# Development of Attached Cavitation at Very Low Reynolds Numbers from Partial to Super-Cavitation
## 3 Results
### Quantitative Characterization of the Different Regimes and Effects of the Reynolds Number  
The type-2 cavities with periodic shrinking are first observed in a very narrow region of the parameter space for \(1200\leqslant Re\leqslant 1350\) and are then present in a wider range of cavitation numbers for \(Re\in[1400;2100]\): they are found to lie in \(\sigma_{2}\in[0.9;1.7]\). The type-4 supercavities have been observed only for one point at very low pressure at \(Re\simeq 1300\) (\(\sigma_{2}\simeq 0.27\)). If supercavities exist for \(Re=1200\) it would be at \(\sigma_{2}\leqslant 0.3\). However, for higher Reynolds numbers, i.e., for \(Re\geqslant 1400\) the zone where supercavities are observed progressively extends up to a constant value of the cavitation number \(\sigma_{2}\leqslant 0.57\). There thus seems to be a progressive transition in the dynamics of attached sheet cavitation at very low Reynolds number between \(Re\simeq 1200\) and \(Re\simeq 1400\). Quantitative measurements of the temporal and spatial features of the attached cavities are analyzed and discussed in the next paragraph. First, the frequency of the periodic shrinking for all the type-2 cavities that have been identified ( in Figure 6) are plotted as a function of the throat velocity in Figure 9. The two quantities are highly correlated: the frequency seems to be proportional to the throat velocity, following a law \(f=3.83V_{throat}\). A Strouhal number based on the throat velocity and on the throat height as a length scale is \(S_{t}=\frac{f_{throat}}{v_{throat}}\). The type-2 regime is thus characterized by a constant Strouhal number of the order of \(S_{t}\simeq 0.0026\). Such a low value is reminiscent of the \"sheet cavity oscillation\" regime described for a turbulent flow in a similar water experiment by [PERSON] et al. (2014) [10] as opposed to the \"cloud cavitation\" regime that is characterized by a Strouhal number greater by almost one order of magnitude. Moreover, in that study [10] the sheet cavity oscillation was observed to dominate the dynamics for short cavities and to disappear as the cavity length increases. The evolution of the average length of the cavities as a function of the outlet cavitation number is plotted in Figure 10. For all Reynolds numbers, the overall trend is an increase of the length with a decrease of the cavitation number, which is not surprising. However, the shape of the curve exhibits a dependence on the Reynolds number. One can indeed notice that the curve becomes steeper as the Reynolds number increases, from \(Re\simeq 800\) to \(Re\simeq 1300\). At very low Reynolds number the cavity grows relatively slowly with a decrease of the cavitation number and the transition to super-cavitation is progressive at \(Re\simeq 1300\). The data obtained for \(Re\geqslant 1400\) then follow a different trend, with first a slow growing until \(L^{*}\simeq 1\) and then a faster growing of the cavity. Moreover, one can notice that for \(Re\geqslant 1300\), the transition between the type-2 regime (\(\blacksquare\)) and the type-3 regime (\(\times\)) corresponds to an average length \(L^{*}\simeq 2\), around \(\sigma_{2}\simeq 1\). Figure 8: One cycle viewed from side in the type-2 periodic shrinking regime (\(\blacksquare\)) at \(Re=1614\), \(\sigma_{1}=4.87\) and \(\sigma_{2}=0.92\). The measured frequency of the cycle is \(34.6~{}Hz\). The dimensionless pressure drop \(K_{p}\) in the experiment without cavitation, i.e., at \(\sigma_{1,2}>>1\), is plotted in Figure 4a as a function of the Reynolds number. Let us recall that \(K_{p}=\sigma_{1}-\sigma_{2}\). As the cavitation develops while decreasing the ambient pressure at constant discharge velocity, the presence of gaseous structures of increasing volume may change the pressure drop. It might thus be interesting to explore the variation of both the inlet and outlet pressure, i.e., in a dimensionless form of both \(\sigma_{1}\) and \(\sigma_{2}\).