Instability mechanisms initiating laminar-turbulent transition past bioprosthetic aortic valves

Abstract

Bioprosthetic heart valves create turbulent flow during early systole which might be detrimental to their durability and performance. Complex mechanisms in the unsteady and heterogeneous flow field complicate the isolation of specific instability mechanisms. We use linear stability analysis and numerical simulations of the flow in a simplified model to study mechanisms initiating the laminar-turbulent transition. The analysis of a modified Orr-Sommerfeld equation, which includes a model for fluid-structure interaction (FSI), indicates Kelvin-Helmholtz and FSI instabilities for a physiological Reynolds number regime. Two-dimensional parametrized FSI simulations confirm the growth rates and phase speeds of these instabilities. The eigenmodes associated with the observed leaflet kinematics allow for decoupled leaflet oscillations. A detailed analysis of the temporal evolution of the flow field shows that the starting vortex interacts with the aortic wall leading to a secondary vortex which moves towards the shear layer in the wake of the leaflets. This appears to be connected to the onset of the shear layer instabilities that are followed by the onset of leaflet motion leading to large-scale vortex shedding and eventually to a nonlinear breakdown of the flow. Numerical results further indicate that a narrower aorta leads to an earlier onset of the shear layer instabilities. They also suggest that the growing perturbations of the shear layer instability propagate upstream and may initiate the FSI instabilities on the valve leaflets.