The onset of roughness effects in the transitionally rough regime

Understanding the relationship between a surface’s topography and its hydraulic resistance is an important, yet elusive, goal in fluids engineering. Particularly poorly understood are the flow conditions at which a given surface will begin to show the effects of roughness in the form of increased wall shear stress above that of the hydraulically smooth wall. This phenomenon is the focus of the present study. The results from a small scale fully-developed turbulent channel flow facility are presented for a hydraulically smooth wall and three types of rough surfaces (a sandpaper surface, two ship bottom paints and painted surfaces smoothed by sanding). Experiments were conducted over a Reynolds number (ReH) range of 5800–64,000 based on the channel height and the bulk mean velocity. The onset of roughness effects occurs for the sandpaper surface at k rms + ∼ 1 or k s + ∼ 5. This value of k s + and the shape of the roughness function in the transitionally rough regime agree rather well with the results of Nikuradse (1933) for uniform sand. The frictional resistance of the two painted surfaces agree within experimental uncertainty despite a factor of two difference in krms. The onset of roughness effects occurs at a maximum peak to trough roughness height, k t + , of ∼10. Painted surfaces sanded with progressively finer sandpaper (60–220 grit) show roughness effects for k rms + ∼ 0.5–0.7 or k t + ∼ 9, while the 400 grit sandpaper displays hydraulically smooth conditions over the entire Reynolds number range. The roughness scale that best predicts the onset of roughess effects is kt, indicating that the largest roughness features have the most influence in determining when a surface ceases to be hydraulically smooth. It is also of note that the roughness functions for the marine paint and painted-sanded surfaces do not exhibit either Nikuradse or Colebrook-type behavior.