Vol 52, No 5 (2017)

The laws of implementation of electrostatic instability of the surface of a cylindrical volume charged jet of an ideal incompressible dielectric liquid moving relative to the ideal incompressible dielectric medium and the stability of bending-deformation capillary waves developed on the surface are investigated analytically. It is found that there are thresholds for the critical conditions of implementation of the instability with respect to the jet velocity relative to the medium (Weber number) and with respect to the electric space charge (relative to the ratio of the electrostatic pressure on the jet surface to the Laplace pressure). The critical analytic dependence between these dimensionless parameters is found.

The problem of constructing uniform asymptotics for the far fields of surface disturbances produced by a localized pulsating source in a heavy homogeneous infinite-depth fluid is considered. The wave pattern of the excited fields is the sum of waves of two types, namely, annular and wedgeshaped. The solutions obtained describe the wave disturbances far from the pulsating source both inside and outside the Kelvin wave wedges.

Arational asymptotic theory is proposed,which describes the turbulent dynamic and thermal boundary layer on a flat plate under zero pressure gradient. The fact that the flow depends on a finite number of governing parameters makes it possible to formulate algebraic closure conditions relating the turbulent shear stress and heat flux with the gradients of the averaged velocity and temperature. As a result of constructing an exact asymptotic solution of the boundary layer equations, the known laws of the wall for velocity and temperature, the velocity and temperature defect laws, and the expressions for the skin friction coefficient, Stanton number, and Reynolds analogy factor are obtained. The latter makes it possible to give two new formulations of the temperature defect law, one of which is identical to the velocity defect law and contains neither the Stanton number nor the turbulent Prandtl number, and the second formulation does not contain the skin friction coefficient. The heat transfer law is first obtained in the form of a universal functional relationship between three parameters: the Stanton number, the Reynolds number, and the molecular Prandtl number. The conclusions of the theory agree well with the known experimental data.

The problem of decomposition of methane hydrate coexisting with water in a highpermeability reservoir is considered. The asymptotic solution is obtained for the decomposition regime in the negative temperature domain. Energy estimates presented show that an impermeable layer saturated with a hydrate-icemixture can be formed in reservoirs with initial positive temperature. The mathematical model of the process of hydrate decomposition is formulated under the assumption on the presence of such a layer in a high-permeability reservoir. In this case the problem is reduced to a purely thermal problem with two unknown moving boundaries. The water-ice phase transition takes place on the leading boundary, while hydrate dissociates at negative temperatures on the slower boundary. The conditions of existence of the layer saturated with a hydrate-ice mixture which is implemented in reservoirs with the high hydrate content are investigated.

Exact solutions to the problem of steady-state axisymmetric flow of an incompressible fluid through rotating rigid body with regard to the centrifugal and Coriolis forces are constructed. The case of the locally transversally isotropic porous skeleton and the quadratic resistance force in the law of flow is considered. Estimates of the practical applicability of the solutions obtained are given. An analysis of increase in the length of the trajectory of a liquid particle due to its deviation from the radial direction in the frame of reference connected with the skeleton is carried out. This is of interest for applications related to deep-bed filtration of suspensions.

The free-molecular rarefied-gas flow in a long channel of elliptic cross-section is considered. The Maxwellian mirror-diffuse reflection model is used as the boundary condition on the channel walls. Under the assumption that a longitudinal temperature gradient is maintained in the channel the mass and heat fluxes are determined as functions of the accommodation coefficient and the ellipse semi-axis ratio. The gas mass velocity profile is obtained. It is shown that for the channels with the same ellipse semi-axis ratios a decrease in the accommodation coefficient leads generally to an increase in the gas mass velocity. The results obtained are compared with those for the case of full gas accommodation on the channel surface.