Large eddy simulations of wall‐bounded flows using a simplified immersed boundary method and high‐order compact schemes

This paper presents a solution algorithm based on an immersed boundary (IB) method that can be easily implemented in high‐order codes for incompressible flows. The time integration is performed using a predictor‐corrector approach, and the projection method is used for pressure‐velocity coupling. Spatial discretization is based on compact difference schemes and is performed on half‐staggered meshes. A basic algorithm for body‐fitted meshes using the aforementioned solution method was developed by A. Tyliszczak (see article “A high‐order compact difference algorithm for half‐staggered grids for laminar and turbulent incompressible flows” in Journal of Computational Physics) and proved to be very accurate. In this paper, the formulated algorithm is adapted for use with the IB method in the framework of large eddy simulations. The IB method is implemented using its simplified variant without the interpolation (stepwise approach). The computations are performed for a laminar flow around a 2D cylinder, a turbulent flow in a channel with a wavy wall, and around a sphere. Comparisons with literature data confirm that the proposed method can be successfully applied for complex flow problems. The results are verified using the classical approach with body‐fitted meshes and show very good agreement both in laminar and turbulent regimes. The mean (velocity and turbulent kinetic energy profiles and drag coefficients) and time‐dependent (Strouhal number based on the drag coefficient) quantities are analyzed, and they agree well with reference solutions. Two subfilter models are compared, ie, the model of Vreman (see article “An eddy‐viscosity subgrid‐scale model for turbulent shear flow: algebraic theory and applications” in Physics and Fluids) and σ model (Nicoud et al, see article “Using singular values to build a subgrid‐scale model for large eddy simulations” in Physics and Fluids). The tests did not reveal evident advantages of any of these models, and from the point of view of solution accuracy, the quality of the computational meshes turned out to be much more important than the subfilter modeling.     

An improved near‐wall modeling for large‐eddy simulation using immersed boundary methods

An improved near‐wall modeling for large‐eddy simulation using the immersed boundary method is proposed. It is shown in this study that the existing near‐wall modeling for the immersed boundary (IB) methods that imposes the velocity boundary condition at the IB node is not sufficient to enforce a correct wall shear stress at the IB node. A new method that imposes a shear stress condition through the modification of the subgrid scale‐eddy viscosity at the IB node is proposed. In this method, the subgrid eddy viscosity at the IB node is modified such that the viscous flux at the face adjacent to the IB node correctly approximates the total shear stress. The method is applied to simulate the fully developed turbulent flows in a plane channel and a circular pipe. It is demonstrated that the new method improves the prediction of the mean velocity and turbulence stresses in comparison with the existing wall modeling based solely on the velocity boundary condition. Copyright © 2015 John Wiley & Sons, Ltd.     

An algebraic variational multiscale–multigrid method for large‐eddy simulation of turbulent pulsatile flows in complex geometries with detailed insight into pulmonary airway flow

The algebraic variational multiscale–multigrid method, an advanced computational approach recently proposed for large‐eddy simulation of turbulent flow, is further developed in this study for turbulent flow simulations in complex geometries. In particular, it is applied to the complex case of pulsatile turbulent flow dynamics of the upper and lower pulmonary airways up to generation 7 and carefully investigated for this important application. Among other things, the results obtained with the proposed method are compared with the results obtained with a rather traditional stabilized finite element method. As opposed to previous large‐eddy simulations of pulmonary airways, we consider a pulsatile inflow condition, allowing the development of turbulence over a pulse cycle to be investigated, which obviously makes these results more physiologically realistic. Our results suggest that turbulent effects in the bronchial airways are rather weak and can completely decay as early as the third generation, depending on geometry and flow distribution. Both methods utilized in this study are able to adequately capture all flow stages from laminar via transitional to turbulent regimes without any modifications. However, the algebraic variational multiscale–multigrid method provides superior results as soon as the flow enters the most challenging, turbulent flow regime. Furthermore, the robustness of the scale‐separation approach based on plain aggregation algebraic multigrid inherent to the algebraic variational multiscale–multigrid method is demonstrated for the present complex geometry. Copyright © 2012 John Wiley & Sons, Ltd.     

A RESIDUAL-BASED UNRESOLVED-SCALE FINITE ELEMENT MODELLING FOR IMPLICT LARGE EDDY SIMULATION 1)

对应于湍流的大尺度与小尺度流场信息, 本文在有限元的框架下, 假设Navier-Stokes方程的解的形函数由大尺度和不可解尺度形函数叠加组成, 引入对应的权函数, 将Navier-Stokes方程的有限元变分形式分解为大尺度和不可解尺度系统. 根据不可解尺度系统, 构建基于Navier-Stokes大尺度方程残差的不可解尺度模型, 将其代入Navier-Stokes方程的大尺度系统, 进而数值求解大尺度系统得到Navier-Stokes方程的大尺度解. 该方法无需像传统的大涡模拟方法那样对方程的解进行过滤, 通过对形函数进行尺度分解实现解的尺度分解. 本文使用该方法的自编程序代码开展了槽道湍流的数值模拟. 通过与有限差分大涡模拟、DNS计算结果的比较, 发现在使用较少网格情况下该方法预测的平均流向速度在近壁区与DNS数据吻合, 在黏性外层略偏高; 该方法对雷诺应力预测偏低导致从流向向垂向方向上湍动能输运略偏低. 流向速度等值面图显示该方法有效捕捉到了大尺度旋涡结构; 同时在近壁区可以观察到明显的低速条带结构.     

An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows

In this paper, an immersed boundary (IB) method is developed to simulate compressible turbulent flows governed by the Reynolds‐averaged Navier‐Stokes equations. The flow variables at the IB nodes (interior nodes in the immediate vicinity of the solid wall) are evaluated via linear interpolation in the normal direction to close the discrete form of the governing equations. An adaptive wall function and a 2‐layer wall model are introduced to reduce the near‐wall mesh density required by the high resolution of the turbulent boundary layers. The wall shear stress modified by the wall modeling technique and the no‐penetration condition are enforced to evaluate the velocity at an IB node. The pressure and temperature at an IB node are obtained via the local simplified momentum equation and the Crocco‐Busemann relation, respectively. The SST k ? ω and S‐A turbulence models are adopted in the framework of the present IB approach. For the Shear‐Stress Transport (SST) k ? ω model, analytical solutions in near‐wall region are utilized to enforce the boundary conditions of the turbulence equations and evaluate the turbulence variables at an IB node. For the S‐A model, the turbulence variable at an IB node is calculated by using the near‐wall profile of the eddy viscosity. In order to validate the present IB approach, numerical experiments for compressible turbulent flows over stationary and moving bodies have been performed. The predictions show good agreements with the referenced experimental data and numerical results.     

Hybrid LES-RANS: An approach to make LES applicable at high Reynolds number

The main bottle neck for using large eddy simulations (LES) at high Reynolds number is the requirement of very fine meshes near walls. Hybrid LES-Reynolds-averaged Navier-Stokes (RANS) was invented to get rid of this limitation. In this method, unsteady RANS (URANS) is used near walls and away from walls LES is used. The matching between URANS and LES takes place in the inner log-region. In the present paper, a method to improve standard LES-RANS is evaluated. The improvement consists of adding instantaneous turbulent fluctuations (forcing conditions) at the matching plane in order to provide the equations in the LES region with relevant turbulent structures. The fluctuations are taken from a DNS of a generic boundary layer. Simulations of fully developed channel flow and plane asymmetric diffuser flow are presented. Hybrid LES-RANS is used both with and without forcing conditions.     

基于Navier-Stokes方程残差的隐式大涡模拟有限元模型

对应于湍流的大尺度与小尺度流场信息, 本文在有限元的框架下, 假设Navier-Stokes方程的解的形函数由大尺度和不可解尺度形函数叠加组成, 引入对应的权函数, 将Navier-Stokes方程的有限元变分形式分解为大尺度和不可解尺度系统. 根据不可解尺度系统, 构建基于Navier-Stokes大尺度方程残差的不可解尺度模型, 将其代入Navier-Stokes方程的大尺度系统, 进而数值求解大尺度系统得到Navier-Stokes方程的大尺度解. 该方法无需像传统的大涡模拟方法那样对方程的解进行过滤, 通过对形函数进行尺度分解实现解的尺度分解. 本文使用该方法的自编程序代码开展了槽道湍流的数值模拟. 通过与有限差分大涡模拟、DNS计算结果的比较, 发现在使用较少网格情况下该方法预测的平均流向速度在近壁区与DNS数据吻合, 在黏性外层略偏高; 该方法对雷诺应力预测偏低导致从流向向垂向方向上湍动能输运略偏低. 流向速度等值面图显示该方法有效捕捉到了大尺度旋涡结构; 同时在近壁区可以观察到明显的低速条带结构.      

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 simple hybrid finite volume solver for compressible turbulence

A simple, explicit, hybrid finite volume method for simulating compressible turbulence is developed by combining a fourth‐order central scheme and a shock‐capturing simple low‐dissipation advection upstream splitting method. The total flux on each of the cell faces is computed as a weighted average of central/nondissipative and upwind/dissipative fluxes. The weights are determined using an unphysical oscillation sensor in addition to a more traditional discontinuity sensor used in earlier studies. Shocks are well captured, but overshoots in density are predicted around contact discontinuities that are normal to the flow. The use of the latter sensor effectively prevents these overshoots from generating spurious oscillations that travel away from the contact lines. The efficacy of the proposed method for direct or large‐eddy simulations of supersonic turbulence is established using several canonical test problems. Copyright © 2015 John Wiley & Sons, Ltd.     

A methodology for high performance computation of fully inhomogeneous turbulent flows

A large‐eddy simulation methodology for high performance parallel computation of statistically fully inhomogeneous turbulent flows on structured grids is presented. Strategies and algorithms to improve the memory efficiency as well as the parallel performance of the subgrid‐scale model, the factored scheme, and the Poisson solver on shared‐memory parallel platforms are proposed and evaluated. A novel combination of one‐dimensional red–black/line Gauss–Seidel and two‐dimensional red–black/line Gauss–Seidel methods is shown to provide high efficiency and performance for multigrid relaxation of the Poisson equation. Parallel speedups are measured on various shared‐distributed memory systems. Validations of the code are performed in large‐eddy simulations of turbulent flows through a straight channel and a square duct. Results obtained from the present solver employing a Lagrangian dynamic subgrid‐scale model show good agreements with other available data. The capability of the code for more complex flows is assessed by performing a large‐eddy simulation of the tip‐leakage flow in a linear cascade. Copyright © 2006 John Wiley & Sons, Ltd.     

Residual‐based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods

In this paper, we present a finite element method with a residual‐based artificial viscosity for simulation of turbulent compressible flow, with adaptive mesh refinement based on a posteriori error estimation with sensitivity information from an associated dual problem. The artificial viscosity acts as a numerical stabilization, as shock capturing, and as turbulence capturing for large eddy simulation of turbulent flow. The adaptive method resolves parts of the flow indicated by the a posteriori error estimates but leaves shocks and turbulence under‐resolved in a large eddy simulation. The method is tested for examples in 2D and 3D and is validated against experimental data. Copyright © 2012 John Wiley & Sons, Ltd.     

A filter‐based,mass‐conserving lattice Boltzmann method for immiscible multiphase flows

Some issues of He–Chen–Zhang lattice Boltzmann equation (LBE) method (referred as HCZ model) (J. Comput. Physics 1999; 152 :642–663) for immiscible multiphase flows with large density ratio are assessed in this paper. An extended HCZ model with a filter technique and mass correction procedure is proposed based on HCZ's LBE multiphase model. The original HCZ model is capable of maintaining a thin interface but is prone to generating unphysical oscillations in surface tension and index function at moderate values of density ratio. With a filtering technique, the monotonic variation of the index function across the interface is maintained with larger density ratio. Kim's surface tension formulation for diffuse–interface method (J. Comput. Physics 2005; 204 :784–804) is then used to remove unphysical oscillation in the surface tension. Furthermore, as the density ratio increases, the effect of velocity divergence term neglected in the original HCZ model causes significant unphysical mass sources near the interface. By keeping the velocity divergence term, the unphysical mass sources near the interface can be removed with large density ratio. The long‐time accumulation of the modeling and/or numerical errors in the HCZ model also results in the error of mass conservation of each dispersed phase. A mass correction procedure is devised to improve the performance of the method in this regard. For flows over a stationary and a rising bubble, and capillary waves with density ratio up to 100, the present approach yields solutions with interface thickness of about five to six lattices and no long‐time diffusion, significantly advancing the performance of the LBE method for multiphase flow simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

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。     

Large eddy simulation of turbulent incompressible flows by a three‐level finite element method

The variational multiscale method provides a methodical framework for large eddy simulation of turbulent flows. In this work, a particular implementation in the form of a three‐level finite element method separating large resolved, small resolved, and unresolved scales is proposed. Residual‐free bubbles are used for the numerical approximation of the small‐scale momentum equation. A stabilizing term is added, in order to take into account the effect of the small‐scale continuity equation. This implementation guarantees the stability of the method without further provisions and offers substantial computational savings on the small‐scale level. Furthermore, it is accounted for the unresolved scales by a specific dynamic modelling procedure. The method is tested for two different turbulent flow situations. Copyright © 2005 John Wiley & Sons, Ltd.     

Effects of radiation on turbulent natural convection in channel flows

A computational study has been carried out to analyse complex interaction of radiation with turbulent natural convective flow of dry and humid air in open-ended channels. Transient flow simulations are undertaken in the channel with one uniformly heated wall and adiabatic side walls for different values of emissivity of active walls with and without participating medium. To adequately present turbulence and radiation, a computational model included large eddy simulations for the turbulent flow coupled with discrete ordinates method for radiation transfer. Spectral line-based weighted-sum-of-grey-gases for the absorption properties of water vapour has been adopted. Complex three-dimensional vortical structures are identified which directly affect the temperature distribution on the heated wall. Including wall to wall radiation resulted in significant changes in the heat transfer, reaching 14 °C temperature drop at the hot wall with wall emissivity of 0.9. Mixing and cooling rates in this case were increased by up to 25%. Including gas radiation for the humid air with the water vapour molar fraction of 0.02 corresponding to saturated conditions at inlet temperature of 25 °C did not have a significant effect on the mean flow and temperature values comparing with wall to wall radiation. However, turbulent statistics have changed significantly resulting in a delayed transition to turbulence near the active wall of the channel and increased turbulent activity near the cold wall. The model developed in the present study is also applicable in fire management, where the aim is to reduce the damage that occurs when a PV module is exposed to high temperatures.     

防风网透流风空气动力学特性大涡数值模拟研究

基于有限体积法建立不可压缩粘性流体运动的大涡模拟模型,采用Smagorinsky-Lilly亚格子模型,并引入浸入边界法(IBM)实现无滑移固壁边界条件,对雷诺数30~30000之间防风网透流风进行模拟研究。基于模拟结果,提出蝶型防风网透流风存在4个典型分区结构,流场中存在由蝶型形态引起的大尺度分层剪切流动,加强流体动能耗散。透流风在雷诺数300时发生层流至湍流的转捩,而在雷诺数增长至3000以上时,湍流充分发展,纵向流速脉动强度可达70%。防风网整体空气阻力远大于单个孔口射流阻力的线性叠加,射流间的相互作用以及大尺度的分层剪切结构大大增加流体阻力损失,这为通过优化孔口布置和网板形态来节省材料提供了科学依据。     

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     

Nonlinear turbulence models for predicting strong curvature effects

Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applications and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent Uduct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models （NLEVM） （quadratic and cubic）, a quadratic explicit algebraic stress model （EASM） and a Reynolds stress model （RSM） developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be employed to simulate the turbulent curved flows in engineering applications.     

大涡模拟及其在湍流燃烧中的应用

大涡模拟作为一种研究湍流流动和湍流燃烧的有效手段,在国际上已经得到广泛应用。本文在回顾了大涡模拟(LES)的基本思想及其实施方法的基础上着重介绍了前人在大涡模拟的亚格子湍流模式和亚格子燃烧模式中的研究成果,同时给出了采用不同亚格子模式的大涡模拟在湍流燃烧中的应用实例,指出了大涡模拟在湍流燃烧中的重要作用,为大涡模拟的进一步发展和应用提供参考。      

Validation of a novel very large eddy simulation method for simulation of turbulent separated flow

The paper describes the validation of a newly developed very LES (VLES) method for the simulation of turbulent separated flow. The new VLES method is a unified simulation approach that can change seamlessly from Reynolds‐averaged Navier–Stokes to DNS depending on the numerical resolution. Four complex test cases are selected to validate the performance of the new method, that is, the flow past a square cylinder at Re = 3000 confined in a channel (with a blockage ratio of 20%), the turbulent flow over a circular cylinder at Re = 3900 as well as Re = 140,000, and a turbulent backward‐facing step flow with a thick incoming boundary layer at Re = 40,000. The simulation results are compared with available experimental, LES, and detached eddy simulation‐type results. The new VLES model performs well overall, and the predictions are satisfactory compared with previous experimental and numerical results. It is observed that the new VLES method is quite efficient for the turbulent flow simulations; that is, good predictions can be obtained using a quite coarse mesh compared with the previous LES method. Discussions of the implementation of the present VLES modeling are also conducted on the basis of the simulations of turbulent channel flow up to high Reynolds number of Re_τ = 4000. The efficiency of the present VLES modeling is also observed in the channel flow simulation. From a practical point of view, this new method has considerable potential for more complex turbulent flow simulations at relative high Reynolds numbers. Copyright © 2013 John Wiley & Sons, Ltd.