Linear stability of flow in a 90-degree bend

TL;DR

This study investigates the flow stability in a 90-degree bend, revealing the existence of separation bubbles, vortex shedding, and the conditions under which flow becomes unstable to perturbations, using high-fidelity numerical methods.

Contribution

It provides the first detailed analysis of the modal stability of flow in a 90-degree bend, including critical Reynolds numbers and unstable modes for both 2D and 3D disturbances.

Findings

Three separation bubbles and vortex shedding observed.

Two-dimensional disturbances have higher critical Reynolds numbers than three-dimensional ones.

Three-dimensional instability is linked to recirculation bubbles after the bend.

Abstract

The paper considers a two-dimensional flow in a channel, which consists of straight inlet and outlet branches and a circularly 90-degree curved bend. An incompressible viscous fluid flows through the elbow under the action of a constant pressure gradient between the inlet and outlet. Navier-Stokes equations were solved numerically using a high-fidelity spectral/hp element method. In a range of Reynolds numbers, an adaptive selective frequency dumping method was used to get a steady-state flow. It was found that three separation bubbles and vortex shedding can exist in the bend. The modal stability of two- and three-dimensional perturbations was investigated. Critical Reynolds number of the two-dimensional disturbances was found as extrapolation by lower Reynolds number results. It is much greater than three-dimensional one, but the two-dimensional flow could subcritically unstable with respect to the imposed small-amplitude white noise. For three-dimensional perturbations, the dependence of the critical Reynolds numbers on the bending radius is obtained. For a case of a moderate bending radius the neutral curve is provided and eigenfunctions are studied in detail: three-dimensional instability can be caused by periodic or monotonically growing mode, these unstable modes regard to the recirculation bubbles that occur after the bend.