Direct numerical simulations of two-dimensional chaotic natural convection in a differentially heated cavity of aspect ratio 4

Abstract

Chaotic natural convection in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is investigated by direct numerical integration of the unsteady two-dimensional equations. Time integration is performed with a spectral algorithm using Chebyshev spatial approximations and a second-order finite-difference time-stepping scheme. Asymptotic solutions have been obtained for three values of the Rayleigh number based on cavity height up to 1010. The time-averaged flow fields show that the flow structure increasingly departs from the well-known laminar one. Large recirculating zones located on the outer edge of the boundary layers form and move upstream with increasing Rayleigh number. The time-dependent solution is made up of travelling waves which run downstream in the boundary layers. The amplitude of these waves grows as they travel downstream and hook-like temperature patterns form at the outer edge of the thermal boundary layer. At the largest Rayleigh number investigated they grow to such a point that they result in the formation of large unsteady eddies that totally disrupt the boundary layers. These eddies throw hot and cold fluid into the upper and lower parts of the core region, resulting in thermally more homogeneous top and bottom regions that squeeze a region of increased stratification near the mid-cavity height. It is also shown that these large unsteady eddies keep the internal waves in the stratified core region excited. These simulations also give access to the second-order statistics such as turbulent kinetic energy, thermal and viscous dissipation, Reynolds stresses and turbulent heat fluxes.