Steady inlet flow in stenotic geometries: convective and absolute instabilities

Abstract

Steady inlet flow through a circular tube with an axisymmetric blockage of varying size is studied both numerically and experimentally. The geometry consists of a long, straight tube and a blockage, semicircular in cross-section, serving as a simplified model of an arterial stenosis. The stenosis is characterized by a single parameter, the aim being to highlight fundamental behaviours of constricted flows, in terms of the total blockage. The Reynolds number is varied between 50 and 2500 and the stenosis degree by area between 0.20 and 0.95. Numerically, a spectral-element code is used to obtain the axisymmetric base flow fields, while experimentally, results are obtained for a similar set of geometries, using water as the working fluid. At low Reynolds numbers, the flow is steady and characterized by a jet flow emanating from the contraction, surrounded by an axisymmetric recirculation zone. The effect of a variation in blockage size on the onset and mode of instability is investigated. Linear stability analysis is performed on the simulated axisymmetric base flows, in addition to an analysis of the instability, seemingly convective in nature, observed in the experimental flows. This transition at higher Reynolds numbers to a time-dependent state, characterized by unsteadiness downstream of the blockage, is studied in conjunction with an investigation of the response of steady lower Reynolds number flows to periodic forcing.

A pressure-gradient mechanism for vortex shedding in constricted channels

“…Stages (a) and (b) in the figure are found in existing research and are present in the current investigation. Although it has been suggested by others (e.g., Varghese et al 6 and Griffith et al 14 ) that an instability may play a role in vortex shedding, the physical mechanism identified by the sequence (c) through (f), through which it leads to vortex splitting and shedding, to our knowledge has not been described previously. In this mechanism, the growing streamwise pressure gradient first leads to an internal vortex splitting characterized by local extrema in the streamfunction and then to external vortex splitting through its action on the low-momentum fluid within the recirculation region.…”

“…Numerical and experimental investigations of stenotic flow in an axisymmetric circular tube having a steady inlet flow are performed by Griffith et al 14 The effect of blockage size on the type of instability (convective or absolute) is studied. At sufficiently large Reynolds numbers, experiments indicate a convective instability occurring downstream of the blockage.…”

“…Convective instabilities may be dominant in the related problem of flow in a partially constricted tube (stenotic flows) with a steady inlet velocity. 6,14,32,34 In addition, convective instabilities are identified in the two-dimensional flow over a bump, 2 the backward-facing step, [30][31][32][33] and separated boundary-layer. 10 In each of these problems, the base flow is strongly nonparallel.…”

“…Griffith et al 14 shows experimentally for stenotic flows that the convective instability plays an important role in the transition of the flow to an unsteady state. For separated boundary-layer problems, unsteadiness in the flow is attributed to convective instabilities from the continuous effects of noise.…”

In vitro validation of flow measurement with phase contrast MRI at 3 tesla using stereoscopic particle image velocimetry and stereoscopic particle image velocimetry-based computational fluid dynamics

“…However, PC-MRI velocity contours at the outlet are noisier compared with the other two sections. This may be explained by the fact that flow distal to the stenosis can be unsteady even in the constant flow cases (see for example (27)), causing spin dephasing. Flow measurement by each method assumes constant velocity over a short period of time.…”