On the flow structure of cloud cavitating flow around an axisymmetric body near the free surface

The influence of the free surface on the cavitating flow is an important issue involved in the design of high speed surface vehicles. In the present paper, unsteady cavitating turbulent flow around an axisymmetric body near the free surface was investigated by both launching experiment and LES simulation. The vortex motion induced by cavity shedding under the effect of the free surface is emphatically analyzed by comparing with the submerged condition. The vortex shedding process around the projectile is not synchronized, while the asymmetric characteristic in collapse process is more remarkable, with the generation of multiple vortex ring structures.


Introduction
Characteristics of cavitating flow, especially unstable structures of cloud cavitating flow, always have close relationship with the vortex motion [1]. Therefore, the turbulence resolution method plays a fatal role on the establishment of numerical approach on unsteady cavitating flow. On the simulation for engineering applications, solving Reynolds-averaged Navier-Stokes (RANS) equations and turbulence models with physical modifications is the main way. Approaches such as modified RNG k-ε turbulence model [2][3][4][5][6] are widely used. In the recent years, large eddy simulation (LES) method is adopted for the research on cavitating flows, which can capture considerable details of large-scale eddies in the flow field with high accuracy [7][8][9][10][11][12][13][14]. For example, an implicit large eddy simulation method was adopted to simulate dynamic cavitation behavior of a propeller by Bensow et al [7]. The cavitation shedding horse-shoe structures were captured numerically by Ji et al [8,14].
The influence of the free surface on the cavitating flow is an important issue involved in the design of high speed surface vehicles, but relative investigations are very limited. Fatingsen et al [15] established a numerical approach based on theoretical models on the supercavitating flow near the free surface. Bal et al presented boundary element methods (BEM) [16][17][18] for cavitating hydrofoils near a free surface. Other similar works are mainly performed concerning stable supercavitating flow structures [19,20]. The influence of the free surface on the unsteady cloud cavitating flow is very lacking in literature.
The present paper focuses mainly on the influence of the free surface on the flow structure of the cloud cavitating flow. Typical evolutions of nonaxisymmetrical cavity shapes around a slender body near the free surface are obtained both by LES method and a launching experiment.  motion induced by cavity shedding under the effect of the free surface is emphatically analyzed by comparing with the submerged condition.

Experimental setup
The launching system is established on the basis of the SHPB technology [21]. It can transiently accelerate the projectile with slight disturbance on surrounding water. The projectile used in this study is a slender cylinder with a conical head. Its material is polished stainless steel. The total length is 246 mm, and the diameter is 37 mm. The conical angle is 90°. Typical photograph of cavitation can be obtained using a high-speed camera with 25000 fps (as shown in Fig.1). The cavitation number is 0.62, while the projectile speed is 17.8 m/s.

Cavity evolution
An additional case without the free surface is also performed. Typical evolution photograghs in experimental and numerical results are as shown in Fig.2. Quasi-periodical variations of cavity shapse are obtained. Typical evolutions of cavity includes growth, re-entry jet development, cavity shedding and collaspe, which are similar for both the process considering and neglecting the effect of the free surface. The cavity shapes affected by the free surface are non-axisymmetrical. The re-entry jet in the upper part of the cavity is generated earlier and has a slightly faster velocity (as shown in Fig.2(a)). When the re-entry jets arrive at the shoulder of the model, the cavity on the lower side is a little longer than the upper side (as shown in Fig.2(b)). The cavity sheds by the interaction between main flow and re-entry jet, and the cavity on the upper side sheds earlier (as shown in Fig.2(c)). The shedding cavity on the lower side is farer away from the main cavity, which collapses more strongly (as shown in Fig.2(d)). Cavity shapes on the lower side are similar with the case without the free surface, but cavity in the latter case is longer. Because the cavity shape is integral and like a ring, the development on the lower side is hindered by the upper side.

Influence on shedding vortex structures
The motion of shedding cavitation clouds has strong correlation with the vortex motion. The flow structures can be visualized based on the Q-criterion. In the present study, the iso-surface of Q=50000 is shown to represent the vortex core, and the colour represents the magnitude of the velocity component in the axial direction. Vortex structures in the shedding process are as shown in Fig.3. For the case without the free surface in the right views, vortexes are rolled outwards gradually, and the upstream parts begin to break apart at first under the influence of the main flow. For the case with the free surface in the left views, the shedding process around the projectile is not synchronized, and the shedding vortex is inclined. The broken vortex is thinner on the upper side under the influence of the free surface.  The shedding vortex breaks up strongly induced by the collapse of the shedding cavity (as shown in Fig.4), which exhibits more remarkable asymmetry during this period under the influence of the free surface. A multiple vortex ring structure is formed after cavity collapse, inducing significant nonuniform distributions of velocity and pressure, which may cause large lateral force and affect the stability of cruising.

Conclusions
Unsteady cavitating turbulent flow around an axisymmetric body near the free surface was investigated by both the launching experiment and the LES simulation. The evolution of flow structures is mainly analyzed, and several conclusions can be drawn as follows: (1) On the upper side near the free surface, the cavity shape and cycle time are both shorter, while cavity shapes on the lower side are similar with the case without the free surface.
(2) The vortex shedding process around the projectile is not synchronized, and the broken vortex is thinner on the upper side under the influence of the free surface.
(3) The vortex collapse process is strongly asymmetric, and a multiple vortex ring structure is formed after cavity collapse. The remarkable asymmetry may cause large lateral force and affect the stability of cruising.