Force Action of a Body with a Permeable Boundary on a Wall in a Fluid

The ideal fluid flow due to fluid penetration through the boundary of an infinitely long solid cylinder in contact with a solid wall is determined. A formula is derived according to which the force exerted by a finite-length part of the cylinder on the wall is directed into the wall and can thus have an arbitrarily large absolute value. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 82–84, January–February, 2006.     

Unsteady-state filtration of a liquid in a fractured-porous stratum to a well with a hemispherical end-face

A study is made of the motion of a liquid toward a well with a hemispherical end-face with unsteady-state spherical-radial filtration in a fractured-porous stratum consisting of hemispherical regions with different values of the permeability of the system of cracks, superposed one on another. A Laplace transform is used to find exact solutions to the problem of the lowering of the stratum pressure as a function of time and distance as well as of the output of a well working with a constant end-face pressure. The article discusses partial cases corresponding to the exploitation of closed and bounded open fractured-porous strata by a central well with a hemispherical end-face. On the basis of numerical calculations, the effect of the parameters of fractured-porous strata on the change in the indices of the process of their exploitation is established. It is established that, with the exploitation of fractured-porous strata, the process of the lowering of the end-face pressure of the well and its output become stabilized with sufficiently large values of the time.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 115–123, November–December, 1973.     

Simulation by a source of a thin jet from a body

An exact analytic solution is found to the following plane hydrodynamic problem. An unbounded flow of an ideal incompressible fluid flows around a plate BB' placed at right angles to the velocity vector of the flow at infinity. The pressure on the free boundary P is equal to the pressure in the flow. From an opening in the center of the plate, a jet with flow rate Q from a cavity with pressure P₀ encounters the flow head-on. As a result of the solution, it is found that for fixed width of the opening the values of Q allowed by the scheme are limited. In the limiting case Q = 0 Chaplygin's flow is obtained with stagnation region at the front [1], and in the limiting case Q = Q_max a jet out of a cavity with pressure P₀ into a cavity with pressure P. As Q varies in this interval, the total drag, regarded as the drag of the plate and the chamber from which the jet emerges, takes a minimal value at a certain point. If the width of the opening tends to the length of the slab, the problem of the collision of two jets is obtained; if the width of the opening tends to zero (Q o), the problem of jet flow past a slab with a source is obtained. It is shown that the replacement of the jet by the source gives a good approximation in both the sense of the force characteristics and in the sense of the behavior of the free streamlines.Translated from Izvestiya Akademii Nauk SSSR, Hekhanika Shidkosti i Gaza, No. 5, pp. 47–54, September–October, 1979.We thank L. I. Sedov for his interest in the work and G. Yu. Stepanov for proposing the method of solution and for a helpful discussion.     

Interaction of a cylinder with a free surface and a jet

The problem of the asymmetric flow around a cylinder of a nonviscous jet is considered and, in particular, of flow with one free boundary. The problem of the choice of circulation is posed, based on a generalization of the Zhukovskii-Chaplygin postulate. Several possibilities are considered and the principle of the minimum of the maximum velocity on a contour is proposed, which qualitatively and quantitatively truly reflects certain aspects of the interaction of the cylinder with the flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 50–58, September–October, 1977.     

Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack

Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified. The project supported by National Natural Science Foundation of China     

On a Paradox in the Motion of a Rigid Particle along a Wall in a Fluid

The results of an experimental investigation of spherical particles with different surface roughnesses rolling under their own weight down an inclined pipe wall in a Newtonian fluid at low Reynolds numbers, both with (friction should be taken into account) and without contact with the wall, are presented. It is shown that a fixed particle moves differently in different fluids with similar viscosities and densities. This fact, as well as the possibility of particle motion without contact with the wall, cannot be explained within the framework of the usual hydrodynamic theories. An example is the dependence of the particle motion on the static pressure.     

Interaction of a rigid punch and a circular plate with a fixed side and a stress-free face

The axisymmetric contact problem of a rigid punch indentation into an elastic circular plate with a fixed side and a stress-free face is considered. The problem is solved by a method developed for finite bodies which is based on the properties of a biorthogonal system of vector functions. The problem is reduced to a Volterra integral equation (IE) of the first kind for the contract pressure function and to a system of two Volterra IE of the first kind for functions describing the derivative of the displacement of the plate upper surface outside the punch and the normal (or tangential) stress on the plate lower fixed surface. The last two functions are sought as the sum of a trigonometric series and a power-law function with a root singularity. The obtained ill-conditioned systems of linear algebraic equations are regularized by introducing small parameters and have a stable solution. A method for solving the Volterra IE is given. The contact pressure functions, the normal and tangential stresses on the plate fixed surface, and the dimensionless indentation force are found. Several examples of a plane punch computation are given.     

Impact of a body with a plane bottom on a thin liquid layer at a small angle

The problem of the impact of a body with a plane bottom (of the type of a box) on a thin liquid layer at a small angle is solved in the two-dimensional formulation. The nonlinear shallow water equations are used, together with the method of matched asymptotic expansions. It is found that at certain values of the input parameters of the problem the liquid pressure diminishes near the lower end of the body and becomes smaller than the atmospheric pressure, which results in liquid separation from the box bottom. The numerical results show that all input parameters of the problem have a considerable effect on the nature of body motion. The liquid separation effect on body motion is analyzed.     

Interaction of a supersonic flow with a transverse jet injected through a circular aperture in a plate

A flow pattern created by the interaction of a supersonic flow with a transverse sonic or supersonic jet injected normally to the direction of the main flow through a circular aperture in a plate is considered. The pressure rises in front of the jet owing to the retarding action of the incident flow. The boundary layer building up on the wall in front of the injection nozzle is accordingly detached. The flow pattern in the region of interaction between the jet and the external flow is illustrated in Fig. 1. The three-dimensional zone of detachment thus formed deflects the incident flow from the wall, and in front of the jet a complicated system of sharp jumps in contraction develops. A three-dimensional system of jumps also develops in the jet itself.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No, 5, pp. 193–197, September–October, 1970.     

Pumping of a fluid through a microchannel by means of a bubble driven by a light beam

A new method of pumping a fluid through a microchannel device using a gas bubble-piston, set in motion by the thermocapillary force induced by a light beam, is proposed. To demonstrate the method, a model micropump has been assembled. The model consists of two reservoirs connected by two channels with a bubble-piston driven by a light beam. The pumping rate and the volume per piston stroke are evaluated experimentally. The method proposed is compared with known microfluid pumping methods. Some advantages of the new method are indicated.     

On the interaction between a dislocation and a crack in a material with a nonlinear stress-strain law

The problem of the interaction of a crack and a dislocation in a medium with a nonlinear stress-strain law is considered for the case of a semi-infinite crack in a displacement loaded strip under longitudinal shear deformation. A power law stress-strain relation is considered and the dislocation is assumed positioned so that the net effect of its interaction with the crack is to produce a zero stress intensity factor when combined with the effect of the applied displacements. Thus the Atkinson-Kay superdislocation model of a relaxed crack tip is extended to the situation where the material satisfies a power-law stress-strain relationship.     

Interaction of a screw dislocation with a notch in a piezoelectric bi-material

Summary The electro-elastic interaction of a screw dislocation and a notch in a piezoelectric bi-material is analyzed. The electro-elastic fields induced by the dislocation are derived using the conformal mapping and the image-dislocation approach, where the solution for a piezoelectric bi-material without a notch is used as a base. The stress and the electric displacement intensity factors of the notch and the image force on the dislocation are given explicitly. We find that intensity factors are expressed in terms of the effective material constants, while the radial component of the image force is independent of the notch angle and the angular position of the dislocation in the polar coordinate system. Numerical results for the image force are provided for the use when one of the two media is purely elastic. They illustrate the behavior of the dislocation in the neighborhood of the notch.     

Mixing of a supersonic stream and a transverse jet injected through a circular hole in a plate

An experimental investigation is conducted of the propagation and mixing of a transverse sonic jet injected into a supersonic gas stream through a circular hole in a plate. The picture of the interaction at the initial section of the injected jet is examined in the majority of papers devoted to this question [1–3]. The aim of this paper is to investigate the mixing of the injected jet with the free stream, and to establish criteria governing the jet insertion and mixing processes.     

Unsteady motion of a source in a fluid under a floating plate

This paper studies the three-dimensional unsteady problem of the hydroelastic behavior of a floating infinite plate under the impact of waves generated by horizontal straight motion of a point source of mass in a fluid of infinite depth. The solution is carried out using known integral and asymptotic methods. The formulas obtained are used to numerically analyze the effect of plate thickness, depth of submergence of the source, and its acceleration, deceleration, and velocity of uniform motion on the deflection of the floating plate.     

Repair of a Plate with a Circular Hole by Applying a Patch

The stressed state of a thin elastic infinite plate with a circular hole covered by a circular patch of a greater radius is considered. The center of the hole coincides with the center of the patch. The patch is attached to the plate along its entire boundary. Stresses are prescribed at infinity on the plate and at the hole boundary. Complex Muskhelishvili potentials are found by the method of power series, and the behavior of stresses on the patch–plate interface and at the hole boundary is studied.     

Motion of a slender body in a fluid under a floating plate

This paper studies the three-dimensional unsteady problem of the hydroelastic behavior of a floating infinite plate under the impact of waves generated by horizontal rectilinear motion of a slender solid in a fluid of infinite depth. An analytic solution of the problem is found based on the known solutions for the unsteady motion of a point source of mass in a fluid of infinite depth under a floating plate. Asymptotic formulas are obtained which model the motion of a solid slender body in a fluid by replacing the body with a source-sink system. These formulas are used to numerically analyze the effect of plate thickness, depth of the body, its dimensions and the velocity of rectilinear motion on the amplitude of deflection of the floating plate. The motion of a submarine under a nonbreakable plate was modeled experimentally. Theoretical and experimental data are in good agreement.     

Stability in a case of motion of a paraboloid over a plane

We solve a nonlinear orbital stability problem for a periodic motion of a homogeneous paraboloid of revolution over an immovable horizontal plane in a homogeneous gravity field. The plane is assumed to be absolutely smooth, and the body–plane collisions are assumed to be absolutely elastic. In the unperturbed motion, the symmetry axis of the body is vertical, and the body itself is in translational motion with periodic collisions with the plane.The Poincare´ section surfacemethod is used to reduce the problemto studying the stability of a fixed point of an area-preserving mapping of the plane into itself. The stability and instability conditions are obtained for all admissible values of the problem parameters.     

Divergence of a helicoidal shell in a pipe with a flowing fluid

This paper considers a solution of the problem of coupled hydroelasticity for a helicoidal shell in a rigid tube with a flowing ideal incompressible fluid, which is of interest for the design of heat exchange systems. The flow is considered potential, and boundary conditions are imposed on the deformed surface. The version of the classical theory of elastic shells as the Lagrangian mechanics of deformable surfaces is used. The longitudinal-torsional vibrations of a long shell and a naturally twisted rod are studied. It is established that the obtained hydrodynamic loads are conservative, so that a divergence type instability is possible. A critical combination of parameters is determined.     

Motion of a load over a floating sheet in a variable-depth pool

A straightline unsteady motion of a load over a floating elastic sheet in a pool whose depth changes in the direction of load motion is studied. The influence of the pool depth, sheet thickness, load size and intensity, and velocity of uniform motion on the amplitude and maximum deflection of the sheet is analyzed.     

Growth of a new phase in a substance in a metastable state

A model of kinetics of phase transitions in a substance in a metastable state is proposed, where the probability of extensive nucleation owing to homogeneous mechanisms is rather large; the model is an alternative to Kolmogorov’s model. The use of this model is demonstrated to offer analytical solutions that describe both the crystallization processes with similar densities of the liquid and solid phases and, for instance, the kinetics of nucleation and growth of bubbles in surface boiling. Solutions obtained by Kolmogorov’s model and by the present model coincide at the initial stage of the process where the volume fraction of the new phase is small. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 75–80, March–April, 2007.