Laminar Flame Edge Dynamics: A Level Set Approach

1. Laminar flame edge dynamics A level set approach Luiza Bondar, Andreas Class(*), Jan ten Thije Boonkkamp, Ronald Rook, Bob Mattheij (*) Institute for Nuclear and Energy Technologies, Forschungszentrum Karlsruhe, Germany

2. Combustion noise Laminar premixed flames • low NOx emission • combustion noise perturbed gas velocity (acoustic perturbation)

3. Combustion noise Transfer function velocity heat release rate

4. Combustion noise Flame Transfer Function (TF) To date the time delay in the flame TF is not yet fully understood experimental data by Viktor Kornilov

5. Combustion noise • understand the TF behaviour • separate different physical phenomena that occur • in flame acoustics interaction • variation of the flame front area • variation of burning velocity due to flame curvature and flow strain • effect of the flame on the flow • near rim phenomena (movement of the flame edge) • study their contribution to flame TF

6. G-equation model Fundamental assumptions burnt gasG>G0 • flame is a thin layer (flame front) • flame is attached at the burner rim flame frontG=G0 G-equation unburnt gasG<G0 area heat release transfer function

7. TF ≈ first order system, no time delay G-equation model analytical models ( Ducruix (2000), Fleifil (1996) ) • flame attachment • no feedback of the flame on the flow • very long flames • burning velocity with constant direction

8. G-equation model Detailed analytical study on the Bunsen flame dynamics results: • analytic solutions for the transient positions of the flame front (perturbed and unperturbed situations) • qualitative information on the stabilisation time • dependence of the boundary conditions on the flow speed and on the laminar burning speed • extension of previous theoretical models: improvement of flame description close to the burner rim improvement of the flame transfer function Bondar(2005, 2006)

9. G-equation model /Comparison with experiments attached flame real boiler situation flow flow flame flame edge trajectory V.Kornilov (2006)

10. extend the G-equation model to account for the flame edge dynamics G-equation model /Comparison with experiments oscillating ring (attached flame) theoretical model (attached flame) oscillating jet (real boiler situation) oscillating ring oscillating jet effect theoretical model flame attachment yes yes no feed back on the flow no no yes

11. Solutions motion of the flame edge normal to the flame front use extended model for (*) along the flame front new modelSE=c(Tedge-Textinction) SL • 2)extended the level set method(for dynamic open curves with moving ends) (*) extended unified model of flames as gasdynamics discontinuities, by A.G. Class, Y. Bronner and B.J. Matkowsky ) G-equation model /Extension Problems 1) motion of the flame edge - controlled by : heat loss & variations in the flame stretch 2)in2D the flame front becomes an open curve the classical level set method can not be applied directly

12. F<0 F>0 flame dynamics evolution equation for G evolution equation for F G-equation model /Extension use 2 level sets to define the flame front / P. Smereka, 2000 edge = points at which at time t=0, SL has a certain value extended G = continuous prolongation of G beyond the edge points G>0 C scalar F = cuts extended G at the edge points G<0 the flame front C is defined by C={x| G(x)=0 and F(x)<0}

13. Orthogonalisation process • replace F with F such that • FG= edge and F G F G>0 C F<0 90o G<0 F>0 steady state F = G-equation model /Extension G F

14. Solution method • to track the evolution of the flame front: the level set method applied separately for F& G • 5th order WENO schemes (Essentially Non Oscillatory) with LLF (SLLF) technique • 3rd order accurate TVD RK timeintegration • coupled reinitialisation - orthogonalisation G-equation model /Extension G-equation model /Extension Test problem • given flow - incompressible and not affected by the flame • temperature equation solved on the lines normal • to the flame front

15. G-equation model /Extension model experiment experimental data by Viktor Kornilov

16. http://www.em2c.ecp.fr Laboratoire Energtique Moleculaire et Macroscopique, Combustion, E.M2.C G-equation model /Extension 1) retains all properties of the classical model • predicts accurately the flame shape and flame dynamics • handles cusping and breaching of the flame front 2) captures the movement of the edge 3) takes into account the dependency of the burning velocity on temperature 4)extension from 1 flame to an array of flames is possible

17. Combustion model Preliminary results

18. Combustion model • extension of the level set method to allow for open curves with moving edges • gives combustion variables without solving the reaction layer • the only “thin layer model” that captures the edge dynamics • allows to switch off(on) various physical phenomenae

19. Conclusions • Analytic results lead to extension of the classical G-equation model • New, extended flame model based on two level-set functions • The extended model allows for an accurate description of the flame edge dynamics • Outlook • Couple the two-level set functions code with the flow code

20. Acknowledgements (random order) Bob Mattheij Jos Jansen Sorin Pop Ronald Rook Bas van der Linden Paul de Haas Pavel Kagan Philip de Goey Koen Schreel Viktor Kornilov Jan ten Thije Boonkkamp Andreas Class Yvan Bronner Jos Maubach Hennie ter Morsche