Using High Performance Computing
to predict Combustion Instabilities
in aeroengines
Franck Nicoud University Montpellier II – I3M CNRS UMR 5149
and
CERFACS
3 November, 2014 EMALCA, Puerto Madryn
MY TWO SCIENTIFIC LIFES
Laboratory of Mathematics and
Modelling of Montpellier
University
CARDIO-VASCULAR BIOMECHANICS -
1ST TALK
European Center for Research and Advanced Training
in Scientific Computing
COMBUSTION INSTABILITIES - 2ND TALK
FRANCE
PARIS
TOULOUSE MONTPELLIER
IN TOULOUSE
IN MONTPELLIER
November, 2014 EMALCA, Puerto Madryn 6
THERMO-ACOUSTIC INSTABILITIES
FLOW VISUALIZATION : RED AREAS DENOTE BURNT GAS.
The Berkeley backward facing step experiment.
Premixed gas
November, 2014 EMALCA, Puerto Madryn 7
THERMO-ACOUSTIC INSTABILITIES
• Self-sustained oscillations arising from the coupling between
a source of heat and the acoustic waves of the system
• Known since a very long time (Rijke, 1859; Rayleigh, 1878)
• Not fully understood yet …
• but surely not desirable …
November, 2014 EMALCA, Puerto Madryn 9
BETTER AVOID THEM …
LPP SNECMA
AIR
FUEL
LPP injector (SNECMA)
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FLAME/ACOUSTICS COUPLING
COMBUSTION
ACOUSTICS
Modeling problem Wave equation
Rayleigh criterion:
Flame/acoustics coupling promotes instability if
pressure and heat release fluctuations are in phase
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OUTLINE
1. A simple case
2. Computing the whole flow
3. Computing the fluctuations only
4. An actual study case
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A TRACTABLE 1D PROBLEM
BURNT GAS
IMPOSED
VELOCITY
IMPOSED
PRESSURE FLAME
n , t
FRESH GAS
0),0(' tu 0),(' tLp
0 L L/2
1T 12 4TT
Kaufmann, Nicoud & Poinsot, Comb. Flame, 2002
• Consider a 1D straight duct hosting an infinitely thin 1D flame which separates unburnt (cold) and burnt (hot) gas
• Assume that the gas are at rest, except for small amplitude acoustic perturbations
• A model describing the response of the flame to acoustic perturbations is needed …
November, 2014 EMALCA, Puerto Madryn 13
MODELING THE FLAME • An actual flame is not steady
• Its shape and size may change if the upstream velocity changes
• Example: Numerical simulation of a 2D flame in a dump
combustor (A. Giauque, CTR SP Stanford, 2006)
Oscillating
flow rate
Moving
Flame
November, 2014 EMALCA, Puerto Madryn 14
MODELING THE FLAME • Here the flame is considered 1D but its heat release may vary to
reflect an actual deforming flame
• the n-t model is used to relate the unsteady heat release to the
acoustic velocity (Crocco, 1952)
• In this view, the flame is just and only an acoustic element (which
is obviously a VERY strong assumption)
𝑛: amplitude of the flame response
τ: time delay of the flame response
𝑞′ 𝑡 ~𝑛 × 𝑢′ 𝑡 − 𝜏
November, 2014 EMALCA, Puerto Madryn 15
EQUATIONS
0),0(' tu 0),(' tLp
0 L
11 ; cT1212 2;4 ccTT
0''
:2
0
2
22
12
2
x
pc
t
p
Lx
0''
:2
2
22
22
2
x
pc
t
p
LxL
CLASSICAL ACOUSTICS
2 wave amplitudes
CLASSICAL ACOUSTICS
2 wave amplitudes
RELATIONS JUMP TWO
,2/''and0'2/
2/
2/
2/t
tLunupL
L
L
L
November, 2014 EMALCA, Puerto Madryn 16
DISPERSION RELATION
• Solve the 4x4 homogeneous linear system to find out the 4 wave
amplitudes
• Consider Fourier modes
• Condition for non-trivial (zero) solutions to exist
tjexptxp )(ˆ),('
03
1
4
1
4
3
4cos
4cos
1
2
1
t
tj
j
ne
ne
c
L
c
L
Coupled modes
mode amplified :0
mode damped :0
Uncoupled modes
November, 2014 EMALCA, Puerto Madryn 17
STABILITY OF THE COUPLED MODES
• Eigen frequencies
• Steady flame n=0:
• Asymptotic development for n<<1:
03
1
4
1
4
3
4cos
1
2
t
tj
j
ne
ne
c
L
,...2,1,0,23
2arccos
4 10,
mm
L
cm
)(sincos
2/sin9
4
shifpulsationComplex
0,0,
10,
10, noj
cLL
cn
t
mm
m
mm
tt
Kaufmann, Nicoud & Poinsot, Comb. Flame, 2002
November, 2014 EMALCA, Puerto Madryn 18
TIME LAG EFFECT
• The imaginary part of the frequency is
• Steady flame modes such that
• The unsteady HR destabilizes the flame if
02/sin 10, cLm
0,
0,
0,0,2
0]2[00sin m
m
mm TT
ttt
t0 2/0,mT 2/3 0,mT 2/5 0,mT0,mT 0,2 mT 0,3 mT
unstable unstable unstable unstable
10,
0,1
2/sin9
sin4
cLL
cn
m
m
t
November, 2014 EMALCA, Puerto Madryn 19
TIME LAG EFFECT
• The imaginary part of the frequency is
• Steady flame modes such that
• The unsteady HR destabilizes the flame if
10,
0,1
2/sin9
sin4
cLL
cn
m
m
t
02/sin 10, cLm
t0 2/0,mT 2/3 0,mT 2/5 0,mT0,mT 0,2 mT 0,3 mT
unstable unstable unstable
0,0,
0,
0,0,2
]2[20sin mm
m
mm TTT
ttt
November, 2014 EMALCA, Puerto Madryn 20
EFFECT OF FLAME-ACOUSTICS
COUPLING
Steady flame
STA
BL
E
UN
STA
BL
E
Real frequency (Hz)
Imagin
ary
fre
quency (
Hz) m 5.0
K 3001
L
T
Unteady flame
n=0.01
t=0.1 ms
STA
BL
E
UN
STA
BL
E
Real frequency (Hz)
Imagin
ary
fre
quency (
Hz)
THE REAL WORLD IS MORE COMPLEX
• Flow physics
– turbulence, partial mixing, chemistry, two-phase flow , combustion
modeling, heat loss, wall treatment, radiative transfer, …
• Acoustics
– complex impedance, mean flow effects, acoustics/flame coupling,
non-linearity, limit cycle, non-normality, mode interactions, …
• Numerics
– Low dispersive – low dissipative schemes, non linear stability,
scalability, non-linear eigen value problems, …
21 November, 2014 EMALCA, Puerto Madryn
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OUTLINE
1. A simple case
2. Computing the whole flow
3. Computing the fluctuations only
4. An actual study case
23 November, 2014 EMALCA, Puerto Madryn
NAVIER-STOKES EQUATIONS
• The 3D PDE’s governing the flow of a constant density (𝜌) fluid are:
Mass conservation (continuity): 𝜕𝑢𝑖
𝜕𝑥𝑖= 0
Momentum: 𝜕𝑢𝑖
𝜕𝑡+ 𝑢𝑗
𝜕𝑢𝑖
𝜕𝑥𝑗= −
1
𝜌
𝜕𝑝
𝜕𝑥𝑖+
𝜕
𝜕𝑥𝑗𝜈
𝜕𝑢𝑖
𝜕𝑥𝑗+
𝜕𝑢𝑗
𝜕𝑥𝑖 , with 𝑖 = 1,2,3
• Remarks: 𝑝 is pressure and 𝜈 is the kinematic viscosity (constant if Newtonian fluid)
The non-linear term 𝑢𝑗𝜕𝑢𝑖
𝜕𝑥𝑗 arises from the inertia effects ; if large enough, it is
responsible for turbulence generation
THE EQUATIONS TO BE SOLVED … • 3D, reacting, multi-species, gazeous mixture …
24 November, 2014 EMALCA, Puerto Madryn
THE EQUATIONS TO BE SOLVED … • 3D, reacting, multi-species, gazeous mixture …
25 November, 2014 EMALCA, Puerto Madryn
THE EQUATIONS TO BE SOLVED … • 3D, reacting, multi-species, gazeous mixture …
26 November, 2014 EMALCA, Puerto Madryn
THE EQUATIONS TO BE SOLVED … • 3D, reacting, multi-species, gazeous mixture …
27 November, 2014 EMALCA, Puerto Madryn
THE EQUATIONS TO BE SOLVED … • 3D, reacting, multi-species, gazeous mixture …
28 November, 2014 EMALCA, Puerto Madryn
THE EQUATIONS TO BE SOLVED …
• 3D, reacting, multi-species, gazeous mixture …
Sensible enthalpy of species k
Specific enthalpy of species k
Sensible enthalpy of the mixture
Specific enthalpy of the mixture
Total enthalpy of the mixture
Total non chemical enthalpy of the mixture
E = H – p/r Total non chemical energy of the mixture
29 November, 2014 EMALCA, Puerto Madryn
THE EQUATIONS TO BE SOLVED …
• 3D, reacting, multi-species, gazeous mixture … as a first step !!
• Do not forget:
– 2-phase flow effects, Turbulence modelling, Complex diffusion, …
– High Performance Computing issues, Huge data management, …
• Large Eddy Simulation is feasible today …
30 November, 2014 EMALCA, Puerto Madryn
EXAMPLE #2
November, 2014 32 EMALCA, Puerto Madryn
Ignition of a Turbomeca combustion chamber
Y. Sommerer & M. Boileau - CERFACS
EMALCA, Puerto Madryn
33
November, 2014
Large Eddy Simulation of a full annular
combustion chamber Staffelbach et al., 2008
• The first azimuthal mode is found unstable from LES, at 740 Hz
• Same mode found unstable experimentally
EXAMPLE #3
November, 2014 EMALCA, Puerto Madryn 34
PARALLEL COMPUTING
• Large scale unsteady computations require huge computing
resources, an efficient codes …
processors
Speed u
p
WHY DO WE NEED MORE ?
• LES/brute force bring a partial answer by giving a picture of what happens when a combustor oscillates
• But it does not really say why, how, under which conditions the instabilities appear. And it is really CPU/memory consuming
• Appropriate low order tools are needed to
– interpret the data and understand the reason why a combustor becomes unstable
– Perform parametric studies to address questions as:
– What is the best strategy to stabilize a combustor which proved unstable
– uncertainty quantification, robust design, margin to stability,…
November, 2014 36 EMALCA, Puerto Madryn
November, 2014 EMALCA, Puerto Madryn 37
OUTLINE
1. A simple case
2. Computing the whole flow
3. Computing the fluctuations only
4. An actual study case
November, 2014 EMALCA, Puerto Madryn 39
LINEARIZED EULER EQUATIONS
assume homogeneous mixture
neglect viscosity
decompose each variable into its
mean and fluctuation
assume small amplitude
fluctuations
0
00
0
1
0
1
;1
ln,,,;1
r
rr
pc
c
pCsTpf
f
fv
u
),()(),( 10 tfftf xxx
November, 2014 EMALCA, Puerto Madryn 40
Linearized Euler Equations
• the unknown are the small amplitude fluctuations,
• the mean flow quantities must be provided
• requires a model for the heat release fluctuation q1
• contain all what is needed, and more …: acoustics + vorticity + entropy
November, 2014 EMALCA, Puerto Madryn 41
Zero Mach number assumption
• No mean flow or “Zero-Mach number” assumption
• Probably well justified below 0.01
rr
pCsTpf
f
ftfftf v ln,,,;1);,()(),(
0
110 xxx
0
00
0
1
10 ;1);,()(),(r
pc
ctt
uxuxuxu
s thicknesflame:th wavelengacoustic: fa LL
November, 2014 EMALCA, Puerto Madryn 42
LINEAR EQUATIONS
0:Mass 01101
rr
ruudiv
t
110011
0:Energy qpTt
TCv
uur
11
0:Momentum pt
ur
0
1
0
1
0
1:StateT
T
p
p
r
r
- The unknowns are the fluctuating quantities
- The mean density, temperature, … fields must be provided
- A model for the unsteady HR q1 is required to close the system
1111 ,,, pTur
THE HELMHOLTZ EQUATION
• Since ‘periodic’ fluctuations are expected, let’s work in the
frequency space
• With this notation:
– Re 𝜔 = 𝜔𝑟 is the angular frequency of oscillation
– Im 𝜔 = 𝜔𝑖 is the growth/decay rate of the fluctuation (unstable if 𝜔𝑖 > 0)
• From the set of linear equations for r1, u1, p1, T1 , the following
wave equation can be derived
qjppp ˆ1ˆˆ1 2
0
0
r
tj
tjtj
eqtq
eteptp
xx
xuxuxx
ˆRe,
ˆRe, ˆRe,
1
11
43 November, 2014 EMALCA, Puerto Madryn
3D ACOUSTIC CODES • Let us first consider the simple steady flame case (no forcing term):
• Boundary conditions may be simple
• Or based on a complex valued boundary impedance, suitable for
nozzles, upstream/downstream acoustic element
0ˆˆ1 2
0
0
ppp
r
atmosphere theoutlet tofor suitable:0ˆ p
44
inlet walls,solidfor suitable:0ˆˆ0 nnu pr
November, 2014 EMALCA, Puerto Madryn
November, 2010 VKI Lecture 45
TUM combustor: first seven modes
f (Hz) type
143 1L
286 1C plenum
503 2C plenum
594 2L
713 3C plenum
754 1C combustor
769 3L
QUESTION
• There are many modes in the low-frequency regime
• They can be predicted in complex geometries
• Boundary conditions and multiperforated liners have first order effect and they can be accounted for properly
• All these modes are potentially dangerous
Which of these modes are made
unstable by the flame ?
46 November, 2014 EMALCA, Puerto Madryn
ACCOUNTING FOR THE UNSTEADY
FLAME • Need to solve the thermo-acoustic problem
• The unsteady heat release must be modelled to close the problem
• This is certainly the most difficult part of the modeling effort required to represent thermo-acoustic instabilities
• As already discussed for the simple 1D configuration, q may be related to the acoustic velocity upstream of the flame
qjppp ˆ1ˆˆ1 2
0
0
r
47 November, 2014 EMALCA, Puerto Madryn
FLAME TRANSFER FUNCTION
• The flame response can be deduced from either
– Theoretical model for simple flames (e.g.: Schuller et al., Comb. Flame, 2003)
– Experimental data (e.g.: Palies et al. Comb. Flame, 2010)
– Large Eddy Simulation (e.g.: Giauque et al., J Turb., 2005)
• In many cases, only information about the volume integrated heat
release is available through a global flame response:
refrefFQ nxu )(ˆ)()(ˆ
dqQ ˆˆ
48 November, 2014 EMALCA, Puerto Madryn
GLOBAL FLAME TRANSFER FUNCTION
ACOUSTIC VELOCITY
AT THE REFERENCE
POSITION
ACOUSTIC
WAVE
refref )(ˆ
)(ˆ)(
nxu
QF
49
GLOBAL HEAT
RELEASE
November, 2014 EMALCA, Puerto Madryn
VALIDATION
• This strategy was used for example by Silva et al. Comb. Flame, 2013
• Swirled stabilized combustor studied at EM2C (Palies et al., Comb. Flame, 2011) with 24 different configurations
50
???????????????????????????????????????????
???????????????????????????????????????????
???????????????????????????????????????????
S: stable regime U: Unstable regime
November, 2014 EMALCA, Puerto Madryn
51
Flame shape by
chemiluminiscence 𝑛𝑙𝑜𝑐𝑎𝑙 𝜏𝑙𝑜𝑐𝑎𝑙
Global Flame transfer Function
from experiment (Palies et al. Comb. Flame, 2010)
Field of Flame Transfer Function
useable in a Helmholtz solver
VALIDATION
November, 2014 EMALCA, Puerto Madryn
• This strategy was used with some success (Silva et al. Comb.
Flame, 2013) …
52
S: STABLE U: UNSTABLE S-U: MARGINAL
EXPERIMENT No activity Strong amplitude Small amplitude
SIMULATION 𝜔𝑖 < 𝑑𝑎𝑚𝑝𝑖𝑛𝑔 𝜔𝑖 > 𝑑𝑎𝑚𝑝𝑖𝑛𝑔 𝜔𝑖 ≈ 𝑑𝑎𝑚𝑝𝑖𝑛𝑔
Only 3 cases (out of 24) with partial disagreement
VALIDATION
November, 2014 EMALCA, Puerto Madryn
November, 2014 EMALCA, Puerto Madryn 53
OUTLINE
1. A simple case
2. Computing the whole flow
3. Computing the fluctuations only
4. An actual study case
• Main contributors:
– L. Benoit, C. Sensiau, E. Gullaud, E. Motheau, P. Salas, C. Silva, K.
Wieczorek, A. Ndiaye, F. Ni
– A. Dauptain, L. Giraud, G. Staffelbach, F. Nicoud, Th. Poinsot
• Support from SAFRAN/SNECMA (since 2000) as well as
ANR and EU
• Integrated in the C3SM framework for generating Human-
Machine Interface
• Now in use in design departments in the SAFRAN Group
November, 2014 54 EMALCA, Puerto Madryn
THE AVSP THERMOACOUSTIC SOLVER
November, 2014 57 EMALCA, Puerto Madryn
CLASSICAL ACOUSTIC ANALYSIS
Which of these modes are made
unstable by the flame ?
P. Salas – PhD thesis - CERFACS
November, 2014 58 EMALCA, Puerto Madryn
FLAME RESPONSE FROM LES
• A large Eddy Simulation (solving the whole set of flow
equations) has been performed to numerically measured
the flame transfer function
• Several pulsed LES were performed since the results
depend on the frequency od excitation
P. Salas – PhD thesis - CERFACS
November, 2014 59 EMALCA, Puerto Madryn
EFFECT OF THE FLAME ON ACOUSTICS
P. Salas – PhD thesis - CERFACS
50 70 90 110 130 150 170 190
Frequency (Hz)
Gro
wth
rate
(s
-1)
210
STABLE MODES
UNSTABLE MODES
STEADY FLAME UNSTEADY FLAME
November, 2014 60 EMALCA, Puerto Madryn
PARAMETRIC STUDY: TIME DELAY
P. Salas – PhD thesis - CERFACS
Mode of interest #1
Mode of interest #2
Mode of interest #3
THE SWIRLER SHOULD BE DESIGNED IN SUCH A WAY TO PRODUCE A
TIME DELAY OF THE FLAME RESPONSE IN THIS RANGE
November, 2014 EMALCA, Puerto Madryn 61
THANK YOU !!
More details, slides, papers, …
http://www.math.univ-montp2.fr/~nicoud/
http://www.cerfacs.fr