485 



lAllA) 

 0.6 r 



05 



0.4 



0.3 



0.2 



(□I 



*'D 3 3 

 A3 4 

 o 4 3 

 • 4 5 



( ) complete collapse 

 no ( ) collapse to max pressure 

 slow pressure increase 

 fast pressure increase 

 very fast pressure increase 

 mean value of 8 samples 



O^ 



bubbles 







5 



1.0 Reduced freq 1.5 



5 10 15 fosc IHz) 20 



FIGURE 25. Normalized collapse time. 



vjhere 



surrounding pressure 



p = vapor pressure 



U = undisturbed velocity 



p = density of water 



a = cavitation number 



Of course this formula at best gives a time 

 proportional to the collapse time of the sheet with 

 maximum length, J^max- ^^ ^^ shown in Figure 26 

 the tendency is simlar to that in Figure 25. The 

 conclusion is that at high f the collapse is 



Osc 



mainly regulated by a surrounding pressure consider- 

 ably higher than the pressure inside the cavity, 

 which results in T^/Tf^' - constant and a violent 

 collapse of the type predicted by classical theory 

 [Rayleigh (1917)]. At low fgsc -"-^ '-^^" ^^ supposed 

 that during collapse the pressures outside and 

 inside the cavity are approximately equal . Then a 

 violent collapse will not occur and T^/T^' becomes 

 considerably larger than for a "free" collapse. 



If the cavity is considered as a monopole source 

 the generated pressure, p, in the far field is 



P 

 4Trr 



d'^V(t - -) 

 c 



dt^ 



(1) 



where 

 V = 

 r = 

 c = 

 t = 



cavity volume 



distance between cavity and hydrophone 



velocity of sound 



time 



Applying this and classical theory of cavity 

 collapse it can be shown [ross (1976) ] that the 

 generated maximum pressure, Pmax' ^^ certain con- 

 ditions is given by 



R AP 



where 



Rjfiajj = the maximum radius of a spherical cavity 



iP = Pfl - Pv 



Pq = surrounding pressure 



p.^, = vapour pressure 

 According to this 



p r/{. AP 

 max 



(2) 



would be an appropriate coefficient to study for 

 different cavities in our case. The parameters are: 

 + 

 p = maximum pressure increase at collapse 



i = maximum chord-wise extension of the sheet 



cavity (for bubbles Vax ~ diameter) 



The distance r is measured individually for 

 every collapse. 



1 9 



AP = - p U'^ a - 9,500 Pa 



Inherent in the coefficient above is an assumption 

 about the collapse dynamics and, as the dynamics 

 are dependent on cavity type, there is no universal 

 value for the coefficient (2) . For our purpose 

 the coefficient may be seen as a measure of the 

 pressure generation efficiency of different types 

 of cavities. For spherical cavities this coefficient 

 was used by Harrison (1952) and Blake et al. (1977). 



Another treatment which leads to a dimensionless 

 pressure coefficient is to suppose that a constant 

 part of the potential energy available for collapse 

 is radiated as noise [Levkovskii (1968)]. The 

 dimensionless parameter derived from this assumption 

 is 



'c max p 



Tc' 



5 - 



4 - 



3.0 



20 



1.0 







/^ very fast pressure increase 

 ■ mean value of 8 samples 



00 



05 



10 Reduced freq. 15 



p = const 



max 



5 10 15 fosclHz)20 



FIGURE 26. Normalized collapse time. 



