Effect of wall proximity on the wake of a rotating and translating sphere (original) (raw)
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The Wake Behind the Sphere; Analysis of Vortices During Transition from Steadiness to Unsteadiness
This paper reports about an experimental investigation of the wake behind a solid sphere on a low velocity hydrodynamical channel for the Reynolds number in the range 250-310. The aim of the work is to analyze the size and shape of the vortices' cores and its change as a function of the Reynolds number. Special attention is paid to the transition from stationary flow, characterized by two counter-rotating longitudinal vortices, to instationary flow. The two-coloured visualization of the wake in steady and unsteady regimes is also presented.
Physical Review Fluids
In many applications, finite-sized particles are immersed in a turbulent boundary layer (TBL) and it is of interest to study wall effects on the instantaneous shedding of turbulence structures and associated mean velocity and Reynolds stress distributions. Here, 3D flow field dynamics in the wake of a prototypical, small sphere (D + = 50, 692 < Re D < 959) placed in the TBL's outer, logarithmic, and buffer layer, were measured using time-resolved tomo-PIV. Increasing wall proximity increasingly tilted the mean recirculating wake away from the wall implying a negative lift force. Mean velocity deficit recovery scaled with the mean wake length with minor effects of wall proximity. Farthest from the wall, streamwise Reynolds normal stresses encircled the mean wake as an axisymmetric tubular "shell," while transverse and wall-normal stresses extended off its tip as axisymmetric tapered cones. Wall proximity removed axisymmetry and attenuated values near the wall. Reynolds shear stresses were distributed as antisymmetric lobes extending off the mean wake displaying increasing values with reducing sphere-wall gap. Instantaneous snapshots revealed a wake densely populated by "archlike" vortices with shedding frequencies lower than for a sphere in uniform flow except in the buffer layer. Tilting of the wake away from the wall resulted from self-induced motion of shed hairpinlike vortices whose symmetry plane was increasingly wall-normal oriented with reduced sphere-wall gap.
Journal of Wind Engineering and Industrial Aerodynamics, 2013
The wake transitions of generic bluff bodies, such as a circular cylinder, near a wall are important because they provide understanding of different transition paths towards turbulence, and give some insight into the effect of surface modifications on the flow past larger downstream structures. In this article, the fundamentals of vorticity generation and transport for the two-dimensional flow of incompressible Newtonian fluids are initially reviewed. Vorticity is generated only at boundaries by tangential pressure gradients or relative acceleration. After generation, it can cross-annihilate with opposite-signed vorticity, and can be stored at a free surface, thus conserving the total vorticity, or circulation. Vorticity generation, diffusion and storage are demonstrated for a cylinder translating and rotating near a wall. The wake characteristics and the wake transitions are shown to change dramatically under the influence of cylinder rotation and wall proximity. At gaps between the cylinder and the wall of less than approximately 0.25 cylinder diameter, the wake becomes three dimensional prior to becoming unsteady, while for larger gaps the initial transition is to an unsteady two-dimensional wake. At a gap of 0.3 cylinder diameter, we observe a sharp increase in the critical Reynolds number at which threedimensionality sets in. As the gap is further increased, the critical Reynolds number initially decreases before increasing to that for an isolated cylinder. The effect of cylinder rotation on these transitions is also quantified, with forward (prograde) rotation enhancing three-dimensional instability and reverse (retrograde) rotation stabilising the wake. High retrograde rotation leads to suppression of threedimensional flow until beyond the highest Reynolds number investigated (Re¼ 750).
Flow dynamics in the turbulent wake of a sphere at sub-critical Reynolds numbers
Computers & Fluids, 2013
Direct numerical simulations of the flow over a sphere have been performed. The computations have been carried out in the sub-critical regime at Re = 3700 and Re = 10000 (based on the freestream velocity and the sphere diameter). A parallel unstructured symmetry-preserving formulation has been used for simulating the flow. Computations have been carried out on unstructured grids obtained by the constant-step rotation about the axis of a two-dimensional grid. With this discretisation, the Poisson equation has been solved by means of a Fourier diagonalization method. Particular attention has been devoted to investigate the shear-layer instabilities and its influence in the vortical structures, as well as the wake configuration. The main features of the flow including power spectra of a set of selected monitoring probes at different positions have been described and discussed in detail. Detailed information about turbulent statistics have also been provided.
Numerical and experimental studies of the rolling sphere wake
Journal of Fluid Mechanics, 2010
A numerical and experimental investigation is reported for the flow around a rolling sphere when moving adjacent to a plane wall. The dimensionless rotation rate of the sphere is varied from forward to reversed rolling and the resulting wake modes are found to be strongly dependent on the value of this parameter. Results are reported for the Reynolds number range 100 < Re < 350, which has been shown to capture the unsteady transitions in the wake. Over this range of Reynolds number, both steady and unsteady wake modes are observed. As the sphere undergoes forward rolling, the wake displays similarities to the flow behind an isolated sphere in a free stream. As the Reynolds number of the flow increases, hairpin vortices form and are shed over the surface of the sphere. However, for cases with reversed rotation, the wake takes the form of two distinct streamwise vortices that form around the sides of the body. These streamwise structures in the wake undergo a transition to a new...
The effects of shear flow on the unsteady wakes behind a sphere at moderate Reynolds numbers
Fluid Dynamics Research, 2000
Numerical simulations to investigate the e ects of shear ow on wakes behind a sphere were carried out using a three-dimensional ÿnite element method. The time-dependent Navier-Stokes equations were solved by a modiÿed explicit time integration scheme. The Reynolds number, deÿned by the sphere diameter and oncoming velocity at its center, ranged from 20 to 500. Linear shear is assumed, and the dimensionless shear rate, deÿned as the vertical gradient of oncoming shear ow, was varied from 0.0 to 0.2. Extensive comparisons were made between the present computed results and available experimental and numerical investigations, and showed that they are in close agreement. Computed lift force was directed toward the low velocity side for Re ¿ 50 whereas it was toward the high velocity side for Re ¡ 50. In addition, drag forces showed slight increases compared to those in a uniform ow. The Reynolds number, at which vortex shedding begins, was found to be lower than that in a uniform ow and was a function of the shear rate. Vortex shedding frequency also increases with the Reynolds number and the shear rate. The irregularity of the vortex shedding and the oscillation of the vortex detachment location appearing in uniform and low shear ows at Re = 500 vanishes when high shear was present.
Kinematics and dynamics of sphere wake transition
2001
The wake of a sphere undergoes a number of symmetry-breaking transitions as it changes from laminar to turbulent. This paper concentrates on the "rst two transitions. At Re"212 a regular transition occurs, when the wake develops a spectacular two-tailed structure consisting of two trailing streamwise vortices. During the second transition at Re"272 the #ow undergoes a Hopf bifurcation. In this case there is a complex interaction between the trailing vortices leading to the periodic shedding of vortex loops. Both these transitions are shown to be supercritical (or nonhysteretic). Landau models are constructed for both transitions and the coe$cients determined. The visual impression of an apparently sudden bifurcation to the two-tailed wake is shown to be due to the focal nature of the trailing vortices, which draws dye into the cores, even if their net circulation is small. A precursor to the second transition to the periodic wake is strong kinking of the trailing vortices about 1 diameter downstream from the back of the sphere. The vorticity structure of the two-tailed wake prior to transition is also quanti"ed which may prove useful for development of models of the transition process. 2001 Academic Press
From the double vortex street behind a cylinder to the wake of a sphere
European Journal of Mechanics - B/Fluids, 2004
In this paper, we review the main results concerning the first instabilities, characterised by the breaking of spatio-temporal symmetries, occurring in the wake of bluff bodies, as the flow speed is increased. Phenomenological wake models are compared to experiments for the geometry of a circular cylinder and of a sphere. The transition from a cylindrical to spherical configuration is also illustrated in various ways, such as the transverse coupling of two sphere wakes and a reduction in length or a wavy deformation of a circular cylinder. Finally, we report preliminary results concerning the fluid-structure interactions in the case of a longitudinally tethered sphere.
Transition to Turbulence in the Wake of a Sphere
Physical Review Letters, 1999
Experimental investigation of the wake of a sphere is reported, namely, the change from steady to periodic flow in the Reynolds number range [100, 360]. First, visualizations have been carried out in a water channel to make precise the geometry of downstream bubble and shedding vortices behind the sphere. Thereafter, measurements have been performed in a wind tunnel and results have been compared successfully to the predictions of the Landau model.