DIRECT NUMERICAL SIMULATION OF A THREE-DIMENSIONAL NATURAL-CONVECTION FLOW IN A DIFFERENTIALLY HEATED CAVITY OF ASPECT RATIO 4

Abstract

The majority of the direct numerical simulations of turbulent and transition natural- convection flows in cavities assume two-dimensional behavior. To investigate the effect of the three-dimensional fluctuations, a complete direct numerical simulation has been carried out, in a cavity with aspect ratio 4, Ra_z  = 6.4 × 10⁸ , and Pr = 0.71, using a low-cost PC cluster. A description of the parallel algorithm and the methodology used to verify the code and the accuracy of the statistics obtained is presented. The main features of the two- and three-dimensional flows are described and compared. Several first- and second-order statistic distributions have been evaluated, including the Reynolds stress tensor. Significant differences are observed between the second-order statistics of the two- and three- dimensional simulations.

This work has been financially supported by the Ministerio de Ciencia y Tecnología, Spain (Projects TIC99-0770 and TIC2003-07970).

Notes

∗Except a situation where A _x  = 2 has been considered.

^†The results discussed in the next paragraphs correspond to simulations A and A2D.

^‡In particular, three digits of the overall Nusselt number are equal.