Bronwyn Stewart

Wake state and energy transitions of an oscillating cylinder at low Reynolds number

This paper reports on an extensive parameter space study of two-dimensional simulations of a circular cylinder forced to oscillate transverse to the free-stream. In particular, the extent of the primary synchronization region, and the wake modes and energy transfer between the body and the fluid are analyzed in some detail. The frequency range of the primary synchronization region is observed to be dependent on Reynolds number, as are the wake modes obtained. Energy transfer is primarily dependent on frequency at low amplitudes of oscillation, but primarily dependent on amplitude at high amplitudes of oscillation. However, the oscillation amplitude corresponding to zero energy transfer is found to be relatively insensitive to Reynolds number. It is also found that there is no discernible change to the wake structure when the energy transfer changes from positive to negative.

The wake behind a cylinder rolling on a wall at varying rotation rates

A study investigating the flow around a cylinder rolling or sliding on a wall has been undertaken in two and three dimensions. The cylinder motion is specified from a set of five discrete rotation rates, ranging from prograde through to retrograde rolling. A Reynolds number range of 20–500 is considered. The effects of the nearby wall and the imposed body motion on the wake structure and dominant wake transitions have been determined. Prograde rolling is shown to destabilize the wake flow, while retrograde rotation delays the onset of unsteady flow to Reynolds numbers well above those observed for a cylinder in an unbounded flow. Two-dimensional simulations show the presence of two recirculation zones in the steady wake, the lengths of which increase approximately linearly with the Reynolds number. Values of the lift and drag coefficient are also reported for the steady flow regime. Results from a linear stability analysis show that the wake initially undergoes a regular bifurcation from a steady two-dimensional flow to a steady three-dimensional wake for all rotation rates. The critical Reynolds number Re c of transition and the spanwise wavelength of the dominant mode are shown to be highly dependent on, but smoothly varying with, the rotation rate of the cylinder. Varying the rotation from prograde to retrograde rolling acts to increase the value of Re c and decrease the preferred wavelength. The structure of the fully evolved wake mode is then established through three-dimensional simulations. In fact it is found that at Reynolds numbers only marginally (~5%) above critical, the three-dimensional simulations indicate that the saturated state becomes time dependent, although at least initially, this does not result in a significant change to the mode structure. It is only at higher Reynolds numbers that the wake undergoes a transition to vortex shedding. An analysis of the three-dimensional transition indicates that it is unlikely to be due to a centrifugal instability despite the superficial similarity to the flow over a backward-facing step, for which the transition mechanism has been speculated to be centrifugal. However, the attached elongated recirculation region and distribution of the spanwise perturbation vorticity field, and the similarity of these features with those of the flow through a partially blocked channel, suggest the possibility that the mechanism is elliptic in nature. Some analysis which supports this conjecture is undertaken.

Numerical and experimental studies of the rolling sphere wake

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 unsteady mode as the Reynolds number increases. During the evolution of this unsteady mode, the streamwise vortices form an out-of-phase spiral pair. Four primary wake modes are identified and a very good qualitative agreement is observed between the numerical and experimental results. The numerical simulations also reveal the existence of an additional unsteady mode that is found to be unstable to small perturbations in the flow.

Flow dynamics and forces associated with a cylinder rolling along a wall

The wake flow structures and the drag force for a cylinder rolling along a wall without slipping were calculated for the Reynolds number range 20<Re<200, covering the two-dimensional shedding regime. Time-dependent numerical computations show the wake undergoes a steady to periodic shedding transition between 85<Re<90. The Strouhal number varies only weakly at higher Reynolds number, and is a factor of 3–4 lower than for an isolated rotating or nonrotating body. Also, within this shedding regime, the wake is characterized by counter-rotating vortex pairs, which propagate away from the wall via mutual induction. These pairs are formed as compact vortex structures from the top separating shear layer induce secondary vorticity at the wall, which is pulled up from the boundary to form the semidiscrete flow structures. Over both the steady and unsteady regimes, the (time-mean) recirculation length and drag are quantified.

Wake formation behind a rolling sphere

Experimental flow visualizations are presented depicting the flow behind a spherical body moving on a plane wall. In the Reynolds number range of 100<Re<350, four distinct wake modes occur which are dependent on the imposed rotation rate of the body. Five different rotation rates are examined: two with forward rolling, one with pure translation (zero rotation), and two with reversed rolling. As the sphere undergoes forward rolling, steady and unsteady wake modes are observed which bear similarities to the flow behind an isolated sphere in a free stream. However, for cases with reversed and zero rotation of the sphere, a new antisymmetric wake mode is discovered.

The Wake Dynamics of a Cylinder Moving Along a Plane Wall with Rotation and Translation

A numerical investigation examined the 2-dimensional flow structures forming around a cylinder moving along a wall with different combinations of rolling and sliding, with Reynolds numbers, Re, ranging from 20 to 500. Past research has shown that both wall effects and rotation can suppress the mechanisms which bring about unsteady flow. Knowing this, it is natural to question how the flow will be affected when both these properties are present, as is the case for the cylinder rolling along a wall. Results indicate that the transition from steady to time-varying flow is strongly influenced by the rate of rotation of the body, and for the case of reversed rolling, the onset of unsteady flow is delayed until Reynolds numbers above 400.