Direct Numerical Simulation of Flow and Heat Transfer in Complex Ducts

A series of Direct Numerical Simulations (DNS) at low Reynolds number is performed to investigate the flow and the heat transfer in ducts with complex geometry, which are frequently encountered in many engineering fields, especially in aeronautics. A finite-difference approach and the immersed-boundary method are adopted to solve the governing equations in the computational domain. The flow and heat transfer phenomena in a circular pipe are studied in detail for laminar and turbulent regimes; thus the code is validated through a comparison of present DNS results with those provided by some trusted references. Straight ducts with regular polygonal cross sections represent the first type of ducts with complex geometry analyzed in this paper. The behavior of the pumping power expenditure is studied when the number of polygonal sides changes. The secondary motions are then investigated, and their effects on the mean velocity and temperature contours are studied. The shapes of vortices in secondary motions are compared with those provided by an analytical approach, which is based on the eigenfunctions of the Laplacian operator. Also the geometries pioneeringly studied by Nikuradse in 1930 are taken into account.