激波诱导含灰气体边界层中的粒子分布

本文研究当激波沿着一个固体表面等速地穿越含灰气体运动时所诱导的层流边界层特性。考虑了作用在气体边界层中球形粒子的 Saffman 升力,建议了一种计算近壁区中弥散相密度剖面的方法,并给出了数值计算结果。本文结果表明:在激波后方存在着一个弯曲的薄层区域,其中的粒子密度可以比其波前原始值增加许多倍。这种粒子聚集效应对于工业中粉尘爆炸等实际问题具有重要意义。     

Radiative cooling of plasma behind a reflected shock front

Calculation of gas flow in a shock tube on the basis of ideal theory [1] leads to results that differ from the real picture. In particular, the calculated velocity of the reflected shock wave exceeds the experimentally measured velocity [2] by about 20%. The calculated parameters of shock-heated gas agree well with the experimental results only directly behind the shock front [3]. The present paper reports a theoretical and experimental investigation of the variation of the plasma parameters behind the front of a reflected shock wave in argon. A picture of the gas-dynamic processes taking place after reflection of the incident shock wave by the end of the shock tube is determined. A method is developed for approximate analytic calculation, this making it possible to determine not only the parameters of the gas directly behind the front of the reflected shock wave for different positions of the wave relative to the end of the shock tube but also the variation of these parameters in other regions behind the reflected shock wave. The calculation takes into account the influence of the boundary layer and radiative cooling in the approximation of a low degree of ionization of the plasma and persistence of equilibrium conditions in the entire region behind the reflected shock wave. The experimental and theoretical profiles of the radiation behind the reflected shock wave are compared.     

Pressure waves in a separated gas-liquid layer in a horizontal duct with a step

Pressure wave propagation into a separated gas-liquid layer in a horizontal duct with a step is investigated analytically. The linear solution is derived assuming a large density ratio of liquid to gas. The solution can be found first for the gas layer and then for the liquid layer. The linear wave in a liquid layer is valid even for fairly large initial pressure ratios, and clearly exhibits the dispersive characteristics of the pressure wave in a liquid layer. As the initial pressure ratio is increased, the pressure wave in the gas layer becomes a shock wave. Thus, its effect on the wave in a liquid layer can be found analytically by modifying the boundary condition in part. The wave in a liquid layer consists of a main wave, which propagates with the shock speed in gas, and a precursor wave, whose front propagates with the speed of sound in liquid. The precursor wave has an oscillatory structure; its amplitude increases with increasing shock strength and also with liquid layer thickness.     

Increase in the density gradient in a thermal inhomogeneity through which a shock wave passes

The amplification of weak perturbations after passing through a shock wave was noted in [1]. In [2], the increase in the density gradient behind a shock wave which decays at the boundary of a weak inhomogeneity was calculated. Growth in the amplitude of acoustic perturbations interacting with a shock wave was demonstrated experimentally in [3]. In the present investigation, the density distribution behind a shock wave propagating through a gas at rest in which the density decreases (but the pressure is constant) was measured. The absolute value of the density gradient within a thermal inhomogeneity was found to increase as a result of the passage of a shock wave. The experimental data agree well with a calculation made under the assumption that the relative change in the density along the inhomogeneity is small. In contrast to [1], quadratic terms are taken into account in the calculation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 170–175, May–June, 1981.     

The flow structure of dilute gas-particle suspensions behind a shock wave moving along a flat surface

The asymptotic and numerical investigations of shock-induced boundary layers in gas-particle mixtures are presented.The Saffman lift force acting on a particle in a shear flow istaken into account.It is shown that particle migration across the boundary layer leads tointersections of particle trajectories.The corresponding modification of dusty gas model isproposed in this paper.The equations of two-phase sidewall boundary layer behind a shock wave moving at aconstant speed are obtained by using the method of matched asymptotic expansions.Themethod of the calculation of particle phase parameters in Lagrangian coordinates isdescribed in detail.Some numerical results for the case of small particle concentration aregiven.     

Lifting of dust particles behind a reflected shock wave sliding above a particle layer

The paper presents results of mathematical simulation of particle lifting behind a shock wave reflected from the face wall and sliding above the particle layer. It is shown that particle lifting occurs in a vortex initiated in the gas when the shock wave is reflected from the wall.     

沉积粉尘的激波点火

采用瞬态阴影技术及红外光电传感器技术实验研究了沉积玉米粉的激波点火过程，并对此进行了理论分析。实验与理论分析结果表明，激波掠射沉积粉尘床后，粉尘颗粒先上扬到一定高度后才点火，颗粒的点火延迟时间与激波波前马赫数、气相氧气含量等因素有关。另外，沉积粉尘的激波点火延迟时间比相同条件下的悬浮粉尘激波点火延迟时间长。     

Formation of blast waves as a result of a low pressure domain decomposition

In this article the formation and propagation of blast wave as a result of a focusing of shock wave in a domain with low pressure and density are examined in the frame of an ideal gas model. We consider the decomposition of a pressure-density discontinuity on the boundary of the spherical (or cylindrical) domain which is filled by a gas whose pressure and density are lower than the pressure and density of gas that filling the external space. At initial moments of this decomposition the rarefaction wave propagates in the external space and the converging shock wave is formed in the domain of low pressure and density. The intensity of the converging shock wave gradually increases, and the wave transitions to the self-similar regime. After implosion, a diverging shock wave is formed which propagates through the disturbed gas. The values of wave intensity, wave impulse and other parameters for some magnitudes of initial parameters have been determined by means of numerical calculations. Received 10 August 1997 / Accepted 13 July 1998     

Dust entrainment in a shock-induced,turbulent air flow

Dust from a layer on the floor of a shock tube is entrained by the air flow behind the unsteady shock wave. The development of the dust mass concentration profiles is measured by means of an optical extinction method. The concentration profiles which can be described by an exponential law approach a stationary limit consistent with the results of pneumatic transport theory. A theoretical model simulating the dust entrainment by a diffusion process is evaluated numerically and compared with the experimental results.     

On flows behind shock waves reflected from a solid wall

The flow fields associated with the interaction of a normal shock wave with a plane wall kept at a constant temperature were studied based on kinetic theory which can describe appropriately the shock structure and its reflection process. With the use of a difference scheme, the time developments of the distributions of the fluid dynamic quantities (velocity, temperature, pressure and number density of the gas) were obtained numerically from the BGK model of the Boltzmann equation subject to the condition of diffusive-reflection at the wall for several cases of incident Mach number:M ₁=1.2, 1.5, 2.0, 3.0, 4.0, 5.0 and 6.0. The reflection process of the shocks is shown explicitly together with the resulting formation of the flow fields as time goes on. The nonzero uniform velocity toward the wall occurring between the viscous boundary layer and the reflected shock wave is found to be fairly large, the magnitude of which is of the order of several percent of the velocity induced behind the incident shock, decreasing as the incident Mach number increases. It is also seen that a region of positive velocity (away from the wall) within the viscous boundary layer manifests itself in the immediate vicinity of the wall, which is distinct for larger incident Mach numbers. Some of the calculated density profiles are compared with available experimental data and also with numerical results based on the Navier-Stokes equations. The agreement between the three results is fairly good except in the region close to the wall, where the difference in the conditions of these studies and the inappropriateness of the Navier-Stokes equations manifest themselves greatly in the gas behavior.This article was processed using Springer-Verlag TEX Shock Waves macro package 1990.     

Boundary layer flows behind constant speed shock waves moving into a dusty gas

Laminar boundary layer flows behind constant speed shock waves moving into a dusty gas are analyzed numerically. The basic equations of two-phase flows are derived in shock fixed coordinates and solved by an implicit finite-difference method for the side wall boundary layer in a dusty gas shock tube. The development of the boundary layer and resulting velocity and temperature profiles, respectively, for the gas and particles are given from the shock front to far downstream. The effects of diaphragm pressure ratio, mass loading ratio of particles and particle size upon the flow properties are discussed in detail.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

振动激发对高超声速气动力/热影响

随着飞行马赫数的不断提高,空气的高温气体效应越来越明显,对高超声速飞行器的气动力/热特性产生重要影响.高温气体效应对气动力/热的影响机理复杂,影响参数众多,迄今为止国内外尚未完全研究清楚.发生高温气体效应时,多个非线性物理过程耦合在一起,地面试验和数值模拟无法将这些过程解耦,无法给出关键物理机理.为了解决这一问题,文章提出一种理论分析与数值模拟相结合的两步渐进新方法:先通过牛顿迭代法得到发生振动激发过程的斜激波无黏解;再将该无黏解的结果作为边界条件,求解边界层的黏性解.利用该方法研究了振动激发过程对二维斜劈的气动力/热特性的影响规律.研究结果表明,振动激发过程对斜激波后的温度、密度、马赫数、雷诺数和斜激波角影响较大,而对压力和速度影响较小.斜激波波后的无黏流动与边界层流动是耦合在一起的.发生振动激发后,斜激波波后雷诺数的增大会导致边界层厚度减小,结合多个物理量的变化,如速度增大和温度减小,共同对边界层内的摩擦阻力和气动热产生影响.对比完全气体的结果发现,振动激发使壁面摩阻升高,而使壁面热流降低.分别通过影响激波层和边界层,振动激发对摩阻的影响是弱耦合的,而对热流的影响则是强耦合的.     

Structure of the heating layer ahead of the front of a strong intensely emitting shock wave

The problem of the structure and brightness of strong shock waves arises in the investigation of such phenomena as the motion of large meteoroids in the atmosphere, optical and electrical discharges, the development of strong explosions, and other similar processes and in the creation of powerful radiation sources based on them. This problem also has a general physics interest. As the propagation velocity of a strong shock wave increases the gas temperature behind its front and the role of emission grow. Part of the radiation emitted by the gas heated and compressed in a shock wave is absorbed ahead of the front, forming the so-called heating layer. The quasisteady structure of a strong intensely emitting shock wave was studied in [1, 2]. In this case a diffusional approximation and the assumption of a gray gas were used to describe the radiation transfer. They introduced the concept of a wave of critical amplitude, when the maximum temperature T_- in the heating layer reaches the temperature T_a determined on the basis of the conservation laws, i.e., from the usual shock adiabat; it is shown that behind a compression shock moving through an already heated gas there is a temperature peak in which the maximum temperature T₊ exceeds T_a. The problem of the quasisteady structure of an emitting shock wave in air of normal density was solved numerically in [3]. The angular distribution of the radiation was approximately taken into account — it was assigned by a simple cosinusoidal law. The spectral effects were taken into account in a multigroup approximation. They introduced 38 spectral intervals, which is insufficient to describe a radiation spectrum with allowance for the numerous lines and absorption bands.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 86–92, September–October, 1978.     

一个改进的电磁波传输激波管实验

在中国科学院力学研究所$\varPhi $ 800 mm高温低密度激波管上进行电磁波在等离子体中传输机理研究时,低密度和强激波条件下,由于气体解离和电离等非平衡过程,使得激波后2区宽度显著减小;同时由于边界层效应造成激波衰减和接触面加速,使得激波后2区长度进一步减小.这两个效应导致激波管2区实验观测 时间减小,2区气体处于非平衡状态,增加了观察数据的不稳定性和数据分析的难度.本文提出在$\varPhi 800 $ mm高温低密度激波 管中采用氩气(Ar)和空气(Air)混合气替代纯空气作为激波管实验介质气体.利用Ar不解离和难电离的特性,减小激波前后压缩比,从而 增加激波后2区实验时间和气体长度. 采用Langmuir 静电探针和微波透射诊断技术测量激波后电子密度,同时利用探针测量激波后2区实验时间.结果显示,在Ar+Air混合气实验中,激波波后电子密度可达与纯Air同样的10$^{13}$cm$^{ - 3}$量级.在与纯Air相同的电子密度和碰撞频率条件下,采用95%Ar+5%Air和90%Ar+10%Air两种混合气,激波后2区实验时间和气体长度约为纯Air条件下的5$\sim $10倍,其中2区实验时间为300$\sim $800 $\mu$s,2区气体长度1$\sim $1.5 m.在$\varPhi $800 mm激波管中采用Ar+Air介质气体进行电磁波传输实验,获得了比在纯Air介质中与理论预测更一致的结果.      

Modelling of dust lifting using the Lagrangian approach

The subject of this paper is dust lifting behind shock waves, a process that is important for the formation of explosive dust clouds in air. While Eulerian–Eulerian has been the standard numerical technique for such simulations, the Eulerian–Lagrangian technique has been used in this paper, making it possible to take into account more physical phenomena, such as particle–particle and particle–wall collisions. The results of the simulations are shown mainly graphically, as snapshots of particle positions at given times after the passing of the shock wave. The results show that the collisions, and the coefficient of restitution assumed for them, is important in determining the mobility and lifting of dust behind shock waves. The results also show that the idea of a horizontally travelling shock wave is an oversimplification: the strong pressure gradient at the surface results in a series of reflected waves generated at the surface and travelling into the gas phase.     

Head on collision of a planar shock wave with a dusty gas layer

The head-on collision of a planar shock wave with a dust-air suspension is studied numerically. In this study the suspension is placed inside a conduit adjacent to its rigid end-wall. It is shown that as a result of this collision two different types of transmitted shock waves are possible, depending on the strength of the incident shock wave and the dust loading ratio in the suspension. One possibility is a partially dispersed shock wave, the other is a compression wave. The flow fields resulting in these two options are investigated. It is shown that in both cases, at late times after the head-on reflection of the transmitted shock wave from the conduit end-wall a negative flow (away from the end-wall) is evident. The observed flow behavior may suggest a kind of dust particle lifting mechanism that could shed new light on the complex phenomenon of dust entrainment behind sliding shock waves.      

Shock induced Richtmyer-Meshkov instability in the presence of a wall boundary layer

An experimental investigation on gaseous mixing zones originated from the Richtmyer-Meshkov instability has been undertaken in a square cross section shock tube. Mass concentration fields, of one of the two mixing constituents, have been determined within the mixing zone when the shock wave passes from the heavy gas to the light one, from one gas to an other of close density, and from the light gas to the heavy one. Results have been obtained before and after the coming back of the reflected shock wave. The diagnostic method is based on the infrared absorption of one of the two constituents of the mixing zone. It is shown that the mixing zone is strongly deformed by the wall boundary layer. The consequence is the presence of strong gradients of concentration in the direction perpendicular to the shock wave propagation. Finally, it is pointed out that the mixing goes more homogeneous when the Atwood number tends to zero.     

Experimental and numerical investigation into the dynamics of dust lifting up from the layer behind the propagating shock wave

In a number of industrial facilities and factory buildings dust layers cover floors, walls, ceilings and various installations. The dust can be easily dispersed by pressure waves generated by weak explosions or as a result of damage of a compressed gas systems. If the obtained explosive dust-air mixture is ignited, a devastating explosion may occur. The aim of the work was to study the dust lifting process from the layer behind the propagating shock wave and to determine some important parameters, which later could be used for development and validation of the numerical model of the process. The experiments were conducted with the use of a shock tube. For measuring the dust concentration in the mixture with air, a special five-channel optical device was constructed, enabling measurements at five positions located in one vertical plane along the height of the tube. The delay in lifting of the dust from the layer and the vertical velocity of the dust cloud were calculated from the dust concentration measurements. The research was carried out for various initial conditions and for various types of dusts. The results obtained in tests with black coal dust are presented in the paper. Three shock wave velocities: 450, 490 and 518 m/s and three dust layer thicknesses, equal to 1.0, 1.5 and 2.0 mm, were taken into consideration. Measurements results of the mean vertical component of the dust cloud velocity between the layer and the first laser beam were used in a new model, where the dust dispersing process is modeled as an injection of the dust from the layer. The numerical simulations were based on the Euler or Lagrange model of the dust phase. In case of Euler model, the dust layer was replaced by injection of dust from the bottom of the channel. The calculations were performed for two models of the investigated process. In the first model, correlation was worked out for all tested dusts and in the new model, the individual correlations for every tested dust were prepared. The results obtained with use of the second model proved to be closer to the experimental results. It appeared, however, that lifting up of the dust from the thick layers, thicker than 1 mm, is a more complex process than that from a thin layers and still requires more research. Probably the problem is, that the shock wave action upon the thick layer causes its aggregation in the first stage of the dispersing process, what makes the dust lifting process more difficult.     

Near-wall imaging using toluene-based planar laser-induced fluorescence in shock tube flow

A quantitative thermometry technique, based on planar laser-induced fluorescence (PLIF), was applied to image temperature fields immediately next to walls in shock tube flows. Two types of near-wall flows were considered: the side wall thermal boundary layer behind an incident shock wave, and the end wall thermal layer behind a reflected shock wave. These thin layers are imaged with high spatial resolution (15μm/pixel) in conjunction with fused silica walls and near-UV bandpass filters to accurately measure fluorescence signal levels with minimal interferences from scatter and reflection at the wall surface. Nitrogen, hydrogen or argon gas were premixed with 1–12% toluene, the LIF tracer, and tested under various shock flow conditions. The measured pressures and temperatures ranged between 0.01 and 0.8 bar and 293 and 600 K, respectively. Temperature field measurements were found to be in good agreement with theoretical values calculated using 2-D laminar boundary layer and 1-D heat diffusion equations, respectively. In addition, PLIF images were taken at various time delays behind incident and reflected shock waves to observe the development of the side wall and end wall layers, respectively. The demonstrated diagnostic strategy can be used to accurately measure temperature to about 60 μm from the wall.     

A self- similar solution of a shock propagation in a mixture of a non-ideal gas and small solid particles

Similarity solutions are obtained for unsteady, one-dimensional self-similar flow behind a strong shock wave, driven by a moving piston, in a dusty gas. The dusty gas is assumed to consist of a mixture of small solid particles and a non-ideal gas, in which solid particles are continuously distributed. It is assumed that the equilibrium flow-condition is maintained and variable energy input is continuously supplied by the piston. Solutions are obtained under both the isothermal and adiabatic conditions of the flow-field. The spherical case is worked out in detail to investigate to what extent the flow-field behind the shock is influenced by the non-idealness of the gas in the mixture as well as by the mass concentration of the solid particles, by the ratio of density of the solid particles to the initial density of the mixture and by the energy input due to moving piston. A comparison is also made between isothermal and adiabatic cases.