Vol 62, No 4 (2017)

The problem on the emission of dust particles from a spherical dimple on a flat horizontal wall with a turbulent stream of a viscous incompressible fluid flowing around it is investigated numerically. With the help of a passive element of control, three various schemes of internal steady flows are reproduced for a dimple with the relative depth h = 0.25, which testifies to the nonuniqueness of the scheme of 3D flow around deep dimples. It is shown that the process of carrying out inertial particles into an external stream depends substantially on the type of internal flow of the scheme implemented in the dimple.

The temporal evolution of the three-dimensional pattern of perturbations superposed on a radialrotational spread or sink of a viscous layer the parameters of which depend on the radial coordinate and time has been studied. The motion of the layer boundaries is specified both in the main motion and in the perturbed motion. Based on the integral relations method applied to the linearized problem in perturbations, sufficient estimates of exponential stability (in particular, on a finite time interval) of the main motion have been derived.

The stability of motion of Maxwell’s pendulum is investigated in a uniform gravity field. By means of several canonic transforms of the equations of pendulum motion and the method of the surfaces of Poincaré sections, the problem is reduced to investigation of the immobile-point stability retaining the area of mapping of the plane into itself. In the space of dimensionless parameters, the stability and instability regions are singled out.

The effect of the diameter of shells of structural steel 45Cr on the parameters of the cumulative numerical distribution of fragments by mass and the cumulative mass distribution of fragments by length has been studied. It is found that the statistical fragment distributions by mass for shells of different diameters are described well by exponential relation, whereas the cumulative mass distributions of fragments by length are described by power functions. The exponents in these relations depend on the shell diameter. Plotting the cumulative mass distribution of fragments by length allows one to relate the mechanisms of dynamic fracture with fragmentation regimes, which differ in the parameters of the power relation characterizing the formation of fragments of the basic spectrum.

An approach to viscous friction is described as nonlocal momentum exchange between different layers of a fluid. The Navier−Stokes equations are replaced by pseudo-differential equations hyperbolic in time. In this case, instead of zero velocity on the boundary, a nonlocal nonlinear boundary condition is set in the form of the velocity dependence of the coefficient before the intensity of the momentum exchange with the boundary. The non-newtonian character of the viscosity of water is shown in experiments with thin insulin needles and explained by the nonlinear character of the momentum exchange of water with the boundary. The calculations agree very well both with our experiments and with the experiments of other authors. Calculations show that the flow decreases more than one-and-a-half times in comparison with the Poiseuille flow for channels with a diameter of 360−390 μm, which is confirmed in experiments.

An analytical solution of the problem on oscillations of ice cover with a rectilinear crack under the action of a local time-periodic load has been obtained. For plates with equal thicknesses, the solution has been obtained in explicit form. It has been found that the contact of plates with different thicknesses is accompanied by the appearance of directions of predominant wave propagation at an angle to the crack in the far field. In the case of a contact of identical plates with free edges and free overlapping, the waveguide mode is excited. The waveguide mode manifests itself especially strongly when the plate has contact with a hard vertical wall.

A simple coarse-grained model of a crystal of normal paraffin (the united-atom model) is considered. By using an original semi-inverse method, it is shown that, alongside with known polymorphic transitions, the model under consideration assumes a dynamic transition, which manifests itself in the localization of vibration energy at a certain threshold value of excitation energy. The prediction of the conditions of this transition requires analytical determination of the spectrum of nonlinear normal modes with arbitrary amplitudes of vibrations because the instability of the mode with the lowest wavenumber is a necessary energy localization condition. The equations obtained make it possible to investigate the resonance interaction between the nonlinear normal modes near the low-frequency edge of the spectrum resulting in capture of the vibration energy by one of the parts of the chain. The conditions of localization of the vibration energy revealed determine the necessary initial data for computer modeling of the predicted dynamic transition in normal paraffins.

The novelty of the results is that the SIBB mode has been implemented without water degassing and without maintaining the surface temperature of the heater constant. The results are of great interest for new medical technologies involving laser destruction of pathological tissues.

Using a test bench the main part of which is a vortex combustion chamber, characteristics describing the initiation of burning of solitary droplets of a typical organic coal–water fuel (OCWF) are established. The oxidizer temperature varied in the range of 600–850 K. The linear motion velocity of the oxidizer in the vortex chamber was about 3 m/s. The configuration of the chamber and parameters of the air flow provided a stable regime of floating for droplets with a size (radius) of about 0.5 mm. The analysis results show that the intensity of initiation of OCWF combustion under conditions of processes occurring in boiler furnaces is significantly (by a factor of 2–4) higher than for droplets that are immovably fixed or freely float in the heated air flow.