Modeling and Simulation of Axisymmetric Stagnation Flames

Laminar flame modeling is an important element in turbulent combustion research. The accuracy of a turbulent combustion model is highly dependent upon our understanding of the laminar flames and their behavior in many situations. How much we understand various phenomena can only be measured by a model that describes the phenomena and by how well the model describes and predicts them. One of the most commonly used methane combustion models is GRI-Mech 3.0. However, how well the model describes the reacting flow phenomena is still uncertain, even after many attempts to validate the model or quantify uncertainties. This is because, in flames, chemisty is coupled with fluid mechanics, thermodynamics, and transport process, and the separation of one from another is not easy, if at all possible.;In the present study, the behavior of laminar flames under different aerodynamic and thermodynamic conditions is studied numerically in a stagnation-flow configuration. The present study follows an experimental study by J. Bergthorson conducted earlier in our group. In numerical study of reacting flows, a one-dimensional model is commonly used to assess the performances of chemical kinetics models. The model describes stagnation flames along the symmetric axis through several key assumptions. One such assumption is a uniform pressure-eigenvalue assumption, i.e., that the curvature of the pressure field is uniform throughout. Although it is shown that this assumption does not hold through more sophisticated numerical studies capable of a two-dimensional description, it is shown that the model works reasonably well in the case of non-reacting (cold) flow and diluted hydrogen flames. However, how well the assumption holds and whether or not the model approximates hydrocarbon flames well are not known. The present study employs the full chemical kinetics model of methane combustion, and a realistic transport model that accommodates differential-diffusion effects within an axisymmetric two-dimensional flow modeling. This allows direct comparisons of two-dimensional and one-dimensional models, as well as numerical and experimental data, to quantify modeling errors that arise from the use of one-dimensional hydrodynamics model and the chemical-kinetics model.;In order to make such a numerical study possible, the spectral element method is reformulated to accommodate the large density variations in methane reacting flows. In addition, a new axisymmetric basis function set for the spectral element method that satisfies the correct behavior near the axis is developed that avoids the well-known singular behavior there. This basis function satisfies all the parity requirements, by construction, that axisymmetric fields must meet. To accomodate computationally expensive detailed methane combustion and transport models, efficient integration techniques are developed to accurately model axisymmetric reacting flow within a reasonable amount of computational time. The numerical method is implemented using an object-oriented programming technique, and the resulting computer program is verified with several different methods.;First, cold-flow simulation is conducted to understand the nature of the underlying flow field without chemical reactions. It is shown that detailed modeling of the experimental apparatus is important for a direct comparison of numerical simulation and experiments to be meaningful.;Reacting flow simulations are conducted in three phases: one-dimensional simulations by Cantera, two-dimensional simulations with an idealized representation of the experimental configuration, and finally, simulations with full details of experimental setup. It is shown that, although the plug-flow boundary condition cannot be used, as is, to predict flame locations, the model can reliably be used to predict flame speed under strain. Through a direct simulation of laboratory flames that allows direct comparison to experimental data, the present study then shows variances with the commonly used GRI-Mech 3.0 chemical kinetics model. It is shown that the methane combustion model based on GRI-Mech 3.0 works well for methane-air mixtures near stoichiometry. However, GRI-Mech 3.0 leads to an overprediction of laminar flame speed for lean mixtures and an underprediction for rich mixtures. This result is slightly different from conclusions drawn in previous work, in which experimental data are compared with a one-dimensional numerical solution. Detailed analysis reveals that flame speed is sensitive to even slight flame front curvature as well as to its finite extension in the radial direction. Neither of these can be incorporated in one-dimensional flow modeling.