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Concept

Tourbillon (physique)

Résumé

vignette|upright=0.65|Tourbillon d'eau dans une bouteille. Un tourbillon est, en dynamique des fluides, une région d'un fluide dans laquelle l'écoulement est principalement un mouvement de rotation autour d'un axe, rectiligne ou incurvé. Ce type de mouvement s'appelle écoulement tourbillonnaire. On en observe à toutes les échelles, depuis le tourbillon de vidange d'une baignoire jusqu'à ceux des atmosphères des planètes, en passant par les sillages observés au voisinage d'un obstacle situé dans un écoulement liquide ou gazeux. Une fois formés, les tourbillons peuvent se déplacer, s'étirer, se tordre et interagir de manière complexe. Une façon simple de visualiser le tourbillon est de considérer un fluide en mouvement dans lequel on délimite un petit volume supposé rigide. Si ce volume tourne par rapport à un référentiel au lieu d'être en translation, il appartient à un tourbillon. Terminologie vignette|upright=1.0|Mouvement d'un petit volume (rigide) de fluide : translat

Source officielle

https://fr.wikipedia.org/wiki/Tourbillon_(physique)

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Growth, timing, & trajectory of vortices behind a rotating plate

Diego Francescangeli

The presence of aerodynamic vortices is widespread in nature. They can be found at small scales near the wing tip of flying insects or at bigger scale in the form of hurricanes, cyclones or even galaxies. They are identified as coherent regions of high vorticity where the flow is locally dominated by rotation over strain. A better comprehension of vortex dynamics has a great potential to increase aerodynamic performances of moving vehicles, such as drones or autonomous underwater vehicles. An accelerated flat plate, a pitching airfoil or a jet flow ejected from a nozzle give rise to the formation of a primary vortex, followed by the shedding of smaller secondary vortices. We experimentally study the growth, timing and trajectory of primary and secondary vortices generated from a rectangular flat plate that is rotated around its centre location in a quiescent fluid. We systematically vary the rotational speed of the plate to get a chord based Reynolds number \Rey that ranges from 800 to 12000. We identify the critical \Rey for the occurrence of secondary vortices to be at 2500. The timing of the formation of the primary vortex is \Rey independent but is affected by the plate's dimensions. The circulation of the primary vortex increases with the angular position

\alpha

of the plate, until the plate reaches 30°. Increasing the thickness and decreasing the chord lead to a longer growth of the primary vortex. Therefore, the primary vortex reaches a higher dimensionless limit strength. We define a new dimensionless time

T^*

based on the thickness of the plate to scale the age of the primary vortex. The primary vortex stops growing when

T^* \approx 10

, regardless of the dimensions of the plate. We consider this value to be the vortex formation number of the primary vortex generated from a rotating rectangular flat plate in a Reynolds number range that goes from 800 to 12000. When

\alpha

> 30°, the circulation released in the flow is entrained into secondary vortices for

\Rey > 2500

. The circulation of all secondary vortices is approximately 4 to 5 times smaller than the circulation of the primary vortex. We present a modified version of the Kaden spiral that accurately predicts the shear layer evolution and the trajectory of primary and secondary vortices during the entire rotation of the plate.We model the timing dynamics of secondary vortices with a power law equation that depends on two distinct parameter:

\chi

and

\alpha_{0}

.The parameter

\chi

indicates the relative increase in the time interval between the release of successive secondary vortices.The parameter

\alpha_{0}

indicates the angular position at which the primary vortex stops growing and pinches-off from the plate.We also observe that the total circulation released in the flow is proportional to

\alpha^{1/3}

, as predicted by the inviscid theory.The combination of the power law equation with the total circulation computed from inviscid theory predict the strength of primary and secondary vortices, based purely on the plate's geometry and kinematics.The strength prediction is confirmed by experimental measurements.In this thesis we provided a valuable insight into the growth, timing and trajectory of primary and secondary vortices generated by a rotating flat plate. Future work should be directed towards more complex object geometries and kinematics, to confirm the validity of the modified Kaden spiral and explore the influence on the formation number.

EPFL2022

Chargement

Vortex rings are very efficient at transporting fluid on long distances and can generate large forces, either thrust or drag. These abilities are influenced by the vorticity distribution within the vortex. Previous work on vortices produced by piston-cylinders showed that the vorticity distribution reaches a steady state when the vortex separates from the apparatus. First, we experimentally investigate the evolution of the vorticity distribution independently of the vortex separation. The vortices are created by impulsively accelerating cones immersed in water. In this configuration, the self-induced velocity of the vortex is directed towards the cone and there is no separation. Particle image velocimetry is carried on at Reynolds numbers around 30000. The vorticity distribution is quantified using the non-dimensional energy of the vortex, which is the energy with respect to the impulse and circulation. After three convective times, the volume of fluid recirculating within the vortex ring is filled with vortical fluid and the non-dimensional energy to a value around 0.3. The vorticity produced on the cone circumvents the vortex and a portion of the vortex volume is lost via tail-shedding. The translational velocity of the vortex ring linearly depends on its circulation and non-dimensional energy. This velocity, relative to the cone, also converges after three convective times and is found to be a more reliable scaling parameter than energy or circulation. It consistently reaches values around 0.9. In a second part, we present models to predict the vortex growth in the wake of disks and cones. Two models are developed. The first model reduces the vortex ring to a core of constant vorticity density. The translational velocity of the vortex is deduced and its trajectory integrated. The model accurately predicts the maximum circulation of the vortex. A second model, based on axisymmetric discrete vortex methods, predicts the growth, vorticity distribution and tail-shedding of the vortex. A third model is developed to explain why the non-dimensional energy consistently converges to values around 0.3. Based on the self similar roll-up of inviscid shear layers, a non-dimensional energy of 0.33 is computed for vortices formed by impulsively accelerated disks or pistons. The model also predicts that a linear acceleration profile leads to a more uniform vorticity distribution, decreasing the non-dimensional energy to 0.18. This result indicates that the vorticity distribution can be controlled by varying the velocity profile of the vortex generator. Another control option is to use permeable disks. We impulsively accelerated perforated disks and observed the vortex formation. A portion of the incoming flow bleeds through the disk and does not circulate around the disk edge, resulting in a lower vorticity maximum. The vortex ring has a more uniform vorticity distribution, as well as a more elongated shape. The non-dimensional energy is brought down to 0.14. Finally, vortex rings have a great potential to transport fluid on long distances, such as extinguishing powder. Their resilience to vortical perturbations is critical for the transport and depends on the vorticity distribution within the vortex. Simulations with nested contour methods are performed to assess that resilience. Vortices with lower non-dimensional energy shed less vortical volume when facing perturbations and qualify as better candidates for fluid transport.

EPFL2021

Chargement

Dynamic stall on an airfoil undergoing VAWT blade angle of attack variations

Sabrina Henne, Sébastien Le Fouest, Karen Ann J Mulleners

Vertical axis wind turbines have several attractive features in the context of energy production in urban areas, but the inherent aerodynamic complexity of the flow around them has challenged their development on a larger scale. They generally operate at low tip speed ratios, where dynamic stall occurs on the blades. The vortex shedding associated with dynamic stall causes highly transient and heavy stress cycles that reduce the aerodynamic performance and increase the risk of fatigue and failure. The flow around an airfoil undergoing VAWT blade angle of attack variations was investigated using particle image velocimetry and force measurements. The formation of vortices and the lift force were studied for different tip speed ratios. A special focus was put on the effect of the asymmetry of the motion. The role of dynamic stall vortices on aerodynamic coeffients was evidenced by comparing experimental data to analytical predictions obtained from Theodorsen's model. For the lowest equivalent tip speed ratio clockwise and counter clockwise rotating dynamic stall vortices formed on the airfoil with increasing and decreasing angle of attack. The asymmetry in motion lead to an asymmetry in size of the clockwise and counter-clockwise vortices. As the asymmetry in motion has a strong effect on the flow behaviour, the local pitch rate was proposed as a governing parameter. The increase of extrema with increasing pitch rate varies for increasing and decreasing angle of attack, indicating an additional influence of the history of the flow development.

2020

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EPFL2021

Growth, timing, & trajectory of vortices behind a rotating plate

Diego Francescangeli

\alpha

T^*

based on the thickness of the plate to scale the age of the primary vortex. The primary vortex stops growing when

T^* \approx 10

\alpha

> 30°, the circulation released in the flow is entrained into secondary vortices for

\Rey > 2500

\chi

and

\alpha_{0}

.The parameter

\chi

indicates the relative increase in the time interval between the release of successive secondary vortices.The parameter

\alpha_{0}

indicates the angular position at which the primary vortex stops growing and pinches-off from the plate.We also observe that the total circulation released in the flow is proportional to

\alpha^{1/3}

EPFL2022