Correlation of internal flow structure with heat transfer efficiency in turbulent Rayleigh-B\'enard convection

TL;DR

This study investigates how different internal flow structures in turbulent Rayleigh-Bénard convection relate to heat transfer efficiency, emphasizing the importance of selecting appropriate Nusselt number definitions for accurate analysis.

Contribution

The paper introduces a detailed analysis of flow mode correlations with heat transfer, highlighting the effectiveness of volume-averaged and kinetic energy dissipation-based Nusselt numbers in capturing flow-structure interactions.

Findings

Single-roll and double-roll modes enhance heat transfer.

Vertically stacked double-roll mode is less efficient.

Volume-averaged Nusselt number best correlates with flow structures.

Abstract

To understand how internal flow structures manifest themselves in the global heat transfer, we study the correlation between different flow modes and the instantaneous Nusselt number ($Nu$) in a two-dimensional square Rayleigh-B\'enard convection cell. High-resolution and long-time direct numerical simulations are carried out for Rayleigh numbers between $10^{7}$ and $10^{9}$ and a Prandtl number of 5.3. The investigated Nusselt numbers include the volume-averaged $Nu_{\text{vol}}$, the wall-averaged $Nu_{\text{wall}}$, the kinetic energy dissipation based $Nu_{\text{kinetic}}$, and the thermal energy dissipation based $Nu_{\text{thermal}}$. The Fourier mode decomposition and proper orthogonal decomposition are adopted to extract the coherent flow structure. Our results show that the single-roll mode, the horizontally stacked double-roll mode, and the quadrupolar flow mode are more efficient for heat transfer on average. In contrast, the vertically stacked double-roll mode is inefficient for heat transfer on average. The volume-averaged $Nu_{\text{vol}}$ and the kinetic energy dissipation based $Nu_{\text{kinetic}}$ can better reproduce the correlation of internal flow structures with heat transfer efficiency than that of the wall-averaged $Nu_{\text{wall}}$ and the thermal energy dissipation based $Nu_{\text{thermal}}$, even though these four Nusselt numbers give consistent time-averaged mean values. The ensemble-averaged time trace of $Nu$ during flow reversal shows that only the volume-averaged $Nu_{\text{vol}}$ can reproduce the overshoot phenomena that is observed in the previous experimental study. Our results reveal that the proper choice of $Nu$ is critical to obtain a meaningful interpretation.