492 



APPENDIX 



HIGH OSCILLATION FREQUENCIES MAINLY GENERATING 

 SHARP PRESSURE PULSES 



LOW OSCILLATION FREQUENCIES MAINLY GENERATING 

 RATHER SLOW PRESSURE PULSES 



The following observations were typical for fosc ~ 



1-3 Hz and ao = 3°, a = 4° (Figure 9) but most of 



the results are also valid for other angle conditions : 



1. The maximum pressure increase is generated 

 before the sheet cavity has disappeared 

 completely. At the moment of maximum pressure 

 increase the collapse Slowed significantly 

 and the rest of the collapse was very slow. 

 Due to hysteresis the total collapse time 



was sometimes longer than the growth time , 

 Tg. Typical for the collapse from maximum 

 extent to maximum pressure was T^/(T^ + Tg) 

 > 0.4. The sheet cavities were attached to 

 the leading edge during the whole collapse 

 and only small parts were separated from the 

 downstream cavity edge . 



2. Already during growth a large part of the 

 cavity is disturbed and consists of one part 

 with a smooth surface and one with thick 

 irregular cavity formations. From this total 

 connected cavity, small parts were separated 

 both during growth and collapse. Only a few 

 of these parts collapsed violently, which is 

 also confirmed by the pressure signals which 

 do not contain many sharp pulses during 

 growth and first part of collapse. 



At very low fog^ (1-2 Hz) these contin- 

 uously occurring collapses of small cavities 

 were, however, the only source of high- 

 frequency noise. At these conditions also 

 most sharp pulses were obtained in the 

 hydrophone (H2) near the trailing edge. 



3. At fQ3(, = 3 and 4 Hz the pressure increase 

 often ends with a sharp pulse. The pulse 

 was, however, not caused by an orderly and 

 violent collapse of the main cavity, but 

 instead by small cavities that separated 

 from the main cavity and then collapsed 

 separately. It was also observed that these 

 rather violent collapses of small cavities 

 mainly occurred during the time when the 

 pressure was high owing to main cavity col- 

 lapse. 



On a more expanded time scale it can also 

 be seen that the sharp pulse is superimposed 

 on a slower pressure increase. If not very 

 clear, this tendency is still detectable in 

 the 7 Hz-condition in Figure 14. This figure 

 shows the pulse (oscillation period 5) in 

 the 7 Hz-condition shown in Figure 10, but 

 with the time axis expanded 40 times . 



4. The cavitation sketches in Figures 9-13 show 

 that for fos^ < 4 Hz the cavitation extent 

 was approximately independent of fosc t)"t 

 that at higher fosc ^^^ cavity did not develop 

 to the full size. One reason for this may 



be that the time variation of the dynamic 

 angle of attack is altered with f,. 



5. Characteristic of low f^- 

 that collapsing cavities show little tendency 

 to rebound. Rebound is only obtained in 

 small bubbles. 



osc ■ 

 is also the fact 



Below some observations are reported regarding the 

 conditions uq = 3°, d = 4° and f^g^, = 10 and 14 

 Hz (Figure 10) . Many of the results are also valid 

 for other similar conditions. Typical observations 

 are : 



1. The sharp pulses are often much higher than 

 slow pressure variations. 



2 . The duration of the final part of the sharp 

 pulses seems (as long as can be determined 



in the recording) independent of fosc (Figure 

 14) . For the earlier parts of the cavitation 

 period the dependency on fos^ ^^ more complex 

 due to different cavity sizes etc. 



3. For this condition (oq = 3°, a = 4°) the 

 complete change of cavity dynamics and 

 pressure generation occurred between fog^ ~ 

 7 and 10 Hz (Figure 14). At 7 Hz the cavity 

 mainly collapsed towards the leading edge. 

 At 10 Hz a large part consisting of thick 

 formations separated and performed a violent 

 collapse at the middle of the hydrofoil (B 

 in Figure 14) . This collapse occurred about 



1.4 milliseconds later than the collapse of 

 those two parts (A) of the sheet that were 

 attached to the leading edge during the 

 whole collapse. Also these two parts col- 

 lapsed rather violently, but a small pulse 

 was generated. The thick separated cavity 



(B) consisted of several parts that did not 

 collapse exactly simultaneously and, thus, 

 a series of collapse and rebound pulses was 

 generated. A significant rebound was only 

 obtained from the separated cavity. The 

 group of rebounded cavities collapsed rather 

 slowly, resulting in a small pulse about 



3.5 milliseconds after the collapse of the 

 separated cavity (B ' ) . In some oscillation 

 periods the separated cavities and those 

 attached to the leading edge collapsed almost 

 simultaneously and it also happened that 

 high pulses were generated at the collapse 



of rebounded cavities. 



4. The cavitation behaviour at fosc ~ "'■^ ^^ "'"^ 

 approximately similar to that at 10 Hz 

 (Figures 10 and 14) . The thick formation 



(C) separated and collapsed at a later stage. 

 The first pulse (Figure 14) was generated 



by the outer cavity (A) attached to the 

 leading edge. About 1.4 milliseconds later 

 the other cavity (B) attached to the leading 

 edge collapsed. This cavity was complex 

 and generated a series of pulses. First 

 about 3.5 milliseconds after the first pulse 

 the thick formation (C) collapsed, generating 

 a sharp pulse. No violent collapses were 

 experienced by rebounded cavities in this 

 case. The overall impression from these 

 two conditions with fosc ~ 1° ^"'^ ^^ ^^ ^^ 

 that normally the separated thick cavities 

 generated the highest pulses , but that in 

 some cases pulses of almost equal height 

 were generated by cavities attached to the 

 leading edge. 

 Another behavior of the signal from the cavitating 

 hydrofoil is a low frequency variation (about 23 Hz) 

 that seems rather independent of fosc' Sequences 



