Flow and Heat transfer Characteristics in a Square Cavity at High Rayleigh Number

Numerical simulations are performed to investigate the flow and heat transfer characteristics in a air-filled (Pr = 0.71), two-dimensional (2-D) cavity where the flow is induced by a buoyancy force due to differential heating of vertical walls at high Rayleigh numbers (10^9, 1.58 × 10^9, 10^(9.5), and 10^(10)). The governing equations are discretized spatially into a fourth-order-accurate compact form and integrated temporally by the second-order-accurate alternating direction implicit (ADI) method. Numerical results of instantaneous and time-averaged flow structures are presented. The time-averaged temperature and vertical velocity near the hot wall are used to generate the mean temperature and velocity profiles in the turbulent boundary layer, and to illustrate the required spatial resolution for simulations of turbulent natural convection. A universal structure is found to exist in the mean velocity and temperature turbulent boundary layer profiles for x^+ ＜ 10. This finding is also in good agreement with reported experimental data.