Tomographic Particle Image Velocimetry of Turbulent Rayleigh-Benard Convection in a Cubic Sample

Abstract

We present an experimental study of turbulent Rayleigh-Bénard convection (RBC) in a cubic cell filled with water using tomographic particle image velocimetry. We developed and installed an RBC apparatus with high optical accessibility and a high power LED array for illumination. At the Prandtl number Pr = 6.9 and the Rayleigh number Ra = 1.0 x 10^10, we studied three dimensional large-scale flow structures (LSC) of RBC. Within the plane of the LSC, nonvanishing out-of-plane components were obtained even in the mean velocity field, indicating the necessity of measuring all three velocity components in volumes. Using the maximum velocity of the LSC, we determined the Reynolds number Re = 6275 which agrees within 5% with the values reported in other studies. Further, based on measured mean velocity profiles, we determined the viscous boundary layer thickness δu = 5.2 mm. Plotting the angular distribution of the maximal velocity measured in the LSC shows a four-leaf clover structure in agreement with the results obtained in Direct Numerical Simulations (DNS). Finally, a procedure to separate the turbulent velocity fluctuations from the measurement noise is discussed and applied to our data. It is shown that the measurement errors increase at the walls, especially in the back of the cell.