Jorge Bailon-Cuba | Searcharxiv

arXiv2011

Low-dimensional model of turbulent Rayleigh-Benard convection in a Cartesian cell with square domain

A low-dimensional model (LDM) for turbulent Rayleigh-Benard convection in a Cartesian cell with square domain, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The empirical eigenfunctions are obtained from a joint Proper Orthogonal Decomposition (POD) of the velocity and temperature fields using the Snapshot Method on the basis of a direct numerical simulation (DNS). The resulting LDM is a quadratic inhomogeneous system of coupled ordinary differential equations which we use to describe the long-time temporal evolution of the large-scale mode amplitudes for a Rayleigh number of 1e5 and a Prandtl number of 0.7. The truncation to a finite number of degrees of freedom, that does not exceed a number of 310 for the present, requires the additional implementation of an eddy viscosity-diffusivity to capture the missing dissipation of the small-scale modes. The magnitude of this additional dissipation mechanism is determined by requiring statistical stationarity and a total dissipation that corresponds with the original DNS data. We compare the performance of two models, a constant so-called Heisenberg viscosity--diffusivity and a mode-dependent or modal one. The latter viscosity--diffusivity model turns out to reproduce the large-scale properties of the turbulent convection qualitatively well, even for a model with only a few hundred POD modes.

physics.flu-dyn↗

arXiv2010

Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection

The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh-Bénard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio $Γ$ of a closed cylindrical cell and the Rayleigh number $Ra$. For small and moderate aspect ratios, the global heat transfer law $Nu=A\times Ra^β$ shows a power law dependence of both fit coefficients $A$ and $β$ on the aspect ratio. A minimum Nusselt number coincides with the point where the LSC undergoes a transition from a single-roll to a double-roll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations. The aspect ratio dependence of the turbulent heat transfer for small and moderate $Γ$ is in line with a varying amount of energy contained in the LSC, as quantified by the Proper Orthogonal Decomposition analysis. For $Γ\gtrsim 8$ the heat transfer becomes independent of the aspect ratio.

physics.flu-dyn↗