In the present study, the overall economic impact of hull fouling on a mid-sized naval surface ship (Arleigh Burke-class destroyer DDG-51) has been analyzed. A range of costs associated with hull fouling was examined, including expenditures for fuel, hull coatings, hull coating application and removal, and hull cleaning. The results indicate that the primary cost associated with fouling is due to increased fuel consumption attributable to increased frictional drag. The costs related to hull cleaning and painting are much lower than the fuel costs. The overall cost associated with hull fouling for the Navy's present coating, cleaning, and fouling level is estimated to be $56M per year for the entire DDG-51 class or $1B over 15 years. The results of this study provide guidance as to the amount of money that can be reasonably spent for research, development, acquisition, and implementation of new technologies or management strategies to combat hull fouling.

Predictions of full-scale ship resistance and powering are made for antifouling coating systems with a range of roughness and fouling conditions. The estimates are based on results from laboratory-scale drag measurements and boundary layer similarity law analysis. In the present work, predictions are made for a mid-sized naval surface combatant at cruising speed and near maximum speed. The results indicate that slime films can lead to significant increases in resistance and powering, and heavy calcareous fouling results in powering penalties up to 86% at cruising speed. The present estimates show good agreement with results from full-scale ship power trials.

Reliable full-scale prediction of drag due to rough wall-bounded turbulent fluid flow remains a challenge. Currently, the uncertainty is at least 10%, with consequences, for example, on energy and transport applications exceeding billions of dollars per year. The crux of the difficulty is the large number of relevant roughness topographies and the high cost of testing each topography, but computational and experimental advances in the last decade or so have been lowering these barriers. In light of these advances, here we review the underpinnings and limits of relationships between roughness topography and drag behavior, focusing on canonical and fully turbulent incompressible flow over rigid roughness. These advances are beginning to spill over into multiphysical areas of roughness, such as heat transfer, and promise broad increases in predictive reliability.

A review of predictive methods used to determine the frictional drag on a rough surface is presented. These methods utilize a wide range of roughness scales, including roughness height, pitch, density, and shape parameters. Most of these scales were developed for regular roughness, limiting their applicability to predict the drag for many engineering flows. A new correlation is proposed to estimate the frictional drag for a surface covered with three-dimensional, irregular roughness in the fully rough regime. The correlation relies solely on a measurement of the surface roughness profile and builds on previous work utilizing moments of the surface statistics. A relationship is given for the equivalent sandgrain roughness height as a function of the root-mean-square roughness height and the skewness of the roughness probability density function. Boundary layer similarity scaling then allows the overall frictional drag coefficient to be determined as a function of the ratio of the equivalent sandgrain roughness height to length of the surface.

The Reynolds number similarity hypothesis of Townsend ͓The Structure of Turbulent Shear Flow ͑Cambridge University Press, Cambridge, UK, 1976͔͒ states that the turbulence beyond a few roughness heights from the wall is independent of the surface condition. The underlying assumption is that the boundary layer thickness ␦ is large compared to the roughness height k. This hypothesis was tested experimentally on two types of three-dimensional rough surfaces. Boundary layer measurements were made on flat plates covered with sand grain and woven mesh roughness in a closed return water tunnel at a momentum thickness Reynolds number Re of ϳ14 000. The boundary layers on the rough walls were in the fully rough flow regime ͑k s + ജ 100͒ with the ratio of the boundary layer thickness to the equivalent sand roughness height ␦ / k s greater than 40. The results show that the mean velocity profiles for rough and smooth walls collapse well in velocity defect form in the overlap and outer regions of the boundary layer. The Reynolds stresses for the two rough surfaces agree well throughout most of the boundary layer and collapse with smooth wall results outside of 3k s. Higher moment turbulence statistics and quadrant analysis also indicate the differences in the rough wall boundary layers are confined to y Ͻ 5k s. The present results provide support for Townsend's Reynolds number similarity hypothesis for uniform three-dimensional roughness in flows where ␦ / k s ജ 40.