A new dynamic formula for determining the coefficient of Smagorinsky model

The most common method to determine the coefficient of Smagorinsky model now is to employ the Germano identity, however it is too complex and expensive in numerical calculation. In this letter we propose a new dynamic formula for determining the coefficient, which is based on the Kolmogorov equation of filtered velocity in physical space. The simplified formula is quite easy to implement in calculation. It is then verified in both homogeneous isotropic turbulence and wall-bounded turbulence by A Priori and A Posteriori tests.     

A new wall-damping function for large eddy simulation employing Kolmogorov velocity scale

A new wall-damping function, based on the Kolmogorov velocity scale, for large eddy simulation (LES) is proposed, which accounts for the near-wall effect. To calculate the Kolmogorov velocity scale, u_ε, the dissipation rate of turbulent energy, ε, is needed. In LES, however, the dissipation rate is generally not solved, unlike in the Reynolds averaged Navier-Stokes (RANS) simulations, e.g., k-ε models. Although, in some previous studies, the dissipation rate of the subgrid-scale (SGS) turbulent energy, ε_SGS, is used instead of ε in calculating the Kolmogorov velocity scale, the scale obtained using such a method overly depends on the grid resolution employed and is generally inappropriate. Accordingly, the wall-damping function using the incorrect velocity scale also depends on the grid resolution and gives an inadequate wall effect. This is because ε_SGS contains only the components in the scale smaller than the grid-filter width, which obviously varies with the grid resolution employed. In this study, to overcome this problem, we propose a method for estimating the Kolmogorov velocity scale with a technique of conversion in LES, and the estimated one is utilized in the wall-damping function. The revised wall-damping function for LES is tested in channel flows and a backward-facing step flow. The results show that it yields a proper near-wall effect in all test cases which cover a wide range of grid resolution and Reynolds numbers. It is also shown that all three kinds of SGS models incorporating the present wall-damping function provide good predictions, and it is effective both in one-equation and 0-equation SGS models. These results suggest that the use of the proposed wall-damping function is a refined and versatile near-wall treatment in LES with various kinds of SGS models.     

基于全局动态Vreman模型的复杂非定常湍流的大涡模拟

在湍流数值模拟方法中,大涡模拟方法可以提供丰富的大涡旋信息,已逐渐成为复杂湍流问题数值研究的重要方法。而大涡模拟中,最重要的一环是尽量准确地构建能反映流场物理本质特征的亚格子应力模型。基于该思想,将一种新型的大涡模拟亚格子应力模型-Vreman亚格子应力模型用于高雷诺数三维后台阶流动的求解,计算结果与实验结果进行对比分析结果较吻合,验证了该模型的可靠性。这是对该模型用于无任何均匀流动方向的高雷诺数复杂湍流非定常流动的首次检验,计算结果优于基于传统的Smagorinsky涡粘性的动态亚格子模型。     

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)     

An improved large eddy simulation of two-phase flows in a pump impeller

An improved large eddy simulation using a dynamic second-order sub-grid-scale (SGS) stress model has been developed to model the governing equations of dense turbulent particle-liquid two-phase flows in a rotating coordinate system, and continuity is conserved by a mass-weighted method to solve the filtered governing equations. In the current second-order SGS model, the SGS stress is a function of both the resolved strain-rate and rotation-rate tensors, and the model parameters are obtained from the dimensional consistency and the invariants of the strain-rate and the rotation-rate tensors. In the numerical calculation, the finite volume method is used to discretize the governing equations with a staggered grid system. The SIMPLEC algorithm is applied for the solution of the discretized governing equations. Body-fitted coordinates are used to simulate the two-phase flows in complex geometries. Finally the second-order dynamic SGS model is successfully applied to simulate the dense turbulent particle-liquid two-phase flows in a centrifugal impeller. The predicted pressure and velocity distributions are in good agreement with experimental results. The project supported by the National Natural Science Foundation of China (50779069 and 90510007), the Start-up Scientific Research Foundation of China Agricultural University (2006021) and the Beijing Natural Science Foundation (3071002).     

A dynamic eddy-viscosity closure model for large eddy simulations of two-dimensional decaying turbulence

This paper puts forth a simplified dynamic eddy-viscosity subgrid-scale model for the vorticity transport equation which is employed in a large eddy simulation study of freely evolving isotropic two-dimensional turbulent flows. The dynamic parameter is averaged in space, thereby retrieving a spatially constant value which only varies in time. The proposed dynamic model is applied to a two-dimensional decaying turbulence problem in a square periodic box, which is a standard prototype of more realistic turbulent flows in the atmosphere and oceans, in order to eliminate any possible errors associated with the boundary conditions or mesh non-uniformities. Compared with high-resolution direct numerical simulations, the performance of the dynamic model is systematically investigated considering various filtering strategies by means of test filters. The effects of the computational resolution and the filtering ratio between the test and the grid filters are also studied by using a huge set of 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.     

适用于浸入边界法的大涡模拟紊流壁面模型

基于近壁定常剪切应力假设,提出了一种新的适用于浸入边界法的大涡模拟紊流壁面模型。通过引入壁面滑移速度,修正了线性速度剖面计算得到的壁面剪切应力,使之满足Werner-Wengle模型。将其应用于平板紊流和高Re数圆管紊流的数值模拟,对比采用和不采用壁面模型的结果得知,采用此模型的速度剖面与实验值吻合良好,验证了此模型的有效性。研究了不同欧拉/拉格朗日网格相对位置对结果的影响,证明了此模型具有较好的鲁棒性,以及可根据局部流动状态和网格精度自动开闭的特点。     

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.     

A low Reynolds number variant of partially-averaged Navier-Stokes model for turbulence

A low Reynolds number (LRN) formulation based on the Partially Averaged Navier-Stokes (PANS) modelling method is presented, which incorporates improved asymptotic representation in near-wall turbulence modelling. The effect of near-wall viscous damping can thus be better accounted for in simulations of wall-bounded turbulent flows. The proposed LRN PANS model uses an LRN k-ε model as the base model and introduces directly its model functions into the PANS formulation. As a result, the inappropriate wall-limiting behavior inherent in the original PANS model is corrected. An interesting feature of the PANS model is that the turbulent Prandtl numbers in the k and ε equations are modified compared to the base model. It is found that this modification has a significant effect on the modelled turbulence. The proposed LRN PANS model is scrutinized in computations of decaying grid turbulence, turbulent channel flow and periodic hill flow, of which the latter has been computed at two different Reynolds numbers of Re = 10,600 and 37,000. In comparison with available DNS, LES or experimental data, the LRN PANS model produces improved predictions over the standard PANS model, particularly in the near-wall region and for resolved turbulence statistics. Furthermore, the LRN PANS model gives similar or better results - at a reduced CPU time - as compared to the Dynamic Smagorinsky model.     

Dissipation in Turbulent Shear Flows: A Wall Function Approach for High Reynolds Numbers

Dissipation effects that are neglected in almost all numerical codes when it comes to turbulent flows are analysed systematically. It is shown how the direct and the indirect dissipation can be implemented into the codes when asymptotic considerations about the flow behaviour close to a wall are taken into account. As an example, adiabatic pipe flow is analysed with special emphasis on the distribution of energy between the mechanical and thermal part of the total energy.     

An investigation of thermally stratified turbulent channel flow with temperature oscillation on the bottom wall by large eddy simulation

Thermally stratified shear turbulent channel flow with temperature oscillation on the bottom wall of the channel is calculated to investigate the behavior of turbulent flow and heat transfer by use of large eddy simulation (LES) approach coupled with dynamic subgrid-scale (SGS) models. The objective of this study is to deal with the effect of the temperature oscillation on turbulent behavior of thermally stratified turbulent channel flow and to examine the effectiveness of the LES technique for predicting statistically unsteady turbulent flow driven by time-varying buoyancy force. To validate the present calculation, thermally stratified shear turbulent channel flow is computed and compared with available data obtained by direct numerical simulation (DNS), which confirm that the present approach can be used to predict thermally stratified turbulent channel flow satisfactorily. Further, to illustrate the effect of the temperature oscillation with different Richardson numbers and periods of the oscillation on turbulence characteristics, the phase-averaged mean value and fluctuation of the resolved velocities and temperature, and instantaneous velocity fluctuation structures are analyzed.     

A complete and irreducible dynamic SGS heat-flux modelling based on the strain rate tensor for large-eddy simulation of thermal convection

In this paper, a general family of explicit algebraic tensor diffusivity functions based on the resolved temperature gradient vector and strain rate tensor is studied and applied to the construction of new constitutive relations for modelling the subgrid-scale (SGS) heat flux (HF). Based on Noll’s formulation, dynamic linear and nonlinear tensor diffusivity models are proposed for large-eddy simulation of thermal convection. The constitutive relations for these two proposed models are complete and irreducible. These two new models include several existing dynamic SGS HF models as special cases. It is shown that in contrast to the conventional modelling approach, the proposed models embody more degrees of freedom, permit non-alignment between the SGS HF and resolved temperature gradient vectors, reflect near-wall flow physics at the subgrid scale, and therefore, allow for a more realistic geometrical representation of the SGS heat flux for large-eddy simulation of thermal convection. Numerical simulations have been performed using a benchmark test case of a combined forced and natural convective flow in a vertical channel with a Reynolds number of and a Grashof number of Gr = 9.6 × 10⁵. The results obtained using the two proposed SGS HF models are compared with reported direct numerical simulation (DNS) data as well as predictions obtained using several conventional dynamic SGS HF models.     

Large eddy simulation and a simple wall model for turbulent flow calculation by a particle method

A turbulent channel flow and the flow around a cubic obstacle are calculated by the moving particle semi‐implicit method with the subparticle‐scale turbulent model and a wall model, which is based on the zero equation RANS (Reynolds Averaged Navier‐Stokes). The wall model is useful in practical problems that often involve high Reynolds numbers and wall turbulence, because it is difficult to keep high resolution in the near‐wall region in particle simulation. A turbulent channel flow is calculated by the present method to validate our wall model. The mean velocity distribution agrees with the log‐law velocity profile near the wall. Statistical values are also the same order and tendency as experimental results with emulating viscous layer by the wall model. We also investigated the influence of numerical oscillations on turbulence analysis in using the moving particle semi‐implicit method. Finally, the turbulent flow around a cubic obstacle is calculated by the present method to demonstrate capability of calculating practical turbulent flows. Three characteristic eddies appear in front of, over, and in the back of the cube both in our calculation and the experimental result that was obtained by Martinuzzi and Tropea. Mean velocity and turbulent intensity profiles are predicted in the same order and have similar tendency as the experimental result. Copyright © 2012 John Wiley & Sons, Ltd.     

A study on the behaviour of high-order flux reconstruction method with different low-dissipation numerical fluxes for large eddy simulation

This work focuses on the numerical dissipation features of high-order flux reconstruction (FR) method combined with different numerical fluxes in turbulence flows. The famous Roe and AUSM+ numerical fluxes together with their corresponding low-dissipation enhanced versions (LMRoe, SLAU2) and higher resolution variants (HR-LMRoe, HR-SLAU2) are incorporated into FR framework, and the dissipation interplay of these combinations is investigated in implicit large eddy simulation. The numerical dissipation stemming from these convective numerical fluxes is quantified by simulating the inviscid Gresho vortex, the transitional Taylor–Green vortex and the homogenous decaying isotropic turbulence. The results suggest that low-dissipation enhanced versions are preferential both in high-order and low-order cases to their original forms, while the use of HR-SLAU2 has marginal improvements and the HR-LMRoe leads to degenerated solution with high-order. In high-order the effects of numerical fluxes are reduced, and their viscosity may not be dissipative enough to provide physically consistent turbulence when under-resolved.     

A coupled model for multiphase fluid flow and sedimentation deformation in oil reservoir and its numerical simulation

A mathematical model for coupled multiphase fluid flow and sedimentation deformation is developed based on fluid-solid interaction mechanism. A finite difference-finite element numerical approach is presented. The results of an example show that the fluid-solid coupled effect has great influence on multiphase fluid flow and reservoir recovery performances, and the coupled model has practical significance for oilfield development.