Monolithic concrete lining is the most popular shaft lining because it is able to endure the rock pressure effects and to exclude large deformations of shaft walls. In the case of starting the reverse ventilation mode in the winter season, a significant negative temperature difference may occur between the warm shaft walls and the cold air from the surface. That temperature difference may have adverse impacts on concrete lining, causing high tensile stresses in it. In this paper, the stress-strain state of the concrete lining and rock mass surrounding the mine shaft is investigated to evaluate the strength of the lining during the reverse ventilation mode in the winter season. The object of the study is the ventilation shaft with surrounding concrete lining and rock mass. Solid and concrete are considered to be isotropic and homogeneous, and their thermodynamic properties are independent of temperature. This allows considering a two-dimensional problem. It is assumed that the temperature drop in lining and rock mass is the only significant factor affecting the stress-strain state of the system. When calculating the temperature of the lining and rock mass, the conductive heat transfer in the volume of rocks and lining, the heat exchange of the lining and rocks with atmospheric air and the heat exchange of the lining with the mine air are taken into account. The presence of moisture in rock mass is not considered. Based on the results of numerical simulation, the following was established. The concrete lining mostly undergoes tensile stresses; the maximum tensile stress acts in a vertical direction. The width of the pre-fracture zone of the lining nonlinearly depends on the duration of the reverse ventilation mode. With an increase in the air temperature in the shaft, the width of the pre-failure zone of the lining decreases, and the permissible duration of the reverse mode significantly increases.

The use of science-based technologies in commercial production makes it possible to obtain high-quality, competitive finished products. The development of new techniques or optimization of existing technological processes involving the in-depth experimental research requires large time and material costs. In this regard, numerical simulation of the technological process under study can be used as an alternative to a physical experiment. The results obtained by numerical methods will make it possible to substantiate the most appropriate regime of billet deformation, providing the required changes in the structure of the material. This paper considers a specific technological process of hot forming of massive billet consisting of two stages: air cooling of the billet while transporting it from the furnace to deforming tools and forming operation - free upsetting of a billet with the aid of a moving upper flat plate and a stationary cutting lower plate. Computer simulation of upsetting of a large billet with the aim to define a change in its shape, temperature distribution over the surface and throughout the billet, and deformation inhomogeneity arising in the process of got forming was carried out using the Deform-2D/3D software package. The initial temperature distribution of material during pressure forming is determined by modeling air cooling of the billet for 45 seconds during its transportation from the furnace to the deforming equipment. For the obtained inhomogeneous temperature distribution, the calculations were performed to evaluate the force required for billet upsetting to the technology specified average diameter of about 1060 mm at the velocity of the die movement of 100 mm/s. Thee Johnson-Mehl-Avrami-Kolmogorov (JMAK) model was used to investigate the evolution of the microstructure (average grain size and recrystallized volume fraction) of the Waspalloy nickel alloy generated as a result of dynamic recrystallization in the process of hot forming of a billet at the strain rate of 100 mm/s.

In this paper, we consider the problem of the stability of an isothermal system of two miscible fluids in a gravity field. Fluids are aqueous solutions of non-reacting substances with different diffusion coefficients. At the very beginning, the solutions uniformly fill half-spaces, which are separated from each other by an infinitely thin horizontal contact surface. Such a configuration can be easily realized experimentally, although it is more difficult for theoretical analysis. We assume that the initial configuration of the system is statically stable. After the start of evolution, the solutions begin to mix, penetrating each other, and creating conditions for the development of the convective instability of double diffusion. An important complicating factor of the problem is the functional dependence of the diffusion coefficients of solutions on their concentration. In recent years, this effect has been actively studied, since its significant influence on convective stability has been proven experimentally. For simplicity, we assume that the diffusion coefficients of solutions depend linearly on concentration. The problem of the stability of a mixture includes the equation of motion in the Darcy and Boussinesq approximation, the continuity equation, and two transport equations for the concentrations. The solution to this problem in the absence of the effect of concentration-dependent diffusion is well known from the literature. If we take into accountsuch a dependence, then we have to deal with the problem of nonlinear diffusion, which can only be solved numerically. To find an analytical solution to the problem, we propose to apply the method of preliminary linearization of Wiedeburg (1890). The method is well known in the theory of thermal conductivity, although it was originally developed specifically for solutions of substances. In our case, we demonstrate that the conditions for convective stability of the base state can be obtained analytically. The comparative analysis of the discrepancy between the Wiedeburg solution and the numerical solution is given. Based on the closed-form analytical solution, we obtain a stability map for the problem under the consideration. We show how the effect of concentration-dependent diffusion affects stability.

Chemoconvective structures in a system of two reacting miscible liquids placed in a cylindrical Hele-Shaw cell that uniformly rotates around the axis of symmetry are studied. Previously, the behavior of similar system has been studied by the authors experimentally and theoretically under the static gravity field. A radially directed inertial field created by the centrifugal force varies in space (along the radius) and can be tuned by the rotation frequency, which gives the system new degrees of freedom. The initial configuration of the system consists of two concentric layers of aqueous solutions, initially separated in space by an infinitely thin diffusion zone. Solutions of acid and base are located respectively closer to the axis of rotation and at the periphery of the cell. The concentrations of reactants are selected in such a way as to guarantee the initial stability of the system with respect to Rayleigh-Taylor disturbances. After bringing fluids into contact, a neutralization reaction begins, which is accompanied by the production of salt. An important role is played by a concentration-dependent diffusion effect, which results in a nonlinear form of the corresponding transfer equations already for the base state characterized by the reaction-diffusion processes. As in the case of static gravity, there exists a density potential well near the reaction front, which determines the nonlinear dynamics of the system. A system of nonlinear equations describing the fluid motion is obtained. The results of numerical simulation of a complete nonlinear problem are presented. We show that cellular convection develops in the potential well at a certain ratio of the initial concentrations and the values of the centrifugal Rayleigh numbers. With an increase in the rotation speed, the periodicity of the structure is violated more and more due to the influence of the DLC instability, which arises near the axis of rotation, and the action of the inertial field, which ejects some cells from the potential well.

Data-driven simulation is a promising approach to the development of heuristic models of complex physical systems. Within this approach, an artificial neural network is trained to directly predict the dynamics of a hydrodynamic model. In this study the data-driven approach is successfully used to approximate saturations of every grid cell for a chosen timestep in a two-phase flow in a porous media setting. The uncertainties that inevitably arise in many specific tasks of the oil and gas industry make research of such heuristic methods highly relevant. In a computational experiment a deep convolutional neural net work is trained with the use of the adversarial training technique. The original architecture and training procedure are used for the training, including a non-trivial sequence of weight updating for the two encoder networks and one decoder/generator. Also, following the methodology of adversarial training, a discriminator network is used, the objective function for which is set to contradict the objective functions of the main training loop. The results of the experiment have proven the ability of the proposed architecture to successfully generalize patterns learned from a set of training data. The developed heuristic model obtains results that are comparable to the reference of traditional numerical simulation for the test initial conditions. The heuristic model exceeds the speed of traditional solvers by 2-3 orders of magnitude. The satisfactory accuracy of the heuristic model makes it applicable to the tasks of synthetic reservoir modelling.

A refined model of viscoelastic-plastic deformation of flexible plates with spatial reinforcement structures has been developed. Strains of the composition materials are assumed to be small and decomposed into plastic and viscoelastic components. Instant plastic deformation of these materials is described by the flow theory with isotropic hardening. Viscoelastic deformation obeys the equations of a linear model of a five-constant body. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The possible weak resistance of composite plates to lateral shear is modeled in the framework of a refined theory of bending. This allows one to determine the displacements of plate points and the stress-strain state in the components of the composition with varying degrees of accuracy. In a first approximation, from the obtained equations and boundary conditions, we obtain relations corresponding to the traditional nonclassical Reddy theory. A numerical solution to the formulated initial-boundary-value problem is sought according to an explicit “cross-type” scheme The viscoelastic-plastic dynamic deformation of rectangular, relatively thin fiberglass plates under the influence of an explosive type load is investigated. The plates have a traditional plane-cross (orthogonal) or spatial reinforcement structure. It is shown that even in the case of relatively thin composite plates the Reddy theory is unacceptable for adequate calculations of their dynamic viscoelastic-plastic deformation. It has been demonstrated that the magnitude and shape of the residual deflections depend not only on the reinforcement structure, but also on the magnitude of the viscoelastic characteristics of the materials of the composition components. It was found that, after dynamic inelastic deformation, the composite plate can have a corrugated residual shape with folds oriented in the longitudinal direction. It is shown that even in the case of a relatively thin plate, replacing the planar-cross reinforcement structure with a spatial structure can significantly reduce the amount of residual deflection and the intensity of residual deformation in the binder material and some fiber families. For relatively thick plates, the effect of such a replacement of the reinforcing structures manifests itself much more.

Practical experience shows that the physical and mechanical properties of the ice cover are unreliable and can strongly depend on various external factors (the presence of snow and wind at the time of freezing, the ambient temperature), if it is reinforced by traditional methods. In this connection, the problem of increasing the bearing capacity of ice by alternative methods, e.g. by introducing reinforcing elements into the ice, is an urgent problem today. The aim of this work is to determine the effect of various reinforcing materials on the carrying capacity of the ice cover. First, a comparison was made between the results of experimental and numerical studies obtained for the maximum deflections and the carrying capacity of ice samples strengthened with steel reinforcement according to the proposed scheme. Secondly, numerical investigation of the strength of ice upon reinforcement with various composite materials was performed. Experiments on strengthening ice samples with A400 steel reinforcement were carried out on a setup specially designed for simulating pure bending conditions. The destruction of the ice cover occurs under the action of pure bending when the vehicle is moving along it. In numerical experiments, the samples were reinforced with surface reinforcing frames with different physical and mechanical properties. Numerical calculations of the stress-strain characteristics of the ice cover were performed in terms of the physically nonlinear deformation model using the FE software package. The paper gives a qualitative and quantitative assessment of the effectiveness of the use of various composite materials as reinforcing elements. It is shown that the application of reinforcing materials to strengthen the ice cover significantly increases its bearing capacity.

The problem of heat transfer intensification using non-homogeneous boundary conditions is of great interest. This paper presents a study of the influence of non-homogeneous, non-periodic distribution of heating on the flow structure and convective heat flux for developed turbulent regimes (Ra = 1,1·109). A numerical simulation of convective turbulence was performed for non-homogeneous heating distribution at the lower boundary in the cubic cavity using open software OpenFoam 4.1. Calculations were carried out for three types of temperature distribution: localized heating at the center of the lower boundary, nine heaters of the same size, equidistant from each other, and fractal heating. All three heating distributions have the same area. The results of numerical simulation showed that in all three cases of non-homogeneous heating distribution in the cavity a large-scale circulation is formed, the dynamics and structure of which depend on the temperature distribution at the lower boundary. Spontaneous reorientations of the large-scale circulation plane by angle ±45° and ±90° were revealed. A comparison of the intensity of heat flux through the layer at a fixed temperature difference at horizontal boundaries was made. It is shown that the intensity of heat transfer weakly depends on the temperature distribution at the lower boundary. The maximum difference in the Nusselt number for three types of a non-uniform heating distribution does not exceed 5%. Comparison of the results of numerical simulation with a uniform and non-uniform temperature distribution for Ra = 1,1·109showed that a decrease in the heating area by 70% leads to a decrease in the Nusselt number by 10%. It is shown that the heat flux decreases with decreasing heating area, at fixed temperatures in the heating and cooling areas, not proportionally to the change in area. For practical applications, an important role is played by the stability of the heat flow, which is characterized by the absence of pulsations. It is shown that the use of fractal heating can significantly reduce the level of heat flux pulsations, without losing heat transfer efficiency

This paper deals with the problems of stability of circular arches supported by inextensible threads that cannot withstand compressive forces. Both ends of the thread are attached to the axis of the arch so that the distance between the attachment points cannot increase during deformation. The problems of stability and supercritical behavior of elastic systems in the presence of unilateral restrictions on the movement lead to the need to study the bifurcation points of the equations or to find the parameters for which some variational problem with restrictions on the desired functions in the form of inequalities has a non-unique solution. In the numerical study, this problem is reduced to finding and studying the bifurcation points of solutions to a nonlinear programming problem. The problem of finding bifurcation points for solutions of nonlinear programming problems is reduced to the problem of identification of conditional positive definiteness of quadratic forms on cones. There are criteria of conditional positive definiteness of quadratic forms on cones in the important special case, when the cone is a positive orthant in Euclidean space. Their application poses the necessity to calculate a large number of determinants, which is computationally extremely inefficient, although in the case of a small number of variables, they offer promise for solving Lyapunov stability problems. The paper proposes and justifies the method of searching for options to solve the problem of nonconvex quadratic programming that arises during the study of the stability of elastic unilateral restrictions on the movement. The results can be used in the design of arches and arch systems to improve their bearing capacity.

A variational formulation of the boundary value problem on the motion of a viscous incompressible fluid with a free surface and changing dynamic boundary angles is proposed. The mathematical description of the process is based on the equations of motion, continuity and natural boundary conditions on the free surface. The traditional feature of the mathematical model on the three-phase contact lines (LTPC) is eliminated by the slip condition. The boundary angle on the LTPC is included in the variational formulation of the problem by replacing the curvature of the free boundary by the Laplace - Beltrami operator and using integration in parts. To describe the dynamic conditions on the LTPC, linking the speed of the LTPC and the dynamic edge angles on the solid walls of the cylinders, the empirical Jiang ratio is used. The numerical solution of the problem is based on the mixed finite element method with approximation of the main variables of the problem (velocity and pressure vector) satisfying the compatibility condition (LBB - condition). In addition, we use a singular finite element and a discontinuous approximation for the pressure to reduce the pressure oscillations in the vicinity of the LTPC. The numerical implementation of the kinematic condition of the free surface motion is performed according to the predictor-corrector scheme. The algorithm is tested on the problems with an analytical solution. Numerical studies of the flow kinematics and the free surface behavior when filling the coaxial gap in terms of the determining parameters of the Reynolds numbers (Re) in the range from 0 to 5, Stokes (W) in the range from 0 to 300 and capillary number (Ca) in the range from 0.0001 to 10 are carried out. The influence of the main parameters of the problem and dynamic conditions on LTPC on the evolution and maximum deflection of the free boundary is shown. For slow filling conditions, gravitational and capillary forces have the greatest influence on the kinematic characteristics of the filling. In this case, the dominant influence on the evolution of the free surface of the capillary forces begins with the values of the capillary numbers less than CA < 0,1. Increasing the flow rate (Re > 1) leads to a significant increase in the deflection of the free surface.