Three types of streamline topology in a Karman vortex street flow are shown under the variation of spatial parameters. For the motion of dilute particles in the Kármán vortex street flow, there exist a route of bifurcation to a chaotic orbit and more attractors in a bifurcation diagram for the proportion of particle density to fluid density. Along with the increase of spatial parameters in the flow filed, the bifurcation process is suspended, as well as more and more attractors emerge. In the motion of dilute particles, a drag term and gravity term dominate and result in the bifurcation phenomenon.
The Karman Vortex Street has been investigated for over a century and offers a reference case for investigation of flow stability and control of high dimensionality, non-linear systems. Active flow control, while of considerable interest from a theoretical point of view and for industrial applications, has remained inaccessible due to the difficulty in finding successful control strategies. Here we show that Deep Reinforcement Learning can achieve a stable active control of the Karman vortex street behind a two-dimensional cylinder. Our results show that Deep Reinforcement Learning can be used…
The splashing of a drop impacting onto a liquid pool produces a range of different sized micro-droplets. At high impact velocities, the most significant source of these droplets is a thin liquid jet emerging at the start of the impact from the neck that connects the drop to the pool. We use ultra-high-speed video imaging in combination with high-resolution numerical simulations to show how the ejecta gives way to irregular splashing. At higher Reynolds number, its base becomes unstable, shedding vortex rings into the liquid from the free surface in an axisymmetric von Kármán vortex street, thu…
Phase reduction theory has been applied to many systems with limit cycles; however, it has limited applications in incompressible fluid systems. This is because the calculation of the phase sensitivity function, one of the fundamental functions in phase reduction theory, has a high computational cost for systems with a large degree of freedom. Furthermore, incompressible fluid systems have an implicit expression of the Jacobian. To address these issues, we propose a new algorithm to numerically calculate the phase sensitivity function. This algorithm does not require the explicit form of the J…
We report on the experimental observation of vortex cluster shedding from a moving obstacle in an oblate atomic Bose-Einstein condensate. At low obstacle velocities $v$ above a critical value, vortex clusters consisting of two like-sign vortices are generated to form a regular configuration like a von Kármán street, and as $v$ is increased, the shedding pattern becomes irregular with many different kinds of vortex clusters. In particular, we observe that the Stouhal number associated with the shedding frequency exhibits saturation behavior with increasing $v$. The regular-to-turbulent transiti…
The vortex streets produced by a flapping foil of span-to-chord aspect ratio of 4:1 are studied in a hydrodynamic tunnel experiment. In particular, the mechanisms giving rise to the symmetry breaking of the reverse Bénard-von Kármán vortex street that characterizes fish-like swimming and forward flapping flight are examined. Two-dimensional particle image velocimetry measurements in the mid-plane perpendicular to the span axis of the foil are used to characterize the different flow regimes. The deflection angle of the mean jet flow with respect to the horizontal observed in the average velocit…
The knifefish species propels itself by generating a reverse Karman street from an anal fin and without significantly moving its body. This unique feature makes this species' propulsion method highly efficient (Blake, 1983). It has been suggested that there is an optimal swimming range for fish based on the amplitude and frequency of the reverse Kármán street. Experiments have been performed to measure the ratio between the amplitude and wavelength of vortices in the wake of a knifefish. It is suggested that by optimizing the thrust created by the reverse Karman street the wave efficiency can …
Although the stability properties of the wake past impervious bluff bodies have been widely examined in the literature, similar analyses regarding the flow around and through porous ones are still lacking. In this work, the effect of the porosity and permeability on the wake patterns of porous rectangular cylinders is numerically investigated at low to moderate Reynolds numbers in the framework of direct numerical simulation combined with local and global stability analyses. A modified Darcy-Brinkman formulation is employed here so as to describe the flow behavior inside the porous media, wher…
The effects of cavitation on the flow around a circular-cylinder array are studied by using a molecular dynamics simulation. Cavitation significantly affects on vortex shedding characteristics. As the cavitation develops,the vibration acting on the cylinders decreases and eventually disappears. The further cavitation development generates a longer vapor region next to the cylinders, and the vortex streets are formed at further positions from the cylinders. The neighboring Karman vortexes are synchronized in the antiphase in the absence of the cavitation. This synchronization is weakened by the…
The two-dimensional flows around a cylinder between two parallel walls at Re=40 and Re=100 are simulated with computational fluid dynamics (CFD). The governing equations are Navier-Stokes equations. They are discretized with finite volume method (FVM) and the solution is iterated with PISO Algorithm. Then, the calculating results are compared with the numerical results in literature, and good agreements are obtained. After that, the mechanism of the formation of Karman vortex street is investigated and the instability of the entire flow field is analyzed with the energy gradient theory. It is …
We study experimentally the vortex streets produced by a flapping foil in a hydrodynamic tunnel, using 2D Particle Image Velocimetry (PIV). An analysis in terms of a flapping frequency-amplitude phase space allows to identify: 1) the transition from the well-known Bénard-von Kármán (BvK) wake to the reverse BvK vortex street that characterizes propulsive wakes, and 2) the symmetry breaking of this reverse BvK pattern giving rise to an asymmetric wake. We also show that the transition from a BvK wake to a reverse BvK wake precedes the actual drag-thrust transition and we discuss the significanc…
Flow past a circular cylinder is investigated in the subcritical regime, below the onset of Benard-von Karman vortex shedding at Re_c ~ 47. The transient response of infinitesimal perturbations is computed. The domain requirements for obtaining converged results is discussed at length. It is shown that energy amplification occurs as low as Re=2.2. Throughout much of the subcritical regime the maximum energy amplification increases approximately exponentially in the square of Re reaching 6800 at Re_c$. The spatiotemporal structure of the optimal transient dynamics is shown to be transitory Bena…
Hysteresis has been observed in a study of the transition between laminar flow and vortex shedding in a quasi-two dimensional system. The system is a vertical, rapidly flowing soap film which is penetrated by a rod oriented perpendicular to the film plane. Our experiments show that the transition from laminar flow to a periodic Kármán vortex street can be hysteretic, i.e. vortices can survive at velocities lower than the velocity needed to generate them.
We study the behavior of an elastic loop embedded in a flowing soap film. This deformable loop is wetted into the film and is held fixed at a single point against the oncoming flow. We interpret this system as a two-dimensional flexible body interacting in a two-dimensional flow. This coupled fluid-structure system shows bistability, with both stationary and oscillatory states. In its stationary state, the loop remains essentially motionless and its wake is a von Kármán vortex street. In its oscillatory state, the loop sheds two vortex dipoles, or more complicated vortical structures, within e…
For problems with multiple bodies, the current integral approach needs the use of auxiliary potential functions in order to have an individual force formula for each body. While the singularity approach, based on an extension of the unsteady Lagally theorem, is restricted to multibody and multivortex flows without bound vortex and vortex production. In this paper, we consider multibody and multivortex flow and derive force formulas, in both forms of singularity approach and integral approach but without auxiliary function, that give individual forces of each body for unsteady two dimensional p…
A comparative assessment of machine learning (ML) methods for active flow control is performed. The chosen benchmark problem is the drag reduction of a two-dimensional Kármán vortex street past a circular cylinder at a low Reynolds number ($Re=100$). The flow is manipulated with two blowing/suction actuators on the upper and lower side of a cylinder. The feedback employs several velocity sensors. Two probe configurations are evaluated: 5 and 11 velocity probes located at different points around the cylinder and in the wake. The control laws are optimized with Deep Reinforcement Learning (DRL) …
A flexible foil undergoing pitching oscillations is studied experimentally in a wind tunnel with different imposed free stream velocities. The chord-based Reynolds number is in the range 1600--4000, such that the dynamics of the system is governed by inertial forces and the wake behind the foil exhibits the reverse Bénard-von Kármán vortex street characteristic of flapping-based propulsion. Particle Image Velocimetry (PIV) measurements are performed to examine the flow around the foil, whilst the deformation of the foil is also tracked. The first natural frequency of vibration of the foil is w…
The flow of a two--layer stratified fluid over an abrupt topographic obstacle, simulating relevant situations in oceanographic problems, is investigated numerically and experimentally in a simplified two--dimensional situation. Experimental results and numerical simulations are presented at low Froude numbers in a two-layer stratified flow and for two abrupt obstacles, semi--cylindrical and prismatic. We find four different regimes of the flow immediately past the obstacles: sub-critical (I), internal hydraulic jump (II), Kelvin-Helmholtz at the interface (III) and shedding of billows (IV). Th…
There are different ways for fluid flow to become turbulent, but usually many instabilities take place before that. Among these instabilities the transition from laminar flow to vortex shedding carries significant practical importance. Here we study a flow, where at high enough flow rates, vortices are generated by a fixed obstacle (cylinder), which penetrates a flowing, quasi-two dimensional soap film. We present experimental results that demonstrate that the transition from laminar flow to a periodic Kármán vortex street can be hysteretic, i.e. changing the mean flow rate $\bar V$ vortices c…
