Low-Prandtl number natural convection in volumetrically heated rectangular enclosures: II. Square cavity, AR=1

Abstract

Following a previous study for a slender enclosure ( AR=4), direct numerical two-dimensional simulations were conducted for the free convective flow of a low-Prandtl number fluid ( Pr=0.0321) with internal heat generation in a square cavity having adiabatic top and bottom walls and isothermal side walls. The Grashof number, Gr, based on conductive maximum temperature and cavity width, ranged from 10 5 to 10 9. For Gr up to ∼10 7, the flow was steady and exhibited left–right symmetry. For Gr≈3×10 7, the spatial symmetry was broken and asymmetric steady-state flow patterns were obtained. For Gr≈5×10 7, the asymmetric flow became time-periodic. Finally, for Gr≥10 8, chaotic flow was predicted; the time-averaged velocity and temperature fields were still markedly asymmetric at Gr=10 8, but reattained bilateral symmetry at higher Gr (10 9), when developed two-dimensional turbulence was observed. For Grashof numbers above ∼10 6, the friction coefficient averaged along the vertical walls scaled roughly with Gr −1/3 (as in the AR=4 cavity), while the Nusselt number (overall/conductive heat transfer) increased roughly as Gr 1/7, i.e. slightly less markedly than in the slender cavity.