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Technical Information - Measurement principle -

Vortex flowmeters use the Von Karman Effect to measure the flow rate of liquids, gases, and steam. This section explains the principle.

The Operating Principle of Vortex Flowmeters

• What Is a Von Karman Vortex?
  In the early 20th century, the Hungarian-born mathematician and physicist Theodore von Karman discovered that when a liquid or gas flows perpendicular to an obstacle, it creates alternating vortices on either side of that obstacle. These rows of vortices are called “Von Karman vortex streets.”

Von Karman further found that the number of vortices generated is proportional to the velocity of the fluid that generates them. This number of vortices generated is called the “Von Karman vortex frequency.” The relationship between the frequency and the flow velocity can be mathematically expressed with the following formula (1). Formula (2) further expresses the relationship with the internal structure of a vortex flowmeter. Putting these two formulas together and expressing them in terms of volumetric flow rate yields formula (3).

f: Von Karman vortex frequency, St: Strouhal number, v: flow velocity, d: width of vortex shedder bar, Q: volumetric flow rate, D: inner diameter of vortex flow meter

The Strouhal number (St) is a dimensionless number determined by the shape and dimensions of the vortex shedder bar, and by properly choosing the shedder bar’s shape, it becomes constant over a wide range of Reynolds number values. Figure 1 shows the relationship between the Reynolds number and the Strouhal number.

Relationship between Reynolds number and Strouhal number (St)

Therefore, if the Strouhal number is known in advance, the flow rate can be determined by measuring the vortex frequency. It has also been found that the volumetric flow rate can be measured irrespective of the pressure, temperature, density, viscosity, etc. of the fluid. However, when measuring volumetric flow or mass flow under standard (reference) conditions, temperature and pressure corrections are required.

• How Is Vortex Frequency Measured?
  When vortices form and pass through a vortex shedder bar (obstacle), the pressure in that area is lower than that in the rest of the fluid. This low pressure creates a pressure differential (dp) on each side of the vortex shedder bar, and stress is applied to the vortex shedder bar from the high-pressure side toward the low-pressure side. The position where the vortices are generated switches regularly, causing the position of the low-pressure area to change and the direction of the stress to shift, causing the vortex shedder bar to oscillate. The frequency of this oscillation is the Von Karman vortex frequency.

The vortices generated create low-pressure and high-pressure areas on both sides of the vortex shedder bar, and force is exerted toward the low-pressure area. As the position of the vortices change from one side to the other, the direction of this force is switched, causing the vortex shedder bar to oscillate.

Several methods are available as means of measuring this oscillation. The most suitable for this application is the piezoelectric crystal sensor. When compressed, the piezoelectric crystal sensor produces an electrical signal that is processed by the flowmeter’s electronics. By measuring the Von Karman vortex frequency (the Strouhal number and the diameter of the cylinder are known), a simple calculation by the flowmeter’s electronics can determine the rate of volumetric flow through the pipe.