The Extension of Eddy Dissipation Concept to the Framework of Large Eddy Simulation

Z.B.Chen, J.X.Wen, B.P.Xu, S.Dembele Centre for Fire and Explosion Studies, Faculty of Engineering, Kingston University, London

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Outline 

Introduction



Combustion Model  Extension of original Eddy Dissipation Concept (EDC) from RANS to LES  Modifications to the original EDC



Soot Model  Extension of Beji et al. (2011) smoke point based model to LES frame  Coupling with the modified/extended EDC



Treatment for radiative heat transfer



Validation results



Conclusions

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Introduction  Mixing based Combustion Models •

Mixture Fraction Model (MFM) ----fast

•

Eddy Dissipation Concept (EDC) ----fast + finite

 Effect of Turbulence on Combustion •

Z  (Yfu, Yo2, Yco2, Yh2o) ???

•

Z + Z” + PDF (MFM)

•

Yfu + Yo2 + Yco2 + YH2o (EDC)

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Introduction  Eddy Dissipation Concept (RANS format)

The reaction rate is associated with the total turbulent kinetic energy (k) and dissipation rate (ε).

Both Ypr and min(Yfu, Yo2/r) can be 0 for some regions in the beginning of the fire----this creates an ignition problem!

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Introduction  Eddy Dissipation Concept (LES format ???)

P1: Is it reasonable to calculate the reaction rate from the replacement of total kinetic energy and dissipation rate with SGS properties?

P2: γ is infinite close to the wall. It can also be huge in the internal domain due to local laminarization. This is non-physical.

P3: The ignition problem due to the χ formulation still exists, no matter what is the turbulence model.

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Combustion Model  Turbulent energy cascade Mean flow W′ u ′, L′, ω ′

q′

W ′′ u ′′, L′′, ω ′′ = 2ω ′

q ′′

W ′′′

Wn u n , Ln , ω n = 2ω n−1

qn

Wn +1

k=f(ksgs, Δ) ??? ε=g(ksgs, Δ) ???

WSGS

{

Structure levels under sub-grid scale

(B.F. Magnussen, 1981-2005)

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uSGS , ∆, ωSGS

qSGS

W1 W* u * , L* , ω *

q*

Combustion Model  Turbulent energy cascade Mean flow W′ u ′, L′, ω ′

q′

W ′′ u ′′, L′′, ω ′′ = 2ω ′

q ′′

W ′′′

Wn u n , Ln , ω n = 2ω n−1

qn

Wn +1 WSGS

{

Structure levels under sub-grid scale

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uSGS , ∆, ωSGS

qSGS

W1 W* u * , L* , ω *

q*

Combustion Model  Turbulent energy cascade Mean flow W′ u ′, L′, ω ′

q′

W ′′ u ′′, L′′, ω ′′ = 2ω ′

q ′′

W ′′′

Wn

k can not be described only as a function of ksgs and Δ. Note that the introduction of k in the EDC reaction rate is only due to the formulation of r.

u n , Ln , ω n = 2ω n−1

qn

Wn +1 WSGS

{

Structure levels under sub-grid scale

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uSGS , ∆, ωSGS

qSGS

W1 W* u * , L* , ω *

q*

Combustion Model  Reacting Fraction of Fine Structures Only the fraction of fine structures, χ, which is sufficiently heated will react. Therefore, where the temperature is higher, the possibility of combustion taking place near this area should be larger.

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Combustion Model  Reacting Fraction of Fine Structures

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Combustion Model  Eddy Dissipation Concept (LES format)

or

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Soot Model 

Detailed soot chemistry • Lindstedt, 1991;



Two conservation equations • Tesner, 1971; Magnussen, 1976, 1989; Moss, 1995



Smoke point concept • Markstein and de Ris (1984), Lautenberger et al. (2005), Chatterjee et al. (2011), Beji et al. (2011)



Soot conversion factor •



Floyd, 2003

Discrete reaction model •

Zhubrin, 2009

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Soot Model  Smoke Point Model (Beji et al. 2011)

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Soot Model  Smoke Point Model (LES)

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Radiation Model  Radiative Transfer Equation (if soot)

 Fixed Radiation Fraction (if no soot)

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FireFOAM Solver Mass

Low Mach number assumption; Finite volume method

Momentum

Total Enthalpy

Species

State of Equation

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Summary of fire scenarios tested EDC with fixed radiative fraction and no soot model

EDC + smoke point based soot model of Beji et al. (2011)

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Validation- EDC + Radiation Fraction  30cm methane fire (Gox, 1980)

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Validation- EDC + Radiation Fraction  30cm methane fire (Gox, 1980)

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Validation- EDC + Radiation Fraction  30cm heptane fire (Gore, 1992)

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Validation- EDC + Radiation Fraction  30cm heptane fire (Gore, 1992)

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Validation- EDC + Soot  30cm heptane fire (Gore, 1992)

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Validation- EDC + Soot  30cm heptane fire (Gore, 1992)

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Validation- Different Radiation Treatment  30cm heptane fire (Gore, 1992)

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Validation- Different Radiation Treatment  30cm heptane fire (Gore, 1992)

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Conclusions  The original RANS based EDC has been extended to the LES frame and modified to overcome some important limitations.  Predictions with the modified EDC in LES frame are in reasonably good agreement with the experiment data for a range of pool fires tested.  The predictions are less satisfactory for small fires which tend to be laminar or with very low level of turbulent mixing.  Further improvement is required for the implementation of the soot model and its coupling with the EDC.

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Acknowledgements The authors gratefully acknowledge financial and technical support from FM Global. Dr Yi Wang from FM Global, in particular, has been of great help in providing technical guidance on the source code and application of FireFOAM.

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