We develop a theory of fluidstructure 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 leadingorderinslenderness 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 twoway coupling the oscillatory flow and the wall deformation via the continuity equation, a onedimensional 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 cycleaveraged pressure (for harmonic pressurecontrolled 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 reducedorder PDE and its perturbative solutions are validated against threedimensional, twowaycoupled 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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Verification and convergence study of a spectralelement numerical methodology for fluidstructure interaction
A highorder in space spectralelement methodology for the solution of a strongly coupled fluidstructure interaction (FSI) problem is developed. A methodology is based on a partitioned solution of incompressible fluid equations on bodyfitted grids, and nonlinearlyelastic solid deformation equations coupled via a fixedpoint iteration approach with Aitken relaxation. A comprehensive verification strategy of the developed methodology is presented, including h, pand temporal refinement studies. An expected order of convergence is demonstrated first separately for the corresponding fluid and solid solvers, followed by a selfconvergence study on a coupled FSI problem (selfconvergence refers to a convergence to a reference solution obtained with the same solver at higher resolution). To this end, a new threedimensional fluidstructure interaction benchmark is proposed for a verification of the FSI codes, which consists of a fluid flow in a channel with one rigid and one flexible wall. It is shown that, due to a consistent problem formulation, including initial and boundary conditions, a highorder spatial convergence on a fully coupled FSI problem can be demonstrated. Finally, a developed framework is applied successfully to a Direct Numerical Simulation of a turbulent flow in a channel interacting with a compliant wall, where the fluidstructure interface is fully resolved.
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 NSFPAR ID:
 10291762
 Date Published:
 Journal Name:
 Journal of computational physics
 Volume:
 10
 ISSN:
 25900552
 Page Range / eLocation ID:
 100084
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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