Branching of secondary modes in the flow between rotating cylinders

The steady secondary flows (Taylor vortices) of a viscous incompressible fluid between concentric rotating cylinders are studied. The range of wave numbers a and Reynolds numbers R in which there are several secondary flow modes is determined. The branching of these modes is studied.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp.47–53, January–February, 1977.     

Dynamics of vorticity at a sphere

The article discusses the two-dimensional flow of an incompressible liquid between two infinitely close concentric spheres, due to an initial distribution of the vorticity differing from zero. The concept of point singularities (vortices, sources, and sinks) at a sphere is introduced. Equations of motion are obtained for point vortices, as well as invariants of the motion, known for the plane case [1]. The simplest case of the mutual motion of a pair of vortices is considered. Equations are obtained for the motion of point vortices at a rotating sphere. Integral invariants for the continuous distribution of the vorticity are obtained, having the dynamic sense of the total kinetic energy and the momentum of the liquid at the sphere. The effect of the topology of the sphere on the dynamics of the vorticity is noted, and a comparison is made with the plane case.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 57–65, November–December, 1977.     

Large-scale turbulence in a thin layer of nonisothermal rotating fluid

The dynamics of large-scale nonisothermal turbulence in a thin rotating layer of fluid are investigated. An hierarchical model, obtained by averaging the initial Boussinesq equations with respect to the vertical coordinates and subsequently projecting the two-dimensional equations onto a basis consisting of a system of axisymmetric spiral vortices of progressively decreasing scale, is proposed. It is shown that the presence of horizontal temperature inhomogeneities leads to a considerable increase in the turbulence decay time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 48–55, July–August, 1988.     

A Numerical Study of the Recirculation Zones During Spin-Up and Spin-Down for Confined Rotating Flows<Superscript>*</Superscript>

This paper reports computational simulations of the Navier–Stokes equations for confined axisymmetric rotating flows induced by rotating the endwalls instantaneously at a different rate to the sidewall. The transient behavior of the recirculation zones in the meridional plane is investigated during the temporal evolution. The changes in the topological structure of the meridional-plane streamline pattern are significant and the temporal evolution from one pattern to another reveals similarities between spin-up and spin-down at the early stages but subsequently differs. As the onset bubble for the first recirculating period always sets out from a certain axial station, a recirculation factor, R_f, is suggested to predict the onset time and location for the first period of recirculation. Accordingly, a stagnation point is observed numerically from a central axial station for low Reynolds numbers around 70–80. The effect of changing the rotation of the sidewall is also discussed, but no substantial influence is observed on the characteristics of the recirculation zones if there is no appearance of the Taylor–Görtler vortices in the sidewall boundary layer.     

Instabilities in multi-hole converging flow of viscoelastic fluids

Studies of the onset of instabilities were conducted on single hole and multi-hole contractions using laser speckle visualization. A well characterized elastic fluid was used with constant viscosity of 13.1 Pa · s and elasticity characterized by a longest relaxation time constant of 2.233 s. The onset of instabilities was characterized in terms of the Deborah number and the contraction ratio. Three types of instabilities were observed: pulsing vortices, azimuthally rotating vortices, and swirling vortices. For the single hole contractions the critical Deborah number for instability increased from 4.4 to 5.07 to 5.25 as the contraction ratio increased from 4: 1 to 8: 1 to 12: 1. The magnitude of the instabilities was much greater for the 4: 1 contraction than for the other two contraction ratios. For the multi-hole contraction a square array of nine holes was used and the ratio of the hole diameter to hole spacing was varied. The height of the vortices is very similar for the single hole and multi-hole contractions at low Deborah numbers. At high Deborah numbers the effect of adjacent holes is to reduce the height of the vortices by a factor of three. For the 4: 1 spacing no secondary vortex was observed below a Deborah number of De = 3.7. Secondary vortices occurred for the 8:1 and 10:1 spacing at all Deborah numbers. Unstable pulsing vortices appeared for all spacings at a critical Deborah number around 5.5. Adjacent holes decreased the strength of the unsteady vortex motions. The centerline velocities were measured for the multi-hole contraction at shear rates of 5, 30, and 300 s^–1. The elongational strain rates are similar at a low shear rate of 5 s^–1. As shear rate is increased the onset of stretching occurs closer to the plane of the contraction for the smaller contraction ratios.     

Large-Scale Streamwise Vortices in the Supersonic Part of a Permeable Nozzle

Large-scale streamwise vortices in the vicinity of a perforated wall in the supersonic part of the nozzle are studied. The governing effect of gas inflow through a perforated wall on origination and parameters of streamwise vortices is experimentally established.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 68–75, September–October, 2005.     

Effect of the acoustic regularization of initial perturbations on the development of ordered structures

Mechanisms are considered by which acoustic oscillations influence the structure of subsonic shear flows. Analysis of the experimental data [1–7] confirms the assumption made in [6] that the regularization of initial perturbations, which causes a higher degree of ordering and an increase in the life of vortices formed because of the development of instability waves or interaction of acoustic oscillations with the edge of the nozzle, is one of the mechanisms by which acoustics influences various shear flows. Photographs are given which show the regularizing effect of acoustics on the development of vortices in the wake behind the edge.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 171–174, January–February, 1986.     

Vortex intensification in convective cells

The intensification of single vortices in convective flows swirled by the Coriolis force is studied numerically. The initial disturbances, specified against the background of a steady cell, are coaxial with the cell flow and have various swirl directions, intensities, and dimensions. It is shown that the vortices are intensified no matter whether the direction of disturbing vortex rotation is co- or counter-directional with the Coriolis force. If the disturbance intensity is small as compared with that of the convective-cell flow, the growth of the azimuthal velocity circulation in the perturbing vortices depends linearly on their initial circulation. For such vortices, the energy increase is proportional to the characteristic vortex radius to the power –5/3.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 62–68. Original Russian Text Copyright © 2004 by Ivanov and Povarnitsyn.     

Flow near a vibrating cylinder

The results are given of experimental investigations into the change in the structure of the secondary steady flows near a circular cylinder vibrating in a fluid at rest in the direction perpendicular to its axis in a wide range of vibration amplitudes at high Reynolds numbers. For vibration amplitudes less than the cylinder diameter, not only viscous waves but also four vortices are generated near the surface of the cylinder and four steady flows at some distance from it. During a period of the vibration, the vortices near the cylinder change their shape and position. At vibration amplitudes comparable with the cylinder diameter, the vortices become separated and form two vortex streets. If the vibration amplitude is increased further, the streets bifurcate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 190–192, July–August, 1982.     

Ekman vortices and the centrifugal instability in counter-rotating cylindrical Couette flow

The finite length of a Taylor–Couette cell introduces endwall effects that interact with the centrifugal instability. We investigate the interaction between the endwall Ekman boundary layers and the vortical structures in a finite-length cavity with counter-rotating cylinders via direct numerical simulation using a three-dimensional spectral method. To analyze the nature of the interaction between the vortices and the endwall layers we consider four endwall boundary conditions: fixed endwalls, endwalls rotating with the outer cylinder, endwalls rotating with the inner cylinder, and stress-free endwalls. The vortical structure of the flow depends on the endwall conditions. The waviness of the vortices is suppressed only very near the endwall, primarily due to zero axial velocity at the endwall rather than viscous effects. In spite of their waviness and random behavior, the vortices generally stay inside of the v=0 isosurface by adjusting quickly to the radial transport of azimuthal momentum. The thickness and strength of the Ekman layer at the endwall match with that predicted from a simple theoretical approach.     

Method of calculating subsonic gas flow with separation past wings

The steady nonlinear problem of subsonic compressible gas flow past a wing of arbitrary shape in plan is considered. A numerical method was devized for solving the problem; this is a further development of the method of discrete vortices. The surface of the body and the vortex wake behind it are simulated by systems of discrete vortex sections, but, in contrast to the case of an incompressible medium, it is necessary in this case for the sources to be distributed outside the wing. The circulations of the attached vortices, the strengths of the sources, and the shape of the wake are determined by iterations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 140–147, July–August, 1984.     

Interaction of helical vortices

A characteristic feature of atmospheric vortices of a convective nature is the powerful radial motions of the medium at their base. In order to take these motions into account in analytical and numerical modeling, it is necessary to use point or distributed vortex sinks (vortex sources), which we will call helical vortices (from the shape of the streamlines of the flows produced) [1]. It seems likely that the interaction of point helical vortices was first considered in the until recently little-known study [2] which was included in the collection [3] and partially overlaps with the more recent studies [4, 5].Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 183–185, July–August, 1995.     

Experimental study of shear flow instability

The results of experiments carried out in order to study the instability of a free shear layer of rotating barotropic fluid at high Reynolds numbers are presented.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 167–173, May–June, 1992.     

Steady disturbed viscous incompressible gas flows in a long cylinder with one closed end

There have been many studies of steady disturbed flows in rotating channels. In [1] the steady disturbed flow between two coaxial rotating cylinders was investigated. In [2, 3] the disturbances of Hagen-Poiseuille flow due to rotation of the pipe were considered. In this article other effects: the propagation of disturbances in a long rotating pipe and their interaction with the end face are examined.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 104–112, September–October, 1993.     

Method of contour dynamics for plane flows of an ideal fluid

The method of contour dynamics is generalized for plane flows of a general form when, apart from vortices, distributed mass sources (or sinks) are present in the fluid. The laws of variation of the vorticity and divergence of the fluid particles with time are obtained for this case which makes it possible to use the method of contour dynamics for piecewise-constant vortex sink distributions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–19, September–October, 1993.     

Influence of large vortices on the structure of turbulent shear flows

Analysis of numerous experimental data reveals an influence of large vortices on the structure and characteristic parameters of flows. An approximate theory is proposed for describing the effect of large vortices on the pressure pulsations, the profiles of the pulsation velocities, the turbulence energy, and the velocity correlations (turbulence friction stresses). Large vortices are shown to have a long-range influence in that they induce pulsations of the pressure and the velocity at large distances, in particular in regions where transverse velocity gradients are absent (jet boundaries, symmetry axis, core of the initial section of a jet, etc.). When the theory is applied to the calculation of the turbulent characteristics of a mixing layer, a planar jet, a combustion jet, and a boundary layer on a flat surface, it is satisfactorily confirmed by the experimental data of a number of authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, p. 10–20, September–October, 1979.I thank A. B. Vatazhin, A. S. Ginevskii, T. A. Girshovich, and A. N. Sekundov for helpful advice.     

The influence of unsteady perturbations on the flow in a forward separation region upstream of a cone

Symmetric and nonsymmetric supersonic separated flows past a cone with a rotating flat-tipped needle mounted at the apex are studied. The influence of unsteady periodic perturbations of the forward separation zone on the aerothermodynamic characteristics of a conical body is analyzed. It is shown that in symmetric flows a rotating needle with a flat tip can be used for reducing the force and thermal loads on the upwind surface of an aircraft.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 132–143, March–April, 1996.     

Velocities and structure of convective motions in a rotating fluid

The velocities in various rotating fluid regimes are investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 165–168, July–August, 1989.The author wishes to thank G. S. Golitsyn for his constant interest in the work.     

Motion of a magnetizable liquid in a rotating magnetic field

Moskowitz and Rosensweig [1] describe the drag of a magnetic liquid — a colloidal suspension of ferromagnetic single-domain particles in a liquid carrier — by a rotating magnetic field. Various hydrodynamic models have been proposed [2, 3] to describe the macroscopic behavior of magnetic suspensions. In the model constructed in [2] it was assumed that the intensity of magnetization is always directed along the field so that the body torque is zero. Therefore, this model cannot account for the phenomenon under consideration. We make a number of simplifying assumptions to discuss the steady laminar flow of an incompressible viscous magnetizable liquid with internal rotation of particles moving in an infinitely long cylindrical container in a rotating magnetic field. The physical mechanism setting the liquid in motion is discussed. The importance of unsymmetric stresses and the phenomenon of relaxation of magnetization are emphasized. The solution obtained below is also a solution of the problem of the rotation of a polarizable liquid in a rotating electric field according to the model in [3].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 40–43, July–August, 1970.     

Determination of the frequencies of the oscillations of a low-viscosity liquid rotating in an axisymmetric vessel

The damping rate and frequencies of the normal modes of a low-viscosity liquid rotating in an axisymmetric vessel are found. The boundary-layer method enables one to express the result in terms of the solutions of the corresponding problem for an ideal liquid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 128–133, March–April, 1980.