Panel Discussion 



Computations of Ship Boundary Layers 



M. Martin 

 Hydronautics, Inc. 

 Laurel, Maryland 



presented by ^ , 



L. Landweber 



INTRODUCTION 



The present study uses the available tools of the linearized potential flow 

 about a ship and the three-dimensional integral turbulent boundary- layer equa- 

 tions to study the characteristics of the boundary -layer on ship forms. The 

 method of Guilloton, as presented by Korvin-Kroukovsky, was used to compute 

 the streamlines and pressures about the ship. Solutions of the boundary- layer 

 equations were obtained using a nonslip boundary condition in the ship surface 

 and the velocity and pressure distributions given by the potential theory as the 

 "outer" conditions. The set of boundary- layer equations was integrated along 

 the streamline using a Runge-Kutta-type technique and, as a result, the momen- 

 tum thickness, shape parameter, and the angle of the boundary-layer flow to the 

 outer flow were calculated. 



The numerical results for series 60/.60 and 60/.80 ships of different lengths 

 at various Froude numbers were presented. 



THREE-DIMENSIONAL TURBULENT 

 BOUNDARY- LAYER EQUATIONS 



The following set of nondimensional boundary -layer equations were derived 

 by Webster and Huang [1] from the three-dimensional turbulent boundary -layer 

 equations presented by Cooke [2] 



3n fi( 1 + n ) 



1 h 



2 /Su 

 u \Sx 



= (1+n) 



a(H) 



( n H+ H+ 1 ) 



Tiy 



o"s 2 e Bs" 



2 



+ — 



Bh 



Bs 



+ 4) (H) 



(H^ + H) u 



( n H+ H+ 1 ) 



1 Bu 



+ •/'(H) 



i(nH+H+ 1) 



1 + H 3u 

 H + 2 3S 



(2) 

 (3) 



■=This is a summary of part of the research carried out at Hydronautics, Inc. 

 by Dr. W . C. Webster and T. T. Huang, between the years 1964 and 1967, on 

 ship boundary layer research. The work was sponsored by the Society of 

 Naval Architects and Marine Engineers under Purchase Order No. 400. 



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