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.     

Approximate calculation of three-dimensional cavitating flow around propeller blades in a viscous capillary fluid

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 83–90, November–December, 1990.     

Nonlinear capillary waves on a viscous fluid jet surface

Capillary instability of a fluid jet is one of the classical problems of hydrodynamics [1]. Studying it is of practical interest, particularly for the optimization of the ignition of a liquid propellant and the development of granulating apparatus in the chemical industry [2]. Until recently, the main attention has been paid to analyzing linear problems. Dispersion equations have been obtained for small perturbations of a jet surface with the viscosity of the external medium taken into account [3]. The construction of a theory of finite-amplitude waves on an ideal fluid jet surface was started in [4, 5]. Up to now this theory has achieved substantial results, as can be assessed by the successful numerical modeling of the dissociation of an inviscid fluid jet into drops [6] (see [7, 8] also). This paper is devoted to a discussion of the nonlinear development stage of viscous fluid jet instability under conditions allowing the influence of the surrounding medium and the gravity field to be neglected.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 179–182, March–April, 1977.The author is grateful to B. M. Konyukhov and G. D. Kuvatov for suggesting this problem and performing the experiment and to M. I. Rabinovich for useful discussions.     

Plane capillary flow of a viscous fluid with mutiply connected boundary in the Stokes approximation

A study is made of the process of relaxation to the equilibrium configuration of an isolated volume of a viscous incompressible Newtonian fluid under the influence of capillary forces. The fluid has the form of an infinite cylinder of arbitrary shape with a smooth compact and, in general, multiply connected boundary. In the course of relaxation, internal cavities collapse, and the cylinder acquires asymptotically a circular configuration. The quasisteady Stokes approximation [1] is used to describe the flow. First proposed by Frenkel' [2], this approximation has been used in the calculation of a dynamic boundary angle [3], the collapse of a circular cylinder [4], and the collapse of a hollow cylinder [5]. The analogy between the hydrodynamic equations in the Stokes approximation and the equations of elasticity theory made it possible [6] to describe the relaxation of a simply connected cylinder by a method close to the one employed by Muskheleshvili [7]. In the present paper, the approach of the author [8] based on work of Grinberg [9] and Vekua [10] is developed. It is shown that the true pressure distribution gives a minimum of the integral of the square of the pressure over the region for fixed integral of the pressure over the boundary. An explicit expression for the pressure is obtained in the form of the projection of a generalized function with support on the boundary onto the subspace of harmonic functions. The velocity field on the boundary of the region is calculated. An upper bound is found for the law of decrease of the perimeter of the region and for the time during which the number of connected components of the boundary remains unchanged.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 117–122, January–February, 1992.     

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.     

Two-dimensional stokes flow of a viscous fluid with a free boundary under the effect of capillary forces

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 47–51, September–October, 1992.     

Cell models for micropolar flow past a viscous fluid sphere

The Stokes axisymmetrical flow of an incompressible micropolar fluid past a viscous fluid sphere and the flow of a viscous fluid past a micropolar fluid sphere are investigated. The appropriate boundary conditions are taken on the surface of the sphere, while the proper conditions applied on the fictitious boundary of the fluid envelope vary depending on the kind of cell-model. These problems are solved separately in an analytical fashion, and the velocity profile and the pressure distribution inside and outside of the droplet are shown in several graphs for different values of the parameters. Numerical results for the normalized hydrodynamic drag force acting, in each case, on the spherical droplet-in-cell are obtained for various values of the parameters representing volume fraction, the classical relative viscosity, the micropolarity and spin parameters are presented both in tabular and graphical forms. Results of the drag force are compared with the previous particular cases.     

Asymptotic theory of flow attachment for a viscous incompressible fluid

A study is made of the two-dimensional laminar flow of a viscous incompressible fluid in the neighborhood of the point of attachment of the flow to a solid surface. The case of large Reynolds numbers is considered. It is assumed that the dimensions of the separation region are of the same order of magnitude as the characteristic dimension of the body around which the flow takes place. The asymptotic theory of such flow is constructed by applying the method of matched asymptotic expansions to the analysis of the Navier-Stokes equations. It is shown that in the neighborhood of the attachment point the flow is locally inviscid and can be described by the complete system of Euler equations. A solution to the corresponding boundary-value problem is constructed numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 63–71, November–December, 1980.     

Numerical calculations of steady viscous incompressible fluid flows

Most authors use the stream function for the calculation of two-dimensional viscous incompressible fluid flows. The velocity field is determined by numerical differentiation, which reduces the computation accuracy significantly. In the following we study steady viscous fluid flow fay a method which makes it possible to avoid this drawback; in this case the problem of the Navier-Stokes equations reduces to a different equivalent problem: an implicit finite-difference scheme constructed on the basis of the results of [1, 2] is proposed for the numerical solution of the resulting system of equations.     

Boundary condition formulation for viscous fluid flow problems

In the solution of the Navier-Stokes equations by difference methods in infinite regions, the question arises as to the nature of the approximate boundary conditions at those portions of the computational region boundary where these conditions are not determined directly by the formulation of the basic problem. In certain cases of practical importance, these boundary conditions may be obtained by coupling the N-S equations with equations which are similar to the boundary-layer equations.In the present paper, we propose boundary conditions for the case of viscous incompressible fluid flow. Their application is illustrated for the problem of flow past the leading edge of a semi-infinite flat plate.The author wishes to thank I. Yu. Brailovskaya and L. A. Chudov for helpful suggestions in the course of this investigation.     

Squeezed flow and heat transfer over a porous surface for viscous fluid

Flow and heat transfer over a permeable sensor surface placed in a squeezing channel is analyzed. A constant transpiration through the sensor surface is assumed. Locally non-similar momentum and energy equations are solved by three different methods, against the transpiration parameter τ, for different values of the squeezing parameter b, and Prandtl number Pr. From the investigation, it is found that when the channel being squeezed, the skin-friction reduces but the heat transfer coefficient increases. Increase in the value of the squeezing parameter onsets reverse flow at the sensor surface when fluid is being injected and the affect is enhanced with the increase of injection through the surface. It is further observed that increase of suction of fluid through the sensor thins the thermal and the momentum boundary layer regions, whereas injection of fluid leads to thickening of both the thermal and the momentum boundary layer regions. Heat transfer from the surface of the sensor increases with the increase of the value of Pr for the entire range of surface mass-flux parameter τ. M. A. Hossain is on leave of absence from University of Dhaka.     

A method for finite element parallel viscous compressible flow calculations

This paper presents the parallelization aspects of a solution method for the fully coupled 3D compressible Navier-Stokes equations. The algorithmic thrust of the approach, embedded in a finite element code NS3D, is the linearization of the governing equations through Newton methods, followed by a fully coupled solution of velocities and pressure at each non-linear iteration by preconditioned conjugate gradient-like iterative algorithms. For the matrix assembly, as well as for the linear equation solver, efficient coarse-grain parallel schemes have been developed for shared memory machines, as well as for networks of workstations, with a moderate number of processors. The parallel iterative schemes, in particular, circumvent some of the difficulties associated with domain decomposition methods, such as geometry bookkeeping and the sometimes drastic convergence slow-down of partitioned non-linear problems.     

Unsteady two-dimensional rotation of a viscous fluid for steady source flow

We obtain the solution of the Navier-Stokes equations for one class of unsteady axisymmetric two-dimensional rotational flows for the case of a line source or sink of constant intensity in the fluid.     

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 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.     

Criticality and transition for a steady reactive plane couette flow of a viscous fluid

Numerical integration is used to determine critical and transitional values of parameters for steady, reactive, viscous, one dimensional plane Couette flow of an incompressible, homogeneous fluid of third-grade with the lower plate at rest while the upper is in uniform motion. The solutions are found for the following cases: (i) Bimolecular (ii) Arrhenius and (iii) Sensitized temperature dependence. Specifically, it is shown that the parameter Λ controlling the non-Newtonian fluid does not affect the flow velocity in any sense while the influence on the viscous dissipation parameter Γ is examined. The results obtained are then compared with similar results in the literature.     

An inviscid/viscous coupling approach for vortex flow field calculations

A new computational approach is developed for the analysis of vortex-dominated flow fields around highly swept wings at high angles of attack. In this approach an inviscid Euler technology is coupled with viscous models, similar to inviscid/boundary layer coupling. The viscous nature of the vortex core is represented by an algebraic model derived from the Navier–Stokes equations. The approach also accounts for the effects of the viscous shear layer near a wing surface through a modified surface boundary condition. The inviscid/viscous coupling consistently provides improved predictions of leading edge separation, vortex bursting and secondary vortex formation at relatively low computational cost. Results for several cases are compared with wind tunnel tests and other Euler and Navier-Stokes solutions.