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A mathematical model of motion of solid particles withselective permeability and a mixture of moving gases is developedwith the use of averaging principles of mechanics of multiphase media.The derived system of quasi-linear partial differential equations isstudied for a particular one-dimensional isothermal case.

Interaction of a shock wave with a system of motionlessor relaxing particles is numerically simulated. Regimes of the gas flowaround these particles are described, and the influence of the initialparameters of the examined phenomenon on the flow pattern is analyzed.The drag coefficient of particles is calculated as a function of theMach number behind the shock wave at a fixed Reynolds number. Thedynamics of heat exchange for particles of different sizes(10$\mu$m--1mm) is determined, and the laws of thermal relaxationafter passing of a shock wave over the system of particles are found.The times of thermal and velocity relaxation of particles are estimatedas functions of the Reynolds number, and the predicted relaxation timeis compared with the corresponding empirical dependences.

Currently available methods of computing thelaminar--turbulent transition (LTT), including methods used ingas-dynamic software packages, are analyzed from the viewpoint of LTTsimulation accuracy.

This paper presents a numerical simulation of the flowresulting from transverse jet injection into a supersonic flow througha slot nozzle, at different pressures in the injected jet and mainflow. Calculations on grids with different resolutions use theSpalart--Allmaras turbulence model, the $k$--$\varepsilon$ model,the $k$--$\omega$ model and the SST model. Based on a comparison ofthe calculated and experimental data on pressure distribution on thewall, the length of the recirculation area and depth of penetration ofthe jet in the supersonic flow, conclusions are made about the accuracyof the calculation results of the different turbulence models and theapplicability of these models for solving similar problems.

A method of designing a supersonic axisymmetric tunnel air inlet based on the problem of an inverted flow in an annular nozzle with isentropic expansion is considered. The nozzle contour is constructed by the method of characteristics. Parameters of one inlet for viscous and inviscid gas flows are calculated.

A mathematical model for hydraulic fracturing is proposed. The model is based on the presentation of the fractured portion of the stratum adjacent to the well as a heterogeneous fractured porous medium. Assumptions usually used in the theory of elastic flow are applied. Formulas for determining the size of the hydraulic fracturing zone and the degree of fracture opening under conditions of relative equilibrium are derived.

This paper describes an experimental study of heat transfer in a channel behind a backward-facing step in the presence of a disturbance in front of it in the form of a single rib in the range of the Reynolds numbers $\Re = 5000\mbox--15\,000$. The influence of the rib position and height on heat transfer intensity behind the backward-facing step is investigated. It is shown that reattachment of the flow disturbed by the obstacle intensifies the heat transfer on the surface behind the backward-facing step.

The influence of two nanomodifiers with different compositions during their homogenization in the AL7 aluminum melt and moulding on the properties of the modified aluminum alloy is studied. Experiments are performed with the use of a centrifugal conductive magnetohydrodynamic pump. The melt is poured into a graphite mould with three cylindrical channels 38 mm in diameter and 160 mm long, which are designed for a metal mass of 500g. Two compositions are used as modifying agents: nano-scale particles of the aluminum nitride powder 40--100nm in size and metallized carbon nanotubes smaller than 25 nm, which are clad with aluminum to improve wetting of their surface. The analysis of the structure of the experimental and reference samples shows that the use of modifiers leads to refinement of the grain structure of the cast metal. According to the Hall--Petch theory, this effect may result in improvement of mechanical characteristics of the cast metal.

The processes of high-velocity oblique collision of metal plates which lead to the formation of their joints (seizure) are considered. It is found that the cleaning of the plate surface necessary for seizure results from a jet flow (particle stream), whose source is at least one of the welded materials or an interlayer of ductile material located in the initial region of collision. It is shown that additional cleaning may occur due to the emergence of rotating microregions in intense gradient flows localized in the joint area; seizure on cleaned surfaces is due to reduction of the surface energy of the system.

Crystal structure parameters, band spectra, distribution maps of the toal and partial electron densities of KN₃ and KSCN are calculated from the first principles using the density functional method and the general properties and distinctions in the band spectra are analyzed. The groups of balance subbands are qualitatively similar; in the upper valence band of KN₃ there is weak hybridization of p states of the complex anion and metal, which is not observed in KSCN. KSCN crystals are direct band gap materials and KN₃ are indirect band gap materials. The existence of weak covalent bonding of complex anions with metal is found from the electron density distribution maps in both crystals and also between metal atoms in KSCN, which is absent in KN₃.