Stratified turbulent Bunsen flames: flame surface analysis and flame surface density modelling

Abstract

In this paper it is investigated whether the Flame Surface Density (FSD) model, developed for turbulent premixed combustion, is also applicable to stratified flames. Direct Numerical Simulations (DNS) of turbulent stratified Bunsen flames have been carried out, using the Flamelet Generated Manifold (FGM) reduction method for reaction kinetics. Before examining the suitability of the FSD model, flame surfaces are characterized in terms of thickness, curvature and stratification.

All flames are in the Thin Reaction Zones regime, and the maximum equivalence ratio range covers 0.1⩽φ⩽1.3. For all flames, local flame thicknesses correspond very well to those observed in stretchless, steady premixed flamelets. Extracted curvature radii and mixing length scales are significantly larger than the flame thickness, implying that the stratified flames all burn in a premixed mode. The remaining challenge is accounting for the large variation in (subfilter) mass burning rate.

In this contribution, the FSD model is proven to be applicable for Large Eddy Simulations (LES) of stratified flames for the equivalence ratio range 0.1⩽φ⩽1.3. Subfilter mass burning rate variations are taken into account by a subfilter Probability Density Function (PDF) for the mixture fraction, on which the mass burning rate directly depends. A priori analysis point out that for small stratifications (0.4⩽φ⩽1.0), the replacement of the subfilter PDF (obtained from DNS data) by the corresponding Dirac function is appropriate. Integration of the Dirac function with the mass burning rate m=m(φ), can then adequately model the filtered mass burning rate obtained from filtered DNS data. For a larger stratification (0.1⩽φ⩽1.3), and filter widths up to ten flame thicknesses, a β-function for the subfilter PDF yields substantially better predictions than a Dirac function. Finally, inclusion of a simple algebraic model for the FSD resulted only in small additional deviations from DNS data, thereby rendering this approach promising for application in LES.

Keywords:

• turbulent combustion
• stratification
• flame surface density model
• direct numerical simulation
• flamelet generated manifold

Acknowledgements

This work received funding from the European Community through the project TIMECOP-AE (project AST5-CT-2006-030828). It reflects only the authors’ views and the Community is not liable for any use that may be made of the information contained herein. Parallelisation of the DNS code has been performed by John Donners from SARA under Project HPC-EUROPA (211437), with the support of the European Community – Research Infrastructure Action under the FP8 ‘Structuring the European Research Area’ Program. The authors would like to thank the Dutch Technology Foundation (STW) under Grant No. SH-178-10 and the support of NCF, the Netherlands Computing Facilities Foundation. Rob Bastiaans of the authors’ Combustion Technology Group is acknowledged for fruitful discussions that resulted in a better understanding of the numerical results.