High Reynolds number trends of centerline mean velocity and normal stress in pipe flow

Abstract

The CICLoPE facility at the University of Bologna in Forli, Italy, is a unique facility that provides fully developed pipe flow up to Reynolds numbers of about $Re_\tau$ of 50,000 with exceptional spatial resolution and stable operating conditions. Measurements obtained over the last two years, on the centerline of the pipe in the fully developed test section, with Pitot probes for the mean velocity in the stream ($\pm 0.2\%$ precision) and hot wires for the intensity of turbulence in the streamwise and the normal stress ( $\pm~5\%$ precision) are reported here and compared to other experimental results and some recent direct numerical simulation (DNS) data. The comparisons reveal that high Reynolds number conditions are only reached when $Re_\tau$ is at least larger than $10,000$. The centerline von K\`arm\`an constant, $\kappa_{CL}$ for pipe flow is confirmed with high confidence to be $0.44$. Unlike previously reported measurements on the pipe centerline of the streamwise turbulence intensity and normal stress reported in the literature with various conflicting trends, both quantities are found in CICLoPE to reach a level trend beyond $Re_\tau$ around $25,000$ with values of approximately $2.9\%$ and $0.85$, respectively. Normalized streamwise velocity spectra on the centerline, with high resolution over seven decades of energy, exhibit a clear and extended $-5/3$ inertial range. Skewness and kurtosis of streamwise velocity are found to be independent of Reynolds number even down to $Re_\tau = 5,000$ and equal to $-0.5$ and $3.5$, respectively.