对流-扩散相互作用结构的不变性

本文提出并证明了不可压缩剪切层流中对流-扩散相互作用结构不变性诸定理:即二难剪切层流与其线性化及非线性扰动存在同一的对流-扩散相互作用结构,且物理尺度(指时间、空间和速度尺度)相同。给出十个推论,例如:对流-扩散相互作用可在剪切层流及其扰动场内“激发“快时间尺度和小空间尺度结构,线性化稳定性原理的约定对剪切流体系统成立等。应用题例导出计及时间-空间尺度效应和非平行流效应的广义Orr-Sommerfeld(GOS)方程,证实它有两个粘性解:阻尼层解和干扰层解;经典OS方程及其两个粘性解:边界层解和Heisenberg临界层解,Triple-deck稳定性理论基本方程及其两个粘性解,均是本文GOS方程及其两个粘性解的特例。     

再冲击载荷作用下流动混合的数值模拟

基于多介质的流体体积分数VOF（volume of fluid）方法和PPM（piecewise parabolic method）方法,给出和发展了可用于多介质粘性流体动力学的数值计算方法和计算代码MVPPM（multi-viscosity-fluid piecewise parabolic method）。为了检验和验证此计算代码,对某激波管实验再冲击载荷作用下的流体动力学不稳定性及其导致的混合过程进行了数值模拟,计算结果与实验结果一致。同时还研究了激波反射冲击作用下流体混合区的演化情况,在反射激波和混合区相互作用的瞬间,混合区的宽度明显减小,之后又迅速增大;另外,混合增长率与初始扰动的频谱有很大关联。通过对有粘性（分子动力学粘性）和无粘性结果的对比,发现粘性对混合区的影响很小。     

弹性曲杆的稳定性问题

本文给出空间任一曲杆在弯扭联合作用下的稳定性问题的一般讨论,并且给出了曲杆某一平衡状态的扰动量所满足的方程组(28)—(36),在适当的边界条件下,这些扰动量的非零解对应于临界状态。文末用这组方程具体讨论了五个实际例子,这些例子有些结果是新的,有些是用新的方法去处理老问题。     

激波与小扰动波的相互作用(激波稳定性问题)

本文讨论朗道和栗弗席兹意义下的激波稳定性问题,也就是求解激波与小扰动波的相互作用问题。在无耗散介质的定常、平面激波两边产生了小扰动。朗道等假定小扰动波传播方向是垂直于激波的,得到的稳定条件是M_>1,M_2<1。我们则把小扰动波取为二维的,即推广为小扰动波可以斜着激波传播的情形,这是更常见的。结论是,无论按群速度方向来区分趋向波和离散波,还是像朗道等那样,按相速度方向来区分趋向波和离散波,既便满足条件M_1>1,M_2<1,对于某些纵向扰动波长与频率范围的声波而言,激波都不稳定。接着提出了几个实验,根据可能的实验结果讨论了趋向波与离散波的定义应按相速度方向还是群速度方向,说明了其意义。 对于管道内的定常激波有类似结果。     

粘性及热传导对于爆轰波的影响

对在满足化学当量比的氢氧混合气体中传播的一维和二维连续旋转爆轰波进行了数值模拟,以此检验粘性和热传导对爆轰波发展和结构的影响。模拟分别基于NS和Euler控制方程,采用二步化学反应模型,对流项采用5阶MPWENO格式求解,时间方向采用3阶TVD Runge-Kutta法,粘性项采用中心差分格式进行离散。结果表明:粘性和热传导不会对爆轰波流场的基本流场结构产生影响;在具体数值上,粘性和热传导的影响值在爆轰波、斜激波、接触间断等速度或温度剧烈变化处相对较大,但总体上其影响量均比爆轰波流场的步进值小三个量级。因此,在没有壁面效应的一维爆轰和二维连续旋转爆轰波流场中,粘性和热传导项作为很小的扰动存在,对爆轰波的流场结构和数值大小基本不会产生影响。     

一维Burgers方程的各种差分格式研究

本文对Burgers方程,一维流体力学动量方程的模型方程,进行了数值实验研究。本文以两类精确解(一类表示定常拟的“激波”解,一类表示非定常的粘性耗散解)为基准。在给定的完全精确的边界条件下,专门探讨各种常用和重要差分格式的优劣。(包括精度、稳定性、计算时间等)。 本文共采用了八种格式(包括Cheng—Allen、修正Cheng格式、MacCormack、分裂格式等)对两类初、边值问题进行了计算和比较。主要的结果是: ①对非定常的粘性耗散问题,采用隐式分裂格式在精度和稳定性方面是各类格式中最好的。 ②对于具有拟“激波”样的定常问题,Cheng的修正格式2具有振幅很小、振动衰减很快的优点,它是各种格式中最佳的。 ③对Mac Cormack格式31,它可以用来算定常和非定常问题,但稳定性很差,要得到好的精度对Re数范围有一定的限制。 ④对于计算含有“激波”的流动,看来差分格式的守恒性是很重要的。 ⑤对像Burgers方程那样的非线性方程,看来Von Neumann的线化稳定性分析仍然是适用的。     

激波稳定性(Ⅰ)

本文先用Ljapunov泛函方法求解在具有任意状态方程的流体介质中传播的一维平面定常激波在一维小扰动下的运动学稳定性问题。 得出激波的运动学稳定条件为—l≤i~2(dv/dp)_H≤1,其中—不i~2是激波Rayleigh线的斜率,(dv/dp)_H是Hugoniot线斜率。此条件与过去从唯象方法得到的条件一致,然后通过对这一条件能量意义的分析,提出一般的激波一维稳定性的能量原理,并由此得出激波能量稳定条件是—1≤i~2(dv/dp)_H≤l—p_o/p_l, 其中P_O、p_l分别是波前、波后压力,这个条件比运动学条件为优,由本文首次得到。     

三维扰动波的非平行边界层稳定性研究

导出了三维扰动波的原始变量形式的抛物化稳定性方程（PSE）,研究了三维空间模态TS波的非平行边界层稳定性问题.采用了法向四阶紧致格式,以提高计算精度.通过给出不会导致奇性的坐标变换、修改外边界条件以及克服平行流初始值的瞬态影响和推进步长的限制,保证了计算的数值稳定.用补全元素带状矩阵法求解块三对角矩阵,大大提高了速度.计算结果清楚地显示了三维扰动波的演化过程和非平行性对边界层稳定性的影响,特别是,观察到非平行性对三维扰动波的影响,有时会使其稳定性出现逆转的现象.还研究了逆压梯度的作用.算例的结果与其他结果符合良好.     

基于商用CFD软件的乘波体气动外形设计方法研究

乘波体设计在超声速和高超声速飞行器设计中已经得到广泛应用,但具体设计方法仍有值得探讨之处.本文针对乘波体的工程设计,探讨了一种基于粘性流场计算的简便设计方法.这种方法以商用CFD软件为工具,首先生成锥形体的超声速粘性流场,然后采用最大压强梯度单元确定激波位置,再用圆柱面相交的方式得到乘波体上表面,利用圆柱面与激波的交线为前缘线,通过流线追踪得到乘波体的下表面,最终得到乘波体构型.本文将所用激波定位方法与存在精确解的无粘锥形流场的计算结果进行了对比,验证了该方法的可靠性.然后以马赫数M=3,设计飞行高度H=15km为设计条件,利用本文提出的方法对其气动性能进行了数值模拟和分析,并特别研究了气动性能随马赫数M和攻角的变化规律.结果表明,利用本文方法所设计的乘波体在设计点和非设计点处都具有良好稳定的气动性能.由于整个设计过程均使用现有商用CFD软件完成,既减少了自行编程所花费的时间,又具有良好的通用性,因此便于在以后的乘波体研究和工程设计中推广.     

计及轴向和剪切变形时压杆的Euler公式

依据平面截面假定, 在计及拉/压和剪切变形的情况下研究压杆的稳定性. 利用线性化 扰动方程, 导出了压杆的挠曲线方程; 根据各种端部约束的边界条件及其积分常数 存在非零解的条件,得到了 Euler临界载荷计算公式. 结果表明, 拉/压和剪切变形对稳定性的影响取决于它们的柔度差.     

Stability of Detonation Profiles in the ZND Limit

Confirming a conjecture of Lyng–Raoofi–Texier–Zumbrun, we show that stability of strong detonation waves in the ZND, or small-viscosity, limit is equivalent to stability of the limiting ZND detonation together with stability of the viscous profile associated with the component Neumann shock. Moreover, on bounded frequencies the nonstable eigenvalues of the viscous detonation wave converge to those of the limiting ZND detonation, while on frequencies of order one over viscosity, they converge to one over viscosity times those of the associated viscous Neumann shock. This yields immediately a number of examples of instability and Hopf bifurcation of reacting Navier–Stokes detonations through the extensive numerical studies of ZND stability in the detonation literature.     

Viscous regularization of the full set of nonequilibrium‐diffusion Grey Radiation‐Hydrodynamic equations

A viscous regularization technique, based on the local entropy residual, was proposed by Delchini et al. (2015) to stabilize the nonequilibrium‐diffusion Grey Radiation‐Hydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, Delchini et al. (2015) only based their work on the hyperbolic parts of the Grey Radiation‐Hydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here, we extend the theoretical grounds for the method and derive an entropy minimum principle for the full set of nonequilibrium‐diffusion Grey Radiation‐Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiation‐hydrodynamic shock simulations. Radiative shock calculations using constant and temperature‐dependent opacities are compared against semi‐analytical reference solutions, and we present a procedure to perform spatial convergence studies of such simulations. Copyright © 2017 John Wiley & Sons, Ltd.     

Interaction of a gasdynamic shock with small disturbances

The stability of shock wave based on the definition of Landau and Lifschitz^[1] is treated in this paper. This is tantamount to solving the problem of interaction of small disturbances with a shock wave. Small disturbances are introduced on both sides of a steady, non-dissipative, plane shock wave. Landau et al.^[1] obtained the stability criterionM ₁>1,M ₂<1 for small disturbances which are travelling in the direction perpendicular to the shock wave. In the present paper, we assume that the small disturbances may be two dimensional, i.e. they may be propagating in the direction inclined to the shock wave. The conclusions obtained are: regardless of whether the incident wave and diverging wave are defined according to the direction of the phase velocity or the group velocity, the shock wave is unstable for some frequencies and longitudinal wave lengths of the disturbances, even if the conditionsM ₁>1,M ₂<1 are fulfilled. Then several experiments are proposed, and the problem of ways to define the incident wave and diverging wave is discussed. The meaning of this problem is illustrated. The same results can be obtained for the steady shock wave in a tube.     

反应金属冲击反应过程的理论分析

基于1维冲击波理论和粉末材料的冲击温度计算模型对反应金属的冲击响应行为、冲击温度及冲击反应过程进行了理论分析,分别考虑了材料密实度、冲击速度对冲击压力、冲击温度的影响;结合粉末材料冲击温度计算结果及冲击反应的化学动力学方法,提出了考虑反应效率的反应金属冲击反应理论模型。利用新模型得到的计算结果与已有实验结果吻合较好。反应金属的冲击反应行为受密实度、冲击速度及材料种类影响明显。 更多还原     

Influence d'une polarisation électrique sur l'instabilité d'une interface liquide/liquide

One studies the influence of the surface tension on the stability of a liquid electrolyte/liquid metal interface. The control of this parameter is obtained by an electric polarization imposed on the liquid metal. The flow is carried out in a cylindrical cavity with turning lid and fixed bottom on the level of which a annular drain filled with liquid gallium is set. One analyzes the phenomenon of appearance of the waves of instability according to the surface tension. The experimental results are compared with a Kelvin–Helmholtz model, purely non-viscous or corrected by taking into account the normal component of the viscous constraints. To cite this article: M. Al Radi et al., C. R. Mecanique 333 (2005).     

Stability of a hypersonic shock layer on a flat plateStabilité d'une couche de choc hypersonique sur une plaque plane.

Stability of a hypersonic shock layer on a flat plate is examined with allowance for disturbances conditions on the shock wave within the framework of the linear stability theory. The characteristics of the main flow are calculated on the basis of the Full Viscous Shock Layer model. Conditions for velocity, pressure, and temperature perturbations are derived from steady Rankine–Hugoniot relation on the shock wave. These conditions are used as boundary conditions on the shock wave for linear stability equations. The growth rates of disturbances and density fluctuations are compared with experimental data obtained at ITAM by the method of electron-beam fluorescence and with theoretical data of other authors. To cite this article: A.A. Maslov et al., C. R. Mecanique 332 (2004).     

Formation of one-dimensional flows of a heat-conducting viscous gas

The article discusses the development of one-dimensional flows in a viscous heat-conducting gas using the example of two flows: 1) the flow arising with the decomposition of a discontinuity of the pressure in the quiescent gas (flow in a shock tube); 2) the flow arising with the application of a constant heat flow at a gassolid interface. For such flows, there has been very little study of the initial stage of the process, right up to the time when nonheat-conducting zones are separated out, described by the Euler equations, as well as dissipation zones of the type of a shock wave or a boundary layer, which can be treated using asymptotic methods [1–3]. With the investigation of the initial stage, the complete solution of the system of Navier—Stokes equations is required. The present article discusses the initial stage of the flows on the basis of a numerical solution of problems 1 and 2. A study is made of the effect of the Prandtl number and of the viscosity coefficient on the behavior of the gas.     

Propagation of Bleustein–Gulyaev wave in 6 mm piezoelectric materials loaded with viscous liquid

The influence of a viscous liquid on acoustic waves propagating in elastic or piezoelectric materials is of particular significance for development of liquid sensors. Bleustein–Gulyaev wave is a shear-type surface acoustic wave and has the advantage of not radiating energy into the adjacent liquid. These features make the B–G wave sensitive to changes in both mechanical and electrical properties of the surrounding environment. The Bleustein–Gulyaev wave has been reported to be a good candidate for liquid sensing application. In this paper, we investigate the potential application of B–G wave in 6 mm crystals for liquid sensing. The explicit dispersion relations for both open circuit and metalized surface boundary conditions are given. A numerical example of PZT-5H piezoelectric ceramic in contact with viscous liquid is calculated and discussed. Numerical results of attenuation and phase velocity versus viscosity, density of the liquid and wave frequency are presented. The paper is intended to provide essential data for liquid senor design and development.     

Stability of the Hypersonic Shock Layer on a Flat Plate

The stability of hypersonic viscous gas flow in a shock layer in the neighborhood of a flat plate is considered. The stability of the velocity, temperature, density, and pressure profiles calculated on the basis of the complete viscous shock layer equations is investigated within the framework of the linear stability theory with allowance for the shock wave relations. The calculated perturbation growth rates and phase velocities are compared with the experimental data obtained by means of electron-beam fluorescence.     

Numerical modeling of the initial stage of the generation of unsteady vortices from sharp corner in plane compressible flow

ＮＵＭＥＲＩＣＡＬＭＯＤＥＬＩＮＧＯＦＴＨＥＩＮＩＴＩＡＬＳＴＡＧＥＯＦＴＨＥＧＥＮＥＲＡＴＩＯＮＯＦＵＮＳＴＥＡＤＹＶＯＲＴＩＣＥＳＦＲＯＭＳＨＡＲＰＣＯＲＮＥＲＩＮＰＬＡＮＥＣＯＭＰＲＥＳＳＩＢＬＥＦＬＯＷＨｕａｎｇＤｕｎ（黄敦）（Ｄｅｐａｒｔ．...