Obtaining Expressions for Time-Dependent Functions That Describe the Unsteady Properties of Swirling Jets of Viscous Fluid

Eugene Talygin and Alexander Gorodkov
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Eugene Talygin: Bakulev National Medical Research Center for Cardiovascular Surgery, 121552 Moscow, Russia
Alexander Gorodkov: Bakulev National Medical Research Center for Cardiovascular Surgery, 121552 Moscow, Russia

Mathematics, 2021, vol. 9, issue 16, 1-8

Abstract: Previously, it has been shown that the dynamic geometric configuration of the flow channel of the left heart and aorta corresponds to the direction of the streamlines of swirling flow, which can be described using the exact solution of the Navier–Stokes and continuity equations for the class of centripetal swirling viscous fluid flows. In this paper, analytical expressions were obtained. They describe the functions C 0 ( t ) and Γ 0 ( t ) , included in the solutions, for the velocity components of such a flow. These expressions make it possible to relate the values of these functions to dynamic changes in the geometry of the flow channel in which the swirling flow evolves. The obtained expressions allow the reconstruction of the dynamic velocity field of an unsteady potential swirling flow in a flow channel of arbitrary geometry. The proposed approach can be used as a theoretical method for correct numerical modeling of the blood flow in the heart chambers and large arteries, as well as for developing a mathematical model of blood circulation, considering the swirling structure of the blood flow.

Keywords: potential swirling flow; Navier–Stokes equations; unsteady swirling flow; tornado-like jets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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