The formation of a secondary shock wave behind a shock wave diffracting at a convex corner

This paper deals with the formation of a secondary shock wave behind the shock wave diffracting at a two-dimensional convex corner for incident shock Mach numbers ranging from 1.03 to 1.74 in air. Experiments were carried out using a 60 mm 150 mm shock tube equipped with holographic interferometry. The threshold incident shock wave Mach number () at which a secondary shock wave appeared was found to be = 1.32 at an 81° corner and = 1.33 at a 120° corner. These secondary shock waves are formed due to the existence of a locally supersonic flow behind the diffracting shock wave. Behind the diffracting shock wave, the subsonic flow is accelerated and eventually becomes locally supersonic. A simple unsteady flow analysis revealed that for gases with specific heats ratio the threshold shock wave Mach number was = 1.346. When the value of is less than this, the vortex is formed at the corner without any discontinuous waves accompanying above the slip line. The viscosity was found to be less effective on the threshold of the secondary shock wave, although it attenuated the pressure jump at the secondary shock wave. This is well understood by the consideration of the effect of the wall friction in one-dimensional duct flows. In order to interpret the experimental results a numerical simulation using a shock adaptive unstructured grid Eulerian solver was also carried out. Received 1 May 1996 / Accepted 12 September 1996     

Ideal gas flow behind a finite-amplitude shock wave

The equations of one-dimensional (with a plane of symmetry) adiabatic motion of an ideal gas are transformed to a form convenient for studying flows between a moving piston and a shock wave of variable intensity. The solution is found for the equations of a motion containing a shock wave which propagates through a quiescent gas with variable initial density and constant pressure. This solution contains four arbitrary constants and, in a particular case, gives an example of adiabatic shockless compression by a piston of a gas initially at rest.     

Interferometric measurement of density in nonstationary shock wave reflection flow and comparison with CFD

We present density measurements from the application of interferometry and Fourier transform fringe analysis to the problem of nonstationary shock wave reflection over a semicircular cylinder and compare our experimental measurements to theoretical results from a CFD simulation of the same problem. The experimental results demonstrate our ability to resolve detailed structure in this complex shock wave reflection problem, allowing visualization of multiple shocks in the vicinity of the triple point, plus visualization of the shear layer and an associated vortical structure. Comparison between CFD and experiment show significant discrepancies with experiment producing a double Mach Reflection when CFD predicts a transitional Mach reflection.Received: 12 November 2003, Accepted: 21 October 2004, Published online: 31 March 2005[/PUBLISHED]PACS: 47.40.-x, 42.40.Kw     

Behavior of sonic lines in a shock layer behind a detached shock wave

A numerical investigation is made into the formation of local supersonic zones in the subsonic flow region between a detached shock wave and the surface of the body in the case of supersonic three-dimensional flow over conical bodies with opening angle _k = 120 ° of the cone in the range of Mach numbers M = 2.5–15.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No.4 pp. 143–145, July–August, 1979.We thank G. I. Petrov for suggesting the problem and for helpful advice and O. M. Belotserkovskii for constant interest in the work.     

Particle and drop dynamics in the flow behind a shock wave

The results of an investigation of the dynamics of hard particles and liquid drops in the flow behind a transmitted shock wave are presented. From the equation of motion of a particle in the shock wave, relations for the displacement, velocity and acceleration as functions of time and certain velocity-relaxation parameters taking into account the properties of the gas and the aerodynamic drag of the particles are obtained for unsteady flow around the particles at an acceleration of 10³–10⁴ m/s². It is shown that the velocity-relaxation parameters are universal. Approaches to finding the aerodynamic drag of freely-accelerating bodies from the dynamics of their acceleration after being suddenly exposed to the flow are considered. It is established that under these conditions the drop dynamics observed can be well described in terms of the same velocity-relaxation parameters with account for linear growth of the transverse drop size. All the kinematic functions obtained are confirmed experimentally.     

Mixing enhancement behind an oblique shock wave

The possibility of mixing enhancement when a design-condition cocurrent jet passes through a stationary oblique shock is investigated. In [4] the effect of such a shock on the mixing layer of flows with Mach numbers M = 3 and 5 was experimentally investigated and it was shown that behind the shock no turbulence is generated. However, irrespective of its effect on the turbulence characteristics, an oblique shock causes deformation of the jet, modifying its dimensions, and in the three-dimensional case the shape of the cross section. The effect of this deformation on mixing, which is shown to be fairly significant, has been investigated theoretically using a numerical method. An approximate relation describing the variation of the maximum admixture concentration in the jet behind the shock is proposed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 61–68, March–April, 1992.The authors are grateful to V. A. Stepanov for useful discussions.     

Transonic transition behind a shock wave traveling through a dust-gas mixture

The results of investigating shock-wave interaction with a particle cloud on the range of transonic relative velocities are presented. Transition of the two-phase flow from the supersonic to the subsonic regime during phase velocity relaxation under conditions of well-expressed gas-phase nonstationarity was observed. The effect of gas acceleration in the subsonic phase interaction region, previously predicted by the authors on the basis of the accelerating screen model, is confirmed experimentally. The presence of a substantial chaotic component of the particle longitudinal velocity, which indicates close internal phase interactions of the collision type, is demonstrated. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 165–173, July–August, 2000. The work received financial support from the Russian Foundation for Basic Research (project N98-01-00722) and INTAS (project N97-2027).     

Vortical regime of the flow behind the bow shock wave

A new nonstationary regime of the flow around a step and a cylinder was found to exist at high free-stream Mach numbers for gas specific heat ratios below 1.2. The main features of the flow are strong vortices in the shock-compressed region with supersonic reversal velocities at the body face. The bow shock wave takes on a complicated shape, fluctuating in time. The vortical regimes can result from local heterogeneities in the free stream. The case of the heterogeneity is studied in this paper in the form of a thin thermal layer of limited length. The vortical regime remains in existence after the source of disturbances is removed. The results have been obtained through computer simulations through the use of Eulerian hydrodynamic equations and by way of several numerical methods: FLIC, Godunov's scheme, TVD, and PPM. The influence of viscosity on the development of the vortical regime has been studied by computer solving the Navier–Stokes equations. Received 21 August 1998 / Accepted 6 June 2001     

Parameter formation behind the reflected wave in a shock tube with a nozzle

The reflection of a shock wave from the inlet of a nozzle of very simple geometry is analyzed on the basis of calculations carried out in the two-dimensional formulation. The nozzle throat is a sharp-edged slit in the end face of the tube leading to an expanding duct with straight generators. In this formulation the results of the investigation are quite general, since they depend on a minimum number of the determining parameters varied in the calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–159, July–August, 1987.The authors wish to thank G. N. Nikolaev and I. M. Naboko for useful discussion of their results.     

Vapor condensation behind a shock wave propagating through a large molecular-mass medium

Measurements of film condensation were made behind the incident shock wave propagating through a vapor-liquid two-phase medium. Major objective of the study is to identify condensing heat transfer rates of the vapor to the shock-tube side wall as well as to learn the condensing main flow field. Ethanol and E-10 (a heavy liquid named Afluid by the manufacturer) were extensively used as working fluid. Steady accumulation of the condensing vapor was confirmed on the wall surface, as similarly seen in the end-wall experiment conducted elsewhere. A most significant result is that "dual-step" shock pressurization was observed in E-10. The first pressure rise is a normal one created by an incident shock front, whereas the second pressure rise is taken place by some large disturbance in the main flow. The reason for this is not certain yet, but is speculated to be a long relaxation time or inefficient compressibility of the fluid. The visualized shock front and its vicinity of E-10 is completely different from those of normal gases. Received May 31, 1994 / Accepted April 20, 1995     

Measurement of parameters of a gas suspension behind a shock wave in foam

A study has been made of the propagation of a shock wave in dry polyhedral foam with cell diameter 1 cm. The experiments were made in a shock tube in the range of Mach numbers M < 1.4 of the shock wave. The interaction of the shock wave with the foam was photographed. This established that the destruction of the foam by the shock wave leads to the formation of a gas-droplet flow behind the shock front. To determine the parameters of the suspension, the flow was probed by He-Ne lasers with different radiation wavelengths. The spectral-transparency method was used to find the modal diameter of the droplets of the gas suspension and the volume concentration of the droplets in the flow. The modal diameter of the droplets was 2m, and the volume concentration of the droplets decreased downstream.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 134–141, May–June, 1993.