Eigenoscillations near a plate in a channel

Acoustic eigenoscillations of a gas near a plate in a rectangular channel, i.e., the eigenfrequency of oscillations as a function of the chord length and the position of the plate in the channel, and the form of the eigenfunctions are studied in a two-dimensional formulation. A mathematical model of eigenoscillations near a plate in a channel has been proposed and substantiated, and the dependence of the eigenfrequency of oscillations on the geometric parameters is studied numerically with the use of this model. 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. 78–90, March–April, 1998.     

Acoustic oscillations near a thin-walled cylindrical obstacle in a channel

The problems of existence of eigenoscillations in infinite cylindrical regions comprising a thin cylindrical obstacle are studied. The existence criteria for eigenoscillations are obtained. For obstacles allowing axial symmetry, the dependence of eigenoscillation frequencies on the obstacle dimensions is studied. The form of eigenoscillations is studied for the first modes. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Science, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 133–142, July–August, 1999.     

Eigenoscillations of a fluid in a canonical domain and functional difference equations

In this work we construct and discuss special solutions of a homogeneous problem for the Laplace equation in a domain with cone-shaped boundaries. The problem at hand is interpreted as that describing oscillatory linear wave movement of a fluid under gravity in such a domain. These solutions are found in terms of the Mellin transform and by means of the reduction to some new functional-difference equations solved in an explicit form (by quadrature). The behavior of the solutions at large distances is studied by use of the saddle point technique. The corresponding eigenoscillations of a fluid are then interpreted as generalized eigenfunctions of the continuous spectrum.     

Visualization of deflagration-to-detonation transitions in a channel with repeated obstacles using a hydrogen–oxygen mixture

The deflagration-to-detonation transition in a 100 mm square cross-section channel was investigated for a highly reactive stoichiometric hydrogen oxygen mixture at 70 kPa. Obstacles of 5 mm width and 5, 10, and 15 mm heights were equally spaced 60 mm apart at the bottom of the channel. The phenomenon was investigated primarily by time-resolved schlieren visualization from two orthogonal directions using a high-speed video camera. The detonation transition occurred over a remarkably short distance within only three or four repeated obstacles. The global flame speed just before the detonation transition was well below the sound speed of the combustion products and did not reach the sound speed of the initial unreacted gas for tests with an obstacle height of 5 and 10 mm. These results indicate that a detonation transition does not always require global flame acceleration beyond the speed of sound for highly reactive combustible mixtures. A possible mechanism for this detonation initiation was the mixing of the unreacted and reacted gas in the vicinity of the flame front convoluted by the vortex present behind each obstacle, and the formation of a hot spot by the shock wave. The final onset of the detonation originated from the unreacted gas pocket, which was surrounded by the obstacle downstream face and the channel wall.     

Laminar slip flow of an electrically conducting incompressible rarefied gas in a channel with a transverse magnetic field

Summary The effects of a constant external magnetic field on the laminar, fully developed flow of an electrically conducting incompressible rarefied gas in a nonconducting parallel-plate channel are studied. Consideration is given to the slip-flow regime, wherein a gas velocity discontinuity occurs at the channel walls. It is found that the magnitude of the slip velocity is unaffected by the magnetic-field strength for a given pressure drop, but that the mean gas velocity and wall friction coefficient are functions of both the velocity slip coefficient and the magnetic-field strength. The effect of a second-order slip-flow boundary condition is briefly discussed.     

Aeroacoustic Self-Oscillations of the Gas Near Two Plates in a Channel

Aeroacoustic self-oscillations of the gas near two thin plates arranged in a tandem manner in a rectangular channel are studied in a two-dimensional formulation. A bifurcation of natural frequencies depending on the distance between the plates is detected, and the frequency of selfoscillations is found as a function of the plate length and the distance from the channel walls. The fields of pressure and gas velocities in the examined range of oscillations are constructed.     

Numerical investigation of rarefied diatomic gas flows through a plane channel into a vacuum

Rarefied flows through a plane microchannel into a vacuum are numerically investigated on the basis of the model kinetic equation for a diatonic gas (nitrogen). The dependence of the gas flow rate through the channel on the Knudsen number, the wall temperature, and the channel length is determined. The energy flux transferred to the cold diatomic gas from the hot channel walls is calculated. The results for diatomic and monatomic gases are compared.     

Unsteady Rarefied Gas Flow with Shock Wave in a Channel

The two-dimensional time-dependent problem of rarefied gas flow in a plane channel, formed by parallel plates of finite length and closed at one end, is solved on the basis of the kinetic S-model. The flow develops as a result of rupture of a diaphragm which separates the gas at rest in the channel and the gas at rest in a reservoir of infinite volume. The effect of gas deceleration at the channel walls under the conditions of diffuse molecular reflection from the channel walls and end face is studied. Decay of a shock wave and disappearance of a homogeneous flow zone behind the shock wave is traced for three variants of conditions at the channel inlet: (1) gas enters the channel from a reservoir of infinite length and width (as the basic variant), the simultaneous motion in the reservoir and channel being studied; (2) the high-pressure reservoir represents a usual channel section; and (3) the motion of the gas in the reservoir is not considered at all, instead of this, the boundary conditions of the evaporation-condensation type under the conditions of gas at rest in the reservoir are imposed in the inlet cross-section.     

Kinematic Parameters of a Two-Phase Flow in a Rectangular Channel

A kinematic two-phase flow pattern formed in a rectangular channel due to the interaction of a gas flow with an initially stationary or moving water layer is investigated. Using laser diagnostics and hot-wire methods, the velocity distributions in the water and the air are found for a stratified flow regime.     

Gas flow in a bent channel

The results are given of experimental investigations of flow of gas (air) in a curvilinear cylindrical channel. Patterns of the streamlines near the wall and the separation region were obtained by blowing cold air through a transparent model. In an investigation of the flow of hightemperature gas, in which an electric arc heater was used to supply the thermal energy, the profiles of the total pressure and the stagnation temperature were measured at different sections of the channel. It was found that the deformation of the profiles after the bend ends earlier for the hot gas than for the cold. The heat flux increases sharply after the bend.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 154–157, September–October, 1981.I thank A. B. Vatazhin for helpful discussions.     

Acceleration of a conducting gas in a strong nonstationary electromagnetic field

The problem of nonstationary acceleration of a conducting gas in a channel is solved, together with the problem of a discharge in an electric-circuit. As distinct from other papers, in which the typical solution assumed a thin cluster subject to acceleration, we examine the case in which the gas flow fills the entire channel. The motion of the gas in the channel is examined in one-dimensional formulation, under the assumption that the particle transit time in the channel is small compared to the discharge time and that the electromagnetic force is large compared to the pressure gradient.For impulsive acceleration of the conducting gas, use is made of a discharge with a certain capacitance. Since the (time-variable) resistance of the channel and, consequently, the behavior of the discharge depend upon the channel flow of the conducting gas, the correct solution of the problem of gas acceleration in the induced electromagnetic field can be obtained only by analyzing simultaneously the magnetogasdynamic channel flow and the discharge process in the entire electric circuit. On the other hand, the acceleration of the gas itself is a function of the instantaneous potential difference at the electrodes. Hitherto, such simultaneous solutions were obtained by many investigators under the assumption, proposed in [1], that a channel gas flow may be treated as the motion of a unique narrow cluster, whose length is negligible as compared to the channel length. Experiments and theoretical estimates show, however, that in many cases the conducting gas fills the entire channel length during the acceleration process, so that the assumption of a narrow cluster is not even approximately fulfilled [4, 5].     

多障碍物通道中激波诱导气相爆轰的数值研究

应用数值模拟方法,研究了直通道中激波经过多块矩形障碍物时诱导 H2/O2混合气体起爆的物理机制. 研究表明：在前导激波强度不足以诱导波后气 体直接起爆的条件下,经过激波压缩的可燃气体也可能在远离激波的障碍物之间的凹槽部位 起爆;障碍物表面产生的压缩波、膨胀波和气流滑移面对可燃气体的起爆、爆轰波的形成和 传播过程有重要的影响;添加不同稀释比的氮气可以影响爆轰波后流场的温度分布;增加障 碍物的间距可以改变可燃气起爆位置.     

Studying the coupled eigenoscillations of an axisymmetric tower-elevated tank system by the multimodal method

Employing the virtual work variational principle and the linear multimodal method for the liquid sloshing in an axisymmetric tank, we study coupled eigenoscillations of a tower and an elevated tank partially filled by a liquid. An emphasis is placed on the case of an upright circular cylindrical tank. Theoretical results are compared with known experimental data.     

Self-similar turbulent compressible gas flows in a channel

In this study we establish for turbulent compressible gas flow (to within a constant factor) the laws governing the variation of the height (radius) and the static pressure along the length of a planar or axisymmetric channel for which the longitudinal velocity component and gas temperature are functions only of the transverse dimensionless coordinate. In such channels the gas density decrease due to friction is compensated by the increase of the cross-sectional area so that the velocity and temperature profiles remain unchanged at all sections of the channel.The results obtained are a generalization to the gas case of the known laws governing the turbulent flow of an incompressible fluid in a cylindrical channel.The author wished to thank A. P. Byrkin for helpful discussions.     

Dynamics of a nonuniformly conducting gas flow in a magnetic field

The dynamics of a nonuniformly conducting gas flow in the channel of a MHD generator are investigated on the basis of numerical modeling. The initial shape of the plasmoids periodically entering the MHD channel qualitatively correspond to that noted in [6, 7]. The alkali metal seed is uniformly distributed over the entire flow. The mechanism of dynamic interaction of the plasmoids and the low-conductivity gas flowing over them, the variation of the shape of the plasmoids and the evolution of the gas dynamic structure of the flow are studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 135–145, September–October, 1989.     

Numerical simulation of compressible gas flow and heat transfer in a microchannel surrounded by solid media

In this study, a numerical model is developed to investigate the coupled compressible gas flow and heat transfer in a microchannel surrounded by solid media. To accommodate the varying flow cross-section, the compressible gas flow model is established in a non-orthogonal curvilinear coordinate system. An iterative numerical procedure is employed to solve the coupled heat transfer and gas flow equations. The computer code for the compressible gas flow is first validated against two test problems, and then extended by including the heat conduction in the solid media. The effect of the inlet Mach number on the Nusselt number is examined. It is found that the pressure difference from the pyrolysis front to the heated surface is induced essentially by the gas addition from the channel wall, instead from the pyrolysis front. The necessity of accounting for the gas compressibility is clearly demonstrated when severe heating is applied. The pressure distribution obtained along the channel axial direction is useful for further structural analysis of composite materials.     

Mechanism of deflagration-to-detonation transitions above repeated obstacles

Experiments are carried out to investigate the mechanism of the deflagration-to-detonation transition (DDT). Because, this mechanism has relevance to safety issues in industries, where combustible premixed gases are in general use. A stoichiometric gas of oxygen and hydrogen (oxy-hydrogen) is ignited in a tube, repeated obstacles are installed, and the DDT behaviours are visualized using a high-speed video camera. The pitch and height of the repeated obstacles and the initial pressure of the oxy-hydrogen premixed gas are varied in an attempt to obtain the optimum conditions that cause DDT a short distance from the ignition source. The experiments identified DDT as being essentially caused by one of the following mechanisms: (1) A deflagration wave is accelerated in terms of a vortex, which is generated behind the obstacle, and the flame acceleration induces a secondary shock wave. Eventually, the shock–flame interaction ahead of the obstacle causes DDT via a very strong local explosion. (2) Each shock wave generated by relatively weak local explosions between the obstacles is not sufficient to cause DDT directly, but DDT results from an accumulation of shock waves. The detonation induction distance is also examined, taking into account the physical and chemical parameters of the obstacles and the oxy-hydrogen premixed gas.     

Flow and heat transport in slotted channels with obstacles

We study the flow conditions in narrow channels with obstacles of various shapes at small and moderate Reynolds numbers. The observed flow conditions are compared with experimental data on heat transfer in a channel with obstacles.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 115–118, January–February, 1971.     

Thermophoretic augmentation of particle deposition in natural convection flow through a parallel plate channel

Present paper deals with temperature driven mass deposition rate of particles known as thermophoretic wall flux when a hot flue gas in natural convection flow through a cooled isothermal vertical parallel plate channel. Present study finds application in particle filters used to trap soot particles from post combustion gases issuing out of small furnaces with low technical implications. Governing equations are solved using finite difference marching technique with channel inlet values as initial values. Channel heights required to regain hydrostatic pressure at the exit are estimated for various entry velocities. Effect of temperature ratio between wall and gas on thermophoretic wall flux is analysed and wall flux found to increase with decrease in temperature ratio. Results are compared with published works wherever possible and can be used to predict particle deposition rate as well as the conditions favourable for maximum particle deposition rate.     

Evaporation from a surface and vapor flow through a plane channel into a vacuum

Two-dimensional steady rarefied-gas channel flow between two parallel walls, from an evaporating face to a perfectly absorbing plane end face, is studied. The vapor is considered to be a monatomic gas. The corresponding problem for the kinetic equation with collision integral in BGK form is formulated and solved numerically by two different finite-difference methods. Attention is focused on the calculation of the total gas flow rate through the channel cross-section. The structure of the gas channel flow as a function of the flow rarefaction, the channel length, and the ratio of the evaporation temperature to the wall temperature is studied.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 150–158, January–February, 1996.