Purdue University Graduate School
Masters_Thesis_Shrihari-Final.pdf (1.34 MB)

Reduced Modelling of Oscillatory Flows in Compliant Conduits at the Microscale

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posted on 2023-04-19, 12:52 authored by Shrihari Dhananjay PandeShrihari Dhananjay Pande

In this thesis, a theory of fluid--structure interaction (FSI) between an oscillatory Newtonian fluid flow and a compliant conduit is developed for  canonical geometries consisting of a 2D channel with a deformable top wall and an axisymmetric deformable tube. Focusing on hydrodynamics, a linear relationship between wall displacement and  hydrodynamic pressure is employed, due to its suitability for a leading-order-in-slenderness theory. The slenderness assumption also allows the use of lubrication theory, which is used to relate flow rate  to the pressure gradient (and the tube/wall deformation) via the classical solutions for oscillatory flow in a channel and in a tube (attributed to Womersley). Then, by two-way coupling the oscillatory flow and the wall deformation via the continuity equation, a one-dimensional nonlinear partial differential equation (PDE) governing the instantaneous pressure distribution along the conduit is obtained, without \textit{a priori} assumptions on the magnitude of the oscillation frequency (i.e., at arbitrary Womersley number).The PDE is solved numerically to evaluate the pressure distribution as well as the cycle-averaged pressure at several points along the length of the channel and the tube. It is found  that the cycle-averaged pressure (for harmonic pressure-controlled conditions) deviates from the expected steady pressure distribution, suggesting the presence of a streaming flow. An analytical perturbative solution for a weakly deformable conduit is also obtained to rationalize how FSI induces such streaming. In the case of a compliant tube, the results obtained from the proposed reduced-order PDE and its perturbative solutions are validated against three-dimensional, two-way-coupled direct numerical simulations. A good agreement is shown  between theory and simulations for a range of dimensionless parameters characterizing the oscillatory flow and the FSI, demonstrating the validity of the proposed theory of oscillatory flows in compliant conduits at arbitrary Womersley number.


Degree Type

  • Master of Science


  • Mechanical Engineering

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Dr. Ivan C. Christov

Additional Committee Member 2

Dr. Steven T. Wereley

Additional Committee Member 3

Dr. Adrian Buganza Tepole

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