Charaoteristios of Ship Boundary Layers 



frequently are designed with zones of reversing curvature, at which 

 boundary-layer profiles with S-shaped cross -flows nnay occur, 



4, At higher Froude numbers the boundary layer will lie 

 over a hull surface area which depends upon the equllibriuna trim 

 and drait and the surface-wave profile cdong the hull at that Froude 

 number. The curvature of the outer streannllnes at the free surface 

 strongly affects the cross-flow components of the boundary- layer 

 velocity profiles [ 6,7] , an effect which Is completely Ignored In 

 boundary-layer studies at zero Froude number. 



5, Near the stern the boundary layer thickness becomes of 

 the same order of magnitude as the radii of curvature, and the 

 methods of thin boundary-layer theory cannot be used without modi- 

 fication. A detailed study of boundary-layer characteristics in this 

 region Is desirable In connection with the development of improved 

 rational methods of computing the viscous drag, and the design of 

 stem appendages from the point of view of strength and cavitation. 

 Of course, if such a calculation could be extended into the near wake, 

 it would be a great boon to the propeller designer, 



6, The draft and trim of a ship may vary greatly, depending 

 upon its cargo. It operates at various speeds or Froude numibers, 

 and if model tests are Involved, the effect of the scale or Reynolds 

 number would be of interest. Since the flow pattern would vary 

 with each of these four parameters, one may wish to calculate the 

 boundary layer for many combinations of parametric values. 



III, SHIP BOUNDARY-LAYER CALCULATIONS 



Ship boundary layers at zero Froude number have been calcu- 

 lated by Uberoi [4] . To determine the outer Irrotational flow he 

 Introduced a distribution of n discrete sources lying within but 

 close to the hull and determined their strengths by solving simul- 

 taneously n linear equations, obtained by satisfying the boundary 

 condition on the hull at n points. This source distribution was then 

 used to calculate the streamlines. 



For calculating the boundary layer, the flow was treated as 

 two-dimensional along each streamline, and the momentum thickness 

 and shape parameter determined by an available two-dimensional 

 seml-emplrlcal procedure [ 10] , A better approximation could have 

 been obtained with little additional effort had one of the available 

 three-dimensional boundary-layer procedures assunalng small cross- 

 flow been used [ 11] , since these would have taken Into account the 

 important three-dimensional property of the spreading of streamlines, 

 Nevertheless, since the spreading of the strecimllnes Is small except 

 near the bow and stern, the results should furnish a useful approxi- 

 mation. 



451 



