Numerical study of roughness model effect including low-Reynolds number model and wall function method at actual ship scale

A numerical study of roughness effects at an actual ship scale is performed. Low-Reynolds number roughness models based on the two-equation turbulence model are employed, meanwhile, a wall function method is also developed. First, the roughness models are examined for the 2D flat plate case at the Reynolds numbers of 1.0×107\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.0 \times 10^7$$\end{document}, 1.0×108\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.0 \times 10^8$$\end{document} and 1.0×109.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.0\times 10^9.$$\end{document} The resistance coefficient increases with roughness height and uncertainty analysis of the resistance coefficient is performed. Additionally, the distributions of the non-dimensional velocities u+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u^+$$\end{document} based on the non-dimensional heights y+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y^+$$\end{document} of the low-Reynolds number models and the wall function method are compared for changing the roughness height. Next, the roughness models and wall function method are applied to the flows around a ship at full scale. The tanker hull form with the flow measurement result from an the actual sea test is selected. The propulsive condition with the free surface effect is achieved by the propeller model. The velocity contours are compared with the measured results of the actual ship. The results of the roughness models show good agreement in comparison with the smooth surface condition. The wall function method leads to reduced grid uncertainty with respect to the resistance coefficient and shows agreement with the measured velocity contours. Consequently, the wall function method is better at full scale.