336 



2 4 6 8 10 12 14 16 18 20 

 Reynolds Number x 10^ 



FIGURE 11. Cavitation inception data for a sharp- 

 edged disk. 



which are dominate at low velocities as will be 

 discussed later. At low Reynolds number the data 

 appear to be satisfied by the empirical relationship 

 discussed by Arndt (1976) : 



0.44 + 0.0036 (Ud/v)' 



(7) 



experiments with disks when the flow was super- 

 saturated. The magnitude of the effect also depends 

 on the number of nuclei in the flow. Gas content 

 effects were noted only in their water tunnel 

 experiments (where there is a healthy supply of 

 nuclei) . No gas content effects on inception were 

 noted in the tow tank (where the flow is highly 

 supersaturated but there is a dearth of nuclei) . 

 Thus the picture becomes more cloudy as the influence 

 of dissolved, noncondensable gas is taken into 

 consideration . 



5. SOME REMARKS ON CAVITATION NOISE 



A complete discussion on cavitation noise would be 

 beyond the scope of this paper. Recognizing the 

 unique features of cavitation inception in 

 turbulent shear flows , it appears appropriate to 

 review what is known about cavitation noise under 

 the same circumstances. 



The general features of cavitation noise were 

 reviewed by Fitzpatrick and Strasberg (1956), Baiter 

 (1974) , and Ross (1976) . The spectrum of cavita- 

 tion noise can in its simplest form be defined as 

 the linear superposition of N cavitation events per 

 unit time. Thus we can write 



It was found that the tow tank data agree with this 

 relationship at relatively high Reynolds numbers. 

 Equation (7) was developed from a model which 

 assumes laminar boundary layer flow on the face of 

 the disk. It would be expected that this condition 

 would be satisfied at higher Reynolds numbers in 

 a tow tank tihan in a highly turbulent water tunnel. 

 At high Reynolds number (and also high velocity 

 where gas content effects are negligible) , there 

 is a continuous upward trend in the data with 

 increasing Reynolds number. This underscores the 

 need for further work as suggested in the intro- 

 duction to this paper. 



A systematic investigation of gas content effects 

 in free shear flow was recently reported by Baker 

 et al. (1976) . Cavitation inception in confined 

 jets, generated either by an orifice plate or a 

 nozzle, was determined as a function of total gas 

 content in the liquid. The results are shown in 

 Figure 12. When the liquid was undersaturated at 

 test section pressure, the critical cavitation 

 index was independent of gas content and roughly 

 equal to that observed by Rouse (1953) for an 

 unconfined jet. When the flow is supersaturated, 

 the cavitation index is found to vary linearly with 

 gas content as predicted by the equilibrium theory, 

 Eq. (6) . This effect occurs even though the 

 Lagrangian time scale is much shorter than typical 

 times for bubble growth by gaseous diffusion. For 

 example, in the cited cavitation data, a typical 

 residence time for a nucleus within a large eddy 

 is roughly 1/15 of a second. At a gas content of 

 7ppm and a jet velocity of approximately 10 m/s , 

 inception occurs at a mean pressure equivalent to 

 a relative saturation level of 1.25. Epstein and 

 Plesset (1950) show that for growth by gaseous _3 

 diffusion alone, 567 seconds is required for a 10 

 cm nucleus to increase its size by a factor of 10. 

 One additional point should be kept in mind here. 

 The local pressure within an eddy is much less than 

 the mean pressure and highly supersaturated con- 

 ditions can occur locally. Arndt and Keller (1976) 

 also reported extreme gas content effects in their 



S(f) = N G(f) (8) 



The function G(f) is the spectrum of a single 

 cavitation event. If p is the instantaneous 

 acoustic pressure due to the growth and collapse of 

 a single bubble, then by definition 



G(f)df 



dt 



Fitzpatrick and Strasberg (19 56) have shown that a 

 characteristic bubble spectrum can be written in 

 the form 



G(fTn) 



r2G(f) 



pR - p 

 m o 



1,5 



1.0 



0.5 







05.08 Cm Dia Nozzle iwater 

 •^5 08 Cm Dia Orifice' 



1/2 pU„ 



!■< 



Rouse 



-a/a > 10 



(a) 



2 4 6 8 10 12 

 Total Gas Content, a (ppm) 



14 



_|^_504cmjl5 24cm 



Sharp -Edged Orifice 



(b) 



J„ 



"^% 504 cm ) 15, 24 cm 

 Contoured Nozzle 



FIGURE 12. Cavitation inception in confined jets. 



