The non-dimensional energy of starting vortex rings typically converges to values around 0.33 when they are created by a cylinder piston or a bluff body translating at a constant speed. To explore the limits of the universality of this value and to analyse the variations that occur outside of those limits, we present an alternative approach to the slug-flow model to predict the non-dimensional energy of a vortex ring. Our approach is based on the self-similar vortex sheet roll-up described by Pullin. We derive the vorticity distribution for the vortex core resulting from a spiralling shear layer roll-up and compute the associated non-dimensional energy. To demonstrate the validity of our model, we consider different velocity profiles of the vortex generator that follow a power-law with a variable exponent m. For a constant velocity (m=0), our model yields a non-dimensional energy of E*=0.33. For a constant acceleration (m=1), we find E*=0.19. For a constant velocity, we obtain realistic vorticity distributions by radially diffusing the vorticity distribution of the Pullin spiral and predict a decrease of the non-dimensional energy from 0.33 to 0.28, in accordance with experimental results. Our proposed model offers a practical alternative to the existing slug flow model to predict the minimum non-dimensional energy of a vortex ring. The model is applicable to piston-generated and wake vortex rings and requires only the kinematics of the vortex generator as input.
The transition from Tayor vortex flow to wavy-vortex flow is revisited. The Self-Sustaining Process (SSP) of Waleffe [Phys. Fluids 9, 883-900 (1997)] proposes that a key ingredient in transition to turbulence in wall-bounded shear flows is a three-step process involving rolls advecting streamwise velocity, leading to streaks which become unstable to a wavy perturbation whose nonlinear interaction with itself feeds the rolls. We investigate this process in Taylor-Couette flow. The instability of Taylor-vortex flow to wavy-vortex flow, a process which is the inspiration for the second phase of t…
Three dimensional roll-type double-diffusive convection in a horizontally infinite layer of an uncompressible liquid is considered in the neighborhood of Hopf bifurcation points. A system of amplitude equations for the variations of convective rolls amplitude is derived by multiple-scaled method. An attention is paid to an interaction of convection and horizontal vortex. Different cases of the derived equations are discussed.
This contribution relates to the simulation of the flow around the tip of a helicopter rotor blade in hovering flight conditions. We here propose a new methodology of framework adaptation, using a comprehensive rotor code and high-fidelity numerical simulations. We construct an equivalent fixed-wing configuration from a rotating blade, in which centrifugal and Coriolis forces are neglected. The effect of this approximation on the solution is analysed. The method is validated by a detailed comparison with wind tunnel data from the literature, concerning aerodynamic properties and tip vortex rol…
A hypothesis is tested and validated for predicting the vortex strength induced by a vortex generator in wall-bounded flow by combining the knowledge of the Vortex Generator (VG) geometry and the approaching boundary layer velocity distribution. In this paper, the spanwise distribution of bound circulation on the vortex generator is computed from integrating the pressure force along the VG height calculated using CFD. It is then assumed that all this bound circulation is shed into the wake to fulfill Helmholtz's theorem and then curl up into one primary tip vortex. To validate this, the traile…
When an object is accelerated in a fluid, a primary vortex is formed through the roll-up of a shear layer. This primary vortex does not grow indefinitely and will reach a limiting size and strength. Additional vorticity beyond the critical limit will end up in a trailing shear layer and accumulate into secondary vortices. The secondary vortices are typically considerably smaller than the primary vortex. Here, we focus on the formation, shedding, and trajectory of secondary vortices generated by a rotating rectangular plate in a quiescent fluid using time-resolved particle image velocimetry. Th…
We present experiments on the instability and fragmentation of volumes of heavier liquid released into lighter immiscible liquids. We focus on the regime defined by small Ohnesorge numbers, density ratios of order one, and variable Weber numbers. The observed stages in the fragmentation process include deformation of the released fluid by either Rayleigh-Taylor instability or vortex ring roll-up and destabilization, formation of filamentary structures, capillary instability, and drop formation. At low and intermediate Weber numbers, a wide variety of fragmentation regimes is identified. Those …
Playing a role in the locomotion of some animals such as the water strider, the formation and dynamics of a semi vortex ring connected to a free surface are experimentally investigated. This semi vortex ring is generated by the circular motion of a flat circular disk in water. Digital Particle Image Velocimetry provides velocity fields and vortex properties. We show how in a broad range of Reynolds numbers, the properties of the semi vortex rings are related to the disk characteristics. In particular, our results highlight a formation process more complex than for a complete vortex ring produc…
We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. An analytical solution is permitted via integration of the Euler equations. Although similar problems were investigated in the 1960's and 70's for special cases of resonance, this is to our knowledge the first general wave interaction (mode coupling) solution derived to second order with a shear current present. Wave interactions are integrable in a spectral convolution to yield the second order dynamics of initial value problems. To seco…
Vortex rings have the ability to transport fluid over long distances. They are usually produced by ejecting a volume of fluid through a circular orifice or nozzle. When the volume and velocity of the ejected fluid are known, the vortex' circulation, impulse, and energy can be estimated by the slug flow model. Vortex rings also form in the wake of accelerating axisymmetric bodies. In this configuration, the volume and velocity of the fluid that is injected into the vortex is not known a priori. Here, we present two models to predict the growth of the vortex behind disks or cones. The first mode…
Flexible broad leaves are thought to reconfigure in the wind and water to reduce the drag forces that act upon them. Simple mathematical models of a flexible beam immersed in a two-dimensional flow will also exhibit this behavior. What is less understood is how the mechanical properties of a leaf in a three-dimensional flow will passively allow roll up into a cone shape and reduce both drag and vortex induced oscillations. In this fluid dynamics video, the flows around the leaves are compared with those of simplified sheets using 3D numerical simulations and physical models. For some reconfigu…
We investigate the various physical mechanisms that underlie the dynamical instability of a quantized vortex array at the interface between two counter-propagating superflows in a two-dimensional Bose--Einstein condensate. Instabilities of markedly different nature are found to dominate in different flow velocity regimes. For moderate velocities where the two flows are subsonic, the vortex lattice displays a quantized version of the hydrodynamic Kelvin--Helmholtz instability (KHI), with the vortices rolling up and co-rotating. For supersonic flow velocities, the oscillation involved in the KHI…
We perform DNS of flow over finite-aspect-ratio NACA 0015 wings to characterize the tip effects on the wake dynamics. This study focuses on the development of three-dimensional separated flow over the wing, and discuss flow structures formed on the wing surface as well as in the far field wake. Vorticity is introduced into the flow in a predominantly two-dimensional manner. The vortex sheet from the wing tip rolls up around the free end to form the tip vortex. At its inception, the tip vortex is weak and its effect is spatially confined. As the flow around the tip separates, the tip effects ex…
Transition to chaos in two-dimensional Rayleigh-Bénard convection: the role of the magnetic field
Government of the State of Goiás (SEDUC-GO)（戈亚斯州政府）；Technological Institute of Aeronautics (ITA)（航空技术学院）；University of Porto（波尔图大学）；Federal Rural University of the Amazon (UFRA)（亚马逊联邦农村大学）
