Some flow fields have an oscillatory pattern which is dependent on Reynolds number. The periodic vortex shedding behind a blunt body immersed in a steady freestream provides one example. Figure 1 shows a sketch of the vortex formation behind a circular cylinder.

A vortex is in the process of formation near the top of the cylinder surface. Below and to the right of the first vortex is another vortex which was formed and shed a short period before. Thus, the flow process in the *wake* of a cylinder or tube involves the formation and shedding of vortices alternately from one side and then the other. This phenomenon is of major importance in engineering design because the alternate formation and shedding of vortices also creates alternating forces, which occur more frequently as the velocity of the flow increases.

When the frequency is in the audible range, a sound can be heard and the body appears to sing. Resonance may occur if the vortex shedding frequency is near the structural-vibration frequency of the body. A dimensionless number, the *Strouhal number* Sr, is commonly used as a measure of the predominant shedding frequency f_{s}. The definition is

where L is a characteristic length (equal to the diameter D in case of a circular cylinder or tube in cross flow) and U∞ the freestream velocity.

The Strouhal number of a stationary tube or circular cylinder is a function of Reynolds number but less of surface roughness and freestream turbulence, see Figure 2.

**Figure 2. Strouhal number versus Reynolds number for circular cylinders (tubes). From Blevins R. D. (1990) Flow Induced Vibrations, Van Nostrand Reinhold Co.**

The variation in the Strouhal number is associated with the changes in the flow structure as described elsewhere (see Tube Crossflow over). From Figure 2 it is found that the Strouhal number is about 0.2 over a large Reynolds number interval. In the Reynolds number range 250 < Re_{D} < 2×10^{5} the empirical formula

is sometimes recommended for estimation of the Strouhal number.

At high Reynolds numbers the vortex shedding does not occur at a single distinct frequency but rather over a narrow band of frequencies.

Noncircular cylinders also shed vortices. It has been suggested to introduce a universal Strouhal number based on the distance between the shear layers. Over a large Reynolds number range a Strouhal number of about 0.2 is then valid regardless of the body geometry.

Vortex shedding also occurs from pair of cylinders, multiple cylinders, arrays of cylinders and heat exchanger tube bundles. However, the pitch-to-diameter ratio (center-to-center distance divided by tube diameter) is important. For two cylinders, placed in-line, vortex shedding occurs behind each cylinder separately if the pitch-to-diameter ratio exceeds a certain value while for smaller values, the two cylinders behave as a single body in terms of vortex shedding. In closely spaced tube bundles, the frequency associated with vortex shedding is not so distinct but might appear as a broadbanded peak. Vortex shedding is one of the mechanisms producing *flow-induced vibration* in shell-and-tube heat exchangers.

#### REFERENCES

Blevins, R. D. (1990) *Flow-Induced Vibration*, 2nd edn., Van Nostrand Reinhold.

Chen, S. S. (1990) *Flow-Induced Vibration of Circular Cylindrical Structures*, Hemisphere.