Decay of a plane shock wave in a two-parameter medium with arbitrary equation of state

Special curves, called shock polars, are frequently used to determine the state of the gas behind an oblique shock wave from known parameters of the oncoming flow. For a perfect gas, these curves have been constructed and investigated in detail [1]. However, for the solution of problems associated with gas flow at high velocities and high temperatures it is necessary to use models of gases with complicated equations of state. It is therefore of interest to study the properties of oblique shocks in such media. In the present paper, a study is made of the form of the shock polars for two-parameter media with arbitrary equation of state, these satisfying the conditions of Cemplen's theorem. Some properties of oblique shocks in such media that are new compared with a perfect gas are established. On the basis of the obtained results, the existence of triple configurations in steady supersonic flows obtained by the decay of plane shock waves is considered. It is shown that D'yakov-unstable discontinuities decompose into an oblique shock and a centered rarefaction wave, while spontaneously radiating discontinuities decompose into two shocks or into a shock and a rarefaction wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 147–153, November–December, 1982.     

Shock-wave structure in the near zone upon explosion of spatial charges in air

Profiles and values of pressure in shock waves are determined for the case of spherical, linear, and spatial charges, such as a coil of a bulk spiral and plane annular coils and Archimedes’ spiral of various lenths, exploded in air. In the case of explosion of rings and spirals, a complex wave structure in the form of a sequence of several shock waves is registered near the charges along the spiral axes; a weaker attenuation of shock waves with distance and pressure amplitudes two to three times higher than in the case of a spherical charge of the same mass are observed. It was found that an increase in the length of a plane spiral does not lead to an increase in the maximum pressure in the shock wave at distances of the order of several pitches of the spiral from its plane. With distance from spatial charges of different shape but identical mass, the pressure values in the shock-wave fronts coincide and tend asymptotically to the parameters of a spherical explosion with a significant increase in the duration of a wave packet generated by the spatial charge. Dependences for evaluation of shock-wave pressure amplitudes in the near zone of the explosion are presented. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 81–90, September–October, 2000.     

气相爆轰波绕射流场显示研究

采用基于红宝石激光器（波长694.3 nm）的纹影系统,对气相爆轰波绕射进行了初步的流场显示研究。采用单色激光和合适半带宽（15 nm）的滤光片,有效地消除了爆轰波自发光对流场显示的影响。合理设置激光器同步控制系统的触发延时,得到了序列的爆轰波阵面纹影照片。结果表明:图像清晰地显示了爆轰波阵面的诱导激波、横波及化学反应区。当爆轰波在左尖点处绕射,受稀疏波作用,诱导激波与化学反应区明显分离,导致爆轰波衰减为爆燃。分离的诱导激波和折皱的化学反应区在纹影图上清晰可见。诱导激波在垂直支管右壁面反射,诱导二次起爆。畸变爆轰波在水平和垂直支管中均发生马赫反射。提高初压,爆轰波受分叉口几何属性的影响减小,畸变爆轰波在水平和垂直支管下游较易恢复为自持爆轰波。     

The moiré method for the study of explosions

Explosives have been used to produce weak shock waves in central cavities of Plexiglas spheres. Shock pressures engendered were less than the so-called stable shock threshold and they resulted in a decomposition of the shock wave into an elastic precursor preceding the so-called plastic shock wave. The differential moiré method has been used to measure simultaneously the precursor and shock-wave velocities, as well as the velocity of the cavity interface. Moreover, the displacement field given by the moiré pattern yields the components of strains and the particle velocity behind each shock.     

高速弹丸诱导斜爆轰激波结构实验研究

斜爆轰推进系统在高超声速推进领域具有广阔的应用前景,其释热迅速、比冲高、燃烧室结构简单的优点吸引研究人员的持续关注.然而,斜爆轰的地面试验同时涉及到高速试验环境模拟、燃料与氧化剂混合、高温燃烧流场结构测量等技术难点,当前国内外系统的试验研究仍然十分有限,难以支撑斜爆轰发动机的研制.为了研究自持传播的斜爆轰激波结构与波面流动特性,基于爆轰驱动二级轻气炮开展了高速弹丸诱导斜爆轰实验研究,使用直径30 mm球头圆柱形弹丸发射进入充满氢/氧可燃混合气体的实验舱中以起爆斜爆轰波,并采用两种阴影技术对实验流动结构进行测量.实验中在不同速度、不同充气压力下观察到三种弹丸诱导激波结构,即激波诱导燃烧、弹丸起爆爆轰波和相对弹丸驻定的斜爆轰波,实验舱充气压力下降则会造成爆轰横波尺度增加与波面流动失稳.实验中,斜爆轰激波角与理论分析结果吻合较好,弹丸气动不稳定带来较大的弹丸攻角会对激波角测量带来一定偏差.通过对斜爆轰波波面法向传播速度的测量发现,随着远离弹丸,斜爆轰传播速度由弹丸飞行速度衰减至接近实验气体CJ速度,弹丸速度的降低会加速斜爆轰波传播速度的衰减.     

Theory of the detonation of weak condensed explosives

The possibilities of detonation taking place in a material characterized by a shock adiabatic containing a sharp break (leading to a double shock-wave configuration) are examined. The range of possible velocities D of a self-sustaining detonation in the second shock wave is determined; D may be subsonic with respect to the original material. However, even for an arbitrarily low velocity of sound the range of subsonic D values above the break point on the adiabat is extremely limited: The minimum detonation velocity D_min coincides (apart from a factor of 0.5–0.8) with the velocity of a longitudinal sound wave in the original material below the break point. This limitation with regard to D is associated with the formation of a wave of rarefaction in the reaction products, For D < D_min the shock wave of rarefaction reaches the Jouguet point and breaks the steady-state complex of the detonation wave. The results obtained are valid not only for weak, but also for powerful, explosive substances, if (by virtue of any kind of losses) low-velocity forms of detonation are realized in these materials.     

3D Steady and Unsteady Bifurcations in a Shock-wave/Laminar Boundary Layer Interaction: A Numerical Study

The principal objective of this paper is to study some unsteady characteristics of an interaction between an incident oblique shock wave impinging a laminar boundary layer developing on a plate plane. More precisely, this paper shows that some unsteadiness, in particular the low frequency unsteadiness, originate in a supercritical Hopf bifurcation related to the dynamics of the separated boundary layer and not necessarily to the coherent structures resulting from the turbulent character of the boundary layer crossing the shock wave. Numerical computations of a shock-wave/laminar boundary-layer interaction (SWBLI) have been compared with a classical test case (Degrez test case) and both two-dimensional and three-dimensional (3D) unsteady Navier–Stokes equations are numerically solved with an implicit dual time stepping for the temporal algorithm and high order AUSM+ scheme for the spatial discretization. A parametric study on the oblique shock-wave angle has been performed to characterize the unsteady behaviour onset. Finally, discussions and assumptions are made about the origin of the 3D low frequency unsteadiness.     

Interference between a centered rarefaction wave and an inclined shock wave

The gas flow in the zone of interaction between an oblique shock and a centered isentropic rarefaction wave is studied using the direct statistical simulation method for solving the Boltzmann equation. The data of calculations of the shock and rarefaction wave structures, flow fields, and streamlines are given for the free-stream Mach number M_∞ = 6, 4 and 2. The formation of the interaction zone is simulated by a gas flow past a double-plane wedge in which the break of the generating line leads to formation of the centered isentropic rarefaction wave. The results of calculations of this flow in solving the Boltzmann equation are given in the Euler approximation.     

一维与二维爆轰传播的时空关联特性数值研究

一维爆轰传播的理论完备、计算准确, 二维斜爆轰传播由于壁面与黏性效应, 大尺度、高精度预测还有一定难度. 利用Euler方程和H₂-Air基元反应模型, 对二维有限长楔面诱导的斜爆轰和活塞驱动一维非定常正爆轰进行计算比较研究, 从时空两个维度方面, 分析了两者在起爆过程、稀疏波传播、爆轰波面演化中的关联特性. 研究结果表明: 在过驱动度相同的条件下, 经过时空变换的活塞驱动一维爆轰传播与二维驻定斜爆轰在起爆区波系结构、波面演化特征和主要参数分布规律方面无论定性或者定量对比均符合较好, 所以, 一维非定常爆轰和二维驻定斜爆轰具有时空相关性. 两者的差异主要体现在过驱动斜爆轰受稀疏波影响过渡到近Chapman-Jouguet (C-J)爆轰状态所需的弛豫时间不同, 原因可能是起源于活塞和壁面稀疏波强度的差异. 本文提出的一维与二维爆轰传播的时空关联方法不仅有助于认知斜爆轰起爆、过驱爆轰产生、胞格爆轰演化的三阶段规律, 还可以对比揭示壁面、边界层和黏性效应的影响, 应用在斜爆轰发动机燃烧室设计中能够有效节约计算时间和成本, 并降低复杂度.      

圆球诱发斜爆轰波的数值研究

斜爆轰发动机是飞行器在高马赫数飞行条件下的一种新型发动机,具有结构简单、成本低和比冲高等优点.但是斜爆轰发动机的来流马赫数范围广,来流条件复杂,为实现斜爆轰波的迅速、可靠引发,采用钝头体来诱发.利用Euler方程和氢氧基元反应模型,对超声速氢气/空气混合气体中圆球诱导的斜爆轰流场进行了数值研究.不同于楔面诱发的斜爆轰波,球体首先会在驻点附近诱发正激波/爆轰波,然后在稀疏波作用下发展为斜激波/爆轰波.模拟结果显示,经过钝头体压缩的预混气体达到自燃温度后,会出现两种流场:当马赫数较低时,由于稀疏波的影响,燃烧熄灭,钝头体下游不会出现燃烧情况;而当马赫数较高时,燃烧阵面能传到下游.分析表明,当钝头体的尺度较小时,驻点附近的能量不足以诱发爆轰波,只会形成明显的燃烧带与激波非耦合结构;当钝头体的尺度较大时,流场中不会出现燃烧带与激波的非耦合现象,且这一特征与马赫数无关.通过调整球体直径,获得了激波和燃烧带部分耦合的燃烧流场结构,这一流场结构在楔面诱发的斜爆轰波中并不存在,说明稀疏波与爆轰波面的相互作用是决定圆球诱发斜爆轰波的关键.     

一种新的运动激波--非定常边界层相互干扰现象

本文探讨了一种新的激波－非定常边界层相互干扰现象，这种激波－边界层干扰现象既不同于定常激波－边界层干扰现象，又不同于激波在端面反射后与该激波所诱导的边界层之间的干扰现象，而是运动激波与稀疏波和第一激波所诱导的非这常边界层之间的干扰现象，本文对这种现象用微波动力学理论进行分析，并把这种干扰现象看成激波的绕射现象，同时在稀疏波破膜的双驱动激波管中进行实验观察，最后把理论分析与实验观察进行了比较。     

Experimental investigation of the interaction between convergent axisymmetric shock waves and sharp and blunt cones in supersonic flow

The interaction between convergent axisymmetric shock waves and sharp and blunt cones has been experimentally investigated in a wind tunnel at M=4.67. During the experiments the effect of the conicity angle of the convergent shock wave, the shape of the model and its position relative to the shock-wave configuration on the structure of the flow and the pressure distribution on the model surface was explored.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 177–182, September–October, 1991.In conclusion, the author wishes to thank Yu. M. Lipnitskii for formulating the problem and E. N. Bogachev for assistance in organizing the research.     

Interaction of rarefaction waves with wet foam

The interaction of rarefaction waves of different shapes with wet water foams is studied experimentally. It is found that the observed values of the pressure are greater, while the surface velocity is lower than the corresponding values predicted by the pseudogas model. The foam breakdown starts as the pressure decreases by 0.3 atm relative to the initial pressure. During downstream propagation of the rarefaction-wave leading edge the propagation velocity decreases.Using of water-based foams as effective screens for damping blast waves in different technological processes has caused considerable interest in studying wave propagation in such systems. The pressure wave dynamics in a foam have been investigated in much detail, both experimentally and theoretically [1–3]. However, the interaction of rarefaction waves with foam has practically never been studied, although it was mentioned in [4] that the unloading phase following the compression wave phase is one of the factors defining the damaging action of blast waves. Besides blast-wave damping, rarefaction wave propagation takes place if such waves are used to breakup foam in oil-producing wells [5].Below, the interaction of rarefaction waves of different shapes with wet water foams is studied. The vertical shock tube described in detail in [3] was used in these experiments.Brest. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 76–82, March–April, 1995.     

The Riemann Solution for the Injection of Steam and Nitrogen in a Porous Medium

We solve the model for the flow of nitrogen, vapor, and water in a porous medium, neglecting compressibility, heat conductivity, and capillary effects. Our choice of injection conditions is determined by the application to clean up polluted sites. We study all mathematical structures, such as rarefaction, shock waves, and their bifurcations; we also develop a systematic method to find fundamental solutions for thermal compositional flows in porous media. In addition, we unexpectedly find a rarefaction evaporation wave which has not been previously reported in any other study.     

Lift-to-drag ratio at supersonic speeds

Wave lift-to-drag ratio is analyzed ignoring friction and using flows behind oblique shock waves and rarefaction waves. It is shown that the lift-to-drag ratio of an infinite oblique plate can surpass considerably that of triangular plates with subsonic, sonic, or supersonic edges. The simplest finite-span oblique wing is a wing with characteristic edges. However, when the normal-to-the-edge flow velocity component behind a shock reaches the speed of sound, the wing contracts into an edge, and other means must be used to exclude the end effect. Several possible variants are indicated. A straight wedge with side plates is the optimal shape for a lifting body with fixed volume, lift, length, and width. Under the same conditions, the cross-section of a pyramidal body formed by stream planes behind one or two plane shocks has practically no effect on the lift-to-drag ratio, while the region of high lift-to-drag ratio is much narrower than for a wedge. If a pyramid fails to provide the required lift-to-drag ratio, it is necessary to turn to forms that better fill the given area. Redistribution of lift between body and wing permits an improvement in the lift-to-drag ratio.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–141, September–October, 1993.     

非定常激波三维双楔面反射的数值研究

采用基于MUSCL-Hancock插值的有限体积方法, 在非结构自适应网格上求解三维Euler方程, 研究了非定常激波在三维垂直双楔面上的反射现象. 研究结果表明, 由于三维效应的影响, 通过二维非定常激波反射理论预测的三维马赫反射区域范围存在着一定的局限, 在该区域范围内出现了一种非典型的三维突起结构, 即第二类三维马赫干. 另外, 对于不同的激波马赫数和楔面倾角组合, 非定常激波在三维双楔面上会形成具有四波结构的三维马赫反射或具有三波结构的三维规则反射.      

Numerical study of spherical blast-wave propagation and reflection

The objective of this study is to understand the flow structures of weak and strong spherical blast waves either propagating in a free field or interacting with a flat plate. A 5th-order weighted essentially non-oscillatory scheme with a 4th-order Runge-Kutta method is employed to solve the compressible Euler/Navier-Stokes equations in a finite volume approach. The real-gas effects are taken into account when high temperature occurs. A shock-tube problem with the real-gas effect is first tested in order to verify the solver accuracy. Moreover, unsteady shock waves moving over a stationary wedge with various wedge angles, resulting in different types of shock wave reflections, are also tested. It is found that the computed results agreed well with the existing data. Second, the propagation of a weak spherical blast wave, created by rupture of a high-pressure isothermal sphere, in a free field is studied. It is found that there are three minor shock waves moving behind the main shock. Third, the problem of a strong blast wave interacting with a flat plate is investigated. The flow structures associated with single and double Mach reflections are reported in detail. It is found that there are at least three local high-pressure regions near the flat plate. Received 27 July 2000 / Accepted 25 January 2002 – Published online 17 June 2002     

Superposition of two incident shocks in R718 vapor flows

Although the positive values of the fundamental gas-dynamic derivative of R718 near vapor-liquid equilibrium line ensures no occurrence of the non-classical behavior like rarefaction shock waves, the occurrence of the homogenous condensations due to rarefaction waves must be taken into account when using the moving shocks and rarefaction waves in wave devices. In this article, the superposition behaviors such as shockwave refraction and reflection of two moving incident shocks for R718 vapor flows near this the vapor-liquid equilibrium zone, have been intensively studied. And the supercharging characteristic of two superposition moving incident shocks for R718 vapor flows achieves remarkable high boosting pressure ratios of about square of those of one primary equal-intensity shock. This inspiring result could be fully used for vapor recompression in multi-effect distillation technology (MED) for brine water treatment.     

Formation conditions for bubble suspensions upon shock-wave loading of liquids

The conditions of development of bubble cavitation in liquid media upon shock-wave loading are found. It is s shown that, for the development of an unbounded cavitation, the bubbles should grow to certain critical sizes sufficient for their transition to a nonequilibrium state owing to the elastic energy transferred by a rarefaction wave to a liquid sample (at the stage of unloading). In contrast to low-viscosity liquids, in high-viscosity ones (such as glycerin) these conditions cannot be satisfied for any really attainable parameters of shock waves. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 53–63, March–April, 2000.     

On Time Reversible Description of the Process of Coagulation and Fragmentation

The process of coagulation is associated with scalar conservation laws, where the adhesion particle dynamics results from shock waves. Conversely, the fragmentation of a massive particle into a number of smaller ones, or into a continuous (dust) distribution, is associated with rarefaction waves. It is generally agreed that a reversible solution of a conservation law can include neither shock waves nor the spontaneous emergence of rarefaction waves. The present paper is an attempt to demonstrate that both coagulation and fragmentation may coexist for a reversible solution, under a natural generalization of the system of conservation law. This is done by introducing an action principle which includes, in addition to the inertial (kinetic energy) term, also an appropriately defined internal energy. The above generalization of the system of conservation law appears as the Euler–Lagrange equations for this action.