Dean Instability in Double-Curved Channels

TL;DR

This paper investigates the Dean instability in double-curved channels using an improved lattice Boltzmann model, revealing complex vortex flow transitions and the influence of channel curvature on critical flow conditions.

Contribution

It introduces an enhanced lattice Boltzmann method for generalized metrics and applies it to analyze vortex flow transitions in double-curved channels with novel findings.

Findings

Validated the method with known critical Dean numbers.

Discovered transitions to 2-, 4-, and 6-cell vortex flows.

Found the critical Dean number has a minimum when curvatures are equal.

Abstract

We study the Dean instability in curved channels using the lattice Boltzmann model for generalized metrics. For this purpose, we first improve and validate the method by measuring the critical Dean number at the transition from laminar to vortex flow for a streamwise curved rectangular channel, obtaining very good agreement with the literature values. Taking advantage of the easy implementation of arbitrary metrics within our model, we study the fluid flow through a double-curved channel, using ellipsoidal coordinates, and study the transition to vortex flow in dependence of the two perpendicular curvature radii of the channel. We observe not only transitions to 2-cell vortex flow, but also to 4-cell and even 6-cell vortex flow, and we find that the critical Dean number at the transition to 2-cell vortex flow exhibits a minimum when the two curvature radii are approximately equal.