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Spatio-temporal linear stability analysis of stratified planar wakes: Velocity and density asymmetry effects

机译：分层平面尾流的时空线性稳定性分析：速度和密度不对称效应

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This paper explores the hydrodynamic stability of bluff body wakes with non-uniform mean density, asymmetric mean density, and velocity profiles. This work is motivated by experiments [S. Tuttle et al., "Lean blow off behavior of asymmetrically-fueled bluff body-stabilized flames," Combust. Flame 160, 1677 (2013)], which investigated reacting wakes with equivalence ratio stratification and, hence, asymmetry in the base flow density profiles. They showed that highly stratified cases exhibited strong, narrowband oscillations, suggestive of global hydrodynamic instability. In this paper, we present a local hydrodynamic stability analysis for non-uniform density wakes that includes base flow asymmetry. The results show that increasing the degree of base density asymmetry generally has a destabilizing effect and that increasing base velocity asymmetry tends to be stabilizing. Furthermore, we show that increasing base density asymmetry slightly decreases the absolute frequency and that increasing the base velocity asymmetry slightly increases the absolute frequency. In addition, we show that increasing the degree of base density asymmetry distorts the most absolutely unstable hydrodynamic mode from its nominally sinuous structure. This distorted mode exhibits higher amplitude pressure and velocity oscillations near the interface with the smaller density jump than near the one with the bigger density jump. This would then be anticipated to lead to strongly non-symmetric amplitudes of flame flapping, with much stronger flame flapping on the side with lower density ratio. These predictions are shown to be consistent with experimental data. These comparisons support the analytical predictions that increased base density asymmetry are destabilizing and that hydrodynamic velocity fluctuation amplitudes should be greatest at the flame with the lowest density jump. (C) 2016 AIP Publishing LLC.
机译：本文探讨了非均匀平均密度，非对称平均密度和速度剖面的钝体尾流的水动力稳定性。这项工作是由实验[S. Tuttle等人，“不对称燃烧的钝体稳定火焰的稀薄吹气行为”，Combust。 Flame 160，1677（2013）]，研究了具有等价比分层的反应尾流，因此研究了基本流量密度曲线的不对称性。他们表明，高度分层的案例表现出强烈的窄带振荡，表明整体流体动力学不稳定。在本文中，我们对包括基流不对称在内的非均匀密度尾流进行了局部水动力稳定性分析。结果表明，增加基本密度不对称度通常会产生不稳定作用，而增加基本速度不对称性则趋于稳定。此外，我们表明，增加基本密度的不对称性会稍微降低绝对频率，而增加基本速度的不对称性会稍微增加绝对频率。此外，我们表明，增加基础密度的不对称程度会从其名义上的曲折结构扭曲最绝对不稳定的流体动力模式。这种畸变模式在密度跳跃较小的界面附近比在密度跳跃较大的界面附近具有更高的振幅压力和速度振荡。然后可以预料这将导致火焰扑动的幅度非常不对称，而密度比较低的一侧的火焰扑动会更强。这些预测显示与实验数据一致。这些比较支持以下分析预测：增加的基本密度不对称会破坏稳定性，并且流体动力学速度波动幅度应在密度跳跃最低的火焰处最大。 （C）2016 AIP出版有限责任公司。

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