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Crystallization processes in the case of modification of the surface layer of an iron-based alloy (Fe-C) subjected to a pulse action of a high-frequency electromagnetic field for substrate heating and melting are numerically simulated. The processes of heating, melting, and subsequent solidification of the metal are studied with the use of a mathematical model that describes thermodynamic phenomena. It is postulated that nano-sized particles with a high melting point uniformly distributed over the melt volume favor rapid crystallization during melt supercooling owing to heterogeneous nucleation. It is found that the nucleation and crystallization conditions in different areas of the melt volume are essentially different, and the maximum number of crystallization centers arise in regions where heat removal proceeds with the greatest rate. The particle size distribution in the crystalline structure in the solidified metal volume is estimated.

The behavior of the velocity component of silicon melt particles tangent to the free boundary during crucibleless zone melting in a magnetic field is studied. It is shown that the neglect of convective terms in the skin layer adjacent to the free boundary leads to erroneous results: the tangential velocity cannot reach a constant value when moving along the normal to the free boundary, which in turn leads, as shown earlier, at full solution of the problem, to an order of magnitude decrease in the characteristic velocity of melt particles outside the skin layer.

To take into account certification modes in optimization problems of the nacelle of a bypass turbojet engine, we developed a method for numerical determination of the characteristics of the air intake in the engine operating regime with a crosswind. The flow and aerodynamic characteristics of the air intake in these regimes were studied. Experiments were carried out in a wind tunnel to validate the calculation method based on the solution of the Reynolds-averaged Navier-Stokes equations. The laminar-turbulent transition was simulated using the the Menter turbulence  -model taking into account the compressibility of the gas.

One of the main methods of searching for gas hydrate deposits is seismic exploration and acoustic logging. For correct processing and interpretation of measurement data, it is necessary to know the acoustic properties of hydrate-containing rocks, which can be studied on the basis of laboratory experiments and adequate mathematical models. In this paper wave propagation in a hydrate-containing porous medium is investigated. The skeleton is considered to consist of grains cemented with gas hydrate, and is modeled by a homogeneous solid phase with effective parameters. The elastic moduli of the composite skeleton of a porous medium are calculated from the elastic moduli of the grain material and hydrate using a well-known method. The velocities and attenuation coefficients of linear waves are calculated within the framework of a two-velocity model of a porous medium. The calculated data are compared with the experimental data of other authors on sound velocities in hydrate-containing porous samples. The influence of the properties of the base rock, the saturating fluid, and hydrate saturation on the propagation of linear waves is studied.

Bypass surgery is widely used in the treatment of cardiovascular diseases. The problem of optimal location of cerebral vascular anastomosis is considered. An electrical circuit model of circulation of large cerebral vessels is constructed whose optimal parameters are determined numerically using swarm intelligence methods. The objective optimization function was taken to be the pressure after shunting compared with the pressure before surgery. This method was first used to solve the problem of formation of cerebral vascular anastomoses. It is shown that the obtained the results are in good agreement with the data of real surgeries.

We study the dynamics of a thin attached cavity formed as a result of an instantaneous stop (impact) of a circular cylinder in a disturbed fluid. The fluid flow immediately following the impact and the initial separation zone are determined using the classical model of impact with separation. To study the cavity collapse process, a direct asymptotic method is used, in which the expansions of the main hydrodynamic characteristics are carried out in terms of a small parameter equal to the dimensionless acceleration of the cylinder before impact. In the leading asymptotic approximation, a problem with one-sided constraints is formulated, from the solution of which the motion of separation points is determined and the process of collapse of a thin cavity is described. Taking into account the special equations of the boundary layer, the analysis of the internal free boundary of the fluid is carried out.

The spreading behavior of liquid droplets bridged by filaments is theoretically studied in this work. In our model, the wetted droplets between the fibers can be in one of three different equilibrium morphologies: barrel, bridge, or liquid column. The results show that small-volume droplets undertake a reversible column-to-bridge transformation. However, two distinct transitions are observed for large-volume droplets: column-to-bridge transition in the case of separated fibers and bridge-to-barrel-to-column transition for closely spaced fibers. Particular attention is paid to a hysteretic behavior of large-volume droplets at various inter-fiber distances. It is found that the our results are in good agreement with available experimental data

Thermofluid features of the flow through ribbed ducts for various rib arrangements and configurations are investigated numerically. Simulations are performed in a wide range of Reynolds numbers. The impacts of roughness factors (rib width, rib pitch, and rib height), rib arrangements, and rib configurations on the thermal performance of ribbed channels are examine.

The problem of fluid withdrawal (or injection) from a reservoir into a well in the presence of a hydraulic fracture perpendicular to the wellbore in the mode of a constant pressure difference between the wellhead and the reservoir is considered. Analytical solutions are obtained that describe the evolution of pressure in the fracture and fluid flow into the well. Approximate solutions are constructed using the method of successive change of stationary states. The comparison of exact and approximate solutions of problems for determining the pressure fields in the fracture and the volumetric flow rate of fluid from the well into the fracture is carried out and it is shown that they practically coincide (the relative difference does not exceed 1-2%). In this case, the calculation time for approximate solutions is significantly reduced. This contributes to the creation of effective calculation algorithms for transient modes of well operation in reservoirs with complicated reservoir characteristics. The influence of reservoir characteristics of a reservoir and a fracture on the evolution of pressure in the fracture and fluid flow into the well is analyzed.

The results of simulation of the process of unsteady fluid filtration in a formation penetrated by a well, which is crossed by a vertical hydraulic fracture of finite length, are presented. Using the method of integral Laplace transformations, an analytical solution of the system of equations describing fluid filtration in a formation and a fracture is constructed. Based on the analysis of the obtained solutions, the main characteristic features of the studied filtration process in the system reservoir - fracture.