Parametric Search for Optimal Channel Shape for Swirling Blood Flow in the Heart and Main Vessels

The study presents a numerical parametric investigation of flow structures in channels with a longitudinal-radial profile zR^N = Const and a spherical dome at the base. The goal of the study was to examine the flow structures in these channels depending on the exponent N of the profile and the height of the dome, to determine the conditions that provide optimal centripetal swirling flow, analogous to blood flow in the heart chambers and major vessels. The investigation was conducted using a comparative analysis of flow structures in channel configurations zR^N = Const, carried out in two stages. In the first stage, the convergence parameter N was varied from 1.25 to 2.75 to identify the value that ensures optimal flow conditions. In the second stage, for the established value of N, the dome height was varied from 2.5 to 15 mm to identify the beneficial effects associated with its presence. The method of investigation involved numerical modeling in a steady-state regime. The results of the study on the influence of the convergence parameter revealed that the profile zR² = Const provides optimal conditions for the formation of swirling flow with minimal specific losses and a uniform distribution of velocity gradients. This channel configuration also showed the best agreement with the analytical solutions for Burgers' vortex, confirming its effectiveness in the static approximation of flows. The parametric investigation of dome height indicated that an optimal dome height of 7 mm contributes to the smoothing of velocity gradients and the reduction of viscous losses due to the optimal enhancement of the centripetal swirling flow scale.