Abstracts - KTH Mechanics

168
Kinematic-dynamic correspondence in flow-driven motion of a
valvular leaflet
G. Pedrizzetti a, F. Domenichini b
When the flow pushes onto the upstream face of a movable door, we think to the
leaflet of a cardiac valve, this opens rapidly with the fluid making little resistance. A
model of a fluid-leaflet interaction should be based on the equations of fluid
mechanics coupled with those of solid mechanics for the structure 1. A fluid is a simple
(Newtonian) material that develops a complex behaviour due to vortices, boundary
layer separation, and turbulence. On the opposite, a solid presents a simpler behaviour
where complexity appears through the material properties that can be non-linear, time
varying, and neither homogeneous nor isotropic. Approximate elastic structures are
usually considered. In physiology, either the material behaviour of a cardiac valve and
its parameters are unknown and difficult to assess. This makes the realistic study of
physiological flows in presence of a moving leaflets often prohibitive.
An asymptotic model of the leaflets dynamics is presented here 2. After assuming
that vortex shedding can only occur from the trailing edge, we consider the limit when
the leaflet moves with the flow such that shedding is inhibited. This kinematic (Kutta)
condition does not depend on either the material structure and elasticity. The relation
between asymptotic condition and actual torque on the solid element is carefully
addressed to show the relation between kinematic condition and actual dynamic
balance on the solid element.
A model problem, made of a leaflet in a two-dimensional channel, is here
considered. The coupled flow-structure dynamics is first recalled in the irrotational
scheme, then analysed numerically at finite Reynolds number (Fig.1). The objectives
of this study are twofold: (i) the introduction of a technique that allows -
asymptotically- a simple solution of the coupled flow-tissue dynamics, and (ii) the
analysis of vortex generation from a freely or constrained moving leaflet.
a Dept. Civil Engineering, University of Trieste, Italy.
b Dept. Civil Engineering, University of Firenze, Italy.
1 De Hart et al., J. Biomech. 36, 103 (2003).
2 Pedrizzetti, Phys Rev Lett. 94, 194502 (2005).
Figure 1: Streamlines and vorticity contours for an accelerated flow in presence of a
freely moving plate. Numerical solution at Re=10 3.