Wall modelled Large Eddy Simulation of natural convection at high Rayleigh number

Alsteens, Louis [UCL] Papalexandris, Miltiadis [UCL]

This work concerns the numerical study of thermal convection in closed cubes at high Rayleigh numbers. In many problems of practical interest involving free convection, the associated Rayleigh number is typically very high, e.g. Re=10⁹and higher. This in turn implies high turbulence intensities. Currently, the computational cost of direct numerical simulation of such flows is prohibitively high. Further, even wall- resolved Large Eddy Simulations (LES) can exhaust current computational resources. An alternative approach is to perform wall-modeled LES. This relies on the development of wall models, which provides near-wall velocity and temperature profiles based on a presumed structure of the hydrodynamic and thermal boundary layers in the flows of interest. In the first part of the talk, we outline the wall models that we employ in our numerical study. For the near-wall velocity profile we employ an algebraic wall model based on the standard law of the wall. Then, an expression for the turbulent viscosity in the first layer of cells is derived from the wall shear stress. This approach is combined with the WALE subgrid model in the bulk of the flow. For the thermal boundary layer, we have implemented two different approaches. The first one is based on the gradient assumption according to which the turbulent conductivity is computed from the turbulent viscosity and a presumed turbulent Prandlt number. In the second approach the turbulent conductivity is computed from a thermal law of the wall, in a manner that is analogous to the wall-modelling of the velocity field. The second part of the talk is dedicated to the presentation and analysis of wall- modeled LES of Rayleigh-Bénard convection at Rayleigh numbers between Ra=108 and Ra=1010. Numerical results obtained with the two different thermal wall models are presented are compared. Finally, we discuss the main features of the flow, and present results for turbulence statistics and the Nusselt number.