Closely spaced co-rotating helical vortices: General solutions
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE（艾克斯马赛大学、法国国家科学研究中心、中央马赛学院、IRPHE）；Departamento de Bioingeniería e Ingeniería Aeroespacial, Universidad Carlos III de Madrid（马德里卡洛斯三世大学生物工程与航空航天工程系）
Andrés Castillo-Castellanos, Eduardo Durán Venegas, Stéphane Le Dizès
In this work, we present general solutions for closely spaced co-rotating helical vortices using a filament approach. For these vortex structures, helical symmetry is broken, but solutions maintain a form of spatial periodicity. We show there exists a moving frame where vortex elements move along the structure without distorting it. These solutions can be used to characterize the evolution of the twin-tip vortices produced in the wake of a tip-splitting rotor blade. The resulting wake has a dual nature. Locally, the structure behaves much like an helical pair aligned with the locally tangent flow. However, as we move away from the vortex structure the induced flow is reminiscent of an 'equivalent' helical vortex with thicker core.
Embedded vortices in turbulent wall-bounded flow over a flat plate, generated by a passive rectangular vane-type vortex generator with variable angle $β$ to the incoming flow in a low-Reynolds number flow ($Re=2600$ based on the inlet grid mesh size $L=0.039\;$m and free stream velocity $U_{\infty} = 1.0\;$m s$^{-1}$) have been studied with respect to helical symmetry. The studies were carried out in a low-speed closed-circuit wind tunnel utilizing Stereoscopic Particle Image Velocimetry (SPIV). The vortices have been shown to possess helical symmetry, allowing the flow to be described in a si…
High resolution direct numerical simulations of rotating and flapping bumblebee wings are presented and their aerodynamics is studied focusing on the role of leading edge vortices and the associated helicity production. We first study the flow generated by only one rotating bumblebee wing in circular motion with $45^{\circ}$ angle of attack. We then consider a model bumblebee flying in a numerical wind tunnel, which is tethered and has rigid wings flapping with a prescribed generic motion. The inflow condition of the wind varies from laminar to strongly turbulent regimes. Massively parallel si…
The presented investigation is motivated by the need to uncover connections between underlying rotor fluid-structure interactions and vortex dynamics to fatigue performance and characterization of flexible rotor blades, their hub, and their supporting superstructure. Towards this effort, temporal stability characteristics of tip vortices shed from flexible rotor blades are investigated numerically. An aeroelastic free-vortex wake method is employed to simulate the helical tip vortices and the associated velocity field. A linear eigenvalue stability analysis is employed to quantify stability tr…
We study the reconnection of vortices in a quantum fluid with a roton minimum, by numerically solving the Gross-Pitaevskii (GP) equations. A non-local interaction potential is introduced to mimic the experimental dispersion relation of superfluid $^4\mathrm{He}$. We begin by choosing a functional shape of the interaction potential that allows to reproduce in an approximative way the so-called roton minimum observed in experiments, without leading to spurious local crystallization events. We then follow and track the phenomenon of reconnection starting from a set of two perpendicular vortices. …
In superfluid helium, vorticity is quantized and constrained on line-like phase singularities, called quantum or quantized vortices. By visualizing the motion of sub-micron frozen particles in superfluid $^{4}$He, we directly observe for the first time the helical Kelvin waves excited after quantized vortex reconnections. We compare the data with self-similar solutions of vortex filament models. We report the results in a fluid dynamic video.
Floating offshore wind turbines (FOWTs) are subjected to platform motion induced by wind and wave loads. The oscillatory movement trigger vortex instabilities, modifying the wake structure, influencing the flow reaching downstream wind turbines. In this work, the wake of a FOWT is analysed by means of numerical simulations and comparison with linear stability theory. Two simplified models based on the stability of vortices are developed for all degrees of freedom of turbine motion. In our numerical simulations, the wind turbine blades are modeled as actuator lines and a spectral-element method…
Two vortex rings can form a localized configuration whereby they continually pass through one another in an alternating fashion. This phenomenon is called leapfrogging. Using parameters suitable for superfluid helium-4, we describe a recurrence phenomenon that is similar to leapfrogging, which occurs for two coaxial straight vortex filaments with the same Kelvin wave mode. For small-amplitude Kelvin waves we demonstrate that our full Biot-Savart simulations closely follow predictions obtained from a simpified model that provides an analytical approximation developed for nearly parallel vortice…
The near wake of a small-scale wind turbine is investigated using Particle Image Velocimetry (PIV) experiments at different tip speed ratios ($λ$). The wind turbine model had a nacelle and a tower mimicking real scale wind turbines. The near wake is found to be dominated by multiple coherent structures including the tip vortices, distinct vortex sheddings from the nacelle and tower, and wake meandering. The merging of the tip vortices is found to be strongly dependent on $λ$. A convective length scale ($L_c$) related to the pitch of the helical vortices is defined which is shown to be a better…
Structured light has emerged as an important tool to interrogate and manipulate matter at micron and sub-micron scale. One form of structured light is an optical vortex beam. The helical wavefront of these vortices carry orbital angular momentum which can be transferred to a Brownian colloid. When the colloid is made of metallic nanostructures, such as silver and gold, resonant optical effects play a vital role, and the interaction leads to complex dynamics and assembly. This brief review aims to discuss some recent work on trapping plasmonic colloids with optical vortices and their lattices. …
We generate vortex tangles using a Hopf flow on a 3-sphere, in place of the standard torus defined by periodic boundary conditions. These tangles are highly anisotropic, with vortices tending to align along the flow direction. Standard power law dependences change accordingly from their values in more isotropic tangles. The line length density $\langle L\rangle$ is proportional to $v_{ns}^{1.28}$, where $v_{ns}$ is the drive velocity, and the reconnection rate depends roughly on $\langle L\rangle^2$. We also discuss the effect of the full Biot-Savart law versus the local induction approximatio…
