A correlation of friction factors for pipe flow over two-dimensional, periodic geometric roughness

Friction effects of two-dimensional, periodic, artificial roughness for fully roughened pipes in turbulent flow were investigated. Friction factor data over many different shapes, sizes, and spacings of roughness were compiled and examined for similarities which could be correlated. Such shapes included fins, round rods, rectangular rods, square bars, v- grooves, and sinusoids. It was found that friction factors for two differently- shaped roughness waveforms of the same spacing, amplitude, and pipe diameter are related by the normalized crosscorrelation coefficient of their waveforms. Such roughness falls into two groups: projections, where the bulk flow interacts with the flow near the wall; and grooves, where captive vortices exist in the roughness cavities and do not interact with the bulk flow. Friction factors were related to sine waves of similar size, modified by linear combinations of roughness dimensions and plotted versus a representing parameter R, which was found to be a dimensionless group containing a measure of spacing, amplitude, and pipe diameter. Two correlation plots were developed, for projections and grooves. These show distinct regions which are shown to delineate geometries where various wall flow processes occur. Predictions can thus be made of friction factor and flow type given only the roughness system geometry and shape.