INVESTIGATION OF A TURBULENT FLOW FROM THE TRANSITIONALLY ROUGH REGIME TO THE FULLY ROUGH REGIME

Abstract

Direct Numerical Simulations (DNS) are carried out in a turbulent rough-wall pipe at low and medium Reynolds numbers. The rough surface, which is comprised of threedimensional sinusoidal roughness elements, was viscously scaled from the transitionally rough regime to the fully rough regime. The main aim of this study is to analyse the behaviour of the near-wall cycle as the surface condition changes from smooth through to fully rough. When analysing the streamwise velocity, a triple decomposition is used to distinguish between the fluctuations due to the spatial variation with the actual turbulent fluctuations. For small roughness height (h+ < 15), the near-wall cycle streaks occurs above the roughness elements. Although the high and low speed streaks look similar to the smooth wall when visually inspected, subtle differences are observed when the premultiplied energy spectra are analysed. When the flow is fully rough, the near-wall cycle is replaced by the stationary features of the flow which dominate within the roughness elements. We also analyse the contribution of the apparent wall shear stress due to form (pressure) drag (τR) expressed as a ratio between form and total shear stress (Rτ = τR τT ). In the fully rough regime, the form drag dominates (Rτ > 0.75) and disrupts the near-wall cycle. Townsend’s outer layer similarity is observed when the wall normal height normalised by the mean radius of the pipe y/R0 is greater than 0.56, where a collapse in the streamwise premultiplied energy spectra is obtained.