The study of heart valve performance (healthy, diseased, and prosthetic) has traditionally involved the examination of transvalvular characteristics, such as pressure gradients and effective and geometric orifice areas. However, recent research has shown that a key downstream flow characteristic, vortex ring formation, should not be overlooked because quantifying this mechanism provides insight into the assessment of valve performance [1]. Vortex ring formation, which is dependent on the valve design [1], is the roll-up of the shear layers shedding past valve leaflets. Governed by a universal time-scale or formation number (FN) that is based on the jet length to diameter ratio (L/D), vortex ring formation provides insight into the kinematics of optimizing effective fluid transport. It has been shown that growth of the leading vortex ring ceases at a FN between 3.5 and 4.5 in various biological systems [2], but most of these studies have assumed a constant or fixed orifice opening. However, incorporating a time-varying jet diameter rather than the constant valve annulus diameter has recently been identified by Dabiri and Gharib as a key factor in the characterization of vortex ring formation and provides a more complete picture of impulse generation and efficiency in vortical flows [2]. This dynamic formation number is governed by the following equation:
where U is velocity, D is diameter, t is time, and the overbar indicates a time average. Estimating (L/D)* can serve as a powerful evaluation tool in comparison to conventional methods of FN calculation that use either an averaged diameter or the valve annulus diameter. Ideally suited for unsteady flows, such as the opening phase and leaflet motions in heart valves, (L/D)* can provide insight into assessing the performance of natural and prosthetic heart valves (PHVs).
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