Mathematical Modeling of the Interaction of a Shock Wave with a Dense Cloud of Particles within the Framework of the Two-Fluid Approach

A parametric numerical study of the interaction of a shock wave with a dense cloud of particles is performed. The problem is solved in the framework of the two-fluid approach, with both the gas and dispersed phases are considered compressible media non-equilibrium in velocity and pressure. The system of governing hyperbolic equations was numerically solved using the Harten–Lax–van Leer method. The statement of the problem corresponds to the arrangement of natural experiments. The simulations revealed the main features of the process, such as the formation of transmitted and reflected waves, the movement of the cloud with a steep leading edge and a smeared tailing edge. The amplitudes of the transmitted and reflected waves, as well as the dynamics of the motion of the cloud, are compared to those observed in real experiments. The influence of the parameters of the equation of state of the dispersed phase and some properties of the computational algorithm on the characteristics of the process is examined.     

一种数值模拟S形进气道内可压缩湍流的隐式迎风增量迭代法

在这篇文章里,我们提出了一个二阶隐式迎风的增量迭代法,用以离散BFC(Body-Fitted Coordinates)坐标变换下的Navier-Stokes方程。使用这种算法结合Lomax两层代数湍流模型数值求解了S形进气道内的可压缩湍流。数值实验表明:计算过程具有较好的稳定性和收敛性。二维Poissuil流动和Couette流动的计算结果和精确解符合良好,两种壁面曲率不同的S形进气道内流场的计算结果也是令人满意的。     

Integrating 1D and 2D hydrodynamic,sediment transport model for dam-break flow using finite volume method

The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume method.It considers interactions among transient flow,strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum equations.An unstructured Quadtree rectangular grid with local refinement is used in the 2D model.The intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all models.The effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux terms.The developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable bed.The results are compared with analytical solution and measured data with good agreement.The simulation results demonstrate that the coupling model is capable of calculating the flow,erosion and deposition for dam break flows in complicated natural domains.     

On the definition of the natural frequency of oscillations in nonlinear large rotation problems

Computational multibody system algorithms allow for performing eigenvalue analysis at different time points during the simulation to study the system stability. The nonlinear equations of motion are linearized at these time points, and the resulting linear equations are used to determine the eigenvalues and eigenvectors of the system. In the case of linear systems, the system eigenvalues remain the same under a constant coordinate transformation; and zero eigenvalues are always associated with rigid body modes, while nonzero eigenvalues are associated with non-rigid body motion. These results, however, cannot in general be applied to nonlinear multibody systems as demonstrated in this paper. Different sets of large rotation parameters lead to different forms of the nonlinear and linearized equations of motion, making it necessary to have a correct interpretation of the obtained eigenvalue solution. As shown in this investigation, the frequencies associated with different sets of orientation parameters can differ significantly, and rigid body motion can be associated with non-zero oscillation frequencies, depending on the coordinates used. In order to demonstrate this fact, the multibody system motion equations associated with the system degrees of freedom are presented and linearized. The resulting linear equations are used to define an eigevalue problem using the state space representation in order to account for general damping that characterizes multibody system applications. In order to demonstrate the significant differences between the eigenvalue solutions associated with two different sets of orientation parameters, a simple rotating disk example is considered in this study. The equations of motion of this simple example are formulated using Euler angles, Euler parameters and Rodriguez parameters. The results presented in this study demonstrate that the frequencies obtained using computational multibody system algorithms should not in general be interpreted as the system natural frequencies, but as the frequencies of the oscillations of the coordinates used to describe the motion of the system.     

三维机翼跨音速颤振的分布式并行计算

以多台微机组成分布式计算系统,利用无限插值方法(TFI)生成三维多块贴体运动网格,以Navier Stokes方程为控制方程,求解三维机翼的跨音速非定常气动力,并与颤振方程耦合迭代计算,求解机翼广义位移响应的时间历程,根据广义位移的时间历程的衰减、等幅和发散振荡等情况确定机翼跨音速颤振临界条件.通过算例验证,计算结果与实验结果和理论分析相吻合.     

Effect of wall temperature on the thermal behavior of a packed bed

The present work is concerned with numerically studying the thermal behaviour of a packed bed storage system under various wall temperatures. The packed bed is mathematically described using a two-phase model, in which the air and solid phases are governed by two coupled partial differential equations representing the energy conservation in each phase separately. The axial and radial conduction in the solid are taken into account while the thermal conductivity of air is ignored. The modeling equations are numerically solved at various fixed wall temperatures, ranging from 5°C to 55°C. The temporal, axial and radial distributions of air and solid temperatures obtained during thermal charging of the bed are studied, and used to compute and investigate the behaviour of energy stored inside the bed as well as the heat loss to the surroundings under such a wide range of wall temperatures.     

Large-scale turbulence modelling via α-regularisation for atmospheric simulations

We study the possibility of obtaining a computational turbulence model by means of non-dissipative regularisation of the compressible atmospheric equations for climate-type applications. We use an α-regularisation (Lagrangian averaging) of the atmospheric equations. For the hydrostatic and compressible atmospheric equations discretised using a finite volume method on unstructured grids, deterministic and non-deterministic numerical experiments are conducted to compare the individual solutions and the statistics of the regularised equations to those of the original model. The impact of the regularisation parameter is investigated. Our results confirm the principal compatibility of α-regularisation with atmospheric dynamics and encourage further investigations within atmospheric model including complex physical parametrisations.     

自然循环过冷沸腾流动不稳定性的研究

本文以氟里昂12作工质,对自然循环过冷沸腾流动不稳定性进行了实验研究,实验过程中发现自然循环系统内可能发生高频脉动和低频脉动两类流动不稳定性,并证实高频脉动属于声波型脉动,低频脉动属于密度波型脉动。本文以两相流漂移模型为基础,对自然循环过冷沸腾流动不稳定性进行了数值模拟,数学模型考虑了热力学非平衡即过冷沸腾和过冷凝结对流动不稳定性的影响。数值模拟结果与实验结果符合良好。     

堆积床内非驻定过滤燃烧的一维研究

多孔介质内气体过滤燃烧不同于自由流中燃烧,燃气与多孔介质强烈换热.热波波速和燃烧波波速是燃烧过程的特征参数.以惰性堆积床内的甲烷/空气的低速过滤燃烧为例,提出一维解析模型,用摄动理论推导出燃烧波波速,用直接求解方法和格林函数方法给出充分发展后的和瞬态的燃烧温度分布,并进行计算验证.     

Coarse-grained computation for particle coagulation and sintering processes by linking Quadrature Method of Moments with Monte-Carlo

The study of particle coagulation and sintering processes is important in a variety of research studies ranging from cell fusion and dust motion to aerosol formation applications. These processes are traditionally simulated using either Monte-Carlo methods or integro-differential equations for particle number density functions. In this paper, we present a computational technique for cases where we believe that accurate closed evolution equations for a finite number of moments of the density function exist in principle, but are not explicitly available. The so-called equation-free computational framework is then employed to numerically obtain the solution of these unavailable closed moment equations by exploiting (through intelligent design of computational experiments) the corresponding fine-scale (here, Monte-Carlo) simulation. We illustrate the use of this method by accelerating the computation of evolving moments of uni- and bivariate particle coagulation and sintering through short simulation bursts of a constant-number Monte-Carlo scheme.     

Numerical investigation of aerodynamics in an apparatus with a circulating fluidized bed

A mathematical model and a numerical algorithm are proposed for investigation of aerodynamics in an apparatus with a circulating fluidized bed. The model is based on the basic assumptions of the theory of interacting interpenetrating continua and two-dimensional nonstationary Navier-Stokes equations. Calculations of the motion of a two-phase mixture in the laboratory apparatus were performed. The computational results are in good agreement with the experimental data.Scientific-Research Institute of Applied Mathematics and Mechanics at Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 63–68, April, 1993.     

h-Multigrid for space-time discontinuous Galerkin discretizations of the compressible Navier–Stokes equations

Being implicit in time, the space-time discontinuous Galerkin discretization of the compressible Navier–Stokes equations requires the solution of a non-linear system of algebraic equations at each time-step. The overall performance, therefore, highly depends on the efficiency of the solver. In this article, we solve the system of algebraic equations with a h-multigrid method using explicit Runge–Kutta relaxation. Two-level Fourier analysis of this method for the scalar advection–diffusion equation shows convergence factors between 0.5 and 0.75. This motivates its application to the 3D compressible Navier–Stokes equations where numerical experiments show that the computational effort is significantly reduced, up to a factor 10 w.r.t. single-grid iterations.     

Simplified models and experimental verification for coupled transmission tower-line system to seismic excitations

The simplified computational models of high-voltage transmission tower-line system under out-of-plane and in-plane vibrations are presented due to seismic excitations in this paper. The equations of motion are derived and the computer program is compiled to obtain the earthquake responses of the coupled system. To verify the rationality of the proposed approaches, the shaking-table experiments of the coupled system of transmission lines and their supporting towers are carried out and the results indicate that the errors of theoretical and testing results of systemic seismic responses are within the acceptable arrange in engineering area. Based on these studies, a simplified analysis method is proposed to make the seismic response calculation of coupled tower-conductor system faster and more effective.     

基于广义交替数值通量的局部间断Galerkin方法求解二维波动方程

波的传播往往在复杂的地质结构中进行,如何有效地求解非均匀介质中的波动方程一直是研究的热点.本文将局部间断Galekin(local discontinuous Galerkin, LDG)方法引入到数值求解波动方程中.首先引入辅助变量,将二阶波动方程写成一阶偏微分方程组,然后对相应的线性化波动方程和伴随方程构造间断Galerkin格式;为了保证离散格式满足能量守恒,在单元边界上选取广义交替数值通量,理论证明该方法满足能量守恒性.在时间离散上,采用指数积分因子方法,为了提高计算效率,应用Krylov子空间方法近似指数矩阵与向量的乘积.数值实验中给出了带有精确解的算例,验证了LDG方法的数值精度和能量守恒性;此外,也考虑了非均匀介质和复杂计算区域的计算,结果表明LDG方法适合模拟具有复杂结构和多尺度结构介质中的传播.     

Dominant frequencies of train-induced vibrations

This paper investigates the dynamic characteristics of ground vibrations induced by moving vehicles including the mass rapid transit system, high-speed train railway, and general railway on bridges, embankments, and in tunnels using field experiments and theoretical solutions. The results indicate that train-induced ground vibrations at the trainload dominant frequencies are significantly large for both subsonic and supersonic train speeds, and the vibrations from carriage natural frequencies and engine frequencies are minor. For trains moving on bridges, the resonant vibrations are serious when the natural frequencies of the bridge are close to the trainload dominant frequencies, but resonance does not occur when the carriage natural frequencies and trainload dominant frequencies match. The trainload dominant frequency and its influence factor can be computed using the two simple equations deducted in this paper.     

h-Multigrid for space-time discontinuous Galerkin discretizations of the compressible Navier–Stokes equations

Being implicit in time, the space-time discontinuous Galerkin discretization of the compressible Navier–Stokes equations requires the solution of a non-linear system of algebraic equations at each time-step. The overall performance, therefore, highly depends on the efficiency of the solver. In this article, we solve the system of algebraic equations with a h-multigrid method using explicit Runge–Kutta relaxation. Two-level Fourier analysis of this method for the scalar advection–diffusion equation shows convergence factors between 0.5 and 0.75. This motivates its application to the 3D compressible Navier–Stokes equations where numerical experiments show that the computational effort is significantly reduced, up to a factor 10 w.r.t. single-grid iterations.     

倾斜井眼中感应测井正演模拟与响应特征

感应测井仪器的发射源可简化为一系列磁偶极子,其在层状地层中产生的电磁场可分解成彼此独立的TE波和TM波叠加,且TE波和TM波完全由两个标量方程确定.首先研究倾斜井眼中磁偶极子场的TE波和TM波分解,推导多层介质中电磁场振幅以及地层界面上广义反射和透射系数的递推公式,给出层状地层电磁场解析解.然后利用数值结果分析考察砂泥岩薄交互层中,地层层厚、井眼倾角变化等对感应测井响应的影响.     

旋转柔性悬臂梁动力学的Bezier插值离散方法研究

在旋转柔性梁变形场描述中,引入Bezier插值离散方法.首先构建旋转运动悬臂梁物理模型,接着采用第二类Lagrange动力学方程和Bezier插值离散方法,在计入柔性梁横向弯曲变形引起的纵向缩短的情况下,推导了旋转柔性梁的刚柔耦合动力学方程,并编制旋转柔性梁的动力学仿真软件,然后通过仿真算例对系统的动力学问题进行研究.最后将仿真结果与有限元法、假设模态法进行分析比较,验证了提出的Bezier插值离散方法的正确性,并得出Bezier插值离散法的计算效率较高;计算精度符合工程实际需要,高速时计算精度大于假设模态法;Bezier插值离散方法在处理大柔性问题时比假设模态法合理.因此在多体系统动力学领域具有优良性能和应用价值的Bezier插值离散方法将具有推广价值.     

Accounting for delay of energy transfer between coupled rooms in statistical-acoustics models of reverberant-energy decay

A statistical-acoustics model for energy decay in systems of two or more coupled rooms is introduced, which accounts for the distribution of delay in the transfer of energy between subrooms that results from the finite speed of sound. The method extends previous models based on systems of coupled ordinary differential equations by using functional differential equations to explicitly model dependence on prior values of energy in adjacent subrooms. Predictions of the model are illustrated for a two-room coupled system and compared with the predictions of a benchmark computational geometrical-acoustics model.     

Time domain finite volume method for the transient response and natural characteristics of structural-acoustic coupling in an enclosed cavity

A time domain finite volume method（TDFVM）based on wave theory is developed to analyze the transient response and natural characteristics of structural-acoustic coupling problems in an enclosed cavity.In the present method,the elastic dynamic equations and acoustic equation in heterogeneous medium are solved in solid domains and fluid domains respectively.The structural-acoustic coupling is implemented according to the continuity condition of the particle velocity along the normal direction and the normal traction equilibrium condition on the interface.Several numerical examples are presented to validate the effectiveness and accuracy of the present TDFVM.Then the effects of water depth on the acoustic and vibration characteristics and the natural characteristics of a structural-acoustic coupling system are analyzed.The numerical results show that the increase of water depth leads to a stronger coupling between the water and structure and the decrease of natural frequencies of coupling system,The computational cost and memory of this method are small and it can be applicable to structural-acoustic coupling problems in the heterogeneous fluid.