Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2026 number 5

To improve the insulating properties of the solid-liquid dielectric interface and to reduce the risk of surface discharges, partial discharges in the liquid dielectric, and dendrite growth in the solid dielectric, it is proposed to minimize polarization and ionic charges at the solid-liquid dielectric interface. For this purpose, nonpolar solid dielectrics with the same permittivity ε as the liquid dielectric are used. Polypropylene and polyethylene, both with ε = 2.3, are suitable for transformer oil with ε = 2.3. Polypropylene has relatively high mechanical strength and is easy to machine, while polyethylene is flexible and deforms without cracking, making it suitable for wire sheaths. This approach makes it possible to increase the dielectric strength of high-voltage pulsed devices, improve insulation reliability, and reduce device dimensions.

A 2.3-mm-thick coating based on titanium aluminides with Cr, Nb, and Si additions is formed on the surface of a VT20 titanium alloy by out-of-vacuum electron-beam surfacing. Energy-dispersive X-ray diffraction combined with energy-dispersive X-ray spectroscopy is used to assess the homogeneity of the coating thickness. The concentrations of aluminum and alloying elements in the deposited layer are found to vary slightly across its thickness, which affects the ratios of the main phases (γ-TiAl, α₂-Ti₃Al, Ti₅Si₃) formed in the coating, while the composition remains qualitatively unchanged. Such variations are not expected to have a significant effect on the coating properties across its thickness. The wear resistance of the deposited layer under dry sliding friction is found to be 2.5-fold higher than that of the base metal, and its mass gain at 1100 °C is 6.5-fold lower than that of the VT20 titanium alloy.

A numerical study is performed to investigate the effect of laser radiation parameters on the dissolution of titanium diboride (TiB₂), a refractory compound used for surface hardening. A spherical TiB₂ particle placed in a titanium melt containing nanoscale refractory modifier particles is considered. The simulation accounts for the nonuniform heating typical of laser powder surfacing. The dependence of the TiB₂ particle dissolution time on laser power and surfacing speed is determined. A comparison with the dissolution of titanium carbide particles is made. The physical properties of TiB₂ are shown to significantly affect the nature and time of its dissolution.

For a multidimensional quantum waveguide with a cylindrical outlet at infinity, various upper and lower bounds on the multiplicity of its discrete spectrum are presented. Some estimates based on the eigenvalues of the integral-differential problem on a resonator are absent from the literature. At the same time, the problem under consideration makes it possible to obtain a sharper sufficient condition for nonemptiness of the discrete spectrum of the waveguide and an estimate of its multiplicity.

A gas-dynamic calculation of the thermal loads and flux parameters of a single-phase flow in the duct of a supersonic exhaust diffuser is performed using a commercial numerical simulation code. The computational model and the challenges of calculating heat fluxes in the pseudo-shock region are described. A combined method for calculating heat fluxes is proposed, based on solving the integral relations for the boundary layer in the supersonic flow region and using the derived engineering formulas for the pseudo-shock region. The proposed approach is tested on a small profiled diffuser. Comparison of the calculated and experimental data shows a difference not exceeding 20 %.

The effect of secondary flows in the form of a paired spiral-vortex structure, formed by flow swirling in an annular channel, on heat transfer is investigated. Local and average heat transfer characteristics in an annular channel under swirling flow conditions are determined experimentally and numerically. The formation of the paired spiral-vortex structure and the resulting nonuniformity in the Nusselt number distribution are examined. The data obtained are compared with known calculated correlations. The largest difference between the numerical simulation results and the experimental data for the distribution of the average heat flux density in the annular channel does not exceed 16 %. Secondary flows are found to form a complex local heat transfer pattern that is not described by existing correlations for the average Nusselt number.

A transient model is proposed for the sedimentation of solid drill cuttings particles in the annulus of a well with arbitrary geometry after circulation of the drilling fluid has stopped. The possibility of plug formation in the annulus is taken into account. The fluid rheology is described by a power-law non-Newtonian model. A numerical scheme is developed that allows the equations of motion to be solved rapidly and efficiently. Examples of modeling particle sedimentation and bed formation are presented for straight, deviated, and J-shaped wellbores. The code developed on the basis of the proposed model makes it possible to determine the distributions of bed thickness and velocity, as well as the suspension density-parameters that can be used to assess the feasibility of wellbore cleanout upon resumption of fluid circulation.

Experimental data on the interaction of weak shock waves with the sharp leading edge of a flat plate and the bow shock at a Mach number M = 2.5 are presented. Measurements are performed with a constant-resistance hot-wire anemometer. Spatial distributions of the mean mass flow rate and its fluctuations under the action of an N-wave are determined in the incoming flow, in the flow above the model, and in the boundary layer. Spectral and statistical analyses of the resulting data are performed. The experimental results show that, when an N-wave passes through the bow shock, its amplitude decreases in the flow above the plate. The statistical distributions of the fluctuation signal in the vicinity of the N-wave fronts deviate significantly from a normal distribution. Outside the N-wave, the probability density distribution of the fluctuation signal is normal. The propagation angles of the N-wave fronts are estimated. The leading front of the N-wave is found to propagate in the incoming flow at an angle of 24.9 ± 0.5°, which agrees with the results of optical measurements. The trailing front of the N-wave propagates at the Mach angle.

The evolution of small perturbations in the joint motion of two uniformly stretched layers of ideal incompressible fluids is investigated. Kinematic and dynamic conditions are satisfied at the free boundaries of the layers and at their interface. The problem of small perturbations in Lagrangian coordinates is shown to admit separation of variables. A system of amplitude equations is derived that contains three Weber numbers, the density ratio and initial thickness ratio of the layers, and the wave numbers, making it possible to determine the evolution of the perturbed motion. Numerical results from an analysis of the amplitude equations are presented, indicating the instability of the motion under consideration.

The feasibility of using physics-informed neural networks (PINNs) to modify the Reynolds-averaged Navier-Stokes (RANS) equations for solving a heat transfer problem in a square channel is explored. A method for approximating solutions to differential equations based on the PINN approach is studied for estimating the mean flow temperature field with various heat transfer fluids. We consider a fully developed turbulent flow at a high Reynolds number (Re = 6100) and small to moderate Prandtl numbers (Pr = 0.025-1.000), typical of fuel elements using liquid metals and gas mixtures as coolants. Two models employing different approaches to approximating the turbulent heat flux are implemented: the gradient diffusion hypothesis (GDH) and an improved GDH hypothesis with two trainable coefficients that accounts for the shortest distance to the channel wall. The use of the PINN approach is shown to allow a significant reduction in computational cost. Model training takes approximately 2 h on a single GPU, whereas direct numerical simulation (DNS) of a similar problem on a supercomputer cluster requires several weeks of computation. The proposed approach is shown to be effective for parametric optimization, especially at small Prandtl numbers. When PINNs are used with DNS data, the accuracy of solving the RANS equations is higher than with conventional RANS modeling. The highest accuracy is achieved by the model using the modified GDH approximation.

The problem of unsteady bilinear flow of a Newtonian fluid in a reservoir with a finite-length vertical automatic hydraulic fracture connecting an injection and a production well is investigated. One well operates at constant pressure, while the other maintains a constant flow rate. Using the Laplace transform, analytical solutions are obtained for the pressure fields in the automatic hydraulic fracturing and in the reservoir, for the flow velocity in the fracture, and for the seepage rate. Conditions for the existence of a bilinear flow regime are determined. A simplified model of fracture flow using specified leakages is proposed, and analytical solutions in which time is a parameter are found.

The problem of proving the local-in-time existence and uniqueness of shock wave solutions to hyperbolic systems of conservation laws with many spatial variables is examined. This problem specifically pertains to the task of finding conditions on the initial data, such that, at each point on the surface of the initial shock wave, a smooth solution to the corresponding free boundary problem exists for small time. Examples of systems of conservation laws in continuum mechanics include the equations of gas dynamics and the equations of elastodynamics for compressible neo-Hookean materials.

The aerodynamic characteristics of a cone-shaped spacecraft model with and without an emergency escape system are compared. The freestream Mach number is M = 2. Jets issuing from the nozzles are shown to significantly affect the aerodynamic characteristics of the model. Compared with the cone-shaped model, the model with the escape system exhibits up to a 5.8-fold reduction in the drag coefficient.

Direct numerical simulation of the laminar-turbulent transition in a zero-pressure-gradient supersonic boundary layer and in the interaction of the boundary layer with an incident shock wave is performed. Transition scenarios caused by the development of a pair of oblique Tollmien - Schlichting waves at the frequency of the most unstable wave of linear theory, as well as by a wave packet, are investigated. Using the method of proper orthogonal decomposition, we performed a comparative analysis of the laminar-turbulent transition scenarios for a zero-pressure-gradient boundary layer and for a flow with a shock wave. Differences in the energy distribution of the flow fluctuations over the eigenmodes in the transition zone and in the wake are demonstrated.

A numerical study is performed on the development of disturbances in weakly underexpanded vibrationally nonequilibrium and equilibrium SF₆ jets issuing from axisymmetric sonic micronozzles into an SF₆ medium. The numerical simulation is based on solving unsteady three-dimensional Navier - Stokes equations using a two-temperature model of relaxing flows. Spectral analysis of the velocity disturbances in the mixing layer with respect to frequencies and azimuthal wave numbers shows that the initial disturbance level of the first asymmetric azimuthal mode determines the position of the laminar-turbulent transition. In a nonequilibrium microjet, this level is an order of magnitude lower than in an equilibrium one, which leads to a longer laminar section of the microjet.

Results of an experimental study of a Bunsen flame using planar laser-induced fluorescence (PLIF) are presented. A conical flame is visualized in the absence and in the presence of a weak transverse electric field. Premixed methane-air and ammonia-hydrogen-air mixtures are used with Reynolds numbers Re = 1000 and 600 and air equivalence ratios φ = 0.92 and 1.00, respectively. Using the PLIF method for two-line OH, an estimate of the temperature field is obtained for the studied regimes in the absence and in the presence of the electric field. The visualization results indicate that, under the action of a weak electric field, the upper part of the flame front of the methane-air mixture becomes rounded and deflected toward the cathode. The effect of a weak electric field on the ammonia-hydrogen-air flame produces no significant changes in the shape of the flame front and no significant deflection toward the electrodes. The temperature field estimate indicates that, in the studied regimes, a weak electric field has no effect on the temperature distribution in the combustion products.

The stabilization of a diffusion flame of gaseous hydrocarbons and hydrogen-containing mixtures is studied both for free discharge into the atmosphere and under the action of an external electric field. Current-voltage characteristics of the flame in an electric field are obtained for various hydrogen volume fractions. A change in the stabilization regime is observed when a constant electric field is applied. The relationship between the flame lift-off height and the homochronicity criterion is examined. The electrohydrodynamic effect on the flame is found to be dual in nature: in addition to the ionic wind, there is another mechanism by which the electric field influences the flame, associated with the induction of a space charge in the reaction region by the external field.

Computational studies of temperature variations in permafrost soils under various external boundary conditions are performed. The calculations use the results of laboratory studies of the thermophysical characteristics of soils in the thawed and frozen states, as well as the results of in situ soil temperature measurements in Norilsk, Russia. The boundary conditions of the computational model at the outer soil surface are specified using the snow cover thickness and the radiation balance. The variation of the radiation balance over the annual cycle is obtained for Norilsk's climatic conditions. A decrease in the moisture content of the surface soil layers is shown to reduce the influence of phase transitions on the thermal inertia of the soil, leading to an increase in the thickness of the soil layer with annual temperature fluctuations, an increase in the thaw depth, and a drop in the soil temperature below the thaw zone. Data are obtained on the temperature distribution over the depth of permafrost soils under various boundary conditions over a long-term cycle for Norilsk's climate.

Within the framework of antiplane shear theory, the equilibrium problem of an elastic composite body containing many thin gradient-elastic inclusions is considered. Each inclusion is geometrically represented by a straight-line segment with endpoints on the edges of the body. The inclusions-fibers or rods-are parallel to one another, and the problem contains a small positive parameter ε describing the distance between two adjacent inclusions. Using a variational formulation of the problem, the behavior of a family of its solutions as ε tends to zero is investigated. The limiting passage as ε → 0+ is justified using the two-scale convergence method. As a result, a correct averaged model of an anisotropic gradient-elastic composite body is constructed. This model describes the effective behavior on a macroscopic scale: on a scale at which it is not necessary to take each individual inclusion into account. Additional smoothness of the solution to the averaged model is proven, and an equivalent mixed formulation is derived on the basis of this proof. Finally, for the averaged problem in the mixed formulation, a numerical algorithm is proposed, and a series of numerical experiments is carried out to confirm the validity of the theoretical conclusions.

The problem of torsion of orthotropic circular rods under a constant torque in the creep regime is considered. Solutions are compared for three types of rods made from a transversely isotropic plate: (1) an isotropic rod with properties corresponding to those in the plane of the plate; (2) a rod oriented normal to the plate, taking into account the transversely isotropic properties of the material; (3) a rod oriented in the longitudinal direction of the plate, taking into account the transversely isotropic properties of the material. In a two-dimensional formulation, analytical solutions and estimates for the angular velocity of twist are obtained under the assumption of steady-state creep and no constraint of displacements at the rod ends along its axis. The resulting solutions are compared with the results of three-dimensional finite element calculations in the ANSYS software package. The possibility of estimating the stress-strain state by the method of characteristic parameters for rods of all three types is demonstrated. The resulting analytical dependences make it possible to determine the shear parameters of the material from torsion tests.

A numerical simulation of non-Newtonian fluid flows with various rheological parameters in a straight microchannel is performed to assess its suitability as a rheometer. Calculations are performed using a rectangular microchannel that is 40 μm high, 400 μm wide, and 13 mm long. A power-law fluid with a consistency index ranging from 0.006-0.6 Pa·sⁿ and a flow index ranging from 0.4 to 0.8 is considered. The Reynolds numbers range from 1 to 100. Based on the simulation data, a correlation is obtained for the constant in the expression for the friction coefficient, and equations are derived for calculating the rheological coefficients of the power-law model from the measured flow rate and pressure drop.