is analyzed using a non‐intrusive polynomial chaos approach for two flow configurations (with or without swirl). Measured quantities including an estimation of the measurement error are then compared with the statistical representation (mean value and variance) of their RANS and LES numerical approximations in order to check whether experiment/simulation discrepancies can be explained within the uncertainty inherent to the studied configuration. The statistics of the RANS prediction are found in poor agreement with experimental results when the flow is characterized by a strong swirl, whereas the computationally more expensive LES prediction remains statistically well inside the measurement intervals for the key flow quantities.Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

A mixed-timescale SGS model for thermal field at various Prandtl numbers

A new subgrid-scale (SGS) model for the thermal field is proposed. The model is an extended version of the mixed-timescale (MTS) SGS model for velocity field by Inagaki et al. (2005), which has been confirmed to be a refined SGS model for velocity field suited to engineering-relevant practical large eddy simulation (LES). In the proposed model for the thermal field, a hybrid timescale between the timescales of the velocity and thermal fields is introduced in a manner similar to velocity-field modeling. Thus, the present model dispenses with an ambiguous SGS turbulent Prandtl number, like the dynamic SGS model. In addition, the wall-limiting behavior of turbulence is satisfied, which is not in the original MTS model, by incorporating the wall-damping function for LES based on the Kolmogorov velocity scale proposed by Inagaki et al. (2010). The model performance is tested in plane channel flows at various Prandtl numbers, and the results show that this model gives the ratio of the timescales between the velocity and thermal fields similar to that obtained using the dynamic Smagorinsky model with locally calculated model parameters. It is also shown that the proposed model predicts better mean and fluctuating temperature profiles in cooperation with the revised MTS model for the velocity field, than the Smagorinsky model and the dynamic Smagorinsky model. The present model is constructed with fixed model parameters, so that it does not suffer from computational instability with the dynamic model. Thus, it is expected to be a refined and versatile SGS model suited for practical LES of the thermal field.     

Large eddy simulation of free surface shallow‐water flow

Shallow‐water flow with free surface frequently occurs in ambient water bodies, in which the horizontal scale of motion is generally two orders of magnitude greater than the water depth. To accurately predict this flow phenomenon in more detail, a three‐dimensional numerical model incorporating the method of large eddy simulation (LES) has been developed and assessed. The governing equations are split into three parts in the finite difference solution: advection, dispersion and propagation. The advection part is solved by the QUICKEST scheme. The dispersion part is solved by the central difference method and the propagation part is solved implicitly using the Gauss–Seidel iteration method. The model has been applied to free surface channel flow for which ample experimental data are available for verification. The inflow boundary condition for turbulence is generated by a spectral line processor. The computed results compare favourably with the experimental data and those results obtained by using a periodic boundary condition. The performance of the model is also assessed for the case in which anisotropic grids and filters with horizontal grid size of the order of the water depth are used for computational efficiency. The coarse horizontal grid was found to cause a significant reduction in the large‐scale turbulent motion generated by the bottom turbulence, and the turbulent motion is predominately described by the sub‐grid scale (SGS) terms. The use of the Smagorinsky model for SGS turbulence in this situation is found inappropriate. A parabolic mixing length model, which accounts for the filtered turbulence, is then proposed. The new model can reproduce more accurately the flow quantities. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

基于大涡模拟的移动粒子半隐式法研究

将大涡模拟(LES)和无网格的移动粒子半隐式法(MPS)相结合, 以求解湍流中的自由表面问题. 对N-S方程进行滤波计算可得到大涡模拟的控制方程, 大涡模拟的控制方程相对于以往的移动粒子半隐式法而言仅多出雷诺应力项, 通过亚粒子应力(sub-particle-scale,SPS)模型并引入Smagorinsky涡黏模型将雷诺应力模型化, 可实现移动粒子半隐式法的大涡模拟. 将MPS-LES应用至具有大变形自由表面的共振晃荡中, 其模拟结果同实验及其他数值模拟结果都相当接近.      

Evaluation of Smagorinsky‐based subgrid‐scale models in a finite‐volume computation

Smagorinsky‐based models are assessed in a turbulent channel flow simulation at Re_b=2800 and Re_b=12500. The Navier–Stokes equations are solved with three different grid resolutions by using a co‐located finite‐volume method. Computations are repeated with Smagorinsky‐based subgrid‐scale models. A traditional Smagorinsky model is implemented with a van Driest damping function. A dynamic model assumes a similarity of the subgrid and the subtest Reynolds stresses and an explicit filtering operation is required. A top‐hat test filter is implemented with a trapezoidal and a Simpson rule. At the low Reynolds number computation none of the tested models improves the results at any grid level compared to the calculations with no model. The effect of the subgrid‐scale model is reduced as the grid is refined. The numerical implementation of the test filter influences on the result. At the higher Reynolds number the subgrid‐scale models stabilize the computation. An analysis of an accurately resolved flow field reveals that the discretization error overwhelms the subgrid term at Re_b=2800 in the most part of the computational domain. Copyright © 2002 John Wiley & Sons, Ltd.     

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 hard-sphere 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.     

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.     

Large eddy simulation using a dynamic mixing length subgrid‐scale model

A novel dynamic mixing length (DML) subgrid‐scale model for large eddy simulations is proposed in this work to improve the cutoff length of the Smagorinsky model. The characteristic mixing length (or the characteristic wave number) is dynamically estimated for the subgrid‐scale fluctuation of turbulence by the cutoff wave‐number, k_c, and the dissipation wave‐number, k_d. The dissipation wave number is derived from the kinetic energy spectrum equation and the dissipation spectrum equation. To prove the promise of the DML model, this model is used to simulate the lid‐driven cubical cavity with max‐velocity‐based Reynolds numbers 8850 and 12,000, the channel flows with friction‐velocity‐based Reynolds numbers 180, 395, 590, and 950, and the turbulent flow past a square cylinder at the higher Reynolds number 21,400, respectively, compared with the Smagorinsky model and Germano et al.'s dynamic Smagorinsky model. Different numerical experiments with different Reynolds numbers show that the DML model can be used in simulations of flows with a wide range of Reynolds numbers without the occurrence of singular values. The DML model can alleviate the dissipation of the Smagorinsky model without the loss of its robustness. The DML model shows some advantages over Germano et al.'s dynamic Smagorinsky model in its high stability and simplicity of calculation because the coefficient of the DML model always stays positive. The characteristic mixing length in the DML model reflects the subgrid‐scale fluctuation of turbulence in nature and thus the characteristic mixing length has a spatial and temporal distribution in turbulent flow. Copyright © 2011 John Wiley & Sons, Ltd.     

Large Eddy Simulations of the Flow in the Near-Field Region of a Turbulent Buoyant Helium Plume

Large eddy simulations are conducted in the near-field region of a large turbulent buoyant helium plume. The CFD package FireFOAM is applied to that purpose. The transient and mean flow dynamics are discussed as a function of grid resolution, with and without the use of the standard Smagorinsky subgrid scale (SGS) model. Small scale structures, formed at the edge of the plume inlet due to baroclinic and gravitational mechanisms and subject to flow instabilities, interact with large scale features of the flow, resulting in a puffing cycle. In general, the LES calculations reproduce the main features of the turbulent plume, with better agreement when the Smagorinsky type SGS model is applied. In particular, the puffing cycle is recovered in the simulations with correct frequency. The mean and rms values of the velocity components are well predicted with use of the SGS model, even on relatively coarse meshes. Agreement for the species mass fraction (mean and rms values) is less satisfactory, but in line with results found in the literature.     

Implicit large eddy simulation of a supersonic flat-plate boundary layer flow by weighted compact nonlinear scheme

The performance of implicit large eddy simulation (ILES) of a supersonic flat-plate turbulent boundary layer flow by weighted compact nonlinear scheme (WCNS) has been investigated. In view of features of WCNS and ILES, it was expected that ILES by WCNS could be an efficient approach to perform LES of supersonic turbulent flows. The flowfield calculated by WCNS was of lower turbulent intensity compared with an explicit LES data obtained by a numerical scheme of the same order of accuracy on a computational grid of similar resolution. It was concluded that the numerical dissipation inherent in WCNS is so large that applying WCNS to ILES of this flowfield is inefficient compared with explicit LES.     

Large eddy simulation of gas-particle turbulent channel flow with momentum exchange between the phases

This paper presents results of a large eddy simulation (LES) combined with Lagrangian particle tracking and a point-force approximation for the feedback effect of particles on the downward turbulent gaseous flow in a vertical channel. The LES predictions are compared with the results obtained by direct numerical simulation (DNS) of a finer computational mesh. A parametric study is conducted for particles with two response times in simulations with and without streamwise gravitational settling and elastic, binary interparticle collisions. It is shown that the classical and the dynamic Smagorinsky turbulence models adequately predict the particle-induced changes in the mean streamwise velocity and the Reynolds stresses of the carrier phase for the range of parameters studied. However, the largest discrepancies between the LES and DNS results are found in the cases of particle-laden flows. Conditional sampling of the instantaneous resolved flow fields indicates that the mechanisms by which particles directly oppose the production of momentum and vorticity of the organized fluid motions are also observed in the LES results. However, the geometric features of the near-wall quasistreamwise vortices are overestimated by the use of both turbulence models compared to the DNS predictions.     

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     

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.     

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.     

Usability of explicit filtering in large eddy simulation with a low‐order numerical scheme and different subgrid‐scale models

Based on a priori tests, in large eddy simulation (LES) of turbulent fluid flow, the numerical error related to low‐order finite‐difference‐type methods can be large in comparison with the effect of subgrid‐scale (SGS) model. Explicit filtering has been suggested to reduce the error, and it has shown promising results in a priori studies and in some simulations with fourth‐order method. In this paper, the effect of explicit filtering on the total simulation error is studied together with a second‐order scheme, where the numerical error should be even larger. The fully developed turbulent channel flow between two parallel walls is used as a test case. Rather simple SGS models are applied, because these models are most likely used in practical applications of LES. Explicit filtering is here applied to the non‐linear convection term of the Navier–Stokes equations, four three‐dimensional filter functions are applied, and the effect of filtering is separated from the effect of SGS modelling. It is shown that the effect of filtering is rather large and smooth filters introduce an additional error component that increases the total simulation error. Finally, filtering via subfilter‐scale modelling is applied, and it is shown that this approach performs better. However, the large‐frequency components of the resolved flow field are not as effectively damped as when the non‐linear convection term is filtered. Copyright © 2007 John Wiley & Sons, Ltd.