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On Flexible Tubes Conveying a Moving Fluid: Variational Dynamics and Spectral Analysis Open Access


Other title
Collapsible tubes
Fluid-structure interaction
Arnoldi algorithm
Variational integrators
Koopman operator
Fluid-conveying tubes
Type of item
Degree grantor
University of Alberta
Author or creator
Canham, Mitchell H
Supervisor and department
Putkaradze, Vakhtang (Mathematical and Statistical Sciences)
Examining committee member and department
Melnikov, Alexander (Mathematical and Statistical Sciences)
Flynn, Morris (Mechanical Engineering)
Putkaradze, Vakhtang (Mathematical and Statistical Sciences)
Hillen, Thomas (Mathematical and Statistical Sciences)
Department of Mathematical and Statistical Sciences
Applied Mathematics
Date accepted
Graduation date
2017-06:Spring 2017
Master of Science
Degree level
This study focuses on the motion of a hollow flexible tube conveying a flowing fluid, also known as the garden-hose instability. This system becomes unstable when the fluid moving through the pipe exceeds a critical flow rate. This non-linear dynamical system involves complex fluid-structure interactions. As the fluid travels down the pipe it can cause deformations to the pipe structure, which consequently changes the flow dynamics. Research into this system began with the work of Ashley and Haviland (1950), who were attempting to explain vibrations which show up in pipelines. It has since garnered considerable interest in scientific literature as it has numerous practical applications. It can be used to model biomechanical systems such as blood flow through arteries or airflow through alveoli in the lungs. It also has applications to aerospace designs as early stage rocket engines require rapid transfer of enormous quantities of fuel through relatively thin and lightweight pipes. My research involves creating a simple model of a hollow tube conveying a fluid and investigating the ordinary differential equations that get produced. This model uses a geometrically exact theory that takes into consideration a tube that has a variable cross section in space and time. This theory is derived in a Lagrangian variational framework. I will also present a physical experiment I created of a flexible tube conveying water. Data is collected from the experiment using a stereoscopic camera set up and a centerline detection algorithm. I suggest a means to analyze this type of data using a Koopman operator, which has never been previously used to investigate the dynamics of the garden hose instability.
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