Viscous laminar flow in a locally constricted axisymmetric pipe

摘要

This paper examines the low Reynolds number viscous flow in the neighbourhood of a constriction in a circular pipe via a method of slow variations. Relationships between flow reversal, associated vanishing pressure gradients, and the volumetric flow rates which produce them are obtained. Critical values of the flow rate are given which distinguish which flow geometry will prevail. We show that vanishing pressure gradient surfaces can originate at points along the central axis of the pipe. An interpretation of results in terms of vortex dynamics is given by the introduction a variable l-the ring circulation-which places at the forefront the role of the central axis. Relevance to cardiovascular flow dynamics studies is noted in the abruptness of pressure gradients seen in the figures here. The algebraic relationships given in this paper should be useful in numerical-experimental studies and in direct numerical simulations with 'standard' models-which are typically characterized by very heavy computational effort for flows involving cylindrical geometries.