Fully-developed laminar flow in trapezoidal ducts with rounded corners: a numerical solution and case study

Abstract

Purpose This paper aims to numerically solve fully developed laminar flow in trapezoidal ducts with rounded corners which result following forming processes. Design/methodology/approach A two-dimensional model for a trapezoidal duct with rounded corners is developed and conservation of momentum equation is solved. The flow is assumed to be steady, fully developed, laminar, isothermal and incompressible. The key flow characteristics including the Poiseuille number and the incremental pressure drop have been computed and tabulated for a wide range of: sidewall angle (θ); the ratio of the height of the duct to its smaller base (α); and the ratio of the fillet radius of the duct to its smaller base (β). Findings The results show that Poiseuille number decreases, and all the other dimensionless numbers increase with increasing the radii of the fillets of the duct; these effects were found to amplify with decreasing duct heights or increasing sidewall angles. The maximum axial velocity was shown to increase with increasing the radii of the fillets of the duct. For normally used ducts in hydrogen fuel cells, the impact of rounded corners cannot be overlooked for very low channel heights or very high sidewall angles. Practical implications The data generated in this study are highly valuable for engineers interested in estimating pressure drops in rounded trapezoidal ducts; these ducts have been increasingly used in hydrogen fuel cells where flow channels are stamped on thin metallic sheets. Originality/value Fully developed laminar flow in trapezoidal ducts with four rounded corners has been solved for the first time, allowing for more accurate estimation of pressure drop.