Cavitation Inception on Rough Bodies 



where y is the distance normal to the surface, and u^ is the velocity at y. The 

 shape parameter H is the following function of the exponent m: 



m+ 2 



(3) 



If S and m are known, it is easy to find the velocity in the oncoming flow at the 

 tip of the roughness where cavitation inception occurs. Similarly, average ve- 

 locities over the roughness can be obtained by simple integrations of Eq. (2). 



Benson used the velocity at the tip of the roughness element u^ in defining 

 a local cavitation number and local Reynolds number. Thus 



local cavitation number 'y. 



2 'm 



local Reynolds number R,^ = huj^/i^ , 



(4) 

 (5) 



where i^ is the kinematic viscosity of the fluid. When <y^^ for Benson's three- 

 dimensional roughness elements is plotted as a function of Rj^ on log-log paper, 

 straight lines can be fitted through the points for each roughness geometry. The 

 curves in Fig. 1 are reproduced from his report (3). 



If the ORL data for two-dimensional circular arc and triangle roughness 

 elements (4) are recomputed in the same way, these data also show a linear 

 variation with Reynolds number (Fig. 2). Despite the fact that these data were 

 obtained in two water tunnels and four boundary layers, the points are well dis- 

 tributed about the mean line. Straight lines of the form 



Fig. 1 - Local cavitation number as a function of the local Reynolds number 

 (DTMB three-dimensional data based on Uj^) 



185 



