A model for tip vortex roll-up in the near field region of three-dimensional foils and the prediction of cavitation onset

A research program known as "Action Concertee Cavitation" initiated in Fran ce in 1991 was aimed at investigating Tip Vortex Cavitation (TVC) in variou s experimental facilities operating over a large range of Reynolds numbers. An original method to analyze the numerous data collected during the progr am was developed. From this method, a correlation model of the roll-up proc ess close to the tip (near held region) of elliptical loading foils is prop osed. It is based on the experimental evidence of a linear relationship, du ring the roll-up process, between a and (Gamma t)(0.5), where a is the loca l vortex core radius, Gamma the local vortex intensity and t the convection time. The care radius and the vortex intensity are modeled with power laws in such a way the linear relationship is satisfied. With the hypothesis of an axisymmetric vortex, the minimum of the pressure coefficient on the vor tex path is computed. It agrees well with the experimental critical cavitat ion number obtained for lift coefficients ranging from 0.2 to 0.6 and for R eynolds numbers ranging from 4 x 10(5) to 6 x 10(6). Moreover, the model sh ows that the actual vortex diffusion appears to be faster than that predict ed by laminar flow hypothesis. This can be explained by an apparent viscosi ty of about two orders of magnitude larger than the molecular viscosity dur ing the roll-up process. Finally, as the model is based on a limited number of parameters to describe a complex phenomenon, it indicates also some imp ortant trends which should be examined by those seeking to mitigate the occ urrence of cavitation on lifting surfaces as designers of pumps, propellers and other fluid machinery. (C) Elsevier, Paris.