Pulsatile flow

In fluid dynamics, a flow with periodic variations is known as pulsatile flow, or as Womersley flow. The flow profiles was first derived by John R. Womersley (1907–1958) in his work with blood flow in arteries. The cardiovascular system of chordate animals is a very good example where pulsatile flow is found, but pulsatile flow is also observed in engines and hydraulic systems, as a result of rotating mechanisms pumping the fluid.

The pulsatile flow profile is given in a straight pipe by

where:

The pulsatile flow profile changes its shape depending on the Womersley number

For ${\displaystyle \alpha \lesssim 2}$, viscous forces dominate the flow, and the pulse is considered quasi-static with a parabolic profile. For ${\displaystyle \alpha \gtrsim 2}$, the inertial forces are dominant in the central core, whereas viscous forces dominate near the boundary layer. Thus, the velocity profile gets flattened, and phase between the pressure and velocity waves gets shifted towards the core.

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