Specific gasdynamical features of spontaneous condensation in an unsteady rarefaction wave

On the basis of numerical modeling, the formation of an unsteady shock wave induced by a condensation shock in a rarefaction wave moving in the high-pressure channel of a shock tube filled with moist air is demonstrated. It is shown that in a fairly long channel a periodic structure consisting of an alternating sequence of condensation shocks and the shock waves they generate may be formed. This structure is a linear unsteady analog of the self-oscillation regime of type IV in the classification [1] for condensing medium flows in the subsonic section of a Laval nozzle. The specific features detected are important for planning and interpreting experiments aimed at investigating spontaneous condensation using a “condensation shock tube”.     

Supersonic low-concentration dusty-gas flow past a plane cylinder in the presence of an oblique shock wave interacting with the bow shock

The motion of an inertial dispersed admixture near a plane cylinder immersed in a steady-state hypersonic dusty flow in the presence of an oblique shock wave interacting with the bow shock is considered. It is assumed that the free-stream particle mass concentration is small and the particles do not affect the carrier flow. The III and IV shock wave interaction regimes are considered. The gas flow parameters in the shock layer are calculated from the numerical solution of the full Navier-Stokes equations for the perfect gas. A TVD second-order finite-difference scheme constructed on the basis of a finite volume method is used. For calculating the dispersed-phase parameters, including the concentration, the full Lagrangian method is used. On a wide range of variation of the particle inertia parameters, the patterns of the particle trajectories, velocity, concentration, and temperature in the shock layer are studied. The possibility of aerodynamic focusing of the particles behind the shock wave intersection point and the formation of narrow beams with a high particle concentration is revealed. These beams impinge on the cylinder surface and result in a sharp increase in the local heat fluxes. The maximal possible increase in the heat fluxes caused by the particles colliding with the cylinder surface is estimated for the flows with and without the incident oblique shock wave.     

Hypersonic flow-past of plane blunt bodies by a nonviscous radiating gas

An analytic solution is obtained in the work in a Newtonian approximation [1] for the flow-past problem for a plane blunt body by a steady-state uniform hypersonic inviscous space-radiating gas flow. The hypersonic flow-past problem for axisymmetrical blunt bodies by a nonviscous space-radiating gas has been previously considered [2–4]. In this case a satisfactory solution of the problem was obtained even in a zero-th approximation by decomposing the unknown values in terms of a parameter equal to the ratio of gas densities before and after passage of the shock wave. The solution of the problem in a zero-th approximation with respect to in the case of flow-past of plane blunt bodies does not turn out to be satisfactory, since the departure of the shock and the radiant flux to the body as gas flows into the shock layer turns out to be strongly overstated under nearly adiabatic conditions. Freeman [5] demonstrated that results may be significantly improved for flow-past of a plane blunt body by a nonradiating gas if a more precise expression is used for the tangential velocity component expressed in a new approximation with respect to the parameter . This refinement is applied in this work for solving the flow-past problem for a plane blunt body by a space-radiating gas. The distribution of the gasdynamic parameters in the shock layer, the departure of the shock wave, and the radiant heat flux to the surface of the body are found. The solution obtained is analyzed in detail for the example of flow-past regarding a circular cylinder.Translated from Zhurnal Prikladnoi Mekhanikii Tekhnicheskoi Fiziki, No. 3, 68–73, May–June, 1975.     

Structure and bifurcations of plane shock waves in a vibrationally excited gas with an external pumping source

The structure of the density profiles in stationary plane shock waves in a vibrationally excited gas is investigated. For self-similar solutions a bifurcation diagram is plotted in the parametric “traveling wave velocity—degree of nonequilibrium” plane. The bifurcation boundaries of the domains of existence of the structures of different types are analytically derived. It is shown that weak plane shock waves are unstable, accelerate, and break down into a sequence of pulses or-at a fairly high pumping rate-waves with nonzero asymptotics, whose amplitude and propagation velocity are independent of the initial disturbance and are determined by the parameters of the medium itself.     

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.     

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.     

冷激波灭火系统中激波对灭火效果和周边环境的影响

为了评估冷激波灭火弹爆炸后形成的激波对灭火效果和周边环境的影响,建立了一套纹影实验装置。通过纹影实验,观察了小尺寸下不同灭火介质爆炸抛撒后激波的形成和传播,并推算了冷激波灭火弹爆炸后油盆边缘附近的波后质点速度。观察发现,水基灭火介质爆炸抛撒后没有形成激波;而粉基灭火介质尽管爆炸抛撒后形成激波,但在油盆边缘附近激波强度较弱,波后质点速度小。与介质抛撒引起的可燃气体介质运动相比,激波对加快可燃气体介质运动的影响可以忽略。最后,通过高速摄影实验验证了激波对灭火效果的影响是可以忽略的。因此,冷激波系统中,激波对灭火效果和周边环境的影响是可以忽略的。     

磁场对激波冲击R22重气柱作用过程影响的数值模拟

为研究平面入射激波与磁化R22重质圆形气柱的作用过程,首先通过数值方法得到了不同初始条件下激波诱导R22气柱的Kelvin-Helmholtz (KH)及Richtmyer-Meshkov (RM)不稳定性导致的重气柱变形过程,并详细讨论了不同情况下透射激波在气柱内聚焦诱导射流的过程;然后在加入磁场的情况下,采用CTU+CT算法进行数值模拟,以保证数值结果满足任意时刻磁场的散度为零。计算结果表明:磁场对激波诱导R22气柱不稳定性具有抑制作用;法向磁场和流向磁场都可以很好地抑制RM不稳定性;对于KH不稳定性,法向磁场的控制效果更好,不仅可以抑制界面上涡串的卷起,还可以阻止主涡的发展,而流向磁场做不到后者;磁场对射流影响不大,射流处的磁能量可以一定程度上抑制射流的衰减,同时法向磁场可以减小聚焦时压力及速度峰值。     

Increase of initial velocity and pressure upon impact on an inhomogeneous target

It is proved on the basis of an analysis conducted by means of the method of (p, u)-diagrams in an acoustic approximation that the mass velocity of the material of a target increases when a shock wave propagates along a target in which the acoustic resistance of the layers decreases in the direction of propagation, and it can even exceed the initial velocity of the striker. An increase in pressure behind the wave front similar to the example of unbounded accumulation in a plane shock wave considered in [2] is observed when a striker impacts on a target in which the acoustic impedance of the layers increases in the direction of propagation of the shock wave. The increase in velocity is experimentially verified.     

Study of the attenuation of a detonation wave with a two-front structure by the boundary (shock) layer method

The possibility that a plane overcompressed detonation wave may undergo a transition to the Chapman-Jouguet mode during its attenuation is considered on the basis of the two-front model, allowing for the change in flow parameters in the interval between the fronts. G. G. Chernyi's approximate method of boundary (shock) layer is used in order to describe the flow of the gas in this interval. The use of this method is justified by the fact that the velocity of propagation of the detonation wave is extremely great (order of several km/sec), and the gas between the compression jump and the combustion front is strongly compressed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 3, pp. 59–65, May–June, 1971.     

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.     

Shock wave structure in a mixture of gas,vapour and droplets

The structure of the relaxation zone behind a shock wave of moderate strength in a mixture of gas, vapour and droplets is analysed. A model is presented for shock induced evaporation, which is based on wet-bulb equilibrium and on the absence of relative motion between droplets and gas. Experimental and numerical data on heterogeneous condensation induced by an unsteady rarefaction wave and on re-evaporation due to shock wave passage are reported for a mixture of water vapour, nitrogen gas and condensation nuclei. Pressure, temperature, saturation ratio and droplet size are experimentally obtained and are very well predicted by a numerical simulation based on the non-linear quasisteady wet-bulb model for phase transition, as well for the expansion wave as for the shock wave. During expansion, droplet number density decays much faster than predicted, which is not yet satisfactorily explained. Shock induced droplet evaporation is studied for post-shock saturation ratios ranging from 5×10^–3 to 0.2, corresponding to shock Mach numbers of 1.2 to 1.9. The evaporation times are well predicted by the theoretical model. No evidence is found for droplet break-up for Weber numbers up to 13, and droplet radii of the order of 1m.On leave at Institute of Fluid Science, Shock Wave Research Center, Tohoku University, Sendai 980, JapanThis article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Investigation of the properties of a shock wave arising in a supersonic flow of plasma,passing through a transverse magnetic field

In a flow of plasma, set up by an ionizing shock wave and moving through a transverse magnetic field, under definite conditions there arises a gasdynamic shock wave. The appearance of such shock waves has been observed in experimental [1–4] and theoretical [5–7] work, where an investigation was made of the interaction between a plasma and electrical and magnetic fields. The aim of the present work was a determination of the effect of the intensity of the interaction between the plasma and the magnetic field on the velocity of the motion of this shock wave. The investigation was carried out in a magnetohydrogasdynamic unit, described in [8]. The process was recorded by the Töpler method (IAB-451 instrument) through a slit along the axis of the channel, on a film moving in a direction perpendicular to the slit. The calculation of the flow is based on the one-dimensional unsteady-state equations of magnetic gasdynamics. Using a model of the process described in [9], calculations were made for conditions close to those realized experimentally. In addition, a simplified calculation is made of the velocity of the motion of the above shock wave, under the assumption that its front moves at a constant velocity ahead of the region of interaction, while in the region of interaction itself the flow is steady-state.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 86–91, January–February, 1975.     

Impact on the surface of a compressible liquid

The evolution of a weak, nearly plane shock wave produced by the impact on the plane boundary of a compressible liquid is considered. At the initial moment the liquid is at rest and occupies the lower half-plane. Then the points of its boundary get instantly velocities directed into the liquid domain. This leads to the formation of a shock wave the intensity of which is non-uniform due to a non-uniform distribution of the impact velocities. Initially the shock wave is plane but then it bends due to the non-linear effects and can later be focused. To analyze the liquid flow, the method of matched asymptotic expansions is used. For finite times the flow and the evolution of the shock wave are described within the framework of the acoustic approximation. For large times the flow becomes non-linear, and the form of the shock front depends essentially on the characteristics of the liquid flow behind it. If the non-uniformity of the impact velocity distribution is slight then the focusing of the shock wave is shown not to occur. The influence of viscosity of the liquid on the structure of its motion is discussed.     

Three-dimensional shock intersection

The flow field in the neighborhood of the three-dimensional intersection of two shocks of different families is investigated when in the plane perpendicular to the line of intersection the flow velocity component is subsonic behind at least one of the departing shocks. In the plane case these flows are not realized. The boundary of the domain of the key parameters for which these flows are possible is determined. The characteristics of the flow field are determined when: (1) behind the departing shocks the flow is homogeneous, and (2) the velocity vectors behind the departing and arriving shocks are parallel to a single plane which contains the intersection line. The flow in Mach-type shock intersection in the neighborhood of the intersection lines (triple points in the plane) is a particular case of the problem considered. It is shown that Mach-type shock intersection is not possible when the intensity of the arriving shocks is less than for their steady-state Mach intersection in the calculation plane. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 137–143, November–December, 1998.     

Analytical Solution for Isothermal Flow in a Shock Tube Containing Rigid Granular Material

Analytical solution of shock wave propagation in pure gas in a shock tube is usually addressed in gas dynamics. However, such a solution for granular media is complex due to the inclusion of parameters relating to particles configuration within the medium, which affect the balance equations. In this article, an analytical solution for isothermal shock wave propagation in an isotropic homogenous rigid granular material is presented, and a closed-form solution is obtained for the case of weak shock waves. Fluid mass and momentum equations are first written in wave and (mathematical) non-conservation forms. Afterwards by redefining the sound speed of the gas flowing inside the pores, an analytical solution is obtained using the classical method of characteristics, followed by Taylor’s series expansion based on the assumption of weak flow which finally led to explicit functions for velocity, density and pressure. The solution enables plotting gas velocity, density and pressure variations in the porous medium, which is of high interest in the design of granular shock isolators.     

Unsteady Rarefied Gas Flow with Shock Wave in a Channel

The two-dimensional time-dependent problem of rarefied gas flow in a plane channel, formed by parallel plates of finite length and closed at one end, is solved on the basis of the kinetic S-model. The flow develops as a result of rupture of a diaphragm which separates the gas at rest in the channel and the gas at rest in a reservoir of infinite volume. The effect of gas deceleration at the channel walls under the conditions of diffuse molecular reflection from the channel walls and end face is studied. Decay of a shock wave and disappearance of a homogeneous flow zone behind the shock wave is traced for three variants of conditions at the channel inlet: (1) gas enters the channel from a reservoir of infinite length and width (as the basic variant), the simultaneous motion in the reservoir and channel being studied; (2) the high-pressure reservoir represents a usual channel section; and (3) the motion of the gas in the reservoir is not considered at all, instead of this, the boundary conditions of the evaporation-condensation type under the conditions of gas at rest in the reservoir are imposed in the inlet cross-section.     

Propagation of pressure waves in two-phase flow

We deal with a pressure wave of finite amplitude propagating in a gas and liquid medium or in the fluid in an elastic tube. We study the effects of pipe elasticity on the propagation velocity of the pressure wave. Pressure waves of finite amplitude progressing in the two-phase flow are treated considering the void fraction change due to pressure rise. The propagation velocity of the two-phase shock wave is also investigated, and the behavior of the reflection of the pressure wave at the rigid wall is analyzed and compared to that in a pure gas or liquid. The results are compared to experimental data of a pressure wave propagating in the two-phase flow in a vertical shock tube.     

Oblique reflection of shock waves from rigid porous materials

A study to determine the general gas dynamic behaviour associated with the impact of a shock wave on a porous wedge has been undertaken. A number of interesting features are noted. The pattern of wave reflection is shown to be significantly affected by the inflow of gas into the wedge. This has the effect of reducing the triple point trajectory angle for cases of Mach reflection and for strongly reducing the reflection angle in regular reflection. The permeability of the wedge has a significant effect on the strength of the reflected wave and in some cases this wave can be attenuated to the extent that it is almost eradicated. Pressure measurements taken under the wedge are characterized by oscillations which are of similar shape, for a given wedge, over a range of shock wave Mach numbers. It is shown that the wave transmitted into the wedge is attenuated to varying degrees depending on the material properties, and that for weak incident waves the mean propagation velocity can be less than the sound speed in the pore fluid. Photographs taken using a specially constructed wedge which allows the transmitted wave to be visualised, show that the transmitted wave is nearly plane.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.