Secondary cells and separation in developing laminar curvedpipe flows
Abstract
Laminar flows through 180° curved bends of circular cross section are investigated numerically. For small curvature ratio, α, defined as pipe radius over mean bend radius, the governing equations could be parabolized. The equations are solved for an α range of from 0.04 to 0.143, a Dean number ( De) range of from 277.5 to 1360, and for a uniform flow, a potential vortex, and a parabolic flow inlet condition. In all these studies a zero crossstream flow at the inlet is assumed. A detailed study of the effects of α, De, and inlet condition on the secondary flow pattern is carried out. Within the range of parameters investigated, up to three secondary cells are found in the crossstream halfplane of a curved pipe. They are the Deantype secondary cell, a secondary separation cell near the inner bend (closest to the center of curvature of the bend), and a third cell near the pipe center. The number of secondary cells in the crossstream halfplane is greatly influenced by the inlet flow, and to a much lesser extent by α and De. For example, only the Dean cell is found in a curvedpipe flow where α and De are small and the inlet flow is either uniform or a potential vortex. When the inlet condition of the same case is changed to a parabolic flow, a threecell structure results. Furthermore, as De increases to 1180, incipient axial flow separation begins at around 23° downstream of the curvedpipe entrance. The formation and extent of the separation and third cells are investigated together with their dependence on the parameters studied. This investigation further shows that, within the range of parameters examined, there is no secondary cell occurring near the outer bend, contrary to some earlier findings on fully developed curvedpipe flows.
 Publication:

Theoretical and Computational Fluid Dynamics
 Pub Date:
 December 1991
 DOI:
 10.1007/BF00271799
 Bibcode:
 1991ThCFD...3..141S
 Keywords:

 Computational Fluid Dynamics;
 Flow Geometry;
 Inlet Flow;
 Laminar Flow;
 Pipe Flow;
 Secondary Flow;
 Axial Flow;
 Incompressible Flow;
 Separated Flow;
 Uniform Flow;
 Vortices;
 Fluid Mechanics and Heat Transfer