Rectangular propulsion nozzles offer thrust-vectoring and air-frame-integration advantages over their more commonly studied circular counterparts. However, they display many distinguishing features which violate assumptions, such as azimuthal homogeneity, typically used in prediction tools for circular jets. In the present paper, we examine the utility of an azimuthal Fourier decomposition for rectangular Mach 1.3 jets of aspect ratio (AR) 1, 4, and 8 using large-eddy simulations, with a circular jet of the same equivalent diameter for reference. The simulations manifest key features of rectangular jets, including higher spreading rates and shorter potential cores with increasing AR, axis switching (AR=4), and azimuthal variation in peak acoustic intensity (AR=8). We show that, after projection on a cylindrical frame, a sine-cosine ansatz for the azimuthal Fourier series affords a more convenient representation of nonaxisymmetric flow features than the commonly used complex exponential ansatz. Fluctuation magnitudes of the higher azimuthal modes show rapid reduction in amplitude, similar to those observed in circular jets, especially if an acoustic fluctuation field based on momentum potential theory is chosen instead of pressure fluctuations. The leading modes differ, however, from those of a circular jet in two important aspects, namely, the mechanisms represented by the sine and cosine coefficients of the first azimuthal mode and the rate of streamwise decay of all modes with increasing AR. These differences are traced to the near- and far-field rectangular jet asymmetry by examining azimuthal inhomogeneity, the implications of which are assessed with a generalized expression for acoustic intensity based on energies of leading modes. The significant simplicity of circular plumes is recovered as a special case of the analysis. Invocation of the twofold mirror symmetry property of rectangular jets eases the prediction procedure so that only two extra terms, representing mechanisms unique to rectangular jets, specifically preferential flapping in the minor axis direction and coupling of axisymmetric and second azimuthal modes, are sufficient to recover the advantages of azimuthal decomposition.

中文翻译：

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通过方位角傅立叶模式表示矩形射流动力学

矩形推进喷嘴提供推力矢量和机身集成优势，而不是更常研究的圆形喷嘴。然而，它们显示出许多违反假设的显着特征，例如方位角均匀性，通常用于圆形射流的预测工具。在本论文中，我们使用大涡模拟检查了方位角傅立叶分解对纵横比 (AR) 1、4 和 8 的矩形马赫数射流的效用，并使用相同等效直径的圆形射流作为参考。模拟显示了矩形射流的关键特征，包括随着 AR、轴切换 (AR = 4) 和峰值声强度的方位变化 (AR = 8) 增加，更高的扩散率和更短的潜在核心。我们表明，在圆柱框架上投影后，方位角傅立叶级数的正弦-余弦 ansatz 比常用的复指数 ansatz 更方便地表示非轴对称流特征。较高方位角模式的波动幅度显示幅度迅速减小，类似于在圆形射流中观察到的幅度，特别是如果选择基于动量势理论的声波波动场而不是压力波动时。然而，领先模式在两个重要方面与圆形射流的领先模式不同，即由第一方位模式的正弦和余弦系数表示的机制以及所有模式随 AR 增加的流向衰减率。通过检查方位角不均匀性，这些差异可追溯到近场和远场矩形射流的不对称性，其含义通过基于领先模式能量的声强度的广义表达式进行评估。圆形羽流的显着简单性作为分析的一个特例得到了恢复。矩形射流的双重镜像对称特性的调用简化了预测过程，因此只有两个额外的项，代表矩形射流独有的机制，特别是短轴方向的优先扑动以及轴对称和第二方位角模式的耦合，足以恢复方位角分解的优点。