Bulletin of Dnipropetrovsk University. Series: Mechanics

9-14

Authors: E. A. Makarenkov, A. V. Siasiev

To consider different elements of constructions, which are used in mechanical engineering, the attention can be paid to the fact that components, in the form of a thick-walled hollow cylinder, which cross-section is a doubly connected area, are used in these elements. The high-temperature speed gas or liquid flow, passing through the inner cavity, creates uneven heating, defined both by conditions of the flow and feature of design. The research arising through this complex thermostressed state is important in the design of mechanical engineering things. Taking into account the fact that we often have to deal with short-term impact of high temperatures, it is important to study unsteady temperature fields to determine their greatest unevenness. The latter thing can give rise to the thermostressed state, leading to disturbance of the operating mode. The proposed paper deals with the task of spreading the heat in the circular cylinder with defined radius and height with the specified starting temperature. The bases of the cylinder are heat-insulated, and along the generatrix is forced heat exchange with the environment. A mathematical statement of the internal problem that satisfies the heterogeneous equation of thermal conduction and homogeneous mixed condition on the generatrix of the cylinder is given. The solution of the problem is carried out by factorization using finite integral transforms of the mixed problem of mathematical physics to the cylinder.

21-28

Authors: T. I. Rusakova, N. N. Belyaev

A numerical model was made for research ventilation underground workings. This model takes into account the most important factors when computing calculations, form underground workings, a rock formation, regime of ventilation, the process of gravitational subsidence pollution. The numerical model is based on solving the multi-dimensional equations of aerodynamics and the equation of convection-diffusion transport of pollutants. Numerical integration of modeling equations is performed using the method of Libman and implicit difference schemes. Realization of difference methods is carried out on an explicit scheme. Numerical modeling is performed on a rectangular grid using the method of marking the computational domain. Program package developed on the basis the numerical model. This allows projections data on distribution of impurity concentration for several seconds. The results of the practical application of the developed numerical model to assess the effectiveness of ventilation excavation for the given parameters of ventilation. The values of the methane concentration is calculated on study area. A comparative analysis of changes in the concentration of this pollutant over time was conducted. Calculations made using the developed numerical model can serve as a practical tool for conducting a series of engineering research to evaluate and maintain the established safety practices parameters of mine atmosphere.

36-42

Authors: N. N. Belyaev, V. I. Nochvay, A. V. Berlov

A numeral model allowing operatively to expect the dynamics of contamination of atmospheric air and risk of toxic defeat of people at an emergency on chemically is worked out dangerous object, attended with the troop landing chemically hazardous substance. To calculate the dispersion of hazardous substances in the ambient air is applied two-dimensional transport equation impurities. The equation takes into account the wind speed and direction, atmospheric diffusion, the intensity of emission of hazardous substances, emission time. For the numerical simulations of impurity transport in the atmosphere is used implicit difference scheme. On the basis of the numerical model is used to compute an experiment to assess the level of air pollution on a scale «county» in the emergency storage of solid rocket propellant on the Pavlograd chemical plant. Model a situation of air pollution in the HCl emission during combustion of solid rocket propellant. Calculated dynamics of air pollution for the two regions of Dnipropetrovsk region.

53-59

Authors: V. Katan

The problem of a disk and an incompressible fluid interaction at different values of the Froude number is examined. The boundary integral equation method (the BIE method) is used to solve tasks. Fredholm boundary integral equation of second kind for low Froude numbers is taken and transformed to clear analytical form consists of integrals obtained from complete elliptic integrals. The analytical solution of the problem of the impact drive at low Froude numbers is represented. Values of the potentials, normal and tangential velocities for the other limit case of impact for high Froude numbers are calculated by known formula. The graph of changes in potentials, normal and tangential velocity on the disk surface and on the free surface are illustrated. The dimensionless coefficient of the associated mass for low Froude numbers is presented. The solution can be used for the debugging programs of numerical calculation of the fluid movement with a free surface as a test.

70-78

Authors: N. N. Belyaev, V. A. Kozachina

In this paper we consider the construction of a numerical model to evaluate the effectiveness of horizontal settler modified structure. The model is based on equations of motion of an ideal fluid and mass transfer equation. The model takes into account the geometric shape of the horizontal settler, the possibility of placing plates having a complex geometric shape, gravitational settling of flocs, unsteady water flow velocity field in the settler and turbulent diffusion. For the numerical solution of modeling equations difference schemes are used. For numerical integration of the equation of mass transfer implicit triangular difference schemes are used. Numerical integration of the equation for the flow function is performed by using A.A. Samarsky implicit difference method. For the numerical integration of the vorticity transport equation is used implicit difference scheme. All difference schemes used to construct a numerical model allow to find the desired value using the formula of the running count, which allows a simple programmed realization of difference equations. The numerical calculation carried out on a rectangular difference grid. For the formation of the computational domain markers are used. The results of a computational experiment are presented.

86-95

Authors: A. A. Grinevich

Exact analytical approach for plane stain investigation of piezoelectric/piezomagnetic bimaterial with an electroded and magnetically permeable electrically conducting crack located at the interface between its components is proposed. It is assumed that a normal and shear stresses field, the electric and magnetic fields paralleled to the crack are given at infinity. First, an open crack is considered, and then it is assumed that the crack faces may be contacted at a certain section of unknown length, which is adjacent to one of the crack tip. For the model of open crack Hilbert problem has been derived. Its exact solution has been obtained in closed form. In the case where the crack faces with frictionless contact conditions the combined Dirichlet-Riemann boundary value problem and Hilbert problem have been formulated for which exact analytical solutions have been written out. For both cases a numerical illustration of the obtained solutions were done for different values of the electric field at infinity. It is proved that the magnetic field does not affect on the crack electromechanical characteristics, and the dependence of these parameters on the mechanical load and electric field were investigated.