Absolute and convective instabilities of a swirling jet/wake shear layer

International audienceThe absolute (AI)/convective (CI) nature of the instability is determined in the family of swirling jet/wake shear layers considered by Martin and Meiburg [Phys. Fluids 6, 424 (1994)] and Lim and Redekopp [Eur. J. Mech. B/Fluids 17, 165 (1998)]. This idealized model includes as essential ingredients both the centrifugal instability associated with the swirl difference and the Kelvin-Helmholtz instability associated with the swirl and axial velocity differences between the core and the outer flow. Centrifugally stabilizing or destabilizing swirl differences are found to promote AI, but a centrifugally destabilizing configuration is more effective in triggering such a transition. For sufficiently large swirl differences, both co-flowing jets and wakes may become AI. In the case of jets, a centrifugally destabilizing swirl difference first brings about AI via the axisymmetric mode m=0 in a large range of mean swirl values. By contrast, a centrifugally stabilizing swirl difference triggers AI via the helical mode m=-8. In the case of wakes, a centrifugally destabilizing swirl difference leads to AI via the bending mode m-1 whereas a centrifugally stabilizing swirl difference triggers AI via various negative helical modes m=-1,-2, etc. © 2000 American Institute of Physics

Reconnexion de vortex 3D : simulation et modelisation

Deux tourbillons initialement quasi rectilignes et tournant en contra-rotation se reconnectent de proche en proche pour former des anneaux. Dans cette étude, on simule une reconnexion unique par simulation numérique directe à Re=1500 (basé sur la circulation des vortex). A cette simulation numérique est associé un modèle 2D par lequel les effets 3D, dus à la courbure des vortex, sont pris en compte à travers la superposition d'un simple champ de déformation 3D uniforme instationnaire issu de la DNS. Des différences avec la description de Saffman (1990) sont mises en évidence, en particulier une éjection de vorticité au moment de la reconnexion, qui affaiblit considérablement les deux vortex dans la région de reconnexion

Interaction vorticité/déformation des monopôles et des dipôles

Par des approches théoriques et numériques, nous généralisons aux vortex non uniformes la relation établie par Moore & Saffman (1971) entre l'ellipticité d'un patch de vorticité et le champ de déformation extérieure qu'il subit. Nous en montrons les implications dans le cadre des monopôles et celui des dipôles

Vortex rings generated by a translating disk from start to stop

In this article, we investigate experimentally and numerically the time evolution of vortex rings generated by the translation of a rigid disk in a fluid initially at rest and submitted to an acceleration followed by a deceleration. The size of the disk and its motion in terms of stroke length and travel time are varied as control parameters. The start-up vortex ring created in the near wake of the disk is characterized experimentally by PIV, and the measurements agree quantitatively with axisymmetric numerical simulations performed with the Basilisk flow solver. The maximum radius and circulation of the annular vortex and its dynamics are shown to follow different power laws with the control parameters. The modeling adapted from Wedemeyer's two-dimensional theoretical calculations [E. Wedemeyer, Ausbildung eines Wirbelpaares an den Kanten einer Platte, Ingenieur-Archiv 30, (1961)] captures the observed scaling laws. Besides, after the disk stops, a secondary ``stopping" vortex ring is generated, which is shown to affect the motion of the main vortex ring

Helical vortex systems: linear analysis and nonlinear dynamics

The near wake behind helicopter rotors, wind turbines and more generally behind rotating devices are dominated by helical vortices. Investigating their stability properties is a necessary step to predict their dynamics. Instabilities in such vortex systems have mainly been studied theoretically (Widnall 1972 [1], Okulov [2] and Sørensen 2007 [3]) in an inviscid framework for small core size vortices. The aim of the present study is to generalize these works to the viscous framework for arbitrary core sizes and vorticity profiles.The base flows considered here are helically symmetric: fields are invariant through combined axial translation of distance z and rotation of angle θ= Δz/L around the z-axis, where 2π L denotes the helix pitch.We first perform a linear temporal stability analysis of these base flows, using an Arnoldi [4] procedure coupled to two different codes : (i) a linearised version of the helical DNS code HELIX [5], (ii) another linear code called HELIKZ, which computes the dynamics of arbitrary perturbations in the vicinity of a helically symmetric base flow. These two codes permit the investigation of different types of instability modes: (i) modes having the same helical symmetry as the base flow which generalize the Okulov modes ; (ii) modes depending on z as exp ikz which generalize the Widnall modes. In the first case (i), instabilities are found to be dominated by displacement modes of the type presented in figure 1 for the case of two vortices. In the second case (ii), modes will be compared to those observed in recent experimental work (Leweke et al. 2014 [6]). We then compute the nonlinear dynamics of a basic flow perturbed with a linear mode of type (i) set at a small initial amplitude. In the helical framework, the displacement mode is shown to be responsible for leap-frog dynamics (cf. figure 2) and/or vortex merging (cf. figure 3) with characteristics depending on the various parameters

Instability of a swirling bubble ring

A toroidal bubble or a cylindrical gas jet are known to be subjected to the Rayleigh-Plateau instability. Air bubble rings produced by beluga whales and dolphins however are observed that remain stable for long times. In the present work, we analyse the generation of such toroidal bubbles via numerical simulations, in particular how the process depends on surface tension. Their stability properties are then briefly analysed. For the estimated Reynolds and Weber numbers relative to the bubbles produced by these animals, the presence of a vortex inside and around the bubble is found to strongly stabilize the Rayleigh-Plateau instability

Free surface flow driven by a rotating end wall in a stationary cylinder: Structure of the axisymmetric base flow

We study the steady free-surface flow of a viscous liquid layer contained in a cylinder with a rotating bottom and a fixed lateral wall. When the disk rotates at large speed, the free surface deforms strongly and three-dimensional instability patterns (rotating polygons) or sloshing motions can arise. In order to get some insight on their formation mechanisms, a study of the axisymmetric base flow is carried out numerically. The flow structure consists of a well-known central fluid column entrained in a motion of solid-body rotation at the disk angular velocity. The fluid region situated at the periphery reveals a complex structure as it is found to be surrounded by four boundary layers. This leads us to discuss the relevance of existing base-flow models used for instability studies of this flow configuration

Dynamics of the three helical vortex system and instability

International audienceMany systems develop helical vortices in their wake (propellers, wind turbines, helicopters). Such flows can be assumed, at least locally, to be helically symmetric, i.e invariant through combined axial translation of distance ∆z and rotation of angle θ = ∆z/L around the same z-axis, where 2π L stands for the helix pitch. In this context, analytical and numerical works describing stationary vortices are mostly restricted to inviscid filaments and patches. Here, we present results obtained using a new DNS code with built-in helical symmetry able to simulate the viscous dynamics of distributed vorticity profiles. This approach contains the effects of 3D vortex curvature and torsion in a simple way and allows one to reach higher Reynolds numbers when compared to a full 3D DNS. In this framework, the long-time (or equivalently far-wake) dynamics of regularly spaced helical vortices is investigated. We focus here on the case of three identical vortices and simulate their dynamics as their pitch L and Reynolds number is varied. At large L, a “classical” three-vortex merging takes place, which resembles the 2D two-vortex merging however with slight differences. When L is reduced, it takes more and more time for the vortices to merge, as their rotation speed around the system axis is slowed down by self-induced vorticity effects. This phenomenon is explained by following the interplay between vorticity and streamfunction in the co-rotating frame of reference, and tracking the locus of hyperbolic points of the streamfunction. At low L-values, typically less than 1, the exponential instability described by Okulov and Sørensen is obtained, resulting in various grouping and merging scenarii at the nonlinear stage of evolution. At intermediate L-values of the order of 1, only viscous diffusion acts, resulting in a, slow, viscous type of merging. Note that other types of instability which are purely 3D are not described within this purely helical framework. Instead, the helical code run on a short period of time allows one to generate a quasi-steady flow state which may then be used to investigate such instabilities. A full 3D Navier–Stokes code is then used, linearized in the vicinity of the basic state, to extract the dominant instability properties

The dynamics of a viscous vortex dipole

International audienceabstrac