# Development of Attached Cavitation at Very Low Reynolds Numbers from Partial to Super-Cavitation
## 3 Results
### Developed Cavitation Regimes Identification in Degassed Oil  
Approximately one hundred of movies have been recorded at various Reynolds numbers and cavitation numbers. Only the cases with no spurious air bubbles coming from upstream and with cavities larger than 1 mm have been reported in Figure 6.  
The data all fall below the numerical inception curves. Four different regimes have been identified. Typical instantaneous side and top views illustrating these four regimes are displayed in Figure 7. The first regime identified with a full circle (\(\bullet\)) corresponds to steady cavities. For \(Re\leqslant 1000\), even at very small cavitation numbers, only steady cavities of this type are observed. The cavity viewed from side is quite flat and its bottom part is detached from the divergent bottom wall.  
For larger Reynolds numbers (\(Re\geqslant 1200\)), the type-1 steady attached cavities are only observed at high cavitation numbers, corresponding to small cavities. When lowering the cavitation number, a second regime arises: the cavity periodically grows and shrinks, which corresponds to spatio-temporal diagrams looking like the one displayed in Figure 3c. A typical cycle of shrinking and growing is illustrated in Figure 8. This second regime, characterized by a \"sawteeth\" spatio-temporal diagram is called \"type-2 cavities with periodic shrinking\" and is displayed with red squares (\(\blacksquare\)).  
Figure 6: Explored map in the Reynolds—cavitation number (\(Re-\sigma_{2}\)) space. Black circles (\(\bullet\)) correspond to type-1 steady small cavities, red squares (\(\blacksquare\)) to type-2 cavities with periodic shrinking, crosses (\(\times\)) to type-3 unsteady cavities with no clear periodic behavior and blue diamonds (\(\blacklozenge\)) to type-4 supercavities with \(L^{\star}\geqslant 7.1\). The solid pale blue line corresponds to the critical cavitation numbers obtained with the single-phase numerical simulations. Images of the cases (a) to (d) are displayed in Figure 7.  
In this regime, the shape of the cavity is different and varies during the cycle. It consists of an elongated bubble with a narrow tail at maximum length and during the shrinking, one can observe that the tail of the cavity turns into a vertical front that collapses towards the throat. For the case illustrated in Figure 8, the length of the cavity varies between \(L_{max}^{*}\simeq 4\) and \(L_{min}^{*}\simeq 0.2\).  
Lowering further the cavitation number, the attached cavity loses this periodic behavior: the spatio-temporal diagrams still show unsteadiness in the flow but with no clear periodic cycle. This third regime is displayed with crosses (\(\times\)) in Figure 6. The variation of its length corresponds this time to the detachment of delta and hairpin vortices as can be seen in Figure 7c. The cavity in this case keeps a length greater than \(L_{min}^{*}\simeq 1\) and has a maximum length of the order of \(L_{max}^{*}\simeq 6\). The characteristic vertical front at the rear part of the cavity that has been noticed in the previous regime is no longer observed.  
Finally, at the lowest cavitation numbers, one can obtain an almost steady cavity that appears to be completely transparent from both top and side view, and whose length is longer than the end of the divergent part of the Venturi profile (i.e., \(L^{*}\geqslant 7.1\)). (see Figure 7d). This fourth type is called \"supercavities\" and is displayed with blue diamonds (\(\blacklozenge\)) in Figure 6.  
Figure 7: Side and top views in different regimes. (**a**): type-1 steady cavity (\(\blacklozenge\)) at \(Re=992\), \(\sigma_{1}=5.96\) and \(\sigma_{2}=0.51\). (**b**): type-2 cavity with periodic shrinking (\(\blacksquare\)) at \(Re=1614\), \(\sigma_{1}=4.87\) and \(\sigma_{2}=0.92\). (**c**): type-3 unsteady cavity with no clear periodic behavior (\(\times\)) at \(Re=1600\), \(\sigma_{1}=4.89\) and \(\sigma_{2}=0.73\). (**d**): to type-4 supercavity (\(\blacklozenge\)) at \(Re=1810\), \(\sigma_{1}=4.66\) and \(\sigma_{2}=0.09\).