A generalized approach to decompose the compressible Navier-Stokes equations into an equivalent set of coupled equations for flow and acoustics is introduced. As a significant extension to standard hydrodynamic/acoustic splitting methods, the approach provides the essential coupling terms, which account for the feedback from the acoustics to the flow. A unique simplified version of the split equation system with feedback is derived that conforms to the compressible Navier-Stokes equations in the subsonic flow regime, where the feedback reduces to one additional term in the flow momentum equation. Subsonic simulations are conducted for flow-acoustic feedback cases using a scale-resolving run-time coupled hierarchical Cartesian mesh solver, which operates with different explicit time step sizes for incompressible flow and acoustics. The first simulation case focuses on the tone of a generic flute. With the flow-acoustic feedback term included, the simulation produces the tone characteristics similar to those obtained by Kühnelt [1] with a Lattice-Boltzmann method. In a contrasting manner, the simulation lacks the proper tone without the feedback term included. As the second simulation case, a thick plate in a duct is studied at various low Mach numbers around the Parker-β-mode resonance. The simulations reveal the flow-acoustic feedback characteristics in very good agreement with results from experiment of Welsh et al. [2]. Simulations and theoretical considerations reveal that the feedback term does not reduce the stable convective flow based time step size of the flow equations.

介绍了一种将可压缩 Navier-Stokes 方程分解为一组等效的流动和声学耦合方程的通用方法。作为标准流体动力学/声学分裂方法的重要扩展，该方法提供了基本的耦合项，它解释了从声学到流动的反馈。导出了一种独特的带反馈的分裂方程系统的简化版本，它符合亚音速流态中的可压缩 Navier-Stokes 方程，其中反馈减少到流动动量方程中的一个附加项。使用尺度解析运行时耦合分层笛卡尔网格求解器对流动-声学反馈情况进行亚音速模拟，该求解器以不同的显式时间步长运行，用于不可压缩的流动和声学。第一个模拟案例侧重于普通长笛的音调。包含流动声学反馈项后，模拟产生的音调特性类似于 Kühnelt [1] 使用 Lattice-Boltzmann 方法获得的音调特性。相比之下，模拟缺乏正确的音调，而没有包含反馈项。作为第二个模拟案例，在 Parker 周围以各种低马赫数研究管道中的厚板 -β-模式共振。模拟结果与 Welsh 等人的实验结果非常吻合。[2]。模拟和理论考虑表明，反馈项不会减少基于稳定对流流动方程的时间步长。