Oscillating viscous flow past a streamwise linear array of circular cylinders

Abstract

This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.

Stationary flow driven by non-sinusoidal time-periodic pressure gradients in wavy-walled channels

“…Although a similar degree of agreement between asymptotic predictions and DNS computations has been found for in other steady-streaming configurations, e.g. for flow about a linear array of cylinders [ 34 ], this result should be taken with caution, in that the relative departures can be dependent on the specific conditions. For instance, the agreement displayed in Fig.…”

Effects of buoyancy on the dispersion of drugs released intrathecally in the spinal canal

“…Their discrete nature may potentially hinder their integration in models based on a slowly varying geometry. Fundamental understanding acquired in connection with oscillatory flows in wavy channels ( Guibert, Plouraboué & Bergeon 2010 ; Alaminos-Quesada et al 2022 , 2023a ) and obstacle arrays ( House, Lieu & Schwartz 2014 ; Bhosale, Parthasarathy & Gazzola 2020 ; Alaminos-Quesada et al 2023b ) can be instrumental to aid these future modelling efforts. In this connection, it is worth mentioning the approximate transport equation proposed recently by Linninger et al (2023) , which incorporates a longitudinal diffusion term with an experimentally fitted diffusivity as a computationally inexpensive means to provide quantification of drug dispersion in the presence of nerve roots.…”