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

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

Combustion noise velocity heat release rate Transfer function

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

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 understand the TF behaviour  separate different physical phenomena that occur in flame acoustics interaction

G-equation model unburnt gas G<G 0 burnt gas G>G 0 flame front G=G 0 G-equation flame is a thin layer (flame front) flame is attached at the burner rim Fundamental assumptions area heat release transfer function

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 TF ≈ first order system, no time delay

G-equation model Detailed analytical study on the Bunsen flame dynamics  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) results:

G-equation model /Comparison with experiments real boiler situationattached flame edge trajectory flame flowflameflow V.Kornilov (2006)

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

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

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

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

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 to track the evolution of the flame front: the level set method applied separately for F& G Solution method 5th order WENO schemes (Essentially Non Oscillatory) with LLF (SLLF) technique 3rd order accurate TVD RK time integration coupled reinitialisation - orthogonalisation

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

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 Laboratoire Energtique Moleculaire et Macroscopique, Combustion, E.M2.C

Combustion model Preliminary results

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

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

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