Radial boundary layer structure and Nusselt number in Rayleigh-Benard convection

TL;DR

This study uses high-resolution direct numerical simulations to analyze the boundary layer structure and heat transfer in Rayleigh-Benard convection, confirming the importance of resolution for accurate Nusselt number calculations.

Contribution

It provides detailed boundary layer profiles and demonstrates the impact of resolution on plume dynamics and heat transfer measurements in Rayleigh-Benard convection.

Findings

Nusselt number agrees with experimental data when simulations are fully resolved.

Boundary layer profiles are closer to Prandtl-Blasius near the cylinder axis.

Underresolved simulations underestimate thermal dissipation near sidewalls.

Abstract

Results from direct numerical simulations for three dimensional Rayleigh-Benard convection in a cylindrical cell of aspect ratio 1/2 and Pr=0.7 are presented. They span five decades of Ra from $2\times 10^6$ to $2 \times10^{11}$. Good numerical resolution with grid spacing $\sim$ Kolmogorov scale turns out to be crucial to accurately calculate the Nusselt number, which is in good agreement with the experimental data by Niemela et al., Nature, 404, 837 (2000). In underresolved simulations the hot (cold) plumes travel further from the bottom (top) plate than in the fully resolved case, because the thermal dissipation close to the sidewall (where the grid cells are largest) is insufficient. We compared the fully resolved thermal boundary layer profile with the Prandtl-Blasius profile. We find that the boundary layer profile is closer to the Prandtl Blasius profile at the cylinder axis than close to the sidewall, due to rising plumes in that region.