Mathematical modelling of a laminar suspension flow in the flat inclined channel

The laminar flow of a suspension consisting of viscous incompressible fluid with solid spherical particles of the same size in a flat inclined channel is investigated in this work. The mathematical model is formulated in a one-fluid approximation in a three-dimensional statement and solved in the OpenFOAM software package. The results of mathematical modeling are compared with experimental data. The study of the dynamics of the distribution of solid spherical particles in the flow and sedimentation along the length of the channel depending on the size of particles and the angle of inclination of the channel relative to the horizon is carried out.

Procedure of the updated calculations of disks of aero – engines with removable blades a finite element method in three – dimensional statement in the environment of Femap/Nastran

Problematic. At adaptation of a design of discs of rotor of air gas-turbine drives (GTD) it is necessary to conduct, in particular, strength calculations for what to create the computer models corresponding to stated designs (delineations) and operation conditions. If creation of a geometrical part of model does not call special difficulties the algorithm of creation of an is finite-element grid models for carrying out of calculations of performances of the disc stress-strain conditions (SSC) with blades can be modified taking into account development of programs for calculate. Research objective. To offer the algorithms allowing with the set exactitude to calculate performance of the SSC of discs with blades on personal computers, and also to represent outcomes in the form of schedules of type "surface". Realization technique. On an example of the disc of 2nd stage of the compressor of GTD the algorithm of construction of a three-dimensional is finite-element grid of the disc of GTD from the separate blocks which have been "pasted together" in a unified grid has been created. Numerical calculations (a contact problem of thermoelasticity, isotropic materials) are carried out. For preparation of construction of schedules of type "surface" the interface program of transformation of the table of columns in the two-dimensional table is created. The results of research. Are created and explicitly techniques of reaching of research objectives are described. Conclusions. The created techniques allow to carry out on the limited computer powers exact enough control calculations of discs with blades in three-dimensional statement, to conduct visualisation of distribution of stresses and contact forces of a zone of a contact "disc-blades" in the form of schedules of type "surface".

Free convective of a linear heterogeneous liquid in a square cavity at side heating

In this work the problem of free convection of the Newtonian poorly stratified liquid in the cell warmed up from left and cooled from right with the heat-insulated horizontal boarders is presented. Liquid with small concentration of salt and initial linear stratification on cell height is considered. The model of double diffusion in a Boussinesq approximation is applied to model the process. The problem is solved both in two - and three-dimensional statement by means of a control volume method and a SIMPLE algorithm. It is shown that vortex structures at the layered mode of convection have quasi-two-dimensional character.

INTERFERENCE OF CLOSABLE CRACKS AND NARROW SLITS IN AN ELASTIC PLATE UNDER BENDING

The problem of bending of an infinite plate containing an array of trough closable cracks and narrow slits is considered in a two-dimensional statement. A crack is treated as a mathematical cut, the edges of which are able to contact along the line on the plate outside. A slit is referred to as a cut with contact stress-free surfaces and the negative jump of normal displacement can occur on this cut. The crack closure caused by bending deformation was studied based on the classical hypothesis of direct normal and previously developed model of the contact of edges along the line. A new boundary problem for a couple of biharmonic equations of plane stress and plate bending with interconnected boundary conditions in the form of inequalities on the cuts is formulated. The method of singular integral equations was applied in order to develop approximate analytical and numerical solutions to the problem. The forces and moments intensity factors near the peaks of defects and contact reaction on the closed edges of the cracks are calculated. A detailed analysis was carried out for parallel rectilinear crack and slit, depending on their relative location. Presented results demonstrate qualitative differences in the stress concentration near the defects of different nature.

FINITE ELEMENT CALCULATION OF THE RIVET JOINT OBTAINED BY NITROGEN COOLING OF THE RIVET

A method for creating a rivet connection using nitrogen cooling of rivets is considered. A rivet, cooled to a temperature of -196 C, is placed in a cylindrical hole in the plates at room temperature. When heated to room temperature, the rivet undergoes a thermal all-round expansion and creates a tight fit. The finite element method solves the contact termal-stress problem for such a connection in the COMSOL MULTIPHYSICS and APM Winmachine software complexes. The problem is solved in a three-dimensional statement. The first stage is the temperature distribution in the rivet-plate system. The resulting temperature field is used as a parameter at the second stage when solving the stress problem. The fields of residual stresses in the plate and rivet are obtained. It is shown that plastic deformations occur in a small part of one of the connected plates. Recommendations for calculating the strength of such compounds are given.

APPLICATION OF A HARDWARE RASTERIZER IN PROBLEMS OF MODELING HYDRODYNAMIC FIELDS IN TRAWL SYSTEMS DURING HYDROLOCATION

The paper proposes a fast method for rebuilding a three-dimensional computational grid for problems of modeling hydrodynamic fields in trawling systems during sound ranging at runtime using a hardware rasterizer of a graphics processor. When the position of a streamlined object changes, it is necessary to periodically update the boundary conditions at the grid nodes near its surface, which, in case of three-dimensional statement, is a laborious task. The suggested method allows a multiple acceleration of the grid update process compared to software implementations. The essence of the method lies in implementation of the pixel shader of the graphics pipeline during rendering, namely, the possibility of outputting the grid nodes into a 3D buffer taking into account information about Z-coordinate of a pixel and a velocity vector of a surface point. The method has been approved using a computer program developed on its basis. The method can be applied both in calculating the influence of hydrodynamic fields on propagation of acoustic waves, and in other applications.

Thickness dimensions of the contact layer of soil-rigid body interaction

Solution of the problems of longitudinal interaction of underground pipelines with soil in a one-dimensional statement requires precise measurements of the thickness of the soil layer contacting with the pipeline. In order to determine the dimensions of the contact layer of soil, the behavior of soil medium under shear interaction of a rigid body with soil is studied. Under straining in soil medium, structural changes denoted by the coefficient of structural destruction are taken into account; the condition of complete adhesion is taken in the contact rigid body – soil boundary. The interaction process under consideration is investigated numerically by the finite difference method. The results of the calculations are presented in the form of graphs and are analyzed. From the obtained results, the maximum values of the thickness of soil contact layer are determined as well as the layers with the corresponding degree of structural destruction depending on the geometric dimensions of the rigid body.

Investigation of the interaction of two parallel shifted cracks in plate bending adjusted for their closure

The problem of interaction of two parallel shifted cracks in plate bending is considered. The cracks closure has been investigated in the classical two-dimensional statement, using the model of smooth contact along a line. The influence of the relative position of cracks and of the contact of their edges on the forces and moment intensity factors has been studied by the singular integral equations method.