Development of flamelet generated manifolds for partially-premixed flame simulations

Accuracy of simulations of combustion processes does not only depend on a meticulous description of the turbulent flow field, its accuracy and detail depends on the representation of combustion chemistry and its interaction with turbulence as well. Simulations with a high level of exactness are very time consuming due the large range in length- and timescales in turbulence and chemical kinetics. The contribution of solving the flow field to the computational cost can be reduced by only solving the major turbulent motions containing the largest part of the turbulent kinetic energy. In this method, the Large Eddy Simulation (LES) method, the influence of small, non-resolved eddies has to be modeled, but good models for this unresolved transport of momentum are readily available. Reducing the chemical kinetics is typically a more difficult job due to the large number of elementary (chemical) reactions to be taken into account and the associated stiffness of the system of equations due to the (very) large range in time scales. The Flamelet Generated Manifold (FGM) reduction method resolves this issue by the creation of a chemical manifold out of one-dimensional flame structures. These one-dimensional flame structures, called flamelets, are computed using detailed chemistry and are subsequently tabulated in composition space as a function of a small number of control variables. During a numerical simulation of a flame, only transport equations for the control variables have to be solved and these variables are typically chosen in a way that the stiffness of the resulting system of equations remains low. The FGM method can thus be interpreted as a combination of flamelet and manifold methods: the low-dimensional chemical manifold which is used in simulations of multi-dimensional flames is based of flame structures containing all transport and chemical phenomena as observed in real-life. A small number of archetypical flamelet types exist of which the premixed and counterflow diffusion are used most commonly. They represent premixed and non-premixed flames, two limiting combustion modes. Partially-premixed combustion is considered to occur somewhere between these two types and no archetypical flamelet type exists for stratified combustion. This doctoral dissertation focusses on the following main research question: Can partially-premixed combustion be adequately modeled by FGM tables based on premixed flamelets, counterflow diffusion flamelets or a combination of both types? The use of the FGM reduction method already can reduce computational costs with a few orders of magnitude [?], but the requirement that the reaction layer should be resolved still claims a large number of grid points in the simulation of turbulent flames. The Flame Surface Density (FSD) model allows much coarser grids to be used, but this method has been specifically defined for premixed flames. In chapter 3 it is shown that the FSD approach can also be used in partially-premixed flames having stratification levels as typically observed in gas turbines. Direct Numerical Simulations (DNS) of turbulent planar Bunsen flames was enabled by the use of the FGM method. A priori analysis of the DNS results indicate that simple Presumed PDF subfilter models for the filtered mass burning rate yield fairly accurate predictions when filter widths of up to eight flame thicknesses are used. The implementation of the FSD model using mass burning rate data from flamelets can therefore be considered to be a feasible possibility for the simulation of turbulent stratified flames in an industrial environment. In chapter 4 the focus shifts from flames with only a moderate stratification towards flames with a larger range of equivalence ratios: the well-documented Sandia Flames. For CO, CO2, H2, H2O and OH mass fractions, a priori comparisons are made with experimentally obtained data from flames with Reynolds numbers ranging from 13.400 for the moderately turbulent Flame C to 44.800 for Flame F in which local quenching plays an important role. It is concluded that counterflow diffusion flamelet-based FGM’s prove to be significantly more accurate than premixed-based ones for H2, CO2 and CO mass fraction predictions. For fuel-rich conditions, premixed flamelet-based FGM’s tend to severely overestimate H2 and CO mass fractions while underestimating CO2 mass fractions. Preferential diffusion effects were only visible at low Reynolds numbers and close to the burner nozzle: in general the unit Lewis number assumption is an appropriate one for these flames. Where all numerical and modeling errors in the Computational Fluid Dynamics (CFD) simulations have been excluded in the a priori analysis in chapter 4, in chapter 5 these are taken into account as well in LES of Sandia Flame D and F. Simulation results appear to be very sensitive to boundary conditions for turbulent velocity fluctuations. However, when outcomes for the reaction progress variable, H2 and CO are viewed in composition space, a fairly good resemblance with experimental results is obtained. Using additional transport equations for H2 and CO instead of interpolating them directly from the FGM table does not improve results. A priori predictions of H2 and CO do show a significant improvement in accuracy compared to LES results. It can be concluded that tabulated FGM chemistry can yield accurate predictions even for difficult species like H2 and CO, provided that the CFD solver predicts control variable fields with high accuracy. For all flames considered in chapters 3 and 5 the type of flamelets to use for the generation of the FGM table was clear, either from literature or from a priori analysis. Chapter 6 tackles the question whether FGM tables based on either premixed or non-premixed flamelets can be combined for the simulation of partially-premixed flames. In many industrially-relevant flames, it is simply not known beforehand which flamelet type is most applicable and therefore an adaptive method is highly desirable. For the two species this dissertation focusses on, H2 and CO, the combination of two FGM tables by means of the proposed smooth transition function does not yield the desired results. Predictions for H2 and CO do not consistently improve when the combined FGM approach is used, although often the results are better then those obtained with the least applicable FGM table. Like in chapter 5, additional transport equations for H2 and CO in which the chemical source term comes from the combination of FGM tables does not improve results either. It can be concluded that the FGM method is a powerful tool which renders DNS and LES of complex flames possible. Without this reduction method, simulations discussed in chapter 3 and 5 would have taken amounts of computational resources which are simply not available. The FGM method obtains accurate predictions for species mass fractions, of which H2 and CO are mainly treated in this dissertation, provided that control variables are accurately predicted by the CFD solver and appropriate assumptions are made for the flamelets from which the FGM table is created. This aspect however, requires a certain insight in combustion physics implying that using the FGM method in partially-premixed flames is not yet "plug-and-play".