Reduced Modelling of Oscillatory Flows in Compliant Conduits at the Microscale
Abstract
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 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
M.S.
Advisors
Christov, Purdue University.
Subject Area
Mechanical engineering|Fluid mechanics
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