定常的キャビテーション気泡について

抄録

One of the reasons, why the intense first subharmonic component is contained in the cavitation noise produced in the relatively weak acoustic field, is often explained to be caused by the re-radiation sound pressure of the parametricly excited bubbles, whose radius is approximately twice the resonance bubble size for the acoustic frequency. However, the reason why such bubbles are produced in the acoustic field has not yet been clarified. In this paper, according to the consideration of the gas diffusion through the wall of the cavitation bubble, we have theoretically verified the fact that the bubbles, with radius approximately twice the resonance bubble size, can stationarily exist in the acoustic field. Considering on the rectified diffusion model of the cavitation bubble, we assumed the followings;(1) There is a spherical diffusion boundary layer of thickness a surrounding the bubble wall. (2) Gas concentration in the boundary layer changes from C_(SR) on the bubble wall(r=R) to C_(S∞) on the outside of the layer(r=R+a). (see Fig. 1)(3) The velocity of diffusion of the gas through the bubble wall is faster than the oscillating velocity of the bubble wall, and the diffusion of gas is always in the static equilibrium state. Under the above assumptions we determined the distribution of gas concentration in the diffusion boundary layer surrounding the bubble wall. (see Eq. (3))Thus the increase of gas content in the bubble at time t, after begining of the pulsating motion of the bubble, is given by the following equation. ΔM=(4πC_<s0>D)/a∫^^t__0((C_<S∞>)/(C_<S0>)R^2-(R^3_0)/R)dt (8)On the other hand, according to the cavitation bubble model, the time change of the bubble radius is governed by the following equation. (d^2R)/(dt^2)+(2R)/3((dR)/(dt))^2=1/(ρR)(P_g-(2σ)/R-P_a+P_0cosωt) (9)According to the increase or decrease of the gas content in the bubble, that is, if ΔM is positive or negative, we decide that the bubble will become to grow or not. If ΔM is equal to zero during the pulsating motion for several cycles of acoustic field, we decide that the bubble is in the equilibrium state. In Fig. 2, one of our calculated results, the domain bounded by the dotted lines gives the equilibrium state of cavitation bubbles. The domain of the stable equilibrium state gives that of the stationarily pulsating cavitation, and the value of the acoustic pressure of the domain of the unstable equilibrium state gives the so-called cavitation threshold value. Comparing the recently published results with out result in Figs. 5 to 7, we can confirm that they have very good agreement with each other. Attending to the bubble radius of the stationarily pulsating cavitation bubble in Figs. 2 and 7, we can confirm that its size is approximately twice the resonance bubble size. Expanding ΔM in power series of β, we obtain the approximate expression of ΔM in the Eq. (17). Moreover, the condition of the stable equilibrium of the bubble is given in Eq. (19), and from this equation we can confirm that the bubbles which have the approximately twice the radius of the resonance bubble can stationarily be exist in the acoustic field. Thus we can make it clear that the first subharmonic component contained in the cavitation noise caused by the re-radiation of sound by the parametricly excited bubbles in the acoustic fields.