345 



25 30 



VELOCITY ~ ft/sec 



45 FIGURE 10. Correlation with cavitation data for 

 basic flow nos. 1, 3, 4, and 5. 



increase. In contrast to this result, the addition 

 of upstream screens causes the cavitation number to 

 decrease as shown in Figure 10. Data in Figure 11 

 show that a decrease in the flow coefficient by 10% 

 causes a dramatic increase in the cavitation number, 

 whereas a 10% increase in the flow coefficient 

 causes the opposite trend which is not shown in the 

 figures. Additional cavitation results are given in 

 Billet (1976). 



determined by the vorticity associated with the 

 vortex but also by the location of the vortex in 

 the primary flow field. 



Considering only the vortex, there are many fac- 

 tors which can influence the minimum pressure coef- 

 ficient. If one models a vortex by a simple 

 rotational core combined with an irrotational outer 

 flow, the Cpmin is found to be 



Cp . = - 2 

 min 



2Tir V„ 

 c 



(7) 



4. CORRELATION OF SECONDARY FLOWS WITH THE CRITICAL 

 CAVITATION NUMBER 



Because of the complicated flow field where the 

 vortex exists, an absolute calculation of Cpj^^^j^ of 

 the cavitating region would be very difficult. The 

 minimum pressure associated with the cavitation 

 occurs within the vortex which is located along the 

 inner wall. This minimiom pressure is not only 



the core. Thus, the factors which influence Cpmin 

 are those which influence the circulation or core 

 size. 



Assuming that secondary flows control the vortex, 

 Eq. (7) can be used to predict changes in critical 

 cavitation number due to changes in the secondary 

 vorticity produced along the inner wall. Therefore, 

 Eq. (7) can be arranged into the form 



VELOCITY ~ ft/sec 



FIGURE 11. Correlation with cavitation data for basic 

 flow nos . 1 and 2 . 



CP„ 



r V 

 l_c " 



CP„ 



r_ V„ 



B 



where T is now the integrated component of stream- 

 wise passage vorticity and r^ is approximated by the 

 characteristic dimension of the resulting passage 

 vorticity. The letters A and B refer to different 

 flow states . 



The passage streamwise vorticity was calculated 

 along several mean streamlines in the blade passage 

 by the method outlined in this paper for four basic 

 flow configurations which are described in the left 

 hand column of Table 2 . For all flow configurations 

 considered, the results show a large amount of 

 streamwise vorticity at the rotor exit plane near 

 the inner wall. An example of the exit streamwise 

 passage vorticity is shown in Figure 8 for Basic 

 Flow No. 1. 



As can be seen in Figure 8, the vorticity near 



