Soft Hydraulics in Channels with Thick Walls: The Finite-Reynolds-Number Base State and Its Stability

TL;DR

This paper investigates the linear stability of flow and deformation in a soft hydraulic conduit with thick walls at finite Reynolds numbers, showing stability under certain conditions and identifying oscillatory eigenmodes.

Contribution

It provides a finite-Reynolds-number analysis of the base state and stability in soft hydraulic channels with thick walls, advancing understanding of fluid-structure interactions.

Findings

Flow is linearly stable to infinitesimal perturbations at fixed upstream flux.

Multiple oscillatory stable eigenmodes are identified.

Results establish a framework for future studies on flow instability and transition.

Abstract

We analyze the linear stability of the base state of the problem of coupled flow and deformation in a long and shallow rectangular soft hydraulic conduit with a thick top wall. Specifically, the steady base state is computed at low but finite Reynolds number. Then, we show that with the upstream flux fixed and the outlet pressure set to gauge, the flow is linearly stable to infinitesimal flow-wise perturbations. Multiple oscillatory but stable eigenmodes are computed in a range of the reduced Reynolds number, $\hat{Re}$, and the so-called fluid--structure interaction (FSI) parameter, $\lambda$, indicating the stiffness of this FSI system. These results provide a framework to address, in future work, the individual effects of various aspects of two-way FSI coupling on instability and flow transition in soft hydraulic conduits.