Generation of abnormal acoustic noise: Singing of a cavitating tip vortex

We present experimental results and a theoretical analysis for the singing of a cavitating tip vortex (SCTV), which has been occasionally observed under special conditions in a few experimental facilities around the world since the 1990s. Due to lack of repeatability, little is known about the generation mechanism of SCTV [R. E. A. Arndt, Annu. Rev. Fluid Mech. 34, 143 (2002)]. In the present work we propose an experimental procedure to produce the SCTV phenomenon at selected flow conditions in the China Ship Scientific Research Center cavitation mechanism tunnel. By analyzing the frequency characteristics of the acoustical signal and the bubble dynamics, it is found that the tone of SCTV matches the natural frequency of radial oscillation of the cylinder bubble and a formulation to predict SCTV is developed. Good agreement is obtained between the proposed formulation and the experimental data from different facilities.

Figure 1

Pictures from the high-speed camera at 2000 fps (a) before, (b) during, and (c) after vortex singing for $W_{\infty }=12.8$ m/s, $\sigma =1.40, \alpha /{\alpha }_s=0.77$, and no nuclei seeding.

Figure 2

Noise spectra of vortex cavitation before, during, and after vortex singing for $W_{\infty }=12.8$ m/s and ${\sigma }_v=1.40$.

Figure 3

Noise spectra of vortex singing for different flow velocities $W_{\infty }=7$, 9, 11, and 12.8 m/s. The first frequency peaks are 297.2, 360.9, 403.4, and 488.3 Hz. Cavitation numbers ${\sigma }_v$ are 1.45, 1.45, 1.45, and 1.40.

Figure 4

Variation of the cavitating vortex radius in different flow states: (a) before singing for $W_{\infty }=12.8$ m/s, (b) during singing for $W_{\infty }=7.0$ m/s, and (c) during singing for $W_{\infty }=12.8$ m/s. The coordinate origin $x=0\mathrm{mm}$ is the hydrofoil's tip.

Figure 5

Primary and second harmonics of singing waves versus incoming current speed $W_{\infty }$ obtained by a hydrophone, as shown by open circles and stars, respectively. Red and blue lines represent the primary frequencies corresponding to $f_1$ and $f_2$. Black lines represent the modulation frequencies corresponding to $\mathrm{\Delta }f=(f_1-f_2)/2$: The solid line is the theoretical curve with the parameter $\beta =0.40$, while the dashed and dotted lines are the results for $\beta =0.45$ and 0.50, respectively.

Figure 6

Comparison among experimental data and the analytical formulation. The solid line is the analytical formulation (7), while dashed lines are $\pm 20\%$ off the exact formulation. Other experimental data are read from [4]. Here SW represents strong water and WW represents weak water.