Author(s): Jean Berlamont
Linked Author(s):
Keywords: Pipe flow; Friction factor; Laminarization; Entropy principle
Abstract: Drag reduction is reported in literatures in which the measured friction factors in pipes is smaller than that one would expect on the basis of state of the art knowledge for a perfectly smooth pipe. This occurs in particular at high Re numbers and in large diameter pipes. This apparently impossible results can not be explained by errors of the measurements. Both from experiments and numerical simulation it is known that rotation causes a certain degree of laminarization of an initially turbulent pipe flow and, accordingly a reduction of the friction factor up to 50%. The reported “smoother than smooth” conditions could indicate that for some reason or another the flow in the pipe has obtained some degree of rotation. Using the “minimum rate of energy dissipation N” principle it can be shown that the most probable flow situation is a flow without any rotation. If however a flow would have obtained for some reason (e.g. the passage of a bend, a flow regulator, …) a certain amount of rotation, it may persist for a long time c. q. for a long distance along the pipe since the corresponding Nvalue is hardly higher than Nmin which corresponds to a flow without rotation. This explains why in a number of circumstances (unintentionally, and unknown to the user or the experimenter) a moderate amount of rotation (N < 0.7 to 1.0) may be present in a straight pipe and why friction factors can be measured which are up to 10% lower than the values for a perfectly smooth pipe according to the White Colebrook Nikuradse (Blasius) formula. Since in a large diameter pipe a small amount of rotation (') produces a relatively large value of N, “smoother than smooth” conditions have been detected preferably in large diameter pipes. If a certain circulation would exist or be imposed in a pipe (e.g. N = 1.0) the reduction of f with, say 10 % would result in an increase of the discharge Q of the order of 5 %. When maintaining the same discharge, a diameter 1 to 2% less could suffice, which is, unfortunately of no practical relevance for design purposes.
Year: 2001