ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The spatial stability of multiple solutions for fully developed laminar flow through a curved tube and through a straight tube in the presence of buoyant effects was studied using a three-dimensional numerical representation of the fully elliptic Navier–Stokes and energy equations. Several recent numerical studies have reported the existence of multiple solutions for fully developed laminar flow in curved tubes; see, for example, Yang and Keller [Appl. Numer. Math. 2, 257 (1986)] or Daskopoulos and Lenhoff [J. Fluid Mech. 203, 125 (1989)]. A similar solution multiplicity for the case of fully developed laminar flow in a heated straight tube has been discussed by Nandakumar et al. [J. Fluid Mech. 152, 145 (1985)]. Each of these studies has reported solutions of a two- and four-cell type, which are symmetric about the midplane of the tube and invariant in the axial (streamwise) flow direction. In addition, the flow visualization study of Cheng and Yuen [J. Heat Trans. 109, 55 (1987)] indicates that two- and four-cell solutions can be obtained experimentally for the flow developing in a curved tube with a 180° bend. The present study investigates the stability of two- and four-cell solutions with respect to perturbations that are asymmetric about the midplane of the tube. Perturbed two- and four-cell solutions are imposed as entrance boundary conditions for three-dimensional simulations of the full tube cross section and the evolution of the flow is observed as it progresses downstream from the entrance plane. For the conditions explored, present results indicate that the two-cell solutions are stable, and asymmetric perturbations are observed to decay as the flow travels downstream. Four-cell solutions are unstable when asymmetric perturbations are introduced, and growth of the perturbations eventually results in a complex three-dimensional transition from four-cell to two-cell flow. Details of the transition flow are described and transition mechanisms are identified.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.858720
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