Vol 54, No 3 (2019)

The problem of the generation of cavitation self-oscillations in a liquid flow in a pipe with two resistances is considered. The first resistance is a cavitator, behind which there is an artificial ventilated cavity, where the mean pressure is greater than the atmospheric pressure, while the liquid and gas outflow into the atmosphere takes place through the second resistance. Investigations show that the self-oscillation frequencies are chiefly determined by the cavity properties and the conditions of the outflow into the atmosphere. The generation of different self-oscillation modes is directly associated with the number of waves formed along the cavity length. It is shown that the pressure pipeline properties and the cavity volume have an effect on the cavitation self-oscillation mode (up to four frequency modes can be observable at the same geometry and hydraulic flow parameters). The question arises of whether the self-oscillations can be used for generating pulsed jets at the outlet. It seems that it is the first mode regime that is most suitable for producing the pulsed jets, since in this case the pressure fluctuations in the cavity are maximum. Using the exponential Voitsekhovskii nozzle the regimes, in which an intermittent jet flow of the liquid is realized at the outlet, are experimentally obtained.

The problem of internal wave propagation in the coastal zone is considered. The solutions describing the evolution of nonlinear waves above the shelf are constructed on the basis of the mathematical three-layer shallow water model. An analysis of the solutions obtained makes it possible to establish the basic laws of transformation of solitary waves and nonlinear wave packets of large amplitude in the shelf zone of the sea. New possibilities of application of analytical and numerical solutions to interpretation of natural experiments are discussed.

A mathematical model is constructed and numerical calculations of the problem of a highspeed longitudinal steady flow of a viscous heat conducting gas with an admixture of liquid droplets over a thermally insulated flat plate are performed. The droplet temperature is assumed to differ from that of the carrier gas. The range of flow parameters is considered, in which the droplet evaporation can be neglected but the temperature of droplets can vary significantly within the boundary layer. The mathematical model of two-phase boundary layer is modified taking into account the temperature nonuniformity inside the droplets. This required, along with solving the macroscopic equations of the two-fluid model, to find a solution of the heat conduction equation inside the droplets. On the basis of parametric calculations, the flow regimes with the formation of a liquid film due to droplet deposition on the wall are investigated. The similarity parameters are found and a range of governing parameters is determined in which, due to the heat exchange with the liquid phase in the boundary layer, a noticeable decrease in the adiabatic-wall temperature is manifested even at very small initial concentrations of the droplets.

The mechanism of formation of three-dimensional internal gravity waves initiated by the start of motion of a disk of given diameter and finite thickness in the horizontal direction along the disk symmetry axis from right to left at a given uniform velocity in an incompressible viscous linearly density-stratified fluid is first considered in detail. The consideration is carried out on the basis of numerical solution of the system of Navier—Stokes equations in the Boussinesq approximation and visualization of the three-dimensional vortex structure of the flow calculated. The obtained fields of the velocity vectors and pressure perturbations possess horizontal and vertical symmetry planes passing through the disk symmetry axis. The process of formation of flow in the upper half-space caused by the shear and gravitational instabilities is described. In this process, two horizontal vortex filaments are initially formed between the back disk face and the place of pulsed start and then transformed into legs of the hairpin vortex loop whose head is located to right of the start point. Thereafter, vortex rings are periodically formed above the start point during half the buoyancy period of fluid. The left-hand halves of the rings are transformed into half-waves occupying space between the disk and the start point.

The problem of unsteady gas flow in a channel between parallel plates initiated by the initial discontinuity of the pressure and density (Riemann problem) in the channel cross-section at the high pressure drops and moderately low Knudsen numbers is solved numerically on the basis of the full system of Navier—Stokes equations. The finite-difference scheme of the second order with respect to the spatial variables and time is used. The effect of the gas viscosity and thermal conductivity on the velocity of the shock wave and the nature of flow behind it is studied under the conditions of long channel and low gas density in the low-pressure section. The numerical solution obtained is compared with the available experimental and computational data.

The present numerical work is devoted to the effect of an external magnetic field on a pulsating flow through an open cavity in a horizontal channel. The cavity is heated uniformly from the bottom wall. The finite volume method is used to solve the energy and Navier—Stokes equations. At the inlet of the channel flow pulsations are produced by adding a sinusoidal component to the velocity. The investigation is conducted for different Strouhal (0 ≤ St ≤1), Richardson (0.25 ≤ Ri ≤1), and Hartmann numbers (0 ≤ Ha ≤50) and for various aspect ratios of the cavity (L/H = 1, 1.5, and 2) at a pulsation amplitude A = 0.1. Various characteristics of the flow, such as isotherms, streamlines, and average and normalized Nusselt numbers are presented. The results indicate that the influence of the external magnetic field on the temperature distribution, flow field, heat transfer mode, and heat transfer enhancement rate vary with the Hartmann number. The effect of pulsations on the heat transfer enhancement is well correlated with the magnetic field intensity, Richardson number, and aspect ratio of the cavity.