Computational Studies of Flame - Flow Interactions

One of the major problems in turbulent combustion is to predict the turbulent burning velocity, which can be increased by the turbulence compared to the laminar burning velocity. This requires the solution to a reacting ow problem, where the turbulence is coupled to the chemical reaction. The diculties lie in the fact that many disparate spatial and temporal scales are present in the convection-reaction-diusion system. The investigator studies several simplied ame/ BLOCKINow interactions, where uid ows have separate large and small scales. The particular aspects considered are the diminished enhancement of turbulent burning velocity when the turbulence intensity is increased above a certain value (the bending phenomenon), and the onset of ame quenching when the turbulence is too strong. The focus is on the often ignored interaction between small scale uid ow and chemical reaction. The approach is to solve the system in two stages: (1) a small scale problem is solved with full interaction between chemistry and uid ow to generate the local burning velocity, which can be quite dierent from the laminar burning velocity; (2) at the large scale level, this local burning velocity is used, together with the large scale uid velocity, to move the ame front, where it is treated as an interface. The turbulent burning velocity is then estimated and the bending phenomenon is analyzed. The investigator uses the projection method for viscous uid and implicit second-order upwind nite dierence methods for the chemical reaction or the front evolution respectively, at two dierent scale levels. The objective is to assess the eects of small scale uid ows on the turbulent burning velocity when the turbulent intensity is large. In another project, the investigator develops a free boundary formulation to model an experiment for chemical fronts propagating in a Hele-Shaw cell, under buoyancy eects. In this model, a mechanism that produces ngers that are dierent from those in the classic viscous ngering phenomenon is identied. The objective is to obtain the wavelength criterion for the ngers which is distinctive in the experiment. The investigator uses a potential theory formulation to solve a simplied model and the level set (G-equation) formulation to solve a more complete model. A method for the evolving temperature that captures its correct jumps across the front is developed. The wavelength of the ngers are important for understanding ame instability caused by buoyancy eects.