Vol 57, No 3 (2016)

The problem of unsteady viscous incompressible fluid flow near a stagnation point is considered. Self-similar solutions describing plane and axisymmetric flows are constructed.

The geometry of flows during separation of pendant drops of liquids with significantly different physical properties (alcohol, water, glycerin, oil) has been studied by high-speed video recording. The dynamics of the processes involving the formation of bridges of two characteristic shapes—slightly nonuniform in thickness and with thinning of the upper and lower ends—has been investigated. It has been shown that the shape change of the separated bridge has a number of stages determined by the properties of the liquid. As a result, the bridge is transformed into a small drop—a satellite drop.

Results of an analysis of two-dimensional unsteady exhaustion of a one-velocity gas–particle medium into vacuum for limiting equilibrium cases of heat transfer between the phases are reported. Domains of existence of a one-dimensional Riemann wave and a lateral expansion wave, as well as boundaries of the flow expansion region are determined. Under thermal equilibrium conditions, the reverse flow is found to occupy a large domain extending beyond the boundaries defined by angles of expansion for an ideal gas and for a gas–particle mixture with thermally insulated phases. Exhaustion of a nonequilibrium (in terms of velocities and temperatures) two-phase medium into vacuum is numerically simulated. It is demonstrated that a barrel-shaped structure with wave expansion of the gas and a combined discontinuity in the expanding gas–particle mixture is formed.

The problem of the stability of the sand bed surface in a rectangular closed conduit with respect to spatially one-dimensional perturbations is formulated. The bed-form stability problem is solved using an analytical formula of bed load which takes into account the effect of bottom pressure on bed-load transport. An analytical dependence of the bed wavelength on hydrodynamic flow parameters and sediment particle diameter is obtained and compared with experimental data.

A 3D numerical study of convective instabilities in a horizontal liquid layer (silicone oil with a Prandtl number Pr = 102) with an upper free surface is presented. The liquid layer is subjected to an inclined gradient of temperature. The influence of both gravity and thermocapillary forces on the formation of convective patterns is studied for different values of the liquid layer depth. Numerical results are found to be in good agreement with experimental data of other authors.

The present paper deals with a flow of a viscous incompressible fluid along a heated vertical cone, with due allowance for variations of viscosity and thermal diffusivity with temperature. The fluid viscosity is assumed to be an exponential function of temperature, and the thermal diffusivity is assumed to be a linear function of temperature. The governing equations for laminar free convection of the fluid are transformed into dimensionless partial differential equations, which are solved by a finite difference method with the Crank–Nicolson implicit scheme. Dependences of the flow parameters on the fluid viscosity and thermal conductivity are obtained.

The paper describes the processes of elastic deformation of thin films under mechanical loading. The film is modeled longitudinally by a compressed plate arranged on an elastic foundation. A computer model of the buckling of the narrow thin plate with a delamination portion located on an elastic foundation is constructed. This paper also touches upon the supercritical behavior of the plate–substrate system. The experiments on the axial compression of a metal strip adhered to a rubber plate are performed, and 2 to 7 buckling modes are obtained therein. The critical loads and buckling modes obtained in the numerical calculations are compared with the experimental data. It is shown that there is the possibility of progressive delamination of the metal plate from the foundation if the critical load is exceeded. It is found that the use of the proposed approach, which, in contrast to other approaches, accounts for the elastic deformation of the substrate, causes the dependence between the critical bending stress and the stiffness of the foundation.

This paper describes an experimental work on a 1: 100 scaled model of a miniature sea-star tension leg platform (TLP) in a wave flume. Two different numerical models are developed: finite element model (FEM) based on the Morison equation and boundary element model (BEM) based on a 3D diffraction/radiation theory. The developed codes are used to calculate hydrodynamic forces and related coefficients. The nonlinear hull/tendon coupled dynamic equation of a mini seastar TLP is solved by using a modified Euler method (MEM). The results of numerical modeling of the motion response behavior of the platform in different degrees of freedom are compared with experimental data. This comparison shows good agreement between the results. Furthermore, this modeling reveals that the first-order diffraction method and quasi-static tendon modeling are sufficient in general for the hydrodynamic analysis of the sea-star TLP.

A mixed convection flow of a third-grade fluid near the orthogonal stagnation point on a vertical surface with slip and viscous dissipation effects is investigated. The governing partial differential equations for the third-grade fluid are converted into a system of nonlinear ordinary differential equations by using a similarity transformation. The effects of various parameters, including the Weissenberg number, third-grade parameter, local Reynolds number, Prandtl number, Eckert number, mixed convection parameter, velocity slip, and thermal slip on the velocity and temperature profiles, local skin friction coefficient, and local Nusselt number are discussed.

The natural and quasi-natural flexural-gravity oscillations of an elastic plate floating on a liquid surface have been studied numerically and analytically based on shallow-water long-wave theory. Dependences of the natural and quasi-natural frequencies on the geometrical parameters of the oscillation region have been investigated for the cases of bounded and unbounded basins. The effect of bottom irregularity in the form of a circular cylinder or a circular truncated cone on the natural and quasi-natural frequencies and functions has been examined.

This paper presents a solution of a sequence of one-dimensional boundary-value problems of thermal stresses defining the elastic–plastic deformation processes used in the shrink fitting of cylindrical bodies. The initiation and development of plastic flow in the materials of the assembly elements are studied taking into account the temperature dependence of the yield stress of these materials. During temperature equalization, the flow can slow down, followed by unloading and formation of a residual stress field providing tension. The conditions of formation and motion of the boundaries of the elastic and plastic states in plastic flow and during unloading are determined.