367 



obtained as the difference between the total pressure 

 coefficient minus the steady part. The steady 

 solution is based on an exact nonlinear theory. 

 The theoretical values obtained from Giesing's 

 program are plotted on Figures 4 and 5 along with 

 the experimental data. 



The phase angles obtained from experiments and 

 calculations will be discussed first. As seen in 

 Figures 4a to 4c, the agreement between experimental 

 measurements and theoretical calculations of pressure 

 and phase angles is quite good for all three pressure 

 locations. The agreement is good between experi- 

 mental measurements and theoretical predictions of 

 magnitudes of dynamic pressure for the cases of 

 X/C = 0.25 and 0.10, as seen in Figures 5a to 5c. 

 At low values of K the measured pressure coefficients 

 are seen to be slightly lower than the values 

 calculated for the case of X/C = 0.033. The exact 

 cause of this small discrepancy between measurements 

 and theoretical calculations has not been determined. 



The cause of small discrepancies between the 

 theory and experiments requires further investigation. 

 Nevertheless, the overall good agreement observed 

 between our experimental measurements and Giesing's 

 method is extremely encouraging. It is noted that 

 Giesing's method is based on unsteady potential 

 flow theory. The combined theoretical and experi- 

 mental results by McCroskey (1975, 1977) indicate 

 that unsteady viscous effects on oscillating airfoils 

 are much less important than the unsteady potential 

 flow effects, if the boundary layer does not interact 

 significantly with the main flow. The present study 

 appears to agree with his conclusion for the case 

 of a fully wetted foil. On the basis of this 

 relatively good agreement between Giesing's method 

 and the experimental data, this method will be used 

 in the next section to predict cavitation inception 

 as a function of the reduced frequency, K. 



4. UNSTEADY EFFECTS ON CAVITATION INCEPTION 



The major objective of this section is to examine 

 what effect unsteadiness has on cavitation inception. 

 The question of the occurrence of cavitation is of 

 particular importance when comparing model test 

 results for marine propellers or hydrofoils with 

 the full-scale prototype data. We would like to 

 know whether a noncavitating model is also free 

 from cavitation in the prototype. When calculating 

 the flow about propeller blades or hydrofoils, it 

 is important to know whether the cavitation bubbles 

 form on the blades, and if so, under what circum- 

 stances. The cavitation number a, defined by 



(8) 



^2 P V ^ 



has proved useful as a coefficient for describing 

 the cavitation process. Here, p and P denote the 

 density and vapor pressure of the fluid and P and 



CO 



V denote the freestream static pressure and the 



Co ^ 



freestream velocity, respectively. 



In addition to the incoming flow properties such 

 as freestream turbulence and nuclei content, the 

 surface finish and boundary layer characteristics 

 on the body surface are also of paramount importance 

 to the cavitation inception process Acosta and 

 Parkin (1975). To limit the scope of the test 



program, air content of the water was not varied. 

 The air content was measured with 70^ saturation 

 in reference to atmospheric pressure at a water 

 temperature of 22.2° C and tunnel pressure of 103.6 

 kPa. 



The foil was pitched sinusoidally around an axis 

 at the quarter chord location aft of the foil leading 

 edge. The cavitation tests were carried out by 

 lowering the ambient pressure from the previous 

 fully wetted tests. The determination of cavitation 

 inception was based on visual observations. For 

 every test condition, 30 pictures were taken to 

 record the cavitation process on the foil. A 

 picture was taken every ten oscillations plus 1/25 

 of the time period of the foil oscillation. Thus, 

 a series of high quality short duration photos 

 were taken that together simulate one and 1/5 cycles 

 of the foil oscillation. A pulse signal was 

 simultaneously recorded on magnetic tape when a 

 picture was taken. In this way, each cavity pattern 

 observed on the foil could be related directly to 

 the instantaneous angle of attack of the foil. 



Analytical Prediction 



A simplified mathematical model will be formulated 

 first to explore the possible effect of unsteadiness 

 on cavitation inception. A significant delay in 

 dynamic stall was observed experimentally and 

 discussed in a recent review paper by McCroskey 

 (1975) , who showed that the pressure gradient dCp/dx 

 around the leading edge was of paramount importance 

 in dynamic stall. The studies by Carta (1971) 

 indicate that the mechanism involved in the delay 

 of dynamic stall is the large reduction of unfavor- 

 able pressure gradient dC /dx during any unsteady 

 motion . ^ 



The mechanism involved in cavitation inception 

 is different from the mechanism of aerodynamic 

 stall. It is generally assumed that cavitation 

 occurs on a body when the local pressure, including 

 the unsteady pressure fluctuations within the 

 boundary layer, falls to or below the vapor pressure 

 of the surroimding fluid, Huang and Peterson (1976). 

 Aside from the effect of nuclei content of the 

 water, it is the value of the local pressure 

 coefficient that governs the occurrence of cavita- 

 tion. Prior to the occurrence of cavitation on 

 an oscillating foil, the foil is in a fully wetted 

 condition. Thus, the knowledge of pressure distribu- 

 tion on the foil in the fully wetted condition 

 can be expected to provide useful information for 

 unsteady cavitation inception prediction. 



As previously mentioned, the combined theoretical 

 and experimental results reviewed and summarized 

 by McCroskey (1977) indicate that unsteady viscous 

 effects on oscillating airfoils are much less 

 important than unsteady potential flow effects, if 

 the boundary layer does not interact significantly 

 with the main flow. In the present study, as 

 discussed in the previous section, the three 

 pressure coefficients measured at three points 

 around the leading edge are predicted reasonably 

 well by Giesing's method both in amplitude and 

 phase within the range of reduced frequencies 

 examined. This unsteady potential flow theory will 

 now be used to investigate cavitation inception. 



In the tests, the foil was oscillated about a 

 mean angle of 3.25°. The mean values of dynamic 

 foil loadings determined from measurements are 



