374 



TABLE 6 



THEORETICAL CALCULATION OF ^a AND a 



4.5 



.5 1.0 1.5 2.0 



REDUCED FREQUENCY, K 



FIGURE 10. Measured cavitation-inception angles for 

 runs 1301 to 1310 and 1501 to 1506. 



pitch amplitude of a^ = 2.8° and cavitation number 

 a = 1.35. The measured cavitation inception angle 

 at the stationary condition was a^g = 4.3°. Within 

 the range of reduced frequency 0.3 2 K ^ 0.77, the 

 measured unsteady cavitation inception angles were 

 a^^ = 5.28°. That is, a significant delay of 

 cavitation inception was observed at nonzero 

 reduced frequencies. The unsteady inception angles 

 computed from Eq. (15) will now be examined. A 

 previous discussion indicates that the suction 

 pressure peak with the foil in oscillation is 

 located at essentially the same X/C position as the 

 suction peak corresponding to the steady condition 



o = Oq. As seen in Figure 7, the steady suction 

 peak occurs at a location near X/C = 0.018. The 

 predicted results based on Eq. (15) for the unsteady 

 cavitation inception are given in Table 4 and plotted 

 in Figure 8 along with the experimental data. The 

 phase angle ((), and the ratio of dynamic to static 

 angular pressure gradients, E,, used in the predic- 

 tion were calculated with Geising's computer program. 

 Reasonably good agreement between theoretical calcu- 

 lations and experimental measurements is observed. 



The test results from runs 1401 to 1406 and runs 

 1407 to 1410 are given in Table 3 and plotted in 

 Figure 9. In these cases, the foil was oscillated 

 around a^ = 3.25° with a pitch amplitude of ai = 

 1.55° and cavitation number of a = 1.14. The 

 measured cavitation inception angle at the stationary 

 condition is ais = 3.5°. The measured unsteady 

 inception angles vary from aiu = 3.9 to 4.2° between 

 K = 0.2 to 1.0 and aiu = 3. 6 to 3. 9° at K= 1.65. 

 The theoretical results obtained from Eq. (15) are 

 given in Table 5 and plotted in Figure 9. Once 

 again, a significant delay in cavitation inception 

 is observed experimentally and predicted theoret- 

 ically at nonzero reduced frequencies. The agree- 

 ment is fair. Part of the discrepancy between theory 

 and experiment may be due to the lack of accurate 

 resolution in measuring foil angles, since only 

 30 pictures were taken to simulate 1 and 1/5 cycles 

 of foil oscillation. The phase angle <t> is seen to 

 change the sign from negative to positive values 

 at K above 1.5. Consequently, at high values of 

 reduced frequencies the amount of reduction in 

 cavitation inception delay is reduced. This trend 

 is observed experimentally and predicted theoret- 

 ically. 



The test results from runs 1301 to 1306, 1307 



TABLE 7 - THEORETICAL CALCULATION OF Aft AND ft 

 AT x/c = 0.018 



iu 



