Flow-rate limitation in a uniform thin-walled collapsible tube, with comparison to a uniform thick-walled tube and a tube of tapering thickness

Bertram, Christopher; Elliott, N. S. J.

doi:10.1016/s0889-9746(02)00160-3

Cited by 35 publications

(33 citation statements)

References 17 publications

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“…Three-dimensional fluid-structure interactions in smooth collapsible tubes have been examined extensively both experimentally, 3,4,7,14,24,25,28,32 and numerically. 22,23,33,40,43 However, it seems that very little attention has been paid to non-Newtonian flow in compliant ducts with staggered baffles.…”

Section: Introductionmentioning

confidence: 99%

Non-Newtonian Bile Flow in Elastic Cystic Duct: One- and Three-Dimensional Modeling

Luo

Chin

et al. 2008

Ann Biomed Eng

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Abstract-Bile flow is thought to play an essential role in the pathophysiological genesis of cholelithiasis (gallstone formation) and in gallbladder pain. In this paper, we extend our previous study of the human biliary system (Li et al., 2007, J. Biomech. Eng., 129:164-173) to include two important factors: the non-Newtonian properties of bile, and elastic deformation of the cystic duct. A one-dimensional (1D) model is analyzed and compared with three-dimensional (3D) fluid-structure interaction simulations. It is found that non-Newtonian bile raises resistance to the flow of bile, which can be augmented significantly by the elastic deformation (collapse) of the cystic duct. We also show that the 1D model predicts the pressure drop of the cystic duct flow well for all cases considered (Newtonian or non-Newtonian flow, rigid or elastic ducts), when compared with the full 3D simulations.

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Section: Introductionmentioning

confidence: 99%

Non-Newtonian Bile Flow in Elastic Cystic Duct: One- and Three-Dimensional Modeling

Luo

Chin

et al. 2008

Ann Biomed Eng

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“…Hence, the domain decomposition discussed previously is not only natural, but it also helps to resolve regions around the membrane ends. We map subdomains [b 1 , 0], [0, 1] and [1, b 2 ] into the [−1, 1] interval, so that the interpolation points represent the extrema of the Nth-order Chebyshev polynomial and we use Chebyshev collocation differential matrices to approximate x-derivatives of functions at the collocation points. The number of collocation points is different in different domains and so are the lengths of the different segments.…”

Section: Appendix B Computational Methodsmentioning

confidence: 99%

“…The resulting matrix is dense since we are using a spectral method for the spatial discretization, but the number of collocation points is relatively small. For b 1 = −10 and b 2 = 11, 200 collocation points in each of the subdomains x ∈ [b 1 , 0] and x ∈ [1, b 2 ], and 20 collocation points for x ∈ [0, 1] was found to be sufficient. Therefore, it is possible to invert the matrices by applying a straightforward LU-decomposition [32].…”

Section: Appendix B Computational Methodsmentioning

confidence: 99%

“…Similar systems have been studied many times before, most notably by Smith [17,18], Bogdanova & Ryzhov [19], Pedley & Stephanoff [20], Pedley [16], Pihler-Puzović & Pedley [21]. We follow Pedley & Stephanoff [20] in assuming that the height of the indentation is much greater than the thickness of the boundary layers which form at the walls, but is still small compared with 1, and σ = O (1). This assumption allows us to proceed to O(ε 2 ) in the x-momentum Navier-Stokes equation to obtain the following equation in the inviscid core:…”

Section: The Modelmentioning

confidence: 96%

“…Similar instabilities are readily observed in experimental collapsible-tube systems, such as the Starling resistor [1], but are yet to be fully understood in all flow regimes [2]. Moreover, although collapsible channels are inherently global systems with self-excited oscillations often being driven or considerably modified by the presence of finite boundaries [3], they are undoubtedly linked to the local instabilities in homogeneous domains with flexible walls [4][5][6][7].…”

Section: Introductionmentioning

confidence: 91%

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Flutter in a quasi-one-dimensional model of a collapsible channel

Pihler-Puzović

Pedley

2014

Proc. R. Soc. A.

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The effects of wall inertia on instabilities in a collapsible channel with a long finite-length flexible wall containing a high Reynolds number flow of incompressible fluid are studied. Using the ideas of interactive boundary layer theory, the system is described by a one-dimensional model that couples inviscid flow outside the boundary layers formed on the channel walls with the deformation of the flexible wall. The observed instability is a form of flutter, which is superposed on the behaviour of the system when the wall mass is neglected. We show that the flutter has a positive growth rate because the fluid loading acts as a negative damping in the system. We discuss these findings in relation to other work on self-excited oscillations in collapsible channels.

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Sensitivity of unsteady collapsible channel flows to modelling assumptions

Liu

Luo

Cai

et al. 2009

Commun. Numer. Meth. Engng.

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SUMMARYWe investigate the influences of modelling assumptions on the dynamic behaviour of collapsible channel flows. The elastic wall is modelled in various different ways: as a large strain Bernoulli-Euler beam, as a small strain Timoshenko beam, and as a 2D-solid model derived from a general virtual work approach, using small strain or large strain assumptions. Different inlet boundary conditions are also considered. The in-house finite element codes and the commercial finite element package ADINA 8.4 are used. The steady results agree very well when using the different models/approaches. The unsteady results, on the other hand, can be quite different. The dynamic behaviour of the system is analysed for a set of chosen parameters, using the full numerical solvers, the linear stability analysis, and the Fourier transform. It is found that the system stability is highly sensitive to the solid modelling assumptions used, numerical solvers adopted, or the boundary conditions imposed. Accuracy of the numerical schemes also has an impact on the system's unsteady behaviour. However, despite the high sensitivity of the unsteady solutions to the modelling assumptions, a cascade stability structure previously revealed by the authors seems to exist when different numerical approaches are used.

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Flow-rate limitation in a uniform thin-walled collapsible tube, with comparison to a uniform thick-walled tube and a tube of tapering thickness

Cited by 35 publications

References 17 publications

Non-Newtonian Bile Flow in Elastic Cystic Duct: One- and Three-Dimensional Modeling

Non-Newtonian Bile Flow in Elastic Cystic Duct: One- and Three-Dimensional Modeling

Flutter in a quasi-one-dimensional model of a collapsible channel

Sensitivity of unsteady collapsible channel flows to modelling assumptions

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