Turbulent flow in a machine honed rough pipe for large Reynolds numbers: General roughness scaling laws

An alternate inner wall variable, for flow over a transitional rough pipe surface, is defined as the ratio of normal coordinate measured above the mean roughness level to the wall roughness scale. The Reynolds equations for mean turbulent flow in a transitional rough pipe, in two layers (inner and outer) are considered. The predictions of the mean velocity and friction factor in fully developed turbulent flow in a rough pipe flow, presented here, covers all types of roughness. The data for a particular case of the machine honed Princeton superpipe roughness, analogous to inflectional type roughness of Nikuradse, is presented, as two expressions using our roughness scale. The velocity profile and friction factor, on a transitional rough wall, are shown to be governed by the new log laws, which are explicitly independent of the transitional wall roughness. Further, the inflectional roughness has also been connected with geometric roughness parameters; like, arithmetic mean roughness, mean peak to valley heights roughness, root mean square (rms), roughness based on texture measure; and the friction factor implicit and approximate explicit formulas have also been proposed. In entire transition region between fully smooth and fully rough wall, monotonic roughness of Colebrook (Moody Chart) over estimaton the friction factor when compared with present inlectional roughness.

► Reynolds mean momentum equation without closure model is considered.
► Mean velocity and friction factor log laws for general roughness.
► Proposed two expressions for roughness due to machine honed/inflectional roughness.
► Inflectional hydraulic to geometric roughness (rms, amean, peakvalley,texture).
► In roughness domain, a Moody type chart is present for inflectional roughness.