Development of a multi-scale projection method with immersed boundaries for chemically reactive flows and its application to examine flame stabilization and blow-off mechanisms

Abstract

High-fidelity multi-scale simulation tools are critically important for examining energy conversion processes in which the coupling of complex chemical kinetics, molecular transport, continuum mixing and acoustics play important roles. The objectives of this thesis are: (i) to develop a state-of-the-art numerical approach to capture the wide spectra of spatio-temporal scales associated with reacting flows around immersed boundaries, and (ii) to use this tool to investigate the underlying mechanisms of flame stabilization and blow-off in canonical configurations. A second-order immersed boundary method for reacting flow simulations near heat conducting, grid conforming, solid object has been developed. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a semi-implicit operator-split projection algorithm. The immersed boundary approach captures the flame-wall interactions. The SAMR framework and the operator-split algorithm resolve several decades of length and time efficiently. A novel "buffer zone" methodology is introduced to impose the solid-fluid boundary conditions such that symmetric derivatives and interpolation stencils can be used throughout the interior of the domain, thereby maintaining the order of accuracy of the method. Near an immersed solid boundary, single-sided buffer zones are used to resolve the species discontinuities, and dual buffer zones are used to capture the temperature gradient discontinuities. This eliminates the need to utilize artificial flame anchoring boundary conditions used in existing state-of-the-art numerical methods. As such, using this approach, it is possible for the first time to analyze the complex and subtle processes near walls that govern flame stabilization. The approach can resolve the flow around multiple immersed solids using coordinate conforming representation, making it valuable for future research investigating a variety of multi-physics reacting flows while incorporating flame-wall interactions, such as catalytic and plasma interactions. Using the numerical method, limits on flame stabilization in two canonical configurations: bluff-body and perforated-plate, were investigated and the underlying physical mechanisms were elucidated. A significant departure from the conventional two-zone premixed flame-structure was observed in the anchoring region for both configurations. In the bluff-body wake, the location where the flame is initiated, preferential diffusion and conjugate heat exchange furnish conditions for ignition and enable streamwise flame continuation. In the perforated-plate, on the other hand, a combination of conjugate heat exchange and flame curvature is responsible for local anchoring. For both configurations, it was found that a flame was stable when (1) the local flame displacement speed was equal to the flow speed (static stability), and (2) the gradient of the flame displacement speed normal to its surface was higher than the gradient of the flow speed along the same direction (dynamic stability). As the blow-off conditions were approached, the difference between the former and the latter decreased until the dynamic stability condition (2) was violated. The blowoff of flames stabilized in a bluff-body wake start downstream, near the end of the combustion-products dominated recirculation zone, by flame pinching into an upstream and a downstream propagating sections. The blow-off of flames stabilized in flow perforated-plate wake start in the anchoring region, near the end of the preheated reactants-filled recirculation zone, with the entire flame front convecting downstream. These simulations elucidated the thus far unknown physics of the underlying flame stabilization and blow-off mechanisms, understanding which is crucial for designing flame-holders for combustors that support continuous burning. Such an investigation is not possible without the advanced numerical tool developed in this work. Based on the insight gained from the simulations, analytical models were developed to describe the dynamic response of flames to flow perturbations in an acoustically coupled environment. These models are instrumental in optimizing combustor designs and applying active control to guarantee dynamic stability if necessary.