Chen Zhibo, Towne Aaron
Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
J Acoust Soc Am. 2021 Sep;150(3):1967. doi: 10.1121/10.0006234.
The acoustic field of high-speed turbulent jets is dominated by a small number of low-wavenumber azimuthal Fourier modes. Accordingly, it is of interest to directly obtain individual azimuthal modes of the acoustic field from simulation data or models of the jet near-field. To this end, we manipulate the Ffowcs Williams and Hawkings (FW-H) equation to obtain a new formulation that lives entirely in the azimuthal Fourier domain-it delivers individual azimuthal modes of the acoustic field as a function of the same azimuthal modes of the near-field FW-H source term or, upon linearization of the source terms, as a function of the same azimuthal modes of the near-field flow variables. As an added benefit, all surface integrals are converted into line integrals in the streamwise-radial plane. After verifying and validating our formulation using a monopole problem with an exact solution and large-eddy simulation data, respectively, we show how our method can be used to efficiently and naturally compute the acoustic field associated with resolvent modes of a Mach 1.5 jet, thus avoiding the need to compute the modes on a large computational domain to capture their acoustic radiation.
高速湍流射流的声场由少数低波数方位傅里叶模式主导。因此，直接从射流近场的模拟数据或模型中获取声场的各个方位模式是很有意义的。为此，我们对Ffowcs Williams和Hawkings（FW - H）方程进行处理，以获得一种全新的公式，该公式完全存在于方位傅里叶域中——它将声场的各个方位模式作为近场FW - H源项相同方位模式的函数给出，或者在源项线性化后，作为近场流动变量相同方位模式的函数给出。另外一个好处是，所有的表面积分都被转换为流向 - 径向平面内的线积分。在分别使用具有精确解的单极子问题和大涡模拟数据对我们的公式进行验证之后，我们展示了如何使用我们的方法高效且自然地计算与马赫数1.5射流的预解模态相关的声场，从而避免了在大计算域上计算模态以捕捉其声辐射的需求。
