Cavitation Inception on Rough Bodies 



good results by assuming that the pressure minimum of the element is propor- 

 tional to the average of the square of the velocity in the boundary layer out to the 

 height of the roughness (5). If a power law boundary layer profile is assumed 

 for the oncoming flow, 



For h < 



U2 H \h 



For h > s 



s^ifir- '" 



2 1 /h\2/'" 



• (8) 



,2 



2 



U2 " ^ m+ 2 h • (9) 



If these expressions are used for the velocity at the tip of two-dimensional 

 roughness elements, the local cavitation number and Reynolds number become 



^ = = -0 (10) 



u^ 

 RI = u.h/i., (11) 



where 



[T?]''\ (12) 



Figure 3 shows the ORL two-dimensional data plotted in terms of cr^^ and R^- 

 The constants A and B of the straight lines fitted through the points are listed in 

 Table 2. 



A comparison of Figs. 2 and 3 shows that the points are shifted somewhat 

 but that there is not much difference in the amount of scatter in the two sets of 

 curves. In both figures, the triangular roughnesses show an increase in local 

 cavitation number with Reynolds number, which is characteristic of cavitation in 

 a separated flow region. 



On both figures, cavitation inception on the circular-arc roughness elements 

 shows very little dependence on Reynolds number. A least- square fit to the data 

 shows a small positive slope to the line in Fig. 2 and a small negative slope in 

 Fig. 3. A different method of computing the local velocity might have produced 

 a horizontal line. Since there was considerable scatter in the data, no further 

 analysis was warranted. An average value of all the circular arc cavitation 

 numbers on Fig. 3 is 1.11. The pressure coefficient, computed by potential flow, 

 has the value 1.083 (5). Although this remarkable agreement may be fortuitous, 

 it appears that the computation of the local flow parameters on the basis of u^ is 

 justified for two-dimensional flows. The constancy of the local cavitation number 



187 



