Numerical Analysis of Laminar Flow in Curved Elliptic Ducts

Abstract

The complete form of the Navier-Stokes equations is solved in this paper for a steady, incompressible, fully developed laminar flow in a curved duct of elliptic cross section. This is achieved by the use of the control volume-based finite difference method via the numerically generated boundary fitted coordinate system. The curvature ratio is included in the primitive variable governing equations, which are solved based on the SIMPLE algorithm. Solutions are obtained for the minor-axis to major-axis ratios of the elliptic duct, 0.2, 0.5, and 0.8, and for Dean numbers ranging from 11.41 to 635.7. It is found that only one pair of vortices appears on the cross-section, even at a Dean number of 635.7. The friction factor and the ratios of the curved duct to straight duct are tabulated and the correlation equation is developed. Furthermore, the distribution of the axial velocity is displayed graphically to illustrate its variations with the Dean number and the minor-axis to major-axis ratio of the elliptic duct on the horizontal symmetry line and on the half-vertical symmetry line. The present method is also applied to solve for a fully developed laminar flow in a curved square flow. The results are compared with the data available in the literature and very close agreement is observed.