A set of nonlinear wave equations based on the acoustic perturbation theory in the frequency domain is developed to simulate vortex-sound interaction and analyze acoustic scattering phenomena from the underwater vortical flow over an airfoil. The vortex can influence the propagation characteristics of an incident plane wave, which generate the vortex scattering. The numerical method is validated according to the computational results compared with the data of previous studies. A case with uniform inlet flow through an airfoil at 30° angle of attack is investigated. Results show that the position of vortex can be evaluated by the position of the peaks of the scattering sound pressure. Studies provide important information for the underwater detection.


When acoustic waves propagate through vortical flow, the flow-sound interaction can affect the sound propagation, resulting in acoustic scattering phenomena. As an effective medium for the long-range underwater transmission of information, acoustic waves are of great significance for detecting the turbulence and vortex flow in the ocean. With the development of underwater noise reduction technology and anechoic materials, underwater target detection has become more and more difficult. The wake generated by the underwater vehicle can evolve the tail vortex with special flow structure. By detecting and analyzing the vortex characteristics of the voyage body, the existence of the structure can be indirectly identified. Previous studies are mainly focused on aeroacoustic scattering with experimental and numerical analysis. However, not much research are found about underwater acoustic scattering from a vortical flow, especially considering the wake flow of solid structure.

To evaluate the effects of vortex scattering on underwater detection, lots of data collection have been performed. Eleni (2012) evaluated the accuracy of k-ω shear stress transport (SST) turbulence model applied in the analysis of the two dimensional flow over NACA0012 airfoil through the comparison of the predictions and the free field experimental measurements for the selected airfoil. Colonius, Lele and Moin (1994) performed direct numerical simulation of the propagation of acoustic wave through the eddy field based on the Nasiver-Stoke (N-S) equations and good results were obtained. It was studied (Blanc- Benon, Lipkens, Dallois, Hamilton and Blackstock, 2002) that the method combining the geometrical acoustic theory and the parabolic approximation was applied to analyze the propagation of a finitude acoustic wave when it passe through a turbulent flow field. It is noted (Ostashev, Wilson, Liu, Aldridge, Symons and Marlin, 2005) that the results of finite-difference, time-domain implementation showed good agreement with Fast Field Program calculations of sound propagation in a stratified moving atmosphere. Iwatsu and Tsuru (2013) solved the linear Euler equation of ideal gas by the symplectic integral method combined the compact finite difference scheme. The scattering acoustic pressure distributions of Rankine vortex and Burgers vortex were respectively simulated and good results were obtained. Ferziger (1974) simulated the low frequency (100Hz) acoustic scattering from aircraft wake vortex by Born approximation method, which can effectively evaluate the vortex size and other characteristics. Zhang, Du, Zhang and Li (2017) analyzed the characteristics of vortex scattering by finitedifference, time-domain method at different monitoring positions when Mach number was approximately 0.3, which lacked further detailed analysis. Brillant, Chillá and Pinton (2004) experimentally studied the wavefront deformation when acoustic waves with different wavelengths propagated through isolated vortex in air. When the wavelength was much smaller than the size of the vortex core, the experimental results were consistent with results based on geometrical acoustics method. Baudet, Ciliberto and Pinton (1991) used ultrasonic waves to measure Karman vortex shedding in cylindrical wake with low Reynolds number (Re = 50) in a wind tunnel. The measured results were consistent with the experimental results obtained by Lund and Rojas (1989), and in agreement with the results of theoretical analysis.

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