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Results of an experimental and numerical study of a supersonic (M_∞ = 4.85) flow around a streamwise-aligned cylinder with a gas-permeable porous insert on the frontal face in the range of Reynolds numbers Re_D = (0.1−2.0) · 10⁵ are presented. The numerical study is performed by using the Ansys Fluent software system and a porous medium model based on a quadratic law of filtration. The parameters of the quadratic dependence are calculated on the basis of experimental data for an air flow in a porous material. Flow fields are obtained, and the wave drag of the model is calculated as a function of the porous insert length and the Reynolds number. Results of numerical simulations are compared with wind tunnel measurements.

An unsteady three-dimensional stagnation-point flow of a nanofluid past a circular cylinder with sinusoidal radius variation is investigated numerically. By introducing new similarity transformations for the velocity, temperature, and nanoparticle volume fraction, the basic equations governing the flow and heat and mass transfer are reduced to highly nonlinear ordinary differential equations. The resulting nonlinear system is solved numerically by the fourth-order Runge−Kutta method with the shooting technique. The thermophoresis and Brownian motion effects occur in the transport equations. The velocity, temperature, and nanoparticle concentration profiles are analyzed with respect to the involved parameters of interest, namely, unsteadiness parameter, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number. Numerical values of the friction coefficient, diffusion mass flux, and heat flux are computed. It is found that the friction coefficient and heat transfer rate increase with increasing unsteadiness parameter (the highest heat transfer rate at the surface occurs if the thermophoresis and Brownian motion effects are absent) and decrease with increasing both thermophoresis and Brownian motion parameters. The present results are found to be in good agreement with previously published results.

The shock-wave loading of a gradient mixture is numerically investigated in the pressure range of 20−150 GPa. The shock compression of a platelet gradient mixture of tungsten and porous copper is considered using a model which is a modification of the model of platelet porous materials supplemented with an algorithm for calculating changes in the thermodynamic and kinematic parameters of each particle and the sample as a whole. It is shown that the calculated parameters of the state of this shock-compressed mixture in the pressure−particle velocity coordinates are consistent with experimental data for a real tungsten−copper mixture.

A mathematical model of the electro−gas−dynamics of a gas−particle system is described. A numerical method for solving the system of equations is proposed, and an analysis is made of the motion of charged solid aerosol particles in gas−particle flow in the electric field produced by the corona electrode of the atomizer, the grounded surface on which deposition is performed, and the charge of the aerosol particles in the interelectrode space. The solution is based on the two−velocity two−temperature model of a monodisperse medium without phase transitions and coagulation assuming that only the carrier medium, described by the Navier−Stokes equations for a compressible gas, has viscosity. The dispersed phase is defined by the equation of conservation of mass, the equations of conservation of momentum components taking into account the Coulomb force and aerodynamic friction, and the equation of conservation of internal energy. The system is written in generalized coordinates in dimensionless form and solved using the explicit McCormack method with splitting over the spatial coordinates and a conservative correction scheme. The velocity and density fields of the gas−particle mixture were investigated in the interelectrode space and near the surface on which solid aerosol particles in the gas−particle flow are deposited.

An analytical algorithm for studying the stability of the equilibrium of compressible hyperelastic sphere with Lagrange variables is proposed. The problem is solved in a spherical coordinate system in a general three-dimensional formulation using linearized stability theory and the method of separation of variables with respect to the radial displacement, the displacement due to the rotation, and the resulting strain in the principal directions. Results of numerical and graphical analysis of the stress--strain state for a three-layer-sphere are used to analyze the gravity stress--strain state of the lithosphere of the Kuril island arc system.

A model of a medium consisting of parallel layers of elastic rectangular blocks separated by deformable viscoelastic interlayers is considered. The model is proposed for describing the low-frequency part of the spectrum in waves propagating in media with such a structure. For a two-dimensional assembly consisting of 36 blocks, the results of numerical calculations are compared with experimental data.

Based on the model of a physical cut and a material layer on its continuation, elastic and elastoplastic problems of determining the stress−strain state inside and outside the layer in the case of loading of cut edges by an antisymmetric system of forces are posed and solved. The solution of the elastic problem is compared with the solution obtained within the framework of the Neuber−Novozhilov model. In contrast to the latter model, the proposed approach provides results consistent with experimental data on the process of formation of fracture regions. Based on the analysis of the discrete solution of the problem, regions of plastic deformation and regions of possible fracture are found.

A new approach is proposed to estimate the fracture of bodies with V-shaped notches under loading of two types. Two examples of quasibrittle fracture are considered: with an initial straight crack and with a sharp V-notch. Experimental data are obtained on the fracture of V-notched specimens under bending.

A boundary singular integral equation of the plane problem was constructed using an approach based on the representation of the unknown Lekhnitskii complex potentials in the form of Cauchy type integrals with unknown densities on the boundary of the region occupied by the body. The contours of the holes and cuts and the shape of the outer boundary are exactly or approximately represented in the form of a sequence of straight and curved (in the form of elliptical arcs) boundary elements. The unknown densities on the boundary elements are approximated by a linear combination of some regular functions or complex functions that have a known singularity. In the numerical solution of the integral equation by the collocation method or by the least-squares method and in the subsequent calculations of the stress--strain state, the integrals of all types along the boundary elements are calculated analytically, which significantly increases the accuracy of the results.

The quality of cutting of low-carbon and stainless steel by beams of fiber and CO₂ lasers with oxygen or nitrogen being used as a process gas is compared. The cut surface roughness for sheets from 3 to 10 mm thick is determined. Domains of optimal (in terms of the minimum roughness criterion) application of lasers of various types in the space of dimensionless parameters (Peclet number and dimensionless power) are found. It is demonstrated that the CO₂ laser is more effective for laser-oxygen cutting, while the fiber laser is more beneficial for cutting with the use of a neutral gas.