椭球面镜声波反射聚焦数值模拟研究

Numerical study on the focusing of sound wave using a concave ellipsoidal mirror

据Hamilton线性理论解,给出沿椭球面镜轴线的电弧放电等离子声源(AD-PSS)反射波计算结果,分析由镜面引起的相位变化对中心波、边缘波及尾波传播影响。在聚焦前区中心波压力为正,边缘波、尾波压力为负;聚焦后区则相反。在线性条件下,反射波压力峰值出现于椭球面镜几何焦点,越过焦点后反射波压力幅值迅速衰减。利用有限元软件COMSOL对椭球面镜声反射过程进行数值模拟,揭示反射波传播演化过程及声场分布规律。据KZK(Khokhlov Zabolotskava Kuznetsov)方程及等效声源法,分析非线性效应对声传播过程影响。研究表明,非线性效应将使椭球面镜实际焦点位置偏离几何焦点,即正压实际焦点出现在几何焦点后,负压实际焦点出现在几何焦点前;随非线性系数增加正压实际焦点后移,负压实际焦点前移。

Based on the Hamilton＇s theoretical linear solution, the numerical results of the reflection waves of arc- discharge plasma sound source （AD-PSS） along the symmetric axis of an ellipsoidal mirror were presented. The propagation characteristics of the center wave, edge wave and wake wave were analyzed. In the front of the far focus of the mirror, the pressure of center wave is positive and those of the edge wave and wake wave are negative. Beyond the far focus, the situation is reversed. Under linear condition, the peak amplitude of the reflection wave collides with the far focus of mirror. The pressure amplitude of the reflection wave decays very quickly when going beyond the far focus. The reflection process of the sound wave was simulated using the FEM software COMSOL, and the evolution of reflection wave and the distribution of sound field were analyzed. Based on the khokhlov zabolotskava kuznetsov （KZK） equation, the influence of nonlinear coefficient on the propagation of reflection wave was discussed.