ABSTRACT 



This report presents refinements of a previous momentum- 

 integral method for calculating three-dimensional turbulent 

 boundary layers on ship hulls. In particular the following refine- 

 ments are made: the small crossflow assumption is removed; 

 numerical calculation of the double model potential flow replaces 

 the slender body potential flow; a more general and versatile or- 

 thogonal coordinate system is used in place of the streamline 

 surface coordinate system; and finally, an improved numerical 

 method is used for solving the momentum- integral boundary-layer 

 equations. It is shown that the boundary layer calculation method, 

 developed here, can be used to calculate certain boundary layer 

 parameters, such as boundary layer thickness or skin friction, 

 with fair accuracy over a large portion of hulls that maintain un- 

 separated flow. The surface coordinate system can also be used in 

 other methods for calculating the boundary layer. 



ADMINISTRATIVE INFORMATION 

 The work reported herein was supported by the General Hydromechanics 

 Research Program under Task Area SR 023-01-01 and Work Unit 1552-070. 



INTRODUCTION 



This report presents some refinements of the momentum- integral method 

 for calculating three-dimensional turbulent boundary-layers as developed by 

 von Kerczek for ship hulls. These refinements include: (1) the removal 

 of the boundary-layer small crossflow approximation; (2) the incorporation 

 of an exact numerical calculation of the double model potential flow in- 

 stead of using the slender-body theory potential flow; (3) the abandonment 

 of the streamline surface coordinate system in favor of a more general and 

 versatile orthogonal surface coordinate system; and (4) an improved 

 numerical method for solving the momentum- integral boundary layer equations. 



The use of momentum- integral methods for calculating three-dimensional 

 boundary layers has come under severe criticism recently by the advocates 



of the differential boundary layer equations (see, for example, Landweber 



2 3 4 



and Patel, Cebeci et al. and Spalding ). The main objection to the inte- 

 gral methods seems to center on the unavailability of a suitable crossflow 

 velocity profile function that adaquately approximates a variety of 



*A complete listing of references is given on page 67, 



