1. ASME Turbo Expo, Charlotte, NC, USA June 29, 2017
GT Predicting Thermoacoustic Instability in an Industrial Gas Turbine Combustor: Combining a Low Order Network Model with Flame LES
Yu Xia, Aimee S. Morgans, William P. Jones
Dept. of Mechanical Engineering, Imperial College London, UK.
Jim Rogerson, Ghenadie Bulat
Siemens Industrial Turbomachinery Ltd., Lincoln, UK.
Xingsi Han
Nanjing University of Aeronautics and Astronautics, PR China.
ASME Turbo Expo, Charlotte, NC, USA June 29, 2017

2. Outline Background & Motivation
Methodology – Combined prediction approach
Low-order network modelling of acoustic waves
Flame describing functions via incompressible flame LES
Results – Predicting thermoacoustic instability
Conclusions and future work

3. Thermoacoustic instability Excessive heat transfer
Background
Traditional fossil fuels (e.g. coal, oil) will remain popular in the next decade*.
NOx emissions from fuel combustion must be controlled due to stricter environmental policies in power and aviation industries.
Lean premixed combustion (LPC) is widely used, but is highly susceptible to thermoacusitc instability – an extremely undesirable phenomenon.
Fatigue failure of
turbine blades
Thermoacoustic instability
Excessive heat transfer
to melt burner
Damaged turbine blades
Melted burner
*International energy agency key world energy statistics.

4. Thermoacoustic instability
Background
Thermoacoustic instability
is caused by an in-phase, two-way interaction between linear acoustic wave perturbation (𝒑′) and unsteady flame heat release fluctuation ( 𝑸′ ):
Limit cycles:
fixed amplitude and frequency p’ Q’

5. Motivation
Project aim: Predicting thermoacoustic instability in an adapted
Siemens SGT-100 gas turbine combustor (single burner)
Built in DLR Stuttgart;
Fuel: German natural gas (98.97% CH4) .
Air/fuel technically premixed;
Tair = 685 K, Tfuel = 305 K
Uair =~5 m/s, Ufuel = ~60 m/s
Lean combustion (∅=0.60)
Mach number 0.02 ~ 0.28
Reynolds number 104 ~ 105
Two operating pressures
(3 bar & 6 bar)

6. Methodology Combined Prediction Approach
Low order network acoustic modelling
Flame describing function (FDF)
1. Geometry simplified into network
3. Simulate flame-acoustic interaction
Upstream
forced velocity u1’
Downstream heat
release rate Q’
2. Wave-based acoustic modelling
4. Construct numerical FDFs
5. Combine into OSCILOS* and calculate thermoacoustic modes
*J. Li, D. Yang, C. Luzzato, A. S. Morgans, OSCILOS Long technical report, 2014.

7. Network simplification of combustor geometry
Step 1: simplify combustor geometry into a network of connected modules:
Complex
combustor
geometry
Swirler
entry
Simplified
network of
connected
modules
Inlet
Thin flame sheet
Exhaust cooling pipe
Air passage
Outlet
Combustion chamber

8. Wave-based modelling of acoustic waves
Step 2: model plane acoustic modes using wave-based method
Cold module
Wave-based equations (k=1, …, 𝑁)
Hot module
Flame jump conditions*
*A. Dowling, S.R. Stow, J. Propulsion and Power 2003

9. Establishment of network transfer matrix
Last module
1st module
BC: damped
open-outlet
BC: fully-closed
inlet
1-D acoustic wave modes are obtained without flame-acoustic interaction:

10. Simulation of flame response to acoustic forcing
To include the flame-acoustic interaction, an additional “flame model” is needed.
Upstream forced velocity
perturbation u’1
Responding flame heat
release rate fluctuation
(Q’ ≠ 0)
(Hydrodynamic disturbance excited by acoustics)
Flame model
Small u1’
Large u1’
Linear
flame transfer function (FTF)
Weakly non-linear
flame describing function (FDF)
E.g. classical 'n−τ’ model*
Simulated by faster incompressible LES solvers
*Crocco L, Proc. Symp. Int. Combust., 1969

11. Computational domain for LES simulations
Step 3: Simulate flame response to acoustic forcing via incomp. LES:
Mesh cells in the whole domain
Measurement
Location
@ x = 28. 7 mm
x = 0 mm
Computational domain
(7.0 million structured mesh cells)
B.C.s: velocity inlet, zero-gradient outlet, adiabatic non-slip walls.
Mesh cells in the refined flame region

12. Numerical settings of LES solvers
Two incompressible LES solvers, BOFFIN and OpenFOAM, are used
BOFFIN (in-house)
OpenFOAM (open-source)
CH4/air reaction
mechanism
15-step +
19 species*
(3 & 6 bar)
4-step +
7 species**
(3 bar)
2-step +
7 species***
(3 bar & 6 bar)
Combustion model
Stochastic field method (Valino, FTaC, 1998)
Partially-Stirred Reactor (PaSR) (Chen, CST, 1997)
SGS turbulence model
Dynamic Smagorinsky
Constant Smagorinsky
Time-step size
5 x 10-7 s
5 x 10-6 s
Time integration
2nd-order Crank-Nicolson scheme
Spatial discretisation
2nd-order Central Difference scheme
Compressibility
Incompressible (state equation: 𝜌(𝑇)= 𝑝 0 /𝑅𝑇)
*Sung et al. Combust. Flame, 2001.
**A. Abou-Taouk, et. al. Combust. Sci. Technol
*** Westbrook & Dryer, Prog. Ener. Combust. Sci., 1984.

13. Simulation results for an unforced case
Contours of flow variables simulated by OpenFOAM with 2-step 3 bar
Axial velocity (m/s)
Static temperature (K)
Heat release rate per unit volume (W/m3)
3D contour of axial velocity (40 m/s)

14. Validation of LES predictions: mean flow variables
LES and measurements match quite well for mean flow variables
Comparison between LES and exp. 3 bar (mean x = 28.7mm)

15. Validation of LES predictions: RMS flow variables
LES and measurement also match well for RMS flow variables (small errors exist)
Comparison between LES and exp. 3 bar (RMS x = 28.7mm)

16. Modelling of acoustic forcing
Step 4: Determine flame describing functions (FDFs)
4.1. Define a harmonic forcing velocity 𝑼 𝒂𝒊𝒓 at swirler air-entry:
𝑈 𝑎𝑖𝑟 = 𝑈 𝑎𝑖𝑟 ∙ 1+ 𝐴 𝑈 ∙ cos 2𝜋∙ 𝑓 𝑈 ∙𝑡 𝑚/𝑠
Mean inflow
Velocity ~5m/s
Velocity forcing
amplitude [-]
Velocity forcing
frequency [Hz]
By controlling both 𝐴 𝑈 and 𝑓 𝑈 , a total of 16 forcing cases (see below) are performed by each LES solver at each pressure.

17. Calculation of total heat release rate fluctuation
(calculated at each time-step)
Local Q ′(x,y,z) spatially
integrated over domain volume V
𝑄 = 𝑄′ x,y,z 𝑑𝑉 𝑉
4.2. Approximate total heat fluctuation 𝑸 by a harmonic expression:
Heat responding amplitude [-]
Heat responding phase [rad]
The values of unknown 𝑨 𝑸 and ∅ 𝑸 are calculated for each forcing case.
𝑄 = 𝑄 ∙ 1+ 𝐴 𝑄 ∙ cos 2𝜋∙ 𝑓 𝑈 ∙𝑡+ ∅ 𝑄 (𝑊/ 𝑚 3 )

18. Heat responding amplitude
𝑄 = 𝑄 ∙ 1+ 𝐴 𝑄 ∙ cos 2𝜋∙ 𝑓 𝑈 ∙𝑡+ ∅ 𝑄 (𝑊/ 𝑚 3 )
Heat responding phase
Heat responding amplitude
Power
spectra of 𝑼 𝒂𝒊𝒓
Power
spectra of 𝑄
𝑨 𝑸 = 0.124
Spectral peak at
forcing frequency
Power spectra via FFT (AU = 0.1, fU = 200 Hz)
Cross-correlation
between 𝑼 𝒂𝒊𝒓 and 𝑄
Location of maximum
cross-correlation magnitude
∅ 𝑸 = rad
Cross-correlation (AU = 0.1, fU = 200 Hz)

19. Flame describing functions (FDFs)
Forced
harmonic velocity 𝑼 𝒂𝒊𝒓
𝑈 𝑎𝑖𝑟 = 𝑈 𝑎𝑖𝑟 ∙ 1+ 𝐴 𝑈 ∙ cos 2𝜋∙ 𝑓 𝑈 ∙𝑡 𝑚/𝑠
Velocity forcing amplitude Velocity forcing frequency
Responding total
heat release rate
fluctuation 𝑄
𝑄 = 𝑄 ∙ 1+ 𝐴 𝑄 ∙ cos 2𝜋∙ 𝑓 𝑈 ∙𝑡+ ∅ 𝑄 (𝑊/ 𝑚 3 )
Heat responding amplitude
Heat responding phase
The FDF is finally defined in frequency domain as:
FDF-Gain: G = A Q / AU
FDF-Phase: ∅ = ∅ Q ±𝑛∙2𝜋
(n: an appropriately selected integer)

20. AU = 0.1 (lower forcing amplitude) AU = 0.2 (higher forcing amplitude)
Flame describing functions (FDFs)
Completed FDFs by polynomially-fitting gain G and phase ∅ over frequency.
@ 3 bar pressure
@ 3 bar pressure
AU = 0.1 (lower forcing amplitude)
AU = 0.2 (higher forcing amplitude)

21. AU = 0.1 (lower forcing amplitude) AU = 0.2 (higher forcing amplitude)
Flame describing functions (FDFs)
At both pressures, the fitted FDFs have small mismatches in FDF-gains, and have generally linearly-distributed FDF-phases.
@ 6 bar pressure
@ 6 bar pressure
AU = 0.1 (lower forcing amplitude)
AU = 0.2 (higher forcing amplitude)

22. Methodology Combined Prediction Approach
Low order network acoustic modelling
Flame describing function (FDF)
1. Geometry simplified into network
3. Simulate flame-acoustic interaction
Upstream
forced velocity u1’
Downstream heat
release rate Q’
2. Wave-based acoustic modelling
4. Construct numerical FDFs
5. Combine into OSCILOS* and calculate thermoacoustic modes
*J. Li, D. Yang, C. Luzzato, A. S. Morgans, OSCILOS Long technical report, 2014.

23. Predicting thermoacoustic instability using OSCILOS
Step 5: use the open source software OSCILOS ( to combine acoustic modes and FDFs to predict thermoacoustic modes.
5. Calculate thermoacoustic
modes
1. Build network geometry
2. Calculate mean flow properties
3. Import and fit numerical FDFs
4. Define acoustic B.C.s

24. Measured thermoacoustic modes from DLR
DLR measurement
Pressure sensor installed
on the top-inner x = 273 mm
6-bar
Measured modes
3-bar
Time-series of measured pressure signals
Power spectra magnitude of pressures

25. Thermoacoustic prediction by OSCILOS
OSCILOS defines a complex plane (X: growth rate, Y: frequency);
Predicted modes are marked by white stars at plane minima;
The frequencies of measured modes are marked by black dash lines.
White stars:
predicted modes
by BOFFIN-FDFs
@ 3 bar, AU = 0.1
Dashed lines:
frequencies of measured modes at 3 bar.
A total of 10
predictions cases
are completed by
OSCILOS

26. Predicted thermoacoustic modes via OSCILOS: 3 bar
3 bar, AU = 0.1
3 bar, AU = 0.1 (left) 4-step (right) 2-step
3 bar, AU = 0.2
3 bar, AU = 0.2 (left) 4-step (right) 2-step

27. Predicted thermoacoustic modes via OSCILOS: 6 bar
BOFFIN
@ 6 bar,
AU = 0.1
OpenFOAM
@ 6 bar, 2-step,
AU = 0.1
BOFFIN
@ 6 bar,
AU = 0.2
OpenFOAM
@ 6 bar, 2-step,
AU = 0.2

28. Comparison of modal frequencies: prediction vs. measurement
The errors for all predicted modal frequencies are <17%.
Modal 3 bar
Exp. data
Modal 6 bar
PSDs of pressure signals measured at x = 231 mm at 3 bar (solid) and 6 bar (dashed-dotted).

29. Comparison of modal growth rates: prediction vs. measurement
The growth rate of the ~368 Hz mode is over-predicted, while the real unstable ~215 Hz mode is under-predicted.
Unstable
mode
Modal growth 3 bar
Exp. data
Unstable
mode
Modal growth 6 bar
PSDs of pressure signals measured at x = 231 mm at 3 bar (solid) and 6 bar (dashed-dotted).

30. Summary on OSCILOS predictions
Based on the thermoacoustic predictions by OSCILOS:
A total number of 7 thermoacoustic modes are predicted for all cases, matching the measured number;
All the predicted modal frequencies accurately match the measured values, with an error less than 17%;
The change of FDFs will considerably modify the mode distribution;
The change of forcing amplitude does not highly affect the mode distribution;
The change of operating condition (e.g., pressure) also has some effects;
The most dynamic predicted mode occurs at ~380 Hz for all cases, mismatching the most dynamic measured mode at ~215 Hz.

31. Conclusion & Future work
This work predicted the thermoacoustic instability in a real industrial gas turbine combustor with complex geometry, having:
Low computational costs (Analytical acoustic modelling + Flame LES);
High prediction accuracy (on frequencies of all thermoacoustic modes);
Convenient prediction process (offered by open source OSCILOS);
Future work will focus on:
Using a refined mesh to study the mesh sensitivity of LES and FDFs;
Studying the mismatch of FDFs and modal growth rates at low frequencies (e.g., adding an upstream air plenum, using a Helmholtz solver, etc.);
Using a simpler reaction mechanism (e.g., 4-step) for BOFFIN LES

32. Acknowledgement Siemens Industrial Turbomachinery (UK)
UK National Supercomputing Service
Centre for Doctoral Training in Fluid Dynamics,
Imperial College London
European Research Council

33. Imperial College London
Thank you very much!
And any questions?
YU XIA
Imperial College London

34. A1. Mesh sensitivity analysis on SGT-100 combustor
Same fixed mass inflow rates for fuel CH4
Coarse mesh: 7.0 m structured cells
Refined mesh: 14.3 m unstructured cells

35. A1. Mesh sensitivity analysis on SGT-100 combustor
The OpenFOAM-FDFs obtained by refined mesh (14M) have close gains and phases compared to BOFFIN & OpenFOAM-FDFs obtained by coarse mesh (7M)
BOFFIN & 3bar pressure (left) AU = 0.1, (right) AU = 0.2

36. A2. Effect of chemical reaction steps on BOFFIN-FDFs
Comparison between 4-step and 15-step chemistry using BOFFIN
4-step chemistry
(Abou-Taouk et al)
15-step chemistry
(Valino)
Fuel
Methane (CH4), 3 bar pressure, equivalence ratio = 0.6
Compressibility
Incompressible (with BOFFIN)
Combustion Model
Stochastic field method
SGS model
Dynamic Smagorinsky model
Time integration
2nd-order Crank-Nicolson scheme
Spatial discretisation
2nd-order central difference scheme

37. A2. Effect of chemical reaction steps on BOFFIN-FDFs
2 spot-check A=0.1, f =600 Hz & A=0.2, f =600 Hz both show close FDF gain and phase
3bar pressure (left) AU = 0.1, (right) AU = 0.2

38. A3. Effect of stochastic field numbers on BOFFIN-FDFs
Comparison between one and eight stochastic fields using BOFFIN
One stochastic field
Eight stochastic field
Fuel
Methane (CH4), 3 bar pressure, equivalence ratio = 0.6
Compressibility
Incompressible (with BOFFIN)
Combustion Model
Stochastic field method
SGS model
Dynamic Smagorinsky model
Time integration
2nd-order Crank-Nicolson scheme
Spatial discretisation
2nd-order central difference scheme

39. A3. Effect of stochastic field numbers on BOFFIN-FDFs
BOFFIN-FDFs are insensitive to the number of stochastic fields
3bar pressure (left) AU = 0.1, (right) AU = 0.2

40. A4. Comparison between Helmholtz and OSCILOS
Geometry
Swirler + Combustor + Exhaust Pipe
Highly simplified
Slightly modified
Air plenum
Flame region
Swirler
Combustor
Exhaust pipe
Exhaust pipe
Swirler
Combustor
Air plenum
Helmholtz solver (COMSOL)
OSCILOS
Acoustic boundary conditions:
Fully closed inlet R1(s) = 1
Open outlet
with damping

41. A4. Comparison between Helmholtz and OSCILOS
With BOFFIN-FDFs (A=0.1) 3 bar pressure
Most unstable mode
correctly captured
All modal frequencies match well
Thermoacoustic modal frequency
Thermoacoustic modal growth rate