turbulent partially premixed methane-air combustion … · turbulent partially premixed methane-air...

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)


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


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


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


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


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


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)


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 =~


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)


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)


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~


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



• 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



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


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


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


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


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


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)


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(~~~

−+=


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 &+∇⋅∇ )(


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


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


Experimental results: OH-PLIF* (extinction)

*OH-PLIF: A. Lantz

Re4000 8000 12000


Experimental results: OH-PLIF* (mean)

*OH-PLIF: A. Lantz

L/DL/D=3 L/D=5 L/D=7


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


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)


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


LES, G-Z approach – Additional results


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


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∫=

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