An official website of the United States government
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.
more »
« less
This content will become publicly available on August 1, 2025
Partitioning method for the finite element approximation of a 3D fluid‐2D plate interaction system
Abstract We consider the finite element approximation of a coupled fluid‐structure interaction (FSI) system, which comprises a three‐dimensional (3D) Stokes flow and a two‐dimensional (2D) fourth‐order Euler–Bernoulli or Kirchhoff plate. The interaction of these parabolic and hyperbolic partial differential equations (PDE) occurs at the boundary interface which is assumed to be fixed. The vertical displacement of the plate dynamics evolves on the flat portion of the boundary where the coupling conditions are implemented via the matching velocities of the plate and fluid flow, as well as the Dirichlet boundary trace of the pressure. This pressure term also acts as a coupling agent, since it appears as a forcing term on the flat, elastic plate domain. Our main focus in this work is to generate some numerical results concerning the approximate solutions to the FSI model. For this, we propose a numerical algorithm that sequentially solves the fluid and plate subsystems through an effective decoupling approach. Numerical results of test problems are presented to illustrate the performance of the proposed method.
more »
« less
- Award ID(s):
- 2348312
- PAR ID:
- 10533392
- Publisher / Repository:
- Numerical Methods for Partial Differential Equations
- Date Published:
- Journal Name:
- Numerical Methods for Partial Differential Equations
- ISSN:
- 0749-159X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A high-order in space spectral-element methodology for the solution of a strongly coupled fluid-structure interaction (FSI) problem is developed. A methodology is based on a partitioned solution of incompressible fluid equations on body-fitted grids, and nonlinearly-elastic solid deformation equations coupled via a fixed-point iteration approach with Aitken relaxation. A comprehensive verification strategy of the developed methodology is presented, including h-, p-and temporal refinement studies. An expected order of convergence is demonstrated first separately for the corresponding fluid and solid solvers, followed by a self-convergence study on a coupled FSI problem (self-convergence refers to a convergence to a reference solution obtained with the same solver at higher resolution). To this end, a new three-dimensional fluid-structure 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 high-order 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 fluid-structure interface is fully resolved.more » « less
-
This experimental study focuses on fluid-structure interaction (FSI) for a thin compliant panel under a shock/boundary layer interaction (SBLI) generated by a 2D compression ramp in a Mach 2 wind tunnel. In previous work, we have studied the FSI for this configuration using simultaneous fast-response pressure-sensitive paint (PSP) and digital image correlation (DIC). Simultaneous PSP/DIC allows for examination of the relationship between the dynamic panel displacement and surface pressure loading, respectively. Spectral analysis showed that pressure fluctuations within the interaction region and shock-foot unsteadiness tend to lock to the first mode resonant frequency of the compliant panel. The current study aims to utilize synchronous high-speed stereoscopic PIV (25 kHz) and DIC (5 kHz) techniques to better understand the coupling between the flow field and the panel displacement field. The PIV is obtained in a streamwise-spanwise plane located at 15% of the boundary layer height. Thin compliant polycarbonate panel with thicknesses of 1 mm is utilized, which has a first-mode vibrational frequency of 407 Hz. The 1 mm panel out-of-plane displacement amplitude was up to 15% of the boundary layer thickness. The analysis includes low-pass and band-pass filtering of the velocity data, including the surrogate separation line, and cross-correlation analysis between panel displacement and velocity. The results indicate a clear coupling of the panel motion and velocity field, but the spectral analysis suffers from limited time records associated with the pulse-burst laser used for PIV. Future work will focus on collecting more data to improve the statistical convergence of the results.more » « less
-
This work presents recent advancements in the study of film cooling in hypersonic flows, considering experimental and numerical investigations, with the aim to characterize the wall-cooling performance in different coolant injection and baseflow conditions in a Mach number range 2–7.7. The study explores the mutual interaction between the injected coolant film and the boundary-layer flow, with emphasis on the effects of wall blowing on the boundary-layer characteristics, stability, and transition to turbulence, as well as the effect of transition on wall-cooling performance. Considered flow configurations include cases of effusion cooling in both wall-normal or slightly inclined and wall-parallel blowing, different types of coolant, cases of favorable pressure gradient compared to zero pressure gradient, as well as transpiration cooling cases at different blowing ratios and surface geometries. For the transpiration cooling case, experiments in different hypersonic wind tunnel facilities are presented for flat plate and cone geometries, with coolant injected through C/C porous samples, whereas numerical simulations of modeled porous injection are presented for a flat plate and a blunt cone, showing results for the boundary-layer receptivity with coolant injection and the associated effects on transition and cooling performance. A summary of the main findings is provided along with a critical analysis based on a comparative study to evaluate the effect of each configuration, injection strategy, and key parameters on the boundary-layer flow and the feedback on wall-cooling performance. Conclusions are drawn about potential directions of study for the further development and optimization of the film cooling technique for future hypersonic vehicles.more » « less
-
Given the complexity of human left heart anatomy and valvular structures, the fluid–structure interaction (FSI) simulation of native and prosthetic valves poses a significant challenge for numerical methods. In this review, recent numerical advancements for both fluid and structural solvers for heart valves in patient-specific left hearts are systematically considered, emphasizing the numerical treatments of blood flow and valve surfaces, which are the most critical aspects for accurate simulations. Numerical methods for hemodynamics are considered under both the continuum and discrete (particle) approaches. The numerical treatments for the structural dynamics of aortic/mitral valves and FSI coupling methods between the solid Ωs and fluid domain Ωf are also reviewed. Future work toward more advanced patient-specific simulations is also discussed, including the fusion of high-fidelity simulation within vivo measurements and physics-based digital twining based on data analytics and machine learning techniques.more » « less
