372 



unsteady effect the inception angle a^Q is generally 



different from a. . Let Aa be 



IS 



Aa = a. - a . 



(14) 



which can be used to measure the magnitude of the 

 unsteady effect. From Eq. (13) , it follows that 



Aa = (a. - a ) ( ^- 1) 

 IS C 



aj sinifi \J1 - ( 



(ai f 0) 



a. a 

 IS - o 



(15) 



ajS 



For the case where the phase angle i) is small at 

 the location of inception, we have 



Aa = (a. 



a ) ( ■=- 

 o 5 



1) 



ai(j) 



ai5 



(16) 



Although a small phase angle, cj), approximation is 

 not required, it is useful to make this approxi- 

 mation for the sake of discussing the implications 

 of Eq. (15) . The first term on the right-hand side 

 represents the effect of the ratio of dynamic to 

 static angular pressure gradients C (K) on unsteady 

 cavitation inception. The second term represents 

 the effect of phase angle, amplitude of oscillation, 

 and the ratio of pressure gradients on cavitation 



1.0 1.5 



REDUCED FREQUENCY, K 



2.0 



FIGURE 8. Measured cavitation- inception angles for 

 test runs 1205 to 1208, ai = 2.8 deg. 



inception. For example, as seen in Figure 4 the 

 phase angles of dynamic pressure response at the 

 leading edge lag behind the foil angle (negative (ji) 

 for values of K less than 1.0 at X/C = 0.033. Due 

 to this phase lag, the occurrence of unsteady cavi- 

 tation inception is further delayed. Contributing 



TABLE 3 - EXPERIMENTAL RESULTS ON UNSTEADY 



CAVITATION-INCEPTION ANGLES, a. 



lu 



