Bifurcation of poloidal field in the flow induced by a radial electric current

A study is made of the steady-state flow of a viscous conducting incompressible fluid in a half-space, induced by an electric current spreading from a point source on a solid surface. There is a critical finite value of the current at which the velocity on the axis becomes infinite. It is shown that for a high-conductivity medium bifurcation of a new MHD regime with nonzero poloidal field and rotation takes place for arbitrarily large values of the current. The axisymmetric MUD dynamo effect detected does not contradict the Cowling-Braginskii antidynamo theorem, since the conditions of the theorem are not fulfilled. In the case of low conductivity the paradox can be resolved using the model of an infinitely narrow turbulent jet. Here, too, self-excitation of the field and rotation are detected and their strengthening leads to suppression of the turbulence and relaminarization of the jet.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 4–11, March–April, 1993.     

Three-dimensional electric potential induced by a point singularity in a multilayered dielectric medium

A simple and effective method is proposed to derive the three-dimensional electric potential induced by a point singularity of any type in an N-phase dielectric medium composed of N-2 intermediate dielectric layers of equal thickness encased in two semi-infinite dielectric media. The point singularity can include a point charge or a point electric dipole. The original boundary value problem for the N-phase medium is reduced to the determination of a single unknown three-dimensional harmonic function through satisfaction of the continuity conditions across all of the N-1 perfect planar interfaces. The single harmonic function can be completely determined after analytically solving the resulting linear recurrence relations, which are independent of the type and the specific location of the singularity. When the singularity is a point charge, we obtain the self-energy of the point charge expressed in terms of a single function and the Coulomb force on the point charge expressed in terms of the negative derivative of this function.     

Free surface deformation due to a source or a sink in Stokes flow

Free surface shape and cusp formation are analyzed by considering two-dimensional viscous flow due to a line source or a line sink below the free surface where the strength of source/sink is given arbitrarily. In the analysis, the Stokes' approximation is used and surface tension effects are included, but gravity is neglected. The solution is obtained analytically by using conformal mapping and complex function theory. From the solution, shapes of the free surface are shown and the formation of a cusp on the free surface is discussed. As the capillary number decreases in negative, the free surface shape becomes singular and in a real fluid a cusp should form on the free surface below some negative critical capillary number. Typically, streamline patterns for some capillary numbers are also shown. As the small capillary number vanishes, the solution is reduced to a linearized potential flow solution.     

Thermal stresses induced by a point heat source in a circular plate by quasi-static approach

The present paper deals with the determination of quasi-static thermal stresses due to an instantaneous point heat source of strength g_pi situated at certain circle along the radial direction of the circular plate and releasing its heat spontaneously at time t = τ. A circular plate is considered having arbitrary initial temperature and subjected to time dependent heat flux at the fixed circular boundary of r = b. The governing heat conduction equation is solved by using the integral transform method, and results are obtained in series form in terms of Bessel functions. The mathematical model has been constructed for copper material and the thermal stresses are discussed graphically.     

Shock wave induced by a high-intensity power source in hypersonic flow

An upstream structure of a parabolic shock wave induced in a hypersonic flow by a steady-state high-intensity heat source is examined. A similarity analysis is used to derive a simple analytic expression that allows one to predict the shock wave upstream stand-off distance. The solution of Navier–Stokes is obtained to provide basis for the validation of the analytic expression; a reasonable agreement is obtained between the analytic and numerical results for a number of power source intensities.     

Free-surface deformation due to spiral flow owing to a source/sink and a vortex in Stokes flow

The free-surface shape and cusp formation are analyzed by considering a viscous flow arising from the superposition of a source/sink and vortex below the free surface where the strength of the source and vortex are arbitrary. In the analysis, Stokes’ approximation is used and surface tension effects are included, but gravity is neglected. The solution is obtained analytically by using conformal mapping and complex function theory. From the solution, shapes of the free surface are obtained, and the formation of a cusp on the free surface is discussed. Above some critical capillary number with a sink, the free-surface shape becomes singular and an apparent cusp should form on the free surface below a real fluid. On the other hand, no cusp would occur for sources of zero or positive strength. Typical streamline patterns are also shown for some capillary numbers. As the capillary number vanishes, the solution is reduced to a linearized potential flow solution.     

Interaction of molecular flow from a point source with a continuous medium

Kutateladze Institute of Thermophysics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 5, pp. 3–6, September–October, 1995.     

Free convective heat and mass transfer flow induced by an instantaneous point source in an infinite porous medium

A simple mathematical theory is proposed for the analysis of the buoyancy-driven heat and mass transfer flow induced by an instantaneous point source in an unbounded fluid-saturated porous medium of uniform porosity, assuming the validity of the Brinkman model. The theory consists of retaining only the leading terms of the series expansions of the dependent variables in terms of the thermal Rayleigh number and is valid within the limit of small Rayleigh numbers only. The heat generating rate is assumed to be not excessive, so that the induced flow is slow. The evolution of the flow field is demonstrated by drawing the streamlines at various times, and the results are delineated by comparing them with those of the Darcy flow model. The significance of the impact of species concentration gradients upon the thermally driven flow has been highlighted. Even though heat was specified to be one of the two diffusion mechanisms, the results apply as well to the case where the source simultaneously generates two different chemical components.     

Free surface deformation due to a source and a sink of equal strength in Stokes flow

Two-dimensional Stokes flow due to a source and a sink of equal strength below the free surface is analyzed and free surface shape and cusp formation are discussed. The source-sink pair below the free surface are aligned vertical to the free surface. In the analysis, the Stokes' approximation is used and surface tension effects are included, but gravity is neglected. The solution is obtained by using conformal mapping and complex function theory. From the solution, typical free surface shapes are shown and formation of a cusp on the free surface is discussed. As the capillary number increases, the converging free surface shape becomes singular and tends to form a cusp for sufficiently large capillary number. Typically, streamline patterns for some capillary numbers are also shown. As the capillary number vanishes, the solution is reduced to the linearized potential flow solution.     

Effect of electric current on migration of point defects near a crack tip

The effect of direct current on migration of point defects dissolved in a crystal near the tip of a crack in tension is estimated. Calculations are carried out with allowance for the plastic strain near the crack tip of a loaded specimen, caused by the motion of dislocations in the active slip planes of the crystal, the Joule heat released, and the effect of gas exchange on the crack edges on the evolution of distribution of interstitial impurity atoms. A numerical analysis is performed for an Fe crystal.     

Heavy particle dispersion from a point source in turbulent pipe flow

Dispersion of heavy particles from a point source in high-Reynolds pipe flow was studied using large-eddy simulation, LES. A stochastic Langevin type Lagrangian model developed by Berrouk et al. was used to account for heavy particle transport by the sub-grid scale motion. In both the LES and in an experiment by Arnason, the larger particles dispersed more than the small ones. The change in diffusivity with particle size is interpreted in terms of the effect of inertia and cross-trajectory effects and qualitatively compared with the analysis of heavy particle dispersion in isotropic turbulence by Wang and Stock. Particle inertia has a much larger influence on the dispersion than the crossing-trajectories effects.     

Stokes flow through a permeable tube

Pressure-driven Stokes flow through a circular tube with a permeable wall is considered as a model of blood flow through a capillary vessel. Fluid penetrates the tube wall over a test section according to Starling law relating the normal fluid velocity to the transmural pressure defined as the difference between the wall and the uniform ambient pressure. The problem is formulated using the integral representation for Stokes flow, and the solution is computed with high accuracy using a boundary-element method for specified values of the wall permeability and percentage of fluid escaping through the walls. The results illustrate the structure of the flow and validate the predictions of a model based on the assumption of locally unidirectional flow for sufficiently small permeability.     

Plane vortex flow induced by a mass source (sink) in a rotating viscous fluid

A solution of the self-similar type, describing the development with time of a plane vortex flow excited by an axisymmetric mass source (sink) in a rotating viscous fluid, is obtained. Sources of two kinds — impulsive and of constant strength — are considered. The solutions for the velocity and vorticity fields are expressed in the form of functions similar to incomplete gamma functions and are presented in the form of graphs for various flow Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 172–175, July–August, 1991.     

Effect of streamwise and spanwise electric fields on transient growth in a two-fluid channel flow

A linear model of a two-fluid channel flow under streamwise/spanwise electric field is built. Both the fluids are assumed to be incompressible, viscous and perfectly dielectric. The effect of the streamwise and spanwise electric fields on transient behavior of small three-dimensional disturbances is studied. The numerical result shows that the streamwise electric field suppresses transient growth of the disturbance with spanwise uniform wave number. The spanwise electric field diminishes transient growth of the disturbance with streamwise uniform wave number. Two peaks of optimal growth are detected in the wave number plane. The peak at relatively large spanwise wave number is dominated by the lift-up mechanism and little influenced by electric field. Differently, the peak at relatively small wave number is associated with the characteristic of the interface and possibly influenced by electric field. The effect of the Weber number, the Reynolds number and the relative electrical permittivity on optimal growth is studied as well. A scaling law is obtained for relatively small Weber numbers and relatively large Reynolds numbers.