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In
fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...
, a Kármán vortex street (or a von Kármán vortex street) is a repeating pattern of swirling
vortices In fluid dynamics, a vortex (: vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in th ...
, caused by a process known as '' vortex shedding,'' which is responsible for the unsteady separation of flow of a
fluid In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...
around blunt bodies. It is named after the engineer and fluid dynamicist Theodore von Kármán, and is responsible for such phenomena as the "
singing Singing is the art of creating music with the voice. It is the oldest form of musical expression, and the human voice can be considered the first musical instrument. The definition of singing varies across sources. Some sources define singi ...
" 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 Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, and first explored by Deardorff (1970). LES is ...
(LES) turbulence models, by numerically solving some dynamic equations such as the Ginzburg–Landau equation, or by use of a bicomplex variable.


Analysis

A vortex street forms only at a certain range of flow velocities, specified by a range of
Reynolds number In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to ...
s (''Re''), typically above a limiting ''Re'' value of about 90. The (''global'') Reynolds number for a flow is a measure of the ratio of
inertia Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newto ...
l to viscous forces in the flow of a fluid around a body or in a channel, and may be defined as a
nondimensional Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...
parameter of the global speed of the whole fluid flow: \mathrm_L=\frac where: *U = the free stream
flow speed In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the ...
(i.e. the flow speed far from the fluid boundaries U_\infty like the body speed relative to the fluid at rest, or an inviscid flow speed, computed through the Bernoulli equation), which is the original global flow parameter, i.e. the target to be non-dimensionalised. *L = a characteristic length parameter of the body or channel *\nu_0 = the free stream
kinematic viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...
parameter of the fluid, which in turn is the ratio:\nu_0 =\frac between: *\rho_0 = the reference fluid density. *\mu_0 = the free stream fluid
dynamic viscosity Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup h ...
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 The hydraulic diameter, , is a commonly used term when handling flow in non-circular tubes and channels. Using this term, one can calculate many things in the same way as for a round tube. When the cross-section is uniform along the tube or channe ...
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
shed A shed is typically a simple, single-storey (though some sheds may have two or more stories and or a loft) roofed structure, often used for storage, for hobby, hobbies, or as a workshop, and typically serving as outbuilding, such as in a bac ...
, as well as with the
kinematic viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...
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 Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
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
asymmetrical Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property of both physical and abstract systems and it may be displayed in pre ...
flow pattern forms around the body and changes the
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
distribution. This means that the alternate shedding of vortices can create periodic lateral (sideways) forces on the body in question, causing it to vibrate. If the vortex shedding
frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
is similar to the
natural frequency Natural frequency, measured in terms of '' eigenfrequency'', is the rate at which an oscillatory system tends to oscillate in the absence of disturbance. A foundational example pertains to simple harmonic oscillators, such as an idealized spring ...
of a body or structure, it causes
resonance Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...
. It is this forced vibration that, at the correct frequency, causes suspended
telephone A telephone, colloquially referred to as a phone, is a telecommunications device that enables two or more users to conduct a conversation when they are too far apart to be easily heard directly. A telephone converts sound, typically and most ...
or
power line An overhead power line is a structure used in electric power transmission and Electric power distribution, distribution to transmit electrical energy along large distances. It consists of one or more electrical conductor, conductors (commonly mu ...
s to "sing" and the antenna on a car to vibrate more strongly at certain speeds.


In meteorology

The flow of atmospheric air over obstacles such as islands or isolated mountains sometimes results in von Kármán vortex streets. When a cloud layer is present at the relevant altitude, the streets become visible. Such cloud layer vortex streets have been photographed from satellites, and can reach over from the obstacle, with vortex diameters normally between .


Engineering problems

In low turbulence, tall buildings can produce a Kármán street, so long as the structure is uniform along its height. In urban areas where there are many other tall structures nearby, the turbulence produced by these can prevent the formation of coherent vortices. Periodic crosswind forces set up by vortices along object's sides can be highly undesirable, due to the vortex-induced vibrations caused, which can damage the structure, hence it is important for engineers to account for the possible effects of vortex shedding when designing a wide range of structures, from
submarine A submarine (often shortened to sub) is a watercraft capable of independent operation underwater. (It differs from a submersible, which has more limited underwater capability.) The term "submarine" is also sometimes used historically or infor ...
periscope A periscope is an instrument for observation over, around or through an object, obstacle or condition that prevents direct line-of-sight observation from an observer's current position. In its simplest form, it consists of an outer case with ...
s to industrial
chimney A chimney is an architectural ventilation structure made of masonry, clay or metal that isolates hot toxic exhaust gases or smoke produced by a boiler, stove, furnace, incinerator, or fireplace from human living areas. Chimneys are typical ...
s and
skyscraper A skyscraper is a tall continuously habitable building having multiple floors. Most modern sources define skyscrapers as being at least or in height, though there is no universally accepted definition, other than being very tall high-rise bui ...
s. For monitoring such engineering structures, the efficient measurements of von Kármán streets can be performed using smart sensing algorithms such as compressive sensing. Even more serious
instability In dynamical systems instability means that some of the outputs or internal states increase with time, without bounds. Not all systems that are not stable are unstable; systems can also be marginally stable or exhibit limit cycle behavior. ...
can be created in concrete
cooling tower A cooling tower is a device that rejects waste heat to the atmosphere through the cooling of a coolant stream, usually a water stream, to a lower temperature. Cooling towers may either use the evaporation of water to remove heat and cool the ...
s, 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 Aeroelasticity is the branch of physics and engineering studying the interactions between the inertial, elastic, and aerodynamic forces occurring while an elastic body is exposed to a fluid flow. The study of aeroelasticity may be broadly classi ...
. Kármán turbulence is also a problem for airplanes, especially when landing.


Solutions


Tuned mass damper (TMD)

To prevent vortex shedding and mitigate unwanted vibrations of cylindrical bodies (such as a tall chimney or mast), a tuned mass damper (TMD) is often used. A tuned mass damper is a device consisting of a mass-spring system specifically designed and tuned to counteract vibrations induced by vortex shedding. It is often attached to the structure through springs or dampers. 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.


Fins & strakes

Another solution to prevent unwanted vibration of such cylindrical bodies is a longitudinal fin that can be fitted on the downstream side, which, provided it is longer than the diameter of the cylinder, prevents the eddies from interacting, and consequently they remain attached. Obviously, for a tall building or mast, the relative wind could come from any direction. For this reason, helical projections (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.


Other countermeasures

Another countermeasure with tall buildings is using variation in the diameter with height, such as tapering - that prevents the entire building from being driven at the same frequency.


Formula

This formula generally holds true for the range 250 < Re''d'' < 200000: \text = 0.198\left (1-\frac\right )\ where: \text=\frac *''f'' = vortex shedding frequency. *''d'' = diameter of the cylinder *''U'' = flow velocity. This dimensionless parameter St is known as the Strouhal number and is named after the Czech physicist, Vincenc Strouhal (1850–1922) who first investigated the steady humming or singing of telegraph wires in 1878.


History

Although named after Theodore von Kármán, he acknowledged that the vortex street had been studied earlier by Arnulph Mallock and Henri Bénard. Kármán tells the story in his book ''Aerodynamics'': In his autobiography, von Kármán described how his discovery was inspired by an Italia
painting
of St Christopher carrying the child
Jesus Jesus (AD 30 or 33), also referred to as Jesus Christ, Jesus of Nazareth, and many Names and titles of Jesus in the New Testament, other names and titles, was a 1st-century Jewish preacher and religious leader. He is the Jesus in Chris ...
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.


See also

* * * * * *


References


External links

* * * * * {{DEFAULTSORT:Karman Vortex Street Vortices Aerodynamics Articles containing video clips