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

Combustion noise low NOx emissioncombustion noise

perturbed gas velocity(acoustic perturbation)Laminar premixed flames

Combustion noise velocity heat release rateTransferfunction

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

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 GG0

flame front G=G0

G-equationflame is a thin layer (flame front)flame is attached at the burner rim Fundamental assumptions areaheat release

transfer function

G-equation model analytical models ( Ducruix (2000), Fleifil (1996) ) flame attachment no feedback of the flame on the flowvery long flamesburning velocity with constant direction

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 functionBondar(2005, 2006)

results:

G-equation model /Comparison with experimentsreal boiler situationattached flameedge trajectoryflameflowflameflowV.Kornilov (2006)

oscillating ring (attached flame)oscillating jet (real boiler situation)nononofeed back on the flowyesyesyesflame attachmenttheoreticalmodel

oscillating ring

oscillating jet

effectG-equation model /Comparison with experimentstheoretical model (attached flame)

G-equation model /Extension 1) motion of the flame edge - controlled by : heat loss & variations in the flame stretch2) in 2D the flame front becomes an open curve the classical level set method can not be applied directly Problems

G-equation model /Extensionthe flame front C is defined by C={x| G(x)=0 and F(x)0G

G-equation model /ExtensionFG

G-equation model /ExtensionG-equation model /ExtensionTest problemgiven flow - incompressible and not affected by the flame

temperature equation solved on the lines normal to the flame front

G-equation model /Extensionexperimentmodelexperimental data by Viktor Kornilov

G-equation model /Extension1) retains all properties of the classical model predicts accurately the flame shape and flame dynamicshandles 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

Combustion modelPreliminary 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

ConclusionsAnalytic 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 MattheijJos JansenSorin PopRonald RookBas van der LindenPaul de HaasPavel KaganPhilip de Goey

Koen SchreelViktor KornilovJan ten Thije BoonkkampAndreas ClassYvan BronnerJos MaubachHennie ter Morsche