Vol 52, No 2 (2017)

The problem of electrohydrodynamic flow of a viscous, low-conducting, polarizable liquid inside and outside a spherical drop in an applied homogeneous constant electric field is analytically solved with account for the effect of both surface conduction current and surface convection current. The influence of the drop deformation on the field and the flow is neglected. The solution is obtained in the form of asymptotic expansions in a small parameter corresponding to weak surface convection electric currents.

The hydrodynamic equations of a viscous incompressible fluid are modified for axisymmetric flows in a pipe of time-varying radius. A new exact time-dependent solution of these equations which generalizes the well-known classic steady-state Hagen–Poiseuille solution for flow in a pipe of constant radius (independent of time) is obtained. It is shown that the law of time variation in the pipe radius can be determined from the condition of the minimum work done to pump a given fluid volume through such a pipe during the radius variation cycle period. A generalization of the optimal branching pipeline in which, instead of the Poiseuille law, its modification based on the use of the exact solution corresponding to the time-dependent M-shaped regime is employed is suggested. It is shown that the hydraulic resistance can be reduced over a certain range of the parameters of the time-dependent flow regime as compared with the steady-state pipe flow regime. The conclusion obtained can be used for the development of the hydrodynamic basis for simulating the optimal hydrodynamic blood flow regime.

The analytic solution of the problem of vibrations of an ice sheet with a rectilinear crack floating on the surface of an ideal incompressible fluid of shallow depth under the action of a local zone of the time-periodic pressure is obtained. The ice sheet is simulated by two thin viscoelastic semiinfinite plates of different thickness. Various conditions on the crack edges are considered. Far field asymptotics are investigated and it is revealed that the predominant directions of wave propagation at an angle to the crack can be distinguished in the far field in the case of contact of two plates of different thickness. In the case of contact of identical plates, a waveguide mode propagating along the crack is excited. It is shown that the waveguide mode is the same for the plates with the free edges and the free overlap since the part of the solution symmetric about the crack is the same while the difference between the solutions is caused by the antisymmetric part of the solution.

The results of a comprehensive investigation including numerical calculations and experiments with models in a wind tunnel and a vehicle under flight conditions aiming to find the ways of reducing the pressure fluctuation levels in an extended cavity at subsonic and transonic freestream velocities are presented. It is shown that the reduction of these loads can be achieved using the means which have demonstrated their effectiveness for cavities with the open-type flows, for example, a permeable deflector and the bevelling of the rear wall but only in the case of a given combination of their geometric parameters. The mechanisms of the action of these devices on the flow, thanks to which the intensity of the wave disturbances generated by the rear wall is reduced, the instability wave growth in the mixing layer behind the deflector is limited, and the fluctuation level in the cavity decreases, are investigated. The results of numerical investigations of the flow in a cavity with a permeable deflector are apparently among the first.

Two versions of the structure of a multi-discharge plasma actuator intended to excite boundary layer perturbations in the neighborhood of the leading swept-wing edge are suggested. The actuator must prevent from appearance and development of the crossflow instability modes leading to laminarturbulent transition under the normal conditions. In the case of flow past a swept wing, excitation of controllable perturbations by the plasma actuator is simulated numerically in the steady-state approximation under the typical conditions of cruising flight of a subsonic aircraft. The local body force and thermal impact on the boundary layer flow which is periodic along the leading wing edge is considered. The calculations are carried out for the physical impact parameters realizable in the near-surface dielectric barrier discharge.

The flow structure of a bubbly impinging jet in the presence of heat transfer between the two-phase flow and the surface is numerically investigated on the basis of the Eulerian approach. The model uses the system of Reynolds-averaged Navier–Stokes equations in the axisymmetric approximation written with account for the inverse effect of the bubbles on the average and fluctuating flow parameters. The influence of the gas volumetric flow rate ratio and the dimensions of the bubbles on the flow structure in a gas-liquid impinging jet is studied, In the presence of gas bubbles the liquid velocity is higher than the corresponding value in the single-phase flow. A considerable, more than twofold, anisotropy between the axial and radial turbulent fluctuations in the gas-liquid impinging jet is shown to exist. An addition of air bubbles leads to a considerable growth in the liquid velocity fluctuations in the two-phase flow (up to 50% compared with the single-fluid liquid impinging jet). An increase in the disperse phase dimensions leads to intensification of turbulence of the liquid.

Macrophotography and high-speed videofilming are used to investigate the material transfer in a falling drop upon collision with the surface of a fluid at rest. In the experiments the drops of colored water, milk, mineral oil, and seed oil fell in pure or colored water. Emphasis was placed on recording the pattern of the drop material spreading over the surface of the receiving fluid. On the continuous surface of the primary cavity and the crown the drop material is concentrated in the form of thin fibers which form a regular streaky or netlike pattern in which triangular, quadrangular, and pentagonal cells are expressed. The cell rows are ordered in the form of layers on the lateral walls and the bottom of the cavity. The fiber dimensions and the degree of their expressiveness vary in the process of flow evolution. The upper row of structures on the crown surface is formed by vertical fibers.

Flow past the airfoil of a civil aircraft wing is numerically modeled in the transonic buffeting regimes. The characteristics of unsteady self-oscillations of the shock on the upper surface of the airfoil are studied. To suppress them a technique of controlling the flow is proposed. It consists in blowing a jet tangent to the upper surface of the airfoil from a small-size slot nozzle. The calculations are carried out within the framework of the unsteady Reynolds equations.