373 



TABLE 4 - THEORETICAL CALCULATION OF A« AND a^^ FOR TEST SERIES 

 1205 TO 1208 AT x/c = 0.018 



NOTE: 



a = 4.30 DEC. 

 Is 



a =• 3.25 DEC. 



o 



Oi = 2.80 DEC. 



to the inception delay is the oscillation amplitude 

 a^. It is noted that the effect of oscillation 

 amplitude on inception angle is strongly coupled 

 with the phase angle. Thus, there will be no effect 

 of aj on inception if there is no phase shift. This 

 is a consequence of the small oscillation amplitude 

 assumption. As the reduced frequency K approaches 

 zero, C"*"l and <t)^0 , and the steady-state inception 

 angle (Aa-K)) is recovered. 



Experimental Results 



The range of Reynolds numbers covered in the cavita- 

 tion tests was 2.4 to 4.1 x 10^. Because it is 

 shown in Acosta and Parkin (1975) and Huang and 

 Peterson (1976) that the existence of laminar 

 separation may trigger premature cavitation in 

 model tests, the boundary layer characteristics on 

 the foil under stationary conditions were calculated. 

 Within the Reynolds number range of the test program, 

 the occurrence of laminar separation around the 

 leading edge was not predicted. Flow visualization 

 with dye injection supported this conclusion. The 

 unsteady effect of foil oscillations on the boundary 

 layer characteristics was not included in the 

 calculation. 



In order to simulate prototype viscous effects 

 as closely as possible, the model was tested at 

 high tunnel speeds (11.5 to 16.4 m/s) . For a 

 given body shape the laminar boundary layer thick- 

 ness based on chord length decreases approximately 

 as (Rn)~-2. The effect of surface roughness on flow 

 characteristics becomes more important at higher 

 Reynolds number. This roughness effect was found 

 in the present model tests with cavitation appearing 

 prematurely in a few "weak" spots even though the 

 surface was highly polished. This caused some 

 difficulty in determining accurate values of 



cavitation inception angle. The relative importance 

 of this uncertainty was minimized by applying the 

 same cavitation inception criteria to both the 

 steady and unsteady test results. 



Six series of oscillating foil tests were carried 

 out. The test conditions and the test results are 

 given in Table 3. Only 30 pictures were taken to 

 cover one and 1/5 cycles of oscillating motion, 

 and thus the angle at which inception occurred can 

 only be related to two successive pictures. There- 

 fore, in some cases, the inception angle is given 

 in terms of a small range of angles instead of a 

 single value. 



The test results from runs 1205 to 1208 are 

 shown in Figure 8. In these cases, the foil was 

 oscillated around a mean angle Uq = 3.25° with a 



4.5 



RANGE OF FOIL ANGLES IN 

 TWO SUCCESSIVE PICTURES 



3.M I 



A RUNS 1401 TO 1406, (J = 1.13 

 O RUNS 1407 TO 1410, ,1= 1.14 



■5 1.0 1.5 2.0 



REDUCED FREQUENCY, K 



FIGURE 9. Measured cavitation-inception angles for 

 runs 1401 to 1410. 



TABLE 5 - THEORETICAL CALCULATION OF to AND a 

 1401 TO 1410 AT x/c = 0.018 



FOR TEST SERIES 



NOTE: 



IS 



3.5 DEC. 



a = 3.25 DEC. 







0!i = 1.55 DEC. 



