Example 3: Karman Vortices

A very common source of oscillation found in many practical situations, like

The resulting vibrations are referred to as flow-induced vibrations. Any structure with a sufficiently bluff trailing edge, if placed in a moving fluid, sheds vortices. These vortices are quite similar irrespective of the shape of the tripping structure. The vortices, called the Karman Vortices are shed alternately clockwise and counter-clockwise in a regular manner from each side of the structure. As a result, the structure is subjected to a periodic sidewise force having the same frequency as that of the vortex shedding.

Figure 4.5: Karman vortices in moving flow

Figure 4.5 schematically shows the Karman vortices in the wake of a cylinder. For such a body, the vortex- shedding frequency f(Hz) can be obtained from the relation

	(4.1)

where D = diameter of the cylinder (m), and V = free stream velocity of the fluid (m/s), S =Strouhal number.The value of the Strouhal number is approximately 0.2 for a cylinder.

For a noncylindrical body, Eqn.(4.1) can still be used when D represents the maximum width of the cross-section normal to the free stream. The value of the Strouhal number for such a body varies from 0.12 to 0.17, depending on the cross-sectional geometry. If the vortex-shedding frequency is close to a natural frequency of the structure, excessive vibration is generated.