Turbulent flow in smooth and rough pipes

Abstract

Recent experiments at Princeton University have revealed aspects of smooth pipe flow behaviour that suggest a more complex scaling than previously noted. In particular, the pressure gradient results yield a new friction factor relationship for smooth pipes, and the velocity profiles indicate the presence of a power-law region near the wall and, for Reynolds numbers greater than about 400x103 (R+>9x103), a logarithmic region further out. New experiments on a rough pipe with a honed surface finish with krms/D=19.4x10-6, over a Reynolds number range of 57x103-21x106, show that in the transitionally rough regime this surface follows an inflectional friction factor relationship rather than the monotonic relationship given in the Moody diagram. Outer-layer scaling of the mean velocity data and streamwise turbulence intensities for the rough pipe show excellent collapse and provide strong support for Townsend's outer-layer similarity hypothesis for rough-walled flows. The streamwise rough-wall spectra also agree well with the corresponding smooth-wall data. The pipe exhibited smooth behaviour for ks+ < or =3.5, which supports the suggestion that the original smooth pipe was indeed hydraulically smooth for ReD< or =24x106. The relationship between the velocity shift, DeltaU/utau, and the roughness Reynolds number, ks+, has been used to generalize the form of the transition from smooth to fully rough flow for an arbitrary relative roughness krms/D. These predictions apply for honed pipes when the separation of pipe diameter to roughness height is large, and they differ significantly from the traditional Moody curves.

Flow in a commercial steel pipe

“…A strong Reynolds number dependence is clearly evident, consistent with observations made for smooth pipes by Morrison et al [10] and rough pipes by Allen et al [1]. Two peaks are evident in the profiles of u 2…”

Evolutionary Optimization of Colebrook&rsquo;s Turbulent Flow Friction Approximations

“…Aside for the Colebrook equation, the presented methodology can be used to fit with the raw and updated measured data, all similar empirical equations which cover the same region of turbulent flow [54,55].…”

“…Despite of that in some tests carried out on pipes that were artificially roughened with grains of sand the curves were inflectional in nature, i.e. the friction factor (λ) decreases to a minimum value with increasing Reynolds number (R) and then rises again to reach a constant value for complete turbulence [53,54], the Colebrook equation is still accepted in engineering practice as sufficiently accurate. It is still widely used in petroleum, mining, mechanical, civil and in all branches of engineering which deals with fluid flow.…”

“…Moody's and Rouse's charts [3,4] represent the plots of the Colebrook equation over a very wide range of the Reynolds number (R from 2320 to 10 8 ) and relative roughness values (ε/D from 0 to 0.05). Beside of some of its shortcomings [54], today, Colebrook's equation is accepted as the informal standard of accuracy for calculation of hydraulic friction factor (λ).…”

“…Hydraulic resistance in general depends on flow rate [53][54][55][56][57][58][59]. To make things even more complex, hydraulic resistance is usually expressed through flow friction factor such as Darcy's (λ) where further pressure drop and flow rate is correlated with the well-known formula by Darcy and Weisbach.…”