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.     

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.     

Large eddy simulation of high-Reynolds-number atmospheric boundary layer flow with improved near-wall correction

It is highly attractive to develop an efficient and flexible large eddy simulation(LES)technique for high-Reynolds-number atmospheric boundary layer(ABL)simulation using the low-order numerical scheme on a relatively coarse grid,that could reproduce the logarithmic profile of the mean velocity and some key features of large-scale coherent structures in the outer layer.In this study,an improved near-wall correction scheme for the vertical gradient of the resolved streamwise velocity in the strain-rate tensor is proposed to calculate the eddy viscosity coefficient in the subgrid-scale(SGS)model.The LES code is realized with a second-order finite-difference scheme,the scale-dependent dynamic SGS stress model,the equilibrium wall stress model,and the proposed correction scheme.Very-high-Reynolds-number ABL flow simulation under the neutral stratification condition is conducted to assess the performance of the method in predicting the mean and fluctuating characteristics of the rough-wall turbulence.It is found that the logarithmic profile of the mean streamwise velocity and some key features of large-scale coherent structures can be reasonably predicted by adopting the proposed correction method and the low-order numerical scheme.     

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.      

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。     

LES of Premixed Methane Flame Impinging on the Wall Using Non-adiabatic Flamelet Generated Manifold (FGM) Approach

In this paper LES of flame wall interaction using a non-adiabatic FGM approach is reported for a premixed methane fuel jet impinging on a spherical disk. Nitrogen is used as co-flow in order to avoid the interaction with the surrounding air and combustion. The flow field is described by means of the Smagorinsky model with Germano procedure for SGS stresses. The SGS scalar flux in scalar transport equations is modeled by the linear eddy diffusivity model. Two aspects are especially addressed in this paper. First focus is on the grid resolution required near the wall without including a special wall-adapted SGS modeling in reacting configurations. The second aspect is devoted to the integration of the near wall kinetic effects into the FGM framework. The results for the flow field, mixing and combustion properties are presented and analyzed in terms of grid resolution, Reynolds number (in reacting and non-reacting case) and adiabaticity. Comparisons with available experimental data show satisfactory agreement. An outline of the thermal and flow boundary layer analysis is subsequently provided.     

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.     

Identification of local extinction topology in axisymmetric bluff‐body diffusion flames with a reactedness‐mixture fraction presumed probability density function model

The effects of finite‐rate chemistry, such as partial extinctions and re‐ignitions, are investigated in turbulent non‐pre‐mixed reacting flows stabilized in the wake of an axisymmetric bluff‐body burner. A two‐dimensional large‐eddy simulation procedure is employed that uses a partial equilibrium/two‐scalar reactedness mixture fraction probability density function (PDF) combustion sub‐model, which is applied at the sub‐grid scale (SGS) level. An anisotropic sub‐grid eddy–viscosity and two equations for the SGS turbulence kinetic and scalar energies complete the SGS closure model. The scalar covariances required in the joint PDF formulation are obtained from an extended scale‐similarity assumption between the resolved and the sub‐grid fluctuations. Extinction due to strong turbulence/chemistry interactions is recognized with the help of a ‘critical’, locally variable, turbulent Damkohler number criterion, while transient localized extinctions and re‐ignitions are treated with a Lagrangian transport equation for a reactedness progress variable. Comparisons with available experimental data suggested that the formulated approach was capable of identifying the effects of large‐scale vortex structure activity, which were inherent in the reacting wake and dominant in the counterpart isothermal flows that otherwise would have been obscured if a standard time‐averaged procedure had been used. Additionally, the post‐extinction and re‐ignition behaviour and its time‐varying interaction with the large‐scale structure dynamics were more appropriately addressed within the context of the present time‐dependent method. Copyright © 2001 John Wiley & Sons, Ltd.     

An immersed boundary method for simulation of inviscid compressible flows

In this paper, an immersed boundary method for simulating inviscid compressible flows governed by Euler equations is presented. All the mesh points are classified as interior computed points, immersed boundary points (interior points closest to the solid boundary), and exterior points that are blanked out of computation. The flow variables at an immersed boundary point are determined via the approximate form of solution in the direction normal to the wall boundary. The normal velocity is evaluated by applying the no‐penetration boundary condition, and therefore, the influence of solid wall in the inviscid flow is taken into account. The pressure is computed with the local simplified momentum equation, and the density and the tangential velocity are evaluated by using the constant‐entropy relation and the constant‐total‐enthalpy relation, respectively. With a local coordinate system, the present method has been extended easily to the three‐dimensional case. The present work is the first endeavor to extend the idea of hybrid Cartesian/immersed boundary approach to compressible inviscid flows. The tedious task of handling multi‐valued points can be eliminated, and the overshoot resulting from the extrapolation for the evaluation of flow variables at exterior points can also be avoided. In order to validate the present method, inviscid compressible flows over fixed and moving bodies have been simulated. All the obtained numerical results show good agreement with available data in the literature. Copyright © 2014 John Wiley & Sons, Ltd.     

Isolating curvature effects in computing wall-bounded turbulent flows

An adjoint optimization method is utilized to design an inviscid outer wall shape required for a turbulent flow field solution of the So–Mellor convex curved wall experiment using the Navier–Stokes equations. The associated cost function is the desired pressure distribution on the inner wall. Using this optimized wall shape with a Navier–Stokes method, the abilities of various turbulence models to simulate the effects of curvature without the complicating factor of streamwise pressure gradient are evaluated. The one-equation Spalart–Allmaras (SA) turbulence model overpredicts eddy viscosity, and its boundary layer profiles are too full. A curvature-corrected version of this model improves results, which are sensitive to the choice of a particular constant. An explicit algebraic stress model does a reasonable job predicting this flow field. However, results can be slightly improved by modifying the assumption on anisotropy equilibrium in the model's derivation. The resulting curvature-corrected explicit algebraic stress model (EASM) possesses no heuristic functions or additional constants. It slightly lowers the computed skin friction coefficient and the turbulent stress levels for this case, in better agreement with experiment. The effect on computed velocity profiles is minimal.     

Vortex dynamics of a cylinder wake in proximity to a wall

Large-eddy simulations (LES) are used to investigate the modifications of wake dynamics and turbulence characteristics behind a circular cylinder placed near a wall for varying gap-to-diameter (G/D) ratios (where G signifies the gap between the wall and the cylinder, and D the cylinder diameter). The three-dimensional (3-D), time-dependent, incompressible Navier–Stokes equations with a dynamic subgrid-scale model are solved using a symmetry-preserving finite-difference scheme of second-order spatial and temporal accuracy. The immersed boundary (IB) method is employed to impose the no-slip boundary condition on the cylinder surface. Flow visualizations along with turbulence statistics are presented to gain insight into the flow structures that are due to interaction between the shear layers and the approaching boundary layer. Apart from the vortex shedding mechanism, the paper illustrates the physics involving the shear layer transition, stretching, breakdown and turbulence generation, either qualitatively or quantitatively, in the presence of a wall for a Reynolds number of Re=1440 (based on D and the inlet free-stream velocity U_∞).     

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.     

An immersed boundary finite difference method for LES of flow around bluff shapes

A three‐dimensional numerical model using large eddy simulation (LES) technique and incorporating the immersed boundary (IMB) concept has been developed to compute flow around bluff shapes. A fractional step finite differences method with rectilinear non‐uniform collocated grid is employed to solve the governing equations. Bluff shapes are treated in the IMB method by introducing artificial force terms into the momentum equations. Second‐order accurate interpolation schemes for all sorts of grid points adjacent to the immersed boundary have been developed to determine the velocities and pressure at these points. To enforce continuity, the methods of imposition of pressure boundary condition and addition of mass source/sink terms are tested. It has been found that imposing suitable pressure boundary condition (zero normal gradient) can effectively reproduce the correct pressure distribution and enforce mass conservation around a bluff shape. The present model has been verified and applied to simulate flow around bluff shapes: (1) a square cylinder and (2) the Tsing Ma suspension bridge deck section model. Complex flow phenomena such as flow separation and vortex shedding are reproduced and the drag coefficient, lift coefficient, and pressure coefficient are calculated and analyzed. Good agreement between the numerical results and the experimental data are obtained. The model is proven to be an efficient tool for flow simulation around bluff bodies in time varying flows. Copyright © 2004 John Wiley & Sons, Ltd.     

格子Boltzmann方法中基于内插值的曲线边界处理新方法

对格子Boltzmann方法提出了一种新的曲面边界条件处理方法。在笛卡尔坐标系中,这种处理方法是现有的格子Boltzmann方法有关边界条件处理与浸入式边界条件的混合,它采用内插值方法计算靠近物理边界的网格点速度,使其保证最低精度为二阶,然后利用格子Boltzmann方法中的边界条件技术得到相应的分布函数。由理论推导和数值计算表明,本文提出的方法比其他方法更稳定且具有二阶精度。     

Fast computation of the wall distance in unsteady Eulerian fluid-structure computations

Highly nonlinear, turbulent, dynamic, fluid-structure interaction problems characterized by large structural displacements and deformations, as well as self-contact and topological changes, are encountered in many applications. For such problems, the Eulerian computational framework, which is often equipped with an embedded (or immersed) boundary method for computational fluid dynamics, is often the most appropriate framework. In many circumstances, it requires the computation of the time-dependent distance from each active mesh vertex of the embedding mesh to the nearest embedded discrete surface. Such circumstances include, for example, modeling turbulence using the Spalart-Allmaras or detached eddy simulation turbulence models and performing adaptive mesh refinement in order to track the boundary layer. Evaluating at each time step the distance to the wall is computationally prohibitive, particularly in the context of explicit-explicit fluid-structure time-integration schemes. Hence, this paper presents two complementary approaches for reducing this computational cost. The first one recognizes that many quantities depending on the wall distance are relatively insensitive to its inaccurate evaluation in the far field. Therefore, it simplifies a state-of-the-art algorithm for computing the wall distance accordingly. The second approach relies on an effective wall distance error estimator to update the evaluation of the wall distance function only when otherwise, a quantity of interest that depends on it would become tainted by an unacceptable level of error. The potential of combining both approaches for dramatically accelerating the computation of the wall distance is demonstrated with the Eulerian simulation of the inflation of a disk-gap-band parachute system in a supersonic airstream.     

Numerical studies on erosive burning in cylindrical solid propellant grain

This paper addresses erosive burning of a cylindrical composite propellant grain. Equations governing the steady axisymmetric, chemically reacting boundary layer are solved numerically. The turbulence is described by the two equation (k-ɛ) model and Spalding’s eddy break up model is employed for the gas phase reaction rate. The governing equations are transformed and solved in the normalized stream function coordinate system. The results indicate that the dominant reaction zone lies within 20% of the boundary layer thickness close to the wall. The sharp gradient of the temperature profile near the wall is found responsible for bringing the maximum heat release zone near the surface and hence enhancement in the burning rate. The model reproduces the experimental observation that erosive burning commences only above a threshold value of axial velocity.     

Subgrid-scale contributions to Lagrangian time correlations in isotropic turbulence

The application of large-eddy simulation （LES） to particle-laden turbulence raises such a fundamental question as whether the LES with a subgrid scale （SGS） model can correctly predict Lagrangian time correlations （LTCs）. Most of the currently existing SGS models are constructed based on the energy budget equations. Therefore, they are able to correctly predict energy spectra, but they may not ensure the correct prediction on the LTCs. Previous researches investigated the effect of the SGS modeling on the Eulerian time correlations. This paper is devoted to study the LTCs in LES. A direct numerical simulation （DNS） and the LES with a spectral eddy viscosity model are performed for isotropic turbulence and the LTCs are calculated using the passive vector method. Both a priori and a posteriori tests are carried out. It is observed that the subgrid;scale contributions to the LTCs cannot be simply ignored and the LES overpredicts the LTCs than the DNS. It is concluded from the straining hypothesis that an accurate prediction of enstrophy spectra is most critical to the prediction of the LTCs.     

A ghost-cell immersed boundary method for large eddy simulation of flows in complex geometries

An efficient ghost-cell immersed boundary (IB) method is proposed for large eddy simulations of three-dimensional incompressible flow in complex geometries. In the framework of finite volume method, the Navier–Stokes equations are integrated using an explicit time advancement scheme on a collocated mesh. Since the IB method is known to generate an unphysical velocity field inside the IB that violates the mass conservation of the cells near the IB, a new IB treatment is devised to eliminate the unphysical velocity generated near the IB and to improve the pressure distribution on the body surface. To validate the proposed method, both laminar and turbulent flow cases are presented. In particular, large eddy simulations were performed to simulate the turbulent flows over a circular cylinder and a sphere at subcritical Reynolds numbers. The computed results show good agreements with the published numerical and experimental data.     

Numerical analysis of wall pressure and heat flux fluctuations in shock-turbulent-boundary-layer interaction

The unsteady, compressible, Reynolds-averaged Navier-Stokes equations are solved numerically for an oblique shock-wave-induced turbulent boundary layer sepration. For the freestream Mach number 6 and the freestream Reynolds number 66·1 × 10⁶ m^?1, a time-dependent computation is performed, using MacCormack's explicit-implicit finite difference method with 82 × 42 grid points. A two-layer eddy viscosity turbulence model is employed in conjunction with a relaxation modification. Comparisons of the mean wall pressure and the mean heat transfer coefficient with the available experimental results are made and the evaluation of unsteady data for surface pressure and heat flux fluctuations is presented. It is found that the fluctuations in heat flux have qualitatively the same features as those of wall pressure but are different quantitatively.     

基于滑移速度壁模型的复杂边界湍流大涡模拟

采用滑移速度壁模型实现了浸入边界方法与壁模型相结合的大涡模拟.本文首先分别采用平衡层模型和非平衡壁模型对周期山状流进行数值模拟,以考查在壁模型中考虑切向压力梯度的作用.数值结果表明,流场的压力对本文所采用的壁模型形式并不敏感,但是考虑切向压力梯度可以显著改进壁面摩擦力的计算结果,并且能够准确的预测强压力梯度区以及分离区内的流动平均统计特性.不考虑压力梯度效应的平衡层模型显著低估了壁面摩擦力的分布,同时无法准确预测分离区内的平均速度剖面.非平衡模型的修正项正比于切向压力梯度和壁面法向距离,因此在强压力梯度区或者网格较粗时,计算得到的平均压力和摩擦力分布以及流动的低阶统计量均与参考的实验和计算结果吻合.在此基础上,通过回转体绕流的大涡模拟考查了该方法用于模拟高雷诺数壁湍流的适用性,非平衡壁模型可以准确地捕捉流动的物理结构并较准确地预测其水动力学特性.结果表明,将浸入边界方法与非平衡滑移速度壁模型相结合的大涡模拟,有望成为数值模拟复杂边界高雷诺数壁湍流的工具.