375 



V. = 5 m/s 



a = 2.5 



o = 3 + 6 Sin «.'t 



= 8 ra/s 

 = 1.18 

 = 3 Sin Mt 



1.0 1.5 



REDUCED FREQUENCY, K 



2.0 



FIGURE H. Measured cavitation-inception angles by 

 Miyata (1972). 



^Q - 3.25° with a pitch amplitude of a^ = 

 and cavitation nximber a = 1.12 to 1.15. The 



to 1310 and 1501 to 1506 are given in Table 3 and 

 plotted in Figure 10. The foil was oscillated 

 around a 

 0.95 



measured cavitation inception angle at the stationary 

 condition is aj_^ = 3.5°. The measured maximum 

 steady inception angles are aj_^ = 3.70 to 3.93°. 

 Once again, a significant delay in cavitation 

 inception at nonzero reduced frequencies is mea- 

 sured. The theoretical calculations based on Eq. (15) 

 are given in Table 6 and plotted in Figure 10. The 

 agreement is reasonably good. 



In order to provide an insight into the effect 

 of a J on cavitation delay, a theoretical example 

 is computed in Table 7 and plotted in Figure 8. 

 The foil is assumed to pitch around a^ = 3.25° with 

 an amplitude of aj = 6.0°. The stationary cavita- 

 tion inception angle is assumed to be a^^g = 4.3°. 

 It is seen in Figure 8 that a significant delay in 

 cavitation inception can be expected if the pitch 

 amplitude is increased. This trend is also observed 

 experimentally by comparing Figures 9 and 10. 



A two-dimensional foil undergoing pitch oscil- 

 lations around an axis located at mid-chord was 

 tested by Miyata et al. (1972). Two of the typical 

 test results are produced in Figure 11 for com- 

 parison. For the data shown the foil was oscillated 

 with a pitch amplitude of aj = 6.0°. As expected 

 (See Figure 8) a significant increase in the angle 

 of cavitation inception is noticed for < K < 1.2. 

 For the second set of data shown in Figure 11, the 

 foil was oscillated with a pitch amplitude of 

 ai = 3.0°. A similarity between Figure 8 and 

 Figure 11 is noticed. Although the foil shapes and 

 the locations of pitch axes are different between 

 Miyata' s experiments and ours, the effect of 

 unsteadiness on cavitation inception is similar for 

 two model tests. A similar trend is also noticed 

 in Ftadhi's experiments (1975). 



In the review papers by Acosta and Parkin (19 75) 

 and Huang and Peterson (1976) , one is clearly 

 reminded that even under steady conditions the 

 cavitation inception process is extremely complex. 



The theoretical prediction of cavitation inception 

 angle under steady conditions is still very difficult. 

 However, if the steady-state inception angle ais is 

 known from model tests, the effect of unsteadiness 

 on cavitation inception may be estimated reasonably 

 well by Eq. (15) . Further investigations are 

 needed to explore discrepancies between theory and 

 experiment and the applicability of Eq. (15) to 

 different foil shapes and for pitch axis different 

 from the ones examined here. 



5. LEADING EDGE SHEET CAVITY INSTABILITY 



Wu (1972) has provided a very useful review of the 

 physics of cavity and wake flows which may help to 

 explain the observations of the present experiment. 

 The essence of his description, applicable to the 

 partial cavity condition, is that the free shear 

 layer enveloping the cavity is unstable. The cavity 

 occupies a portion of what can be referred to as 

 the wake bubble or near wake, physically delineated 

 in steady flow by a dividing streamline that is 

 characterized by a constant or nearly constant 

 pressure. For the condition where the cavity within 

 the near wake is unsteady, the region is, strictly 

 speaking, not defined by a streamline but by a 

 material line which is difficult to observe experi- 

 mentally. Because of this difficulty, we will 

 initially assume that a quasisteady approximation 

 is valid. When the cavity is just beyond the 

 inception condition, its surface should be smooth 

 as would be expected with a laminar shear layer. 

 As the cavity grows in length the free shear layer 

 would tend to become unstable. Transition from a 

 laminar to turbulent shear layer initially takes 

 place at the downstream end of the near-wake. A 

 further extension of the cavity length causes 

 transition to gradually move upstream along the 

 free shear layer and the far-wake becomes irregular. 

 This is comparable to the bursting of a short laminar 

 separation bubble in a single phase fluid. With a 

 continued increase in cavity length, transition 

 can begin at the leading edge of the cavity. 



In applying here the general features of the 

 near-wake outlined by Wu (1972) no assumption is 

 made as to whether the cavity occupies all of the 

 near-wake region since the detailed physics of the 

 region downstream of the cavity trailing edge are 

 uncertain. One possibility is that the roll-up of 

 the shear layer into vortices is completed at the 

 near-wake closure where the vortices break away. 

 If this occurs, it is reasonable to expect a 

 periodicity in this shedding process. 



The variation in foil pressure at the Pj location 

 (see Figure 1) can give a useful insight into what 

 is happening both downstream of the cavity and 

 within the cavity when the foil is oscillaing with 

 a pitch amplitude (aj) of 1.55°. Figure 12 shows 

 an oscillograph record of the pressure variation 

 Pi for a cavity that reaches its maximum length 

 downstream of the gage location. (A) is the 

 region where the foil surface is fully wetted and 

 the pressure appears to follow the variation 

 expected as the angle of attack, a, is varied. At 

 point (B) , the cavity begins to cover the gage and 

 in this example the pressure drops from the fully 

 wetted pressure of 31.7 kPa to the cavity pressure 

 in 0.003 seconds. The cavity pressure remains 

 constant, except for several pressure spikes (C) of 



