1.State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China 2.Key Laboratory of Aerodynamics Noise Control, China Aerodynamics Research and Development Center, Mianyang 621000, China
Fund Project:Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 11732016), the Sichuan Science and Technology Program (Grant No. 2018JZ0076), and the National Numerical Windtunnel Project.
Received Date:25 December 2020
Accepted Date:05 March 2021
Available Online:14 May 2021
Published Online:20 May 2021
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 ${M_v}$ and the length-scale ratio $\lambda /R$. 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 ${M_v} - \lambda /R$ plane is divided into three subdomains. As the vortex strength ${M_v}$ increases and the length-scale ratio $\lambda /R$ 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 ${M_v}{\left( {\lambda /R} \right)^{ - 2}}$. In particular, the directivity of the scattered field with a very low Mach number and a very long wavelength behaves as ${M_v}{\left( {\lambda /R} \right)^{ - 2}}\left| {\sin \left( {\theta /2} \right)} \right|$. In the resonance domain, the beams in the opposite direction to the incident waves decay rapidly. The rest of two beams follow the ${M_v}$ 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. Keywords:acoustic scattering/ vortex strength/ length-scale ratio/ scaling laws
图8给出了低马赫数$\left( {{M_v} = 0.015625} \right)$、大波长$\left( {\lambda /R \geqslant 8} \right)$时的散射声场指向性分布(r = 16R). 从图8可以看出, 随着波长的增加, 指向性分布逐步接近四个等强度的波束(参考曲线). 我们可以得到在极低马赫数、极大波长时散射声场的分布函数有如下形式: 图 8 低马赫数大波长下的散射声压均方根指向性分布 Figure8. Directivity for root-mean-square pressure of the scattered fields with low Mach number and long wavelength.
针对共振散射区的短波散射, 如图12所示, 两道主要的波束逐渐向声波入射方向靠拢, x轴负方向的散射彻底消失. 从图13可以看出随着旋涡强度的增加, 两道波束发生干涉, 标志着散射由共振散射区转向几何声学区. 图 12t = 60时的散射声压, 其中${M_v} = 0.125$, $\lambda /R = 1$ Figure12. Snapshot of scattered pressure with ${M_v} = 0.125$ and $\lambda /R = 1$ at t = 60.
图 13 旋涡强度对共振散射区小波长散射声场指向性的影响 Figure13. Directivity for root-mean-square pressure of the scattered fields in resonance domain with relatively small wavelength at different vortex strength.
图 15 不同旋涡强度对几何声学区散射声场指向性的影响 Figure15. Directivity for root-mean-square pressure of the scattered field in geometrical acoustics domain at different vortex strength.