Resumen de Numerical simulation of turbulent diffusion flames using flamelet models on unstructured meshes
Jordi Ventosa Molina
The present thesis aims at developing numerical methods and algorithms for the efficient simulation of diffusion flames in the flamelet regime. To tackle turbulent chemically reacting flows a double framework is used in the present thesis. On the one hand, flow description is performed in the context of Large Eddy Simulation (LES) techniques. On the other hand, thermochemistry is modelled by means of flamelet models. The flamelet regime is characterised by the split of the combustion process into a flame structure case and flow transport case. Therefore, to study chemically reacting flows it is required an algorithm for computing variable density flows and a model to describe chemical kinetics. In order to accomplish these goals the thesis is divided into five chapters, each one describing and analysing a specific aspect of the required numerical methods. In first place, in Chapter 1 the basic formulation for describing chemically reacting flows is detailed. Chemical kinetics are briefly described and transport terms for multicomponent flows are detailed. Then, an introduction to turbulent combustion is performed, where the challenges of simulating these flows using finite rate kinetics are stated. It is then argued that specific models are required. Before proceeding to describe the combustion model, an algorithm for the simulation of variable density flows is described and studied in Chapter 2. Furthermore, the study revolves around the use of unstructured meshes. A temporal integration scheme, specifically a multi-step scheme, and two spatial discretisation schemes, namely collocated and staggered schemes, are described and studied. In Chapter 3 a flamelet model for the simulation of diffusion flames is described. First, the flamelet regime is described and the flame equations in mixture fraction space are presented. Then, a Flamelet/Progress-Variable model is used to fully describe the flame. The two main parameters of the model are the mixture fraction and the progress-variable. Additionally, a finite differences method for the solution of the flamelet equations is presented. Since the target flames are turbulent, assumed probability density functions are introduced in order to restate the flamelet solutions as stochastic quantities. The model allows precomputing the flame thermochemistry and storing it into a database, which is accessed during simulations in physical space. The next two chapters deal with the parameters used to represent the flamelet database. First, Chapter 4 studies the definition of the progress-variable, which is required to unambiguously represent the chemical state. The definition of this parameter has been reported to be case sensitive. The present work evidences a dependence on the diffusion model. Definitions found valid for Fickian diffusion are shown to result in non-monotonic distributions when differential diffusion is considered. Furthermore, in the chapter two detailed chemical mechanism are considered. Tests include a CH4/H2/N2 diffusion flame and a self-igniting CH4 flame, where the fuel issues into a vitiated coflow. In the latter case, chemical mechanisms are shown to play a central role in the prediction of the flame stabilisation distance. Lastly, when turbulent flames are considered, the flamelet database is stated as a function of stochastic parameters. Among them, the mixture fraction variance, which represents mixing at the subgrid level, requires modelling. Since chemical reactions in the flamelet regime occur at scales smaller than the Kolmogorov scale, the correct characterisation of subgrid mixing is a critical issue. Hence, in Chapter 5 different models for the evaluation of the subgrid variance are studied. The study case is the methane/hydrogen/nitrogen diffusion flame. The study shows that correct description of the subgrid mixing is critical in accurately predicting the flame stabilisation.
