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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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= i0.491.

8. 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= i0.491.

9. 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.

10. 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.

11. 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)

12. 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