Wall friction relations in wall-bounded shear flows

Abstract

The widespread use of available skin friction relations in engineering and in turbulence research is ample justification to examine their validities and limitations of use. The Prandtl–von Kármán logarithmic friction law (Prandtl, 1932), for instance, is vitally important for decades for predicting wall skin friction. There have been, however, rising concerns regarding its accuracy due to the deficit of the flow similarity assumption adopted in the vicinity of the wall and in the core/outer region of the flow field. Hence, the wall skin friction could possibly be doubtful when predicted using the Prandtl–von Kármán relation, in particular at high Reynolds numbers compared with values obtained from direct measurements. We therefore briefly review the recent advances in the logarithmic friction relation based on the latest pipe, channel, and boundary layer wall friction data over a wide range of Reynolds numbers. Common similarities and differences among those flows, particularly in terms of the mean flow and the wall skin friction data are highlighted. Recent pipe friction relations (Mckeon et al., 2005) are compared with the Prandtl–von Kármán logarithmic friction law and verified with new accurate pipe friction data. A revisited logarithmic skin friction relation for plane-channel flows (Zanoun et al., 2009) is reported, predicting the wall friction with an accuracy of better than ±1.44%. A modified logarithmic skin friction relation for external flows introduced by Nagib et al. (2007) is presented and discussed. We believe that having a concise review and summary of the often used friction relations in wall-bounded shear flows in a single article will be of interest to fluid mechanics readers.