Direct numerical simulation of a differentially heated cavity of aspect ratio 4 with Rayleigh numbers up to 10~(11) - Part I: Numerical methods and time-averaged flow

摘要

A set of direct numerical simulations of a differentially heated cavity of aspect ratio 4 with adiabatic horizontal walls is presented. The five configurations selected here (Rayleigh numbers based on the cavity height Ra = 6.4 × 10~8, 2 × 10~9,10~(10), 3 × 10~(10) and 10~(11), Pr = 0.71) cover a relatively wide range of Ra from weak to fully developed turbulence. A short overview of the numerical methods and the methodology used to verify the code and the simulations is presented. The time-averaged flow results are presented and discussed in this first part. Significant changes are observed for the two highest Ra for which the transition point at the boundary layers clearly moves upstream. Such displacement increases the top and bottom regions of disorganisation shrinking the area in the cavity core where the flow is stratified. Consequently, thermal stratification values are significantly greater than unity (1.25 and 1.41, respectively).