About the Porous Media Flow Through Circular and Elliptical Anisotropic Inhomogeneities

In this article, we describe horizontal groundwater flow due to a uniform flow at infinity around a cylindrical or elliptical inhomogeneity, where the permeability inside the inhomogeneity is anisotropic and different from the isotropic domain outside the inhomogeneity. The orientation of the uniform flow with respect to the orientation of the ellipse is arbitrary as well as the orientation of the anisotropy inside the ellipse. We derive an expression for the ratio of the flow through the ellipse with respect to the flow in the homogeneous case.     

Stability of a binary-mixture advective flow in a plane horizontal layer with perfectly heat conducting boundaries

The stability of a steady-state advective flow of a binary mixture in a plane horizontal layer with perfectly heat conducting solid boundaries in the presence of a uniform longitudinal temperature gradient is investigated. The problem is solved with account for thermodiffusion. The limits of the stability of the steady-state flow with respect to long-wave disturbances are found analytically. The stability of the main flow with respect to plane and spiral disturbances with finite wavelengths is studied numerically. The stability maps in the “Rayleigh number-Sorét parameter” plane are constructed for a number of typical liquid and gaseous mixtures.     

On the comparison of two different solutions in the form of series of the governing equation of an unsteady flow of a second grade fluid

In this paper, two different solutions in the form of series of the governing equation of unsteady flow of a second grade fluid are considered. These are series expansions with respect to inverse power of time and a perturbation expansion. Two illustrative examples are given. One of them is the unsteady flow of a second grade fluid over a plane wall suddenly set in motion and the other is the diffusion of a line vortex in a fluid of second grade. It is a remarkable fact that the expression of the series expansion with respect to inverse power of time is exactly in the same form as that of the perturbation expansion. Thus, it is possible to replace a series expansion with respect to inverse power of time with a perturbation expansion.     

Hard excitation of auto-oscillations in a Hagen-Poiseuille flow

Sufficiently powerful perturbations of the flow of a liquid moving in circular pipes results in turbulence, starting with Reynolds numbers of the order of 2200–2300 [1]. It has been established theoretically [2, 3] that the flow of a viscous incompressible liquid in a pipe of circular section (Hagen-Poiseuille flow) is stable with respect to infinitesimally small perturbations for all Reynolds numbers. Attempts to obtain finite-amplitude flow instability by considering only two-dimensional perturbations [4, 5] were also unsuccessful. This paper shows that the considered flow is unstable with respect to three-dimensional perturbations of finite amplitude.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–183, September–October, 1984.The author wishes to express sincere gratitude to G. I. Petrov and S. Ya. Gertsenshtein for their interest in his work.     

Stability of poiseuille flow of a viscoplastic fluid with respect to perturbations of finite amplitude

The study made in [1] revealed that the Poiseuille flow of a viscoplastic fluid is stable with respect to infinitely small perturbations. At the same time, it is a known fact that at large Reynolds numbers a turbulent-flow regime of a viscoplastic fluid has been observed experimentally (see [2]). The divergence in the results from the linear theory of hydrodynamic stability of the experimental data indicates the need for investigating the stability of the Poiseuille flow of a viscoplastic fluid with respect to finite amplitude perturbations; this forms the main content of the present paper.     

Numerical simulation of confined laminar jet flows

Two‐dimensional incompressible jet development inside a duct has been studied in the laminar flow regime, for cases with and without entrainment of ambient fluid. Results have been obtained for the flow structure and critical Reynolds number values for steady asymmetric jet development and for the onset of temporal oscillations, at various values of the duct‐to‐jet width ratio (aspect ratio). It is found that at low aspect ratios and Reynolds numbers, jet development inside the duct is symmetric. For larger aspect ratios and Reynolds numbers, the jet flow at steady state becomes asymmetric with respect to the midplane, and for still higher values, it becomes oscillatory with respect to time. When entrainment is present, the instabilities of asymmetric development and temporal oscillations occur at a much higher critical Reynolds number for a given aspect ratio, indicating that the stability of the jet flow is higher with entrainment. Copyright © 2000 John Wiley & Sons, Ltd.     

Translationally nonequilibrium free jet boundary layer in the wake behind a wedge

Macroscopic equations obtained as a thin-layer version of the 13-moment Grad equations derived from kinetic considerations are used for describing the translationally nonequilibrium monatomic gas flow in a hypersonic free jet boundary layer formed in the wake behind a wedge. This model makes it possible to investigate flows with strong violations of equilibrium with respect to the translational degrees of freedom. A method of constructing the solution of this kinetically justified problem based on the solution of an analogous problem in the Navier-Stokes interpretation is proposed. It is established that for the kinetic variant of the problem considered the gas flow velocity distribution along the separating streamline in a plane orthogonal to the wedge generator coincides with the distribution obtained in solving the Navier-Stokes variant. It is found that taking into account the nonequilibrium nature of the flow with respect to the translational degrees of freedom of the gas particles has no effect on the base pressure and the wake angle.     

Taylor instability of a fluid film on a body

The Taylor instability develops in a parallel flows when the body force acts in the direction from the heavier fluid toward the lighter [1]. It has been suggested that an increase in flow vorticity may have a stabilizing influence on the Taylor instability [2]. In studying the hydrodynamic stability of a viscous film on a body in a flow of a low-viscosity fluid [3], the author noted some stabilization of the Taylor instability with increase in Reynolds number, and suggested that cases of complete stabilization of the flow with respect to two-dimensional disturbances are possible with some increase in Reynolds number. In the present investigation, calculations revealed cases in which with increase in Reynolds number the Taylor instability goes over into a Helmholtz instability, which increases with increase in Reynolds number, and also cases in which the Taylor instability completely disappears at some value of the Reynolds number before a Helmholtz instability has developed, i.e., cases of complete stabilization of the flow with respect to two-dimensional disturbances as a result of an increase in Reynolds number.     

Stability of flow of a nonlinear viscous power-law hardening medium in a deformable channel

A dynamical model of flow of a nonlinear viscous power-law hardening medium in a cylindrical deformable channel is considered. The flow and deformation are axisymmetric. Stationary solutions and their stability with respect to small perturbations are studied. Stability domains are found in the space of dimensionless parameters.     

Stability of the advective flow in a horizontal rectangular channel with adiabatic boundaries

The steady-state advective flow in a long horizontal rectangular channel with rigid adiabatic boundaries in the presence of a uniform longitudinal pressure gradient is investigated. The stability of this flow with respect to perturbations of various types is studied. The dependence of the critical Rayleigh number on the Prandtl number is found for various aspect ratios.     

Stability of viscous flow between rotating and stationary disks

The linear problem of the stability of viscous flow between rotating and stationary parallel disks is solved in the locally homogeneous formulation using the method of normal modes. The main flow is assumed to be selfsimilar with respect to the radial coordinate. The system of sixth-order equations, derived for the amplitude functions of the disturbances, is integrated by a finite difference method. The stability characteristics with respect to disturbances of four types are calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 79–87, November–December, 1991.     

Resistance of a circular pipe with pulsatory variation of the flow rate

The results of an experimental investigation of the hydraulic resistance of a circular pipe for turbulent flow with periodic flow rate fluctuations are presented. The presence of resonance phenomena in the pipe is revealed. It is established that, for hydrodynamic nonstationarity, the pipe resistance is a nonmonotonous function of the frequency of the imposed flow rate fluctuations and differs from the pipe resistance in the stationary flow regime. Under the conditions considered, to find the pipe resistance it is necessary to take into account the variation of the flow kinetic energy with respect to the phase of the imposed flow rate fluctuations due to the deformation of the velocity profile.     

Laminar heat transfer near an asymmetric stagnation point

This paper considers the laminar boundary layer at an obstacle near the stagnation point of a three-dimensional incompressible potential flow, asymmetric with respect to this point (e.g., for a jet incident at an angle on an obstacle). The effect of compressibility is investigated in the example of a plane subsonic flow. The solution in the close vicinity of the stagnation point is obtained by expanding in series with respect to the longitudinal coordinate, and for the more distant vicinity, the problem is solved by the method of local similarity. It is shown that in this case (in contrast with a symmetric flow [1, 2]) the maximum heat flux does not coincide with the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 140–145, November–December, 1976.The author thanks V. V. Lunev for stating the problem and for scientific guidance.     

On the consistency of four different control surfaces used for finite area blade-to-blade flow calculations

The aim of this contribution is to investigate the consistency and order of accuracy of different control surfaces used for finite area blade-to-blade flow calculations. The following cases will be treated: a hexagonal element, a trapezoidal element, a bitrapezoidal element and a quadrilateral element. Finally, the consistency conditions will be discussed and compared with respect to a cascade flow application.     

An experimental study on a wake behind a torus using the UVP monitor

 The flow around a torus has a complicated three-dimensional structure. Measuring the spatiotemporal field of velocity by means of conventional methods such as hot-wire anemometers and other one-point measuring instruments is thus difficult. Research is made on the spatiotemporal structure of the wake behind the torus by using a flow-visualizing technique and an ultrasonic velocity profile (UVP) monitor, in which two kinds of tori with different diameter ratios or solidity are set in a uniform flow with zero inclination and oblique postures. For the torus with zero inclination, there are two modes of flow structure according to the diameter ratio; at lower ratio, a disk mode is dominant, and at higher ratio, a ring wake mode appears. For the torus set with an oblique posture, the structure of the wake changes with respect to the oblique angle in a complicated fashion. The power spectra of the fluctuating velocities reveal an aspect of the character of this structural change. The Strouhal numbers estimated from the power spectra suggest that the flow patterns can be classified into four categories with respect to the oblique angle. Received: 15 May 1997/Accepted: 10 September 1998     

On the orbital motion of a rotating inner cylinder in annular flow

In this paper, numerical calculations have been performed to analyse the influence of the orbital motion of an inner cylinder on annular flow and the forces exerted by the fluid on the inner cylinder when it is rotating eccentrically. The flow considered is fully developed laminar flow driven by axial pressure gradient. It is shown that the drag of the annular flow decreases initially and then increases with the enhancement of orbital motion, when it has the same direction as the inner cylinder rotation. If the eccentricity and rotation speed of the inner cylinder keep unchanged (with respect to the absolute frame of reference), and the orbital motion is strong enough that the azimuthal component (with respect to the orbit of the orbital motion) of the flow‐induced force on the inner cylinder goes to zero, the flow drag nearly reaches its minimum value. When only an external torque is imposed to drive the eccentric rotation of the inner cylinder, orbital motion may occur and, in general, has the same direction as the inner cylinder rotation. Under this condition, whether the inner cylinder can have a steady motion state with force equilibrium, and even what type of motion state it can have, is related to the linear density of the inner cylinder. Copyright © 2006 John Wiley & Sons, Ltd.     

VORTEX SHEDDING RESONANCE FROM A ROTATIONALLY OSCILLATING CYLINDER

Vortex shedding resonance of a circular cylinder wake to a forced rotational oscillation has been investigated experimentally by measuring the velocity fluctuations in the wake, pressure distributions over the cylinder surface, and visualizing the flow field with respect to cylinder oscillations. The vortex shedding resonance occurs near the natural shedding frequency at small amplitude of cylinder oscillations, while the peak resonance frequency shifts to a lower value with an increase in oscillation amplitude. The drag and lift forces acting on the cylinder at fixed forcing Strouhal number indicate that the phase lag of fluid forces to the cylinder oscillations increases with an increase in oscillation amplitude, supporting the variation of resonance frequency with oscillation amplitude. The comparative study of the measured pressure distributions and the simultaneous flow visualizations with respect to cylinder rotation shows the mechanisms of phase lag, which is due to the strengthened vortex formation and the modification of the surface pressure distributions.