Abstract
The Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation has been widely used in the simulation and calculation of nonlinear sound fields. However, the accuracy of KZK equation reduced due to the deflection of the direction of the sound beam when the sound beam is inclined incidence. In this paper, an equivalent sound source model is proposed to make the calculation direction of KZK calculation model consistent with the sound propagation direction after acoustic refraction, so as to improve the accuracy of sound field calculation under the inclined incident conditions. The theoretical research and pool experiment verify the feasibility and effectiveness of the proposed method.
Highlights
Due to the nonlinear effect of the medium, when the parametric acoustic array transmitted two similar frequency primary sound waves, the difference, sum, and harmonic frequency waves will be generated in the radiated sound field [1,2,3]. e parametric array technology can generate broadband, high directivity, and side-lobe suppressed low-frequency sound beams by using a small aperture array [4,5,6]. is parametric sound feature makes the parametric sonar more suitable for high-directivity sound beam noninvasive measurement and high-resolution sub-bottom profiling [7,8,9]
In the nonlinear sound field numerical analysis, the KZK equation was solved with the finite-difference time-domain method (FDTD) for the acoustic field from a rectangular aperture parameter array source. e staggered grid system at inclined plane boundary is described in Figure 2. e four terms on the right side of equation (1) represent diffraction in ux, uy axial directions, attenuation, and nonlinearity, respectively
To confirm the numerical results, the sound pressure distributions at primary, sum, and difference frequencies through inclined plane were measured using a TC4038 hydrophone, as shown in Figure 6. e water pool used in the experiments was 20 m long, 6 m wide, and 5 m deep. e German SES2000 parametric array (0.22 m × 0.22 m) was used as a rectangular sound source, and the signal is collected by Tuopu’s multichannel dynamic signal acquisition analyzer
Summary
Due to the nonlinear effect of the medium, when the parametric acoustic array transmitted two similar frequency primary sound waves, the difference, sum, and harmonic frequency waves will be generated in the radiated sound field [1,2,3]. e parametric array technology can generate broadband, high directivity, and side-lobe suppressed low-frequency sound beams by using a small aperture array [4,5,6]. is parametric sound feature makes the parametric sonar more suitable for high-directivity sound beam noninvasive measurement and high-resolution sub-bottom profiling [7,8,9]. When the parametric sound is obliquely irradiated into different media, the acoustic propagation path changes due to the medium parameters, which has a certain influence on the application of the parametric sound. Such as the direction of sound propagation will be deflected when the high-intensity focused ultrasound used in the noninvasive treatment of solid tumors and inversion error of shallow depth parameter due to inclined seabed. Vander Meulen and Haumesser constructed the model of finite amplitude sound beam propagation for the vertical incident baffle, and the nonlinearity coefficient of the aluminum plate medium has been measured and evaluated by the in-depth analysis of the second harmonic in the sound field [20]. The results of the aluminum plate were verified by the pool test
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