Fluctuations of the wall shear stress vector in a large-scale natural convection cell

R Du Puits,C Bruecker

doi:10.1063/5.0006610

Abstract

We report first experimental data of the wall shear stress in turbulent air flow in a large-scale Rayleigh–Bénard experiment. Using a novel, nature-inspired measurement concept [C. H. Bruecker and V. Mikulich, PLoS One 12, e0179253 (2017)], we measured the mean and fluctuating part of the two components of the wall shear stress vector at the heated bottom plate at a Rayleigh number Ra = 1.58 × 1010 and a Prandtl number Pr = 0.7. The total sampling period of 1.5 h allowed us to capture the dynamics of the magnitude and the orientation of the vector over several orders of characteristic timescales of the large-scale circulation. We found the amplitude of short-term (turbulent) fluctuations to be following a highly skewed Weibull distribution, while the long-term fluctuations are dominated by the modulation effect of a quasi-regular angular precession of the outer flow around a constant mean, the timescale of which is coupled to the characteristic eddy turnover time of the global recirculation roll. Events of instantaneous negative streamwise wall shear occur when rapid twisting of the local flow happens. A mechanical model is used to explain the precession by tilting the spin moment of the large circulation roll and conservation of angular momentum. A slow angular drift of the mean orientation is observed in a phase of considerable weakening of mean wind magnitude.

Highlights

Since Ludwig Prandtl’s pioneering work, we know that the local heat transport at a surface with a temperature differing from that of the surrounded fluid is linked to the local momentum transport across the fluid layer close to the surface
First simulation data, published by Scheel and Schumacher,3 show the existence of singularities in the wall shear stress vector field similar to those reported in Bruecker
Because of the modulation effect, which the outer flow enforces on the signal on the floor, the wall shear stress (WSS) signals should reveal the footprint of this wiggling motion

Summary

Introduction

Since Ludwig Prandtl’s pioneering work, we know that the local heat transport at a surface with a temperature differing from that of the surrounded fluid is linked to the local momentum transport across the fluid layer close to the surface. Measurements of the local wall shear stress (WSS) may, contribute to a better understanding of the convective heat transfer process. Following Prandtl’s idea, Ludwieg carried out a first analysis of the relationship between the heat and momentum transport in thermal convection He did not have the appropriate metrology, and he could obtain only the time-averaged WSS from measurements of the profile of the velocity parallel to the wall.. Due to the lack of sufficiently sensitive sensors of the WSS, the current status quo in such data knowledge is solely available from Direct Numerical Simulations (DNS) Such simulations provide the local WSS vector information in time but usually for a limited simulation period of only a few tens of minutes. First simulation data, published by Scheel and Schumacher, show the existence of singularities in the wall shear stress vector field similar to those reported in Bruecker.4 These singularities are considered as footprints of large eruptions of fluid parcels from the wall, which significantly affect the heat transport.. First simulation data, published by Scheel and Schumacher, show the existence of singularities in the wall shear stress vector field similar to those reported in Bruecker. These singularities are considered as footprints of large eruptions of fluid parcels from the wall, which significantly affect the heat transport. It is, the authors’ conclusion that the information on the magnitude and the angle of the WSS vector as well as the information on its temporal behavior are crucial to understand the local momentum and heat transport processes at the wall

Methods

Results

Conclusion