<p>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.</p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/22654300 |
| Date | 19 April 2023 |
| Creators | Shrihari Dhananjay Pande (14551670) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Reduced_Modelling_of_Oscillatory_Flows_in_Compliant_Conduits_at_the_Microscale/22654300 |
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