Summary
In the present paper a perturbation method is developed in order to study viscous laminar flows through wavy-walled channels. The stream function of the flow is expanded in a series thereby the wall amplitude being the perturbation parameter. The walls of the channel are transformed into parallel straight lines in order to simplify the boundary conditions of the problem on the wall. Flow field and wall-shear stresses are calculated numerically up to the first perturbation order.
The position of the beginning separation on the channel walls and the associated critical Reynolds number are determined, as well as the extension of the region of the separated flow. The position of separation and reattachment points are given as functions of Reynolds numbers lying above the critical Reynolds number. The results are discussed and compared with the experimental results of other papers and further theoretical analysis.
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References
D.C. Belinfante, On viscous flow in a pipe with constrictions.Proceed. Cambr. Phil. Soc. (Math. and Phil. Soc.) 58 (1962) 405–416.
J.C. Burns and T. Parkes, Peristaltic motion,J. Fluid Mech. 29 (1967) 731–743.
L.C. Cheng, M.E. Clark and W.C. Peng, The effect of oscillatory frequency in plane wavy conduit flows,J. Biomechanics 10 (1977) 607–609.
J.C.F. Chow and K. Soda, Laminar flow in tubes with constriction,The Phys. of Fluids 15 (1977) 1700–1706.
J.H. Forrester and Y.C. Young, Flow through a converging-diverging tube and its implications in occlusive vascular disease, Parts I and II,J. Biomechanics 3 (1970) 297–316.
P. Hall, Unsteady viscous flow in a pipe of slowly varying cross-section,J. Fluid Mech. 64 (1974) 209–226.
S-T. Hsu and J.F. Kennedy, Turbulent flow in wavy pipes,J. Fluid Mech. 47 (1972) 481–502.
M.J. Manton, Low Reynolds number flow in slowly varying axisymmetric tubes,J. Fluid Mech. 49 (1971) 451–459.
A. Ramachandra Rao and R. Devanathan, Pulsatile flow in tubes of varying cross-sections,ZAMP 24 (1973) 203–213.
I.J. Sobey, On flow through furrowed channels. Part 1: Calculated flow patterns,J. Fluid Mech. 96 (1980) 1–26.
K.D. Stephanoff, I.J. Sobey and B.J. Bellhouse, On flow through furrowed channels. Part 2: Observed flow patterns,J. Fluid Mech. 96 (1980) 27–32.
K. Stewartson and P.G. Williams, Self-induced separation,Proc. Roy. Soc. A 312 (1969) 181–206.
K. Stewartson, Multistructured boundary layers on flat plates and related bodies. In: Chia-Shun Yih (ed.),Advances in Applied Mechanics, Vol. 14, pp. 145–239, Academic Press, New York-San Francisco-London (1974).
K. Stewartson, High Reynolds-number flows. In: R. Rautmann (ed.), Approximation methods for Navier-Stokes problems,Lecture Notes in Mathematics vol. 771, pp. 505–518, Springer-Verlag, Berlin-Heidelberg-New York York (1980).
N. Talukder, P.E. Karayannacos, R.M. Nerem and J.S. Vasko, An experimental study of the fluid dynamics of multiple noncritical stenoses,Transactions of the ASME, J. Biomechanical Engineering 99 (1977) 74–82.
S. Tsangaris and E. Leiter, Analytical solutions for weakly-stenosed channels at low Reynolds numbers,Proc. 1st Int. Conf. Mech. Med. & Biol. (1978) 289–292.
K. Vajravelu, Fluid flow and heat transfer in horizontal wavy channels,Acta Mechanica 35 (1980) 245–258.
D.F. Young and F.Y. Tsai, Flow characteristics in models of arterial stenoses; I. Steady flow,J. Biomechanics 6 (1973) 395–410; II. Unsteady flow,J. Biomechanics 6 (1973) 547–559.
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Supported by “Fonds zur Förderung der wissenschaftlichen Forschung”, Vienna, Austria, Project Number 3214.
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Tsangaris, S., Leiter, E. On laminar steady flow in sinusoidal channels. J Eng Math 18, 89–103 (1984). https://doi.org/10.1007/BF00042729
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DOI: https://doi.org/10.1007/BF00042729