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Turbulent Partially Premixed Methane-Air Combustion in a Conical Burner
E. Baudoin, Y. Rixin, X.S Bai
Dept. Of Energy Sciences, Lund University, Sweden
Fluid Mechanics Seminar Series, 24-03-2010
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Outline
• Motivation
• Description of the conical burner
• Overview of some experimental results
• LES: modeling based on two scalar fields (Z-G approach)*
• LES: modeling based on the progress variable approach
• Conclusions
* Bo L. et Al., Proc. Combust. Inst. (2009)
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Motivation
• Partially Premixed Combustion (PPC) is found in many engineering applications …
– Combustion engines (PPC)
– Gas turbines (spray combustion)
• ... due to its potential to reduce pollutant emissions
• BUT PPC involves complex phenomena
– PPC affects strongly the stabilization of the flame
• if it is uncontrolled possibility of flashback, instabilities...
– Combustion characteristics are not well understood
• Improved prediction and understanding → LES
– laboratory scale test case for model development
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
The conical burner - Description
• Methane-air mixture
– Fuel supply: outer tube
– Air supply: inner tube
• Mixing length (L/D) adjustable
– L/D=0 non-premixed
– L/D>20 premixed
• Operating conditions
– Φg=3 (mass flows)
– Uc=20m/s (cone inlet)
– Re=12000
– L/D=3,5 and 7 ( in stable
regime)
8.0mm 6.8mm
D=9.7mm
19mm L
PIV window : 96*77mm
70mm
PLIF window : 66*66mm
AIR
CH4 CH4
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Experimental results - Stability curves
––Re=12000, ---Re=8000, ...Re=4000
Symbols: available experimental data
Obtained by decreasing fuel supply
until global quenching, B. Yan (2009)
• For Re=12000, an optimum is found for L/D~2.5
– PPC is more stable
• Diffusion flamelet theory
– Air on fuel side: χc < χ0,c
– Stability should increase as
L/D decreases
• Premixed front propagation
– Lower fuel gradient as L/D
increases
– Stability should increase as
L/D increases
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Experimental results: OH-PLIF / PIV*
*OH-PLIF: A. Lantz and PIV: S.M. Hosseini
L/DL/D=3 L/D=5 L/D=7
• OH layer thinner with higher composition gradient
• Leading flame fronts are stabilized in the recirculation zones introduced by the entrained air flow near the wall of cone
• Existence of local flame extinction holes in all cases
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Experimental results: Stabilization
• Mean leading flame front stabilized at the same position, x/D=1.5
• Entrained air flow and recirculation zone structures insensitive to
the degree of partial premixing
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Experimental results - Summary
• From stability curve, PPC is more stable
– For L/D>2.5
• Premixed front propagation is expected (triple flame) to stabilize the flame
– For L/D<2.5
• Stabilization diffusion control? or ”weak” triple flame?
• For L/D>2.5: Experimental results show lift-off inside the cone
– Similar stabilization location for L/D=3,5 and 7
• OH-PLIF / PIV images suggest local extinction inside the cone
• All those observations should be predicted by LES ...
– Focus on case L/D=5 (all L/D similar behavior in stable regime)
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES models - Equations for the flow
• Continuity equation
(–) spatial filter with the width (∆) and (~) density weighted as
• Spatial filtered Navier-Stokes equations with low mach number assumption
• Sub-grid scale stresses modeled using Scale Similarity Model
( )ijij
jj
i
jij
iji uuuuxx
u
xx
P
x
uu
t
uρρµ
ρρ−
∂
∂+
∂
∂
∂
∂+
∂
∂−=
∂
∂+
∂
∂ ~~~~~~
0
~
=∂
∂+
∂
∂
j
j
x
u
t
ρρ
ρρ ii uu =~
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Numerical methods - Schemes
• Staggered Cartesian grid – stretched
• Flow transport equation schemes
– Convective and diffusive terms: explicit scheme
– Convective term: 5th order WENO scheme
– Diffusive term: 4th order central difference scheme
– 2nd order Adam-Bashforth scheme for time stepping
• G-equation transport equation schemes
– 3th order WENO scheme
– 3th order TVD Runge-Kutta scheme for time stepping
• Time step: ~5·10-6s (CFL~0.1)
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, G-Z approach - Why?
• Diffusion flamelet model failed
– Flame is attached to the cone
inlet
– Inner stoichiometric surface is
ignited
– Low scalar dissipation is
predicted in the cone
• Lift-off is not due to high scalar dissipation rate
• Triple flame propagation at the leading fronts BUT the trailing edge is supposed to be of diffusion type
Experimental data
CH and temperature field (LES)
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, G-Z approach - Level-set G equation
• Level-set G equation model for flame front tracking
• Ssgs should take into account: sub-grid scale flame wrinkling, laminar flamelet propagation speed and possibly quenching mechanisms (χ)
* with model constant (~1)
• >0: possible burnable domain where the diffusion flamelet canbe applied
• <0: mixture is assumed chemically inert
* Proposed by Peters et Al. (2000) for RANS
21~~~~
~
∂
∂
∂
∂=
∂
∂+
∂
∂
jj
sgs
j
c
jx
G
x
GS
x
Gu
t
G
)1()( ,0 csgsLsgs auZSS χχ/−+= a
G~
G~
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, G-Z approach – Results
• LES corresponds well with the CH PLIF image
– Only the outer stoichiometric surface is
burnable
– Thin wrinkled CH layers are captured
• Zero-th level-set distribution indicates that partially premixed flame is blown upward at the centre jet
• Flame front is located near but not always at Zst due to
– Flame propagation
– Local flow velocity
Experimental data
Zst isoline (gray) and CH layers
from LES
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, G-Z approach – Results
• LES corresponds well with the CH PLIF image
– Only the outer stoichiometric surface is
burnable
– Thin wrinkled CH layers are captured
• Zero-th level-set distribution indicates that partially premixed flame is blown upward at the centre jet
• Flame front is located near but not always at Zst due to
– Flame propagation
– Local flow velocity
Experimental data
Z>Zst field (yellow), T-field and
G0 isoline (white) from LES
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, G-Z approach – Results
x/D=2: Exp (o), LES (solid line)
x/D=4: Exp (×), LES (dashed line)
• Air entrainment is observed in the cone near the wall
– Streamlines
– Axial velocity statistics
• In between reverse flow and the rich fuel/air mixture there is a low speed zone
– Shear layer is generated
– Favorable for triple flame
front stabilization
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, G-Z approach - Predicted CH layer
• 2D normalized FSD (max. value 0.2mm-1)
• Experimental data
– 200 CH-PLIF images
• LES data
– 10000 samples (0.05s)
• Along radial direction at x=0.027m (a)
– Thickness of mean CH zone is ~15mm
• Along radial direction at x=0.057m (b)
– Mean CH zone is thicker
– Mean flame brush merge
• Good agreement in terms of
– Thickness of mean flame brush
– Shape of FSD profile
LES PLIF
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, G-Z approach - Flame Surface Density
(a)
(b)
• 2D normalized FSD (max. value 0.2mm-1)
• Experimental data
– 200 CH-PLIF images
• LES data
– 10000 samples (0.05s)
• Along radial direction at x=0.027m (a)
– Thickness of mean CH zone is ~15mm
• Along radial direction at x=0.057m (b)
– Mean CH zone is thicker
– Mean flame brush merge
• Good agreement in terms of
– Thickness of mean flame brush
– Shape of FSD profile
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, G-Z approach - Predicted CH2O layer
LES PLIF
• Instantaneous CH2O distribution above the cone
– LES (left) and PLIF (right) results
• Thicker CH2O layer observed with PLIF than predicted by LES
– Longer life time than CH radicals
– Transport of CH2O can occur
• More interactions between CH2O and the flow have to be taken into account
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, G-Z approach - Summary
Iso-surfaces of λ2=3.6·10-6
and T=1000K
• Diffusion-Flamelet model can not predict the flame lift-off inside the cone
• Flamelet model coupled with G-equation gives reasonable solution
– Triple flame propagation
– Air entrainment influence
• Limitations => improvement!
– G incorrect in inner flame
– Stationary diffusion flamelet
is not accurate in simulating
the flame holes
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, C-Z approach - Principle
• From transport of a reactive scalar and mixture fraction
• If progress variable defined such
where in reactants and in equilibrium products
• An equation for can be derived* for
• Models are need... or simplifications (restrictive assumptions)
• Terms vanish under stratified premixed regime assumption
∂∂
∂+
∂
∂+
∂
∂+×
∂∂+∇⋅∇=⋅∇+
∂
∂cZ
nZ
nc
ni
n Zc
Y
Z
Y
c
Y
cYcDuc
t
c,
2
2
2
2
21
)()( ρχρχρχωρρρ
&
[ ]),(),,(),( txZtxcYtxY iinin =
nnn
n YDuYt
Yωρρ
ρ&+∇⋅∇=⋅∇+
∂
∂)()(
0),( =txc i 1),( =txc i
),( txc i
* Domingo et Al. (2002)
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, C-Z approach - Principle
• Filtered equations with (–) spatial filter and (~) density weighted
• Closure needed
• Both equation can defined an ideal regime: coupling needed
– Flame index defined as *
with
– Giving
* Takeno et Al. (1996)
ccDuccucut
cωρρρρρ &+∇⋅∇+−⋅∇=∇+
∂
∂)()~(~
~
)()~
(~
~
ZDuZZuZut
Z∇⋅∇+−⋅∇=∇+
∂
∂ρρρρρ
−=
OF
OF
p
,
,1
2
1
χ
χξ OFOF D ∇⋅∇−=,χ
dppp φξφξφ~
)~
1(~~~
−+=
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, C-Z approach - Preliminary results
• Try to get a proper stabilization (stratified premixed approach)
– Closure for : FPI approach
– Closure for : Flame Surface Density
(details on closure at the end)
• Diffusion branch... Or how to predict local quenching?
– Finite rate chemistry effect
– Effect of dilution
– Flamelet approach? –> Generation? Conditions?
• Coupling between the two approaches
– ”simple” ON/OFF based on a given value of c
• Diffusion flame modeling critical
– Flame index in this flame not straightforward
• diffusion approach may suffice
cω&
ccD ωρ &+∇⋅∇ )(
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Conclusions – modeling PPC
• G-Z approach has been extended to LES and applied to PPC
– Insight on the stabilization mechanism (triple flame)
– Reasonable agreement with available experimental data
• G-Z approach has also limitations
– The G-Z coupling is limited to an On/Off situation
• Inner region of the flame not properly modeled
– The steady diffusion flamelet used failed to predict
• local extinction
• CH2O layer
• Towards C-Z approach (ongoing work)
– Evaluation of available premixed model (FPI - FSD)
• More insight on the dynamics of the flame
– Improvement of the diffusion flamelet approach is needed
– Better coupling between premixed and nonpremixed possible
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Conclusions – Conical burner
• Burner more stable when fuel and air are partially premixed
– Optimum L/D=2.5
– Due to premixed front propagation at the leading edge
• While operating in a stable regime
– OH layer in the cone is found to be thicker as L/D increases
– Local extinction in the cone are observed
– The stabilization location is the same for L/D=3,5 and 7
• For L/D=5
– Thin and wrinkled CH layer detected in the cone
– Exp. and LES explained stabilization mechanism
– CH layer outside the cone exhibits local extinction
– CH2O layer outside the cone is thick
Thank you for your attention
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Experimental results: OH-PLIF* (extinction)
*OH-PLIF: A. Lantz
Re4000 8000 12000
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
Experimental results: OH-PLIF* (mean)
*OH-PLIF: A. Lantz
L/DL/D=3 L/D=5 L/D=7
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES - Computational domain (ref. grid)
• Parallelized in-house code
• Domain size
– 39.45D x 21.1D x 21.1D
• Divided into 4 blocks
– Mesh for each block 1283
– 8 million cells
• Streching function
– arctangent function
– Resolution up to 0.35mm in
cross section direction along
centre line
– Fixed ∆x=0.75mm
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES - Computational domain (fine grid)
• Parallelized in-house code
• Domain size
– 20D x 21.1D x 21.1D
• Divided into 24 blocks
– Mesh for each block 1283
– 50 million cells
• Streching function
– Fixed resolution inside cone
∆x= ∆y = ∆z =0.485mm
– arctangent function (outside)
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES – Boundary conditions
• At the wall (cone + far field BC)
– Non-slip condition for velocity
– Zero gradient for all scalar
• Co-flow (surrounding of the cone)
– Top hat velocity U=0.2m/s
• Domain outlet
– Convective outflow conditions
• Cone inlet
– Read-in inflow library generated from mixing chamber simulation
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, G-Z approach – Additional results
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, C-Z approach – FPI approach
• Freely propagated premixed flamelet for various Z (Φ) gererated
giving a tabulation of reaction rates, species as f(Z,c)
• Closure for
– MILES:
– Presumed pdf*:
With
and **
ccDuccucut
cωρρρρρ &+∇⋅∇+−⋅∇=∇+
∂
∂)()~(~
~
)()~
(~
~
ZDuZZuZut
Z∇⋅∇+−⋅∇=∇+
∂
∂ρρρρρ
)~,~
(),( cZcZ cc ωω && =
),( cZcω&
dZdccZcZPcZcZ cZcc ∫∫ ⋅= ),,~,~
,,(),(),( δδωω &&
≤−≤−
=
otherwise
ccandZZifcZcZP
cZ
cZcZ
,0
5.0~5.0~
,1
),,~,~
,,(δδ
δδδδ
XXCX
~~2 ∇⋅∇∆= ∆δ
*Duwig et Al (2008) where c is the temperature ** Pierce et Al. (1998
Lund university / Dept. Of Energy Sciences / Fluid Mechanics Seminar Series / 24-03-2010
LES, C-Z approach – FSD approach
• can be transported or expressed as an algebraic form*
with SGS wrinkling factor and the c-filter size
• Then the transport equation for (c) is
– Models needed + constant
– and
Σ=+∇⋅∇ )()(0
luc scD ρωρ &
*Boger et Al (1998)
Σ
c
cc
∆
−Ξ=Σ
)~1(~64
π
Ξ c∆
c
LucL
u
ccSc
Succucu
t
c
∆
−Ξ+
∇
∆⋅∇+−⋅∇=∇+
∂
∂ )~1(~~4~
616
~
)~(~~
ηρπ
ρρρρρ
dZZZPZsS ZlL ),~
,()(~
1
0
0 δ∫=