Stability Analysis of Multiple Reacting Wakes

摘要

Hydrodynamic instabilities in reacting shear flows control a variety of combustion system phenomena, such as combustion instabilities, mixing and entrainment, and blow off. A large body of literature exists pertaining to the dynamics of single "element" (e.g., jets, wakes) hydrodynamics, but not on the multi-element systems that are often found in combustion applications. The objective of this work is to investigate the stability of multiple reacting wakes, simulating the arrays of bluff body stabilized flames which are routinely used in applications. Spatio-temporal stability analyses are conducted on model velocity and density profiles, with key parameters being the density ratio across the flame, the backflow ratio (or shear ratio) and wake spacing. In the case of an unconfined single planar wake, the most absolutely unstable mode is always sinuous (asymmetric). In contrast, the most absolutely unstable mode in a single planar jet is varicose (symmetric). However, in the case of the two wake system, the most absolutely unstable mode may be either sinuous or varicose. Interestingly, the maximum absolute growth rate varies non-monotonically as wake separation distance is varied, which is associated with a mode switching between the sinuous and varicose modes. The behavior of the multi-wake system converges to that of the single bluff body system in the two limits of large or small spatial separation. These results demonstrate the important, but non-monotonic, dependence of flameholder separation distance and flame density ratio on the dynamics of combustion systems.