Direct numerical simulation of turbulent flow in pipes with realistic large roughness at the wall

We carry out direct numerical simulation (DNS) of turbulent flow in rough pipes. Two types of irregular roughness are investigated, namely a grit-blasted and a graphite surface. A wide range of Reynolds numbers is tested, from the laminar up to the fully rough regime, attempting to replicate Nikuradse's pioneering study. Despite the large relative roughness, outer-layer similarity is achieved at high Reynolds number as hypothesised by Townsend, with deviations from the smooth wall case of 4% for the grit-blasted surface and 13% for the graphite surface. This makes it possible to define a roughness function and the equivalent sand-grain roughness. The results are compared with those obtained in plane channels, with small differences pointing to the residual influence of the duct cross-sectional shape in the presence of relatively large roughness. The computed friction factors behave similar to those Nikuradse's chart, with differences in terms of the friction factor in the laminar region and of the critical Reynolds number, which are partly absorbed by using the hydraulic radius as reference length scale. The distributions of the velocity fluctuations intensities point to a isotropisation of turbulence in the near-wall region resulting from the roughness, with influence of the roughness geometry. Comparison of the computed equivalent sand-grain roughness height suggest that existing correlations suffer from poor predictive power, at least for surfaces with large relative roughness.

Automated summary

In this research, direct numerical simulation (DNS) is used to study turbulent flow in rough pipes. Two types of irregular roughness, grit-blasted and graphite surfaces, are investigated. A wide range of Reynolds numbers is tested, and outer-layer similarity is achieved at high Reynolds numbers despite the large relative roughness. A roughness function and an equivalent sand-grain roughness are defined. The results are compared with those obtained in plane channels, and the computed friction factors behave similarly to Nikuradse's chart. However, there are differences in terms of the friction factor in the laminar region and the critical Reynolds number, which are partly absorbed by using the hydraulic radius as a reference length. The distributions of velocity fluctuations intensities show turbulence isotropization in the near-wall region due to roughness, with influence from the roughness geometry. The calculated equivalent sand-grain roughness height suggests that existing correlations have poor predictive power for surfaces with large relative roughness.