Entrainment and topology of accelerating shear layers

2021

Phys. Rev. Fluids

Ring vortices are efficient at transporting fluid across long distances. They can be found in nature in various ways: they propel squids, inject blood in the heart, and entertain dolphins. These vortices are generally produced by ejecting a volume of fluid through a circular orifice. The impulse given to the vortex rings moving away results in a propulsive force on the vortex generator. Propulsive vortex rings have been widely studied and characterised. After four convective times, the vortex moves faster than the shear layer it originates from, and separates from it. This separation corresponds to a maximum circulation of the vortex and a maximal spread of the vorticity in the vortex, quantified by the non-dimensional energy. The simultaneity of these three events obfuscate the causality between them. To analyse the temporal evolution of the non-dimensional energy of ring vortices independent of their separation, we analyse the spatiotemporal development of vortices generated in the wake of cones. Cones with different apertures and diameters were accelerated from rest to produce a wide variety of vortex rings and their energy, circulation, and velocity were extracted based on time-resolved velocity field measurements. The vortex rings that form behind the cones have a self-induced velocity that cause them to follow the cone and they continue to grow as the cone travels well beyond the limiting vortex formation times scales observed for propulsive vortices. The non-dimensional circulation, based on the vortex diameter, and the non-dimensional energy of the drag vortex rings converge after three convective times to values comparable to their propulsive counterparts. This results proves that vortex pinch-off does not cause the non-dimensional energy to reach a minimum value. The limiting values of the non-dimensional circulation and energy are mostly independent of the cone geometry and translational velocity and fall within an interval of 10% around the mean value. With only 6% of variation, the velocity of the vortex is the most unifying quantity that governs the formation of vortex rings behind cones.

Section: Spatial and Temporal Development Of A Drag Vortex Ringmentioning

confidence: 99%

Scaling of the translational velocity of vortex rings behind conical objects

Guyon

2021

Phys. Rev. Fluids

“…The life of vortices around bluff bodies often begins with a shear layer (Jeon & Gharib 2004;Fernando & Rival 2016;Fernando et al 2017;Rosi & Rival 2017;Corkery, Babinsky & Graham 2019). When a bluff body moves relative to a fluid flow, a thin layer of fluid emerges at the edge of the body where non-zero shear flow gradients are present.…”

Section: Introductionmentioning

confidence: 99%

“…This range corresponds to a Strouhal number around 0.2, according to the plate geometry and kinematics used by the authors. The secondary vortex shedding frequency behind a vertical flat plate increases with increasing acceleration of the flat plate according to Rosi & Rival (2017). It is crucial to define a scaling parameter, such as the Strouhal frequency for the cylinder case, that allows for a more universal relationship between the shedding frequency or formation time of primary and secondary vortices as a function of the Reynolds number.…”

Section: Introductionmentioning

confidence: 99%

Discrete shedding of secondary vortices along a modified Kaden spiral

Francescangeli

2021

J. Fluid Mech.

“…However, there is no consensus about the exponent value of the proposed relationship. Prasad and Williamson (1997) indicated that an exponent value of 0.67 works for Re up to 10 5 and Wei and Smith (1986) (Rosi and Rival, 2017).…”

Section: Introductionmentioning

confidence: 99%

“…Every kind of two-dimensional motions can be decomposed into a pure rotation and a translation. An extensive body of literature can be found that discusses the vortex formation behind translating objects (de Guyon and Fernando and Rival, 2016;Rosi and Rival, 2017;Paraz et al, 2016). The vortex formation process on a rotation object has received less attention.…”

Section: Introductionmentioning

confidence: 99%

Strength and timing of primary and secondary vortices generated by a rotating plate

Francescangeli

2023

Preprint

Accurate predictions of how vortices grow, evolve, and separate from aerodynamic objects are desirable for various applications ranging from autonomous aerial vehicles to wind turbines. Here, we present an experimental characterisation of the formation process of vortices created by the rotation of a thin rectangular flat plate. The plate is rapidly accelerated from rest up to a constant rotational velocity that was varied to explore the effect of the Reynolds number on the limit strength and the timing of successively generated vortices at the tip of the plate. The total non-dimensional positive circulation released at the tip of the plate during the entire rotation varies solely as a function of the angular position of the plate. Initially, all this circulation accumulates in a primary or starting vortex until this vortex separates after a constant non-dimensional time for all rotational velocities and different plate dimensions tested. An empirical model of the prediction of the limit strength of the primary vortex based on the constant non-dimensional formation is presented. The limit strength of the primary vortex is independent of the Reynolds number. After the primary vortex separates, a series of smaller secondary vortices form at the tip of the plate. These secondary vortices are discretely released at increasing time intervals. The timing of the release of the secondary vortices and their non-dimensional strength depend on the Reynolds number, and an empirical prediction model is presented.