Numerical simulation on compressible turbulence by spectral method

The numerical and physical issues of simulations on compressible turbulence are reviewed in the present paper. An outline of the global spectral methods and the progress of recent local spectral methods are illustrated. Several typical subjects in this field are studied, including homogeneous isotropic turbulence, autoignition in premixed turbulence, interaction between flames and turbulence, and shock wave in turbulence. The results of the numerical simulations are discussed, enabling us to discover and to understand the physical phenomena which have not been solved by experiments.     

Numerical simulation of laminar jet-forced flow using lattice Boltzmann method

In the paper, a numerical study on symmetrical and asymmetrical laminar jet-forced flows is carried out by using a lattice Boltzmann method （LBM） with a special boundary treatment. The simulation results are in very good agreement with the available numerical prediction. It is shown that the LBM is a competitive method for the laminar jet-forced flow in terms of computational efficiency and stability.     

High-resolution algorithms of sharp interface treatment for compressible two-phase flows

In this paper, a kind of arbitrary high order derivatives (ADER) scheme based on the generalised Riemann problem is proposed to simulate multi-material flows by a coupling ghost fluid method. The states at cell interfaces are reconstructed by interpolating polynomials which are piece-wise smooth functions. The states are treated as the equivalent of the left and right states of the Riemann problem. The contact solvers are extrapolated in the vicinity of contact points to facilitate ghost fluids. The numerical method is applied to compressible flows with sharp discontinuities, such as the collision of two fluids of different physical states and gas–liquid two-phase flows. The numerical results demonstrate that unexpected physical oscillations through the contact discontinuities can be prevented effectively and the sharp interface can be captured efficiently.     

Numerical simulation of viscoelastic flow through a sudden contraction using a type dependent difference method

Numerical simulation of the flow of upper convected Maxwell fluid through a planar 4:1 contraction has been performed using type dependent difference approximation of the vorticity equation. For creeping flow assumption, the numerical convergence has been achieved up to much higher values of the elasticity parameter than those obtained by conventional finite difference methods. For non-vanishing Reynolds number flow, it is shown that the corner vortices disappear, which is in good qualitative agreement with existing experimental results. In doing so, spatial distributions of stream function, vorticity and stresses are considered in relation to a change of type of vorticity.     

Numerical simulation and homogenization of two-phase flow in heterogeneous porous media

A mathematically rigorous method of homogenization is presented and used to analyze the equivalent behavior of transient flow of two incompressible fluids through heterogeneous media. Asymptotic expansions and H-convergence lead to the definition of a global or effective model of an equivalent homogeneous reservoir. Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method. Numerical experiments involving the simulation of incompressible two-phase flow have been performed for each heterogeneous medium and for the homogenized medium as well as for other averaging methods. The results of the simulations are compared in terms of the transient saturation contours, production curves, and pressure distributions. Results obtained from the simulations with the homogenization method presented show good agreement with the heterogeneous simulations.     

Numerical simulation of compressible plane jets

Two- and three-dimensional spatial direct numerical simulations of a compressible plane jet exhausting into a parallel stream are described. These simulations reveal the inadequacy of a two-dimensional model in capturing the totality of the flow physics. In two dimensions, instabilities evolve into highly organized large-scale mixing events; two-dimensional time-averaged turbulence quantities also suffer from artificial vortex organization. Mean normal velocity profiles show a significant reduction in entrainment with increased compressibility, while the effect is much less pronounced in three dimensions. While streamwise and spanwise turbulence intensities exhibit no change with increased compressibility, normal intensity and shear stress are significantly reduced.     

考虑活塞回复的侧向后喷武器两相流数值模拟

为研究活塞回复运动对火药燃气流动的影响,基于两相流理论对活塞控制侧向后喷武器的发射过程进行了数值模拟研究。考虑控制侧向后喷通道开闭的活塞-弹簧系统的往复运动,建立了结合膛内气固两相流、活塞腔内流固耦合和侧向排气管内气体瞬态流动的武器发射过程数学模型,并将数值模拟结果与相关文献进行了比较验证。得到了该武器发射过程中膛内流场分布与稀疏波传播特性,并与普通武器的膛内流场进行了对比分析。进一步研究了活塞回复运动对火药燃气流动和减后坐效率的影响。结果表明:相对于不考虑活塞的回复运动,在弹丸初速都降低1.52%的情况下,因为活塞回复关闭后喷通道,其减后坐效率由38.86%下降到32.88%,说明在此类武器研究中,不可忽视活塞回复运动。     

基于贴体网格的VOF方法数模流场研究

提出了一种基于VOF方法的模拟具有复杂边界形状结构物附近流场的新算法,BFC—SIMPLE—VOF算法。采用坐标变换方法实现了任意复杂区域的结构化网格划分,在贴体网格下对二维不可压缩粘性流体的控制方程进行了离散。提出了基于交错网格的修正SIMPLE算法来迭代求解压力一速度场,修正了贴体坐标下的界面跟踪方法（VOF方法）...     

Direct simulation of compressible turbulence in a shear flow

The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. We find that the growth of the turbulent kinetic energy decreases with increasing Mach number—a phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressure-dilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. We previously obtained the following results for isotropic turbulence: first, the normalized compressible dissipation is of O(M _t ² ), and, second, there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both these results have now been substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.Dedicated to Professor J.L. Lumley on the occasion of his 60th birthday.This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665, U.S.A.     

Numerical simulation of annular two-phase flow considering the four involved mass transfers

In the present study, a numerical model is developed for simulation of annular two-phase flow considering bubbly flow regime in the liquid film along with the four involved mechanisms of mass transfer those are evaporation, entrainment, deposition and condensation. In the numerical approach, liquid film accompanied by fine nucleated bubbles are simulated with innovative model named suction model, the whole domain containing liquid film and the vapor core is simulated by volume of fluid model. While the vapor and the entrained droplets are treated as homogeneous flow. The interface between the liquid and the vapor is traced by level set formulation. The model is then validated by experimental models of Lee & Lee and Stevanovic et al. and shows a good precision such that it predicts the experimental results of Stevanivic et al. Better than their own numerical model. This issue is due to the least possible simplifying assumptions along with considering the effect of boiling in liquid film and all mechanisms of mass transfer in the fluid flow.     

Numerical simulation of compressible gas flow and heat transfer in a microchannel surrounded by solid media

In this study, a numerical model is developed to investigate the coupled compressible gas flow and heat transfer in a microchannel surrounded by solid media. To accommodate the varying flow cross-section, the compressible gas flow model is established in a non-orthogonal curvilinear coordinate system. An iterative numerical procedure is employed to solve the coupled heat transfer and gas flow equations. The computer code for the compressible gas flow is first validated against two test problems, and then extended by including the heat conduction in the solid media. The effect of the inlet Mach number on the Nusselt number is examined. It is found that the pressure difference from the pyrolysis front to the heated surface is induced essentially by the gas addition from the channel wall, instead from the pyrolysis front. The necessity of accounting for the gas compressibility is clearly demonstrated when severe heating is applied. The pressure distribution obtained along the channel axial direction is useful for further structural analysis of composite materials.     

Hyperbolicity and one-dimensional waves in compressible two-phase flow models

Hyperbolic models for compressible two-phase flows including a conservative symmetric hyperbolic model are reviewed. The basis for a theory of shock waves is developed within the framework of the latter. The analysis of small amplitude discontinuities allows us to conclude that in general there are two types of shocks corresponding to two sound waves. The problem of transition between a pure phase and a mixture (the phase vacuum problem) is analysed. It is proved that for some models the smooth centred wave solution can not provide such a transition. Within the framework of our conservative model there is the possibility of constructing discontinuous solutions which can resolve the phase vacuum problem.PACS: 47.55Kf, 47.40.-xE. Romenski: On leave from Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk 630090, Russia     

基于反馈力浸入边界法模拟复杂动边界流动

浸入边界法是模拟流固耦合的重要数值方法之一。本文采用反馈力浸入边界方法,对旋转圆柱和水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟。其中,固体边界采用一系列离散的点近似代替,流体为不可压缩牛顿流体,使用笛卡尔自适应加密网格,利用有限差分法进行求解。固体对流场的作用通过构造适宜的反馈力函数实现。本文首先通过旋转圆柱绕流的计算结果同实验结果进行对比,吻合较好,验证了该计算方法的可靠性。然后针对水电站水力过渡过程中水轮机活动导叶旋转摆动绕流后的动边界流场进行数值模拟,得到导叶动态绕流后的流场分布特性和涡结构的演化特性。     

亚、跨、超音速及不可压流动的数值分析方法的研究

为了对亚、跨、超音速及不可压无粘流动进行数值模拟,将LU－SGS方法与预处理方法结合,给出了PLU－SGS方法。方程离散基于有限体积法,采用高阶精度AUSMPW格式。方程求解采用了特征边界条件。通过典型算例的数值试验对比分析,表明PLU－SGS方法可以有效地对亚、跨、超音速及不可压流动进行数值模拟,并具有较高的计算精度和收敛速度。     

Numerical simulation of compressible multifluid flows using an adaptive positivity-preserving RKDG-GFM approach

The Runge-Kutta discontinuous Galerkin method together with a refined real-ghost fluid method is incorporated into an adaptive mesh refinement environment for solving compressible multifluid flows, where the level set method is used to capture the moving material interface. To ensure that the Riemann problem is exactly along the normal direction of the material interface, a simple and efficient modification is introduced into the original real-ghost fluid method for constructing the interfacial Riemann problem, and the initial conditions of the Riemann problem are obtained directly from the solution polynomials of the discontinuous Galerkin finite element space. In addition, a positivity-preserving limiter is introduced into the Runge-Kutta discontinuous Galerkin method to suppress the failure of preserving positivity of density or pressure for the problems involving strong shock wave or shock interaction with material interface. For interfacial cells in adaptive mesh refinement, the data transfer between different grid levels is achieved by using a L² projection approach along with the least squares fitting. Various numerical cases, including multifluid shock tubes, underwater explosions, and shock-induced collapse of a underwater air bubble, are computed to assess the capability of the present adaptive positivity-preserving RKDG-GFM approach, and the simulated results show that the present approach is quite robust and can provide relatively reasonable results across a wide variety of flow regimes, even for problems involving strong shock wave or shock wave impacting high acoustic impedance mismatch material interface.     

The circular disk straddling the interface of a two-phase flow

The motion is determined for a thin circular disk straddling the plane interface of an immiscible two phase creeping flow and moving parallel or perpendicular to the interface. Expressions are derived for the drag coefficient on the disk.     

A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave

A Free-Lagrange numerical procedure for the simulation of two-dimensional inviscid compressible flow is described in detail. The unsteady Euler equations are solved on an unstructured Lagrangian grid based on a density-weighted Voronoi mesh. The flow solver is of the Godunov type, utilising either the HLLE (2 wave) approximate Riemann solver or the more recent HLLC (3 wave) variant, each adapted to the Lagrangian frame. Within each mesh cell, conserved properties are treated as piece-wise linear, and a slope limiter of the MUSCL type is used to give non-oscillatory behaviour with nominal second order accuracy in space. The solver is first order accurate in time. Modifications to the slope limiter to minimise grid and coordinate dependent effects are described. The performances of the HLLE and HLLC solvers are compared for two test problems; a one-dimensional shock tube and a two-dimensional blast wave confined within a rigid cylinder. The blast wave is initiated by impulsive heating of a gas column whose centreline is parallel to, and one half of the cylinder radius from, the axis of the cylinder. For the shock tube problem, both solvers predict shock and expansion waves in good agreement with theory. For the HLLE solver, contact resolution is poor, especially in the blast wave problem. The HLLC solver achieves near-exact contact capture in both problems. Received May 25, 1995 / Accepted September 11, 1995