Some dynamical characteristics of a non-spherical bubble in proximity to a free surface

Estimating depth and explosive charge weight for an extremely shallow underwater explosion of the ROKS Cheonan sinking in the Yellow Sea

“…In particular, we see broad amplitude spectra from Z and E-W components indicating that the hydroacoustic waves have the vertical and radial properties of the reflected P waves from the hull of the ship at around 17.5 and 35 Hz (Figs. 4 and 5), whereas the bubble pulses (1.01, 1.72 Hz) (Kim and Gitterman, 2013) are well revealed on the vertical component after 0.990 s since the bubble collapse occurred off the portside near the surface by means of the buoyant force and the Bjerknes effect (Li et al, 2012). There are many different acoustic phases 31 s after P-wave arrival from the spectrogram of the Z component implying that the UWE took place at a very shallow underwater resulting in sonic boom (see Fig.…”

“…Although we used the Rayleigh-Willis equation which was originated from the free surface, the surface effect for this shallow underwater explosion does not influence the calculation of NEW because relative errors of bubble pulse periods between both observation versus free surface (2.32%) and observation versus 3D simulation with BEM (4.04%) are insignificant. Even if the non-contact UWE occurred off the portside of the ship, the nearer the bubble pulse from the hull of the ship, the longer the life time (bubble pulse period) sustains due to the Bjerknes effect assuming that the non-contact UWE occurred off the portside of the ship (Zhang et al, 2008a;Li et al, 2012). Fig.…”

The jet characteristics of bubbles near mixed boundaries

“…When the γ h reaches 4.0, as a result of the small distance between the bubble and free surface, strong nonlinear interaction 6 between them always makes the bubble generate a downward jet no matter how close the bubble is to the vertical wall. Even though the vertical wall exert an extraordinary impact on the bubble, the high pressure 15,57 between the bubble and the free surface would also drive the liquid jet directed downward, as the condition γ h = 4.0 (5.0) in Fig. 10.…”

“…As γ h increases at fixed γv, the jet angle gradually increases, reaching 90 ○ when the bubble approaches the free surface with a high pressure zone forming beneath the free surface; 54,57 this increase in the jet angle means the increase of the Bjerknes force in the vertical direction; so in a sense this may prove that the effect of the Bjerknes force from the free surface is greater than that of the bottom wall under the same conditions, which also may be deduced in the numerical simulations of Blake. 16,17 With an increase in γv at fixed γ h , the Bjerknes force exerted on the bubble in the vertical direction is constant, but that in the horizontal direction decreases, causing the joint force to rotate clockwise.…”

Study on Load Characteristics of Underwater Explosion Using RKDG-LS-DGF and BEM

“…Qi et al [11] applied BEM in the simulation of dynamic characteristic of two neighboring cavity bubbles. Li et al [12] proposed that the motions of a gas bubble in proximity to a free surface with and without buoyancy force, as well as in shallow water, can be simulated based on a numerical time integration coupled with three-dimensional boundary integral spatial solution. Zhang et al [13][14][15][16] investigated the bubble dynamics in free field and both vicinity to free surface and rigid boundary, combining the numerical simulation and the experimental results.…”