Womersley.hpp File Reference

Womersley Analytical Solution. More...

#include <complex>
#include <lifev/core/LifeV.hpp>
#include <lifev/core/filter/GetPot.hpp>

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Data Structures
class	Womersley

Namespaces
	LifeV
	Default Physical Solver.

Detailed Description

Womersley Analytical Solution.

Author

Mauro Perego mauro.nosp@m.@mat.nosp@m.hcs.e.nosp@m.mory.nosp@m..edu

Contributor:

Umberto Villa uvill.nosp@m.a@em.nosp@m.ory.e.nosp@m.du

Maintainer:

Umberto Villa uvill.nosp@m.a@em.nosp@m.ory.e.nosp@m.du

Date

11-12-2009

Analytic solution of Womersley for unsteady Navier-Stokes 3D on the cylinder having axis x, origin (0,0,0), diameter D and height L. Solution of incompressible NS equation in a cylindrical vessel with a sinusoidal pressure drop (deltaP = A cos(wt) ) between the inflow and the outflow and no-slip conditions on the vessel wall. this solution works also in the 2D-axisymmetric formulation (geometry [0, L]x[0, D/2]).
The Womersley number arises in the solution of the linearized Navier Stokes equations for oscillatory flow (presumed to be laminar and incompressible) in a tube. When is small (1 or less), it means the frequency of pulsations is sufficiently low that a parabolic velocity profile has time to develop during each cycle, and the flow will be very nearly in phase with the pressure gradient, and will be given to a good approximation by Poiseuille's law, using the instantaneous pressure gradient. When is large (10 or more), it means the frequency of pulsations is sufficiently large that the velocity profile is relatively flat or plug-like, and the mean flow lags the pressure gradient by about 90 degrees.

Definition in file Womersley.hpp.