Impact of Combustion Modeling on the Spectral Response of Heat Release in LES

ABSTRACT

This work assesses the effect of using different closure concepts for the spatially filtered mean reaction rate on the resolved spectral response of turbulent heat release in large eddy simulations (LESs). Two well-known combustion models, the turbulent flame speed closure (TFC) and the dynamically thickened flame (DTF) models have been applied to a premixed turbulent jet flame with otherwise identical numerical setups. Although the flame front is artificially thickened in the DTF model, it reproduces a thinner flame and, hence, stronger flame–turbulence interactions compared to the TFC model. As the time-averaged quantities from both methods are comparable, the DTF approach shows overall higher fluctuations of local and integral heat release rates in the spectral domain compared to the TFC model, particularly in the high-frequency range. A better agreement with measured sound pressure density is observed for TFC in the low-frequency range and for DTF in the high-frequency range. TFC simulations with different source formulations, that is, ${\overline{\dot{\omega }}}_c\propto \tilde{c}(1-\tilde{c})and{\overline{\dot{\omega }}}_c\propto |\nabla \tilde{c}|$, showed comparable flame thicknesses and spectra of heat release, but the averaged flow quantities calculated with ${\overline{\dot{\omega }}}_c\propto |\nabla \tilde{c}|$, however, deviate largely from measured data for the current setup. In the second step, the same formulations for the mean rate are applied to an excited plane-jet flame (two-dimensional (2D)) using equidistant grid cells and forced inflow conditions, thereby excluding the influence of varying grid resolution and broadband turbulent fluctuations. This setup is specifically tailored for a detailed analysis of flame response to flow unsteadiness and grid resolution. The formulation of the reaction rate according to the TFC approach again results in a considerably thicker flame compared to results obtained from the DTF model and direct numerical simulation, even on a sufficiently fine mesh. Therefore, the DTF formulation of the reaction rate shows overall stronger responses of heat release rates to forced fluctuations than the TFC formulation. Differences are smaller in the low-frequency range, indicating a stronger damping of heat release fluctuations with increasing frequency for the TFC formulation. Coarsening the grid leads to a much stronger damping of heat release fluctuations in the DTF formulation compared with the TFC formulation, so that the benefit of the DTF formulation decreases with decreasing grid resolution. This reflects the different sensitivity behavior of these models with respect to unsteady flows and grid resolutions, which is of great importance for computing thermoacoustic problems with LES, for example, combustion noise.

KEYWORDS:

• Large eddy simulation
• turbulent premixed flame
• turbulent flame speed
• thickened flame approach
• OpenFOAM

Acknowledgments

This work was supported by the German Research Council (DFG) through Research Units Bo 693/26-2 and DFG-PA920/12. The authors thank for the financial support from the Helmholtz Association of German Research Centres (HGF) through the Research Unit EMR as well as the computing resources provided by the High Performance Computing Center Stuttgart (HLRS) at the University of Stuttgart and the Steinbuch Centre for Computing (SCC) at the Karlsruhe Institute of Technology.

Additional information

Funding

This work was supported by the Deutsche Forschungsgemeinschaft [Bo 693/26-2 and DFG-PA920/12];Helmholtz-Gemeinschaft [EMR].