Date of Award


Publication Type

Doctoral Thesis

Degree Name



Mechanical, Automotive, and Materials Engineering


Engineering, Mechanical.




The problem of steady, laminar, incompressible flow through curved ducts of varying cross-sectional area is investigated numerically. The area change is attained by keeping the upper and lower walls at a constant angle of inclination with respect to the horizontal. Since the angle of divergence or convergence used is small and the Reynolds numbers employed are high, the governing equations are simplified by applying the parabolic assumptions. In most of the previous studies, a Neumann boundary value problem in the correction potential is solved to estimate the velocity corrections which are used to enforce continuity satisfaction in the cross stream plane. In the present study, a simple technique is developed to calculate these velocity corrections. It is achieved by solving two mixed boundary value problems in the velocity correction. The finite difference form of the momentum equations are solved using an alternating direction implicit method. The velocity correction equations and the Poisson equation for pressure are solved using the successive line over relaxation scheme and the strongly implicit procedure respectively. Results are obtained for flows with uniform axial velocity at the inlet with the Dean number ranging from 50 to 300. The ratio of the duct outlet to the inlet area varied from 0.8 to 6.0 in the current study. The procedure to calculate the velocity corrections is shown to be correctly formulated and that it provides accurate results. The variation of the centerline velocity with the streamwise distance shows that the effect of area change is realized only beyond a certain axial distance and that the variation is linear in this region. The axial presssure drop as well as centerline velocity variation indicate that the location of axial flow separation moves closer to the inlet when the Dean number increases. The secondary flow is suppressed or enhanced depending on the divergence or convergence of the cross-sectional area respectively. The area change has a non-uniform effect on the secondary flow, in the case of diverging ducts. The area change has a definite effect on the secondary flow separation also.Dept. of Mechanical, Automotive, and Materials Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1986 .K853. Source: Dissertation Abstracts International, Volume: 47-09, Section: B, page: 3922. Thesis (Ph.D.)--University of Windsor (Canada), 1986.