Modeling laminar partially premixed flames with complex diffusion in OpenFOAM

Modeling laminar partially premixed flames withcomplex diffusion in OpenFOAM R©

Danny Messig, Jens Keller, Bernd Meyer, Christian Hasse

Institute of Energy Process Engineering and Chemical EngineeringFreiberg, Germany

Sixth OpenFOAM WorkshopPennstate

Contents

1 Introduction

2 Theoretical background

3 Validation

4 Flamelet results

5 Conclusions

2

Contents

1 Introduction


3 Validation

4 Flamelet results

5 Conclusions

3

IntroductionScope:

Numerical simulation of a laminar flame with complex diffusion

What is diffusion?Transport phenomenon caused by concentration andtemperature gradients

What is flamelet?Subgrid model, representing chemistry, kinetics and transportPhysical representation of interaction between chemicalreactions and transport

Why flamelet?Solving detailed chemistry conventional⇒ computational expensiveFLUT’s (Flamelet Look Up Table)⇒ enormous speed up

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Contents

1 Introduction


3 Validation

4 Flamelet results

5 Conclusions

5

Theoretical background

Governing equations:

∂ρ

∂t+∇ · (ρv) = 0

∂

∂t(ρv) +∇ · (ρvv) = −∇p+∇ · τ + ρg

∂

∂t(ρh) +∇ · (ρvh) = −∇ ·q +

Dp

Dt+ Q̇Radiation

∂

∂t(ρYi) +∇ · (ρvYi) = −∇ · ji +Ri

OpenFOAM standard:

∂

∂t(ρh) +∇ · (ρvh) = ∇ ·

(λ

cp∇h)

+Dp

Dt

∂

∂t(ρYi) +∇ · (ρvYi) = ∇ · (µ∇Yi) +Ri

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Radiation model based on RADCAL [1]:

Q̇Radiation = −4σpN∑

i=1

Xiai

(T 4 − T 4

∞)

Laminar heatflux q and species fluxes ji:

q =N∑

i=1

hiji︸︷︷︸Inter-diffusion

−λ∇T︸︷︷︸Fourier’s law

−N∑

i=1

RT

MiXiDT,i∇Xi︸︷︷︸

Dufour effect

ji = ρuiYi, (ui diffusion velocity)

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Diffusion velocities ui:

ui = uD,i + uT,i + uC

uD,i = − 1Lei

λ

ρcp

1Xi∇Xi, Fickian diffusion

Lei =λ

cpρDm,i, Lewis number

uT,i = −DT,i

ρYi

1T∇T, Soret effect

uC = −n∑

i=1

(uD,i + uT,i)Yi, correction to ensureN∑

i=1

ji = 0

Different modelling approaches for Lei, respectivelymixture-average diffusion coefficient Dm,i

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Flamelet:Mixture fraction Z:

ρ∂Z

∂t+∇ · (ρvZ) = ∇ · (ρDZZ)

Combustion in a diffusion flame takes place in the closevicinity of the surface of stoichiometric mixture Zst

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Flamelet:

Changes are mainly in orthogonal direction on iso-mixturefraction surfacesChanges of temperature and composition are expressed as afunction of the orthogonal coordinate

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Flamelet:Coordinate transformation and assumption leads to simplified1D flamelet equations:

ρ∂Yi

∂t=

ρχ

2Lei∂2Yi

∂Z2+Ri

Mixture fraction Z is now the independant coordinateFull 1D flamelet equations can be found in [2]

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new solver: lamReactingFoam:Full transport equations for mixture-average diffusionimplemented!Different diffusion models availableAdded radiation [1]Neglecting Dp/Dt for open laminar flamesImplemented in OpenFoam-1.5.x usingalternateChemistryModel [3]

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Contents

1 Introduction


3 Validation

4 Flamelet results

5 Conclusions

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Validation

Validation against:

1 Fluent calculations2 Experimental data

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Validation against Fluent

Case setup:

Laminar, diffusiondominated gas flowspecies properties fromsame databaseRi = Q̇Radiation = 0

Domain with L = 0.25 m

Inlet YO2 YH2O YCH4 YH2 YCO2 YN2 T ux

[−] [−] [−] [−] [−] [−] [K] [m/s]1 0 0.2 0 0 0 0.8 300

0.12 0.38 0 0.4 0.2 0.02 0 1000

boundary conditions

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Validation against Fluent

Results:CO2-profile along outlet

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Validation against experimental data

Flame characterisation:

premixed, partially premixed and non-premixed flame (f.l.t.r)

Primary equivalence ratio: Φ =

(V̇prim. Air

)st

V̇prim. Air

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Case setup:

Domain L = 20 cm

Geometry data from [4]Extruded domain (z < 0 cm)Fully developed velocity profile at inlets24100 non-uniform volume cells3D structured 2◦ wedge mesh

Inlet 1 Inlet 2Φ V̇CH4 V̇prim. Air V̇sec. Air

[−] [cm3/min] [cm3/min] [cm3/min]∞

3300

440002.464 1050

Bennett-flame [4] configuration

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Numerical setup:Diffusion models:

Full transport: Full transport equations for mixture-averagediffusion with Lei 6= const. 6= Le and radiationLe = 1: Full transport equations with Lei = Le = 1 andradiationOriginal: alternateReactingFoam with Sc = ν/Dm,i = 1,no Soret/Dufour effects and no radiation

Chemical Mechanism: GRI-Mech 1.2

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Results:Temperature profiles on centerline

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Results:OH mole fraction profiles on centerline

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Comparison of maximum centerline temperature Tmax,C, flameheight HT , flame height HOH:

Source Tmax,C HT HOH[K] [cm] [cm]

Φ =∞Experimental by Bennett et. al. [4] 1960 5.7 5.9

CFD by Bennett et. al. [4] 1868 8.0 8.2CFD by Claramunt et. al. [5] 1908 5.9 6.1

lamReactingFoam 1928 5.7 6.0Φ = 2.464

Experimental by Bennett et. al. [4] 2090 3.8 4.2CFD by Bennett et. al. [4] 1999 3.4 3.8

CFD by Claramunt et. al. [5] 2030 4.0 4.5lamReactingFoam 2042 3.9 4.3

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Contents

1 Introduction


3 Validation

4 Flamelet results

5 Conclusions

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Flamelet results

Scope:Compare different radial profiles of CFD-calculation oflamReactingFoam with results produced by an inhouse flameletcodeVerification for using the flamelet model in OpenFOAM R©

More details of the coupling between FLUT’s andOpenFOAM R© is given in talk „A CFD-Flamelet model basedtime scale analysis of multi-feed stream in a high pressuregasifier“ in the next session [6]

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Flamelet results

Set up:Bennett-flame configuration [4]Diffusion models:

Unity Lewis-Number Lei = Le = 1Non-unity constant Lewis-Number Lei = const. 6= Le

Flamelet calculations:Full flam.: Full set of flamelet equationsSimple flam.: Simplified set of flamelet equationsAnalytical approach for profiles of scalar dissipation rate χ

CFD: lamReactingFoamChemical mechanism: GRI-Mech 1.2No radiation

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Flamelet results

Unity Lewis-Number Lei = Le = 1

CO2 mass fraction and temperature T as functions of Z

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Flamelet results

Non-unity constant Lewis-Number Lei = const. 6= Le

CO2 mass fraction and temperature T as functions of Z

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Contents

1 Introduction


3 Validation

4 Flamelet results

5 Conclusions

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Conclusions

Full laminar diffusion transport equations in OpenFOAM 1.5successfully implementedVerification of corresponding diffusion methods in OpenFOAM1.5 with Fluent 12.0 and Cantera 1.8CFD improvement compared to published num. results forBennett-flame [4]Flamelet results in good agreement with full transport solutions

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Acknowledgement

The results described above were obtainedin the research project „HotVeGas“.The project was supported with public funding by theGerman Federal Ministry of Economics and Technology(Project ID 0327773B)

This research has been also funded by theGerman Federal Ministry of Education and Research in theframework of Virtuhcon(Project ID 040201030)

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Literatur I

[1] W. L. Grosshandler.RADCAL: A Narrow-Band Model for Radiation Calculations ina Combustion Environment.Technical report, NIST technical note 1402, 1993.

[2] J. Keller.Influence of molecular diffusion flux modeling on the structureof non-premixed and partially premixed flames.Master’s thesis, TU Bergakademie, 2011.

[3] Gschaider B., Rehm M., Seifert P., Meyer B.Implementation of an alternative chemistry library intoopenfoam.In Open Source CFD International Conference 2008, Berlin,2008.

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Literatur II

[4] B. A. V. Bennett, C.S. McEnally, L. D. Pfefferle, M.D. Smooke.Computational and Experimental Study of Axisymmetric CoflowPartially Premixed Methane/Air Flames.Combustion and Flame, 123:522–546, 2000.

[5] K. Claramunt, R. Consul, C. D. Pérez-Segarra and A. Oliva.Multidimensional mathematical modeling and numericalinvestigation of co-flow partially premixed methane/air laminarflames.Combustion and Flame, 137:444–457, 2004.

[6] Vegendla P., Weise S., Messig D., Hasse C.A CFD-Flamelet model based time scale analysis of multi-feedstream in a high pressure gasifier.In 6th OpenFOAM Workshop, 2011.

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Modeling laminar partially premixed flames with complex diffusion in OpenFOAM

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