462 



f(£) = 



v3l3 



e exp 



v2l 



(2) 



20 10 60 



Am Content (ppm) 



FIGURE 16. Effect of air content on MDDR 

 (NACA 16021, H2102-2, C = 40 mm, a = 4 deg. 

 V = 41.7 m/s, a = 0.443) . 



bination [e.g. Hammitt et al . (1969)], have also 

 been proposed by several researchers. 



The present test results are also compared with 

 those material properties, i.e., hardness, engi- 

 neering strain energy, and ultimate resilience. 

 Hardness seems to give the best representation as 

 seen in Figure 18. This will be discussed in Section 

 5 dealing with modeling the erosion mechanism. 



5. THEORETICAL CONSIDERATIONS 



Review of Erosion Scaling Theory 



Thiruvengadam has made several theoretical consid- 

 erations on scaling of erosion. In 1971, he 

 introduced a scaling formula [Thiruvengadam (1971) ] . 

 He assumed a statistical distribution of air nuclei 

 and derived the efficiency of erosion, 9, as. 



where f is the distribution function of energy 

 density, e, reached on the material surface. Then 

 a scaling law for cavitation erosion was derived 

 using an empirical formula for the erosion resis- 

 tance of materials. A comparison with only the 

 pealc erosion intensity taken from Thiruvengadam' s 

 tests showed good agreement [Kato (1975)]. 



Consideration on Effect of Cavitation Number 



As mentioned before, MDDR has a peak value of a 

 certain cavitation number. This is due to a 

 combination of the following two reasons . There is 

 an increase in the collapsing cavity volume as the 

 cavitation number decreases which causes increased 

 erosion. On the other hand, the decrease of cavita- 

 tion number causes an increase in the cavity length 

 so the eroded area shifts towards the trailing edge 

 of a foil. Also when the cavity length exceeds the 

 chord length, the cavity does not collapse on the 

 foil surface, causing no cavitation erosion. 

 Usually the cavity length fluctuates and the erosion 

 intensity will change continuously with the cavita- 

 tion number. Although there seems to be a consider- 

 able decrease in the collapsing pressure of cavity 

 decreasing cavitation number, the control factor 

 of erosion intensity is the change of cavity length 

 as mentioned above. 



The decrease of erosion intensity at the right 

 hand side of the MDDR peak in Figure 19 is caused 

 by the lack of cavity and by too long a cavity on 

 left hand side. By increasing the cavitation number, 

 the cavity becomes intermittent, and if the cavity 

 is stabilized by roughing the leading edge, the 

 MDDR peak shifts to a higher cavitation number 

 where the peak value is increased. This was verified 

 in the authors' experiments as shown in Figure 20. 



°,A„>'5 -2.67 



(1) 



where 6, a, Aa, and W are nondimensional nuclei 

 size, cavitation number, degree of cavitation, and 

 Weber number respectively. Equation (1) is very 

 attractive because it has no empirical constants. 

 However the calculated values are quite different 

 from the experimental values. While 8 should be 

 the order of 10 by the calculation, the G obtained 

 from model tests typically has an order of 10" . 

 This discrepancy comes from the assumption that the 

 total energy of the cavity bubbles generates the 

 erosion. The theory shows that when the cavitation 

 number is reduced, the efficiency, 9, increases 

 from the point of cavitation inception to a maximum 

 and then decreases to zero when cavitation number 

 reaches zero. This tendency agrees qualitatively 

 with experiments. It is expected, since the actual 

 cavity becomes a supercavity at a certain cavitation 

 number causing the erosion intensity to decrease 

 greatly and in a practical sense reach zero. 



One of the authors has proposed a model of erosion 

 mechanism in which the discharged energy of the 

 collapsing bubble is assumed to be distributed 

 statistically as: 



0,06 



100 300 



Hv (kg/mm ) 

 (b) Copper and Brass 



0.3 

 0.1 



0.01 

 1000 15 



Hv (kg/mm ) 

 (a) Steel 



100 300 

 Hv (kg/mm^) 



(c) Aluminum Alloy 



FIGURE 17. Vickers hardness vs. erosion 

 resistance (Heymann (1959)]. 



