A prediction model for two-dimensional pressure distribution from underwater shock wave focusing by an ellipsoidal reflector.

Underwater shock wave focusing by ellipsoidal reflector is an important method for medical treatment, detection, and acoustic warfare. However, its pressure field is difficult to predict due to complicated physics. In this study, the pressure by focusing is modeled based on theories of shock wave propagation, nonlinear reflection, and nonlinear focusing, and the calculation domain is determined by approximate equations of wave fronts and lines. The pressure field during the whole process is described by combining direct and focusing pressures in the time and space domains. On this basis, the focusing behavior is simulated, and obtained pressure profiles are compared with experimental results, and the influence of reflector length on focusing performance is also discussed. The results indicate that although there are some rough assumptions, this model can simulate the underwater focusing in some detail and does a good job of predicting the pressure distribution, especially for the positive peak pressure, with an error below 10%; as the reflector length increases, the dynamic focus tends to move linearly forward to the other geometric focus, and the pressure gain increases continuously but the growth rate decreases.