Pickering Ethan, Towne Aaron, Jordan Peter, Colonius Tim
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125, USA.
University of Michigan, Ann Arbor, Michigan 48109, USA.
J Acoust Soc Am. 2021 Oct;150(4):2421. doi: 10.1121/10.0006453.
Resolvent analysis has demonstrated encouraging results for modeling coherent structures in jets when compared against their data-educed counterparts from high-fidelity large-eddy simulations (LES). We formulate resolvent analysis as an acoustic analogy that relates the near-field resolvent forcing to the near- and far-field pressure. We use an LES database of round, isothermal, Mach 0.9 and 1.5 jets to produce an ensemble of realizations for the acoustic field that we project onto a limited set of resolvent modes. In the near-field, we perform projections on a restricted acoustic output domain, r/D=[5,6], while the far-field projections are performed on a Kirchhoff surface comprising a 100-diameter arc centered at the nozzle. This allows the LES realizations to be expressed in the resolvent basis via a data-deduced, low-rank, cross-spectral density matrix. We find that a single resolvent mode reconstructs the most energetic regions of the acoustic field across Strouhal numbers, St=[0-1], and azimuthal wavenumbers, m=[0,2]. Finally, we present a simple function that results in a rank-1 resolvent model agreeing within 2 dB of the peak noise for both jets.
与高保真大涡模拟（LES）中通过数据推导得到的对应结构相比，预解式分析在模拟射流中的相干结构方面已显示出令人鼓舞的结果。我们将预解式分析公式化为一种声学类比，将近场预解式强迫与近场和远场压力联系起来。我们使用一个关于圆形、等温、马赫数为0.9和1.5的射流的LES数据库，来生成一组声场的实现结果，并将其投影到一组有限的预解式模态上。在近场中，我们在一个受限的声学输出域r/D = [5,6]上进行投影，而远场投影则在一个以喷嘴为中心、直径为100的圆弧组成的基尔霍夫曲面上进行。这使得LES实现结果能够通过一个数据推导的、低秩的、互谱密度矩阵以预解式基表示。我们发现，单个预解式模态能够在斯特劳哈尔数St = [0 - 1]和方位波数m = [0,2]范围内重构声场中能量最高的区域。最后，我们给出了一个简单的函数，该函数生成的秩为1的预解式模型与两种射流的峰值噪声相差在2 dB以内。
