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G-equation modelling of thermo-acoustic oscillations of partially-premixed flames

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Semlitsch, Bernhard  ORCID logo
Orchini, A 
Dowling, AP 
Juniper, MPJ 


Numerical simulations aid combustor design to avoid and reduce thermo-acoustic oscillations. Non-linear heat release rate estimation and its modelling are essential for the prediction of saturation amplitudes of limit cycles. The heat release dynamics of flames can be approximated by a Flame Describing Function (FDF). To calculate an FDF, a wide range of forcing amplitudes and frequencies needs to be considered. For this reason, we present a computationally inexpensive level-set approach, which accounts for equivalence ratio perturbations on flames with arbitrarily-complex shapes. The influence of flame parameters and modelling approaches on flame describing functions and time delay coefficient distributions are discussed in detail. The numerically-obtained flame describing functions are compared with experimental data and used in an acoustic network model for limit cycle prediction. A reasonable agreement of the heat release gain and limit cycle frequency is achieved even with a simplistic, analytical velocity fluctuation model. However, the phase decay is over-predicted. For sophisticated flame shapes, only the realistic modelling of large-scale flow structures allows the correct phase decay predictions of the heat release rate response.



Thermoacoustic instability, non-linear combustion modelling, flame describing function, equivalence ratio perturbation

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International Journal of Spray and Combustion Dynamics

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European Commission (641453)
This work was conducted within the EU 7th Framework Project Joint Technology Initiatives - Clean Sky (AMEL- Advanced Methods for the Prediction of Lean-burn Combustor Unsteady Phenomena), project number: JTI-CS-2013-3-SAGE- 06-009 / 641453. This work was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (, provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and funding from the Science and Technology Facilities Council.