Absolute instability of impinging leading edge vortices in a submodel of a bileaflet mechanical heart valve

Bileaflet mechanical heart valves (BMHVs) have been related to the production of unphysiological turbulent flow in the ascending aorta. These valves comprise a pair of rigid blunt plates (leaflets), which are immersed in a confined flow with Reynolds numbers up to 10 000. They are prone to develop impinging leading-edge vortex (ILEV) instabilities [K. Hourigan et al., J. Fluids Stud. 15, 387 (2001); S. Deniz and T. Staubli, ibid. 11, 3 (1997)] on the leaflets because of their relatively large chord-to-thickness ratio and their low angle of incidence. These instabilities can produce strong disturbances between the leaflets which may contribute to the onset and intensity of turbulent flow in the wake of the valve. The complex nature of the flow around BMHVs prevents a detailed theoretical analysis of the underlying instability mechanisms. Therefore, we defined a two-dimensional submodel of the flow with fixed leaflets, which renders the problem accessible to the rich toolbox of hydrodynamic stability theory. High-order numerical simulations of this flow configuration indicated the systolic development of unstable ILEVs on the inner side of the leaflets during systolic acceleration of the flow. We found that the ILEV instabilities can only be observed with sufficiently high spatial resolution, which may explain why these phenomena have not been observed so far in most computational studies of BMHV flow. Orr-Sommerfeld eigenmodes with high growth rates confirmed the unstable character of this flow. We further identified a pocket of absolute instability which acts as a wave maker between the leaflets. Finally, we confirmed that this wave-maker region has a direct effect on the nonlinear breakdown in the wake of the valve. To this end, the leaflet geometry was modified such that the ILEV (and the associated wave maker) was eliminated and it was shown numerically that the wake remains laminar for the modified geometry. The results of this study are a first step toward a detailed understanding of the hydrodynamic instability mechanisms which lead to turbulent flow past BMHVs.