Experimental and Theoretical Investigation 

 of Ship Boundary Layer and Wake 



Shuji Hatano, Kazuhiro Mori and Takio Hotta 

 Hiroshima University , Hiroshima , Japan 



ABSTRACT 



Characteristics of the boundary layer and wake flow 

 of ships are investigated experimentally and at- 

 tempts are made to estimate their velocity distri- 

 butions . 



Boundary layer characteristics , before the onset 

 of separation, are studied; a three-dimensional 

 boundary layer calculation is carried out by the 

 integral method, while examining the boundary layer 

 assumptions and the validity of auxiliary equations 

 by direct measurements of velocity and static pres- 

 sure profiles in boundary layer as well as skin 

 friction distribution on hull surface. 



Assuming that the wake is the domain of influ- 

 ence of the boundary layer and consists of three 

 sub-regions, i.e., vorticity diffusion region, 

 separated retarding region, and viscous sublayer, 

 different governing equations for each stib-region 

 are derived by local asymptotic expansions. 



Velocity distribution in the vorticity diffusion 

 region is estimated in two steps: first, vorticity 

 distribution is found by solving the vorticity 

 diffusion equation, then velocity distribution is 

 calculated from the obtained vorticity distribution 

 by invoking Biot-Savart' s law. 



Satisfactory agreements are attained between 

 calculations and measurements both for boundary 

 layer and wake. 



1. INTRODUCTION 



Introductory Remarks 



The prediction of the viscous flow field around 

 ship hulls, boundary layer on the hull surface, and 

 the wake, is one of the most important problems in 

 ship hydrodynamics. Important design-conditions, 

 such as estimations of viscous resistance or wake 

 distribution on a propeller disk, are all closely 

 connected with this problem. Instabilities of ship 



maneuvering and propeller-excited-vibrations are 

 also presently urgent problems in practice; they 

 are also fundamentally connected with the viscous 



Calculations of a ship boundary layer have been 

 carried out by many investigators during the last de- 

 cade; e.g., Uberoi (1969), Gadd (1970), Webster and 

 Huang (1970), Hatano et al . (1971), Himeno and Tanaka 

 (1973) , and Larsson (1975) . They have solved bound- 

 ary layer equations in integral forms. Cebeci et al . 

 (1975) , as well as Soejima and Yamazaki (1978) , has 

 tried to solve them by the finite-difference method. 



Such remarkable progress in ship boundary layer 

 calculations are mainly due to studies of two- 

 dimensional boundary layers and to the use of high 

 speed computers. Though some of them yield good 

 results, an absence of experimental examination of 

 boundary layer assumptions or auxiliary equations 

 can be found when applying them to shiplike bodies. 

 Experimental examinations are very important because 

 most of auxiliary equations are derived from two- 

 dimensional experiments. 



On the other hand, as to the ship wake, many 

 experimental studies have been carried out not only 

 for ship models but also for full scale ships, e.g., 

 Yokoo et al., (1971) and Hoekstra, (1975) mainly 

 discussed the prediction of full scale wake charac- 

 teristics based on model wake survey. 



Rational theoretical studies are still more im- 

 portant. As to theoretical studies of wake, we 

 must retreat to problems of flow behind rather 

 simple obstacles like flat-plates, circular cylin- 

 ders, or bodies of revolution. Even in such cases, 

 most treatments are based on potential theory such 

 as free-streamline theory or cavity-flow theory, 

 reviewed by Wu, (1972). However, because vortici- 

 ties existing within wakes are mainly generated in 

 boundary layers of hull surfaces and shed into wakes 

 viscously and convectively through separations , the 

 prediction of wake flow should be treated in close 

 relation to boundary layer flow. 



The previous works by Hatano et al . , (1975, 1977), 



169 



