In fluid dynamics, a Kármán vortex street (or a von Kármán vortex street) is a repeating pattern of swirling vortex, caused by a process known as vortex shedding, which is responsible for the unsteady flow separation of a fluid around Blunt body.
It is named after the engineer and fluid dynamicist Theodore von Kármán,Theodore von Kármán, Aerodynamics. McGraw-Hill (1963): . Dover (1994): . and is responsible for such phenomena as the "singing" of suspended telephone or power lines and the vibration of a car antenna at certain speeds.
Mathematical modeling of von Kármán vortex street can be performed using different techniques including but not limited to solving the full Navier-Stokes equations with k-epsilon, SST, k-omega and Reynolds stress, and large eddy simulation (LES) turbulence models, by numerically solving some dynamic equations such as the Ginzburg–Landau equation,Albarède, P., & Provansal, M. Quasi-periodic cylinder wakes and the Ginzburg–Landau model. Journal of Fluid Mechanics, 291, 191-222, 1995.Farazande, S. and Bayindir, C., The Interaction of Von Kármán Vortices with the Solitons of the Complex GinzburgLandau Equation. International Conference on Applied Mathematics in Engineering (ICAME) September 1–3, 2021 - Balikesir, TurkeyMonkewitz, P. A., Williamson, C. H. K. and Miller, G. D., Phase dynamics of Kármán vortices in cylinder wakes. Physics of Fluids, 8, 1, 1996. or by use of a bicomplex number.
For common flows (which can usually be considered as incompressible or isothermal), the kinematic viscosity is everywhere uniform over all the flow field and constant in time, so there is no choice on the viscosity parameter, which becomes naturally the kinematic viscosity of the fluid being considered at the temperature being considered. On the other hand, the reference length is always an arbitrary parameter, so particular attention should be put when comparing flows around different obstacles or in channels of different shapes: the global Reynolds numbers should be referred to the same reference length. This is actually the reason for which the most precise sources for airfoil and channel flow data specify the reference length at the Reynolds number. The reference length can vary depending on the analysis to be performed: for a body with circle sections such as circular cylinders or spheres, one usually chooses the diameter; for an airfoil, a generic non-circular cylinder or a bluff body or a revolution body like a fuselage or a submarine, it is usually the profile chord or the profile thickness, or some other given widths that are in fact stable design inputs; for flow channels usually the hydraulic diameter about which the fluid is flowing.
For an aerodynamic profile, the reference length depends on the analysis. In fact, the profile chord is usually chosen as the reference length also for aerodynamic coefficient for wing sections and thin profiles in which the primary target is to maximize the lift coefficient or the lift/drag ratio (i.e. as usual in thin airfoil theory, one would employ the chord Reynolds as the flow speed parameter for comparing different profiles). On the other hand, for fairings and struts the given parameter is usually the dimension of internal structure to be streamlined (let us think for simplicity it is a beam with circular section), and the main target is to minimize the drag coefficient or the drag/lift ratio. The main design parameter which becomes naturally also a reference length is therefore the profile thickness (the profile dimension or area perpendicular to the flow direction), rather than the profile chord.
The range of Re values varies with the size and shape of the body from which the eddies are Vortex shedding, as well as with the kinematic viscosity of the fluid. For the wake of a circular cylinder, for which the reference length is conventionally the diameter d of the circular cylinder, the lower limit of this range is Re ≈ 47. Eddies are shed continuously from each side of the circle boundary, forming rows of vortices in its wake. The alternation leads to the core of a vortex in one row being opposite the point midway between two vortex cores in the other row, giving rise to the distinctive pattern shown in the picture. Ultimately, the energy of the vortices is consumed by viscosity as they move further down stream, and the regular pattern disappears. Above the Re value of 188.5, the flow becomes three-dimensional, with periodic variation along the cylinder. Above Re on the order of 105 at the drag crisis, vortex shedding becomes irregular and turbulence sets in.
When a single vortex is shed, an Symmetry flow pattern forms around the body and changes the pressure distribution. This means that the alternate shedding of vortices can create Frequency lateral (sideways) forces on the body in question, causing it to vibrate. If the vortex shedding frequency is similar to the natural frequency of a body or structure, it causes resonance. It is this forced vibration that, at the correct frequency, causes suspended telephone line or to "sing" and the antenna on a car to vibrate more strongly at certain speeds.
Even more serious instability can be created in concrete , especially when built together in clusters. Vortex shedding caused the collapse of three towers at Ferrybridge Power Station C in 1965 during high winds.
The failure of the original Tacoma Narrows Bridge was originally attributed to excessive vibration due to vortex shedding, but was actually caused by aeroelastic flutter.
Kármán turbulence is also a problem for airplanes, especially when landing.
The effectiveness of a tuned mass damper in mitigating vortex shedding-induced vibrations depends on factors such as the mass of the damper, its placement on the structure, and the tuning of the system. Engineers carefully analyze structural dynamics and characteristics of the vortex shedding phenomenon to determine the optimal parameters for the tuned mass damper. In many cases, the spring is represented by suspending the mass on cables such that it forms a pendulum system with the same resonance frequency. The mass is carefully tuned to have a natural frequency that matches the dominant frequency of the vortex shedding.
As the structure is subjected to vortex shedding-induced vibrations, the tuned mass damper oscillates in an out-of-phase motion with the structure. This counteracts the vibrations, reducing their amplitudes and minimizing the potential for resonance and structural damage.
Obviously, for a tall building or mast, the relative wind could come from any direction. For this reason, helical strakes resembling large screw threads are sometimes placed at the top, which effectively create asymmetric three-dimensional flow, thereby discouraging the alternate shedding of vortices; this is also found in some car antennas.
In his autobiography, von Kármán described how his discovery was inspired by an Italian painting of St Christopher carrying the child Jesus whilst wading through water. Vortices could be seen in the water, and von Kármán noted that " The problem for historians may have been why Christopher was carrying Jesus through the water. For me it was why the vortices". It has been suggested by researchers that the painting is one from the 14th century that can be found in the museum of the San Domenico church in Bologna.
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