undissolved void fraction (10 to 10 ). The pressure was found to vary 



strongly with both frequency and void fraction when operating in a non- 



-4 

 uniform wake except at very high void fractions (10 ) where the results 



appeared to be independent of frequency. These interesting observations 

 show, again, the importance of the presence of microbubbles on the extent 

 of cavitation, and they raise the question of tunnel interaction through 

 the confining effect of the surrounding walls on a dynamic experiment. 



We turn, now, to the immediate objectives of the present section. We 

 first touch upon the available analytic methods that can be used to esti- 

 mate these interaction effects for the types of cavitation mentioned, 

 and we then discuss some recent experimental work aimed at characterizing 

 unsteady flows through cavitating pumps. 



Analytic Methods for Internal Cavitation 



We refer now, briefly, to Table 5 for the types of cavitation to be 

 considered. We are concerned here, primarily, with unsteady problems. It 

 is clear from previous experience that attached unsteady cavities can be 

 dealt with on the basis of linearized potential flow (Wu 1972) . There 

 are, however, still difficult problems for the proper formulation of 

 unsteady, growing, attached cavities with realistic geometries. The tip 

 vortex flow is also complex; dynamic treatment of these flows appear to 

 be lacking. Pumps and propellers reveal attached cavities, as well as 

 bubbly tip-clearance flows and inflows. The global properties of a 

 volume of such bubble flow can be established with bubble mechanics for 

 unsteady pressure fluctuations. But the concentration of bubbles in such 

 flows must be small, otherwise the full two-phase fluid dynamic equations 

 for the mixture of cavitating bubbles and liquid must be used. These 

 equations are evidently not yet well developed analytically.* 



In the following sections, we sketch a sample problem intended to 

 illustrate some of these dynamic features for a pump. 



*Private communication with Prof. L. van Wijngaarden. 



73 



