Towards a classification of models for the numerical simulation of premixed combustion based on a generalized regime diagram

The inner structure, and the physical behaviour of turbulent premixed flames are usually described, and classified by means of the regime diagram introduced by Borghi and Peters. Thereby properties related to both the flame and the (turbulent) flow are considered. In this work a diagram valid for all physical regimes, comprising suitable requirements for laminar simulations, direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds averaging based numerical simulation (RANS) is proposed. In particular the diagram describes essential situations within the validity limits of the “Borghi, Peters diagram” which physical phenomena are resolved by the simulation, and which have to be modelled. This information is used for systematic classification of various models by suggesting specific models that are appropriate depending on the regime and numerical resolution, and may provide guidance for numerical simulation methods and model development in turbulent premixed combustion. This might help users as a guideline in choosing appropriate models for a given device, and numerical effort available. The regime diagram suggested by Pitsch and Duchamp de Lageneste, which includes DNS and LES by explicitely accounting for the numerical related variable filterwidth, emerges here as one of the special two-dimensional cases possible. In contrast to the generalized regime diagram, their diagram does not include laminar simulations, and RANS based considerations, while transition between wrinkled and corrugated flamelets is not clearly established.

Keywords:

• Premixed combustion
• Generalized regime diagram
• Numerical requirements

Acknowledgements

The authors gratefully acknowledge the financial support by the German Research Council (DFG) through “Graduiertenkolleg Modellierung und numerische Beschreibung technischer Strömungen”, and Collaborative Research Center SFB 568 “Flow and Combustion in Future Gas Turbine Combustion Chambers”.

Notes

^‡Consequences of a variable Schmidt number on regime diagrams are outlined in the appendix.

^§CPB: Cant, Pope, Bray, CFM: Coherent Flame Model, Mb: Mantel and Borghi, Cd: Cheng And Diringer.

^¶An exception is given by the MB-model. All terms on the right hand side of (17) are modelled proportional to turbulent quantities, Σ reduces to a passive scalar, which cannot represent the flamefront.