Mathematical simulation of conjugate mixed convection in a rectangular region with a heat source

Conjugate convective-conductive heat transfer in a rectangular region with forced flow and a heat source is simulated numerically. Distributions of the thermal and hydrodynamic characteristics of the flow regimes studied are obtained. The evolution of the process analyzed is shown. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 69–81, November–December, 2008     

Vibrational Convection in the Hele-Shaw Cell. Theory and Experiment

The influence of high-frequency horizontal vibrations on convection in the Hele-Shaw cell located in a uniform gravity field is considered experimentally and theoretically. Nonlinear regimes of vibrational convection in the supercritical region are examined. It is shown that horizontal vibrations (directed toward the wide sides of the cell) decrease the threshold of quasi-equilibrium stability. Regions of existence of one- and two-vortex steady flows are found, and unsteady regular and random regimes of thermal vibrational convection are considered. New random regimes in the Hele-Shaw cell are found, which result from nonlinear interaction of the “lower” modes responsible for the formation of regular supercritical convective regimes. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 40–48, March–April, 2006.     

Flow regimes of a high-viscosity polymer mass bounded by the free surface in the region of drastic expansion of a channel

Flow regimes of the polymer mass filling cylindrical variable-section molds are studied by means of the numerical solution of the problem of a nonlinear viscoplastic fluid flow with a free surface in cylindrical channels of geometrically complicated shapes. A mathematical formulation of the problem is given, and factors affecting the molding process are analyzed. Numerical experiments performed in a wide range of problem parameters make it possible not only to elucidate the specific features of the hydrodynamic behavior of the free surface of the moving polymer mass, but also to establish the existence of two flow regimes depending on the ratio of the generalized Reynolds number to the Froude number. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 81–88, January–February, 2008.     

Gravitional penetration of a nonwetting fluid into a porous medium. Classification of regimes

The existence of capillary-gravitational equilibrium is detected in the problem of the penetration of a nonwetting fluid into a porous medium from the top. Using a numerical simulation method, three qualitatively feasible regimes of operation of the system are distinguished: total penetration of the soil; penetration to a finite depth, i.e., starting from a certain moment of time the gravitational head is weaker than the capillary resistance of the medium; no penetration of the soil. The existence of these three regimes makes it possible to distinguish critical parameters of the process expressed in terms of the Bond number. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 95–103, March–April, 1998.     

Bifurcation of self-similar solutions describing a thermocapillary flow of a fluid in a thin layer

Thermocapillary flows of a fluid in a lamina with a rigid lower wall and a free upper surface, along which the temperature gradient is given in the radial direction, are investigated for large Marangoni numbers. Self-similar solutions which describe the axisymmetric flow regimes of a fluid without the circumferential velocity component are constructed numerically and asymptotically for a system of Prandtl equations. It is shown that a pair of new self-similar flow regimes of a fluid with rotation branches off from the regimes obtained. The new regimes ere calculated numerically and asymptotically. Rostov State University, Rostov-on-Don 344090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 137–142, May–June, 1999.     

Regimes of laminar lateral flow separation due to jet exhaust

Numerical simulation of the separation flow on the lateral surface of an aircraft due to interaction between the engine exhaust plume and the external air-stream is carried out on the basis of the full Navier-Stokes equations. Three separated flow regimes are revealed, namely, closed, open and periodic. The conditions under which each of these three regimes may exist are determined. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 132–138, January–February, 1994.     

Excitation of subharmonic oscillations in an axisymmetric flow with coherent structures in the regime of aeroacoustic resonance

Conditions of origination of aeroacoustic resonance phenomena near an axisymmetric body in the form of a thick-walled tube in an air flow in a rectangular channel are studied experimentally. Dependences of the eigenfrequency of acoustic oscillations on the model length are determined. By studying the mechanism of origination of oscillations in the wake flow, it is shown that the process of generation of annular coherent structures in resonant regimes is characterized by evolution of nonlinearities including a subharmonic packet. Possible methods of flow control are discussed. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i, Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 59–68, July–August, 2000.     

Numerical modeling of the forming of fiber bundles from polymer melts

A mathematical model for the process of forming of synthetic fibers moving as a bundle is formulated. Three main versions are considered: forming of exposed bundles, forming in shafts with blowing, and stretching of fibers by means of an ejector. Low and high-speed forming regimes are also considered within the framework of the Maxwell model of a viscoelastic fluid. The calculations performed showed that the parameters of the fiber bundle produced depend on the method of forming used and on the local conditions in high-speed stretching, accompanied by oriented crystallization. Dnepropetrovsk State University, Dnepropetrovsk 320625. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 184–192, January–February, 1999.     

The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Unsteady gas well operating regimes

A model of a gas well containing liquid is considered, the nature of the steady-state regimes is investigated, and the causes of cyclical output are analyzed. In formulation the problem resembles the oil well gushing problem studied in [1]. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 162–164, November–December, 1986.     

Appearance of a “cold” layer upon explosive compacting of powders

Explosive compacting of powders is numerically simulated in the two-dimensional formulation. Different flow regimes depending on the detonation velocity are considered. Based on the calculations, the nature of the appearance of a “cold” layer upon explosive compacting of powders is revealed. 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. 192–197. January–February, 2000.     

Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos

We apply the recently improved version of the 0–1 test for chaos to real experimental time series of laser droplet generation process. In particular two marginal regimes of dripping are considered: spontaneous and forced dripping. The outcomes of the test reveal that both spontaneous and forced dripping time series can be characterized as chaotic, which coincides with the previous analysis based on nonlinear time series analysis.     

On an integral relation in magnetohydrodynamics

In the case of an incompressible fluid, an integral relation for change in the total pressure flux in magnetohydrodynamic (MHD) channels is obtained. Expressions for the reversible and irreversible changes in the total pressure flux are found. Various MHD-flow regimes are considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 184–187, January–February, 1998.     

Formation of thermal localized structures in a weld in pulse-arc welding by a nonmelting electrode

The technological regimes of welding that promote uniform distribution of the properties over the length of a welded joint are studied by numerically modeling the formation of a weld seam by a nonmelting electrode. Institute of Physics of Strength and Materials Science, Siberian Division, Russian Academy of Sciences, Tomsk 634021. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 172–177, November–December, 1998.     

Stability of wave regimes in film flow along a vertical surface

The stability of nonlinear traveling waves with respect to all possible two-dimensional infinitesimal perturbations is numerically investigated. The stability zones are determined for two families. It is shown that regimes of the second family, which in the limit go over into positive solitons, are the more stable. Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 126–131, September–October, 1988.     

Changes of a porous structure in flow of a monodisperse medium

The motion of fluids with suspended particles in porous media is considered. A mathematical model for the interaction of a monodisperse suspension with a porous structure is proposed. Changes in the parameters of the medium and the flow are studied for equilibrium regimes. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 113–121, March–April, 2000.     

Calculation of oscillatory regimes in couette flow in the neighborhood of the point of intersection of bifurcations initiating taylor vortices and azimuthal waves

Self-oscillating regimes of motion of a fluid close to Couette flow between rigid oppositely-rotating cylinders are investigated in a small neighborhood of the point of intersection of the neutral curves of the monotonic and oscillating instabilities. Bifurcation theory methods, together with computer calculations make it possible to detect transitions associated with the generation of both quasiperiodic oscillations and chaotic attractors. Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 81–93, July–August, 1998.     

Critical gas outflow from nozzles

The possibility of critical gas flow from Laval nozzles in overexpanded regimes behind a bridge shock is investigated theoretically with and without allowance for viscous mixing at the edge of the jet. The influence of the mixing effect and flow separation from the nozzle walls on the critical flow conditions is analyzed. It is shown experimentally that these regimes coincide closely with the displacement of the normal shock to the nozzle exit and cessation of the emission by the jet of a discrete tone. Mariupol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 180–184, July–August, 1994.