Flow in pipes with non-uniform curvature and torsion

Gammack, David; Hydon, Peter E.

doi:10.1017/s0022112001003548

Cited by 34 publications

(25 citation statements)

References 36 publications

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“…An extensive review on flow in curved tubes was provided by Berger et al [5]. Gammak and Hydon [6] studied steady and unsteady flows in pipes with small slowly varying curvature and torsion. They found that the azimuthal wall shear stress (WSS) was increased by the introduction of torsion.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Effects of Dynamic Change in Curvature and Torsion on Pulsatile Flow in a Helical Tube

Selvarasu

Tafti

2012

Journal of Biomechanical Engineering

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Cardiovascular diseases are the number one cause of death in the world, making the understanding of hemodynamics and the development of treatment options imperative. The effect of motion of the coronary artery due to the motion of the myocardium is not extensively studied. In this work, we focus our investigation on the localized hemodynamic effects of dynamic changes in curvature and torsion. It is our objective to understand and reveal the mechanism by which changes in curvature and torsion contribute towards the observed wall shear stress distribution. Such adverse hemodynamic conditions could have an effect on circumferential intimal thickening. Three-dimensional spatiotemporally resolved computational fluid dynamics (CFD) simulations of pulsatile flow with moving wall boundaries were carried out for a simplified coronary artery with physiologically relevant flow parameters. A model with stationary walls is used as the baseline control case. In order to study the effect of curvature and torsion variation on local hemodynamics, this baseline model is compared to models where the curvature, torsion, and both curvature and torsion change. The simulations provided detailed information regarding the secondary flow dynamics. The results suggest that changes in curvature and torsion cause critical changes in local hemodynamics, namely, altering the local pressure and velocity gradients and secondary flow patterns. The wall shear stress (WSS) varies by a maximum of 22% when the curvature changes, by 3% when the torsion changes, and by 26% when both the curvature and torsion change. The oscillatory shear stress (OSI) varies by a maximum of 24% when the curvature changes, by 4% when the torsion changes, and by 28% when both the curvature and torsion change. We demonstrate that these changes are attributed to the physical mechanism associating the secondary flow patterns to the production of vorticity (vorticity flux) due to the wall movement. The secondary flow patterns and augmented vorticity flux affect the wall shear stresses. As a result, this work reveals how changes in curvature and torsion act to modify the near wall hemodynamics of arteries.

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Section: Introductionmentioning

confidence: 99%

Investigation of the Effects of Dynamic Change in Curvature and Torsion on Pulsatile Flow in a Helical Tube

Selvarasu

Tafti

2012

Journal of Biomechanical Engineering

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“…The first results regarding the stationary problem in curved pipes are found in [14,15] where the author performs an asymptotic analysis depending on a parameter related with the curvature radio of the pipe and its cross section. Also, in [16][17][18][19] the flow behaviour inside the pipe is related with the curvature and torsion of its middle line. In [16] the main term of the asymptotic expansion of the solution is compared with a Poiseuille flow inside a pipe with rigid walls.…”

Section: Introductionmentioning

confidence: 99%

“…Also, in [16][17][18][19] the flow behaviour inside the pipe is related with the curvature and torsion of its middle line. In [16] the main term of the asymptotic expansion of the solution is compared with a Poiseuille flow inside a pipe with rigid walls. In [17,18] the authors use asymptotic methods to derive a one dimensional model justified with error estimates.…”

Section: Introductionmentioning

confidence: 99%

Rigorous justification of the asymptotic model describing a curved‐pipe flow in a time‐dependent domain

et al. 2018

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This paper is devoted to the mathematical justification of an asymptotic model of a viscous flow in a curved tube with moving walls by proving error estimates. To this aim, we first construct the space correctors near the pipe's inlet and outlet due to the boundary layer phenomenon. In order to guarantee the adequate properties for these correctors we study what we called modified Leray's problem defined in a semi-infinite strip. We ensure the existence and uniqueness of an exponential decaying solution when the axial variable tends to infinity. Then, by deriving a Poincaré's type inequality and other estimates for the boundary value problems taking into account the condition on the pipe's lateral boundary, we evaluate the difference between the asymptotic approximation and the exact solution of the problem. K E Y W O R D Sasymptotic analysis, curved pipe, error estimates, Navier-Stokes equations, time-dependent domain

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“…While the above mentioned work was primarily concerned with 0020-7683/$ -see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2009.09.022 rigid pipes there has been a body of research devoted to flow in flexible and rigid pipes (Berger et al, 1983;Zabielski and Mestel, 1998;Gammack and Hydon, 2001;Roberts, 2004) with applications ranging from the instabilities exhibited by pipes (Lundgren et al, 1979;Gregory and Paidoussis, 1966a;Gregory and Paidoussis, 1966b) to blood flow in arteries (Caro et al, 1996;Pedley, 1980).…”

Section: Introductionmentioning

confidence: 99%

The nonlinear dynamics of elastic tubes conveying a fluid

Beauregard

Goriely

Tabor

2010

International Journal of Solids and Structures

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a b s t r a c tThe Kirchhoff equations for elastic tubes are modified to include the effect of fluid flow. Using the techniques of linear and nonlinear analysis specially developed for the Kirchhoff equations, the effect of the fluid flow on the basic twist-to-writhe instability is investigated. The results suggest an intriguing modification of the bifurcation threshold due to the flow. Beyond threshold the buckled tube acquires a slight curvature which modifies the flow rate and results in a correction to nonlinearity of the amplitude equation governing the deformation dynamics.

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Flow in pipes with non-uniform curvature and torsion

Cited by 34 publications

References 36 publications

Investigation of the Effects of Dynamic Change in Curvature and Torsion on Pulsatile Flow in a Helical Tube

Investigation of the Effects of Dynamic Change in Curvature and Torsion on Pulsatile Flow in a Helical Tube

Rigorous justification of the asymptotic model describing a curved‐pipe flow in a time‐dependent domain

The nonlinear dynamics of elastic tubes conveying a fluid

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