Gas Nuclei Trajectories and Cavitation Inception 



-1.2 -1.0 -0,8 -0.6 -0.4 -lA -0.2 0.2 ( 



LONGITUDINAL POSITION/HALF ULTIMATE BODY WIDTH - x 



Fig. 3 - The influence of the starting point in the y direction 

 on the gas nuclei trajectories (h = 0.6 inch; U = 50 fps) 



become statically unstable. Since the radius of bubbles being pushed away from 

 its streamline are of the order of several hundredth of h in the present prob- 

 lem, it is therefore decided to use y^ = 0.01 for all the calculations. 



Figures 4 and 5 show the influence of initial bubble size on its trajectory 

 and thus its stability at u = 50 fps and cr^ = 0.4 and 0.58. Figures 4 and 5 illus- 

 trate that the larger bubbles may indeed remain stable while smaller ones be- 

 come unstable. In Fig. 4, two bubbles of initial radius Rg = 0.04 and 0.24 were 

 traced along the dividing streamline. It is interesting to note that these bubbles 

 will temporarily stand still at a point where the drag force and the pressure 

 gradient acting on the bubble are in equilibrium. This occurs at x = -0.478 for 

 Rq = 0.04 and x = -0.833 for Rg = 0.24. Afterward, the bubbles will be moved 

 away from the dividing streamline by the perturbations in the vertical direction. 

 Figure 5 shows that certain bubbles collide with the body at some distance from 

 the nose. It is assumed that after collision the bubble surface will remain tan- 

 gent to the surface of the body as it moves past the body. Thus, if the collision 

 occurs before the location of minimum pressure of the body, the bubble will 

 definitely encounter the minimum pressure of the body in its trajectory; on the 

 other hand, if the collision occurs after the location of minimum pressure of the 

 body, the bubble will not encounter the minimum pressure in the flow field. 



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