Turbulent convection in a Rayleigh-Bénard cell with solid horizontal plates of finite conductivity

Kurzfassung

Turbulent Rayleigh-Bénard convection (RBC) is one of the classical problems of fluid dynamics. In spite of the great effort made in the past to understand the complex physical mechanisms in this type of flow, there are still many open questions which must be answered. In order to understand the effect of conductive horizontal plates on the flow structure in a Rayleigh-Bénard cell the differences between finite and infinite conductivity of the horizontal plates were the aim of many experimental and numerical studies, see (Brown et al., 2005; Johnston and Doering, 2009; Verzicco and Sreenivasan, 2008). Actually, the horizontal plates are assumed to be isothermal in most numerical simulations while they are conductive in experiments. Even more, the finite conductivity of the plates is one explanation for discrepancies between results obtained in experiments and numerical simulations. A fixed temperature boundary condition corresponds to infinite thermal conductivity of the plates while an imposed heat flux models poorly conducting plates. The effect of these two boundary conditions was recently compared by (Verzicco and Sreenivasan, 2008). Their studies indicated that the heat transfer is suppressed for Ra>109 in simulations with plates of finite conductivity whereas for lower Ra the two cases leed to similar flows which agree with observations by (Johnston and Doering, 2009). They concluded that below Ra≈1010 the plate conductivity plays no significant role in the Nu∼Ra 2/7 scaling. Nevertheless, the results of (Verzicco and Sreenivasan, 2008) as well as those of (Johnston and Doering, 2009) refer to a cell with infinitely thin plates while the finite thickness of the plates is considered in our simulations. In the present study the scaling exponent β in the Nusselt-Rayleigh relation, i.e. Nu∼Ra β obtained for the cell with highly conducting aluminium plates is similar as those obtained by (Kaczorowski and Wagner, 2007), who studied RBC in the same convection cell and for the same Pr and similar Ra. However, the scaling exponent obtained for the cell with poorly conducting plexiglas plates is found to be slightly lower than those obtained by (Kaczorowski and Wagner, 2007).