Direct Numerical Simulation of a Low Prandtl Number Rayleigh–Bénard Convection in a Square Box

Direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) are used to study the steady-state Rayleigh–Bénard convection (RB) in a two-dimensional unit aspect ratio box. The steady-state RB convection is characterized by analyzing the time-averaged temperature-field, and flow field for a wide range of Rayleigh number (2.1 × 10⁵ ⩽ Ra ⩽ 2.1 × 10⁸). It is seen that the time-averaged and space-averaged Nusselt number $(Nuh¯)$ at the hot-wall monotonically increases with the increase in Rayleigh number (Ra) and the results show a power law scaling $Nuh¯∝Ra0.2593$⁠. The current Nusselt number results are compared with the results available in the literature. The complex flow is analyzed by studying the frequency power spectra of the steady-state signal of the vertical velocity at the midpoint of the box for different Ra and probability density function of dimensionless temperature at various locations along the midline of the box.