Aspect-ratio dependency of Rayleigh-Bénard convection in box-shaped containers

Abstract

We report on a numerical study of the aspect-ratio dependency of Rayleigh-Bénard convection, using direct numerical simulations. The investigated domains have equal height and width while the aspect ratio Γ of depth per height is varied between 1/10 and 1. The Rayleigh numbers \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ra}}$\end{document}Ra for this study variate between 105 and 109, while the Prandtl number is \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Pr}} = 0.786$\end{document}Pr=0.786. The main focus of the study concerns the dependency of the Nusselt number \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Nu}}$\end{document}Nu and the Reynolds number \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Re}}$\end{document}Re on \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ra}}$\end{document}Ra and Γ. It turns out that due to Γ, differences to the cubic case (i.e., Γ = 1) in \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Nu}}$\end{document}Nu of up to 55% and in \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Re}}$\end{document}Re of up to 97% occur, which decrease for increasing \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ra}}$\end{document}Ra. In particular for small Γ sudden drops in the \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ra}}$\end{document}Ra-scaling of \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Nu}}$\end{document}Nu and \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Re}}$\end{document}Re appear for \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ra}}\approx 10^6$\end{document}Ra≈106. Further analysis reveals that these correspond to the onset of unsteady motion accompanied by changes in the global flow structure. The latter is investigated by statistical analysis of the heat flux distribution on the bottom and top plates and a decomposition of the instantaneous flow fields into two-dimensional modes. For \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ra}}$\end{document}Ra slightly above the onset of unsteady motion (i.e., \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ra}}\approx 10^6$\end{document}Ra≈106) for all considered Γ ⩽ 1/3 a four-roll structure is present, which corresponds to thermal plumes moving vertically through the domain's center. For \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ra}}\ge 10^7$\end{document}Ra≥107, also for small Γ, a single-roll structure is dominant, in agreement with two-dimensional simulations and experiments at larger \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Ra}}$\end{document}Ra and \documentclass[12pt]{minimal}\begin{document}$\mbox{\textit {Pr}}$\end{document}Pr.

Multiscale Modeling of Multiphase Fluid Flow

“…Note at the top and bottom surfaces are not instantaneously equal in this case, instead, they are identical in a sense of time average. Similar phenomena of is also recently reported in a square container with a thin depth (1/10) at Pr = 0.786 and Ra = 10 6 [234]. Figure 8-13b shows that the surface-averaged Nusselt number at the top and bottom surfaces almost have a phase difference of 180º.…”

“…Moreover, the flow and heat transfer process are also affected by the aspect ratio and boundary conditions of the enclosure. Therefore, many studies of natural convection in a cavity focus on the effects of relative strength of buoyancy and viscous forces [230], various fluids properties [231][232][233], aspect ratio [230,234,235], and boundary conditions [236][237][238].…”

Reversals of the large-scale circulation in quasi-2D Rayleigh–Bénard convection

“…the mean time between successive reversals has a strong Ra dependence in the former and is essentially Ra-independent in the latter (Brown & Ahlers 2006;Xi & Xia 2007). The importance of the corner rolls was also found later by a number of numerical and experimental studies in the 2D/quasi-2D system (Chandra & Verma 2011, 2013Vasilev & Frick 2011;Yanagisawa et al 2011;Wagner & Shishkina 2013). As the dynamics of flow reversals appears to have quite different dimensional dependence, the question then is whether flow reversals in the RB system in the 2D and 3D cases can be described by a unified framework.…”

Dynamics of large-scale quantities in Rayleigh-Bénard convection

“…According to GL scaling, for small and moderate Pr's, Pe ∼ √ RaPr, but for large Pr, Pe ∼ Ra 3/5 . The above scaling have been verified in many experiments [14][15][16][17][18][19][20][21] and numerical simulations [22][23][24][25][26][27][28][29][30]. In this paper we derive a general formula for Pe, of which the aforementioned relations are limiting cases, by comparing the relative strengths of the nonlinear, pressure, buoyancy, and viscous terms, and quantifying them using the numerical data.…”