Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2024 number 2

Investigations (mainly those performed by the authors) of air blowing through a perforated section on a body of revolution with a large aspect ratio in an axisymmetric incompressible flow are summarized. Result of numerical and experimental studies of the flow properties, efficiency of the turbulent boundary layer control and prospects of using it for a body of revolution at small subsonic velocities equivalent to the take-off and landing regimes for a modern subsonic cargo aircraft are analyzed.

Optimization of tangential jet blowing on the upper surface of a supercritical transonic airfoil in the buffet mode was carried out. Two-dimensional Unsteady Reynolds Averaged Navier-Stokes equations were solved to simulate the flow past the airfoil. The Spalart-Almaras turbulence model was used to close the equations. The position of the slot nozzle and the intensity of the jet blowing out of it were varied. The optimal position for blowing with the minimum jet intensity to suppress buffet was determined.

This paper presents the results of a study of the influence of various sources of magnetic field on the size of droplets formed in microfluidic flows. Direct and reverse emulsions in a microfluidic device with flow focusing were obtained using magnetic fluids based on oil and water which are a continuous phase. Non-magnetic inclusions of various volumes were formed depending on the selected parameters: continuous phase flow rate, magnetic field configuration, and the position of the magnet relative to the axis of the device.

A periodic flow of an incompressible fluid around plates at large Reynolds numbers and small Keleghan-Carpenter numbers is considered. The energy dissipation over the oscillation period and the resistance coefficients of the plates are determined. Two-dimensional problems are studied on translational and angular vibrations of a flat plate and a plate in the shape of a circular arc, on translational vibrations of a circular cylinder with ribs symmetrically located on it, on angular vibrations of cruciform plates, as well as the problem of periodic flow around an inclined edge on a flat wall. A three-dimensional problem of translational and angular vibrations of a thin circular disk is considered. All obtained dependences for energy dissipation and drag coefficients are presented in analytical form through velocity intensity coefficients, which characterize the velocity singularity at the sharp edges of the plates with a potential flow around an ideal fluid. Some obtained dependencies are compared with the available numerical and experimental data.

Numerical modeling of a flow around a symmetrical thick drop-shaped airfoil in a non-stationary formulation was carried out at Reynolds numbers Re = 10⁴ ÷ 10⁵ and in the range of angles of attack α = –10 ÷ 10°. The calculations were performed in the approximation of the unsteady Reynolds-averaged Navier-Stokes equations (URANS) using the implicit large-eddy method (ILES). In the URANS approach, the position of the laminar-turbulent transition was determined based on the models k–kl–ω, k–ω–γ–Re_θ (Menter model) and (k–ω)-SST models with a given laminar flow region. It is shown that the position of the laminar-turbulent transition region has a significant impact on the flow structure and aerodynamic characteristics of the airfoil. Comparison of the results obtained using the ILES approach with experimental data showed that they are in good agreement. URANS calculations did not allow obtaining results consistent with experimental data. Fixing the laminar-turbulent transition point in the URANS calculation in some cases made it possible to correct the results.

Ceramic composites based on B₄C with a mole fraction of CrB₂ 0-30% were obtained by reactive hot pressing of a mixture of B₄C, Cr₂O₃, and nanofibrous carbon at a press force of 17.5 MPa, a temperature of 2000 °C and an exposure time of 10 min. The possibility of the chemical reduction reaction of metal oxide with boron carbide during hot pressing was studied. During the synthesis of CrB₂, the density of B₄C was found to increase due to the formation of the CrB₂-B₄C eutectic liquid phase. The relative density of all B₄C-CrB₂ composites obtained under these conditions exceeds 90%. The dependences of the microhardness and elastic modulus of samples on the concentration of the plastic phase were obtained. The dependence of the elastic modulus of the heterogeneous material on the volume fraction of chromium diboride taking into account porosity was determined by sequentially using the Reuss and Voigt averaging schemes

Uniaxial tension and three-point bending tests were performed for polymer composite samples made of Crystal 85-5 epoxy resin modified with MHG-4E (average particle size 5-15 µ m) and FV-530D (average particle size 25 µ m) photoluminescent powders. The dependence of the elastic modulus on the filler concentration was obtained. The photoluminescent properties of the resulting composites were studied. The dependence of the has been established afterglow intensity on the filler content in the composite was determined.

A problem of mathematical modeling of a section of a fuel element (fuel element), including a number of fuel pellets and a shell fragment, in an axisymmetric formulation is considered. It is assumed that the shell is a thermoelastic-plastic body, and the tablet is a thermoelastic body, taking into account the cracking of the material. To numerically simulate the thermal and mechanical contact of tablets with each other and with the shell, various variants of the domain decomposition method were used. The results of calculations are presented, which describe the achievement of the nominal power of a section containing 10 pellets, the influence of cracking of pellets on the thermomechanical state of the fuel rod is assessed.

A new technique has been proposed and implemented that allows for time-frequency analysis of data obtained using the PIV method, taking into account the readings of the surface sensor of a hot-wire anemometer. The technique is based on calculating the correlation coefficients between the data obtained by the PIV method and the data from the hot-wire anemometer sensor, which were previously filtered in a given frequency range. Using this approach makes it possible to obtain data on the unsteady characteristics of flows throughout the entire measurement range in the frequency range, the boundaries of which extend beyond the boundaries of the frequency range of the PIV method. Using the proposed method, a study of non-stationary processes in the region of interaction of a shock wave with a boundary layer at the Mach number M = 1.43 was carried out.

The feasibility of joining of the 6061 aluminum alloy to double-layer oxygen-free copper (TU1) by laser welding technology is reported. The weld formation and microstructure of the Cu-Cu-Al welding joint for various technological parameters are analyzed. The assessment of experimental results is based on macro- and microstructure observations of the weld using the AxioObserver D1M and Gemini SEM 300 scanning electron microscopes. The width and depth of the molten pool and the mechanical properties of the Cu-Cu-Al welding joint are tested by the Eagle-MD semi-automatic image measuring instrument and the YH-9002 computerized tension and compression machine. Among the nine tested samples, the most favorable weld parameters values are obtained with a laser power at 1600 W and a welding speed of 90 mm/s. The aluminum side area has a richer metallographic structure than the copper side area after welding.

Based on the solution of the cellular problem of the theory of elasticity, an analysis of the main types of deformation of the binder cross-reinforced with fibers of the composite was carried out. It is shown that all previously predicted possible types of local deformation of the binder fiber composite are revealed in numerical solutions of the cell problem of the averaging theory. The local stress-strain state of the binder significantly depends on the cross-sectional shape of the fibers. In the case of fibers with a square cross-section, it is possible to estimate the stress-strain state using explicit formulas, while for fibers with sections of other shapes, a computer must be used to calculate the stress-strain state.

It has been found that the heat release in the homogenized composite model is described by Joule-Lenz law for the averaged current strength and voltage. It has been shown that the local electric field strength and the local electric current in a real composite are usually significantly different from those in the averaged model despite the fact that the electric field potentials in the averaged model and the real composite are close.

Various crossovers of the effective permeability of certain analytically treatable models of the Darcy flow in porous media are studied. They account for the critical behavior as well for the regimes with low concentrations of obstacles. Transverse permeability of spatially periodic arrays of impenetrable cylinders is found in an analytical form and accounts for various asymptotic regimes. Longitudinal permeability for a square array of cylinders is found as well. Transverse flows past hexagonal and square arrays of cylinders are also considered based on expansions for small concentrations and lubrication approximation for high concentrations of cylinders. Three-dimensional periodic arrays of spherical obstacles are considered as well. Formulas for the drag force exerted by various lattices of obstacles are derived from low-concentration expansions. The Stokes flow through two-dimensional and three-dimensional channels enclosed by two wavy walls is studied by means of expansions for small waviness amplitudes. Compact formulas for permeability are derived in the form of factor approximants for arbitrary values of waviness. Various power laws are accounted for in the regime of large waviness parameters, as well as the existing expansions at small amplitudes.

The classical time-harmonic plane strain problem for a fluid-loaded cylindrical elastic shell is revisited. The results of the low-frequency asymptotic analysis, including explicit formulae for eigenfrequencies, are presented. A refined version of the semi-membrane shell theory is formulated. It is shown that the shell inertia does not affect significantly the lowest eigenfrequencies. It is also demonstrated that the ring stress component has a parabolic linear variation.

The effective thermal characteristics of composite materials used in the theory of solid-state cooling are studied. Two classes of composites are considered: layered structures consisting of a large number of nano-sized layers and two-phase granular composites. It is assumed that the boundaries between media are imperfect. At these boundaries, the temperature experiences a Kapitsa jump. The effective characteristics of layered structures are obtained using the matrix averaging method. The Averaging of the characteristics of granular composites is based on the Bruggeman approach. Formulas taking into account the influence of the Kapitsa interlayer resistance on the average thermal characteristics of the structure are obtained. Expressions for average values of heat sources are derived.

A method of transition from the three-dimensional piezoelastic problem for a composite material to the one-dimensional problem for a piezoelastic beam is presented. This is done using an asymptotic method of homogenization based on the separation of fast and slow variables in the solution. A special feature of the problem is the presence of two small parameters, one of which characterizes the microstructure of the composite material, and the other the cross-sectional size. Averaged relations describing the piezoelastic beam and fast correctors were obtained. Their joint use makes it possible to correctly describe the total stress-strain state of the initial three-dimensional body. The proposed method is suitable for solving the three-dimensional problem of deformation of an extended bodies with an arbitrary periodic structure and new problems (e.g., the torsion problem) that have no analogues in the theory of piezoelastic plates.

The stress-strain elastic field in a square array of N non-overlapping circular inclusions is described by approximate analytical formulas. In particular, soft inclusions are studied by an asymptotic analysis. The case with N = 1 yields a regular square array of disks of radius r embedded in an elastic matrix. The computations of Natanzon and Filshtinsky are based on an infinite system of linear algebraic equations solved by the truncation method. The infinite system determines the Taylor series coefficients of the Kolosov-Muskhelishvili complex potentials. A method of functional equations is used to write the series coefficients in symbolic form up to terms of the order of O ( r ^2s) at a fixed value of s . Approximate analytical formulas for local elastic fields are derived.

A small-sized elastic isotropic strip-beam loaded with variable body and surface forces is considered. On the front surfaces, surface shear stress and inertia are taken into account within the framework of the Gurtin-Murdoch surface elasticity theory. Asymptotically correct equations describing the long-wavelength bending deformation of micro/nano-beams taking into account shears and surface effects are derived by asymptotic integration of the two-dimensional elasticity equations over the strip thickness. The influence of surface stress and inertia on the lower spectrum of natural vibrations of metal micro/nano-beams is studied. It has been shown that surface inertia has the same effect on the spectrum of natural frequencies of bending vibrations as surface stresses.

The process of buckling of the von Mises truss in the case of material instability, i.e., with allowance for the loss of ellipticity, is considered. Strain diagrams are constructed. Results that allow one to study buckling of thin-walled structures (arcs or shells) made of materials for which the loss of ellipticity of equilibrium equations is possible are obtained.

The problems of indentation of a rigid stamp of finite dimensions with a surface microrelief into a multilayer elastic strip are considered. Boundary variational formulations of problems using the Poincare-Steklov operator, which maps contact stresses into displacements, are presented. When approximating this operator, a discrete Fourier transform was used; to calculate the transfer function, an algorithm based on the variational formulation of the boundary value problem for displacement transformants was used. As a result of approximation of the original contact problem, a quadratic programming problem with constraints in the form of equalities and inequalities was obtained, for the numerical solution of which an algorithm based on the conjugate gradient method was used. A number of patterns of contact interaction have been established.