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.     

Reflection of a strong shock wave from a sphere and a cylinder

We examine the flow on the axis in the vicinity of the stagnation point for reflection of a strong plane shock wave (with uniform parameters behind the wave) from a sphere and a circular cylinder whose generators are parallel to the incident wave front.The small parameter method [1, 2] is used to obtain, in closed form, relations which define the time variation of the velocity profile, pressure, enthalpy, and reflected shock wave standoff.As the time t , these relations reduce to the known formulas [3, 4] which define the steady flow on the axis for the flow behind the incident shock wave about a body, if account is taken of the leading terms containing the small parameter.The solution is extended to the case in which account for equilibrium dissociation and ionization is necessary.Comparison of the results with measurement [5] of the reflected shock wave distance from a sphere, as a function of time, shows satisfactory agreement.     

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.     

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.     

Reflection of a spherical blast wave from a planar surface

Numerous authors have carried out rather extensive studies in the last twenty to thirty years of the problem of the interaction of shock and blast waves with obstacles in their paths. Owing to the complexity of the problem, they assumed certain limiting cases for the shock wave interactions in which the parameters behind the shock wave were usually taken to be constants. The first wave diffraction studies involving variable parameters behind the front were presented in [1, 2], wherein a development of the theory of “short waves” (blast waves at a substantial distance from the center of an explosion) and their reflection from a planar surface was given. The theory of short waves assumes that the jump in pressure at the wave front and the region over which the parameters vary are small. The problem concerning reflection of a blast wave from a surface was also considered in [3, 4], wherein a solution in the region behind the reflected wave was obtained at initial times. The initial stage in the reflection of a blast wave from a planar, cylindrical, or spherical surface (the one-dimensional case) was studied in [5]. In this paper we investigate the interaction of a spherical blast wave, resulting from a point explosion, with a planar surface; we consider both regular and non-regular reflection stages. In solving this problem we use S. L. Godunov's finite-difference method. We obtain numerical solutions for various values of the shock strength at the instant of its encounter with the surface. We present the pressure fields in the flow regions, the pressure distribution over the surface at various instants of time, and the trajectories of the triple point. The parameter values at the front of the reflected wave are compared with results obtained from the theory of regular reflection of shock waves.     

Shock-tube experiments on the stability of regular reflection in the dual-solution domain

Regular reflection (RR) and Mach reflection (MR) are theoretically both possible in the dual-solution domain of oblique shock reflection. The physical difference between the two types of reflection is the pressure behind the reflected shock wave: that of MR is lower than that of RR for strong shock reflection. The magnitude relation of these pressures is inverted for weak shock reflection. In the present paper, we performed two kinds of experiment, depending on whether the oblique shock reflection is weak or strong. For strong shock reflection, we decreased the pressure behind the reflected wave of RR using a convex double-wedge. For weak shock reflection, we increased this pressure using a concave double-wedge. Thus, we investigated the stability of RR against pressure disturbances. The results indicate that RR in a shock tube is stable, in the dual-solution domain, for both weak and strong incident shocks.     

Experimental investigation of the interaction of a shock wave with a magnetic field

We present certain results of an experimental investigation of the propagation of a shock wave S through a magnetohydrodynamic channel of the Faraday type. Under conditions of short circuiting of the induced currents in the supersonic stream that follows the shock wave, we registered the occurrence of a shock front T. The x-t diagrams of the motion of the S and T shock waves in the channel and behind it are determined. For a number of fixed sections in the channel, we have measured the density and degree of ionization of the gas and determined their time dependence. The investigations were performed in argon, and the ionizing shock wave propagated with Mach numbers 12–13. The magnetic field intensity was 1.5 T.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 153–183, May–June, 1971.     

Comparative study of amorphous and crystalline Zr-based alloys in response to nanosecond pulse laser ablation

In shock tube experiments, the interaction between the reflected shock and boundary layer can induce shock bifurcation and weak ignition. The weak ignition can greatly affect the ignition delay time measurement in a shock tube experiment. In this work, two-dimensional simulations considering detailed chemistry and transport are conducted to investigate the shock bifurcation and non-uniform ignition behind a reflected shock. The objectives are to interpret the formation of shock bifurcation induced by the reflected shock and boundary layer interaction and to investigate the weak ignition and its transition to strong ignition for both hydrogen and dimethyl ether. It is found that the non-uniform reflection of the incident shock at the end wall produces a wedge-shaped oblique shock foot at the wall. The wedge-shaped structure results in strong interactions between reflected shock and boundary layer, which induces the shock bifurcation. It is demonstrated that the local high-temperature spots at the foot of the bifurcated shock is caused by viscous dissipation and pressure work. As the post-reflected shock temperature increases, the transition from weak ignition to strong ignition in a stoichiometric hydrogen/oxygen mixture is observed. The relative sensitivity of ignition delay time to the post-reflected shock temperature is introduced to characterize the appearance of weak ignition behind the reflected shock. Unlike in the hydrogen/oxygen mixture, weak ignition is not observed in the stoichiometric dimethylether/oxygen mixture since it has a relatively longer ignition delay time and smaller relative sensitivity.

     

Airflow behind strong shock front with account for nonequilibrium ionization and radiation

We consider the gas state behind a shock wave front in air with a velocity v10 km/sec. Nonequilibrium ionization and radiative transport are taken into account. We take into consideration the real air spectrum — the numerous lines, bands, and continuua. Account for the radiation leads to an integrodifferential system of equations for which a solution method is developed. As a result we obtain the gas parameter profiles behind the shock wave, which are affected by the relaxation processes and radiative cooling. The calculations were made for v=10–16 km/sec and a pressure p=10^–5–10^–2 atm ahead of the front.In order to obtain realistic results, we consider only the gas layer bounded by the shock and a surface parallel to it. It is assumed that the gas bounded by these planes is not irradiated from without. In this formulation still another defining parameter appears—the distancel between the planes. The calculations were made forl=1–100 cm.     

Nonequilibrium ionizatlon of air behind a shock wave front at speeds of 5–10 km/sec

The solution of the problem of nonequilibrium ionization of dissociating air in a shock wave propagating with a speed of 5–10 km/sec has shown that the electron concentration distribution has a maximum behind the wave front for speeds below 9 km/sec.The formation of this maximum is caused by the high associative ionization rate in comparison with the nitrogen dissociation rate. In the nonequilibrium region behind the shock wave front there is formed a considerable concentration peak of the molecular ions which are formed as a result of associative ionization and charge exchange.The author wishes to thank V. P. Stulov for useful discussions.     

竖直平面激波与水平热层作用后流场的理论计算方法研究

围绕竖直平面激波与固壁附近水平热层作用问题,提出了流动进入准自相似阶段后固壁附近流场参量的理论计算方法。与已有的Mirels方法相比,本文的方法在下列三个方面进行了改进:（1）舍弃“热层内激波速度与入射激波速度相等”的假定,分析了热层内激波的传播过程,并基于几何激波动力学理论计算热层内激波强度;（2）假定在与入射激波后流体而非入射激波阵面固连的坐标系中,波后流体在定常等熵波作用下,形成沿固壁运动的“活塞”,驱动其前方的热层气体运动;（3）“活塞”内流体与其毗邻的热层气体满足压力和速度连续,不再引入速度比例系数。利用改进后的方法,对于马赫数为2.00的竖直平面激波,在不同热层密度条件下进行计算。本文方法得到的热层内激波强度以及物质界面处的压力、速度和密度等参量,与数值模拟结果偏差均小于10%,优于Shreffler和Mirels计算方法。对于马赫数为1.36的竖直平面激波,当其传播速度小于热层内气体声速时,Shreffler和Mirels计算方法不再适用,而本文中提出的方法得到的计算结果与数值模拟结果和已有实验数据基本吻合,最大偏差约20%。上述结果表明,本文中提出的理论计算方法提高了现有方法的合理性,扩大了适用范围。     

Structure of a shock wave in which multiple ionization of the atoms is taking place

Ionization relaxation in a shock wave of very large amplitude is considered, the atoms behind the front of the shock wave being multiply ionized. In calculating the structure of the shock wave and the kinetics of ionization, allowance is made for the electron component of the thermal conductivity which plays an important role in this. A simplified method of calculating the kinetics of multiple ionization is proposed, and an application of this method is presented. The results of the structure calculation show that, as a result of heating by thermal conduction, the gas is considerably ionized even in front of the jump in compression, while the electron component of the thermal conductivity passes through a maximum.Translated from Zhurnal Prikladnoi Mekhnika i Tekhnicheskoi Fiziki, No. 5, pp. 11–21, September–October, 1970.     

Impact of vacuum degree on the aerodynamics of a high-speed train capsule running in a tube

Motivated by the growing scientific and engineering interest in evacuated tube railway transportation systems, in this paper we numerically study the influence of the vacuum degree on the flow field around a train capsule running in an evacuated tube with circular section. The vacuum degree is increased by lowering the nominal pressure inside the tube. The numerical simulations are fully verified by wind-tunnel experimental data of supersonic flows around a blunt body and in a scramjet combustion chamber, as well as by several numerical results in other related studies. The flow around the train capsule is characterized by a compression region in front of the train, a chocked flow near the train, and a complex highly unsteady region behind the train, where expansions waves and reflecting oblique shock waves exist. The total aerodynamic drag and the vacuum degree are found to be linearly related, revealing that lowering the nominal pressure can have a significantly beneficial effect on the aerodynamic performance of the train capsule. The aerodynamic heating due to compressibility effects and the increased pressure are more prominent along the centreline of the tube than on the tube wall. As the vacuum degree increases, the temperature and pressure differences between the front and the tail of the train and the intensity of the reflected shock waves become less significant, so that the extension of the expansion region in the train wake shortens.     

Regular reflection of a shock wave from a solid wall in a stream of fuel mixture

The two-dimensional stationary problem of regular reflection of a shock wave from a plane solid wall in a fuel gas mixture is examined in the case when the mixture is ignited at the intersection of the incident wave with the wall and a flame front is formed behind the reflected shock wave. The shock waves and the flame front are considered plane surfaces of discontinuity. The fuel mixture and the reaction products are considered perfect, inviscid, and non-heat-conducting gases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 161–163, July–August, 1978.     

A revised three-shock solution for the Mach reflection of weak shocks (1.1<M i<1.5)

It is well known that the classical three-shock theory of von Neumann (1943) does not adequately describe the configuration of the shocks close to the triple-point of a Mach reflection of an incident shock with a Mach number less than about 1.5. The assumptions on which the three-shock theory is based have been examined and several of them are shown to be invalid. The assumption that may be of most significance is that the normal components of the flows behind the reflected and the Mach stem shocks are parallel. Dropping this assumption removes an essential equation in the three-shock solution. An alternative assumption, based on experimental observation, is that there is an approximate linear relationship between the pressure behind the reflected shock and the triple-point trajectory angle. This assumption permits a revised three-shock solution which gives results that are in agreement with experimental observations of reflections of incident shocks with Mach numbers between 1.1 and 1.5.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.     

平面激波冲击并排液滴的三维数值模拟研究

采用三维守恒清晰界面数值方法, 研究平面激波冲击并排液滴的动力学过程. 研究的焦点在于激波接触液滴后的复杂波系结构生成, 以及并排液滴相互耦合作用诱导的单个液滴非对称界面演化. 首先, 分析并排液滴之间界面通道内的波系结构发展, 发现在冲击初期由于反射激波相交而形成新的反射激波以及马赫杆; 这些流动现象与液滴另外一侧 (非通道侧) 由激波反射所形成的弯曲波阵面截然不同, 而且所导致的液滴横向两侧流场差异是中后期冲击过程液滴两侧界面非对称演化的主要原因. 其次, 研究冲击中期时, 特别是入射激波已运动至液滴下游并远离并排液滴, 界面形态的演化过程和规律, 揭示通道下游出口处由于气流膨胀导致的界面闭合、以及随后气流阻塞导致的界面破碎等新的流动现象. 最后, 研究液滴间距对并排液滴相互作用的影响规律, 发现液滴间距大小与通道内压力峰值具有明显的关联关系. 研究表明, 更小的液滴间距不仅带来更大的压力峰值, 而且使得峰值出现的时间更早.      

Hot spot formation from shock reflections

Heterogeneities sensitize an explosive to shock initiation. This is due to hot-spot formation and the sensitivity of chemical reaction rates to temperature. Here, we describe a numerical experiment aimed at elucidating a mechanism for hot-spot formation that occurs when a shock wave passes over a high-density impurity. The simulation performed is motivated by a physical experiment in which glass beads are added to liquid nitromethane. The impedance mismatch between the beads and the nitromethane results in shock reflections. These, in turn, give rise to transverse waves along the lead shock front. Hot spots arise on local portions of the lead front with a higher shock strength, rather than on the reflected shocks behind the beads. Moreover, the interactions generated by reflected waves from neighboring beads can significantly increase the peak hot-spot temperature when the beads are suitably spaced.     

Least energy as a criterion for transition between regular and Mach reflection

A new criterion is suggested to define the point of transition between regular and Mach reflection. The suggested criterion is based on the natural tendency of a physical system to minimize its energy. The increases of the specific energy behind the reflected shock of a regular reflection and behind the Mach stem of a Mach reflection are calculated. It is hypothesized that the type of reflection that will occur is that which produces the smaller change of specific energy. The transition angles predicted using this criterion show better agreement with experimental results than those predicted using the detachment criterion for incident shock waves with Mach numbers between 1.1 and 2.0.This article was processed using Springer-Verlag TEX Shock Waves macro package     

矩形凹槽管道中激波传播的数值研究

基于二维Euler方程,结合五阶加权基本无振荡(weighted essentially nonoscillatory,WENO)格式以及自适应网格加密(adaptive mesh refinement,AMR)技术对入射激波在矩形凹槽管道内传播过程进行了数值模拟。数值结果清晰地显示了入射激波传播过程中与多个矩形凹槽作用以及在凹槽内变化的整个过程,且与已有的实验结果吻合较好。另外,结果还揭示了入射激波与单个凹槽作用时,会发生绕射产生膨胀波,还会发生碰撞从而诱导反射激波。膨胀波会导致入射激波压力降低,而反射激波则导致其升高,但膨胀波的影响占主导作用,因而入射激波波阵面强度出现振荡下降。     

Reflection of a plane shock wave from a rigid concave wall

We present the results of an experimental study of the reflection of a plane stationary shock wave with Mach number in the range 1.21–1.35 from a rigid cylindrical concave wall. The experiments were carried out in a shock tube. In experimental shock tube technology the reflection of a shock wave from a rigid wall is often used for obtaining high temperatures [1]. This circumstance is associated with the fact that the temperature behind the reflected wave is significantly higher than that behind the incident wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 33–39, July–August, 1970.