An experimental investigation of low Reynolds number secondary streaming effects associated with an oscillating viscous flow in a curved pipe

Bertelsen, Arnold F.

doi:10.1017/s0022112075002169

Cited by 33 publications

(8 citation statements)

References 2 publications

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“…His analytical study showed that a new vortex pair appears and coexists with Dean cells (Lyne instability). Zalosh and Nelson [6] obtained the same results, and later experimental work of Bertelsen [7] confirmed previous work. Sudo et al [8] characterized the secondary flow by the Womersley number in fully developed oscillatory flow and classified secondary flow structures into five patterns.…”

Section: Introductionsupporting

confidence: 82%

Mixing by Time-Dependent Orbits in Spatiotemporal Chaotic Advection

Karami

Shirani²,

Jarrahi

et al. 2014

Journal of Fluids Engineering

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The simultaneous effects of flow pulsation and geometrical perturbation on laminar mixing in curved ducts have been numerically studied by three different metrics: analysis of the secondary flow patterns, Lyapunov exponents and vorticity vector analysis. The mixer that creates the flow pulsation and geometrical perturbations in these simulations is a twisted duct consisting of three bends; the angle between the curvature planes of successive bends is 90 deg. Both steady and pulsating flows are considered. In the steady case, analysis of secondary flow patterns showed that homoclinic connections appear and become prominent at large Reynolds numbers. In the pulsatile flow, homoclinic and heteroclinic connections appear by increasing b, the ratio of the peak oscillatory velocity component of the mean flow velocity. Moreover, sharp variations in the secondary flow structure are observed over an oscillation cycle for high values of b. These variations are reduced and the homoclinic connections disappear at high Womersley numbers. We show that small and moderate values of the Womersley number (6 a 10) and high values of velocity amplitude ratio (b ! 2) provide a better mixing than that in the steady flow. These results correlate closely with those obtained using two other metrics, analysis of the Lyapunov exponents and vorticity vector. It is shown that the increase in the Lyapunov exponents, and thus mixing enhancement, is due to the formation of homoclinic and heteroclinic connections.

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Section: Introductionsupporting

confidence: 82%

Mixing by Time-Dependent Orbits in Spatiotemporal Chaotic Advection

Karami

Shirani²,

Jarrahi

et al. 2014

Journal of Fluids Engineering

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“…As a increases to 6 the centres move towards the inside of the bend and remain there a t a = 10. This thickening of the vortex core on the inside of the curve was attributed to finite-curvature effects by Bertelsen (1975), but from these results it would appear to depend on G when a 2 6. The full time-dependent streamlines for a = 5 are shown in figure 7.…”

Section: Resultsmentioning

confidence: 84%

“…Lyne's findings were verified experimentally by Bertelsen (1975) and Munsen (1975and Munsen ( , 1976. They investigated the nature of the steady secondary-flow component using flow-visualization techniques.…”

Section: Introductionmentioning

confidence: 89%

Oscillatory flow in curved pipes. Part 2. The fully developed case

Mullin

Greated

1980

J. Fluid Mech.

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A theoretical and experimental investigation of oscillatory flow in curved pipes is presented. The equations for fully developed laminar flow are found to depend on an amplitude parameterGand a frequency parameter α. Initially the Navier–Stokes equations are expanded in terms ofGand the resulting linearized equations are solved numerically using finite Hankel integral transforms. A further expansion is used for the case α → 0 and closed-form solutions are presented.Laser-Doppler anemometry has been used to obtain velocity information in oscillatory air flow in small-diameter curved glass tubes. Using this technique, low-Reynolds-number experiments were carried out and comparison between theory and experiments is presented.For α [les ] 1 the velocity distributions found are essentially those for steady flow, while for α [ges ] 11·0 the results are not at variance with earlier work. It is for the transition stage between these two regimes that unexpected behaviour is recorded, but a satisfactory explanation is found in terms of general trends within the flow.

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“…Numerical studies of toroidal pipes have shown that, under certain conditions, a four-vortex solution exists for both steady flow (Dennis & Ng 1982;Nandakumar & Masliyah 1982;Yanase, Gotoh & Yamamoto 1989) and unsteady flow (Lyne 1971;Zalosh & Nelson 1973). A stable four-vortex solution was also observed in the experimental work of Bertelsen (1975).…”

Section: Introductionmentioning

confidence: 89%

Flow in pipes with non-uniform curvature and torsion

Gammack

Hydon

2001

J. Fluid Mech.

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This paper describes steady and unsteady flows in pipes with small, slowly varying curvature and torsion. Four new pipe shapes are studied, using Germano's extension of the Dean equations. Analytic and numerical solutions are obtained for flows driven by a steady pressure gradient. Oscillatory flows in pipes with non-uniform curvature are obtained by numerical methods. The effects of the non-uniformities in curvature and torsion are discussed, with particular reference to wall shear stress.

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An experimental investigation of low Reynolds number secondary streaming effects associated with an oscillating viscous flow in a curved pipe

Cited by 33 publications

References 2 publications

Mixing by Time-Dependent Orbits in Spatiotemporal Chaotic Advection

Mixing by Time-Dependent Orbits in Spatiotemporal Chaotic Advection

Oscillatory flow in curved pipes. Part 2. The fully developed case

Flow in pipes with non-uniform curvature and torsion

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