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The interaction between deformable surfaces and oscillatory driving is known to produce complex secondary time-averaged flows due to inertial and elastic nonlinearities. Here, we revisit the problem of oscillatory flow in a cylindrical tube with a deformable wall, and analyse it under a long-wave theory for small deformations, but for arbitrary Womersley numbers. We find that the oscillatory pressure does not vary linearly along the length of a deformable channel, but instead decays exponentially with spatial oscillations. We show that this decay occurs over an elasto-visco-inertial length scale that depends on the material properties of the fluid and the elastic walls, the geometry of the system, and the frequency of the oscillatory flow, but is independent of the amplitude of deformation. Inertial and geometric nonlinearities associated with the elastic deformation of the channel drive a time-averaged secondary flow. We quantify the flow using numerical solutions of the perturbation theory, and gain insight by developing analytic approximations. The theory identifies a complex non-monotonic dependence of the time-averaged flux on the elastic compliance and inertia, including a reversal of the flow. Finally, we show that our analytic theory is in excellent quantitative agreement with the three-dimensional direct numerical simulations of Pandeet al.(Phys. Rev. Fluids, vol. 8, no. 12, 2023, 124102).
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Spatio-temporal relationship between three-dimensional deformations of a collapsible tube and the downstream flowfield
The interactions between fluid flow and structural components of collapsible tubes are representative of those in several physiological systems. Although extensively studied, there exists a lack of characterization of the three-dimensionality in the structural deformations of the tube and its influence on the flow field. This experimental study investigates the spatio-temporal relationship between 3D tube geometry and the downstream flow field under conditions of fully open, closed, and slamming-type oscillating regimes. A methodology is implemented to simultaneously measure three-dimensional surface deformations in a collapsible tube and the corresponding downstream flow field. Stereophotogrammetry was used to measure tube deformations, and simultaneous flow field measurements included pressure and planar Particle Image Velocimetry (PIV) data downstream of the collapsible tube. The results indicate that the location of the largest collapse in the tube occurs close to the downstream end. In the oscillating regime, sections of the tube downstream of the largest mean collapse experience the largest oscillations in the entire tube that are completely coherent and in phase. At a certain streamwise distance upstream of the largest collapse, a switch in the direction of oscillations occurs with respect to those downstream. Physically, when the tube experiences constriction downstream of the location of the largest mean collapse, this causes the accumulation of fluid and build-up of pressure in the upstream regions and an expansion of these sections. Fluctuations in the downstream flow field are significantly influenced by tube fluctuations along the minor axes. The fluctuations in the downstream flowfield are influenced by the propagation of disturbances due to oscillations in tube geometry, through the advection of fluid through the tube. Further, the manifestation of the LU-type pressure fluctuations is found to be due to the variation in the propagation speed of the disturbances during the different stages within a period of oscillation of the tube.
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- Award ID(s):
- 2145189
- PAR ID:
- 10502880
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of Fluids and Structures
- Volume:
- 127
- Issue:
- C
- ISSN:
- 0889-9746
- Page Range / eLocation ID:
- 104122
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jfluidstructs.2024.104122
