Experimental investigation of periodic flow in curved pipes

Swanson, Chris J.; Stalp, Steven R.; Donnelly, Russell J.

doi:10.1017/s002211209300271x

Cited by 11 publications

(4 citation statements)

References 2 publications

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“…Furthermore, the studies all imposed symmetry across the centreplane of the pipe (the plane containing the centreline of the pipe), so that asymmetric solutions were not permitted. Periodic flows in curved pipes have also been investigated experimentally (Lin & Tarbell 1980;Sudo et al 1992;Swanson, Stalp & Donnelly 1993;Chandran, Yearwood & Wieting 1979). While the above studies all considered curved pipes with zero torsion (so that the pipe centreline remained in the plane), flow in helical pipes has also been considered.…”

Section: Introductionmentioning

confidence: 99%

Unsteady flows in pipes with finite curvature

Siggers

Waters

2008

J. Fluid Mech.

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Motivated by the study of blood flow in a curved artery, we consider fluid flow through a curved pipe of uniform curvature, δ, driven by a prescribed oscillatory axial pressure gradient. The curved pipe has finite (as opposed to asymptotically small) curvature, and we determine the effects of both the centrifugal and Coriolis forces on the flow. In addition to δ, the flow is parameterized by the Dean number, D, the Womersley number, α, and a secondary streaming Reynolds number, R s . Asymptotic solutions are developed for the case when δ 1, α 1 and the magnitude of the axial pressure gradient is small, using regular perturbation techniques. For intermediate values of the governing parameters, a pseudospectral code is used to obtain numerical solutions. For flows driven by a sinusoidal pressure gradient (D = 0), we identify three distinct classes of stable solutions: 2π-periodic symmetric, 2π-periodic asymmetric, and asymmetric solutions that are either quasi-periodic, or periodic with period 2πk for k ∈ N. The transition between solutions is dependent on the value of δ; thus pipes with finite curvature may exhibit qualitatively different transitions between the solution classes as the governing parameters are varied from those of curved pipes with asymptotically small curvature. When α 1, matched asymptotic expansions are used to simplify the system, and the resulting equations are solved analytically for R s 1, δ 1 and numerically for larger parameter values. We then determine the effect of a non-zero steady component of the pressure gradient (D = 0), and show that, for certain parameter values, when D is above a critical value the periodic asymmetric solutions regain spatial symmetry. Finally, we show that the effects of finite curvature can lead to substantial quantitative differences in the wall shear stress distribution and discuss briefly the physiological implications of the results for blood flow in arteries.

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Section: Introductionmentioning

confidence: 99%

Unsteady flows in pipes with finite curvature

Siggers

Waters

2008

J. Fluid Mech.

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“…The 1/7 ratio was selected because of its frequent use in the existing body of literature on pulsatile flow through curved geometries. A 180 • bend was similarly selected due to its prevalence in the literature and to ensure that both the axial and secondary flows were developed (Swanson, Stalp & Donnelly 1993). A 3 mm deep recess was machined into each end of the bend apparatus to accommodate the glass tubing, which was affixed to the bend using silicone caulk.…”

Section: • Bend 421 Design Of Bendmentioning

confidence: 99%

“…In pulsatile flow, Talbot & Gong (1983) found that the axial flow separated from the inner wall during deceleration, and they discovered the presence of helical structures in the Dean's vortices. Swanson, Stalp & Donnelly (1993) looked at flow development in curved pipes experimentally and suggested that flow becomes fully developed near 165 • in a 180 • bend. Komai & Tanishita (1997) simulated flow around a curved tube for several curvature ratios, Womersley numbers, and intermittency parameters (ratio of systolic time to the total cardiac period).…”

Section: Introductionmentioning

confidence: 99%

The influence of inlet velocity profile and secondary flow on pulsatile flow in a model artery with stenosis

Peterson¹,

Plesniak²

2008

J. Fluid Mech.

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The results of an experimental investigation to determine the influence of two physiologically relevant inlet conditions on the flow physics downstream of an idealized stenosis are presented. The two inlet conditions are an asymmetric mean inlet velocity profile and an asymmetric mean inlet velocity profile plus secondary flow, as found downstream of a bend. The stenosis is modelled as an axisymmetric 75 % area reduction occlusion with a length-to-diameter ratio of 2. The flow was forced by a 10-harmonic carotid artery-inspired waveform with mean, maximum and minimum Reynolds numbers of 364, 1424 and 24, respectively, and a Womersley number of 4.6. Laser Doppler velocimetry and particle image velocimetry were used to characterize the spatial and temporal evolution of a baseline case (no disturbances) as well as the two physiologically relevant inlet conditions. The asymmetric inlet velocity profile was found to reduce the region of influence of the stenosis by forcing the stenotic jet towards the tube wall via an induced non-uniform radial pressure gradient, similar to the Coanda effect. Curvature-induced secondary flow was found to play a minor role in the near-stenosis region. Vortex ring formation was relatively unaffected by the mean velocity gradient and secondary flow. Evidence of remnants of the starting vortex ring was observed far downstream in all cases. † Present address:

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“…Because it was believed that the knowledge of the flow in an arbitrary U tube can contribute to the understanding of the process of arteriosclerosis in a human aorta, the steady and the unsteady flow in a U tube were studied intensively by a number of research groups as early as the early 1970s (23–40). Collins and Dennis published totally developed steady axial velocity profiles (24) for Dean numbers 66.1, 77.1, 190.9, and 369.5.…”

Section: Introductionmentioning

confidence: 99%

Validation of the Coupling of Magnetic Resonance Imaging Velocity Measurements with Computational Fluid Dynamics in a U Bend

et al. 2002

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Magnetic resonance imaging (MRI) can be used in vivo in combination with computational fluid dynamics (CFD) to derive velocity profiles in space and time and accordingly, pressure drop and wall shear stress distribution in natural or artificial vessel segments. These hemodynamic data are difficult or impossible to acquire directly in vivo. Therefore, research has been performed combining MRI and CFD for flow simulations in flow phantoms, such as bends or anastomoses, and even in human vessels such as the aorta, the carotid, and the abdominal bifurcation. There is, however, no unanimity concerning the use of MRI velocity measurements as input for the inflow boundary condition of a CFD simulation. In this study, different input possibilities for the inflow boundary conditions are compared. MRI measurements of steady and pulsatile flow were performed on a U bend phantom, representing the aorta geometry. PAMFLOW (ESI Software, Krimpen aan den Ussel, The Netherlands), an industrial CFD software package, was used to solve the Navier-Stokes equations for incompressible flow. Three main parameters were found to influence the choice of an inflow boundary condition type. First, the flow rate through a vessel should be exact, since it proves to be a determining factor for the accuracy of the velocity profile. The other decisive parameters are the physiology of the flow profile and the required computer processing unit time. Our comparative study indicates that the best way to handle an inflow boundary condition is to use the velocities measured by MRI at the inflow plane as being fixed velocities. However, before using these MRI velocity data, they first should be corrected for the partial volume effect by filtering and second scaled in order to obtain the correct flow rate. This implies that a reliable flow rate measurement absolutely is needed for CFD calculations based on MRI velocity measurements.

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Experimental investigation of periodic flow in curved pipes

Cited by 11 publications

References 2 publications

Unsteady flows in pipes with finite curvature

Unsteady flows in pipes with finite curvature

The influence of inlet velocity profile and secondary flow on pulsatile flow in a model artery with stenosis

Validation of the Coupling of Magnetic Resonance Imaging Velocity Measurements with Computational Fluid Dynamics in a U Bend

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