Tip vortices that are generated by marine lifting surfaces such as propeller blades, ship rudders, hydrofoil wings, and anti-roll fins can lead to cavitation. Prediction of the onset of this cavitation depends on model tests at Reynolds numbers much lower than those for the corresponding full-scale flows. The effect of Reynolds number variations on the scaling of tip vortex cavitation inception is investigated using a theoretical flow similarity approach. The ratio of the circulations in the full-scale and model-scale trailing vortices is obtained by assuming that the spanwise section lift coefficient distributions are the same between model and full-scale. The vortex pressure distributions and core sizes are derived using the Rankine vortex model and McCormick's assumption about the dependence of the vortex core size 9n the boundary layer thickness at the tip region. Using a logarithmic law to describe the velocity profile in the boundary layer over a large range of Reynolds number, the boundary layer thickness becomes dependent on the Reynolds number to a varying power. In deriving the cavitation inception scaling in the traditional scaling format of σ_(if) / σ_(im)= (Re_f/Re_m)~n, the values of n are not constant and depend on the values of Ref and Rem themselves. This contrasts traditional scaling for which n is treated as a fixed value that is independent of Reynolds numbers. At very high Reynolds numbers, the present theory predicts the value of n to approach zero, consistent with the trend of these flows to become inviscid. Comparison of the present theory with available experimental data shows promising results, especially with recent results from high Reynolds number tests. Numerical examples are given of the values of n for different model to full-scale sizes and Reynolds numbers.
展开▼
