468 



5.0 



Injection Rate (d/V • S) 



10.0 

 xlO"' 



FIGURE 25. Effect of air injection on MDDR erosion 

 index [NACA 16021, pure Al (H2102-2) , C = 40 mm, 

 a = 4 deg. , V = 41.9 m/s , a = 0.438]. 



factors such as cavitation number, water velocity, 

 etc. 



(3) Modelling of cavitation erosion has been made 

 assuming a statistical distribution of cavitation 

 bubble. Using the model, a theory of erosion scaling 

 was established which contains two constants given 



by the experiment. The erosion scaling of cavita- 

 tion number, velocity, chord length, and material 

 can be made by the theory. The theory has been 

 shown to give good agreement with the authors ' and 

 Thiruvengadam' s tests . 



(4) Another two-dimensional foil section (NACA 

 16021) was also tested, but in this case the side 

 wall effect was so large that the results were not 

 compared with the theoretical calculations . 



(5) The paint test also was made with the same 

 foil section (NACA0015) . The results of paint 

 test agreed with that of the aluminum erosion test 

 although it gives qualitative data. 



(6) The effect of air content and air injection 

 method was also investigated experimentally. The 

 air injection was found to be very effective in 

 preventing erosion. 



ACKNOWLEDGMENTS 



This research work was financially supported by 

 the Grant in Aid for Developmental Scientific 

 Research (2) , Ministry of Education, Japan (Research 

 No. 185087) and the authors are grateful for the 

 support. 



NOMENCLATURE 



A, 



B 



C 



c 



Cp 



d 



E 



Et 

 e 



F 



f 



"v 



Kl 



K2 



L 



1 



MDD 



MDDR 



MDP 



MDDR 



N 



n 



P 



Q 



R 



s 



SR 



T 

 V 

 a 

 6 



«e 



e 



n 

 A 

 X 

 P 

 



K2 



constants 



span 



constant, chord length 



constant 



pressure coefficient 



depth 



energy 



total energy of bubbles 



energy density 



force 



energy density distribution function 



Vickers hardness 



constants 



constants 



reference length (chord length) 



length 



mean depth of deformation 



mean depth of deformation rate 



mean depth of penetration 



mean depth of penetration rate 



total number of cavity bubbles 



distribution function of bubble number 



pressure 



volumetric flow rate 



bubble radius 



area 



surface roughness 



time 



velocity 



attack angle, air content 



thickness 



cavity thickness at the end 



energy density rate 



probability 



aspect ratio 



cavity length 



density 



cavitation number 



yield stress 



volume 



The authors would like to express their acknowledg- 

 ments to Prof. S. Tamiya and members of the High 

 Speed Dynamics Laboratory, University of Tokyo, for 

 their many valuable discussions and help during 

 the research work. They also wish to thank Mr. T. 

 Komura, Mr. R. Latorre , and Miss N. Kaneda for 

 their sincere help during the preparation of the 

 paper . 



REFERENCES 



Ahmed, 0., and F. G. Hammitt (1969). Determination 

 of particle population spectra from water tiinnel 

 using Coulter counter. Univ. of Michigan, Cav. 

 and Multiphase Flow Lab. Rep. 01357-4-1, 08466-7-1. 



