Borden 



cavitation inception over three-dimensional roughness elements embedded in the 

 boundary layer of a flat plate. This relationship became apparent when the cavi- 

 tation number and Reynolds number were computed in terms of the local veloc- 

 ity in the oncoming flow at the point of cavitation and the roughness height. The 

 Reynolds number dependency was further confirmed when similar two-dimensional 

 data were analyzed in the same way. These data were obtained in two water tun- 

 nels, in four different boundary layers, and at temperatures ranging from 76 to 

 86 °F. Although the temperature range was not large enough to establish a true 

 viscous effect in the two sets of boundary layer experiments, it is reasonable to 

 assume that viscosity would play the same role in a shear flow as in a uniform 

 flow. Specifically, when cavitation originates in a vortex resulting from flow 

 separation on a blxoff roughness, viscosity of the fluid will affect the cavitation 

 inception speed. There will be no viscous effects on gently curving protuber- 

 ances on which there is no flow separation. The results discussed here tend to 

 support these hypotheses. 



The cavitation inception data obtained at the Model Basin and at ORL have 

 been reduced to local velocity conditions. Analytical curves have been fitted to 

 the data for each roughness geometry. Using Holl's formulas for computing 

 cavitation inception on a rough parent body, sets of curves and tables have been 

 compiled for use in computing cavitation speeds for a cavitating rough body of 

 known pressure distribution and boundary layer characteristics operating at dif- 

 ferent depths in the ocean. 



SCALING OF CAVITATION INCEPTION 

 ON ROUGHNESS ELEMENTS 



Two sets of experiments have been performed to measure cavitation incep- 

 tion over two- and three-dimensional roughness elements embedded in the 

 boundary layer on a flat plate (3,4). The cavitation number measured in terms 

 of the velocity at the outher edge of the boundary layer has been defined as 



-0 = "-^. (1) 



where p is the static pressure in the water tunnel at the location of the rough- 

 ness element, p^ is the vapor pressure of the liquid, p is the density of the 

 liquid, and u is the velocity at the outer edge of the boundary layer. For a par- 

 ticular roughness element, (^^ is a function of h, the height of the roughness; ^, 

 the boundary layer thickness; H, the shape parameter of the boundary layer pro- 

 file; and the velocity of flow. In order to develop scaling laws for predicting 

 cavitation inception, it is necessary to determine the flow in the immediate 

 vicinity of the roughness. 



In turbulent flow, the velocity profile of a boundary layer is well approxi- 

 mated by a power law of the form 



y 

 U 



(2) 



184 



