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Reduced-order model of a reacting, turbulent supersonic jet based on proper orthogonal decomposition
Theoretical and Computational Fluid Dynamics ( IF 3.4 ) Pub Date : 2020-01-09 , DOI: 10.1007/s00162-019-00513-y
Antoni Alomar , Aurélie Nicole , Denis Sipp , Valérie Rialland , François Vuillot

The present article deals with the spatiotemporal reduction of a reacting, supersonic, turbulent jet. A flowfield dataset is first obtained from a LES simulation including chemical reactions. The spatial reduction is accomplished by performing successively a Fourier transform in the azimuthal direction and a proper orthogonal decomposition (POD), while the temporal reduction is obtained through a selection of Fourier modes in the leading temporal POD modes (chronos). A prior low-pass temporal filter has been used to eliminate a significant portion of high-frequency content, the resulting reduced-order model (ROM) focusing only on the low-frequency, large-scale structures of the jet. The leading axisymmetric ( $$m=0$$ m = 0 ) POD mode describes a very low-frequency pulsation of the shock cells. The second and third axisymmetric POD modes are paired and describe a wave packet amplified along the potential core and with a rapid decay downstream. The two leading helical ( $$m=1$$ m = 1 ) POD modes, which are complex modes, appear to be mixed and together describe convecting wave packets of a longer wavelength and a lower frequency. They can be associated to the instability of the shear layer downstream of the potential core. Strong global cross-correlations are observed between the mass fractions and the axial velocity and temperature fields, which lead to similar energy decay rates and POD modes when they are included in the POD. The temporal reduction of the leading sets of chronos via an energy-based selection of Fourier modes has been shown to complement efficiently the spatial reduction, providing a complete spatiotemporal ROM of the flowfield.

中文翻译:

基于适当正交分解的反应性湍流超音速射流的降阶模型

本文涉及反应性、超音速、湍流射流的时空减少。流场数据集首先从包括化学反应的 LES 模拟中获得。空间缩减是通过在方位角方向上连续执行傅立叶变换和适当的正交分解 (POD) 来实现的,而时间缩减是通过在领先的时间 POD 模式 (chronos) 中选择傅立叶模式来获得的。先前的低通时间滤波器已被用于消除大部分高频内容,由此产生的降阶模型 (ROM) 仅关注喷流的低频、大规模结构。领先的轴对称 ( $$m=0$$m = 0 ) POD 模式描述了冲击单元的极低频脉动。第二个和第三个轴对称 POD 模式成对出现,描述了一个沿潜在核心放大的波包,并在下游快速衰减。两个领先的螺旋 ($$m=1$$m=1) POD 模式是复杂模式,似乎混合在一起,描述了更长波长和更低频率的对流波包。它们可能与潜在核心下游剪切层的不稳定性有关。在质量分数与轴向速度和温度场之间观察到强烈的全局互相关,当它们包含在 POD 中时,会导致类似的能量衰减率和 POD 模式。通过基于能量的傅立叶模式选择来减少领先的计时组的时间减少已被证明可以有效地补充空间减少,
更新日期:2020-01-09
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