Ventilated cloud cavitating flow around a blunt body close to the free surface

Ventilated cavitation occurs as a complicated problem if the free surface is close to the cavity boundary around a high-speed underwater vehicle. The present study investigate the cavitating flow around a blunt axisymmetric body very near the free surface. A typical experiment is conducted by using a launching system with a split Hopkinson pressure bar device, and a numerical scheme is established based on large eddy simulation and volume-of-fluid methods. Unsteady behavior, including air entrainment and shedding of the cloud cavity, is observed, and high consistency is achieved between numerical and experimental results. Distinctions of evolution features between the cavities on the upper and lower sides are presented and analyzed. First, strong entrainment of noncondensable air occurs and changes the fluid property inside the cavity, which makes the cavity larger. Moreover, given the small distance between the vehicle and the free surface, the re-entrant jet generated in the upper part is thin and cannot completely cut off the main cavity, which causes the upper part of the cavity to remain approximately unchanged after the growth stage without the occurrence of the shedding phenomenon. Finally, the evolution of vortex structures is also discussed by comparisons with the motions of the air entrainment, re-entrant jet, and shedding cavity.

Figure 1

Components of the underwater launch system.

Figure 2

Typical cavitation photograph. The cavity length on the upper and lower side of the projectile is marked by $L_{\mathrm{up}}$ and $L_{\mathrm{down}}$. The free surface is pointed out by an arrow.

Figure 3

Calculated domain and boundary conditions in the simulation. The defined velocity-inlet, pressure-outlet, and wall boundary conditions are marked.

Figure 4

Mesh near the head of the projectile.

Figure 5

Comparison of the cavity profiles between the experimental figures and the simulated results of the original mesh and refined mesh.

Figure 6

The comparison of the variation of cavity length between numerical and experimental results.

Figure 7

Time evolution of cavitation patterns obtained from the experiment and simulation in the stage of cavity growth and air entrainment. The translucent isosurface represents where the volume fraction of liquid water is 0.9, while the blue isosurface represents where the volume fraction of vapor is 0.5, which can demonstrate the front of the air entrainment.

Figure 8

Time evolution of cavitation patterns obtained from the experiment and simulation in the earlier part of the re-entrant jet action stage. The translucent isosurface represents where the volume fraction of liquid water is 0.9.

Figure 9

Time evolution of cavitation patterns obtained from the experiment and simulation in the later part of the re-entrant jet action stage. The translucent isosurface represents where the volume fraction of liquid water is 0.9.

Figure 10

Time evolution of cavitation patterns obtained from the experiment and simulation in the cavity shedding stage. The translucent isosurface represents where the volume fraction of liquid water is 0.9.

Figure 11

Time evolution of cavitation patterns obtained from the experiment in the submerged case. The time interval is 2 mm for each view.

Figure 12

Flow field of the air entrainment at the beginning (the flow time is equal to 2 ms, and the line represents the interfaces where the volume fraction of the liquid water is equal to 0.5, while the color represents the velocity in the $X$ direction)

Figure 13

Distribution of the air entrainment at the beginning (the flow time is equal to 2 ms, translucent surfaces represent the cavity boundary and the free surface, line represents the volume fraction of air, and the color represents the velocity in the $Y$ direction)

Figure 14

Flow field of the air entrainment at the end (the flow time is equal to 4 ms, and the line represents the interfaces where the volume fraction of the liquid water is equal to 0.5, while the color represents the velocity in the $X$ direction).

Figure 15

Distribution of the air entrainment at the end (the flow time is equal to 4 ms, translucent surfaces represent the cavity boundary and the free surface, line represents the volume fraction of air, and the color represents the velocity in the $Y$ direction).

Figure 16

Shape of the re-entrant jet at the moment of 7 ms. Translucent surfaces represent the cavity boundary and the free surface, line represents the volume fraction of air, and the color represents the velocity in the $X$ direction on the cylindrical surface where the radial coordinate is equal to 1.1 times of radius of the projectile section.

Figure 17

The development of the re-entrant jet in the upper part of the cavity on the symmetric plane. The line represents the interfaces where the volume fraction of the liquid water is equal to 0.5, while the color represents the velocity in the $X$ direction. The jet front is pointed out by the white arrow in each view.

Figure 18

Profiles of the re-entrant jet inside the cavity on the upper side of the projectile at $t=5,6,7$, and 8 ms.

Figure 19

Profiles of the re-entrant jet inside the cavity on the lower side of the projectile at $t=5,6,7$, and 8 ms.

Figure 20

The development of the re-entrant jet in the lower part of the cavity on the symmetric plane. The line represents the interfaces where the volume fraction of the liquid water is equal to 0.5, while the color represents the velocity in the $X$ direction. The jet front is pointed out by the white arrow in each view.

Figure 21

The development of the re-entry jet inside the cavity on the symmetric plane. The iso-surface represents the interfaces where the volume fraction of the liquid water is equal to 0.5, while the color represents the velocity in the $X$ direction. The trajectory of the jet front is pointed out by the red arrow in each view.

Figure 22

The development of the re-entrant jet in the cavity on the symmetric plane for the simulated case with 40 mm distance between the upper side of the projectile and the free surface. The line represents the interfaces where the volume fraction of the liquid water is equal to 0.5, while the color represents the velocity in the $X$ direction.

Figure 23

Vortex structures in the cavity development and shedding process. The isosurfaces represent where $Q=5\times {10}^6$, color represents the velocity component in the axial direction, and the outer translucent surfaces represent the cavity boundary and the free surface. Key structures are marked by arrows and lines. The time interval is 2 ms and the first view is at the moment of 2 ms.

Figure 24

Velocity distribution on the added isosurface of vortex-stretching magnitude is $5\times {10}^6$ at $t=4,8,12$, and 16 ms of the simulated cases with and without free surface.

Figure 25

Velocity distribution on the added isosurface of vortex-dilatation magnitude is $5\times {10}^6$ at $t=4,8,12$, and 16 ms of the simulated cases with and without free surface.

Figure 26

Velocity distribution on the added isosurface of baroclinic torque magnitude is $5\times {10}^6$ at $t=4,8,12$, and 16 ms of the simulated cases with and without free surface.