Vol 53, No 5 (2018)

The solutions of initial and boundary value problems of the outflow of an ideal (inviscid and non-heat-conducting) gas from cylindrical and spherical sources into a vacuum are obtained. Time is measured from the moment, when the source is turned on; at this moment the source is surrounded by a vacuum. The entropy, flow rate, and the Mach number of the gas outflowing from the source are given, together with the source radius; the Mach number can be greater of or equal to unity. If the source radius is greater than zero, then the flow domain in the “radial coordinate–time” plane consists of the stationary source flow and adjoining non-self-similar centered expansion wave consisting of C⁻-characteristics. The stationary flow is described by the known formulas, while the expansion wave is calculated by the method of characteristics. The calculations by this method confirm the earlier obtained laws for large values of the radial coordinate. The interface between the vacuum and the expansion wave is the straight trajectory of particles and, at the same time, a unique rectilinear C⁻-characteristic. For the source of zero radius (“pointwise” source) the velocity, density, and speed of sound of the outflowing gas are infinite. The gas velocity remains infinite everywhere, while the density and speed of sound become zero for any non-zero values of the radial coordinate. For the pointwise source the problem of outflow into a vacuum is self-similar. In the plane of the “self-similar” velocity and speed of sound its solution is given by three singular points of a differential equation in these variables. At one of these points the self-similar velocity is infinite, the self-similar speed of sound is zero, and the self-similar independent variable varies from zero to infinity, with the exception of the extreme values.

The problem of the far field of internal gravity waves generated by an oscillating point perturbation source moving in a vertically infinite layer of a stratified medium of variable buoyancy is considered. The analytical solution of the problem is obtained by two ways for a model quadratic buoyancy frequency distribution. In the first case the solution is expressed in terms of the eigenfunctions of the vertical spectral problem and the Hermite polynomials. In the second case the solution in the form of the Green’s characteristic function is represented in terms of the functions of parabolic cylinder. The analytical solutions obtained make it possible to describe the amplitudephase characteristics of the far fields of internal gravity waves in a stratified medium with variable Brunt-Väisäläfrequency.

Periodic perturbations in the core of a thin isochronous vortex ring in an inviscid incompressible fluid are investigated in the linear approximation. The aim of the study is to construct the system of basic displacements, namely, the complete system of solutions of the Helmholtz equation for vorticity perturbations inside the core of a vortex ring with a given frequency in the form of expansion in the ring thinness parameter μ. The structure of basic displacements depends substantially on the fact to what extent the frequency of the forcing action is close to the resonance frequencies of the system. If the difference between these frequencies is small, then, in addition to the ring thinness μ, the second small parameters arises in the problem. This leads to significant complication of the procedure of obtaining the solution and appearance of considerable corrections in the subsequent approximations of the expansion procedure. The case of isochronous vortex ring in which the periods of revolution of liquid particles are identical is considered. Obtaining the threedimensional oscillations in such flows turns out to be the simplest since there are no perturbations of the continuous spectrum for the isochronous ring. The system of basic displacements is the necessary element in deriving the dispersion relation for the eigen-oscillations of the vortex ring. The solutions obtained can also serve as an instrument to analyze the reaction of flows with curvilinear vortex lines or flows localized in toroidal regions to the external excitation.

The results of numerical simulation of the processes of two-phase flow through a porous medium in three-dimensional digital models of the porous space of three natural sandstone samples are given. The calculations are carried out using the lattice Boltzmann equations and the digital field gradient model over a wide range of the capillary numbers and the viscosity ratios of injected and displaced fluids. The conditions of flow through a porous medium with capillary fingering, viscous fingering and with stable displacement front are revealed.

The mechanism of replacement of methane by carbon dioxide in the hydrate in the process of CO₂ injection into a reservoir with formation of fronts of methane hydrate dissociation and carbon dioxide hydrate generation is investigated. It is found that such a replacement regime can be implemented in both low- and high-permeability reservoirs. It is shown that in the highintensity injection regime the heat flux from the well does not affect propagation of the fronts of methane hydrate dissociation and carbon dioxide hydrate generation. In this case the replacement regime is maintained by only the heat released at formation of carbon dioxide hydrate. An increase in the injection pressure may lead to suppression of methane hydrate dissociation and termination of the replacement reaction. The critical diagrams of existence of the regime of conversion of methane hydrate to carbon dioxide hydrate are constructed.

Experiments on heat transfer in supersonic underexpanded high-enthalpy air jets are conducted on the VGU-4 induction plasmatron at the pressure in the compression chamber of 8.5 hPa. At the air flow rate of 3.6 g/s and the high-frequency generator powers of 45 kW(regime 1) and 64 kW (regime 2) the heat fluxes to the copper surface at the stagnation point of watercooled cylindrical models along the axes of dissociated air jets are measured. The models, 30 mm in diameter, could have a flat face or a hemispherical nose. In the same regimes, the stagnation pressures are measured using the Pitot tube in the shape of a cylinder, 30 mm in diameter, having either a flat face or a hemispherical bluntness with a receiving hole, 14 mm in diameter. For the experimental conditions calculations of flows in the plasmatron discharge channel and supersonic underexpanded jets issuing from the discharge channel are performed within the framework of the Navier–Stokes and Maxwell equations. The heat fluxes to the experimental models are computed and compared with the experimental data.