Motion of a nonrectilinear fiber in a viscous fluid flow

The plane problem of dynamic interaction of a laminar viscous fluid flow and an inextensible pliable fiber of finite length is solved using the perturbation method. Two types of rheological twodimensional flows — pure shear and simple shear — are considered. Formulas are obtained for the evolution of the tensile force and the shape of the fiber. Results of asymptotic and numerical calculations are compared.     

Motion of a spherical particle in a viscous nonisothermal fluid

The Stokes and Hadamard-Riabouchinsky formulas are generalized to the case of steady motion of a solid spherical particle or drop in an incompressible fluid whose viscosity depends exponentially on the temperature. It is shown that for finite temperature differences between the surface of the particle and the region far from it the drag is determined by an effective viscosity with value close to the geometric mean of the viscosity on the surface of the particle and far from it.     

Unsteady jet flow of a viscous fluid

A solution is obtained, within the framework of the boundary layer theory, to the problem of the unsteady flow created by a two-dimensional jet source for a given momentum flux variation with time. In particular, aperiodic and periodic momentum variations are examined, and a qualitative analog with turbulent flow is noted for the latter.     

Pulsating laminar flow of a viscous fluid in a capillary

The possibility of using the hypothesis of quasistationarity for a pulsating laminar flow of viscous fluid in a capillary has been tested experimentally. It is shown that for the given parameters the use of this hypothesis leads to a satisfactory agreement between theory and experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 175–176, May–June, 1982.     

The viscous flow through a slightly distorted flexible tube

The high Reynolds number structure is examined for a viscous Newtonian flow through a thin axisymmetric flexible Hookean tube. Linear and nonlinear solutions are examined for a number of cases encompassing both large and small tube compliances. Particular cases studied are a flexible tube with a flexible stenosis/dilatation and a flexible tube supported between two rigid tubes. Novel vacillating free-interactions are identified at low tube compliances. These free-interfactions are believed to have application to general viscous-inviscid interactions. Solutions are also found which appear to terminate at a critical level of tube dilation for the slightly constricted tube.This study was supported by a National Science Foundation Presidential Young Investigator Award.     

Cylinder in viscous incompressible fluid flow

We present a technique for calculating the temperature field in the vicinity of a cylinder in a viscous incompressible fluid flow under given conditions for the heat flux or the cylinder surface temperature. The Navier-Stokes equations and the energy equation for the steady heat transfer regime form the basis of the calculations. The numerical calculations are made for three flow regimes about the cylinder, corresponding to Reynolds numbers of 20, 40, and 80. The pressure distribution, voracity, and temperature distributions along the cylinder surface are found.It is known that for a Reynolds number R>1 the calculation of cylinder drag within the framework of the solution of the Oseen and Stokes equations yields a significant deviation from the experimental data. In 1933 Thom first solved this problem [1] on the basis of the Navier-Stokes equations. Subsequently several investigators [2, 3] studied the problem of viscous incompressible fluid flow past a cylinder.It has been established that a stable solution of the Navier-Stokes equations exists for R40 and that in this case the calculation results are in good agreement with the experimental data. According to [2], a stable solution also exists for R=44. The possibility of obtaining a steady solution for R>44 is suggested.Analysis of the results of [2] permits suggesting that the questions of constructing a difference scheme with a given order of approximation of the basic differential relations which will permit obtaining the sought solution over the entire range of variation of the problem parameters of interest are still worthy of attention.Calculation of the velocity field in the vicinity of a cylinder also makes possible the calculation of the cylinder temperature regime for given conditions for the heat flux or the temperature on its surface. However, we are familiar only with experience in the analytic solution of several questions of cylinder heat transfer with the surrounding fluid for large R within the framework of boundary layer theory [4].     

Motion of a sphere down an inclined plane in a viscous flow

The motion of a rigid particle near a wall in a fluid flow is an important element of particle transport by fluids. The aim of this study was to carry out an experimental and theoretical investigation of the gravity-induced motion of a rigid sphere in a viscous fluid in the presence of a transverse flow. The experimental study of this configuration is a way of understanding the specific features of the hydrodynamically constrained particle motion. It is established that the transverse motion of the fluid substantially increases the particle settling velocity, which grows with increase in the transverse flow velocity. This effect is most pronounced for small angles of inclination of the plane. The difference in the particle settling velocities in the presence and absence of the transverse flow could reach a factor of two.     

Motion of a chain of bubbles in a vertical channel with a viscous fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 87–91, May–June, 1991.     

Numerical simulation of plate autorotation in a viscous fluid flow

A general formulation of the plane coupled dynamical and aerodynamical problem of the motion of a rigid body with a rotational degree of freedom in a viscous incompressible fluid flow is given. A computation technique for solving the Navier-Stokes equations based on the meshless viscous vortex domain method is used. The autorotation of a single plate and a pair of plates is investigated. The effect of the reduced moment of inertia and the Reynolds number on the angular rotation velocity is determined. The time dependences of the hydrodynamic loads are compared with the corresponding instantaneous flow patterns. The increased the autorotation velocity of two plates in tandem is detected.     

Nonisothermal flow of a viscous incompressible fluid in a two-dimensional diffuser

The velocity and temperature distributions in a viscous incompressible fluid flow in a two-dimensional diffuser are analyzed. Fully developed flow is considered, i.e., the influence of the entrant section is disregarded. It is assumed that the diffuser walls are maintained at a temperature depending on the polar radius. The dynamic viscosity is considered to be an exponential function of the temperature. The problem is reduced to the solution of a system of ordinary differential equations, which is solved by the method of successive approximations. The convergence of the iterative scheme is proved.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 40–48, July–August, 1973.The author is indebted to L.A. Galin and N. N. Gvozdkov for assistance with the study.     

Flow of a viscous fluid past a flexible membrane at low Reynolds numbers

The numerical calculation of a steady two-dimensional viscous flow past a flexible membrane is treated. Both edges of the membrane are fixed in the flow and its chord is set normal to the flow. The Navier-Stokes equation in terms of the stream function and the vorticity is transformed to the body fitted coordinate system. The numerical calculations, based on a finite difference method and relaxation method, are carried out for several values of the membranes tension for cases when the Reynolds numbers are 5, 10 and 20. It is found that two different shapes of the membranes are possible at a given value of tension and Reynolds number: one with a small deformation, and the other with a large deformation. Two vortices appear in the concave region of the membrane if its deformation increases beyond a certain extent.     

Motion of a viscous fluid and a wall in the presence of a stationary wall

The problem of damping motion of a hydromechanical system consisting of a viscous fluid and its bounding rigid walls is solved. A condition under which there is an abrupt deceleration of the hydromechanical system is determined.     

Cavitation flow calculations for a viscous and capillary fluid

Developed cavitation calculations, where the cavity forms a void directly adjoining and stationary relative to the body, have been carried out almost exclusively within the framework of ideal fluid mechanics [1, 2]. Experiments (for example, [2, 3]), however, indicate that viscosity and capillarity have an undoubted influence on cavitation flows. In the case of developed cavities behind nonlifting bodies this effect has been taken into account [4] in terms of the dependence of the arc abscissa of the beginning of the cavity on the Weber and Reynolds numbers We and Re for a given value of the cavitation number. In calculating a partial cavity (of a length not exceeding that of the body in the flow) it is necessary to take into account the development of the boundary layer on the cavity and the presence of viscous separation zones not only in front of but also behind it. In this paper a method of calculating partial cavitation satisfying these requirements is proposed, and problems relating to the justification of the method are discussed. The cavitation calculations presented employ the flow model described in [5], which takes into account the presence of the boundary layer on the body and the cavity, together with the viscous separation zones. The calculation method is a development of that described in [6] and makes important use of an idea derived from [2, 7]. In this connection, the fact that the characteristics of the boundary layer in cavitation flow past bodies have not been sufficiently studied has made it necessary to resort to a numerical experiment to close the semiempirical relations used in the calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 45–51, November–December, 1985.