Spall damage in aluminum-alloy

A void growth relations for ductile porous materials under intense dynamic general loading condition is presented. The mathematical model includes the influence of inertial effects, material rate sensitivity, as well as the contribution of void surface energy and material work-hardening. Numerical analysis shows that inertia appears to resist the growth of voids. The inertial effects increase quickly with the loading rates. The theoretical analysis suggests that the inertial effects cannot be neglected at high loading rates. Plate-impact tests of aluminum alloy are performed with light gas gun. The processes of dynamic damage in aluminum alloy are successfully simulated with a finite-difference dynamic code in which the theoretical model presented in this paper is incorporated.

Dynamic failure in ductile porous materials

In this paper, a mathematical model of dynamic fracture in porous ductile materials under intense dynamic general loading is developed. The mathematical model includes the influence of inertial effects and material rate sensitivity, as well as the contribution of surface energy of a void and material work-hardening. In addition, the condition of the void compaction is considered as well. The threshold stresses for the void growth and compaction are obtained. A simple criterion for ductile fracture which is associated with material distention and plastic deformation is adopted. As an application of the theoretical model, the processes of two-dimensional spallation in LY12 aluminum alloy are successfully simulated by means of two-dimensional finite-difference Lagrangian code.

Numerical-simulation of low supersonic-flow around a sphere

The controlled equations defined in a physical plane are changed into those in a computational plane with coordinate transformations suitable for different Mach number M(infinity). The computational area is limited in the body surface and in the vicinities of detached shock wave and sonic line. Thus the area can be greatly cut down when the shock wave moves away from the body surface as M(infinity) --> 1. Highly accurate, total variation diminishing (TVD) finite-difference schemes are used to calculate the low supersonic flowfield around a sphere. The stand-off distance, location of sonic line, etc. are well comparable with experimental data. The long pending problem concerning a flow passing a sphere at 1.3 greater-than-or-equal-to M(infinity) > 1 has been settled, and some new results on M(infinity) = 1.05 have been presented.

Computation of turbulent-flow in a square duct - aspects of the secondary flow and its origin

A numerical study of turbulent flow in a straight duct of square cross-section is made. An order-of-magnitude analysis of the 3-D, time-averaged Navier-Stokes equations resulted in a parabolic form of the Navier-Stokes equations. The governing equations, expressed in terms of a new vector-potential formulation, are expanded as a multi-deck structure with each deck characterized by its dominant physical forces. The resulting equations are solved using a finite-element approach with a bicubic element representation on each cross-sectional plane. The numerical integration along the streamwise direction is carried out with finite-difference approximations until a fully-developed state is reached. The computed results agree well with other numerical studies and compare very favorably with the available experimental data. One important outcome of the current investigation is the interpretation analytically that the driving force of the secondary flow in a square duct comes mainly from the second-order terms of the difference in the gradients of the normal and transverse Reynolds stresses in the axial vorticity equation.

Numerical study of bluff body flow structures

Our recent progress in numerical studies of bluff body flow structures and a new method for the numerical analysis of near wake flow field for high Reynolds number flow are introduced. The paper consists of three parts. In part one, the evolution of wake vortex structure and variation of forces on a flat plate in harmonic oscillatory flows and in in-line steady-harmonic combined flows are presented by an improved discrete vortex method, as the Keulegan-Carpenter number (KC) varies from 2 to 40 and ratios of U-m to U-0 are of O(10(-1)), O(10) and O(10), respectively. In part 2, a domain decomposition hybrid method, combining the finite-difference and vortex methods for numerical simulation of unsteady viscous separated flow around a bluff body, is introduced. By the new method, some high resolution numerical visualization on near wake evolution behind a circular cylinder at Re = 10(2), 10(3) and 3 x 10(3) are shown. In part 3, the mechanism and the dynamic process for the three-dimensional evolution of the Karman vortex and vortex filaments in braid regions as well as the early features of turbulent structure in the wake behind a circular cylinder are presented numerically by the vortex dynamics method.

Diffusion analogy and shock capturing for solving aerodynamic equations

Improving the resolution of the shock is one of the most important subjects in computational aerodynamics. In this paper the behaviour of the solutions near the shock is discussed and the reason of the oscillation production is investigated heuristically. According to the differential approximation of the difference scheme the so-called diffusion analogy equation and the diffusion analogy coefficient are defined. Four methods for improving the resolution of the shock are presented using the concept of diffusion analogy.

A consistent model of isolated force-free magnetic arches

The magnetic flux tube concentrating strong magnetic field is the basic configuration of magneticfield in the solar atmosphere. In the present paper, the equilibrium of isolated magnetic flux tube inthe solar atmosphere is discussed. In the viewpoint of mathematics, the boundary condition is nonlinearand the position of boundary needs to be determined by the physical condition although the equation ofmagnetic potential is linear for the linear force-free field. Analytical solutions to the arches of bothuniform circular cross-section and non-uniform cross section have been obtained. The results show thatthe nonlinear problem may have or not have any solution according to different azimuthal components of the magnetic field; the number of solutions to the nonlinear problem is four at most, and two in some cases. In the present paper, the analytical solutions to the approximations of both fat and slender arches are given in detail, and the general features of magnetic arch structure are shown.

Coupled deformation-flow analysis for methane hydrate production by depressurized wells

A formulation for coupled flow-deformation analysis of methane-hydrate extraction problems is presented. By assuming that the hydrate does not flow, a two phase flow formulation is considered, based on Darcy's law and capillary pressure relation. The formulation is implemented in the finite difference code FLAC. The code was used to investigate the stability of a methane extraction well by depressurizing the well. © 2005 Taylor & Francis Group, London.

Diffusive waves in a channel with concentrated lateral inflow

In the current paper an analytical solution for diffusive wave equation with the concentrate-distributed lateral inflow is yielded. Finite-difference numerical method is also employed to validate this model. The backwater effects drawn from lateral inflow on the mainstream are examined finally.

可压缩流气动声场的数值模拟

气动声学是一门流动力学和声学之间的交叉学科，主要研究流动及其与物体相互作用产生噪声的机理。动用计算技术研究气动声学问题的手段称为计算气动声学。本文的目的是，基于高精度数值算法的研究，分别运用Lighthill比拟理论、Kirchhoff积分和直接数值模拟等方法，针对翼型绕流、激波-涡干扰和轴对称射流，研究了物面非定常脉动压力、涡脱落、激波-涡干扰以及涡对并等产生噪声的机理。首先针对声场与主流场在能级和特征尺度等方面的差异，从空间离散角度分析了几种差分格式，表明迎风紧致格式/对称紧致格式有较小的数值色散、耗散和各向异性误差，因而适用于气动噪声的计算。以Runge-Kutta格式为例，对时间离散带来的误差进行了分析。指出对声波计算来说，仅考虑格式稳定性是不够的，时间步长还受到允许色散误差和耗散误差的限制。基于保色戎关系的思想，构造了优化Runge-Kutta格式。处例显示优化Runge-Kutta格式相对于经典格式有更高的计算效率。采用3阶迎风紧致格式和3阶Runge-Kutta格式数值模拟了NACA0012翼型的可压缩非定常绕流流场，并将此流场作为近场声源，运用声学比拟理论对偶极子声和四极子声进行研究。结果指出，主流速度对远场声压有决定性影响，在来流马赫数较大时，四极子噪声和偶极子噪声具有相同量级，不能被忽略，表明了可压缩效应对声场的影响。采用5阶迎风紧致格式和4阶Runge-Kutta格式求解非定常可压缩Navier-Stokes方程，对激波-单涡/双涡干扰导致的声场进行了直接数值模拟。详细研究了激波-涡干扰产生噪声的机理，指出噪声的产生及其性质和激波变形密切相关。研究了近场噪声衰减和传播距离r的关系，发现噪声衰减大致和r~(4/5)而不是r~(1/2)成反比关系，提出这种差异是由流场的非线性效应引起的。构造了Kirchhoff积分和非定常流动计算相结合的算法。采用5阶迎风紧致格式和3阶Runge-Kutta格式对亚声速轴对称射流进行直接数值模拟。将射流流场作为近场声源，结合Kirchhoff方法求解远场 气动噪声。数值结果表明远场噪声具有方向性，噪声声压在离开对称轴20°处达到最大值。随着传播距离增大，噪声方向性逐渐减弱。

可压平面混合层稳定性分析及数值模拟

可压平面混合层是包含复杂多时空尺度运动的非定常流体力学部问题，具有深刻的理论意义和广泛的应用背景。针对该问题所涉及内容的多面性，本文的目的是，基于高精度、高分辨率数值算法的构造、发展和数值行为分析，采用线性稳定性分析和直接数值模拟方法。从理论和计算两方面集中研究压缩性效应、粘性效应、初值效应以及燃烧反应放热效应等对可压平面混合层早期稳定性行为和大尺度拟序涡结构非线性演化的影响。以混合层已有研究成果的分析和综述为开端，论文主体共包括四部分：第一部分是可压平面混合层时间/空间模式数值线性稳定性分析。实现了高精度对称紧致差分格式（SCD）对可压粘性扰动线性稳定性边值问题的求解，对导出的线性和非线性离散特征值问题，提出了两个高效局部解法。研究涉及二维/三维扰动波、无粘/粘性扰动波、特征函数和特征值谱、第一/第二模态、超声速快/慢模态、速度比和密度比等。验证了对流Mach数Mc为一个合理的压缩性参数。指出压缩性效应和粘性效应对最不稳定扰动波的波数（频率）和增长率呈相拟的抑制作用，且时间模式稳定性分析结果在许多方面是可信的。从随机和线性扰动场出发，采用高精度五阶迎风紧致和六阶对称紧致混合差分算法（UCD5/SCD6）对可压平面混合层的稳定性特征进行了直接数值模拟，揭示了初始主导线性扰动与一些实际涡结构非线性作用形态间的内在关联，印证了线性稳定性分析方法的合理性和有效性。第二部分是高精度迎风紧致差分格式（UCD）时空全离散数值行为分析。导出了其一维/二维一般色散表达式。研究表明，UCD格式在高波数区具有内在的全离散耗散和色散特性；其数值群速度的快/慢特征可因CFL数不同而改变；在稳定CFL数下简单附加人工粘性可强化UCD格式在高波数区的耗散量；提高时间精度可放宽稳定CFL数限制；UCD格式的二维全离散色散介质中存在三个不同性质的数值波，其全离散稳定性由数值声波主控。第三部分实现了高精度UCD5/SCD6差分算法对空间发展可压平面混合层的直接数值模拟。通过亚谐扰动波的个数和扰动频率的控制，捕捉到了基频涡的饱和、一次和二次对并等现象，显示了大尺度涡结构与入中初始扰动方式之间的内在联系。利用参数Mc观察了压缩性效应对大尺度涡空间演化及其相互作用的影响。第四部分实现了高精度UCD5/SCD6差分算法对非预混扩散火焰化学反应平面混合层的直接数值模拟。研究指出，放热效应可抑制和延迟涡的形成，使基频涡卷拉伸甚至丧失，混合层Reynolds 应力ρu'v'和流向速度波动关联项u'v'下降，以致涡结构与外流动量交换和标量输运减少，脉动输运能力被削弱，从而混合效率、产物生成率和混合层增长率下降，放热主要通过膨胀效应和斜压效应来抑制大尺度涡的演化。

摄动有限体积算法及其在两相流中应用

采用一种全新的摄动有限体积(PFV)算法和水平集(Level Set)技术对液液两相系统中液滴坠落进行数值模拟,数值结果表明,PFV新算法具有节点少、精度高,效率高,编程方便等优点,能成功模拟液液两相流动,为两相流动数值模拟提供了一种新的途径.

Effect of coal-over-coal reburn on furnace temperature and heat flux distributions in 1 MW tangentially fired furnace

The furnace temperature and heat flux distributions of 1 MW tangentially fired furnace were studied during coal-over-coal reburn, and the influences of the position of reburn nozzle and reburn fuel fraction on furnace temperature and heat flux distributions were investigated. Compared with the baseline, the flue gas temperature is 70–90 C lower in primary combustion and 130–150 C higher at furnace exit, and the variations of the flue gas temperature distributions along furnace height are slower. The temperature distribution along the width of furnace wall decreases with the increase of the relative furnace height. In the primary combustion zone and the reburn zone, the temperature and heat flux distributions of furnace wall are much non-uniform and asymmetric along the width of furnace wall, those of furnace wall in the burnout zone are relatively uniform, and the temperature non-uniformity coefficients of the primary combustion zone, the reburn zone and the burnout zone are 0.290, 0.100 and 0.031, respectively.

A singularly perturbed linear two-point boundary-value problem

We consider the following singularly perturbed linear two-point boundary-value problem:

Ly(x) ≡ Ω(ε)D_xy(x) - A(x,ε)y(x) = f(x,ε) 0≤x≤1 (1a)

By ≡ L(ε)y(0) + R(ε)y(1) = g(ε) ε → 0^+ (1b)

Here Ω(ε) is a diagonal matrix whose first m diagonal elements are 1 and last m elements are ε. Aside from reasonable continuity conditions placed on A, L, R, f, g, we assume the lower right mxm principle submatrix of A has no eigenvalues whose real part is zero. Under these assumptions a constructive technique is used to derive sufficient conditions for the existence of a unique solution of (1). These sufficient conditions are used to define when (1) is a regular problem. It is then shown that as ε → 0^+ the solution of a regular problem exists and converges on every closed subinterval of (0,1) to a solution of the reduced problem. The reduced problem consists of the differential equation obtained by formally setting ε equal to zero in (1a) and initial conditions obtained from the boundary conditions (1b). Several examples of regular problems are also considered.

A similar technique is used to derive the properties of the solution of a particular difference scheme used to approximate (1). Under restrictions on the boundary conditions (1b) it is shown that for the stepsize much larger than ε the solution of the difference scheme, when applied to a regular problem, accurately represents the solution of the reduced problem.

Furthermore, the existence of a similarity transformation which block diagonalizes a matrix is presented as well as exponential bounds on certain fundamental solution matrices associated with the problem (1).