335 



FIGURE 8. Collation of cavitation inception data. 



1 2 3 4 5 6 7 

 Time (m sec) 



FIGURE 9. Sample bubble growth data [after Arndt 

 and Ippen (1968)] . 



wherein 



'f = 



2Tj,/pU Boundary Layer Flow 



1^2 Free Shear Flows 



In this expression C^ is computed either from the 

 measured wall shear in the case of boundary layer 

 flows or from turbulence measurements made in the 

 air at comparable Reynolds numbers for the case of 

 a free jet and a wake. The measured value of C is 

 only significant for the case of the disk wake and 

 the pressure data was determined from the experi- 

 mental work of Carmodi (1964) . The available data 

 seem tc be well approximated by the relation 



a + C = 16 C^ 

 c p f 



which was originally proposed for boundary layer 

 flow by Arndt and Ippen (1968) . These data would 

 seem to imply that a relatively simple scaling law 

 already exists and would further imply that the 

 previous discussion in this paper on turbulence 

 effects is superfluous. This is not the case . 

 Arndt and Ippen (1958) made observations of the 

 bubble growth in turbulent boundairy layers . Some 

 of their results are depicted in Figures 9 and 10. 

 Figure 9 shows sample bubble growth data. The 

 growth rate is observed to stabilize at a constant 

 value during most of the growth phase. Using Eq. 

 (4) , the levels of local tension are found to be 

 quite small, of the order 20 to 100 millibar. These 

 data correspond to observations in a rough boundary 

 layer. Of particular interest is the fact that, 

 in all cases, the life time for bubble growth is 

 a fraction of the Lagrangian time scale, :7 = S/u' . 

 In fact growth times were observed to be of the 

 order h/u . Unfortunately there is not enough 



*Tb was estimated from Eq. (5) using observed values 

 of Rj, reported in Arndt and Ippen (1967) . For 

 convenience, the results are normalized to equivaleni: 

 sand grain roughness, hg. 



experimental evidence available to completely 

 illuminate this point. As shown in Figure 10, 

 cavitation occurs roughly in the center of the 

 boundary layer with a tendency for the zone of 

 maximum cavitation to shift inward as u*Tg/hg 

 decreases from about 1.5 to approximately 0.1*. 

 In the cited boundary layer experiments , Cp is 

 negligible. Thus a„ = 16 Cf. Noting that p' is 

 approximately 2.5 pu* at the wall, we estimate 

 that cavitation is incited by negative peaks in 

 pressure of order 5 p' . This compares favorably 

 with Rouse's (1953) data for jet cavitation which 

 indicate that negative peaks of order 10 p' are 

 responsible for cavitation. 



A strong dependence on Reynolds number can be 

 observed even in free shear flows. Figure 11 

 contains cavitation data for a sharp edged disk. 

 These data were obtained in both water tunnels 

 and a new depressurized tow tank facility located 

 at the Netherlands Ship Model Basin. The water 

 tunnel data are for cavitation desinence, whereas 

 the tow tank data are for cavitation inception 

 determined acoustically. The cross hatched data 

 were determined in a water tunnel at high velocities 

 by Keermeen and Parkin (1957) . All the other data 

 were obtained at relatively low velocities (2 - 10 

 m/sec) . There is considerable scatter in these 

 data and this is traceable to gas content effects 



all bubbles 

 covitating bubbles 



4 6 



y/s 



FIGURE 10. Observation of cavitation in turbulent 

 boundary layers [after Arndt and Ippen (1968)]. 



