Direct numerical simulation of a turbulent rough-walled pipe

Direct Numerical Simulations (DNS) of turbulent pipe flow have been conducted at low to medium Reynolds numbers. The surface of the pipe is varied from a smooth-wall pipe to a rough-wall pipe, where the roughness is comprised of three-dimensional sinusoidal elements. Parametric tests were carried out to analyse the effects of the height and the wavelength of the sinusoidal surface. An analysis of the mean statistics convincingly supports Townsend's outer-layer hypothesis. Higher-order statistics such as skewness and flatness are also gathered and show reasonable collapse in the outer layer of the pipe for different roughness cases. Even at a mean-to-peak roughness height of 2.5 wall units, which is within the viscous sublayer of the pipe, the roughness effected a centerline velocity shift of 0.50 friction velocities. When the roughness height is increased to a mean-to-peak roughness height of 20 wall units, the flow can be considered to be in the fully rough regime, with a centerline velocity shift of 7.1 friction velocities.