管道内激波的不稳定性

本文将无限大激波阵面的激波不稳定性理论[1]推广到矩形截面管道内的激波不稳定性问题.首先,给出这个问题的数学提法,包括扰动方程与三类边界条件.其次,给出扰动方程的普遍解.上游和下游的普遍解分别含有5个待定常数.再次,在一类边界条件和一个假定下,证明了激波前扰动为0,激波后两个声扰动之一为0.边界条件是,X→±∞处扰动物理量为0.假定只讨论激波不稳定性问题,从而可先设ω=iγ,γ是不稳定性增长率,为正实数.另一类边界条件是管壁上法向速度扰动为0,它使波数只能取一组离散值.最后,用扰动激波上的5个守恒方程这一边界条件来决定激波后4个待定常数和扰动激波振幅这个未知量时,导出了色散关系.结果表明,正实数γ确是存在.不稳定激波有两种模式,一种模式为γ=-W·k(W<0)它代表激波的绝对不稳定性,是新得到的模式.另一种模式与过去工作中给出的[2,3]大体相同.本文则进一步给出了这种模式的激波不稳定性增长率,并指出j2((?V/?P)_H=1+2M为最不稳定点(即无量纲化的不稳定性增长率Г=∞).如果不假定ω是纯虚数,而是复数,其虚部为正实数Im(ω)≥0.本文也严格证明了其不稳定性判据仍有两种模式,ω仍为纯虚数.     

反射型激波风洞中激波与边界层的相互作用

本文研究了反射型激波风洞中由于非完全反射对激波与壁面边界层相互作用的影响,给出了在反射激波坐标系中计算边界层速度分布、温度分布和马赫数分布的计算方法.算例表明,在计及氮气的平衡真实气体效应的情形下,随着入射激波马赫数M_s的增大,边界层的最小马赫数从壁面处移到边界层内;随着喷管喉道面积的增大,边界层的最小马赫数、反射激波的分叉角α和分叉区后的射流速度均随之减小.计算结果与实验值相比是一致的.     

Stability of One-Dimensional Steady Flows with Detonation Wave in a Channel of Variable Cross-Sectional Area

Computational Mathematics and Mathematical Physics - The stability of one-dimensional steady flows of an ideal (inviscid and non-heat-conducting) gas in channels of variable cross section with...     

Flow Structure behind a Shock Wave in a Channel with Periodically Arranged Obstacles

We study the propagation of a pressure wave in a rectangular channel with periodically arranged obstacles and show that a flow corresponding to a discontinuity structure may exist in such a channel. The discontinuity structure is a complex consisting of a leading shock wave and a zone in which pressure relaxation occurs. The pressure at the end of the relaxation zone can be much higher than the pressure immediately behind the gas-dynamic shock. We derive an approximate formula that relates the gas parameters behind the discontinuity structure to the average velocity of the structure. The calculations of the pressure, velocity, and density of the gas behind the structure that are based on the average velocity of the structure agree well with the results of gas-dynamic calculations. The approximate dependences obtained allow us to estimate the minimum pressure at which there exists a flow with a discontinuity structure. This estimate is confirmed by gas-dynamic calculations.     

Numerical Investigation of Shock Wave Interference Heating in Chemical Nonequilibrium

A Navier‐Stokes solver is extended by a nonequlibrium gas model to investigate heat transfer rates in hypersonic flow. The nonequlibrium model is shortly discussed and results for a type IV interaction on a cylinder are presented and compared to experimental measurements. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Simple Approximate Solution for the Interaction of a Shock Wave with an Area Change

An approximate solution of the equations for the interactionof a shock with a divergence has been found and used to startan iterative process to obtain the exact solution.     

An Interaction of a Rarefaction Wave and a Transonic Shock for the Self-Similar Two-Dimensional Nonlinear Wave System

We study a two dimensional Riemann problem for the self-similar nonlinear wave system which gives rise to an interaction of a transonic shock and a rarefaction wave. The interesting feature of this problem is that the governing equation changes its type from supersonic in the far field to subsonic near the origin. The subsonic region is then bounded above by the sonic line (degenerate) and below by the transonic shock (free boundary). Furthermore due to the rarefaction wave in the downstream, which interacts with the transonic shock, the problem becomes inhomogeneous and degenerate. We establish the existence result of the global solution to this configuration, and present analysis to understand the solution structure of this problem.     

非传播孤立波及其相互作用的数值模拟

通过数值求解由Miles导出的目前公认的的非传播孤立波的控制方程——一个带复共轭项的非线性立方SchrLdinger方程,对非传播孤立波进行研究。讨论了Miles方程中的线性阻尼系数α的值,计算表明,线性阻尼α对形成稳定的非传播孤立波影响很大,Laedke等人关于非传播孤立波的稳定性条件只是一个必要条件,而不是充分条件。模拟了两个非传播孤立波的相互作用,数值模拟表明,两个波的作用模式依赖于系统的参数,对不同的初始扰动及其演化的计算表明,只有适当的初始扰动才能形成单个稳定的非传播孤立波,否则扰动可能消失或发展成多个孤立波。     

直管束流固耦合振动的数值模拟

为了研究反应堆结构中的诸如燃料棒、蒸汽发生器和其它换热器传热管束等的流体-结构交互作用问题,利用有限体积法离散大涡模拟(large eddy simulation, LES)的流体控制方程,用有限元方法求解结构动力学方程,并结合动网格技术,建立三维流体诱发振动的数值模型,模拟直管束中流体的流动及结构振动,实现计算结构动力学(computational structure dynamics, CSD)与计算流体力学(computational fluid dynamics, CFD)之间的联合仿真．首先,基于流固耦合方法对单管的流致振动特性进行了详细分析,得到了其动力学响应与流场特性;其次基于建立的传热管束流致振动计算模型,研究了两并列管、两串列管以及3×3正方形排列管束的流致振动行为．     

三维矩形槽道中颗粒沉降的数值模拟

采用三维格子Boltzmann方法对矩形通道中的颗粒沉降进行了模拟研究．单颗粒沉降的模拟结果表明,颗粒最终的稳定沉降位置沿槽道中心线,不受颗粒初始位置和直径的影响．颗粒和壁面之间的两体相互效应可以用无因次沉降速度定量描述,无因次沉降速度的模拟结果和实验结果定量上吻合一致．模拟分析了双颗粒沉降的DKT（drafting, kissing and tumbling）过程,探讨了颗粒直径比以及壁面效应对DKT过程的影响．模拟发现当颗粒直径相同时,双颗粒的沉降过程为周期性的DKT过程,从而形成双螺旋形式的沉降轨迹,此螺旋沉降轨迹的频率和振幅受颗粒初始位置影响．从模拟结果中还得到颗粒群的最终稳定构型,并进行了构型对比分析．最后对包含49个颗粒的颗粒群沉降行为进行了模拟,说明多体相互作用在对称性的情况下可以简化．     

运动壁面槽道流动的直接数值模拟

采用谱方法,在曲线坐标系下对不可压缩Newton流体的N-S方程进行求解,采用定义在物理空间中的流动物理量以避免使用协变、逆变形式的控制方程．在计算空间采用Fourier-Chebyshev谱方法进行空间离散,时间推进采用高精度时间分裂法．为了减小时间分裂带来的误差,采用了高精度的压力边界条件．与其他求解协变、逆变形式控制方程的谱方法相比,该方法在保持谱精度的同时减小了计算量．首先通过静止波形壁面和行波壁面槽道湍流的直接数值模拟,对该数值方法进行了验证;其次,作为初步应用,利用该方法研究了槽道湍流中周期振动凹坑所产生的流动结构．     

声波方程高阶差分方法数值模拟结果研究

首先,给出了声波方程时空域高阶差分格式.证明了差分格式在时间上是二阶精度,在空间上最高可以达到2M精度.其次,对该高阶差分格式优缺点评价,新的差分格式是一种关于一个方向上所用到的临近网格节点数目一半的可变长度的差分算子,为不同精度需求提供了灵活可变的差分算子公式.另外一种意义上说,新的差分格式是依赖于频率的,同一种差分格式对于不同频率的震源,其频散的程度也不一样,因此只有采用了合适的差分形式才能够达到最好的效果.最后,给出了一系列数值模拟实例,验证了文中所得到的结论.     

外卷边槽钢辊弯成型过程数值模拟

拓展了结构分析有限条法,基于固体力学有限形变理论的更新拉格朗日法(U.L.法),建立了弹塑性大变形样条有限条法,并将其用于模拟外卷边槽钢辊弯成型过程,分析了带材的变形特点,获得了变形带材的三维位移场、应变场和应力场。算例表明,变形带材的角部出现横向压应变峰值,外卷边轧辊前部位出现纵向拉应变峰值。另外,带材的横向变形是主要的,纵向变形较小。     

Interaction of Weak Shock Waves with Magnetohydrodynamic Boundary Layers

The interaction of weak shock waves with magnetohydrodynamicboundary layers is investigated. An approximate model is usedin which the main stream is supersonic, and the laminar boundarylayer is replaced by a stationary or shear layer in the xy-plane.The inviscid semi-infinite fluid is continuous and perfectly-electricallyconducting. The fluid velocity U(y) varies monotonically fromzero at the non-conducting wall, y = 0, to a supersonic valueat the outer edge of the shear layer where y = , beyond whichthe supersonic velocity remains uniform. In practice, we shallassume that the velocity profile in the region y < is linear;also that the fluid density in the basic flow, and the soundspeed c, are independent of y. A uniform magnetic field, alignedparallel to the free stream at infinity, is assumed to be appliedthroughout the flow field. Perturbations to the flow are assumedto be small so that the governing equations can be linearized.Disturbances to the flow are found to propagate upstream farmore than in the corresponding non-magnetic problem, and anincident compression wave is reflected locally as a compressionwave upstream and an expansion wave downstream of the incidentdisturbance.     

Accuracy of MUSCL-Type Schemes in Shock Wave Calculations

Doklady Mathematics - The central-difference Nessyahu–Tadmor (NT) scheme is considered, which is built using second-order MUSCL reconstruction of fluxes. The accuracy of the NT scheme is...