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Is the vortex flowmeter reliable?
When the fluid moves around the surface, boundary layer separation is easy to occur, especially when the fluid is a poor streamlined cylinder, and the vortex separation is more intense. According to experimental observations, when the fluid bypasses the non-streamlined cylinder, the vortex generated by the flow separation has a certain regularity due to the instability of the boundary layer. When the Reynolds number is high, when the vortex is formed and separated on one side of the cylinder, it is impossible to form a vortex on the other side, but only for the formation and separation of the vortex. Only when a certain side of the vortex leaves the cylinder for a certain distance, the other side can form a vortex, so that alternating, regular vortex rows are formed on both sides of the cylinder. This is the vortex flowmeter. Strauhal first used experimental methods to find the whirl of the wake behind the bluff body After periodicity, after more than 30 years, Kaman observed the stability of the vortex street through a large number of experiments, and found that there is a constant ratio between the distance between the two columns of vortices and the distance between the vortices of the same column. When the flow rate is constant, the vortex frequency in the wake actually remains stable. He mathematically derived the conditions that proved the stability of the vortex street and came to the following important conclusions: (1) A single vortex column is unstable; (2) The two vortex columns arranged symmetrically are also unstable; (3) Two vortex rows arranged alternately. If the vortex of the upper row rotates clockwise, and the following vortex rotates counterclockwise, it is usually unstable due to the interaction between the vortices. Only when the two columns of vortex arrangements satisfy certain conditions are stable. Let us discuss the stability of the vortex flowmeter. The distance between two adjacent vortices in the same column is i. The position of a vortex in the upper vortex is z, and the vortex intensity is r1; in the next vortex, the position of the vortex immediately adjacent to the vortex is z2, and the vortex intensity is r2. It can be seen from the theory of vortex motion that a point z that does not coincide with any one of the two vortices in the complex plane is taken, and the complex potential of the point is