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

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.