Decay of shock waves in a dusty-gas shock tube

A numerical study is performed for the unsteady nonequilibrium flow of a gas-particle mixture in a shock tube, where a semi-empirical formula for a single particle is assumed to calculate the drag and heat transfer rate of the particle cloud. To simulate actual flows of the mixture in which the size of the particles is distributed over a finite range, the motion of the particles is analyzed by dividing them into several groups according to their different diameters. It is shown that the particles of diameter larger than the average value cause a significant delay in the relaxation of the gas-particle flow. Good agreement is obtained between the numerical and the experimental results of the decrease in the shock propagation velocity, except for strong shock waves transmitted into dusty gas with a high loading ratio.     

Reflection of shock waves from a solid boundary in a mixture of condensed materials. 1. Equilibrium approximation

The process of reflection of shock waves (SW) from a solid wall in a two-component mixture of condensed materials is studied within the framework of mechanics of heterogeneous media. The velocity of a reflected SW and the values of the parameters behind its front are analytically determined as functions of the velocity of the incident wave and the initial parameters of the mixture. It is shown that the absolute value of the velocity of the reflected SW can be greater than the velocity of the incident SW in mixtures with a small content of the light component and at low velocities of the incident shock wave. The nonmonotonic character of the dependence of pressure in the final equilibrium state behind the incident SW on the initial volume concentration of particles is demonstrated. The velocity of the incident SW is estimated for the case where a similar effect is also observed behind a reflected SW. It is established that, for weak shock waves, the dependence of the amplification factor of the reflected SW on the initial volume concentration of the light component is nonmonotonic and has a local maximum. It is noted that, as the velocity of the incident SW increases, the effect of compacting of the mixture (increase in concentration of the heavy component) behind the reflected SW becomes much less pronounced than in a passing SW. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences. Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 73–78, September–October, 1999.     

Experimental study of planar shock wave interactions with dense packed sand wall

A dense packed sand wall is impacted by a planar shock wave in a horizontal shock tube to study the shock-sand wall interaction. The incident shock Mach number ranges from 2.18 to 2.38. A novel device for actively rupturing diaphragm is designed for the driver section of the shock tube. An apparatus for loading particles is machined by the electrical discharge cutting technique to create a dense packed particle wall. High-speed schlieren imaging system and synchronized pressure measurement system are used together to capture the wave structures and particle cloud velocity. The dynamic evolution model from dense packed particles to dense gas–solid cloud at the initial driving stage is established. The blockage and permeation effects of the sand wall work together and influence each other. The high pressure gas behind the incident shock wave blocked by the sand wall pushes the upstream front of the wall forward like a piston. Meanwhile, the high speed gas permeating through the sand wall drags the sands of the most downstream layer forward. The incident shock strength, initial sand wall thickness and particle diameter are varied respectively to investigate the shock attenuation and the wall acceleration. Increasing the sands diameter or mixing in small diameter sands can significantly attenuate the incident shock. The smaller particles or the particles in thinner wall can be dispersed into a larger range in the process of transform from dense packed particles to dense gas–solid cloud. Moreover, the stronger incident shock can disperse the particles into a larger region.     

Aerodynamic characteristics of solid particles�� acceleration by shock waves

In this study, the interaction of a planar shock wave with a group of particles has been investigated using high-speed photography and dynamic pressure measurements. Experiments were carried out in a horizontal circular shock tube. The influence of the particle loading ratio, particle diameter, driving gas and shock wave Mach number on the acceleration was studied. It was found that the higher the particle loading ratio, the greater was the particle velocity. This is due to the higher driving pressure. Helium and nitrogen gases play quite different roles in acceleration. Pressure multiplication during shock wave interaction with particles also appears. Based on the experimental results, the discussion regarding partial quantitative velocities and accelerations of particle groups, as well as the attenuation factors when shock waves pass through the particles, is given.     

Some properties of strongly nonequilibrium flows with population inversion in shock waves

The effect of incident flow parameters and composition of a CO₂ + N₂ + H₂O(He) mixture on population inversion in the relaxation zone of a normal shock wave is considered.     

Interaction of a shock wave with a loose dusty bulk layer

The interaction of a planar shock wave with a loose dusty bulk layer has been investigated both experimentally and numerically. Experiments were conducted in a shock tube. The incident shock wave velocity and particle diameters were measured with the use of pressure transducers and a Malvern particle sizer, respectively. The flow fields, induced by shock waves, of both gas and granular phase were visualized by means of shadowgraphs and pulsed X-ray radiography with trace particles added. In addition, a two-phase model for granular flow presented by Gidaspow is introduced and is extended to describe such a complex phenomenon. Based on the kinetic theory, such a two-phase model has the advantage of being able to clarify many physical concepts, like particulate viscosity, granular conductivity and solid pressure, and deduce the correlative constitutive equations of the solid phase. The AUSM scheme was employed for the numerical calculation. The flow field behind the shock wave was displayed numerically and agrees well with our corresponding experimental results.      

A physical model of the structure and attenuation of shock waves in metals

In this paper, a physical model of the structure and attenuation of shock waves in metals is presented. In order to establish the constitutive equations of materials under high velocity deformation and to study the structure of transition zone of shock wave, two independent approaches are involved. Firstly, the specific internal energy is decomposed into the elastic compression energy and elastic deformation energy, and the later is represented by an expansion to third-order terms in elastic strain and entropy, including the coupling effect of heat and mechanical energy. Secondly, a plastic relaxation function describing the behaviour of plastic flow under high temperature and high pressure is suggested from the viewpoint of dislocation dynamics. In addition, a group of ordinary differential equations has been built to determine the thermo-mechanical state variables in the transition zone of a steady shock wave and the thickness of the high pressure shock wave, and an analytical solution of the equations can be found provided that the entropy change across the shock is assumed to be negligible and Hugoniot compression modulus is used instead of the isentropic compression modulus. A quite approximate method for solving the attenuation of shock wave front has been proposed for the flat-plate symmetric impact problem.     

Specific features of incident and reflected blast waves

On the basis of numerical modeling specific features of shock wave reflections were analyzed. It was found, that after diaphragm rupture self-modeling pressure and velocity distributions nearby the shock front establish. But in some special cases the temperature behind the shock front can rise. This peculiarity should be taken into account when performing experiments with high reactive gaseous mixtures. The temperature on the shock front and the velocity gradient behind it are uniform in the case of strong blast wave reflections. This effect is observed in the zone with an elevated temperature profile behind the incident blast wave. The reflected triangular waves conserve a quasi-self-modeling character by pressure. Typical experiments were carried out to verify the theoretical predictions. The effects of reflected wave acceleration in the case of triangular waves and the self-similar character of the pressure profiles were observed.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Particle image velocimetry measurements of a shock wave/turbulent boundary layer interaction

Particle image velocimetry is used to investigate the interaction between an incident shock wave and a turbulent boundary layer at Mach 2.1. A particle response assessment establishes the fidelity of the tracer particles. The undisturbed boundary layer is characterized in detail. The mean velocity field of the interaction shows the incident and reflected shock wave pattern, as well as the boundary layer distortion. Significant reversed flow is measured instantaneously, although, on average no reversed flow is observed. The interaction instantaneously exhibits a multi-layered structure, namely, a high-velocity outer region and a low-velocity inner region. Flow turbulence shows the highest intensity in the region beneath the impingement of the incident shock wave. The turbulent fluctuations are found to be highly anisotropic, with the streamwise component dominating. A distinct streamwise-oriented region of relatively large kinematic Reynolds shear stress magnitude appears within the lower half of the redeveloping boundary layer. Boundary layer recovery towards initial equilibrium conditions appears to be a gradual process.     

A multiphase shock tube for shock wave interactions with dense particle fields

Currently there is a substantial lack of data for interactions of shock waves with particle fields having volume fractions residing between the dilute and granular regimes. To close this gap, a novel multiphase shock tube has been constructed to drive a planar shock wave into a dense gas–solid field of particles. A nearly spatially isotropic field of particles is generated in the test section by a gravity-fed method that results in a spanwise curtain of spherical 100-micron particles having a volume fraction of about 20%. Interactions with incident shock Mach numbers of 1.66, 1.92, and 2.02 are reported. High-speed schlieren imaging simultaneous with high-frequency wall pressure measurements are used to reveal the complex wave structure associated with the interaction. Following incident shock impingement, transmitted and reflected shocks are observed, which lead to differences in particle drag across the streamwise dimension of the curtain. Shortly thereafter, the particle field begins to propagate downstream and spread. For all three Mach numbers tested, the energy and momentum fluxes in the induced flow far downstream are reduced about 30–40% by the presence of the particle field.     

两相正激波松弛流的数值研究

对气、固两相正激波松弛流动进行了数值研究,方程中考虑了压力梯度及非匀速运动引起的附加质量力。给出了完整的计算方法,对三种不同固相容积比、不同固相颗粒直径和不同马赫数分别进行了数值计算,所得计算结果给出了气、固两相的速度、温度、压力、密度、固相容积比及熵值沿流向分布情况。文章对气、固两相参数在松弛区中的变化规律进行了讨论。     

气相爆轰波冲击气固界面的透反射特性

为了研究气相爆轰波冲击气固界面过程中透射波和反射波的相关特性,建立爆轰波冲击气固界面的一维理论模型,对不同初始压力条件下爆轰波到达气固界面后的界面两侧的压力和界面速度变化进行分析。利用时空守恒元求解元方法对气相爆轰波冲击气固界面过程进行数值模拟,分析气体部分反射波的压力分布和速度变化规律及透射入固体中应力波的波形和波速特征,并搭建气相爆轰波冲击活塞实验装置进行进一步验证。结果表明:气体爆轰波到达气固界面后,在固体中透射指数形式的弹性波,并在界面处向气体区反射一道激波。爆轰波后的稀疏波与反射激波相交,削弱反射激波,最终形成稳定激波回传。气固界面在稀疏波和反射稀疏波的作用下,压力和速度逐渐下降,最终也形成稳定状态。在不同混气初始压力情况下,爆轰波冲击过程中产生的最高压力和爆压的比值基本保持不变。理论模型对特征点相关物理量的计算值和实验数据符合的较好。     

Dense particle cloud dispersion by a shock wave

A dense particle flow is generated by the interaction of a shock wave with an initially stationary packed granular bed. High-speed particle dispersion research is motivated by the energy release enhancement of explosives containing solid particles. The initial packed granular bed is produced by compressing loose powder into a wafer with a particle volume fraction of $\phi _\mathrm{p} = 0.48$ . The wafer is positioned inside the shock tube, uniformly filling the entire cross-section. This results in a clean experiment where no flow obstructing support structures are present. Through high-speed shadowgraph imaging and pressure measurements along the length of the channel, detailed information about the particle shock interaction was obtained. Due to the limited strength of the incident shock wave, no transmitted shock wave is produced. The initial solid-like response of the particle wafer acceleration forms a series of compression waves that eventually coalesce to form a shock wave. Breakup is initiated along the periphery of the wafer as the result of shear that forms due to the fixed boundary condition. Particle breakup is initiated by local failure sites that result in the formation of particle jets that extend ahead of the accelerating, largely intact, wafer core. In a circular tube, the failure sites are uniformly distributed along the wafer circumference. In a square channel, the failure sites, and the subsequent particle jets, initially form at the corners due to the enhanced shear. The wafer breakup subsequently spreads to the edges forming a highly non-uniform particle cloud.     

Particle relaxation and its influence on the particle image velocimetry cross-correlation function

A study of some aspects of tracer particle responses to step changes in fluid velocity is presented. The effect of size distribution within a seed material on measured relaxation time is examined, with polydisperse particles of the same median diameter shown to possess a significantly higher relaxation time than their monodisperse counterparts when measured via a particle image velocimetry algorithm. The influence of a shock wave–induced velocity gradient within a PIV interrogation window on the correlation function is also examined using the noiseless cross-correlation function of Soria (Turbulence and coherent structures in fluids, plasmas and nonlinear media. World Scientific, Singapore, 2006). The presence of a shock is shown to introduce an artificial fluctuation into the measurement of velocity. This fluctuation is a function of the shock position, shock strength, spatial ratio and particle distribution. When the shock is located at the middle of the window, the magnitude of the fluctuation increases monotonically with increasing spatial ratio, increases asymptotically with shock strength, and decreases for increasing particle polydispersity. When the shock is located at the left-hand edge of the window, the magnitude of the artificial fluctuation is highest for intermediate spatial ratios, going to zero at infinitely high and low values. In this instance, particle polydispersity acts to increase the magnitude of fluctuations in measured velocity. In both cases, particle polydispersity serves to broaden the PDF of measured velocity. For the cases presented herein, with a shock located within the interrogation window, the root mean square of the artificial velocity fluctuations reaches values in excess of 30% of the freestream velocity.     

基于CN自由基的火星再入流场温度测量

利用氰自由基（CN）B2Σ+→X2Σ+ 电子带系的发射光谱温度测量技术诊断模拟火星再入流场高温气体的温度. 以双原子分子光谱理论为基础,通过确定CN 自由基B2Σ+→X2Σ+ 电子带系中 Δv = 0 振动带系发射光谱的跃迁波数、Einstein 跃迁几率以及不同振转能级粒子数等参数,得到了任意转动温度和振动温度下的理论光谱强度分布,结合经窄线宽半导体激光器标定的仪器展宽（Lorentz 线型,半宽度FWHM 为0.154 nm）,为CN自由基B2Σ+→X2Σ+ 电子带系发射光谱测温技术提供理论依据. 利用激波管模拟火星再入流场环境,通过分析激波波后不同时刻处高时间、空间分辨率的CN 自由基发射光谱,得到了激波波后高温气体不同时刻处的转动温度和振动温度,并根据得到的温度信息给出了激波诱导时间和弛豫时间.      

氢氧燃烧及爆轰驱动激波管

分析并观察了沿驱动段轴向分布多火塞燃烧驱动段的性能．提出主膜处同一管截面均匀分布三火花塞引燃的点火方法．用这种点火方法驱动产生的入射激波强度重复性较高,激波后气流速度、温度和压力的定常性亦大大改善,可满足气动试验实际要求．提出在驱动段尾端串接卸爆段来消除爆轰波反射高压,从而可使反向爆轰驱动段用来产生高焓高密度试验气流．这种反向爆轰驱动产生的入射激波重复性高,激波衰减弱．在主膜处的收缩段产生的反射波可缓解爆轰波后跟随的稀疏波的不利影响,从而使前向爆轰驱动具有实用性．在产生的入射激波强度相同条件下,前向爆轰驱动所需的爆轰驱动段可爆混合气初始压力可较反向爆轰低近一个量级．     

Acceleration of a sphere behind planar shock waves

The paper presents the results of an investigation on the motion of a spherical particle in a shock tube flow. A shock tube facility was used for studying the acceleration of a sphere by an incident shock wave. Using different optical methods and performing experiments in two different shock tubes, the trajectory and velocity of a spherical particle were measured. Based upon these results and simple one-dimensional calculations, the drag coefficient of a sphere and shading effect of sphere interaction with a shock tube flow were studied.     

Measurement and simulation of the two-phase velocity correlation in sudden-expansion gas-particle flows

In this paper the present authors measured the gas-particle two-phase velocity correlation in sudden expansion gas-particle flows with a phase Doppler particle anemometer(PDPA) and simulated the system behavior by using both a Reynolds-averaged Navier-Stokes(RANS) model and a large-eddy simulation(LES).The results of the measurements yield the axial and radial time-averaged velocities as well as the fluctuation velocities of gas and three particle-size groups(30 μ m,50 μ m,and 95 μ m) and the gas-particle velocity correlation for 30 μ m and 50 μ m particles.From the measurements,theoretical analysis,and simulation,it is found that the two-phase velocity correlation of sudden-expansion flows,like that of jet flows,is less than the gas and particle Reynolds stresses.What distinguishes the two-phase velocity correlations of sudden-expansion flow from those of jet and channel flows is the absence of a clear relationship between the two-phase velocity correlation and particle size in sudden-expansion flows.The measurements,theoretical analysis,and numerical simulation all lead to the above-stated conclusions.Quantitatively,the results of the LES are better than those of the RANS model.     

Interaction of a high-speed combustion front with a closely packed bed of spheres

The head-on collision of a combustion front with a closely packed bed of ceramic-oxide spheres was investigated in a vertical 76.2 mm diameter tube containing a nitrogen diluted stoichiometric ethylene–oxygen mixture. A layer of spherical beads in the diameter range of 3–12.7 mm was placed at the bottom of the tube and a flame was ignited at the top endplate. Four orifice plates spaced at one tube diameter were placed at the ignition end of the tube in order to accelerate the flame to either a “fast-flame” or a detonation wave before the bead layer face. The mixture reactivity was adjusted by varying the initial mixture pressure between 10 and 100 kPa absolute. The pressure before and within the bead layer was measured by flush wall-mounted pressure transducers. For initial pressures where a fast-flame interacts with the bead layer peak pressures recorded at the bead layer face were as high as five times the reflected Chapman–Jouget detonation pressure. The explosion resulting from the interaction developed by two distinct mechanisms; one due to the shock reflection off the bead layer face, and the other due to shock transmission and mixing of burned and unburned gas inside the bead layer. The measured explosion delay time (time after shock reflection from the bead layer face) was found to be independent of the incident shock velocity. As a result, the explosion initiation is not the direct result of the shock reflection process but instead is more likely due to the interaction of the reflected shock wave and the trailing flame. The bead layer was found to be very effective in attenuating the explosion front transmitted through the bead layer and thus isolating the tube endplate. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Reconstruction of velocity fields from wall pressure measurements in a shock wave/turbulent boundary layer interaction

We present here experimental results in a shock wave/turbulent boundary layer interaction at Mach number of 2.3 impinged by an oblique shock wave, with a deflection angle of 9.5°, as installed in the supersonic wind tunnel of the IUSTI laboratory, France. For such a shock intensity, strong unsteadiness are developing inside the separated zone involving very low frequencies associated with reflected shock motions.The present work consists in simultaneous PIV velocity fields and unsteady wall pressure measurements. The wall pressure and PIV measurements were used to characterize the pressure distribution at the wall in an axial direction, and the flow field associated. These results give access for the first time to the spatial-time correlation between wall pressure and velocity in a shock wave turbulent boundary layer interaction and show the feasibility of such coupling techniques in compressible flows. Linear Stochastic Estimation (LSE) coupled with Proper Orthogonal Decomposition (POD) has been applied to these measurements, and first results are presented here, showing the ability of these techniques to reproduce both the unsteady breathing of the recirculating bubble at low frequency and the Kelvin–Helmholtz instabilities developing at moderate frequency.