No abstract

When acoustic waves propagate through a volume of vortical flows, the strong nonlinear scattering lead the amplitude, the frequency, and the phase of the incident waves to change obviously. As one of the most significant problems in the area of aeroacoustics, the scattering of acoustic waves by a vortical flow plays a main role in industrial applications and scientific research. In this study, we start from an elementary vortex model. The scattering of plane acoustic waves from a Taylor vortex is investigated by solving two-dimensional Euler equations numerically in the time domain. To resolve the small-amplitude acoustic waves, a sixth-order-accurate compact Padé scheme is used for spatial derivatives and a fourth-order-accurate Runge-Kutta scheme is used to advance the solution in time. To minimize the reflection of outgoing waves, a buffer zone is used at the computational boundary. The computations of scattered fields with very small amplitudes are found to be in excellent agreement with a benchmark provided by previous studies. Simulations for the scattering from a Taylor vortex reveal that the amplitude of the scattered fields is strongly influenced by two dimensionless quantities: the vortex strength <inline-formula><tex-math id="M1">\begin{document}${M_v}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M1.png"/></alternatives></inline-formula> and the length-scale ratio <inline-formula><tex-math id="M2">\begin{document}$\lambda /R$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M2.png"/></alternatives></inline-formula>. Based on a global analysis of scale effects of these two dimensionless quantities on the scattering cross-section, the whole scattering domain defined on the <inline-formula><tex-math id="M3">\begin{document}${M_v} - \lambda /R$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M3.png"/></alternatives></inline-formula> plane is divided into three subdomains. As the vortex strength <inline-formula><tex-math id="M4">\begin{document}${M_v}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M4.png"/></alternatives></inline-formula> increases and the length-scale ratio <inline-formula><tex-math id="M5">\begin{document}$\lambda /R$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M5.png"/></alternatives></inline-formula> decreases, the acoustic scattering from a compact vortex goes through the long-wavelength domain, the resonance domain, and the geometrical acoustics domain in turn. The associated scattered fields with the increasing of intensity show more irregularities. The scattering in the long-wavelength domain possesses four primary beams described by half-sine functions, which scales as <inline-formula><tex-math id="M6">\begin{document}${M_v}{\left( {\lambda /R} \right)^{ - 2}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M6.png"/></alternatives></inline-formula>. In particular, the directivity of the scattered field with a very low Mach number and a very long wavelength behaves as <inline-formula><tex-math id="M7">\begin{document}${M_v}{\left( {\lambda /R} \right)^{ - 2}}\left| {\sin \left( {\theta /2} \right)} \right|$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M7.png"/></alternatives></inline-formula>. In the resonance domain, the beams in the opposite direction to the incident waves decay rapidly. The rest of two beams follow the <inline-formula><tex-math id="M8">\begin{document}${M_v}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20202206_M8.png"/></alternatives></inline-formula> scaling. The scattered fields are concentrated around the direction of the incident wave in the geometrical acoustics domain, where the primary beams are surrounded by several small sub-beams. The physical mechanism of the acoustic scattering caused by a vortex involves two different mechanisms, namely nonlinear scattering effect and linear long-range refraction effect.

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The scattering of acoustic waves by a vortex is a fundamental problem of the acoustic waves propagation in complex flow field, which plays an important role in academic research and engineering application for sound source localization, acoustic target recognition and detection, the far field noise prediction, such as aircraft wake vortex identification, detection and ranging, acoustic target forecasting in turbulent shear flow, acoustic measurement and sound source localization in wind tunnel test, etc. The nonlinear scattering phenomenon occurs when acoustic wave passes through the vortex, which is mainly related to the length-scale ratio between the wavelength of acoustic wave and the core radius of the vortex. In this paper, a plane acoustic wave passing through a stationary isentropic vortex is numerically simulated by solving a two-dimensional compressible, unsteady Euler equation. A sixth-order linear compact finite difference scheme is employed for spatial discretization. Time integration is performed by a four-stage fourth-order Runge-Kutta method. The eighth-order spatial compact filter scheme is adopted to suppress high frequency errors. At the far field boundaries, buffer layer is applied to handle the outgoing acoustic wave. Under the matching condition, the accuracy of the numerical results is verified by comparing with the previous direct numerical simulation results. The acoustic scattering cross-section method is introduced to analyze the effects of different length-scale ratio on the acoustic pulsation pressure, acoustic scattering effective sound pressure and acoustic scattering energy. Scattering occurs when sound waves pass through the vortex, the acoustic field in front of the vortex is basically unaffected, and the acoustic wave front remains intact. A “vacuum” region is formed slightly below the acoustic field directly behind the vortex, and two primary interference bands and several secondary interference bands are formed on the upper and lower sides of the vortex. As the length-scale ratio increases, the sound scattering decreases and the influence of the vortex flow field on the acoustic field gradually weakens. The influence region of effective sound pressure of acoustic scattering is mainly concentrated behind the vortex. With the increase of the length scale ratio, the influence gradually increases and extends to the upstream, and then the influence region gradually decreases to the vicinity of the vortex. When the length scale ratio is greater than or equal to 6, the location of the maximum effective sound pressure of sound scattering jumps from the upper right to the lower right of the vortex. The influence of acoustic wave wavelength change on the acoustic scattering energy can be divided into three parts. With the increase of the length scale ratio, the maximum sound scattering energy presents four different stages.

A data-driven and physical property-based hydrodynamic and acoustic mode decomposition method combining dynamic mode decomposition and Helmholtz decomposition is proposed. It allows decomposition and fast prediction of hydrodynamic and acoustic components of the flow field. The method is tested by a two-dimensional subsonic open cavity flow and a supersonic cold jet, and the hydrodynamic and acoustic features are revealed. For the cavity flow, it is found that the acoustic velocity inside the cavity is composed of several pairs of standing waves. The propagating trajectory of the acoustic waves in the cavity is well captured. The dynamic relation between the hydrodynamic and acoustic motion is investigated. For the supersonic jet, the method successfully identifies the screech in the far field and the “trapped wave” within the potential core.