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We develop a theory of fluid--structure interaction (FSI) between an oscillatory Newtonian fluid flow and a compliant conduit. We consider the canonical geometries of a 2D channel with a deformable top wall and an axisymmetric deformable tube. Focusing on the hydrodynamics, we employ a linear relationship between wall displacement and hydrodynamic pressure, which has been shown to be suitable for a leading-order-in-slenderness theory. The slenderness assumption also allows the use of lubrication theory, and the flow rate is related 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 (\textit{i.e.}, at arbitrary Womersley number). We find 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 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. We find good agreement 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.
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Code and data for "Theory and simulation of elastoinertial rectification of oscillatory flows in two-dimensional deformable rectangular channels"
Oscillatory flows between deformable boundaries frequently occur in various processes within engineered and biological systems. The fluid–structure interaction problem, and specifically the two-way pressure-deformation coupling that arises due to the flow in a compliant channel, is central to applications. A complete understanding of oscillatory flow in a compliant 2D channel (a canonical configuration) has not been achieved; specifically, developing the elastoinertial theory and benchmarking its predictions against detailed simulation data remains a knowledge gap. The goal of this work is to address these knowledge gaps.
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- Award ID(s):
- 2245343
- PAR ID:
- 10675534
- Publisher / Repository:
- Purdue University Research Repository
- Date Published:
- Edition / Version:
- 1.0
- Subject(s) / Keyword(s):
- CFD Mechanical Engineering FOS: Mechanical engineering fluid-structure interactions microfluidics lubrication theory viscous fluid flow soft hydraulics elastic deformation mathematical modeling oscillatory flow Finite-element method
- Format(s):
- Medium: X Size: 24 files; 467 MB Other: text/plain; text/x-script.python; application/zip; image/png
- Size(s):
- 24 files 467 MB
- Sponsoring Org:
- National Science Foundation
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