Concept
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:
| { |
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| u |
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| r |
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| t |
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| α |
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| ω |
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| n |
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| P'n |
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| ρ |
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| μ |
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| R |
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| J0(·) |
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| i |
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| Re{·} |
| } |
| The pulsatile flow profile changes its shape depending on the Womersley number |
| For , viscous forces dominate the flow, and the pulse is considered quasi-static with a parabolic profile. |
| For , 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. |
| The Bessel function at its lower limit becomes |
| which converges to the Hagen-Poiseuille flow profile for steady flow for |
| or to a quasi-static pulse with parabolic profile when |
| In this case, the function is real, because the pressure and velocity waves are in phase. |
| The Bessel function at its upper limit becomes |
| which converges to |
| This is highly reminiscent of the Stokes layer on an oscillating flat plate, or the skin-depth penetration of an alternating magnetic field into an electrical conductor. |
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