447 



TABLE 2. Length of Sheet Cavity Over Diameter, 

 Lsc/D, and length of Separation Bubble Over 

 Diameter, L/D, for SST Hemispherical Nose. 



Re 



10" 



SC 



L/D 



0.94 

 1.27 

 1.54 

 2.03 



0.156 

 0.124 

 0.070 

 0.074 



0.124 

 0.096 

 0.084 

 0.068 



Appearance on Blunt Model 



The type of cavitation occurring on the blunt nose 

 is typically travelling bubble cavitation. An 

 example is shovm in Figure 30a (a = 0.33). When 

 a is reduced, a single transient cavity may develop, 

 as shown in Figure 30b (a = 0.28). The transient 

 character of the cavities occurring on the blunt 

 nose is clearly observed in the photographs taken 

 from multiple exposure holograms. Figure 31 shows 

 a photograph taken from a hologram, where three 

 pulses were generated by the ruby laser with pulse 

 separations of 50 ysec and 100 ysec respectively. 

 The flow is from right to left. The picture shows 

 the growth of a cavity near the nose of the model. 

 The cavity is attached to the model and its shape 

 is a spherical segment. The cavity grows (its 

 radius increases) and, at the same time, travels 

 along the surface with a velocity slightly below 

 that of the surrounding fluid. When the cavity 

 reaches a certain height, its shape becomes more 

 like an attached bubble, as shown in Figure 32. 

 In this figure, the flow is from left to right. 

 The attached bubble hardly grows, travels along 

 the surface, and finally collapses. 



The streamwise distance to cavitation separation 

 on the blunt nose obtained from a series of holograms 

 taken at various values of a and Re, is plotted in 

 Figure 33. Also plotted are data points where no 

 cavitation was observed in the hologram on either 

 one or both sides of the model. It is found that 



the streamwise distance to cavitation separation 

 decreases with increasing Re (apart from the scatter, 

 typical for travelling bubble cavitation) . For 

 Re = 2.08 X 10 , cavitation separation is located 

 at a short distance from the pressure minimum 

 [(s/D)p = 0.37]. 



The observations of the cavity growth as 

 represented in Figure 31, enables a comparison with 

 theory. Plesset (1949) analyzed experimental 

 observations by Knapp and Hollander (1948) and 

 compared the growth and collapse of bubbles on a 

 1.5 caliber ogive with the equation of motion for 

 a bubble. The agreement was quite satisfactory. 

 Recently, Persson (1975) introduced some refinements 

 in the comparison. The present analysis is based 

 on the so-called Rayleigh-Plesset equation according 

 to Hsieh (1965). For a vapor bubble, the motion 

 of the bubble wall is given by the equation 



(RR + y R ) 



P - P - 



2S 



R 



4pR 

 R 



(6) 



where p is the liquid density, R the instantaneous 

 bubble radius, P^^ the vapor pressure, P the instan- 

 taneous ambient pressure, S the surface tension, 

 and y the dynamic viscosity. The dots indicate 

 differentiation with respect to time t. The 

 multiple exposure hologram (Figure 31) provided 

 data on Ro(to), Rl (to+50us) , and R2 (to+150vJs) , 

 whereas P(t) could be derived from Figures 31 and 

 4. Equation (6) was solved numerically to obtain 

 a theoretical value of R2 - The results of the 

 computations are given in Table 3. To compare the 

 significance of the right-hand side terms of Eq. 

 (6) , numerical values of these terms are presented 

 in Table 4. The main conclusion to be derived from 

 Table 3 is that the experimentally observed growth 

 of the cavity on the blunt nose is fairly well 

 represented by the Rayleigh-Plesset equation of 

 motion. This is mainly due to the fact that the 

 blunt nose does not exhibit laminar flow separation 

 and viscous effects seem to be small. 



The appearance of developed cavitation on the 

 blunt nose with polymer injection was essentially 

 the same as that without polymers . Details are 

 given by Van der Meulen {1976b) . 



FIGURE 30. Photographs showing cavitation on blunt nose. The flow is from left to right. V =12.8 m/s . 

 (a) a = 0.33; (b) a = 0.28. ° 



