ALBERT

Description: We analyse the wind and boundary layer properties of turbulent Rayleigh-Bénard convection in a cylindrical container with aspect ratio one for Prandtl number Pr = 0.786 and Rayleigh numbers (Ra) up to 10 9 by means of highly resolved direct numerical simulations. We identify time periods in which the orientation of the large-scale circulation (LSC) is nearly constant in order to perform a statistical analysis of the LSC. The analysis is then reduced to two dimensions by considering only the plane of the LSC. Within this plane the LSC is treated as a wind with thermal and viscous boundary layers developing close to the horizontal plates. Special focus is on the spatial development of the wind magnitude and the boundary layer thicknesses along the bottom plate. A method for the local analysis of the instantaneous boundary layer thicknesses is introduced which shows a dramatically changing wind magnitude along the wind path. Furthermore a linear increase of the viscous and thermal boundary layer thickness along the wind direction is observed for all Ra considered while their ratio is spatially constant but depends weakly on Ra. A possible explanation is a strong spatial variation of the wind magnitude and fluctuations in the boundary layer region. © 2012 Cambridge University Press.

Description: To approximate the velocity and temperature within the boundary layers in turbulent thermal convection at moderate Rayleigh numbers, we consider the Falkner-Skan ansatz, which is a generalization of the Prandtl-Blasius one to a non-zero-pressure-gradient case. This ansatz takes into account the influence of the angle of attack β of the large-scale circulation of a fluid inside a convection cell against the heated/cooled horizontal plate. With respect to turbulent Rayleigh-Bénard convection, we derive several theoretical estimates, among them the limiting cases of the temperature profiles for all angles β, for infinite and for infinitesimal Prandtl numbers Pr. Dependences on Pr and β of the ratio of the thermal to viscous boundary layers are obtained from the numerical solutions of the boundary layers equations. For particular cases of β, accurate approximations are developed as functions on Pr. The theoretical results are corroborated by our direct numerical simulations for Pr= 0. 786 (air) and Pr= 4. 38 (water). The angle of attack β is estimated based on the information on the locations within the plane of the large-scale circulation where the time-averaged wall shear stress vanishes. For the fluids considered it is found that β 0. 7 π and the theoretical predictions based on the Falkner-Skan approximation for this β leads to better agreement with the DNS results, compared with the Prandtl-Blasius approximation for β = π. © 2013 Cambridge University Press.

Description: Direct numerical simulations (DNS) of turbulent thermal convection in a box-shaped domain with regular surface roughness at the heated bottom and cooled top surfaces are conducted for Prandtl number Pr = 0.786 and Rayleigh numbers Ra between 106 and 108. The surface roughness is introduced by four parallelepiped equidistantly distributed obstacles attached to the bottom plate, and four obstacles located symmetrically at the top plate. By varying Ra and the height and width of the obstacles, we investigate the influence of the regular wall roughness on the turbulent heat transport, measured by the Nusselt number Nu. For fixed Ra, the change in the value of Nu is determined not only by the covering area of the surface, i.e. the obstacle height, but also by the distance between the obstacles. The heat flux enhancement is found to be largest for wide cavities between the obstacles which can be 'washed out' by the flow. This is also manifested in an empirical relation, which is based on the DNS data. We further discuss theoretical limiting cases for very wide and very narrow obstacles and combine them into a simple model for the heat flux enhancement due to the wall roughness, without introducing any free parameters. This model predicts well the general trends and the order of magnitude of the heat flux enhancement obtained in the DNS. In the Nu versus Ra scaling, the obstacles work in two ways: for smaller Ra an increase of the scaling exponent compared to the smooth case is found, which is connected to the heat flux entering the cavities from below. For larger Ra the scaling exponent saturates to the one for smooth plates, which can be understood as a full washing-out of the cavities. The latter is also investigated by considering the strength of the mean secondary flow in the cavities and its relation to the wind (i.e. the large-scale circulation), that develops in the core part of the domain. Generally, an increase in the roughness height leads to stronger flows both in the cavities and in the bulk region, while an increase in the width of the obstacles strengthens only the large-scale circulation of the fluid and weakens the secondary flows. An increase of the Rayleigh number always leads to stronger flows, both in the cavities and in the bulk. © 2014 Cambridge University Press.