Force acting on a deformable contour moving in an arbitary fluid stream

A solution is given for the plane nonstationary motion of an arbitary deformable contour in the potential flow of an ideal incompressible fluid. The problem was solved by conformal mapping. A simple formula is obtained for the force acting on a small size contour.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 4–8, January–February, 1973.The author is grateful to L. I. Sedov and Yu. L. Yakimov for formulating the problem and supervising the research.     

Circulation flow around airfoils by a steady plane-parallel flow of a heavy liquid of finite depth with a free surface

Steady problems of a circulation flow around bodies by a flow of a heavy liquid bounded by a free surface and a straight bottom are solved. The method of complex boundary elements is used, which is based on the integral Cauchy formula written for a complex-conjugate velocity. Results of numerical calculations of the flow around a circular contour and the Joukowski airfoil are presented. Shapes of the free surface and the most important hydrodynamic characteristics of the process (velocity circulation over the airfoil and the lifting force and its moment relative to the sharp edge of the airfoil) are given. Kemerovo State University, Kemerovo 650043. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 101–110, May–June, 2000.     

Calculation of flow around a lifting surface in the case of large deformations

Many studies have been made of the nonstationary flow of an ideal incompressible fluid around a lifting surface. The present state of the numerical methods of solution of this problem is reviewed in [1]. The present paper studies three-dimensional nonstationary flow around a lifting surface which undergoes deformation and behind which a wake vortex surface is formed. The lifting and wake vortex surfaces are represented in parametric form. The metrics of these surfaces are used, and the introduced vortex function is approximated by bicubic splines. For the convenient application of the theory developed here to the flapping flight of insects, for which it is sometimes difficult to distinguish the lateral and trailing edges of the wings, the following terminology is introduced. The part of the edge of the lifting surface from which the wake vortex surface is shed is called the trailing edge. The remaining part is called the leading edge. On the leading edge, the velocity has a singularity. Test calculations have demonstrated the effectiveness of the method.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 72–79, July–August, 1980.     

Construction of asymmetric nozzles of maximum moment given additional conditions on the geometrical and force characteristics

A solution is given to the variation problem of constructing asymmetric plane nossles which realize the maximum moment relative to some point. The contours of the nozzle are assumed to be noninteracting. The method of the undetermined control contour is used [1]. The solution of this problem contains as a special case the solution to the problem of constructing a nozzle of maximum thrust, including also the case of a given lifting force [1–3]. It is shown that the construction of a nozzle of maximum moment under additional conditions on the thrust and the lifting force, or on the moment relative to another point, reduces to the construction of a nozzle of maximun moment relative to some auxiliary point.Translated from Izvestiya Akademi Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 148–152, September–October, 1984.The author thanks A. N. Kraiko for useful discussions and for his appraisal of the study.     

Motion of a deformed contour in a flow of an ideal incompressible liquid with a constant vorticity

The article gives a solution to the plane problem of the motion of a deformed contour in a flow of an ideal incompressible liquid with a constant vorticity. An explicit expression is obtained for the hydrodynamic force when the velocity of the external flow depends linearly on the coordinates. In the case of a contour of small dimensions, this expression is valid also for an arbitrary external flow.     

Hydrodynamic action of the fluid slowly flowing around a spheroidal particle covered by a viscous film

A steady problem of a slow axisymmetric flow of a viscous incompressible fluid around an oblate spheroid covered by a viscous film is solved analytically with the use of the Stokes approximation. Surface tension on the interface between the fluids is taken into account. Expressions for velocity components and stream functions are presented. A formula for determining the force action of the incoming flow onto the oblate spheroid is derived.     

Interaction of a three-dimensional boundary layer with an extensive obstacle

A special variant is considered of the theory of longitudinal—transverse interaction in which the pressure field in the perturbed region of flow forms under the influence of centrifugal forces which lead to a change in the pressure across the boundary layer. This regime of flow is realized in flow of an incompressible fluid, when the two-dimensional boundary layer developing along the smooth section of the contour of a solid body enters into interaction with a three-dimensional irregularity on the surface around which flow is taking place, a projection or a depression. On the assumption that the height of the irregularity is not great, a solution is constructed for the linearized problem of interaction. It is shown that the properties of the flow of fluid in the region of interaction, in particular the possibility of penetration of perturbations into the boundary layer in front of an irregularity, depend on the sign of the curvature exhibited by the contour of the body.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 39–48, January–February, 1988.     

Stability of a disperse-mixture flow in a boundary layer

The hydrodynamic stability of a dilute disperse mixture flow in a quasi-equilibrium region of a boundary layer with a significantly nonuniform particle concentration profile is investigated. The mixture is described by a two-fluid model with an incompressible viscous carrier phase. In addition to the Stokes drag, the Saffman lifting force is taken into account in the interphase momentum exchange. On the basis of a numerical solution of the boundary-value problem for a modified Orr-Sommerfeld equation, neutral stability curves are analyzed and the dependence of the critical Reynolds number on the governing parameters is studied. It is shown that taking into account the particle concentration nonuniformity in the main flow and the Saffman lifting force significantly changes the stability limits of the two-phase laminar boundary layer flow. The effect of these factors on the boundary layer stability is considered for the first time.     

Force acting on a particle in unsteady flow of a pseudoplastic fluid

The accelerated flow of a pseudoplastic fluid around a quiescent sphere at Reynolds numbers Re = 0–200 and dimensionless acceleration Ga = 10–10⁴ is studied by numerical simulation. It is shown that the analytical expression of the added mass force for an ideal fluid is appropriate for a pseudoplastic fluid. An expression for calculating the hereditary Basset force for a pseudoplastic fluid is proposed.     

Low-velocity viscous incompressible fluid flow around a hollow porous sphere

The problem of a viscous incompressible fluid flow around a hollow porous sphere in the Stokes approximation, in which the filtration flow through the sphere shell obeys the Darcy law, is solved. The force acting on the sphere from the fluid is calculated. The limiting cases are considered. The stream function is constructed.     

Effect of proximity of barrier on lifting force produced by vertical solid jets

The effect of proximity to the ground on the lifting force generated by a vertical solid jet is studied in connection with development of vertical takeoff and landing devices and of air cushion devices. Such a study was made in [1 ] for planar flow by an incompressible ideal fluid. There a generalization of the results obtained on a compressible fluid was made by the approximation method. In the present work the planar problem of streamline flow past a dihedral barrier of a gas jet emerging from a channel with parallel walls was solved by the Chaplygin-Fal'kovich method [2, 3], The results of [1, 4–9] follow as a particular case from the solution obtained. Calculations were carried out clarifying the effect of the proximity of a barrier and the lifting effect of a fluid on flow characteristics at subsonic speeds.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 123–131, September–October, 1971.     

Effect of surface and internal waves on the hydrodynamic characteristics of a contour in the linear approximation

A method of solving the problem of the motion of an elliptic contour in a three-layer fluid is developed within the framework of the linear theory. The results of calculating the hydrodynamic contour loads and the shape of the interfaces are presented for the following problems: the motion of a contour beneath an interface between two media and in a two-layer fluid both beneath a rigid lid and a free surface. On the basis of the numerical experiment it is concluded that surface and internal waves have a significant effect on the hydrodynamic characteristics of the contour. Omsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 121–127, May–June, 1998. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00093).     

On the nonlinear theory of the wing in a plane unsteady flow

The main aspects of the nonlinear theory of the wing in a plane unsteady fluid flow are generalized on the basis of the author’s previous results. An initial-boundary problem for complex velocity is formulated. A system of differential equations with conditions at points of vortex wake shedding is presented, which allows a large class of problems to be solved correctly. The Cauchy problem is solved by using a standard discretization procedure. The boundary-value problem is reduced at each time step to singular integral equations of the first and second kind. The accuracy of solving these equations by the method of discrete vortices and by the method of panels is compared. Specific features of pressure calculations in the case of a separated flow around the airfoil contour are discussed     

Asymptotic theory of a wing moving near a solid wall

In this study we use the method of matched asymptotic expansions to obtain an approximate solution of the problem of the nonstationary motion of a lifting surface near a solid wall. The region of flow is provisionally subdivided into characteristic zones, in which, using the appropriate coordinates, we construct asymptotic expansions for the velocity potential, which thereafter coalesce in the regions of common validity. In the first approximation (extremely small heights of flight) the problem reduces to the solution of a Poisson equation in a plane region bounded by the contour of the wing in the horizontal plane with boundary conditions established from the coalescence.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 115–124, November–December, 1977.     

Viscous lifting and drainage of a conducting fluid in the presence of a transverse magnetic field

A theoretical investigation of the effects of a transverse magnetic field on the combined problem of viscous lifting and drainage of a conducting fluid on a plate is presented. The effects of inertia and transverse magnetic field on the liquid film thickness is studied for two cases namely a plate withdrawn with a constant velocity and one withdrawn with a constant acceleration. The expressions for the flow rate and the free surface profiles are obtained for the above two cases. It is found that the free surface profiles are convex in nature as in the non-magnetic case thus showing that the inertia does not effect the general pattern of flow, and the effect of the magnetic field is to retard both the lifting and drainage of the fluid.     

Problem of the Sand Production in a Producing Well

The problem of sand production (dilatant-plastic reservoir fragmentation) in the process of pumping-out fluid through an uncased borehole is considered. Taking the dilatant change in reservoir porosity into account makes it possible to find a relation between the fluid and solid mass flow rates. There is no steady-state solution if the elasto-plastic boundary does not coincide with the supply contour. In this case a self-similar problem of well start-up with a constant production rate is considered.     

Oscillations of a cylinder piercing a linearly stratified fluid layer

The plane problem of the small steady-state oscillations of a horizontal cylinder arbitrarily located in a three-layer fluid whose upper and lower layers are homogeneous and whose middle layer is linearly stratified is considered in the linear formulation using the Boussinesq approximation. The fluid is assumed to be ideal and incompressible. The method of mass sources distributed along the body contour is used in the internal wave generation regime and an integral equation for the fluid pressure is derived in the non-wave regime. The hydrodynamic load acting on the body is calculated as a function of the oscillation frequency of the cylinder and its location. The results are compared with experimental data.     

Plane Elastic Boundary Value Problem Posed by Displacement and Force Orientations on a Closed Contour

A boundary value problem (BVP) of the plane elasticity posed in terms of the orientations of forces and displacements is considered. The main aim of the present paper is to investigate the solvability of BVPs of this kind. Firstly, analysis of two cases is performed: the case of a circle with special orientations of force and displacement vectors on the circumference and the case of an arbitrary contour with coaxial orientations of these vectors. The solutions obtained indicate that the problem can have a certain number of solutions or be unsolvable. Then the BVP is reduced to a boundary integral equation and its solvability is investigated for the general case of a smooth simple-connected closed contour. As a result, the number of linearly independent solutions is determined. This number only depends upon the angle between the force and displacement vectors. This revised version was published online in July 2006 with corrections to the Cover Date.     

Convective stability of fluid in a rotating horizontal annulus

The convective stability of quasi-equilibriumof a fluid layer formed by two horizontal coaxial cylindrical surfaces which have different temperatures and rotate at the same angular velocity about the axis of symmetry is investigated theoretically and experimentally. Consideration is carried out from the standpoint of thermal vibrational convection caused by the average lifting force generated as a result of vibrations of a nonisothermal fluid with respect to the cavity. The vibrations are induced by an external field. The action of the centrifugal force field is also taken into account. Stability of mechanical quasi-equilibrium with respect to monotonic plane perturbations, which are, as shown experimentally, the most dangerous, is studied within the framework of the linear analysis. The stability boundaries are constructed for layers of various relative thickness in the plane of control parameters, the centrifugal and vibrational Rayleigh numbers. The thresholds of excitation of two-dimensional convective structures obtained experimentally are in good agreement with the theoretical ones.     

Fundamental solutions for axi-symmetric translational motion of a microstretch fluid

The fundamental solution for the axi-symmetrictranslational motion of a microstretch fluid due to a concentrated point body force is obtained.A general formula for thedrag force exerted by the fluid on an axi-symmetric rigid particle translating in it is then deduced.As an application to theobtained drag formula,this paper has discussed the problemof creeping translational motion of a rigid sphere in a microstretch fluid.The slip boundary condition on the surfaceof the spherical particle is applied.The drag force and theother physical quantities are obtained and represented graphically for various values of the micropolarity and slip parameters.