344 



wise vorticity was divided into tangential and axial 

 components whereby the former, (i^g ' "'''s ' ) sin62/ 

 causes a radial gradient of axial velocity and the 

 latter leads to an equation for a stream function 

 describing the radial and tangential velocities in 

 the exit plane , r , 6 . 



The form of the secondary stream function equation 

 is 



TABLE 1. Deviation Angles for Basic Flow No. 1 



8r r 3r ^2 ^^2 



- (u 



S2 



-co ')sec6o 



2 dr 



F(r). 



(rtanB2) 



(5) 



where v^ is the secondary axial velocity and is 

 obtained from the solution of the tangential com- 

 ponent of streamwise vorticity. The solution to 

 Eq. (5) was found by applying standard differential 

 techniques. The solution and the necessary boundary 

 conditions will not be discussed in this brief paper. 



The deviation angle due to the secondairy flow 

 can be calculated using 



A6 



N cos^ 62 

 2tiV 



2TT/N 



3m ^ 

 T— dr 

 dr 



(6) 







where N is the nuntier of blades and V is obtained 

 from the solution of Eq. (5). The axial velocity, 

 Vx, and outlet angle, Bz- are determined in the 

 calculation of the primary flow field. 



The results of the secondary flow calculations 

 for various basic flows indicate that the effects 

 are significant only near the inner wall where the 

 incoming vorticity is the largest. The deviation 

 angles calculated for Basic Flow No. 1 are shown 

 in Table 1. 



3. CAVITATION EXPERIMENTS 



The cavitation experiments were conducted in the 

 48-inch diameter water tunnel located in the Garfield 

 Thomas Water Tunnel Building of the Applied Research 

 Laboratory at The Pennsylvania State University. In 



Normalized Distance 

 from Surface 



R/R 

 R 



0.00 



0.04 



0.14 



0.24 



0.34 



0.44 



0.54 



0.64 



Deviation Angles 



A6 

 s 





 -5.4 



o 

 -2.9 





 -1.0 



<0.2 



all cases, desinent cavitation was employed as the 

 experimental measure of the critical cavitation 

 number. The cavitation in the vortex system occurred 

 on the rotor cap. Also, the occurrence of the 

 cavitation was very sporadic. 



The air content of 3.1 ppm was chosen for all of 

 the cavitation experiments because gas effects are 

 reduced and the relative saturation level was always 

 much less than unity. Desinent cavitation number 

 data were obtained for different incoming velocity 

 profiles to the rotor. The incoming velocity profile 

 was varied by changes in the configuration of the 

 upstream surface in addition to varying the rotor 

 flow coefficient. Results were obtained with/without 

 upstream struts, with/without a screen on the upstream 

 surface, and on/off design rotor flow coefficients. 

 In all, there were sixteen different flow configura- 

 tions or Basic Flow Nos . tested. 



Figures 9-11 display the effects on the desinent 

 cavitation number over a range of velocities due to 

 variations in the inflow velocity distribution. In 

 general, the cavitation number increased for in- 

 creasing free stream velocity for all flow config- 

 urations shown. As shown in Figure 9, the addition 

 of upstream struts which consisted of four struts 

 placed at the 0°, 90°, 180°, 270° points on the 

 upstream surface caused the cavitation number to 



FIGURE 9. 

 flow nos. 



Correlation with cavitation data for basic 

 1 and 4. 



25 30 



VELOCITY ~ Hfsec 



