Numerical exploration of turbulent air natural-convection in a differentially heated square cavity at Ra = 5.33 × 10~9

摘要

The turbulent air natural-convection in a differentially heated square cavity is certainly a benchmark problem in thermo-hydrodynamics. Using large eddy simulation (LES), the natural convection at a Rayleigh number of 5.33 × 10~9 is numerically explored, in which a sub-grid scale model constructed by non-dimensional analysis on the basis of the swirling-strength and the harmonically-averaged grid interval is utilized. A factor of swirling strength intermittency (FSI), which is defined by the ratio of the swirling strength to the magnitude of the complex eigenvalue of the filtered velocity gradient tensor, is used instead of the near-wall length scale decaying factor in the description of the near-wall sub-grid viscosity. The cavity with the height-width-depth ratio of 1:1:2 is partitioned by a non-uniform staggered grid, whose resolution is obtained by the grid number of 100 × 100 × 120 . It was found that to some extent the LES results agree well with the existing experimental data, suggesting that the swirling-strength based sub-grid scale model used in the LES is of potential. Subjected the influences of the loop wall jet and the assigned temperature in the horizontal walls, as can be seen from the t-z averaged FSI distribution in the square section, the heterogeneity of the averaged FSI in the near wall regions is more evident, but in the core region of the square cavity, this heterogeneity decreases and the natural convection tends to become relatively homogeneous. The turbulent natural convection at Rayleigh number 5.33 × 10~9 certainly has its own geometry-dependent intermittency of turbulence.