NUMERICAL STUDY OF INCOMPRESSIBLE FLOW AND HEAT TRANSFER IN NON-CIRCULAR DUCTS WITH CUSP CORNERS

Abstract

A numerical finite-volume calculation method was used for application to fully-developed flow and heat transfer in straight ducts with 2-Cusp, 3-Cusp and 4-Cusp cross-sectional area. The method was formulated with reference to a non-orthogonal curvilinear coordinate system which was fitted exactly into duct shape. In turbulent flow, the Reynolds stresses were calculated by using the coupled algebraic stress model of Launder and Ying (1973) with a (k ) transport model. This turbulent stress model enabled secondary flows to be included in the non-circular duct calculations. In heat transfer solution, three thermal boundary conditions were investigated. Predictions were compared with available numerical and experimental data. The turbulent flow predictions of secondary and axial velocity, wall shear stress and Nusselt number were in reasonable agreement with experiment for the fully-developed flow cases. It is concluded that, although the maximum secondary flow was found to be (1.5%-2.5%) of the mean axial flow, the absence of this flows have significant influence on the flow and heat transfer parameters. Moreover, these flows will increase when the corners of a duct become more acute. Heat transfer results showed that the peripheral temperature variation around the duct has a significant effect on the heat transfer results, and confirmed the inadequacy of the hydraulic radius concept in the cases of the very non-circular ducts when comparison is made with Blasius correlation.