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.     

Interaction of a reflected shock from a concave wall with a flame distorted by an incident shock

Observations are presented from calculations where a laminar spherical CH₄/air flame was perturbed successively by incident and reflected shock waves reflected from a planar or concave wall. The two-dimensional axi-symmetric Navier–Stokes equations with detailed chemistry were used. The computational results were qualitatively validated with experiments which were performed in a standard shock tube arrangement. Under the influence of the incident shock wave, a Richtmyer–Meshkov instability is induced in the flame, and the distorted flame finally takes the form of two separated elliptical burning bubbles in the symmetric cross plane. Then, under subsequent interactions with the shock wave reflected from the planar or the concave wall, the flame takes a mushroom-like shape. Transverse waves produced by the shock reflection from the concave wall can compress the flame towards the axis, and the focusing shock generated on the concave wall will lead to a larger mushroom-like flame than that induced by the planar reflection.      

Shock-wave structure in the near zone upon explosion of spatial charges in air

Profiles and values of pressure in shock waves are determined for the case of spherical, linear, and spatial charges, such as a coil of a bulk spiral and plane annular coils and Archimedes’ spiral of various lenths, exploded in air. In the case of explosion of rings and spirals, a complex wave structure in the form of a sequence of several shock waves is registered near the charges along the spiral axes; a weaker attenuation of shock waves with distance and pressure amplitudes two to three times higher than in the case of a spherical charge of the same mass are observed. It was found that an increase in the length of a plane spiral does not lead to an increase in the maximum pressure in the shock wave at distances of the order of several pitches of the spiral from its plane. With distance from spatial charges of different shape but identical mass, the pressure values in the shock-wave fronts coincide and tend asymptotically to the parameters of a spherical explosion with a significant increase in the duration of a wave packet generated by the spatial charge. Dependences for evaluation of shock-wave pressure amplitudes in the near zone of the explosion are presented. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 81–90, September–October, 2000.     

On the Chaotic Dynamics of a Spherical Pendulum with a Harmonically Vibrating Suspension

The equations of motion for a lightly damped spherical pendulum are considered. The suspension point is harmonically excited in both vertical and horizontal directions. The equations are approximated in the neighborhood of resonance by including the third order terms in the amplitude. The stability of equilibrium points of the modulation equations in a four-dimensional space is studied. The periodic orbits of the spherical pendulum without base excitations are revisited via the Jacobian elliptic integral to highlight the role played by homoclinic orbits. The homoclinic intersections of the stable and unstable manifolds of the perturbed spherical pendulum are investigated. The physical parameters leading to chaotic solutions in terms of the spherical angles are derived from the vanishing Melnikov–Holmes–Marsden (MHM) integral. The existence of real zeros of the MHM integral implies the possible chaotic motion of the harmonically forced spherical pendulum as a result from the transverse intersection between the stable and unstable manifolds of the weakly disturbed spherical pendulum within the regions of investigated parameters. The chaotic motion of the modulation equations is simulated via the 4th-order Runge–Kutta algorithms for certain cases to verify the analysis.     

Start shock waves and the vortex structures arising in the formation of jets

Experimental studies were made of the state behind a shock wave arising in front of a pulse jet in formation, and the development of the vortex structure of the jet itself. A comparison was made of the experimental axial density distribution in the jet in the region between the front of the gas and the primary shock wave with the solutions to the problem of an expanding spherical piston and the nonself-similar problem of a point explosion. Moscow Translated from Izvestiya, Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 146–150, September–October, 1988.     

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.     

Interaction of a high-speed combustion front with a closely packed bed of spheres

The head-on collision of a combustion front with a closely packed bed of ceramic-oxide spheres was investigated in a vertical 76.2 mm diameter tube containing a nitrogen diluted stoichiometric ethylene–oxygen mixture. A layer of spherical beads in the diameter range of 3–12.7 mm was placed at the bottom of the tube and a flame was ignited at the top endplate. Four orifice plates spaced at one tube diameter were placed at the ignition end of the tube in order to accelerate the flame to either a “fast-flame” or a detonation wave before the bead layer face. The mixture reactivity was adjusted by varying the initial mixture pressure between 10 and 100 kPa absolute. The pressure before and within the bead layer was measured by flush wall-mounted pressure transducers. For initial pressures where a fast-flame interacts with the bead layer peak pressures recorded at the bead layer face were as high as five times the reflected Chapman–Jouget detonation pressure. The explosion resulting from the interaction developed by two distinct mechanisms; one due to the shock reflection off the bead layer face, and the other due to shock transmission and mixing of burned and unburned gas inside the bead layer. The measured explosion delay time (time after shock reflection from the bead layer face) was found to be independent of the incident shock velocity. As a result, the explosion initiation is not the direct result of the shock reflection process but instead is more likely due to the interaction of the reflected shock wave and the trailing flame. The bead layer was found to be very effective in attenuating the explosion front transmitted through the bead layer and thus isolating the tube endplate. This paper is based on work that was presented at the 21th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, July 23–27, 2007.     

Forced nonlinear oscillations of a gas bubble in a large spherical flask (resonator) filled with a fluid

Radial oscillations of a gas bubble in a large spherical flask filled with a fluid are considered. We derive an equation of the change of the bubble radius by the known law of pressure variation at the boundary of the liquid volume (the law of motion of the piston) for a period of time during which, repeatedly reflected from the piston, the leading front of the reflected-from-the bubble perturbations reaches the bubble. For further calculations of the change of the bubble radius, recurrent relations which include the wave reflected from the bubble in the previous cycle and its subsequent reflection from the piston are obtained. Under harmonic action of the piston on the fluid-bubble system, a certain periodic regime with a package of bubble oscillations is established. Institute of Mechanics, Ural Scientific Center, Russian Academy of Sciences, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 77–87, September–October, 1998.     

Uniform expansion of a gravitating gas in the presence of a pressure gradient

Within the framework of the Newtonian mechanics, we studied the possibility of the formation of a uniformly expanding gravitating gas due to the passage of a detonation wave through a freely compressible medium (dust). The formulation of the problem is associated with the modeling of the large-scale expansion of the Universe. At the same time, the results obtained can also be applied to the calculation of the consequences of the spherical collapse of other gaseous masses. A class of exact solutions taking the pressure gradient into account is derived. Possible changes in the system behavior, as compared to with case of uniform pressure studied in [1], are analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 176–182, July–August, 1998. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 97-01-00196).     

Numerical simulation of gas dynamics in a bubble during its collapse with the formation of shock waves

The specific features of calculation of a gas in a spherical bubble located in the center of a spherical volume of weakly compressible fluid are considered. The problems of motion of a cold gas to a point and a spherical piston converging to a point are used to evaluate the algorithm. It is shown that significant errors can arise in calculation of spherical waves in the vicinity of the pole. These errors can be substantially reduced by means of artificial viscosity in the Riemann problem. Institute of Mechanics and Machine Building, Kazan’ Scientific Center, Russian Academy of Sciences, Kazan’ 420111. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 101–110, March–April, 1999.     

Stability of small radial oscillations of a spherical layer of liquid

An isothermal spherical layer of a viscoelastic liquid described by the one-parameter Maxwell model is considered. When the model parameter is taken equal to zero, a model of a purely viscous Newtonian fluid is obtained. The stability of the spherical layer of liquid with respect to small radial perturbations of the velocity and pressure is investigated for both types of liquids. Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 170–171, September–October, 1988.     

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.     

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.     

Experimental and numerical studies on interactions of a spherical flame with incident and reflected shocks

Observations are presented from experiments and calculations where a laminar spherical CH4/air flame is perturbed successively by incident and reflected shock waves. The experiments are performed in a standard shock tube arrangement, in which a high-speed shadowgraph imaging system is used to record evolutions of the flame. Numerical simulations are conducted by using second-order wave propagation algorithms, based on two-dimensional axisymmetric Navier-Stokes equations with detailed chemical reactions. Qualitative agreements are obtained between the experimental and numerical results. Under actions of incident shock waves, Richtmyer-Meshkov instability responsible for the flame deformation is induced in the flame, and the distoned flame takes a barrel shape. Then, under subsequent actions of the shock wave reflected from a planar wall, the flame takes an inclined non-symmetrical kidney shape in a symmetric cross section, which means a mushroom-like shape of the flame comes finally into being. The vorticity direction in the ring cap has been altered by the reflected shock＇s action, which makes the head of the mushroom-like flame extend quickly to the side wall.     

Gravity-induced motion of a uniformly heated solid particle in a gaseous medium

The steady motion of a uniformly heated spherical aerosol particle in a viscous gaseous medium is analyzed in the Stokes approximation under the condition that the mean temperature of the particle surface can be substantially different from the ambient temperature. An analytical expression for the drag force and the velocity of gravity-induced motion of the uniformly heated spherical solid particle is derived with allowance for temperature dependences of the gaseous medium density, viscosity, and thermal conductivity. It is numerically demonstrated that heating of the particle surface has a significant effect on the drag and velocity of gravity-induced motion. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 74–80, January–February, 2008.     

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.     

On the scattering of spherical waves by a cylindrical object

Summary The connection between plane wave and spherical wave scattering from an infinitely cylindrical object is investigated. If the distance of the source and the observer from the axis of the cylinder are denoted by ϱ₀ and ϱ, respectively, the ratio of the scattered field to that for plane wave excitation [ϱ0/(ϱ0 + ϱ)]^1/2.     

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.     

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).     

Structure of a turbulent bore in a homogeneous liquid

A mathematical model for the propagation of nonlinear long waves is constructed with allowance for nonhydrostatic pressure distribution and the development of a surface boundary layer due to wave breaking. The problem of the structure of a bore in a homogeneous liquid is solved. In particular, the transition of a wave bore to a turbulent bore as its amplitude increases is described within a single model. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 56–68, March–April, 1999.