REDIM reduced modeling of quenching at a cold wall including heterogeneous wall reactions

In this work, the Reaction-Diffusion-Manifold (REDIM) is applied for Flame-Wall-Interactions with heterogeneous wall reactions. There are two major issues that have to be considered: A reduced description that text captures transient regimes like flame quenching has to be generated, and the boundary condition for the reduced system that accounts for heterogeneous wall reactions has to be specified. Since the extinction at the wall is governed by at least two processes (chemical reactions and heat loss to the wall), a two-dimensional manifold is chosen for the reduced description to construct a REDIM which can handle heat loss and extinction. For solving the issue of the boundary conditions, two different types of boundaries have to be defined. The boundary condition for the wall is specified via a gradient estimate which is given via the surface reaction rate. For those boundaries, which are not defined as boundaries in physical space, the gradient guess is projected onto the tangential space of the manifold's boundary. Before solving the REDIM evolution equation, a spatial gradient estimate and an initial guess for the manifold have to be defined. Both are obtained from detailed sample solutions of the transient system, which were performed with the in-house program INSFLA. Afterwards, the REDIM evolution equation is integrated to the stationary state and the necessary data for subsequent simulations are stored in REDIM-tables. The problem of a head-on flame quenching at a cold wall is studied for premixed methane-air-flames at different pressures. In order to validate the reduced model, the generated REDIM-tables are used for computations with the same model configuration than the detailed computation, and species like CO are investigated as a function of the temperature T for different positions near the wall (such an investigation for experimental results was also carried out in Mann et al. for the pressure of 1 bar and the mass fraction of CO Mann et al., 2014). The reduced model reproduces the behavior of the extinction very well and both the detailed as well as the reduced simulations show a good agreement with the experimental results.