Resonances in pulsatile channel flow with an elastic wall

TL;DR

This paper investigates how pulsatile flow interacts with elastic vessel walls, revealing resonance phenomena and providing analytical predictions for oscillation amplitudes in a simplified model relevant to physiological and engineering flows.

Contribution

It introduces a numerical and analytical study of pulsatile flow in elastic channels, identifying resonance conditions and characterizing the system as a forced harmonic oscillator with unique damping.

Findings

Resonance occurs under specific flow conditions.

The system behaves as a forced harmonic oscillator.

Analytical predictions match numerical results.

Abstract

Interactions between fluids and elastic solids are ubiquitous in application ranging from aeronautical and civil engineering to physiological flows. Here we study the pulsatile flow through a two-dimensional Starling resistor as a simple model for unsteady flow in elastic vessels. We numerically solve the equations governing the flow and the large-displacement elasticity and show that the system responds as a forced harmonic oscillator with non-conventional damping. We derive an analytical prediction for the amplitude of the oscillatory wall deformation, and thus the conditions under which resonances occur or vanish.