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.     

Method of <Emphasis Type="Italic">A</Emphasis>-operators and conservation laws for the equations of gas dynamics

An algorithm is proposed which allows all conservation laws for a system of differential equations to be to obtained from its one zero-order conservation law for which the general rank of the Jacobi matrix is equal to the number of independent variables of the system. The efficiency of the algorithm is shown by examples of the equations of gas dynamics, for which new conservation laws are derived. For the equations considered, additional symmetry properties related to these conservation laws are established. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 53–60, March–April, 2009.     

Characteristics, conservation laws, and symmetries of the kinetic equations of motion of bubbes in a fluid

Generalized characteristics and Riemann invariants that are preserved along the characteristics are found for a kinetic model of motion of bubbles in a fluid. Conditions that ensure the hyperbolicity of a set of equations of a bubbly flow are obtained. It is shown that the set of equations of motion has an infinite number of conservation laws. An infinite series of generalized symmetries admitted by the equations is constructed. Solutions that are invariant under the generalized symmetries of solution and describe the propagation of running and simple waves in a bubbly fluid are found. 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. 86–100, March–April, 1999.     

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.     

Thermohydrodynamics of continuous-wave CO2 lasers with a closed cycle of the flow

The problem of pressure losses upon gas motion along a closed circuit containing channels in which heat is supplied to and removed from the gas is studied. The object where the pressure losses are studied is a CO₂ laser with a crossflow. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, 630090 Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 3–13, January–February, 2000.     

Motion and heat and mass transfer in a disperse admixture in turbulent nonisothermal jets of a gas and a low-temperature plasma

The motion and heat and mass transfer of particles of a disperse admixture in nonisothermal jets of a gas and a low-temperature plasma are simulated with allowance for the migration mechanism of particle motion actuated by the turbophoresis force and the influence of turbulent fluctuations of the jet flow velocity on heat and mass transfer of the particle. The temperature distribution inside the particle at each time step is found by solving the equation of unsteady heat conduction. The laws of scattering of the admixture and the laws of melting and evaporation of an individual particle are studied, depending on the injection velocity and on the method of particle insertion into the jet flow. The calculated results are compared with data obtained with ignored influence of turbulent fluctuations on the motion and heat and mass transfer of the disperse phase. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 95–108, May–June, 2008.     

Shadow Waves: Entropies and Interactions for Delta and Singular Shocks

This paper deals with two key problems for delta (or singular) shock solutions to systems of conservation laws: that of their entropy admissibility conditions (which is connected to the notorious uniqueness problem) and that of their interaction. We choose to represent systems of conservation laws by nets of functions which are piecewise constant (or constant with respect only to the space variable), here called shadow waves. All the calculations can then be done on each element of such nets using only the usual Rankine–Hugoniot conditions. A 3 × 3 pressureless gas dynamics model is the main example in the paper.     

Conservation laws and group properties of equations of isentropic gas motion

A system of equations of isentropic gas motion with n ⩾ 2 is classified in terms of zero-order conservation laws with the use of the method of A-operators. New conservation laws are found to be valid only for potential isentropic motion of the Chaplygin gas. In this case, the greatest number of nontrivial conservation laws is obtained, with n scalar conservation laws being nonlocal. Additional properties of symmetry of the considered equations associated with these conservation laws are indicated.     

Inertial steady flow of a bed of granular material down a surface with microrelief with allowance for finite time of intergranular contacting

An inertial flow of a granular material can be described by the laws of conservation of mass, momentum, and energy of random motion of solid particles by invoking some closing relations. In this work, these closing relations are inferred from the dimensional theory. The system of equations obtained is used to determine characteristics of a steady flow of a bed of a granular material down an inclined surface with a microrelief for various Richardson numbers and finite contact times of the particles during their collisions. Novosibirsk Military Institute, Novosibirsk 630103. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 128–132, November–December, 1999.     

Compaction of copper nanopowder

The problem of void filling in a copper nanocell under external loading generated by a spherical piston is solved. It is demonstrated by computations that a copper nanocell is an unstable system. Small perturbations generated by piston motion lead to void filling under the action of surface tension and to release of significant amounts of thermal energy. After the voids are filled, the initial crystalline structure of nanoparticles is violated and becomes amorphous. When the nanocell is rapidly compressed, a metastable state with a strongly distorted crystal lattice arises, which transforms to an amorphous state with significant amounts of heat released. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 133–141, May–June, 2007.     

Behavior of the unsteady jet of a mixture of a pressurized gas and dispersed particles discharged from a circular duct into the atmosphere

The unsteady axisymmetric jet produced by discharge of a mixture of a pressurized gas and dispersed particles from a circular duct into the atmosphere is studied within the framework of two-velocity, two-temperature gas dynamics. An attempt is undertaken to allow for the effective pressure due to random particle motion. The collision mechanism is found to be essential to radial expansion of the flow. Experimental data that support the results obtained are reported. Mozhaiskii Military Spacecraft Engineering Academy, St. Petersburg 197082. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 151–157, January–February, 1999.     

Partially invariant solutions for a submodel of radial motions of a gas

All partially invariant solutions in terms of the group of extensions for a model of radial motions of an ideal gas are found. The solutions are obtained by the method of separation of variables in an equation containing functions of one variable but different functions of different independent variables. The solutions predict different continuous unsteady convergence or expansion of the gas under the action of a piston with a point sink or source. If the sink or source affects all particles simultaneously, a collapse or an explosion occurs. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 26–34, September–October, 2007.     

A gas pendulum

It is shown that a periodic two-dimensional isentropic motion of a gas exists and it is described by an exact solution of the equations of gas dynamics. A polytropic gas that fills a circular cylinder rotates and oscillates (in the radial direction) simultaneously under the action of periodically changing external pressure. The solution obtained belongs to the class of solutions with a velocity field that is linear in the coordinates (with homogeneous deformation). 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. 115–119, September–October, 2000.     

Fractal First-Order Partial Differential Equations

The present paper is concerned with semi-linear partial differential equations involving a particular pseudo-differential operator. It investigates both fractal conservation laws and non-local Hamilton–Jacobi equations. The idea is to combine an integral representation of the operator and Duhamel's formula to prove, on the one hand, the key a priori estimates for the scalar conservation law and the Hamilton–Jacobi equation and, on the other hand, the smoothing effect of the operator. As far as Hamilton–Jacobi equations are concerned, a non-local vanishing viscosity method is used to construct a (viscosity) solution when existence of regular solutions fails, and a rate of convergence is provided. Turning to conservation laws, global-in-time existence and uniqueness are established. We also show that our formula allows us to obtain entropy inequalities for the non-local conservation law, and thus to prove the convergence of the solution, as the non-local term vanishes, toward the entropy solution of the pure conservation law.     

Numerical analysis of the stability of nonisothermal couette flow

The stability of convective motion of a liquid between two rotating heated cylinders is investigated in the absence of external forces. The mathematical model for describing the convection is obtained from the general equations [1, 2] on the assumption that the density of the liquid, the thermal conductivity, the specific heat and the viscosity coefficients depend only on temperature, and that the work done by the pressure forces and the viscous dissipation are negligibly small. The thermal expansion coefficient of the liquid is not assumed to be small, which distinguishes the models in question from the classical Oberbeck-Boussinesq model [1, 3, 4]. Rostov-on-Don. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 70–76, September–October, 1988.     

Complete systems of conservation laws for two-layer shallow water models

A well-posedness criterion for a complete system of conservation laws is proposed that assumes maximum compatibility of the convexity domain of the closing conservation law with the domain of hyperbolicity of the model used. This criterion is used to obtain well-posed complete systems of conservation laws for the models of two-layer shallow water with a free-surface (model I) and with a rigid lid (model II). 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. 23–32, September–October, 1999.     

Mathematical simulation of gas cloud motion following the atmospheric explosion of a meteoroid

The gasdynamic consequences of the explosion of a meteoroid in a dense atmosphere are studied. The gas motion is simulated on the basis of a high-accuracy numerical method using adaptive movable networks. Some effects which could not be reproduced using coarser networks are revealed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 29–37, January–February, 1998. The study was carried out with the support of the Russian Foundation for Fundamental Research (project No. 96-01-00448).     

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.     

Use of high pressures for solving problems of hypersonic aerodynamics

The use of high pressures in a hypersonic aerodynamic experiment is founded on physical grounds. Calculation results of Mach and Reynolds numbers reachable at the line of gas condensation are given as functions of the temperature and pressure in the plenum chamber. Approaches to solving problems of designing ultrahigh-pressure facilities that ensure outflow with pressures up to20,000 atm are described. These problems include the stop of the first-stage piston at the point of maximum pressure, suppression of the reaction force, provision of normal operation of seals of the moving piston, and reduction of friction forces in the seals. The principles considered are used in an actually operating facility. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 103–114, September–October, 2000.     

Suppression of oscillations of piston-aided wind tunnels

The method chosen to compensate for the forces acting on the barrel in the course of compression and confinement of the test gas in the settling chamber of a hypersonic wind tunnel with a free locking piston is justified. A method is proposed to compensate for the effect of adverse factors by optimizing the mass of an auxiliary piston introduced into the system. The effectiveness of the method is validated experimentally. As a result, for the case of gas compression to 200 MPa, the displacement of the center of mass of the barrel is reduced from 50 to 0.25 mm, which is smaller than the amplitude of elastic axial extension corresponding to the maximum pressure of the gas. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 212–220, September–October, 2008.