Experimental study and direct numerical simulation of the evolution of disturbances in a viscous shock layer on a flat plate

The evolution of disturbances in a hypersonic viscous shock layer on a flat plate excited by slow-mode acoustic waves is considered numerically and experimentally. The parameters measured in the experiments performed with a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵ are the transverse profiles of the mean density and Mach number, the spectra of density fluctuations, and growth rates of natural disturbances. Direct numerical simulation of propagation of disturbances is performed by solving the Navier-Stokes equations with a high-order shock-capturing scheme. The numerical and experimental data characterizing the mean flow field, intensity of density fluctuations, and their growth rates are found to be in good agreement. Possible mechanisms of disturbance generation and evolution in the shock layer at hypersonic velocities are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 3–15, September–October, 2006.     

Numerical simulation of receptivity of a hypersonic boundary layer to acoustic disturbances

Direct numerical simulations of the evolution of disturbances in a viscous shock layer on a flat plate are performed for a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵. Unsteady Navier-Stokes equations are solved by a high-order shock-capturing scheme. Processes of receptivity and instability development in a shock layer excited by external acoustic waves are considered. Direct numerical simulations are demonstrated to agree well with results obtained by the locally parallel linear stability theory (with allowance for the shock-wave effect) and with experimental measurements in a hypersonic wind tunnel. Mechanisms of conversion of external disturbances to instability waves in a hypersonic shock layer are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 84–91, May–June, 2007.     

Approximate analytical calculation of the mach configuration of steady shock waves in a plane constricting channel

An approximate analytical model for calculation of the parameters of a steady gas flow inside a plane constricting channel formed by two symmetrically positioned wedges is suggested. A Mach configuration of shock waves (triple point) is formed in the channel when the wedge angles are larger than some critical value. The flow calculation in a constricting channel reduces to the solution of the iterative problem for a system of nonlinear algebraic equations. The configurations of shock waves, the slipstream, and the sonic line are described by the proposed model of a gas flow. A comparison of the results obtained using this model allows a fairly accurate calculation of the Mach stem and the length of the subsonic-flow region. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 52–58, May–June, 1998.     

Shock wave standoff distance for a sphere slightly above Mach one

This paper describes a numerical simulation of bow shock formation ahead of a sphere at steady supersonic flow in the Mach number range of 1.025–1.20. Turbulent viscous flow results are presented using the Spalart–Allmaras turbulence model. The purpose of this study is to determine the shock standoff distance for a spherical projectile at slightly supersonic free flight speeds. Results are compared to experimental data, including double exposure holographic interferograms obtained from a 40 mm polycarbonate sphere launched by a light gas gun. The shock standoff distance was determined from the interferograms. The present numerical simulations were found to agree with previously published data, and reached down to M = 1.025—a range where almost no previously published data exists. The computed flow structure and shock wave locations agree well with recently obtained free-flight interferograms.     

Gas content factor in the interaction of shock waves of different intensity in a two-phase gas-liquid medium

The transition from regular to Mach interaction is investigated in connection with the interaction of two plane weak or moderate shock waves of different intensity in a two-phase gas-liquid medium over the entire range of gas contents. A nonmonotonic dependence of the transition limit and the flow parameters on the gas content is detected. The investigation extends the results of [1] corresponding to the reflection of a shock wave from a wall. At intermediate gas contents in the case of opposing shock waves, analogous to the normal reflection of a shock wave from a solid wall, the results are in agreement with [2]. In the case of weak shock waves non-linear asymptotic expansions [3] are employed. In the extreme cases of single-phase media the results coincide with the findings of [3, 4]. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 172–174, November–December, 1986.     

Nonregular interaction of shock waves in magnetohydrodynamics

The nonregular quasisteady interaction of plane-polarized shock waves in a magnetic field is considered. Within the framework of the magnetohydrodynamic approximation, a Mach interaction pattern is proposed and investigated. This pattern contains the Mach shock wave moving between the initial shocks and connecting their branch points. Unlike the gasdynamic case, in the vicinity of both branch points the flow contains, in addition to the Mach shock, up to five waves whose qualitative structure cannot be predicted in advance. Numerical methods of solving the problem are elaborated. The numerical simulations of the phenomenon under consideration were carried out by means of a specially designed software package with the entire range of all the upstream parameters being covered. It was found that the velocity and inclination of the Mach shock depend significantly on the vector of the magnetic induction in the initial state. The wave pattern of the developing flow is a function of all the key parameters, being particularly sensitive to the inclination of the magnetic field. The values of the parameters for which catastrophic restructurings of the wave pattern occur are determined. Sudden changes in the flow and the magnetic field occur in a zone behind the colliding shock waves. The interaction of the shock waves at different angles and for different magnetic fields are analyzed in detail.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 184–198, May–June, 1993.The authors wish to thank G. G. Chernyi, A. B. Vatazhin, A. G. Kulikovskii, and G. A. Lyubimov for helpful discussions of their results.     

Type of reflection of a near-wall shock wave in the process of diffraction from a square channel

The results of an experimental and numerical investigation of the process of diffraction of shock waves from a square channel at a ninety-degree convex corner are presented for various incident shock wave Mach numbers M₀ (1.4<M₀<7). The type of reflection of the near-wall fragment of the diffracting shock wave from the wall and the wave velocity are determined as functions of M₀, direction, and time. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 145–151, January–February, 2000. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 96-02-16170a).     

Numerical simulation of blast flow fields induced by a high-speed projectile

Numerical investigations on the launch process of a projectile in a nearly realistic situation have been performed in this article. The Arbitrary Lagrangian–Eulerian (ALE) of Euler equations is solved by the AUSMDV scheme and the dynamic chimera grid technique are used for describing the moving of the projectile. Based on our numerical results, the muzzle blast flow field of the transient launch process of a projectile at a relative high Mach number of 3.0 has been visualized numerically, and the prominent characteristics including the propagation of first and second blast waves, the generation of bow shock wave and moving of the projectile, etc. have been discussed in detail.      

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     

Effect of yaw on the starting point of curvature for reflected diffracted shock wave (subsonic and sonic cases)

Lighthill (Proc. R. Soc. A 198, 454–470, 1949) considered the diffraction of a normal shock wave passing over a small bend. The bend being small Lighthill was able to linearize the flow equations and solved the problem through several mathematical techniques. Following Lighthill (Proc. R. Soc. A 198, 454–470, 1949), Srivastava and Chopra (J. Fluid Mech. 40, 821–831, 1970) extended the work to the diffraction of oblique shock waves. Srivastava (AIAAJ 33, 2230–2231, 1995) considered the problem of starting point of curvature and extended the work to yawed wedges (Srivastava in Proceedings of the 14th International Mach reflection symposium Sun Marina Hotel, Yonezawa, Japan, 1–5 October 2000, pp. 225–249, 2002). Srivastava (Shock waves 13, 323–326, 2003) considered the problem for starting point of curvature when the relative outflow behind reflected shock before diffraction has been subsonic and sonic. The present work is an extension of the work published in Srivastava (Shock waves 13, 323–326, 2003) when the wedge has been yawed through an angle. The results have been obtained for two angles χ = 60° and χ = 40° (χ is the angle of yaw).      

Gas-dynamic flow structure of a system of plane supersonic intersecting jets in a hypersonic flow

Turbulent motion is described by a system of parabolized Novier-Stokes equations which is closed by the (k-ε) model of turbulence. In the numerical calculations performed by the method of decomposing the flow vectors, the complex pattern of the interaction between perturbation waves is shown. In addition, it is shown that the system of shock waves on a gas-dynamic site causes the production of the pulsation-motion energy and the appearance of dissipative cellular structures in the field of kinetic turbulence energy. Al-Farabi Kazakh National State University, Almaty 480121. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 108–114, January–February, 1999.     

A rapid opening sleeve valve for a diaphragmless shock tube

This paper describes a novel pneumatically operated diaphragmless shock tube valve that is capable of generating well-formed shock waves within a driven tube which has a length to diameter ratio of 122. Its development was motivated by the requirement for an automated shock tube—an application for which the conventional bursting diaphragm method is not suited. The valve operates reliably, without any need for adjustment to its setup, over a wide range of driver pressures. Shock waves of up to Mach 2.4 have been generated in test gas at atmospheric pressure. A model for assessing the performance of the valve was developed and calibrated with experimental data. It indicated that opening times in the region of 0.5 ms were attained. By comparison, the opening time of a burst diaphragm is approximately 0.2–0.3 ms. Features of the valve include a streamlined flow path, which helps optimise the efficiency of the shock tube, automated operation and a test turn around time of the order of a few minutes.     

Unsteady and nonequilibrium airflow near a stagnation line

The propagation of shock waves in a medium with a nonuniform distribution of the parameters is the subject of recently published research [1–3]. The present paper deals with the problem of the gas flow ahead of the forward point of a blunt body moving at supersonic speed in air with variable parameters. The chemical reaction processes behind the shock front are taken into account. As a result of numerical calculations by the method of characteristics with isolation of the forward shock the time-dependent position of the shock front and the distributions of the composition and gas dynamic parameters in the shock layer are found. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 170–172, November–December, 1986.     

Shock-wave-initiated lifting of particles from a cavity

The dynamics of particles of the disperse phase in a turbulent gas flow in planar shock waves sliding along a solid surface with a trapezoid cavity is examined numerically. Lifting of particles from the cavity walls is calculated in the approximation of a rarefied gas suspension. It is shown that the intensity of the transient shock wave and the initial positions of particles have a significant effect on the particle-lifting properties. The height of particle lifting is found to nonmonotonically depend on the initial streamwise coordinate and shock-wave Mach number. It is shown that zones of aggregation and subtraction of particles may be formed at the cavity bottom. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 24–34, January–February, 2007.     

Characteristics of unsteady type IV shock/shock interaction

Characteristics of the unsteady type IV shock/shock interaction of hypersonic blunt body flows are investigated by solving the Navier–Stokes equations with high-order numerical methods. The intrinsic relations of flow structures to shear, compression, and heating processes are studied and the physical mechanisms of the unsteady flow evolution are revealed. It is found that the instantaneous surface-heating peak is caused by the fluid in the “hot spot” generated by an oscillating and deforming jet bow shock (JBS) just ahead of the body surface. The features of local shock/boundary layer interaction and vortex/boundary layer interaction are clarified. Based on the analysis of flow evolution, it is identified that the upstream-propagating compression waves are associated with the interaction of the JBS and the shear layers formed by a supersonic impinging jet, and then the interaction of the freestream bow shocks and the compression waves results in entropy and vortical waves propagating to the body surface. Further, the feedback mechanism of the inherent unsteadiness of the flow field is revealed to be related to the impinging jet. A feedback model is proposed to reliably predict the dominant frequency of flow evolution. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.     

Differential characteristics of the flow field in a plane overexpanded jet in the vicinity of the nozzle lip

A method of theoretical investigation of the flow field in a two-dimensional (plane-parallel or axisymmetric) overexpanded jet of an ideal perfect gas in the vicinity of the nozzle lip is described. The changes in curvature of the shock wave emanating from the lip, as well as the shock-wave intensity and flow parameters behind the shock are analyzed as functions of the Mach number, pressure ratio in the plane jet, and ratio of specific heats of the gas. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 72–83, May–June, 2006.     

Density reconstruction from laser schlieren signal in shock tube experiments

Using a diffraction approach the convolution-type integral equation for the laser schlieren signal created by an arbitrary disturbance at low pressure, where refractive index of disturbance is close to unity, in a shock tube (thin optical layer) has been deduced. In the equation electric circuit relaxation processes were taken into account by a response function. The equation was solved with the aid of the regularization method worked out for ill-posed problems. The density structures of the strong shock waves in air have numerically been reconstructed from experimental data ranging shock wave Mach number of –30, and –30 Pa. Received 7 April 1996 / Accepted 20 June 1996     

The shock–vortex interaction patterns affected by vortex flow regime and vortex models

We have used a third-order essentially non-oscillatory method to obtain numerical shadowgraphs for investigation of shock–vortex interaction patterns. To search different interaction patterns, we have tested two vortex models (the composite vortex model and the Taylor vortex model) and as many as 47 parametric data sets. By shock–vortex interaction, the impinging shock is deformed to a S-shape with leading and lagging parts of the shock. The vortex flow is locally accelerated by the leading shock and locally decelerated by the lagging shock, having a severely elongated vortex core with two vertices. When the leading shock escapes the vortex, implosion effect creates a high pressure in the vertex area where the flow had been most expanded. This compressed region spreads in time with two frontal waves, an induced expansion wave and an induced compression wave. They are subsonic waves when the shock–vortex interaction is weak but become supersonic waves for strong interactions. Under a intermediate interaction, however, an induced shock wave is first developed where flow speed is supersonic but is dissipated where the incoming flow is subsonic. We have identified three different interaction patterns that depend on the vortex flow regime characterized by the shock–vortex interaction.      

August Toepler — The first who visualized shock waves

The scientific investigation of the nature of shock waves started 130 years ago with the advent of the schlieren method which was developed in the period 1859–1864 by August Toepler. At the very beginning applied to the visualization of heat and flow phenomena, he immediately turned to air shock waves generated by electric sparks, andsubjectively studied the propagation, reflection and refraction of shock waves. His new delay circuit in the microsecond time regime for the first time made it possible to vary electrically the delay time between a spark generating a shock wave and a second spark acting as a flash light source in his chlieren setup. In 1870 Toepler, together with Boltzmann, applied Jamin's interferometric refractometer and extended the visualization to very weak sound waves at the threshold of hearing. Toepler's pioneering schlieren method stimulated Ernst Mach and his team toobjectively investigate the nature of shock waves: they improved Toepler's time delay circuit; continued the study on the reflection of shock waves; introduced shadowgraphy as a modification of the schlieren method; photographed the propagation of shock waves generated by an electric spark and by supersonic projectiles, and improved interferometry. Based on a large number of original documents the paper illuminates the concomitant circumstances of the invention of the schlieren method and its first applications by others. Although the schlieren method is only one of the many methods I had to use, it is a very important one, and I believe that you will enjoy the results as much as I do. Ernst Mach