Vol 60, No 5 (2019)

Numerical simulation of physical processes in the electron-optical system of a DUET accelerator was carried out using the ERA-DD code. The calculations were made on adaptive quasi-structured grids developed by the authors. A mathematical model for the emission plasma surface deformable when solving the problem is proposed. In this model, the problem is considered in a two-dimensional axisymmetric approximation and the front of the electron entrance to the computational domain is represented as a set of circular arcs connected by necks. In order to increase the accuracy of the calculations, it is proposed to divide the multi-scale extended domain into two subdomains and alternately solve self-consistent problems in the subdomains using the Schwarz alternating method. The beams are simulated by the method of current tubes, and the electric field potential is calculated by the finite volume method. The obtained characteristics of the beam are compared with experimental data. It is shown that for the operating parameters of the beam source, its losses on the accelerator components are minimal and can be caused primarily by the imperfect alignment of the holes in the mask and the support grid, as well as by deviations of electron beams generated by the structures located on the periphery of the emission electrode.

The two-dimensional problem of vertical separation impact of a circular cylinder under the free surface of a heavy liquid is considered. The problem is studied in a linearized formulation corresponding to low velocities of the body and liquid and taking into account the dynamics of the points of separation of the cavitation zone. A coupled nonlinear problem is formulated, which includes a mixed boundary-value problem of potential theory with one-sided constraints on the surface of the body and an equation defining the law of motion of the cylinder. Examples demonstrating the dynamics of separation points during forced or free cylinder motions are considered. Numerical results obtained using the proposed mathematical model are compared with the results of asymptotic analysis of the initial nonlinear problem for small times.

This work deals with the creeping flow of an incompressible viscous fluid through a membrane. It is assumed that the membrane is composed of nonhomogeneous porous cylindrical particles with radially varying permeability enclosing a cavity. The flow within the nonhomogeneous porous medium is governed by the Darcy equation. The flow inside the cavity and outside the nonhomogeneous porous region is governed by the Stokes equations. An analytical solution of the problem is obtained by using the cell model technique. Exact expressions for the drag force acting on the membrane and hydrodynamic permeability of the membrane are derived. The influence of radially varying permeability on flow parameters is considered. The effects of various parameters of the problem on hydrodynamic permeability of the membrane are discussed for four models. Some previous results for hydrodynamic permeability are verified as special limiting cases.

This paper describes a cylindrical container of finite dimensions, filled with two quiescent immiscible heat-conducting liquids with a common flat interface. The side walls and bases of the vessel are solid, there are no external forces, and the contact angle of the interface with the side wall of the container is π/2. The interface has a surface tension whose strength linearly depends on temperature. When one of the container bases is heated to a critical temperature, there is movement inside the vessel. When modeling takes into account the energy spent on the interface deformation. The emerging spectral problem is solved by the modified Galerkin method. For various liquids, in the case of monotonous vibrations, the dependence of a critical Marangoni number on a container size and a temperature ratio, specified on the cylinder bases, is obtained, and a perturbed motion velocity field is constructed.

Barotropic geostrophic flows are investigated using rectangular and polar coordinate systems. It is shown that, for the analysis of geostrophic flows with radial symmetry, the use of a polar coordinate system is preferable. Relations between the hydrodynamic characteristics, including the expressions of the fluid particle velocity components and vorticity through pressure, are obtained. It is established that, in the case of stationary barotropic flows, isobaths coincide with current lines. Stationary radially symmetric geostrophic flows are considered.

A theoretical model of the development of a high-viscosity oil reservoir using the technology of paired horizontal wells is presented. The problem was solved numerically assuming that the two-well system is replaced by one hypothetical well through which simultaneous heating of the reservoir and oil recovery are performed. The heat consumption for heating the reservoir, the change in flow rate, and the mass of extracted oil for a certain period of time were analyzed for different values of the heating temperature, pressure difference, and induction period of the well. The obtained solutions can be used to determine heating conditions optimal in energy consumption.

This paper presents a three-dimensional thermo-elastic analysis of a rotating cylindrical functionally graded shell subjected to inner and outer pressures, surface shear stresses due to friction, an external torque, and a uniform temperature distribution. A power-law distribution is considered for thermal and mechanical properties of the material. The first-order shear deformation theory (FSDT) is employed to express the displacement field. The system of six constitutive differential equations of the problem includes the Euler equations for the energy functional. It is found that the material grading index has a significant effect on the stress and displacement fields.

This paper presents the theory of irreversible deformations that allows one to analyze large deformations of metals and determine the characteristics of the stress-strain state, deformation damage, and structural characteristics at various structural levels.

This paper describes energy distribution in a block medium simulated by a one-dimensional chain of masses joined by springs and dampers. Equations describing the motion of masses are solved by the methods of the theory of ordinary differential equations. The effect of the block medium parameters on energy dissipation is investigated. An approximate analytical solution is obtained that describes the total energy of a block medium at large values of time.

Within the framework of a model of a perfectly plastic body, the strength of a two-layer water shut-off baffle adjacent to the trunk of a production well in a porous medium is investigated. The baffle is formed by pumping (with subsequent hardening) synthetic resin into the porous layer through the production well. In the problem parameter space, the domains with the satisfied strength and yield conditions of the outer and inner layers of the baffle are determined.

Oscillations of a structure of a catastrophic type, comprised of a bearing and controlling surfaces are under study. It is shown that this process is self-oscillatory. Calculation results are given.

A laboratory technique for accelerating a measuring probe in a ballistic experiment was used to perform a series of experiments with high-speed video recording of the process from the start of movement of the measuring probe and electric wire in the launching device to the end of movement of the probe in the target. Advantages of the developed probing technique are discussed. The results of video recording of the dynamic gas flow in the launching device and the evolution of the electric wire shape were used to determine conditions and technical solutions that provide continuous recording of the movement parameters of the measuring probe on the flight path and in the target medium.