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

  • Author / Creator
    Canham, Mitchell H
  • 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.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Putkaradze, Vakhtang (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Melnikov, Alexander (Mathematical and Statistical Sciences)
    • Flynn, Morris (Mechanical Engineering)
    • Hillen, Thomas (Mathematical and Statistical Sciences)
    • Putkaradze, Vakhtang (Mathematical and Statistical Sciences)