Direct Numerical Simulation on a Cartesian Mesh of the Flow through a Tube Bundle

In this paper, we present a three-dimensional direct numerical simulation (DNS) of a turbulent flow through a staggered tube bundle. The Navier–Stokes equations are discretized on a staggered Cartesian grid with the help of the finite-volume approach. The complex geometry of the tube bundle is implemented by the diagonal cartesian method (DCM). The advantage of this method, in comparison with body-fitted coordinate approaches, is that it leads to less complicated algorithms and, therefore, to more efficient computations. The principle of this method is described in this paper. Simulations of the flow through a tube bundle are carried out at on four different meshes with various grid spacings. Results of the simulations on the finest mesh are compared with the experimental data of Simonin and Barcouda [Measurements of fully developed turbulent flow across tube bundle. In 3ème Conférence Internationale sur les Applications de l'Anéemometrie Laser à la Mécanique des Fluides, 1986] and with the large-eddy simulations (LES) of Rollet-Miet et al. [“LES and RANS of turbulent flow in tube bundles”, Int. J. Heat Fluid Flow, 20 (1999) pp. 241–254]. Based on this comparison we conclude that an accurate simulation of a flow through a tube bundle can be performed with the DCM.