Ablation of a hydrogen pellet in a light-gas gun bore

An ablation model for a hydrogen pellet accelerating in a thermonuclear facility fuel-injector bore is developed. The model is based on the Lagrange internal-ballistic problem complemented by the Stefan conditions on the ablating surface of the pellet Calculations demonstrate that, during pellet motion in the bore under the action of the gas, the pellet length remains almost unchanged, while due to the heat exchange with the bore walls the pellet diameter decreases by 4–10% St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–11, January–February, 1999.     

On a class of internal solitary waves in a two-layer fluid

Solitary waves on an interface between two fluids are considered. A uniform asymptotic expansion is constructed for internal solitary waves with flat crests (of the plateau type) that degenerate into a bore in the limit. It is shown that, in this case, in contrast to a Korteweg-de Vries wave, the wave amplitude is of the same order of smallness as the longwave approximation parameter. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 55–61, September–October, 1999.     

Bore impact on a vertical plate

This paper describes the technique and results of an experimental study of the longitudinal force component, the vertical coordinate of its application point, and the overturning moment for the impact of a bore on a vertical plate. The bore was generated by removal of a shield which produced the initial free-surface level difference in the channel (in the model formulation of the dam-break problem). It is shown that the greatest forces and overturning moments occur at the ratio of the initial headwater and tailwater levels at which a bore with a developed head roller is formed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 45–54, November–December, 2008.     

Special case of a traveling wave in one model of a multicomponent medium

The Kuropatenko model for a multicomponent medium whose components are polytropic gases is considered. It is assumed that, as x → ±∞, the multicomponent medium is in a homogeneous state with constant gas-dynamic parameters — velocity, pressure, and temperature. For the traveling wave flows, conditions similar to the Hugoniot conditions are obtained and used to uniquely determine the flow parameters for x → −∞ from the flow parameters x → +∞ and traveling wave velocity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 39–47, July–August, 2009.     

Propagation of a thermal detonation wave in a water-corium system

The problem of the unsteady propagation of a thermal detonation wave in a high-temperature-melt-water system up to the steady-state regime is considered on the basis of the three-dimensional and three-temperature vapor explosion model. The basic laws of wave evolution are analyzed and the wave structure is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 115–125, July–August, 2000. The work was supported by the Russian Foundation for Basic Research (project No. 98-02-17766) and the International Science and Technology Center (project No. 408).     

Determination of the shape of the shocks ahead of a transverse jet injected into a supersonic flow

The three-dimensional shape of the shock wave formed ahead of a sonic jet flowing out into a supersonic flow through the surface of a sharp cone is determined. The shape of the wave in the longitudinal and transverse cross-sections of the model is constructed using schlieren photographs taken for various angles of rotation and freestream Mach numbers M=1.75–3. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 41–44, March–April, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 95-01-00709a).     

Numerical simulation of wave flows caused by a shoreside landslide

A mathematical model is developed for formation and propagation of discontinuous waves caused by sliding of a shoreside landslide into water. The model is based on the equations of a two-layer “shallow liquid” with specially introduced “dry friction” in the low layer, which allows one to describe the joint motion of the landslide and water. An explicit difference scheme approximating these equations is constructed, and it is used to develop a numerical algorithm for simulating the motion of the free boundaries of both the landslide and water (in particular, the propagation of a water wave along a dry channel, incidence of the wave on the lakeside, and flow over obstacles). Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 109–117, July–August, 1999.     

On forced oscillations of a simple model for a novel wave energy converter

The dynamics of a simple model for an ocean wave energy converter is discussed. The model for the converter is a hybrid system consisting of a pair of harmonically excited mass–spring–dashpot systems and a set of four state-dependent switching rules. Of particular interest is the response of the model to a wide spectrum of harmonic excitations. Partially because of the piecewise-smooth dynamics of the system, the response is far more interesting than the linear components of the model would suggest. As expected with hybrid systems of this type, it is difficult to establish analytical results, and hence, with the assistance of an extensive series of numerical integrations, an atlas of qualitative results on the limit cycles and other forms of bounded oscillations exhibited by the system is presented. In addition, the presence of unstable limit cycles, the stabilization of the unforced system using low-frequency excitation, the peculiar nature of the response of the system to high-frequency excitation, and the implications of these results on the energy harvesting capabilities of the wave energy converter are discussed.     

Hydraulic jump structures in the presence of an ice sheet

Jumps of the bore type arising in a fluid layer with an ice sheet are investigated. These jump structures are considered for a determining mechanism in the form of dispersion due to the presence of an ice sheet. For this purpose a generalized Korteweg-de Vires equation [1] is used. The structure of these jumps consists of a wave zone that expand with time. On the boundary of the wave zone there are transitions between uniform and periodic states which can be locally considered as jumps. Among them are jumps which can be regarded as steady in the coordinate system moving with the boundary of the wave zone. These are jumps between a sequence of solitons and a uniform state (jumps of soliton type) on the boundary of the wave zone and jumps between periodic and uniform states (jumps with radiation). In addition, there are jumps which are unsteady even from the standpoint of a local analysis. In order to investigate the effect of dissipation processes on the jumps considered a system of generalized Boussinesq equations is derived with allowance for bottom slope and bottom and ice friction. The jump damping process is investigated numerically. This system of equations also makes it possible to investigate undamped jumps of the floodwater wave type. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 139–146. July–August, 2000.     

Nonlinear characteristics of the interaction of a turbulent boundary layer with a wavy surface

A nonlinear interaction of a turbulent boundary layer with a wavy surface of a solid body or a liquid whose level has a deviation in the form of a traveling monochromatic wave is studied. For the waviness of small curvature, a calculation procedure is proposed for the amplitude dependence of the drag coefficient and complex elasticity which characterizes the back action of the flow on the surface inflection. The analysis is based on the use of an isotropic algebraic model of turbulent viscosity and an orthogonal system of curvilinear coordinates that follow the surface inflections. The interaction between the flow and the surface wave is described within the framework of a quasi-linear model, and a two-scale, mean-flow model is used to determine the transverse structure of the flow in a smoothly expanding boundary layer. Institute of Applied Physics, Russian Academy of Sciences, Nizhnii Novgorod 603600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 72–84, November–December, 1998.     

Propagation of pressure waves in a gas-liquid medium with a cluster structure

Propagation of a stepwise shock wave in a liquid containing spherical gas-liquid clusters is experimentally studied. Measured results are compared with available theoretical models. It is shown that resonant interaction of gas-liquid clusters in the wave can increase the amplitude of oscillations in the shock wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 50–60, May–June, 2005.     

Evolution of a laser-generated shock wave in iron and its interaction with martensitic transformation and twinning

Effects of shock waves (generated by a nanosecond laser pulse in plates of Armco-iron) on structural changes are analysed. Localisation of processes of martensitic transformation and twinning – for various values of laser pulse duration – is studied both experimentally and numerically. A proposed model accounts for interaction of shock wave propagation and structure changes. Realisation of martensitic transformation and twin formation influences wave front modification. A stress amplitude decrease with increasing distance from a microcrater determines, together with the pulse duration, a character of spatial localisation of structural changes. Numerical results are compared with experimental data and serve as a basis for additional interpretation of phenomena. Received 9 August 1994 / Accepted 30 June 1997     

Edge waves in a shallow fluid beneath a fractured elastic plate

It is shown that a fracture in an elastic plate floating on the surface of a shallow liquid layer is a waveguide along which wave energy can be transported. The edge wave velocity is less than the velocity of flexural-gravity waves. The existence of an antisymmetric edge wave mode depends on the Poisson's ratio of the elastic plate. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 185–189, July–August, 1994.     

Uniform far field asymptotics of internal gravity waves from a source moving in a stratified fluid layer with smoothly varying bottom

The far field asymptotics of internal waves is constructed for the case when a point source of mass moves in a layer of arbitrarily stratified fluid with slowly varying bottom. The solutions obtained describe the far field both near the wave fronts of each individual mode and away from the wave fronts and are expansions in Airy or Fresnel waves with the argument determined from the solution of the corresponding eikonal equation. The amplitude of the wave field is determined from the energy conservation law along the ray tube. For model distributions of the bottom shape and the stratification describing the typical pattern of the ocean shelf eract analytic expressions are obtained for the rays, and the properties of the phase structure of the wave field are analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 111–120, May–June, 1998. This work was financially supported by the Russian Foundation for Basic Research (project No. 96-01-01120).     

Head-on Collision of a Detonation with a Planar Shock Wave

The phenomenon that occurs when a Chapman–Jouguet (CJ) detonation collides with a shock wave is discussed. Assuming a one-dimensional steady wave configuration analogous to a planar shock–shock frontal interaction, analytical solutions of the Rankine–Hugoniot relationships for the transmitted detonation and the transmitted shock are obtained by matching the pressure and particle velocity at the contact surface. The analytical results indicate that there exist three possible regions of solutions, i.e. the transmitted detonation can have either strong, weak or CJ solution, depending on the incident detonation and shock strengths. On the other hand, if we impose the transmitted detonation to have a CJ solution followed by a rarefaction fan, the boundary conditions are also satisfied at the contact surface. The existence of these multiple solutions is verified by an experimental investigation. It is found that the experimental results agree well with those predicted by the second wave interaction model and that the transmitted detonation is a CJ detonation. Unsteady numerical simulations of the reactive Euler equations with both simple one-step Arrhenius kinetic and chain-branching kinetic models are also carried out to look at the transient phenomena and at the influence of a finite reaction thickness of a detonation wave on the problem of head-on collision with a shock. From all the computational results, a relaxation process consisting of a quasi-steady period and an overshoot for the transmitted detonation subsequent to the head-on collisions can be observed, followed by the asymptotic decay to a CJ detonation as predicted theoretically. For unstable pulsating detonations, it is found that, due to the increase in the thermodynamic state of the reactive mixture caused by the shock, the transmitted pulsating detonation can become more stable with smaller amplitude and period oscillation. These observations are in good agreement with experimental evidence obtained from smoked foils where there is a significant decrease in the detonation cell size after a region of relaxation when the detonation collides head-on with a shock wave.     

Shallow-water equations with dispersion. Hyperbolic model

A hyperbolic shallow-water model is constructed with allowance for nonlinear and dispersive effects. The model describes solitonlike solutions in a range of wave velocities and predicts the breaking of smooth waves when the limiting amplitude is attained. The model is found to be adequate by comparison with experimental data on the evolution of a wave packet generated by the moving lateral wall of a channel. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 40–46, March–April, 1998.     

Criterion of formation of a shock wave reflected from a cloud of particles

The problem of the formation of a “collective” shock wave reflected from a cloud of particles, which was previously observed in experiment, is considered. A criterion of formation of a reflected shock wave is obtained based on the numerical and analytical solutions of the problem. 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. 44–51, May–June, 1998.     

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.      

Formation of a petal-shaped structure at the front of an axisymmetric liquid film induced by collision of a drop with a flat surface

A model for the formation of a petal-shaped structure is proposed that is based on Rayleigh-Taylor instability occurring at the stage of transition of supersonic flow to forced flow. At this stage, there is abrupt deceleration of the flow, reaching (10 ⁸–10¹⁰)g. A dispersion relation is derived that allows one to obtain the length of the wave whose amplitude increases with maximum rate. The number of petals formed is determined assuming that this quantity is constant in time. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 91–96, November–December, 1999.     

Effect of Wave Formation during Shock-Wave Compaction of Powders

The problem of shock-wave compaction of a metal powder enclosed in a metal container with a transverse partition is solved. A model of wave formation on the partition and in the compact adjacent to the partition is proposed; the model is based on the loss of strength in the powder due to collapsing of pores and to development of instability of the partition being compressed in the shock wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 119–130, January–February, 2006.