Cavitation Inception on Rough Bodies 



element appeared to be a reasonable value for computing the local flow parame- 

 ters. With this choice of local flow velocity, u^^ becomes equal to u, the veloc- 

 ity at the edge of the boundary layer, as soon as the roughness protrudes through 

 the boundary layer. Unfortunately no data were obtained for roughness elements 

 with heights of the same magnitude as the boundary layer thickness. 



COMPUTATION OF CRITICAL HEIGHTS OF 

 ROUGHNESS ELEMENTS 



Holl (4) has postulated that the cavitation inception data obtained in the 

 boundary layer on a flat plate can be used to predict cavitation inception on an 

 isolated roughness element embedded in the boundary layer of a smooth hydro- 

 dynamic body having an arbitrary pressure distribution. Although he recog- 

 nized the importance of matching boundary layer profiles and roughness height 

 to boundary layer thickness ratios, he failed to recognize the importance of 

 Reynolds number scaling. With the use of local cavitation number and local 

 Reynolds number scaling, the data can be used in a great variety of boundary 

 layer conditions. In order to use the roughness data quantitatively for a given 

 hydrodynamic body, it is necessary to know the pressure distribution, boundary 

 layer thickness, and velocity profile on the parent body. On the other hand, an 

 estimate of the effect of isolated roughness on a parent body can be obtained 

 from a reasonable estimate of the pressure distribution and boundary layer 

 development. 



If a roughness element is placed on a smooth parent body at a point where 

 the pressure coefficient is Cp, the cavitation inception number at the roughness 

 is 



^R= -Cp+ (1-Cp)cx„, (13) 



where o-^ is the cavitation inception number of the roughness computed in terms 

 of the velocity u at the edge of the flat plate boundary layer which has the same 

 velocity profile as the parent body. Inasmuch as the boundary layer profiles are 

 the same, u may also be interpreted as the velocity at the edge of the boundary 

 layer of the parent body. Therefore, the factor 



l-Cp=uVu^2 (14) 



converts cr^ to free- stream flow conditions. If the isolated roughness is at a 

 water depth H^ on the parent body. 



_ Pc-Py _ 2g (H^+H^-H^) 



(15) 



where Hg is the pressure head of the atmosphere and H^ is the pressure head of 

 the vapor pressure. 



Thus o-Q in Eq. (13) is determined as a function of the free -stream velocity 

 u„, the pressure coefficient Cp, the water depth H^, the atmospheric pressure 



189 



