Implementation of REDIM reduced chemistry to model an axisymmetric laminar diffusion methane–air flame

Abstract

The goal of this work is to analyze the use of automatically reduced chemistry by the Reaction–Diffusion Manifold (REDIM) method in simulating axisymmetric laminar coflow diffusion flames. Detailed chemical kinetic models are usually computationally prohibitive for simulating complex reacting flows, and therefore reduced models are required. Automatic reduction model approaches usually exploit the natural multi-scale structure of combustion systems. The novel REDIM approach applies the concept of invariant manifolds to treat also the influence of the transport processes on the reduced model, which overcomes a fundamental problem of model reduction in neglecting the coupling of molecular transport with thermochemical processes. We have considered a previously well studied atmospheric pressure nitrogen-diluted methane–air flame as a test case to validate the methodology presented here. First, one-dimensional and two-dimensional REDIMs were computed and tabulated in lookup tables. Then, the full set of governing equations are projected on the REDIM and implemented in the object-oriented C++ Gascoigne code with a new add-on library to deal with the REDIM tables. The projected set of governing equations have been discretized by the Finite Element Method (FEM) and solved by a GMRES iteration preconditioned by a geometric multigrid method. Local grid refinement, adaptive mesh and parallelization are applied to ensure efficiency and precision. The numerical results obtained using the REDIM approach have shown very good agreement with detailed numerical simulations and experimental data.

Keywords:

• automatically reduced chemistry
• reaction–diffusion manifold
• axisymmetric laminar coflow diffusion methane–air flames
• finite element method
• adaptive mesh

Acknowledgments

This work is a result of a joint project between the Interdisciplinary Center for Scientific Computing of the University of Heidelberg and the Graduate Program in Applied Mathematics of the Federal University of Rio Grande do Sul. Pedro Henrique de Almeida Konzen is grateful to Prof. Dr. Álvaro Luiz de Bortoli for making this project possible. This author is also grateful for financial support from the Deutscher Akademischer Austausch Dienst (DAAD).