Technische Universität München
Tackling Combustor Design Problems with Large Eddy Simulation of Reacting Flows
Wolfgang PolifkeFachgebiet für ThermodynamikTechnische Universität München
Acknowledgements:Joao Carneiro, Patrick Dems, Stephan Föller, Thomas Komarek, Rohit Kulkarni, Luis Tay, Matthieu Zellhuber
AG Turbo, Alstom, DFG, DST, KW21, Siemens
MUSAF II ColloquiumSep. 18-20, 2013, CERFACS, Toulouse
Technische Universität München
W. Polifke - MUSAF II, Sep. 2013
Overview
Gas turbine combustor design challenges
• stability
• emissions
This talk
• mixing and auto-ignition in turbulent flow
• flame dynamics from system identification
• spray dispersion, evaporation & combustion
2
control & optimization,
c
ode couplingreacting flo
w
multi-physis, multi-scale
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Sequential combustion in Alstom GT24/26
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multi-stream mixing in swirling, turbulent flow
auto-ignition & flame propagation
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Composite PV lookup from PSRs
4Mixture fraction!
Prog
ress
var
iabl
e! s
ourc
e!
Progress variable!
Technische Universität München!
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0! 0.2! 0.4! 0.6! 0.8! 1!
Yc!
Z!
Yeq!
Chemistry simplification:!
Yc!
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Prog
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ourc
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Progress variable!
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Yp!
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Autoignition tabulation (0D reactors):!
Tabulated Chemistry Concept!
10!
Technische Universität München!
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Chemistry simplification:!
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Prog
ress
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ourc
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Progress variable!
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Yp!
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Autoignition tabulation (0D reactors):!
Tabulated Chemistry Concept!
10!
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W. Polifke - MUSAF II, Sep. 2013
Stochastic fields for subgrid scale fluctuations
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Technische Universität München!
Turbulence-Chemistry Interaction models!
Presumed PDF! Transported PDF!
Deterministic transport equations! Stochastic partial differential equations!
Turbulence chemistry interaction!
Lagrangian/Particle! method!
Eulerian/Fields !method!
(ITO formulation)!11!
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W. Polifke - MUSAF II, Sep. 2013
Stochastic fields, composite progress variable
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0!
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940! 950! 960! 970! 980! 990!
Aut
oign
ition
leng
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Air temperature [K]!
Experiment!Presumed PDF!Stochastic fields!
Implemented in Fluent and OpenFOAMValidation:
Markides & Mastorakos, Cabra, Delft, SEVH2, n-Heptane, CH4
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Cabra-H2-Flame with Li-Dryer mechanism
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see papers by Kulkarni, Zellhuber, Collonval ...
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Thermo-acoustic combustion instabilities
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from Lieuwen & Yang, 2006
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Feedback between heat release and acoustics
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W . Polifke / divide et impera — Ercoftac TecTag / 2
Thermo-Akustische Instabilität
(p’, u’) (p’, u’)Q’
!!Q !p d""# > 0.
Rückkopplung zwischen Fluktuationen
der Strömung (p’,u’) und der Wärmefreisetzung Q’
-> Selbsterregte Schwingungen !
Stabilitätskriterium nach Rayleigh:
Eingeschlossene Flamme
Rayleigh’s criterion: Instability requires�p� Q̇� dt > 0,
Premix flames are velocity sensitive: Q̇� = Q̇�(��),
System acoustics controls phase p� ↔ ��: Z =p�
��.
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Multi-physics interactions with feedback
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FlameFuel Supply
Air Supply
Combustor
Equivalence Ratio
Position and Area of Flame
Burning Velocity Q’
p’, u’u’
p’
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Combustion LES captures (in principle) all relevant effects:
but:
• turbulent, reacting, compressible flow at low Ma-#
• acoustic boundary conditions !?
• wide range of length and time scales
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“brute force” LES for combustion dynamics?
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“divide et impera”
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Stability analysis by combined use of
• “system model” for combustor acoustics
• reduced order model (ROM) of heat source dynamics
This strategy may be adopted to
• network models
• state-space models
• Galerkin models
• FE/FV-based solvers for Helmholtz / APE / LEE
this is code-coupling, too !!
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ROMs of input-output systems
Matrix-based methods (for state-space models)
• Truncated Balanced Realization
• Krylov methods (moment matching)
Data-based models
• PODs & Galerkin Projection
• System Identificationnon-parametric model (e.g. spectral analysis)
parametric models
- Black Box models (e.g. time-delay models)
- Gray Box models (e.g. state space models)
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Time-delay ROMs for linear systems
present response depends on present & previous signals
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and previous responses ... and noise, too
+
trade offs: accuracy - uncertainty - # of coefficients - flow/flame physics
FrequencyResponse F
F(ω)
F(ω) =�
k hke−�ω�tk
z-transform
Unit ImpulseResponse h
h
� · h = cWiener filter equation
Auto-correlation �Cross-correlation c
�, c
��j ∼�
k sk−�sk−j
c� ∼�
k sk−�rk
Time Series(��B(k�t); Q̇
�(k�t))
s, r
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Flame transfer function from LES
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Signal
� �� �Q̇�
��B
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Turbulent premix swirl burner
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Komarek et al, ‘09, ’10; Tay et al, ’10, ‘11
URANS LESSolver CFX AVBP
Turb./Sub-grid model
SST WALE
Combustion Model
TFC DTFM1 step Kin.
Time step [s] 5e-5 1.25e-7
Spatial/temp. Discretization
Second order
Second order
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LES/SI for premix swirl burner
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Validation: FTF from CFD/SI vs experiment
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Daubechieswavelets
Tychonov Regularization for inversion of Wiener Filter:
hα =��T�+ α2RRT�−1
�Tc
Generation of optimal excitation signals:
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Advanced SI for low signal-to-noise
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maximumentropy
non-Gaussiansimulation
Föller & Polifke, ICSV ’11:Transmission and reflectionof sound at duct discontinuity
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Aero-acoustic scattering at an orifice
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input to excite acoustic eigenmodes of the pipe network. If the acoustic lossesare weaker than the acoustic gain provided by the orifice the eigenmode willgrow rapidly and the system becomes acoustically unstable.
Due to the high amplification potential and the regular appearance in pipenetworks, orifices were studied by several research groups. Experimentally,the scattering coefficients of cylindrical orifices with different diameters andthicknesses were determined and analyzed by Testut et al. [TAMH09]. In com-parison to experimental studies, orifices were investigated more frequently byresearches with different numerical approaches. Kirkegaard et al. [KAEÅ12]applied the linearized Navier-Stokes equations to solve for the scattering coef-ficients of a 2-dimensional orifice configuration. Rupp et al. [RCS10] analyzednumerically the aero-acoustic interactions in the vicinity of an orifice geom-etry based on unsteady 3-dimensional Navier-Stokes simulations. In previ-ous years, results for the scattering coefficients and for the whistling crite-rion [AS99] of the here introduced geometry were already published by La-combe et al. [LMF+10, Lac11, LFJ+13]. All these results base on the SI method-ology presented by Föller et al. in 2012 [FP12] where a FIR model structurewithout individual time lag adaption was employed.
The aero-acoustical network element representation of the orifice configu-ration is shown in Fig. 6.2. There are potentially two directions for incidentacoustic waves with fu as the corresponding upstream ingoing characteris-tic wave amplitude and gd as the downstream ingoing counterpart. The twooutgoing characteristic wave amplitudes are upstream gu and downstreamfd, respectively. Since the orifice configuration represents a 2x2 aero-acoustic
Figure 6.2: Acoustical network element representation of the cylindrical orifice in a pipe
MIMO system, its scattering matrix (Eq. (6.1)) agrees with the acoustic ele-
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6.3 Results
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.2
0.4
0.6
0.8
1
1.2
1.4
Sr
|T+ |
(a) upstream transmission
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.2
0.4
0.6
0.8
1
1.2
Sr
|R! |
(b) downstream reflection
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
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1.2
Sr
|R+ |
LES/SI99% Conf. Int.Lacombe, exp.
(c) upstream reflection
0 0.1 0.2 0.3 0.4 0.5 0.6 0.70
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Sr
|T! |
(d) downstream transmission
Figure 6.5: Amplitudes of the scattering coefficients for the cylindrical orifice in a pipe vs. Srnumber; LES/SI results with 99% confidence intervals at 2 M numbers (MLES/SI =0.0252: black, MLES/SI = 0.0349: red) in comparison with experimental data of La-combe [Lac11] (Mexp = 0.026: black, Mexp = 0.0335: red)
highest model frequency of interest fmax,mod. The remaining frequency con-tent in ranges above fmax,mod in the acoustic responses gu and fd is not mod-eled and thus, causes a reduction of the prediction quality.
Comparing the results in Figs. 6.5 and 6.6 to the LES/SI results presentedin earlier publications [LMF+10, LFJ+13], methodological improvements ledto the significant better quality of the solutions. Especially, the occurrenceof wavy deviations over the entire frequency range could be successfully re-
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M = 0.026M = 0.034
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Summary
Status Quo
• LES/SI can give flame dynamics with quantitative accuracy
Ongoing work
• optimal model structures for identification
• non-linear effects
• high frequencies, acoustic losses
• combustion noise
• LES model for (partially) premixed (spray) combustion
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Poly-Celerity MOM for polydisperse sprays
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Test case: sedimentation of bubbles
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2.4 Test Case
Figure 2.2: Contours of the Sauter Mean Diameter obtained with the Moments Model in Open-FOAM.
Figure (2.4) shows the evolution of the bubble size distribution function at several positionsinside the channel (corresponding to axial positions x = 1,5; 5,7 cm and vertical positions y =0,1; 10; 19,9 mm). As bubbles tend to move towards the upper side of the channel, the numberdensity is higher for the vertical coordinate corresponding to y = 19,9 mm, and smaller at y =0,1 mm. Furthermore, a very reasonable agreement can be noted between both methods, withthe Moments Model being able to reproduce not only the shape of the distribution function, butalso its variation along the channel. However, the distribution obtained with the Moments Modelnear the upper wall at the most downstream axial position in the channel deviates considerablyfrom that of the Multi-Fluid solution. This occurs because the shape of the spectral distributionat that location is dominated by the high accumulation of big bubbles near the top wall, whichis not appropriately reproduced by a Gamma distribution.
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(Carneiro et al)
Experiments (Sommerfeld & Qiu, ’91) vs. LES (Dems et al, 2012)
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Polydisperse multi-phase turbulent swirl flow
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Results for Sommerfeld & Qiu - Axial Velocity
!"#$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&!'
(#)%%%%%%%%%%%*#+,-./"
Gas phase Particles
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Comparison Against Experiment of Sommerfeld & Qiu (1991)
!"#$%&%'()*+,-.(/01234( !"5$%&%6-17+(8*8,(91
:70,
:70,%;%<*/,9=(1
Swirl air
Particles & air
D = 200 mm
Axial velocities
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Conclusions
Large Eddy Simulation is relevant for R&D in industry
Industrial applications imply special modelling requirements
Reduced Order Models can be an interesting alternative to code-coupling for multi-physics, multi-scale problems
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Thank you !