Stability of helical tubes conveying fluid

TL;DR

This paper develops a geometric variational approach to analyze the linear stability of helical and collapsible tubes conveying fluid, providing a comprehensive method for arbitrary three-dimensional configurations and revealing stability loss mechanisms.

Contribution

It introduces a novel methodology based on geometric variational principles for stability analysis of collapsible, helical tubes, enabling treatment of complex 3D configurations with constant coefficient equations.

Findings

Stability loss in straight tubes due to cross-sectional area change.

Complete stability analysis for arbitrary 3D helical configurations.

Numerical validation of the stability theory for straight and helical tubes.

Abstract

We study the linear stability of elastic collapsible tubes conveying fluid, when the equilibrium configuration of the tube is helical. A particular case of such tubes, commonly encountered in applications, is represented by quarter- or semi-circular tubular joints used at pipe's turning points. The stability theory for pipes with non-straight equilibrium configurations, especially for collapsible tubes, allowing dynamical change of the cross-section, has been elusive as it is difficult to accurately develop the dynamic description via traditional methods. We develop a methodology for studying the three-dimensional dynamics of collapsible tubes based on the geometric variational approach. We show that the linear stability theory based on this approach allows for a complete treatment for arbitrary three-dimensional helical configurations of collapsible tubes by reduction to an equation with constant coefficients. We discuss new results on stability loss of straight tubes caused by the cross-sectional area change. Finally, we develop a numerical algorithm for computation of the linear stability using our theory and present the results of numerical studies for both straight and helical tubes.