Effect of isothermal rough boundaries on the statistics of velocity and temperature fluctuations in turbulent Rayleigh–Bénard convection

Abstract

Using direct numerical simulations, we investigate the effect of surface roughness on the statistics of fluctuations in a 2D rectangular cell of aspect ratio Γ = 2 with air as the working fluid. We consider roughly two decades of Rayleigh number, 108≤Ra≤4.64×109, with three roughness configurations of R1, R2, and R3 characterized by their maximum heights of 5%, 10%, and 20% of the cell height, respectively. We show that roughened cells trigger stronger fluctuations, which further gets augmented with increasing Ra. Vertical variations of velocity and temperature fluctuations show different trends. While the temperature fluctuation becomes homogeneous in the bulk, it exhibits strong inhomogeneous vertical velocity fluctuations. The comparison of global heat flux with smooth case shows a significant increment beyond Ra=2.15×108. Surface roughness impacts local heat flux through augmented plumes, which is qualitatively ascertained by instantaneous temperature field. Furthermore, probability distribution functions reveal no particular trend for the taller roughness configurations, though the magnitude is amplified. Through identification of plumes and background regions, we show their behavior as a function of Ra for different rough cases. Finally, we decompose the shear production into its three components (based on the nature of mechanical forces) to understand the energy interaction between the mean flow and fluctuating flow field.