Transition and gas leakage mechanisms of ventilated cavities around a conical axisymmetric body

In this paper, we present an experimental investigation on gas entrainment and gas leakage mechanisms of different ventilated cavity flow patterns around a conical axisymmetric body, by high-speed video and theoretical analysis. The ventilated cavity is generated around a conical axisymmetric body and studied in the closed-loop water tunnel at Lab of Fluid Machinery and Engineering, Beijing Institute of Technology. The experimental studies revealed three distinct cavity patterns, namely, the foamy cavity (FC), the intermittent and transitional cavity (ITC), and the continuous and transparent cavity (CTC) under different Froude and $C_Q$ values. All patterns contain the transparent region at the cavity rear (except FC) and the recirculating vortex that generates foam shedding at the cavity rear. The qualitative gas entrainment and leakage process are then explained based on the schematics of internal gas flow and surrounding water flow. As the flow pattern varies from FC to CTC with increasing ventilation rate, it is observed that the size of shedding foam grows larger while the shedding frequency gradually reduces, leading to balanced gas injection and leakage. Moreover, the mechanism controlling the hysteresis of the ITC-to-CTC transition is quantitatively explained using a gas leakage model of ITC cavities, which assumes the foam is periodically shed in the form of a vortex ring. After extensive validation by both current measurements and previous research, the model can accurately predict the ventilation rate required for the ITC-to-CTC transition. Finally, the mechanism causing closure discrepancy between CTC cavities in this paper and free-standing supercavities (without cavitator body) in past studies are investigated. Due to the impact of stagnation points on the cavitator body, the adverse pressure gradient (APG) in the streamwise direction of CTC cavities is estimated to be 6.8 times that of free-standing supercavities under the same flow conditions, leading to water flow separation at the cavity rear. As a result, after the ventilation hysteresis, the recirculating vortex closure is still observed in CTC cavities under the impact of large APG, different from free-standing supercavities that form vortex tube closure.

Figure 1

Schematics of experimental setup and the cavitator. (a) The experimental setup with ventilation system for imaging the ventilation cavity. (b) The test section and the position of the cavitator. All dimensions are in millimeters.

Figure 2

Side views of the ventilated cavitation observed in the experiments: (a) Foamy cavity (FC) at $\mathrm{Fr}=17.07$, $C_Q=0.028$. (b) Intermittent and transitional cavity (ITC) at $\mathrm{Fr}=17.07$, $C_Q=0.059$. (c) Continuous and transparent cavity (CTC) at $\mathrm{Fr}=14.25$, $C_Q=0.110$.

Figure 3

Globe flow patterns of ventilated cavities around an axisymmetric cavitator.

Figure 4

(a) Experimental observation and (b) schematic illustration of the cavity flow field and bubble dynamics of the foamy cavity (FC) at $\mathrm{Fr}=12.27$, $C_Q=0.026$.

Figure 5

(a) Experimental observation and (b) schematic illustration of the cavity flow field and bubble dynamics of the intermittent and transitional cavity (ITC) at $\mathrm{Fr}=12.27$ and $C_Q=0.051$.

Figure 6

(a) Experimental observation and (b) schematic illustration of the cavity flow field and bubble dynamics of the continuous and transparent cavity (CTC) at $\mathrm{Fr}=12.27$ and $C_Q=0.102$.

Figure 7

The boundary lines separating contiguous flow patterns.

Figure 8

Schematic of dimension and shedding frequency measurements. The cavity length $\left(L_c\right)$ and maximum diameter $\left(D_c\right)$ of (a) the intermittent and transitional cavity (ITC) and (b) the continuous and transparent cavity (CTC). Wake bubble break-off and shedding tracking at (c) $t=t_0$ and (d) $t=t_1$.

Figure 9

The variation of cavity length $\left(L_C\right)$ and maximum radius $\left(R_C\right)$ with different ventilation $C_Q$ under $\mathrm{Fr}=9.62$, 12.27, and 14.22.

Figure 10

(a)The schematic of the vortex ring shedding model applied in intermittent and transitional cavities (ITCs). (b)The shed vortex rings have an averaged cross-sectional radius of $(R_C-R_n)/2$ and a central axis length of $\pi (R_C+R_n)$.

Figure 11

Normalized maximum radius $R_C/R_n$ of the cavity developed on the conical cavitator over the range of tested Fr cases. All data are obtained from the cavity under maximum ventilation coefficient. The error bars shown here correspond to the standard deviation of the 50 independent measurements. The results by Shao et al. [32] and Garabedian [49] are presented under the same flow conditions as ours for comparison purposes.

Figure 12

The Strouhal number distribution under (a) a global and (b) a specific range of Re for intermittent and transitional cavities (ITCs) in our experiments. For comparison, all data marked by black squares are from Roshko [54], and the dashed line, 0.21, corresponds to conclusion from Houghton and Carpenter [55].

Figure 13

(a) The distribution of parameter $K$ calculated on intermittent and transitional cavities (ITCs), with projections on Fr and $C_Q$ axes for clear observation of $K$ values. The dashed lines mark out the averaged $K$ (0.36). (b) The estimated critical $C_Q$ from Eq. (2) by substituting the largest $R_C/R_n$ under different Fr cases.

Figure 14

Schematic of gas flow inside and water flow surrounding (a) the continuous and transparent cavity (CTC) formed on the conical axisymmetric cavitator and (b) the free-standing supercavity formed after a backward-facing strut from Wu et al. [23]. Points $A_1$ and $A_2$ are located at the potential water flow close to the gas-water interface. Points $B_1$ and $B_2$ are on the same streamline as $A_1$ and $A_2$, respectively.