Karman vortex street is an important phenomenon in fluid mechanics, which is often encountered in nature. When the steady incoming flow under certain conditions bypasses some objects, the two sides of the object will periodically shed out the double row line vortex with opposite rotation direction and regular arrangement. After nonlinear action, Karman vortex street is formed.If the water flows through the pier, and the wind blows through the tower, chimney, wire, etc., Carmen vortex street will be formed.Karman Vortex Street has some important applications, so it is necessary to understand its research history and relevant applications.
Under certain conditions, when the steady incoming flow bypasses some objects, the two sides of the object will periodically fall off from the opposite rotating direction and form a regular double row line vortex.At the beginning, the two linear vortices keep their own motion forward, and then they interfere with each other, attract each other, and the interference is growing, forming a nonlinear so-called vortex street.Karman vortex street is a phenomenon studied by viscous incompressible fluid dynamics.Karman vortex street occurs when fluid flows around tall chimneys, high-rise buildings, electric wires, oil pipelines and tube bundles of heat exchangers.
Carmen Vortex Street
In 1911, German scientist T. von Kamen found the theoretical basis of this vortex stability from the viewpoint of aerodynamics.yesFlow around a cylinderThe frequency f of each single vortex in the vortex street is proportional to the flow velocity v and inversely proportional to the cylinder diameter d, that is, f=Sr (v/d).Sr is the Strouhal number, which is mainly related to Reynolds number.When Reynolds number is 300~3 × 10 ^ 5, Sr is approximately constant (0.21);When the Reynolds number is 3 × 10 ^ 5~3 × 10 ^ 6, the regular vortex street no longer exists;When the Reynolds number is greater than 3 × 10 ^ 6, the Karman vortex street will automatically appear again, and then Sr is about 0.27.When vortex street appears, the fluid will produce a periodic alternating transverse force on the object.If the frequency of the force is close to the natural frequency of the object, it will cause resonance and even damage the object.This vortex street once made the submarine's periscope unable to observe, the strait bridge was damaged, and the boiler's air preheater tube box vibrated and cracked.However, using this periodic and alternating nature of the Karman vortex street, the Karman vortex street flowmeter can be made, and the velocity or flow of the fluid can be determined by measuring the shedding frequency of the vortex.
In the 1960s, American scientist F.H. Harlow and others successfully simulated the Karman vortex street in subsonic flow with a high-speed electronic computer.Figure 1 shows the schematic diagram of the formation process of Karman vortex street obtained by numerical simulation,
Where a represents the initial state of two vortex layers with opposite rotating directions;B indicates that the two vortex layers are in unstable motion respectively;C indicates that the unstable motion of the two vortex layers interferes with each other;D indicates the formation of Karman vortex street.
Carmen Vortex Street
The formation of Karman vortex street is related to Reynolds number Re.When Re is 50~300, the vortex shedding from the object has a periodic rule (Figure 2);When Re>300, the vortex begins to fall off randomly;As Re continues to increase, the randomness of vortex shedding also increases, and finally turbulence is formed.
After studying the stability of two rows of straight parallel vortex wires, Carmen pointed out that in general, this vortex street is unstable, and only when the spatial scale of the vortex street is h/a=0.281, it is stable for small disturbances (Figure 3).This is very close to the measured results.
Discoverer
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Von Karman （Theodore von Kármán 1881~1963）He is an American Hungarian ergologist and one of the founders of modern mechanics. He was born in Budapest, Hungary, on May 11, 1881 and died in Aachen, Germany, on May 7, 1963.Among his graduate students at California Institute of Technology, there are Chinese scholars Qian Xuesen, Guo Yonghuai, Qian Weichang, and Chinese American scholar Lin Jiaqiao. His academic ideas have played a positive role in the development of China's mechanics.He is good at seeing through phenomena, grasping the physical essence of things, refining mathematical models, establishing a style of study that closely combines mathematical theory with engineering practice in modern mechanics, and establishing the basic direction of modern mechanics.He has made many outstanding achievements and received medals from many countries, including the first National Science Medal of the United States.
Research History
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Von Kamen was born in a family of an education professor in the Austro Hungarian Empire. He graduated from the Royal Institute of Technology in Budapest in 1902. In 1906, he went to the University of Gö ttingen in Germany to study. Under the guidance of Professor Ludwig Prandtl 1875-1953, he obtained a doctor's degree in 1908.Von Carmen was an assistant professor at the University of Gottingen in 1911. Professor Plunt's research interest at that time was mainly focused on the boundary layer problem.The task Prandt assigned to Karl Hiemenz, a doctoral student, was to design a water tank so that the flow splitting behind the cylinder could be observed, and the splitting point calculated according to the boundary layer theory was checked by experiment.For this reason, it is necessary to know how the pressure intensity around the cylinder is distributed in a steady flow.Haymends made the water tank, but unexpectedly, when carrying out the experiment, he found that the water flow in the tank was constantly swinging violently.
Karman vortex street photographed by satellite
After Haymendes reported this situation to Professor Plunt, Plunt told him: "Obviously, your cylinder is not round enough.".However, after Haymends made a very fine processing of the cylinder, the water continued to swing.Plunt added: "The sink may be asymmetric.".Haymends then began to carefully adjust the sink, but still could not solve the problem.
Von Kamen's project at that time had nothing to do with the work of Haymends, but every morning when he entered the laboratory, he always ran to him and asked: "Mr. Haymends, is the flow stable now?" Haymends replied very regretfully: "It's always swinging.".
At this time, Von Carmen thought that if the current kept swinging, there must be an internal objective reason for this phenomenon.One weekend, Von Karman tried to calculate the stability of the vortex system with a rough calculation method.He assumes that only one vortex can move freely, and all other vortices are fixed.Then move the vortex slightly to see what the calculated result will be.Von Kamen came to the conclusion that if the vortex is symmetrically arranged, it must be farther and farther away from its original position;For the antisymmetric arrangement, although the same result is obtained, when the distance between the rows and columns has a certain ratio to the distance between adjacent vortices, the vortex stays near its original position and moves in a small circular path around the original position.
When he went to work on Monday, Von Carmen reported his calculation results to Professor Plunt and asked him how he thought about this phenomenon?Plunt said, "There is some truth in this. Write it down. I will submit your paper to the college.".When Von Carmen recalled it later, he wrote about it: "This is my first paper on this issue. Later, I felt that my assumption was a bit arbitrary. So I re studied a vortex system where all vortices can move. This requires a slightly more complicated mathematical calculation. After several weeks of calculation, I wrote my second paper.Someone asked me: 'Why did you put forward two papers in three weeks?One must be wrong.In fact, it's not wrong. I just draw a rough approximation first, and then refine it. Basically, the results are the same;But the value of the critical ratio obtained is not exactly the same ".
Von Kamen studied the vortex arrangement in the flume experiment of Haymendes.Later, because of the detailed and successful study of its mechanism by von Kamen, people crowned it with the surname of Carmen, called it Carmen Vortex Street.
Von Carmen himself later wrote in his book: "I don't claim that I found these eddies. Before I was born, everyone knew that there were such eddies. The first thing I saw was a picture in Bologna Church in Italy. On the picture, St. Christopher crossed the river with a young Jesus in his arms. The painter painted crisscross eddies behind Christopher's bare feet."Von Kamen also said that before him, a British scientist, Henry Reginald Arnulpt Mallock (1851-1933), had also observed the crisscross eddies behind the obstacles and took pictures.Another French professor, Henry B é nard (1874-1939), also made a lot of research on this issue.However, Bernard mainly investigated the vortices in viscous liquids and colloidal suspensions, and his perspective of investigation was that of experimental physics rather than aerodynamics.
Von Kamen believed that his contributions to the study of this problem from 1911 to 1912 were mainly in two aspects: first, he found that the vortex street was stable only when the vortex was antisymmetric and the distance between the rows and columns had a certain ratio to the spacing between two adjacent vortices in the same row;The second is to link the momentum carried by the vortex system with the resistance.
stability
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When the vortex grows continuously, the swing is strengthened, and the unstable symmetric vortex is broken, the periodic and alternate shedding Karman vortex street will be formed.The research shows that the Karman vortex street is unstable in most cases. Through calculation, the stability condition of Karman vortex street is h/l=0.281, and Re=150.
Dropout frequency
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The research shows that, in the range of Re=200~15000, the vortex behind the cylinder is periodically and evenly shedding, and the shedding frequency f of the vortex is proportional to the incoming flow speed U and inversely proportional to the cylinder diameter d.When Re>1000, the Strouhal number is approximately equal to the constant 0.21.At this time, the shedding frequency f is proportional to the incoming flow speed. The vortex flowmeter is based on this principle to measure the shedding frequency of the vortex around the flow cylinder in the flow field, so as to measure the velocity and flow.
event
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In the 1940s, the tragic lesson of the wind damage accident of Tacoma Narrow Bridge in the United States made people realize the important role of Carmen Vortex Street in building safety.
In 1940, a suspension bridge with a main span of 853.4 meters was built in Tacoma Canyon in Washington State, USA, at a cost of 6.4 million dollars.Four months after completion, a wind with a wind speed of 19 m/s was encountered on November 7 of the same year.Although the wind was not strong, the bridge experienced severe torsional vibration, and the amplitude was getting larger and larger (nearly 9 meters) until the bridge deck tilted to about 45 degrees, so that the suspenders were pulled apart one by one, causing the steel beams on the bridge deck to break and collapse, falling into the canyon.At that time, a Hollywood film team was shooting a film with the bridge as the location, recording the whole process of the bridge from the beginning of vibration to the final destruction. It later became a valuable information for the Federal Highway Administration to investigate the cause of the accident.When people investigated the accident and collected historical data, they were surprised to find that from 1818 to the end of the 19th century, at least 11 suspension bridges had been destroyed by bridge vibration caused by wind.
After the Second World War, people studied the causes of the wind damage accident of Tacoma Bridge.At the beginning, there were two different opinions in dispute. -Some aviation engineers believe that the vibration of Tacoma Bridge is similar to the flutter of wings;The hydrodynamics experts represented by Von Kamen believe that the main beam of Tacoma Bridge has a blunt head H-shaped section, which is different from the streamlined wing. There is obvious vortex shedding, which should be explained by the vortex induced resonance mechanism.In 1954, Von Kamen wrote in the book "Development of Aerodynamics" that the destruction of the Takoma Strait Bridge was caused by the resonance of the periodic vortex.The designer wanted to build a cheaper structure and used flat sheet metal instead of truss as the side wall.Unfortunately, these flat plates caused vortex emission, which started the torsional vibration of the bridge body.The destruction of this bridge is caused by the resonance between vibration and vortex emission.
In the 1960s, the calculation and experiment proved that von Karman's analysis was correct.The wind damage accident of Tacoma Bridge is the Karman vortex street when the fluid with a certain flow velocity flows through the side wall;The alternative emission of vortex behind the Karman vortex street will generate alternating lateral force perpendicular to the flow direction on the object, forcing the bridge to vibrate. When the emission frequency is coupled with the natural frequency of the bridge structure, resonance will occur, causing damage.
Karman vortex street not only appears behind the cylinder, but also forms behind other shaped objects, such as high-rise buildings, TV transmission towers, chimneys and other buildings.The vibration of these buildings caused by wind is often related to Carmen vortex street.Therefore, calculation and wind tunnel model test should be carried out during the design of high-rise buildings to ensure that the buildings will not be damaged by Karman Vortex Street.It is understood that before the construction of the TV transmission towers in Beijing and Tianjin, and the Oriental Pearl TV Tower in Shanghai, model experiments were conducted in the wind tunnel of the Department of Mechanics and Engineering Sciences of Peking University.
Acoustic effect
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When the Karman vortex street falls off alternately, it will produce vibration and sound effect. This sound is caused by the pressure fluctuation in the fluid caused by the periodic fall off of the Karman vortex street. For example, the sound of wind blowing wires heard in daily life is caused by the vortex street falling off.
Cause resonance
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If the alternating shedding frequency of the vortex street coincides with the acoustic standing wave frequency of the object, resonance will also occur.Industrial preheaters, boilers, etc. are mostly composed of circular tubes. When the fluid flows around the circular tube, the alternating shedding of Karman vortex street will cause the vibration of the air column in the preheater box. If the alternating shedding frequency of the vortex street coincides with the acoustic standing wave frequency of the object, it will cause acoustic resonance, causing severe vibration of the tube box. In serious cases, the vibration drum of the preheater tube box will stagger, or even break.If the natural frequencies of the header and gas are changed to stagger with the shedding frequency of the Karman vortex street to avoid resonance, the damage of the equipment can be prevented.
application
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In fact, Carmen Vortex Street does not always cause unfortunate accidents. It also has very successful applications.For example, the Karman vortex flowmeter, which has been widely used in industry, is a kind of flowmeter made of Karman vortex phenomenon.When the vortex generator is vertically inserted into the fluid, the fluid will bypass the generator and form a Karman vortex street. Under certain conditions, the asymmetric vortex train can remain stable. At this time, the vortex frequency f is proportional to the flow velocity v of the fluid and inversely proportional to the front width d of the vortex generator, which can be expressed as: f=Stv/d
Where StIs the Strouhal number, which is constant under normal working conditions.
Karman vortex flowmeter has many advantages: it can measure the flow of liquid, gas and steam;The precision can reach ± 1% (indicated value);Simple structure, no moving parts, reliable and durable;The piezoelectric element is encapsulated in the generator, and the detection element does not contact the medium;Wide range of operating temperature and pressure, operating temperature up to 400 ℃;It has automatic adjustment function, and can use software to automatically adjust pipeline noise.
misunderstanding
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Many people believe that Karman vortex street can only be generated when a fluid flows around a cylinder. In fact, Karman vortex street may be generated whenever boundary layer separation occurs. Therefore, some facilities, such as underwater buildings or aviation equipment, are streamlined to avoid the destructive effect of Karman vortex street.
reference
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1. Entries Author: Zhang Deliang, Encyclopedia of China, Volume 74 (the first edition), Entries in mechanics: Fluid Mechanics, Encyclopedia of China Press, 1987:492
