编号 1 (2024)

Continuum models of media with zero pressure are widely used in various branches of physics and mechanics, including studies of a dilute dispersed phase in multiphase flows. In zero-pressure media, the particle trajectories may intersect, “folds” and “puckers” of the phase volume may arise, and “caustics” (the envelopes of particle trajectories) may appear, near which the density of the medium sharply increases. In recent decades, the phenomena of clustering and aerodynamic focusing of inertial admixture in gas and liquid flows have attracted increasing attention of researchers. This is due to the importance of taking into account the inhomogeneities in the impurity concentration when describing the transport of aerosol pollutants in the environment, the mechanisms of droplet growth in rain clouds, scattering of radiation by dispersed inclusions, initiation of detonation in two-phase mixtures, as well as when solving problems of two-phase aerodynamics, interpretation of measurements obtained by LDV or PIV methods, and in many other applications. These problems gave an impetus to a significant increase in the number of publications devoted to the processes of accumulation and clustering of inertial particles in gas and liquid flows. Within the framework of classical two-fluid models and standard Eulerian approaches assuming single-valuedness of continuum parameters of the media, it turns out impossible to describe zones of multi-valued velocity fields and density singularities in flows with crossing particle trajectories. One of the alternatives is the full Lagrangian approach proposed by the author earlier. In recent years, this approach has been further developed in combination with averaged Eulerian and Lagrangian (vortex-blob method) methods for describing the dynamics of the carrier phase. Such combined approaches made it possible to study the structure of local zones of accumulation of inertial particles in vortex, transient, and turbulent flows. This article describes the basic ideas of the full Lagrangian approach, provides examples of the most significant results which illustrate the unique capabilities of the method, and gives an overview of the main directions of further development of the method as applied to transient, vortex, and turbulent flows of “gas-particle” media. Some of the ideas discussed and the results presented below are of a more general interest, since they are also applicable to other models of zero-pressure media.

The diffusion stability of a single cavitation bubble in a spherical liquid cell surrounded by an infinite elastic solid is considered. The time-periodic pressure in the solid far away from the liquid cell is used as an external driving, which initiates bubble oscillations along with the gas diffusion process in the bubble-in-cell system. The work is based on the engineering approximation according to which the bubble growth/reduction is considered on average, assuming that during the period of the external driving the mass of gas in the bubble does not noticeably change. This theory predicts the existence of stably oscillating bubbles in confined liquid undergoing an external driving force. Three possible diffusion regimes are revealed: 1) total bubble dissolution, 2) partial bubble dissolution, and 3) partial bubble growth, where the last two regimes provide the diffusion stability in the bubble-in-cell system. The parametric study of the influence of the gas concentration dissolved in the liquid on the resulting stable bubble size is conducted. The obtained results are compared with the results for the case of the stable bubble oscillations in the pressure sound field in a bulk (infinite) liquid. The theoretical findings of the present study can be used for improvement of the modern applications of ultrasound technology.

The results of numerical study of supersonic flow in a channel with cavity are given. The calculated oscillation spectra are analyzed using the fast Fourier transform. Two types of oscillatory modes can be distinguished in the resulting periodic self-oscillatory regime. The first type of the modes corresponds to acoustic vibrations caused by the passage of sound waves along the cavity and calculated using the modified Rossiter formula. The second type of the modes corresponds to the frequencies of flow-rate oscillations caused by mass transfer between the cavity and the external flow. It is shown that the flow structure is modified when fuel is supplied in front of the cavity. Active combustion occurs in the layer of mixing fuel and oxygen from air. The flow pattern demonstrates the onset of Kelvin–Helmholtz instability on the interface between the main flow and the reacted gas. It is shown that an increase in the supplied fuel pressure leads to a decrease in the oscillation frequency and an increase in the characteristic size of oscillations.

The behavior of an ice cover on the surface of an ideal incompressible fluid of finite depth under the action of a pressure domain that moves rectilinearly at a constant velocity in the presence of a current with velocity shift in the upper layer is studied. It is assumed that the ice deflection is steady in the coordinate system moving with the load. The Fourier transform method is used within the framework of the linear wave theory. The critical velocities, the deflection of ice cover, and the wave forces are studied depending on the current velocity gradient, the shear layer thickness, the direction of motion, and the compression ratio.

The problem of constructing the transverse contour of a conical body having the minimum wave drag in the range of supersonic velocities provided that the length and the volume are preserved is considered. A cone is taken as the initial body, an assumption about locality of the relation between variations in the geometric parameters and the pressure on the surface is made, and the quadratic approximation of this relation is used. The found solution is compared with the results obtained within the framework of the Newton model. These solutions are proposed to combine being based on the assumption of the power-law relation between the radius and the derivative of radius with respect to the angular coordinate. In this case, a class of contours in which half of the cycle consists of the element with monotonic variation in the radius and arc of the circle is distinguished. These contours can be described by specifying a single geometric parameter, namely, the exponent. Using the inviscid perfect gas model, direct numerical optimization of the shape of transverse contour is carried out and the possibility of reducing the wave drag as compared to the star-shaped bodies with plane faces is demonstrated.

The two-dimensional electrogasdynamic problem of anomalous glow discharge on the surface of a sharp plate in supersonic flow of a perfect gas is solved using the system of Navier-Stokes equations to describe thermogasdynamic processes in the boundary layer and the two-temperature two-fluid diffusion-drift model of gas-discharge plasma to determine the electrodynamic structure of the discharge. The near-electrode regions of space charge and the external electrical circuit consisting of a power source and an ohmic resistance are taken into account. The influence of the magnetic field which is transverse to gas flow and has the induction of up to 0.03 T on the structure of boundary layer and glow discharge is studied. The electrogasdynamic structure of anomalous near-surface discharges is studied numerically over a wide range of gas flow velocities (M = 5–20), the free-stream pressures (p = 0.6–5 Torr), the electrode voltages, and the electric currents through the discharges. The electrodynamic structure of the gas-plasma flow near the electrodes and the effect of the glow discharge on the pressure and temperature distributions along the surface of the plate are also studied.