Ventilated supercavitation around a moving body in a still fluid: observation and drag measurement

Abstract

This experimental study examines ventilated supercavity formation in a free-surface bounded environment where a body is in motion and the fluid is at rest. For a given torpedo-shaped body and water depth ($H$), depending on the cavitator diameter ($d_{c}$) and the submergence depth ($h_{s}$), four different cases are investigated according to the blockage ratio ($B=d_{c}/d_{h}$, where $d_{h}$ is the hydraulic diameter) and the dimensionless submergence depth ($h^{\ast }=h_{s}/H$). Cases 1–4 are, respectively, no cavitator in fully submerged ($B=0$, $h^{\ast }=0.5$), small blockage in fully submerged ($B=1.5\,\%$, $h^{\ast }=0.5$), small blockage in shallowly submerged ($B=1.5\,\%$, $h^{\ast }=0.17$) and large blockage in fully submerged ($B=3\,\%$, $h^{\ast }=0.5$) cases. In case 1, no supercavitation is observed and only a bubbly flow (B) and a foamy cavity (FC) are observed. In non-zero blockage cases 2–4, various non-bubbly and non-foamy steady states are observed according to the cavitator-diameter-based Froude number ($Fr$), air-entrainment coefficient ($C_{q}$) and the cavitation number ($\unicode[STIX]{x1D70E}_{c}$). The ranges of $Fr$, $C_{q}$ and $\unicode[STIX]{x1D70E}_{c}$ are $Fr=2.6{-}18.2$, $C_{q}=0{-}6$, $\unicode[STIX]{x1D70E}_{c}=0{-}1$ for cases 2 and 3, and $Fr=1.8{-}12.9$, $C_{q}=0{-}1.5$, $\unicode[STIX]{x1D70E}_{c}=0{-}1$ for case 4. In cases 2 and 3, a twin-vortex supercavity (TV), a reentrant-jet supercavity (RJ), a half-supercavity with foamy cavity downstream (HSF), B and FC are observed. Supercavities in case 3 are not top–bottom symmetric. In case 4, a half-supercavity with a ring-type vortex shedding downstream (HSV), double-layer supercavities (RJ inside and TV outside (RJTV), TV inside and TV outside (TVTV), RJ inside and RJ outside (RJRJ)), B, FC and TV are observed. The cavitation numbers ($\unicode[STIX]{x1D70E}_{c}$) are approximately 0.9 for the B, FC and HSF, 0.25 for the HSV, and 0.1 for the TV, RJ, RJTV, TVTV and RJRJ supercavities. In cases 2–4, for a given $Fr$, there exists a minimum cavitation number in the formation of a supercavity while the minimum cavitation number decreases as the $Fr$ increases. In cases 2 and 3, it is observed that a high $Fr$ favours an RJ and a low $Fr$ favours a TV. For the RJ supercavities in cases 2 and 3, the cavity width is always larger than the cavity height. In addition, the cavity length, height and width all increase (decrease) as the $\unicode[STIX]{x1D70E}_{c}$ decreases (increases). The cavity length in case 3 is smaller than that in case 2. In both cases 2 and 3, the cavity length depends little on the $Fr$. In case 2, the cavity height and width increase as the $Fr$ increases. In case 3, the cavity height and width show a weak dependence on the $Fr$. Compared to case 2, for the same $Fr$, $C_{q}$ and $\unicode[STIX]{x1D70E}_{c}$, case 4 admits a double-layer supercavity instead of a single-layer supercavity. Connected with this behavioural observation, the body-frontal-area-based drag coefficient for a moving torpedo-shaped body with a supercavity is measured to be approximately 0.11 while that for a cavitator-free moving body without a supercavity is approximately 0.4.