Vortex formation and decay - The scaling of vortex-wall interaction
EuHIT project "ANNI: Vorticity annihilation at high Reynolds numbers - A question of initial conditions?"
Dr. David E. Rival, Queen's University, Kingston, Ontario, Kanada
Dr. Joel Sommeria, CNRS, Grenoble, France
The formation of vortices is ubiquitous in many flow occuring in nature. For instance, a large variety of swimmers and flyers accelerate their propulsors (i.e. wings or flippers) to obtain flow separation and the subsequent roll-up of a vortex. In case the vortices stay attached to the propulsor, the interaction of the pressure minimum in the vortex with the propulsor itself can be utilized to produce thrust and/or lift while maintaining a high degree of maneuverability. Dimension analysis on the kinematics of various animals revealed similarities concerning the stroke frequencies (Strouhal number, 0.2<St<0.4) and the importance of rotational accelerations for the long-term stability of a vortex (Rossby number, Ro<4). Interestingly, St and Ro remain in a small margin for a wide range of Reynolds numbers (Re) reaching from the laminar (small insects) to the highly turbulent regime (large mammals). The present project strives to gain insights into Re-effects on vortices. In particular, it is investigated how turbulence influences vortex formation and decay.
Figure 1: Left side and middle: Lagrangian visualization of the turbulent flow in an impulsively-stopped, rotating cylinder at two time instances (DNS data). Right side: PIV setup at the CORIOLIS platform.
The project is subdivided into three subprojects. The first two projects aim towards a fundamental understanding of the cross-annihilation of vorticity in vortex-wall interaction. The boundary layer between a propulsor and an attached vortex is unique as it is dominated by the interaction of the vorticity inside the vortex and the opposite-signed vorticity in the boundary layer. Such a boundary layer is abstracted by impulsively stopping a cylinder, containing a fluid in solid body rotation. A temporally-developing boundary layer forms and passes through multiple stages before the flow is quiescent. Each of the stages contains flow features that result from the interaction of opposite-signed vorticity. In addition, the behavior of all stages (i.e. transition, turbulence, the decay of turbulence) is influenced by Re. In the first project, a highly resolved direct numerical simulation (DNS) is performed for the impulsively-stopped cylinder at small to medium Re. In the second project, the Re range is extended to very high Re by measurements at the CORIOLIS platform in Grenoble. The 13m-diameter platform (containing ~180m³ of water) is decelerated to rest and the boundary-layer formation is captured by means of large-scale planar and stereo particle image velocimetry (PIV) measurements.
Figure 2: Left side: PIV setup at Queen's University. Middle and right side: three-dimensional vortex wakes reconstructed from PIV for a circular plate and a plate with edge undulation.
The third project shifts the focus on the influence of turbulence on vortex formation. In a 15m-long towing tank at Queen's University, a circular plate is accelerated perpendicular to its orientation, resulting in a vortex wake behind the plate. Hereby, the separated shear layer that rolls up to the vortex is influenced by varying Re and by aplying multiple distinct modifications of the propulsors circumferential vortex-forming edge. Both, a wide range of Re and various undulatory edge modifications of different wavelengths are tested. This allows to address the effects of small scale three-dimensional flow structures (increase of Re) and large scale disturbances (large wavelengths of the edge undulation) on vortex formation, vortex stability, and the obtained propulsion force.