Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-19T12:15:54.640Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodic flows through curved tubes: the effect of the frequency parameter

Published online by Cambridge University Press:  26 April 2006

Costas C. Hamakiotes  and
Stanley A. Berger
Costas C. Hamakiotes
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
Stanley A. Berger
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In a previous paper we reported on the effect of Dean number, κm, on the fully developed region of periodic flows through curved tubes. In this paper we again consider a sinusoldally varying volumetric flow rate in a curved pipe of arbitrary curvature ratio, δ, and investigate the effect of frequency parameter α, and Reynolds number Rem on the flow. Specifically, we report on the flow-field development for the range 7.5 [les ] α [les ] 25, and 50 [les ] Rem [les ] 450. The results, obtained by numerical integration of the full Navier–Stokes equations, reveal a number of characteristics of the flow previously unreported. For low values of Rem the secondary flow consists of a single vortex (Dean-type motion) in the half-cross-section at all times and for all values of α studied. For higher Rem we observe inward ‘centrifuging’ (Lyne-type motion) at the centre. This motion always occurs during the accelerating period of the volumetric flow rate. It appears at lower α for higher Rem and, for the given Rem at which it appears, it occurs at earlier times in the cycle for lower a. A striking feature is observed for α = 15 for the range 315 [les ] Rem [les ] 400: period tripling. The flow field varies periodically with time for the duration of three volumetric-flow-rate cycles then repeats for the subsequent three cycles, and so on. The computed axial pressure gradient also varies periodically with time but with the same period as the volumetric flow rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 210 , January 1990 , pp. 353 - 370
Copyright
© 1990 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Berger, S. A., Talbot, L. & Yao, L.-S. 1983 Flow in curved pipes. Ann. Rev. Fluid Mech. 15, 461.Google Scholar
Caro, C. G., Fitz-Gerald, J. M. & Schroter, R. C. 1971 Atheroma and arterial wall shear. Observation, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis.. Proc. R. Soc. Lond. B 177, 109.Google Scholar
Chorin, A. J. 1968 Numerical solution of the Navier-Stokes equations. Maths Comput. 22, 745.Google Scholar
Cvitanović, P. (Ed.) 1984 Universality in Chaos. Bristol: Adam Hilger.
Dean, W. R. 1927 Note on the motion of fluid in a curved pipe. Phil. Mag. 4, 208.Google Scholar
Dean, W. R. 1928 The stream-line motion of fluid in a curved pipe. Phil. Mag. 5, 673.Google Scholar
Dennis, S. C. R. & Ng, M. C. 1982 Dual solution for steady laminar flow through a curved tube. Q. J. Mech. Appl. Maths 35, 305.Google Scholar
Feigenbaum, M. J., Kadanoff, L. P. & Shenker, S. J. 1982 Quasiperiodicity in dissipative systems: A renormalization group analysis. Physica 5D, 370.Google Scholar
Friedman, M. H., Hutchins, G. M., Bargeron, C. B., Deters, O. J. & Mark, F. M. 1981 Correlation between intimal thickness and fluid shear in human arteries. Atherosclerosis 39, 425.Google Scholar
Fry, D. L. 1968 Acute vascular endothelial changes associated with increased blood velocity gradients. Circul. Res. 22, 165.Google Scholar
Fry, D. L. 1973 Responses of the arterial wall to certain physical factors In Atherogenesis: Initiating Factors. Ciba Symposium vol. 12, p. 93. North-Holland: Elsevier. Excerpta Medica.
Gollub, J. P. & Benson, S. V. 1980 Many routes to turbulent convection. J. Fluid Mech. 100, 449.Google Scholar
Gong, K. O. 1979 Experimental study of unsteady entrance flow in a curved pipe. Ph.D. thesis. University of California, Berkeley.
Guckenheimer, J. & Holmes, P. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.
Hamakiotes, C. C. 1988 Periodic flows through curved tubes. Ph.D. thesis. University of California, Berkeley.
Hamakiotes, C. C. & Berger, S. A. 1988 Fully developed pulsatile flow in a curved pipe. J. Fluid Mech. 195, 23.Google Scholar
Ito, H. 1987 Flow in curved pipes. JSME Intl J. 30, 543.Google Scholar
José, J. V., Kadanoff, L. P., Kirkpatrick, S. & Nelson, D. R. 1977 Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model.. Phys. Rev. B 16, 1217.Google Scholar
Ku, D. N., Giddens, D. P., Zarins, C. K. & Glagov, S. 1985 Pulsatile flow and atherosclerosis in the human carotid bifurcation. Arteriosclerosis 5, 293.Google Scholar
Lennie, T. B., McKenzie, D. P., Moore, D. R. & Weiss, N. O. 1988 The breakdown of steady convection. J. Fluid Mech. 188, 47.Google Scholar
Libchaber, A. & Maurer, J. 1982 A Rayleigh Bénard experiment: helium in a small box. In Nonlinear Phenomena at Phase Transitions and Instabilities (ed. T. Riste), p. 259. Plenum.
Lyne, W. H. 1971 Unsteady viscous flow in a curved pipe. J. Fluid Mech. 45, 13.Google Scholar
Nandakumar, K. & Masliyah, J. H. 1982 Bifurcation in steady laminar flow through curved tubes. J. Fluid Mech. 119, 475.Google Scholar
Nandakumar, K. & Masliyah, J. H. 1986 Swirling flow and heat transfer in coiled and twisted pipes. In Advances in Transport Processes, vol. 4 (ed. A. S. Mujumdar and R. A. Masliyah). Wiley Eastern.
Nerem, R. 1981 Arterial fluid dynamics and interactions with the vessel walls. In Structure and Function of the Circulation, vol. 2 (ed. C. J. Schwartz, N. T. Werthessen & S. Wolf). Plenum.
Schettler, G. et al. (Eds.) 1983 Fluid Dynamics as a Localizing Factor for Atherosclerosis. Springer.
Wersinger, J.-M., Finn, J. M. & Ott, E. 1980 Bifurcation and “strange” behavior in instability saturation by nonlinear three-wave mode coupling. Phys. Fluids 23, 1142.Google Scholar
Winters, K. H. 1984 A bifurcation study of laminar flow in a curved tube of rectangular cross-section. Harwell Rep. AERE-TP, 1104.Google Scholar
Winters, K. H. & Brindley, R. C. G. 1984 Multiple solutions for laminar flow in helically-coiled tubes. Harwell Rep. AERE-R, 11373.Google Scholar
Yang, Z. & Keller, H. B. 1986 Multiple laminar flows through curved pipes. Appl. Numer. Maths 2, 257.Google Scholar