Dr. Alessandra Bigongiari Study of instabilities in a BRS burner using a Green’s Function Approach Dr. Alessandra Bigongiari

Introduction: the method Analysis of the combustion instabilities in a BRS burner combining the Green’s function method with CFD simulations: FLAME RESPONSE TO PERTURBATIONS Flame Describing Function Reflection coefficients Reflection coefficients Integral Equation Q,G Acoustic field u Q(t,τ) Green’s function Q (u) from FDF

ωn=resonant frequencies Green’s function Response of the system to a point source located in x’ and firing at t’ ωn=resonant frequencies Tailored: same boundary conditions as the acoustic field Modal amplitudes gn and frequencies ωn are calculated for the BRS L GOVERNING EQUATION g1

Integral equation & heat release model Integral equation derived from: Governing equation for G Acoustic Analogy equation Integral equation derived from: Governing equation for G Acoustic Analogy equation Numerical Iteration FDF calculated from the model Heat release model Time-lag distribution Tailored green function Heat release law: FEEDBACK Low pass filter behaviour

FDF from full CDF simulations (3D) 3D Simulations performed by Dmytro Iurashev, in the OpenFOAM environment -Different values of the perturbation amplitudes A/U(%) -Wiener Hopf Inversion and single frequency method (for high perturbation amplitudes) Tailored green function Heat release law: FEEDBACK Fit using the FDF from our model

Heat release law: FEEDBACK STABILITY MAPS Stability map for the control parameter L (total length). Green=unstable, White=stable Gaussian time-lag distribution Other parameters Sratio = 0.13 (ratio of cross-sectional areas) xj =0.16m (position of the temperature jump) xq = 0.21m (flame position). R0=1 (rigid end), RL =-1(open end) Heater power/mass flow Tailored green function Heat release law: FEEDBACK Discrete time-lag distribution

LOSSES Stability map for the control parameter L (total length). Green=unstable, White=stable Gaussian time-lag Distribution RL=-0.9 Other parameters Sratio = 0.13 (ratio of cross-sectional areas) xj =0.16m (position of the temperature jump) xq = 0.21m (flame position). R0=1 (rigid end) Heater power/mass flow Tailored green function Gaussian time-lag Distribution RL=-0.576-i0.491.

Validation Validation is still in progress. First results show that the system is more stable than map predictions. P(x=21 cm)~Flame position Initial condition lInf=10cm Tailored green function Gaussian time-lag Distribution RL=-0.576-i0.491.

CONCLUSIONS & WORK IN PROGRESS We have produced stability maps for a BRS burner using a Flame Describing Function extracted from full CFD simulations. We have used a heat release model with a distribution of time-lags and produced stability maps. We are studying a different heat release model introducing a distribution for the time-lags where 2 time-lags are considered. Further analysis of losses (described by reflection coefficients) is in progress.

THANKS FOR YOUR ATTENTION The presented work is part of the Marie Curie Initial Training Network Thermo-acoustic and aero-acoustic nonlinearities in green combustors with orifice structures (TANGO). We gratefully acknowledge the financial support from the European Commission under call FP7-PEOPLE-ITN-2012.

My new research topic in Pisa… Instabilities in an optical cavity (with a laser), generated by the delayed response (dilatation) of an irradiated membrane. Pictures represent the instabilities in the transmitted field (green) and the oscillations at the membrane surface (blue)

My new research topic in Pisa… Cavity resonance λ=nL before expansion λ’=n(L-dL) after exp. Ligth cause the thermal expansion of the membrane in a time τ Laser τ Delay associated to thermal expansion: I(λ)=light intensity at resonance > thermal expansion with delay τ >cavity resonance condition changes: decay of the intensity until a new resonance condition is reached >contraction of the membrane with delay τ >superposition of waves gives damping or unstability