TY - JOUR
T1 - A multi-state description of roughness effects in turbulent pipe flow
AU - She, Zhen Su
AU - Wu, You
AU - Chen, Xi
AU - Hussain, Fazle
PY - 2012/9
Y1 - 2012/9
N2 - Despite persistent efforts over the last century, a theory for predicting the effects of surface roughness on the mean flow is still missing. Here, we extend a recently proposed multi-state theory to incorporate roughness effects. A formula for the roughness function is constructed by applying the Lie-group invariance theory, giving excellent agreement with the fully collapsed data of both the Nikuradze sand-coated and Princeton honed pipes. A major advantage of the theory is its ability to successfully describe the non-universality-either inflectional or monotonic variations-in a transitionally rough regime with a single sharpness parameter. This model then yields an analytic prediction for the friction factor and mean velocity profiles in rough pipes, agreeing with the empirical data. Consistent with classical understanding (e.g. Townsend's similarity hypothesis), our results confirm the multi-layer theory of wall turbulence, regardless of smooth or rough surfaces.
AB - Despite persistent efforts over the last century, a theory for predicting the effects of surface roughness on the mean flow is still missing. Here, we extend a recently proposed multi-state theory to incorporate roughness effects. A formula for the roughness function is constructed by applying the Lie-group invariance theory, giving excellent agreement with the fully collapsed data of both the Nikuradze sand-coated and Princeton honed pipes. A major advantage of the theory is its ability to successfully describe the non-universality-either inflectional or monotonic variations-in a transitionally rough regime with a single sharpness parameter. This model then yields an analytic prediction for the friction factor and mean velocity profiles in rough pipes, agreeing with the empirical data. Consistent with classical understanding (e.g. Townsend's similarity hypothesis), our results confirm the multi-layer theory of wall turbulence, regardless of smooth or rough surfaces.
UR - http://www.scopus.com/inward/record.url?scp=84867025883&partnerID=8YFLogxK
U2 - 10.1088/1367-2630/14/9/093054
DO - 10.1088/1367-2630/14/9/093054
M3 - Article
AN - SCOPUS:84867025883
SN - 1367-2630
VL - 14
JO - New Journal of Physics
JF - New Journal of Physics
M1 - 093054
ER -