On the Impact of the Aspect Ratio on the Formation of Large-Scale Structures in Turbulent Mixed Convection in a Cuboidal Sample

Abstract

Temperature measurements combined with Particle Image Velocimetry (PIV) were performed in a cuboidal convection sample with a square cross section (width / height). The objective of the study is to analyze the influence of the aspect ratio $\Gamma_{xz}=L/H$ and the Archimedes number $Ar$ on the large-scale coherent structures in mixed convection. Air at ambient pressure was used as working fluid ($Pr=0.7$). The aspect ratio was varied between $1\leq\Gamma_{xz}\leq4$ (length / height) and the variation of the Archimedes number was achieved by prescribing the inflow velocity of an air jet, which was superimposed on the thermally induced flow via an inlet and outlet channel. The Rayleigh number was kept constant at $Ra=2.0\times10^8$. A model, adopted from pure thermal convection, was used to extract the number of convection rolls from the circumferential temperature distribution measured along the sidewalls of the convection sample. For a fixed Archimedes number ($Ar\approx4$), the number of thermally induced large-scale circulations (LSC$_\mathrm{TC}$) increased with the aspect ratio of the sample. Specifically, starting with $\Gamma = 2$, a linear dependence with unity slope was found. A decrease of the Archimedes number led to a transition from the single LSC$_\mathrm{TC}$ structures to FC-dominated LSCs (LSC$_\mathrm{FC}$) for $\Gamma=1$ and $\Gamma=2$, whereas the multi-roll structures found for $\Gamma=3$ and $\Gamma=4$ were more stable even for higher inflow velocities.