# 含气泡液体中声场能量的传播Propagation of Sound Energy in Bubbly Liquids

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Aiming at the problem of sound wave propagation in bubbly liquids, an idea of using energy propagation to establish a model is proposed. The vibration of the bubble and the mechanical energy of the sound are combined to establish an energy propagation model of the sound field in the bubbly liquids, and the model is used as a single numerical simulation of the mechanical energy change of the bubble caused by bubble cavitation, the mechanical energy loss of the driven sound field and the influence of bubble vibration on the propagation process of the sound field during the model Through numerical analysis, it’s found that the more the volume change of a single bubble during the vibration process, the more obvious the change of mechanical energy, and the greater the mechanical energy loss of the corresponding driving sound field; if the bubble is cavitation under the action of the driving sound field, a small cavitation area is formed near the sound source, and the size of the area is affected by the number of bubbles and the intensity of the sound field. Finally, the proposed and applied sound field energy propagation model in bubbly liquids can be conveniently used to deal with the propagation of sound fields in bubbly liquids.

1. 引言

2. 声场能量传播模型

2.1. 气泡振动的能量模型

$\rho \left(R\stackrel{¨}{R}+\frac{3}{2}{\stackrel{˙}{R}}^{2}\right)={P}_{g}-\frac{2\sigma }{R}-4\mu \frac{\stackrel{˙}{R}}{R}-P$ (1)

$P={P}_{\infty }+{P}_{r}$ (2)

${P}_{g}=\left({P}_{0}+\frac{2\delta }{{R}_{0}}\right){\left(\frac{{R}_{0}}{R}\right)}^{3\gamma }$ (3)

$P\cdot dV=-\rho \left(R\stackrel{¨}{R}+\frac{3}{2}{\stackrel{˙}{R}}^{2}\right)\cdot dV+{P}_{g}\cdot dV-\frac{2\delta }{R}\cdot dV-\frac{4\mu \stackrel{˙}{R}}{R}\cdot dV-{P}_{\infty }\cdot dV$ (4)

2.2. 声场能量传播模型

${E}_{0}=\frac{{V}_{0}}{2}\rho \left({\upsilon }^{2}+\frac{1}{{\rho }^{2}{c}^{2}}{P}_{r}^{2}\right)$ (5)

$\Delta E=\frac{3\beta {V}_{0}}{4\pi {R}_{0}^{3}}{P}_{r}\cdot dV$ (6)

${E}^{\prime }={E}_{0}-\Delta E$ (7)

$\frac{{V}_{0}}{2}\rho \left({\upsilon }^{2}+\frac{1}{{\rho }^{2}{c}^{2}}{P}_{r}{}^{2}\right)-\frac{3\beta {V}_{0}}{4\pi {R}_{0}^{3}}{P}_{r}\cdot dV=\frac{{V}_{0}}{2}\rho \left({{\upsilon }^{\prime }}^{2}+\frac{1}{{\rho }^{2}{c}^{2}}{{P}^{\prime }}_{r}^{2}\right)$ (8)

3. 数值模拟分析

Figure 1. Bubble radius, mechanical energy and mechanical energy loss of driving sound field change with time

Figure 2. Influence of bubble content and sound field amplitude on sound field propagation

4. 结论

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