DIRECT NUMERICAL SIMULATIONS OF 2-DIMENSIONAL CHAOTIC NATURAL-CONVECTION IN A DIFFERENTIALLY HEATED CAVITY OF ASPECT-RATIO-4

Chaotic natural convection in a differentially heated air-filled cavit y of aspect ratio 4 with adiabatic horizontal walls is investigated by direct numerical integration of the unsteady two-dimensional equation s. Time integration is performed with a spectral algorithm using Cheby shev spatial approximations and a second-order finite-difference time- stepping scheme. Asymptotic solutions have been obtained for three val ues of the Rayleigh number based on cavity height up to 10(10). The ti me-averaged flow fields show that the flow structure increasingly depa rts 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 ampl itude of these waves grows as they travel downstream and hook-like tem perature patterns form at the outer edge of the thermal boundary layer . At the largest Rayleigh number investigated they grow to such a poin t that they result in the formation of large unsteady eddies that tota lly disrupt the boundary layers. These eddies throw hot and cold fluid into the upper and lower parts of the core region, resulting in therm ally 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 strati fied core region excited. These simulations also give access to the se cond-order statistics such as turbulent kinetic energy, thermal and vi scous dissipation, Reynolds stresses and turbulent heat fluxes.