## Abstract

The development of complex velocity fields in curved ducts from an initially parabolic profile is studied using a three-dimensional numerical model of the parabolized Navier-Stokes equations. The velocity profiles are influenced strongly by a geometrical parameter R_{c} (the radius of curvature) and a dynamic parameter Dn (Dean number, Re/√R_{c}). For R_{c} < 10 and Dn up to 200, the velocity fields develop into the previously observed two- and four-cell solutions that are axially invariant and symmetric about the midplane. For R_{c} = 100 and Dn > 125 oscillatory solutions develop which me periodic in the axial direction, but are asymmetric about the midplane. Increasing the Dean number over a narrow range results in a significant increase in the frequency of such oscillations. Grid sensitivity tests indicate that such oscillations are not a numerical artifact. Development of oscillatory solutions is delayed with decreasing radius of curvature. Thus for R_{c} = 10, axially invariant two-dimensional solutions that retain the symmetry about the midplane could be obtained for Dn as high as 300. This trend is consistent with one of the earliest observations by Taylor [Proc. R. Soc. London Ser. A. 124, 243 (1929)] that steady, symmetric laminar flows can be observed over a larger range of Dean number in tightly coiled tubes. However, when an asymmetric perturbation is imposed at the inlet, oscillatory solutions develop even for low R_{c}, indicating that symmetric two-dimensional solutions are not stable to asymmetric perturbations, as indicated by Winters [K. W. Winters and R. C. G. Brindley (private communication)]. Numerical results are also presented for flow through curved ducts with periodic step changes in curvature.

Original language | English |
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Pages (from-to) | 1348-1359 |

Number of pages | 12 |

Journal | Physics of Fluids |

Volume | 31 |

Issue number | 6 |

State | Published - 1988 |

Externally published | Yes |