Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2018 number 2

Exact solutions of a nonlinear Boltzmann kinetic equation with a source are constructed in the case of an isotropic distribution function and Maxwell model of isotropic scattering. These solutions are constructed with the use of an equivalence group such that one of its transformations uniquely identifies the class of the source functions that are linear in terms of the distribution function; moreover, the transformed equation has a zero right side. As a result, one can explicitly find invariant solutions of the type of the Bobylev-Krook-Wu solutions, in particular, those that admit physical interpretation.

This paper describes the study of electroconvection of low-conductivity fluid in a capacitor with boundary conditions of adhesion on a solid surface in the case of rapid charge relaxation. The linear stability of fluid equilibrium in a constant electric field is investigated. The model describing the averaged fluid flow in a high-frequency electric field. The nonlinear modes of electroconvection are described. A mode map is constructed. It is established that, depending on the frequency of the external field, the transition to chaotic state occurs through quasiperiodic or intermittent structures.

The nonlinear integral model of a turbulent thermal is extended to the case of the presence of a horizontal component of its motion with respect to the medium (for example, the rise of a thermal in shear flow). In contrast to traditional models, the possibility of heat release in the thermal is taken into account. For a piecewise constant vertical horizontal velocity profile medium and a constant vertical velocity shear, analytical solutions are obtained which describe different dynamic modes of thermals. The nonlinear interaction between the horizontal and vertical components of thermal motion because each of them influences the rate of entrainment of the ambient medium, i.e., the rate of increase in the size of the thermal and, hence, its mobility. It is shown that the enhancement of the entrainment of the medium due to the interaction of the thermal with the cross flow can lead to a significant decrease in the mobility of the thermal.

A numerical solution is found for the problem of evolution of two oppositely rotating vortices in a viscous incompressible fluid near a solid surface. The mechanism of vortex dissipation is determined. The trajectory of vortex motion is constructed.

The dynamics of a heavy cylindrical body in a liquid-filled horizontal cylindrical cavity with a time-varying rotation rate is experimentally investigated. The body is near the cavity boundary under a centrifugal force and undergoes solid-body rotation together with the liquid and the cavity at a fixed rotation rate. The dependence of the body dynamics on the amplitude and frequency of the rotation rate modulation is investigated. It is found that at a critical amplitude of modulation (at definite frequency), the heavy body repulses from the cavity boundary and comes into a steady state at some distance from the wall. It is found that the average lift force (repulsive one) is generated by the azimuthal oscillation of the body in the rotating frame of reference and manifests itself at a distance comparable to the thickness of the viscous boundary layer. In the experiments, we observed an azimuthal drift of the body due to asymmetric azimuthal oscillations of the body. In the limit of high frequency of the rotation rate modulation, the dependence of the lift force coefficient on the gap between the body and the wall is determined.

Natural aeroacoustic oscillations of the gas near two thin plates arranged in a tandem manner in a rectangular channel are studied in a two-dimensional formulation. A bifurcation of natural frequencies depending on the distance between the plates is detected, and the frequency of natural oscillations is found as a function of the plate length and the distance from the channel walls. The fields of pressure and gas velocities in the examined range of oscillations are constructed.

An invariant submodel of gas dynamics equations constructed on a three-dimensional subalgebra with a projective operator for the case of monatomic gas is under consideration. The submodel is reduced to an Abel equation, with integral curves constructed for it. For a separatrix of a saddle, an approximate solution is studied. Such solutions describe the vortex scattering of gas along plane curves placed on the surface of revolution.

The power supply of an electromagnetic accelerator of solids (railgun) from a source of electromagnetic energy with a magnetohydrodynamic generator and a transformer with superconducting windings is calculated and analyzed. The laws and equations for electrical circuits are used, which are solved analytically and numerically. It is shown that a transformer with superconducting windings can be used to accumulate electromagnetic energy from a magnetohydrodynamic generator and to power a railgun in burst mode operation.

This paper considered the behavior of a semi-infinite ice cover on the surface of an ideal incompressible fluid of finite depth under the action of a load moving at a constant velocity along the edge of the cover at some distance from it. The ice cover is simulated by a thin elastic plate of constant thickness. In a moving coordinate system, the deflection of the plate is assumed to be steady. An analytic solution of the problem is constructed using the Wiener-Hopf technique. The wave forces, the deflection of the plate, and the elevation of the free surface of the fluid at different speeds of the load are considered.

A semi-analytical method for determining the productivity of a radial system of horizontal wells in an anisotropic layer is proposed. Results of calculations of the productivity and distribution of fluid flow along the length of the wellbores of the radial system of horizontal wells using the proposed method are compared with the data of experimental studies based on electrolytic modeling and engineering calculations. The effects of the number of wellbores, their location in the reservoir, and the hydraulic pressure loss on the distribution of the fluid flow along the length of horizontal wellbores are investigated.

The problem of unsteady coupled heat and mass transfer in the course of motion of a spherically blunted conical body fabricated with the use of thermal protection materials is considered. Numerical integration is applied to study the characteristics of heat and mass transfer at constant stagnation parameters (Mach number 6, altitude 15 km, and flight time 600 s), which impose severe constraints on the choice of materials for thermal protection. It is demonstrated that the use of advanced ceramic materials ensures an admissible temperature regime and maintaining the initial geometry of the body, including its motion at an angle of attack.

The purpose of the present study is to investigate the heat transfer performance due to free convection of nanofluids with variable properties inside 2D and 3D channels with trapezoidal cross sections. The governing equations are solved numerically using the finite volume method and the SIMPLER algorithm. In this study, the effect of the nanoparticle volume fraction, Rayleigh number, side wall angles of the trapezoidal section, and axial slope of the 3D channel are examined. The presented results include the average Nusselt number, flow circulation streamlines, and isothermal contours. The heat transfer rate (i.e., Nusselt number) is seen to increase in both 2D and 3D channels with an increase in the Rayleigh number. In 2D trapezoidal enclosures, the Nusselt number decreases with an increase in the nanoparticle volume fraction from zero to 2% and increases if the nanoparticle volume fraction is greater than 2%. In 3D channels, an increase in the axial slope of the channel leads to an increase in the Nusselt number.

This paper analyzes the effect of the time-dependent shape of a load pulse on the spall strength of materials. Within the framework of a classical one-dimensional scheme, triangular pulses with sections of signal increment and attenuation and without sections of signal increment are considered. Calculation results for the threshold characteristics of fracture for rail steel are given. The possibility of optimization of fracture by selecting a loading time with the use of an introduced characteristic of dynamic strength (pulse fracture capacity) is demonstrated. The study is carried out using a structure-time fracture criterion

A strength condition is obtained that takes into account the deformation anisotropy and the effect of uniform pressure on the mechanical properties of materials.

The one-dimensional dynamic problem of the interaction of the unloading wave with the elastic-plastic boundary is considered within the theory of large elastic-plastic deformations. It is shown that before the formation of the unloading wave, the increasing pressure gradient leads to quasistatic deformation of the elastic-viscoplastic material filling the round tube, which is retained in the tube due to friction about its wall, resulting in the formation of near-wall viscoplastic flow and an elastic core. The unloading wave is initiated at the moment when the material begins to slip on the inner wall of the tube. Calculations were conducted using the ray method of constructing approximate solutions behind strong discontinuity surfaces, and ray expansions of the solutions behind the cylindrical surfaces of discontinuities were obtained.

Friction stir spot welding is a new technique used in industries for spot joining dissimilar combinations. In this investigation, dissimilar combinations of Al5052 aluminium and C10100 copper are joined by using this technique with variations of important process parameters, such as the tool rotational speed, dwell duration, and plunging depth. A central composite design model is developed for establishing empirical relationships between the process parameters and the fatigue life of the joints (number of cycles to fracture). The analysis of variance is used for determining the significance of the developed model. The response surface methodology is used for maximizing the fatigue strength. By confirmation experiments, the model is validated, and the error is found to be within four percent.

A closed mathematical model is formulated, which takes into account elastoplastic deformations and the medium capability of accumulating the energy of internal self-balanced stresses. Satisfaction of the diffeomorphism postulate (assumption of displacement field smoothness) is not required; as a result, the strains depend on the stresses and second derivatives of the stresses with respect to the coordinates. The model involves a linear structural parameter. Relations that take into account local bending of the elementary volumes of the medium are derived.

A plane hydrofracture problem for the Khristianovich-Geertsma-de Klerk model is extended and solved in the case where a confining stress closing a fracture is not constant in the direction of its propagation. A method is developed for solving the problem with an arbitrary stress contrast. It is stated that the transition through a contact with positive (negative) contrast occurs with fracture arresting (acceleration), whose intensity is controlled by a dimensionless parameter derived from theoretical considerations and numerical results

A previously developed technique is used to solve problems of strength and stability of discretely reinforced noncircular cylindrical shells made of a composite material with allowance for the moments and nonlinearity of their subcritical stress-strain state. Stability of a reinforced bay of the aircraft fuselage made of a composite material under combined loading with bending and twisting moments is studied. The effects of straining nonlinearity, stiffness of longitudinal ribs, and shell thickness on the critical loads that induce shell buckling are analyzed.

A quasi-one-dimensional nonstationary model for the waterproofing of main cracks using Herschel-Bulkley viscoplastic fluid is presented. The mathematical model developed in a one-dimensional isothermal approximation with the hydrodynamic parameters (pressure and velocity) averaged over the cross section of the crack can be used to determine the optimal technological parameters of the waterproofing process and the size of gel barriers to ensure their stability on exposure to an intense filtration flow after crack waterproofing. The ranges of flow rates which provide waterproofing of a crack of fixed width for the selected gel are determined. The stability of the established gel barriers is estimated.

This paper considers the dynamic problem of a semi-infinite crack in an elastic space that suddenly begins to grow with a constant speed. At the initial time, the crack faces at some distance from its tip are subjected to normal tensile concentrated forces which then move along the crack faces at a speed different from the speed of the crack tip. The stress intensity factor is calculated. Various special cases are examined.

Minimax criterion is used to carry out the theoretical analysis of normal displacement of points at the boundary of a circular disk weakened by arbitrarily placed rectilinear cracks. This paper presents a criterion and method for solving the problem of fracture of the circular disk with mixed conditions on its boundary. A closed system of algebraic equations is constructed, which allows for minimization of stress intensity factors. The normal displacement of points at the boundary of the circular disk, for which the bearing capacity of the disk increases.