Vortex Dynamics in the Sinus of Valsalva

Figures

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  Figure 8. Pressure coefficient difference along the normalized valve length, calculated as suction side minus pressure side during the (a) opening, (b) fluttering, and (c) closure stages. The small inset plot (depicted with the black curve) illustrates the aortic opening area during systole, with the red dot marking the instantaneous time.

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  Figure A1. (a) Maximum intra-cycle flow rate through the valve (achieved when the valve is fully open) plotted against fluid mesh lengths, and (b) logarithmic relation of error variation with mesh size.

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  Figure 1. Parametrized two-dimensional model of the aortic wall with the aortic valve. The aortic sinus and leaflets within the black box are shown in a zoomed-in depiction to the right, with annotated dimensions for clarity.

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  Figure 2. Transvalvular pressure gradient is defined as the difference in pressure between the left ventricle and the aortic outflow tract.

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  Figure 3. (a) Pressure coefficient distribution in the sinus of Valsalva in steady flow and (b) pressure coefficient distribution with Hill’s spherical vortex model in steady flow. The velocity distribution is shown using streamlines, with intermediate arrow markers to indicate the flow direction.

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  Figure 4. Comparison of experimental results of Bellhouse et al. (1969) [5] and numerical results for cases of different stiffness in (a) temporal evolution of valve opening area and (b) pressure differences during valve closure where Δp=pc−pa.

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  Figure 5. Comparison of experimental results of Bellhouse et al. (1969) [5] and numerical results for cases of different leaflet stiffness in (a) temporal evolution of flow into the aorta, (b) flow into the cusp–sinus cavity at closure phase, and (c) stress–strain curves for different leaflet stiffness.

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  Figure 6. Velocity and vorticity distributions for (a–c) pre-peak systole, (d,e) peak systole, and (f) post-peak systole. Secondary vortical structures forming after the development of the primary vortex are indicated with red and green arrows. The small inset plot (with the black curve) shows the aortic opening area during the systolic phase, with the red dot indicating the instantaneous time.

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  Figure 7. (a) The trajectories of the main vortex derived from three stiffness models; (b) evolution of the maximum vorticity of the vortex region with time.