Roughness effects in turbulent pipe flow

Abstract

Mean flow measurements are presented for fully developed turbulent pipe flow over a Reynolds number range of $57\,{\times}\,10^3$ to $21\,{\times}\,10^6$ where the flow exhibits hydraulically smooth, transitionally rough, and fully rough behaviours. The surface of the pipe was prepared with a honing tool, typical of many engineering applications, achieving a ratio of characteristic roughness height to pipe diameter of 1 : 17000. Results for the friction factor show that in the transitionally rough regime this surface follows a Nikuradse (1933)-type inflectional relationship rather than the monotonic Colebrook (1939) relationship used in the Moody diagram. This result supports previous suggestions that the Moody diagram in the transitional regime must be used with caution. Outer scaling of the mean velocity data shows excellent collapse and strong evidence for Townsend's outer layer similarity hypothesis for rough-walled flows. Finally, the pipe exhibited smooth behaviour for scaled roughness height $k_s^+ \,{\le}\, 3.5$, which supports the suggestion by Zagarola & Smits (1998) that their pipe was hydraulically smooth for $Re_D\,\,{\leq}\, 24\,{\times}\,10^6$.