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.     

Irregular reflection of a strong shock wave from a thin wedge

The problem of irregular reflection of a strong shock wave from a rigid wall has been studied [1–3] mainly within the framework of the linear theory. It has been found that near the front of a shock wave there exist a region of large gradients of gasdynamic parameters in which the linear theory is no longer valid [4]. In the present paper we consider the nonlinear problem of Mach reflection when there is interaction between a shock wave of high intensity and a thin wedge. The solution of the problem is constructed on the assumption that the ratio of densities along the front of the impinging shock wave is small [5, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 55–61, September–October, 1974.In conclusion, the authors wish to express their gratitude to A. A. Grib for his interest in the subject and to L. A. Rumyantsev for his help in carrying out the calculations.     

Initial stage of the collision of blast waves

The collision of two blast waves is analyzed for the case of variable parameters of the gas behind the wave front and wave reflection at a plane, a cylindrical, and a spherical obstacle. The reflection of a blast wave from a nonmoving obstacle is investigated in detail. The problem of the collision of two shock waves with constant parameters behind the front is solved both in the symmetrical case (reflection from a nonmoving wall) and in the case of waves of different amplitudes by a system of algebraic relations for the compression shocks. The reflection of a strong point-source spherical shock wave from a wall has been treated in [1, 2]. The present article examines the initial stage of wave collision for an arbitrary distribution of the parameters behind the front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–48, September–October, 1971.The authors are grateful to V. P. Korobeinikov for a discussion of the results and to V. P. Kolgan for furnishing the numerical solutions.     

On regular reflection of detonation waves

The boundaries of regular reflection of detonation waves by a rigid wall are calculated. It is assumed that detonation is initiated at the point of reflection when a shock wave is incident on the wall at a finite angle in a gas fuel mixture, the detonation propagating instantaneously along the reflected front.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 178–180, March–April, 1983.     

Theory of regular and mach reflection of shock waves in a two-phase gas-liquid medium

An equilibrium model of a two-phase gas-liquid medium, with allowance for the proportion, density, and compressibility of the components, and with a difference from [1] in that the adiabatic velocity of sound is introduced, has been used in order to study the regular and Mach (elementary theory) reflection of a shock wave of moderate intensity from a solid wall throughout the whole range of gas proportions. A complicated nonmonotonic variation has been found for the pressure on the wall behind the reflected wave, the angle of reflection, and the angle of departure of the triple point as functions of the gas proportion, the angle of incidence, and the intensity of the incident wave. In particular, it is shown that oblique reflection for moderate and low gas contents leads to the formation of a stronger reflected shock wave than does normal reflection. The effect of the gas proportion on the position of the boundary between the regions of regular and Mach reflection has already been studied in [2]. The results are described of serial calculations of the parameters of reflection for an air-water mixture, and these results agree fairly well for normal reflection with the known experimental data [3] for low and moderate gas contents. In the limiting case, the results agree with the known results for single-phase media [4, 5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 188–190, March–April, 1985.     

Regular reflection of a magnetohydrodynamic shock wave from a conducting wall

In two-dimensional supersonic gasdynamics, one of the classical steady-state problems, which include shock waves and other discontinuities, is the problem concerning the oblique reflection of a shock wave from a plane wall. It is well known [1–3] that two types of reflection are possible: regular and Mach. The problem concerning the regular reflection of a magnetohydrodynamic shock wave from an infinitely conducting plane wall is considered here within the scope of ideal magnetohydrodynamics [4]. It is supposed that the magnetic field, normal to the wall, is not equal to zero. The solution of the problem is constructed for incident waves of different types (fast and slow). It is found that, depending on the initial data, the solution can have a qualitatively different nature. In contrast from gasdynamics, the incident wave is reflected in the form of two waves, which can be centered rarefaction waves. A similar problem for the special case of the magnetic field parallel to the flow was considered earlier in [5, 6]. The normal component of the magnetic field at the wall was equated to zero, the solution was constructed only for the case of incidence of a fast shock wave, and the flow pattern is similar in form to that of gasdynamics. The solution of the problem concerning the reflection of a shock wave constructed in this paper is necessary for the interpretation of experiments in shock tubes [7–10].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 102–109, May–June, 1977.The author thanks A. A. Barmin, A. G. Kulikovskii, and G. A. Lyubimov for useful discussion of the results obtained.     

Transition from regular reflection to mach reflection when a shock wave interacts with a wall in a two-phase gas—liquid medium

A study is made of the transition from regular reflection to Mach reflection when a plane moderately strong or weak shock wave interacts with a wall in a two-phase gas—liquid medium. An equilibrium model that differs from the model of Parkin et al. [1] by the introduction of the adiabatic velocity of sound is used to investigate shock wave reflection in the complete range of gas concentrations. For the reflection of weak shock waves, nonlinear asymptotic expansions [2] are used. In the limiting cases, the results agree with those already known for single-phase media [2, 3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 190–192, September–October, 1983.     

Reflection of a blast-profile shock wave from the end wall of a shock tube

The flow in the shock tube, which models the flow conditions behind a blast wave, is calculated for an inviscid non-heat-conducting perfect gas with a constant value of the specific heat ratio. The results are compared with the authors' experimental data.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 141–148, May–June, 1992.The authors are grateful to V. A. Levin for assisting with the work and useful discussions.     

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.     

Guderley reflection for higher Mach numbers in a standard shock tube

An experimental study shows that the Guderley reflection (GR) of shock waves can be produced in a standard shock tube. A new technique was utilised which comprises triple point of a developed weak Mach reflection undergoing a number of reflections off the ceiling and floor of the shock tube before arriving at the test section. Both simple perturbation sources and diverging ramps were used to generate a transverse wave in the tube which then becomes the weak reflected wave of the reflection pattern. Tests were conducted for three ramp angles (10°, 15°, and 20°) and two perturbation sources for a range of Mach numbers (1.10–1.40) and two shock tube expansion chamber lengths (2.0 and 4.0 m). It was found that the length of the Mach stem of the reflection pattern is the overall vertical distance traveled by the triple point. Images with equivalent Mach stem lengths in the order of 2.0 m were produced. All tests showed evidence of the fourth wave of the GR, namely the expansion wave behind the reflected shock wave. A shocklet terminating the expansion wave was also identified in a few cases mainly for incident wave Mach numbers of approximately 1.20.     

Unsteady reflection of a shock wave from a body with a cylindrical recess

In a number of cases of supersonic flow past bodies with recesses pulsations in the flow arise [1–3]. Experiments [4, 5] indicate that stabilization of the steady supersonic flow past the body with a recess on which a shock wave is incident takes place after a series of oscillations of the bow wave. Numerical calculation of the interaction of a supersonic jet with a cylindrical cavity [6] reveals that damped pressure pulsations arise inside the cavity if the jet is homogeneous, and undamped pulsations it is inhomogeneous. The authors explain the damping of the pulsations by the influence of artificial viscosity. This paper investigates experimentally and theoretically (by numerical methods) the oscillations of the bow shock wave and the parameters of the flow behind it in the case of unsteady reflection of a shock wave from a body with a cylindrical recess turned towards the flow. The problem is posed as follows. A plane shock wave with constant parameters impinges on a cylinder with a cavity. The unsteady flow originating from this interaction is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 199–202, September–October, 1984.     

Reflection of pressure waves of moderate intensity at a solid wall in a liquid with bubbles of a readily soluble gas

The present paper is concerned with an experimental study of the process of gas dissolution behind a shock wave in a liquid with bubbles of a readily soluble gas, the influence of gas dissolution on the wave evolution, and strengthening of the shock wave after reflection from a solid wall. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 19–24, September–October, 1998.     

Head-on collision of normal shock waves with rigid porous materials

The head-on collision of a planar shock wave with a rigid porous material has been investigated experimentally in a 75 mm × 75 mm shock tube. The experimental study indicated that unlike the reflection from a flexible porous material (e.g., polyurethane foam) where the transmitted compression waves do not converge to a sharp shock wave, in the case of a rigid porous material (e.g., alumina) the transmitted compression waves do converge to a sharp shock wave, which decays as it propagates along the porous material. In addition to this major difference, many other differences were observed. They are outlined in the following sections.Based on these observations a suggestion modifying the phenomenology of the reflection/interaction process in the case a porous material with large permeability is proposed.     

Emission and radiative cooling of xenon plasma behind a strong shock front

A numerical and experimental investigation of the emissivity and radiative cooling of xenon plasma in strong shock waves with Mach numbers M=16–45, including experimentally up to M=28, has been made. It is shown that under these conditions the equilibrium temperature behind the shock wave can be reduced by cooling by 1.5–2 times.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 155–162, January–February, 1992.     

Shear layer behavior resulting from shock wave diffraction

All previous studies on shock wave diffraction in shock tubes have spatial and temporal limitations due to the size of the test sections. These limitations result from either the reflection of the expansion wave, generated at the corner, from the top wall and/or of the reflection of the incident diffracted shock from the bottom wall of the test section passing back through the region of interest. This has limited the study of the evolution of the shear layer and its associated vortex, which forms a relatively small region of the flow behind the shock with an extent of only a few centimeters, and yet is a region of significant interest. A special shock tube is used in the current tests which allow evolution of the flow to be examined at a scale about an order of magnitude larger than in previously published results, with shear layer lengths of up to 250 mm being achieved without interference from adjacent walls. Tests are presented for incident shock wave Mach numbers of nominally 1.3–1.5. Studies have been undertaken with wall angles of 10, 20, 30 and 90°. Significant changes are noted as the spatial and temporal scale of the experiment increases. For a given wall angle, the flow behind the incident shock is not self-similar as is usually assumed. Both shear layer instability and the development of turbulent patches become evident, neither of which have been noted in previous tests.     

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.     

Shock strengthening in a wedge-shaped cavity

The unsteady problem of the entry of a shock wave of arbitrary intensity into a wedge-shaped cavity is examined. An exact solution of the non-linear problem of reflection of a plane wave from a nonplanar wall is found for certain cavity angles. Numerical wave focusing calculations are carried out for arbitrary cavity angles. A single scaling law is obtained for gas flows with waves of moderate and high intensity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 123–129, September–October, 1987.     

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.     

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.     

Reflection of an Oblique Shock Wave in a Reacting Gas with a Finite Relaxation–Zone Length

Reflection of an oblique shock wave in a reacting gas with a finite length of the chemical–reaction zone is studied. Shock polars for an arbitrary heat release behind the oblique shock wave are constructed. Transition criteria from regular to Mach reflection and back are obtained. It is shown that transition criteria are significantly changed if the reaction–zone length is taken into account.