Axisymmetric equilibrium shapes of a fluid in a toroidal vessel under conditions of weightlessness

The axisymmetric problem of the evolution of the free surface of a fluid during the filling of a toroidal vessel under conditions of weightlessness is considered. Despite its interest [1, 2], this topical problem of the hydrodynamics of weightlessness remains unsolved for lack of an effective method of solution. This paper employs the iteration-difference approach proposed in [3–5] for calculating simply and doubly connected axisymmetric equilibrium figures. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 154–156, November–December, 1986.     

Numerical simulation of aerosol sampling from an air flow to an input tube

The processes of sampling (aspiration) to an input tube of an aspiration probe from an ambient air flow are studied numerically. The air flow is simulated on the basis of three-dimensional Navier-Stokes equations for an incompressible fluid. The method proposed allows calculation of the aspiration efficiency in the case of rather complicated shapes of the limiting trajectories of the particles. Dependences of the aspiration efficiency on the mean velocity of suction of air into the tube and the size of particles for a given free-stream velocity are obtained. Research Institute of Aerobiology, State Research Center of Virusology and Biotechnology “Vector,” Novosibirsk Region, Kol’tsovo 633159. Institute of Computing Technologies, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 113–122, September–October, 1999.     

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).     

Stability of a plane conducting fluid layer under convection in a vertical magnetic field

The nonlinear convective instability of a plane horizontal conducting fluid layer placed in a uniform vertical magnetic field is studied [1]. A similar problem was previously considered in [2] but with allowance only for so-called weakly nonlinear third-order effects. In the present paper attention is concentrated on the study of the finite-amplitude instability mechanisms associated with the "hard" excitation of vibrations. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 23–28, January–February, 1998.     

Deposition of inertial particles from a turbulent pipe flow

An explicit formula is derived for the rate of deposition of large particles (droplets) on a tube wall in two-phase turbulent flow. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 68–75, March–April, 1998. The work was financially supported by the International scientific foundation INTAS (grant No. 94-4348) and by the Russian Foundation for Fundamental Research (project No. 97-01-00398).     

Optimization of shock-wave action on a spherical bubble in an ideal incompressible liquid

The possibility of controlling the oscillations of a spherical gas bubble in an ideal incompressible liquid is subjected to theoretical analysis. Liquid surface tension forces are not taken into account. The optimization process realizing a maximum of the radius amplitude and a maximum of the gas pressure in the bubble for a given impulsive change of pressure at infinity is considered. A shock-resonance bubble oscillation procedure giving stepwise pressure changes at the extrema of the radius is constructed. This problem is of interest in connection with the investigation of cavitation erosion [1] and processes in biological tissues [2–4]. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1988.     

Optimization of the shape of a wing in a hypersonic nonequilibrium gas flow

A variational technique of obtaining the optimal shape of a low-aspect-ratio wing with allowance for the nonequilibrium character of the flow is developed. The technique is applied to the problem of determining optimal wing shapes under terrestrial atmosphere conditions. The real-gas effect on the optimal shapes and maximum lift-drag ratio is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 160–170, March–April, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-00629).     

Reynolds analogy in a dusty laminar boundary layer

The nonisothermal Blasius problem for a gas suspension is considered on the basis of the equations of a quasiequilibrium two-phase laminar boundary layer [1–3]. Approximate analytical expressions are obtained for the friction and heat transfer coefficients and their region of applicability is estimated; the Reynolds analogy between friction and convective heat transfer processes [4] is extended to the case of a dusty quasiequilibrium laminar boundary layer. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 160–162, November–December, 1986.     

Two-front mathematical model of water injection into a steam-saturated geothermal reservoir

A mathematical model of the process of water injection into a high-temperature steam-saturated geothermal reservoir is proposed. In the reservoir there is a zone of co-existence of steam and water which is separated from the steam and water zones by moving interfaces (phase transition fronts) whose location is determined in the process of solving the problem. Within the framework of the proposed model the thermodynamic contradiction that exists in the single-front case for low permeabilities, expressed as supercooling of the steam in the corresponding zone ahead of the interface [1, 2], is not observed. With increase in the permeability the two-front solution obtained goes smoothly over into a noncontradictory single-front solution. Neutral curves separating the domains of existence of the different types of solution in parameter space are constructed. Moscow. e-mail: barmin@inmech.msu.su. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 105–112, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 99-01-01042).     

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).     

Two-parameter model of a turbulent flow with a dispersed-particle admixture

Using a two-point probability density function for the particle distribution over velocities and coordinates, a closed model of the particle effect on the turbulent flow characteristics is formulated. The processes of turbulent dissipation and turbulent energy transfer across the spectrum are studied. Different models of two-phase turbulence are compared. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 40–56, July–August, 1998. The work received financial support from INTAS (grant No. 94-4348) and the Russian Foundation for Basic Research (project No. 98-01-00-353).     

Two-dimensional instability of a tangential discontinuity in dispersive media

The instability of a tangential discontinuity in a compressible dispersive medium with respect to small two-dimensional perturbations is demonstrated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 16–23, January–February, 1997. The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 96-01-01340).     

Nonlinear gas oscillations in a closed tube driven by the aperiodic motion of a piston

Nonlinear gas oscillations in a closed tube driven by the aperiodic motions of a piston as a result of the action of the external and internal pressure drop are studied. The external pressure takes two values alternating at the moment of change of direction of motion of the piston. Two models of the motion of the gas are considered. Model 1 is formed by a system of equations representing the mass, momentum, and entropy conservation laws. As distinct from model 1, model 2 includes the total energy conservation law in place of the entropy conservation laws. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 134–142, March–April, 1998. The work was carried out with partial support from the Russian Foundation for Fundamental Research (project No. 96-01-00484).     

Resonant interactions of two waves in a model of a two-layer fluid

The behavior of long-wave perturbations on the interface between two layers of different fluids with interfacial interaction taken into account, which can be described by the quasiperiodic solutions of a pseudodifferential equation, is considered. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 92–98, January–February, 2000. The work was supported financially by the Russian Foundation for Basic Research (project No. 96-01-01766) and by the Siberian Branch of the Russian Academy of Sciences (project No. IG-43-97).     

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).     

Subsonic compressible cavitation flow past a plate at small cavitation numbers

A solution of the problem of symmetric inviscid compressible cavitation flow past a plate at small cavitation numbers is presented. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–104, July–August, 1998. This research was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00111).     

Particle interaction in a flow with a parabolic velocity profile

The hydrodynamic interaction of two rigid spherical particles in a viscous incompressible fluid with the velocity at infinity represented by a second-degree polynomial in the coordinates is considered. An analytical solution of the problem is suggested. The forces and torques exerted on the particles and also the linear and angular particle velocities are calculated. The results are compared with previous theoretical and experimental data. Saransk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 84–91, January–February, 2000. The work received financial support from the Russian Foundation for Basic Research (project No. 98-01-03295).     

Modeling the dynamics of colliding particles in a turbulent shear flow

A kinetic model for the probability density function (PDF) of the particle velocity in a turbulent flow with account for particle collisions is presented. The model is tested by comparison with the results of a numerical experiment for a nonstationary homogeneous shear layer. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 105–112, July–August, 1998. The study received financial support from the International Science Foundation INTAS (project No. 94-4348) and the Russian Foundation for Basic Research (project No. 97-01-00398).     

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.     

Numerical model of the aspiration system of an internal combustion engine

A physicomathematical model of flow in the aspiration system of an internal combustion engine operating in a “cold” regime, i.e., for a prescribed motion of the crankshaft, has been constructed. An ideal single-species gas is used. Results of a series of calculations for a time interval of five operation cycles are presented. Deceased. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 125–131, November–December, 1998.