A local integral model of chemically reacting flows, including finite rate effects.

A new local integral model for simulating molecular mixing and chemical reactions in complex flows has been developed and tested. This model is based entirely on the fact that, for small values of the dimensionless diffusivity, gradients tend to concentrate in locally one-dimensional structures. A local parabolization of the governing equations leads to a canonical set of local integral equations for the gradient quantities on a material surface. The governing transport equations are thus reduced from partial differential equations to ordinary differential equations. The underlying approximation becomes increasingly accurate as the Reynolds, Schmidt, and Damkohler numbers increase in precisely this range of parameters in which direct simulations become impractical and in which traditional modeling approaches based on non-physical assumptions become unreliable. Here, this local integral method has been applied to three broad types of problems involving molecular mixing and chemical reactions. Unsteady strained diffusion-reaction layers undergoing one-step temperature-dependent finite rate chemistry are simulated and compared to full finite difference calculations. The model was also coupled with a flow field simulation to allow explicit calculation of a one-step reaction with temperature-dependent kinetics in a time-evolving shear layer. Global quantities compare well with finite difference results and remarkably, even structural features of these fields agreed well with the simulations. Lastly, the model was coupled with complex equilibrium and non-equilibrium reaction chemistries through conserved scalar formulations.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/103920/1/9423157.pdfDescription of 9423157.pdf : Restricted to UM users only