Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika židkosti i gaza

The study of steady-state axisymmetric Poiseuille flow of a Newtonian fluid induced by streamwise pressure and temperature gradients in the case of the dynamic viscosity coefficient dependent on the temperature is reduced to finding solutions to a three-parameter boundaryvalue problem for a third-order ordinary differential equation. In the domain of the parameter space corresponding to negative axial temperature gradients, there exist two branches of solutions describing flows accompanied by heat removal from the fluid. When the branches meet, they form a boundary in the phase space beyond which no solutions to the Poiseuille-type problem exist. One of the branches can be continued into the domain of non-negative values of the streamwise temperature gradient and contains an isothermal Poiseuille solution. Along this branch, curve of the flow rate as a function of the dimensionless axial temperature gradient has a minimum in the domain of positive values of the latter. In this part of the parameter space, the heat exchange regime with the external medium depends on the relation between all three dimensionless numbers of the problem. The heat exchange regime affects the nature of flow, slowing down the flow near the rigid wall during heat transfer, and forming a more filled velocity profile when heat is absorbed by fluid.

The time evolution of the three-dimensional pattern of initial disturbances imposed on an unsteady flow, which is a combination of one-dimensional rθ and rz-shears of Newtonian viscous fluid in a cylindrical layer infinite in length, is studied. The annular and axial velocities of both cylindrical boundaries, which do not vary in the disturbed motion, are specified. The formulation of the linearized problem in terms of variations in the velocities, the strain rates, the pressure, and the stress deviator is given. To analyze this problem, the method of integral relations is developed. The method makes it possible to obtain sufficient estimates of the development of disturbances in the Hilbert space H2, in particular, Lyapunov stability and asymptotic stability. These estimates include both the kinematic parameters of main flow and harmonics of the annular disturbances and wavenumbers of axial disturbances. For the steady-state main flow in the layer, exponential estimates of stability take place.

Vapor flow in a gap between a liquid droplet and a hot wall caused by evaporation of liquid is considered. It is assumed that the wall temperature is higher than the minimum film boiling temperature, and there is no direct contact with liquid. In particular, the problem of such a flow arises in modeling post-crisis heat transfer, when droplets from a vapor-liquid flow fall onto the heated surface and partially evaporate on it, making a significant contribution to heat transfer. Within the framework of the problem under consideration, the gap between the droplet and the wall is assumed to be plane, and the vapor flow to be laminar and axisymmetric. An exact solution to the corresponding hydrodynamic problem is given.

The results of experimental and numerical investigations of the development of two- dimensional determininistic disturbances in the case of Rayleigh–Taylor instability and transition to turbulence on the gas–liquid interface are presented. The experiments were performed on a light-gas gun. Disturbances at the interface were produced by means of gun oscillations using a special device. The disturbance wavelength varied from 5.4 to 8.8 mm, their amplitude from 0.3 to 0.4 mm, and the liquid layer acceleration from 5.2 to 18.8 mm/ms2. Water was used as a fluid and compressed air as a gas. The experimental data on the disturbance transition to the turbulent stage are obtained. The experiments are accompanied by the numerical modeling using the EGAK code. The criteria of instability transition to the turbulent stage are proposed.

A theoretical model of a metering pump based on magnetic fluid containing a body of magnetizable material controlled by an applied variable uniform magnetic field is proposed. The model takes into account the nonlinear dependence of the magnetization of the magnetic fluid on the magnetic field. This makes it possible to consider the case of any (including strong) magnetic fields. Within the framework of this model, calculations of lifting a piston separating the magnetic and pumped fluids in various uniform magnetic fields are performed. The calculations based on the proposed model are compared with previous and new experiments. A good agreement between theory and experiment is obtained.

The vapor flow near an interphase surface is studied by solving jointly the kinetic Boltzmann equation and the equations of continuum mechanics in the case of evaporation. It is shown that the flow structure formed in this case represents the totality of several zones, namely, the kinetic nonequilibrium region (Knudsen layer), the uniform flow region, where the velocity, density, and temperature are coordinate-independent, the contact discontinuity, and a region of uniform flow behind a closing shock wave. An approach is proposed, which makes it possible to construct the flow structure in the case of time-dependent evaporation without solving the kinetic Boltzmann equation. The results of the application of this approach are compared with numerical calculations obtained using the joint solution of the kinetic Boltzmann equation and the continuum mechanics equations and also by means of the direct statistical Monte-Carlo simulation.

The distinctive features of pressure wave dynamics in the presence of a porous partition (layer) saturated with a bubbly fluid are considered. It is shown that, depending on the parameters of the gas mixture and the porous medium (volume gas content, bubble dispersion, and porosity), reflection of a wave pulse from the porous partition saturated with a bubbly mixture is similar to reflection from the free boundary or from the rigid wall.