Presently, engineers lack an accurate technique for predicting the drag of a generic rough surface, regardless of years of comprehensive measurements and recent computations of boundary layer flow over rough surfaces. The technique in use currently was first defined by Schlichting (1936) as the size of the sand grains from the experiments of Nikuradse (1933) that gave effectively the same frictional resistance as the roughness under consideration. Through the years, subsequent studies have been undertaken, such as those by Ligrani & Moffat 1986; Shockling, Allen & Smits 2006; Schultz & Flack 2007, yet the Nikuradse (1933) remains the most complete study of the fully rough regime to date. Reproducing Nikuradse’s original surfaces has encountered a great inhibition owing his idiosyncratic experimental approach.
In the Moody diagram, the equivalent roughness height which is the same as the equivalent sand-grain roughness height (ks), which is a hydraulic scale and not a physical scale is normally used. It would be therefore right for one to presume that the word equivalent has often been ignored and the words roughness height have been used. Consequently, the Moody diagram is only accurate for surfaces with known ks in the fully rough regime. Therefore, following recent technological advances that have enabled researchers to computationally model rough wall flows, the applicability of the Moody diagram has been called in to question, since it is only accurate for surfaces with known ks in the fully rough regime.
To this note, a recently published paper in the Journal of Fluid Mechanics, by Professor Karen Flack from the Department of Mechanical Engineering at United States Naval Academy contributed a new perspective of the Moody Diagram based on a recent paper by Thakkar et al. The recent contributions by Thakkar et al. were the first to employ Direct Numerical Solution (DNS) to study turbulent boundary layer flow over a realistic irregular roughness, similar to the sand grain roughness of Nikuradse, for the entire range of roughness Reynolds numbers, from hydraulically smooth to fully rough.
In brief, her aim was to clear the misunderstanding regarding the mechanisms responsible for the transition from hydraulically smooth to fully rough, highlighting the inherent drawback in the Colebrook-White transition equation-derived Moody diagram. She assessed the simulation’s ability to identify the theoretical issues related to the approach to hydrodynamic smoothness, since neither the Colebrook curve nor Bradshaw’s quadratic law was close to the DNS results.
In a nutshell, the study by Karen Flack focused on creating a better understanding with regard to prediction of frictional drag on rough surfaces. In her work, she does not discredit the Moody diagram but instead recommends its modification/review, specifically, the Colebrook function which represents a monotonic variation in the skin-friction, asymptotically approaching the limits of hydraulically smooth and fully rough regimes. In general, her work poised a daunting question on whether the engineering community was ready to move beyond the Moody diagram and the characterization of roughness by ks. Altogether, since this is still an active research area, it is anticipated that this work and other computations, coupled with validation experiments, will ultimately lead to improved frictional drag predictions.
Karen A. Flack. Moving beyond Moody. Journal of Fluid Mechanics (2018), volume 842, page 1-4.Go To Journal of Fluid Mechanics (2018)