19th International Conference on the Discrete Simulation of Fluid Dynamics (DSFD 2010), July 5-9 Rome, Italy

1. 19th Discrete Simulation POLITECNICO DI TORINO
of Fluid Dynamics DEPARTMENT OF ENERGETICS
Radiative lattice Boltzmann method
applied to combustion simulation
and reduced chemical kinetics
A. F. Di Rienzo, E. Chiavazzo, P. Asinari
July 5-9, 2010 – Rome, Italy
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2. POLITECNICO DI TORINO Introduction
GOAL OF THE TALK
To point out (a) the derivation of the lattice Boltzmann model for
solving radiative heat transfer in an absorbing and emitting
medium and (b) how this model can be coupled with combustion
simulation via lattice Boltzmann and reduced chemical kinetics.
KEY POINTS
Combustion: to decouple fast and slow dynamics.
Radiation: to compute radiative source term to be used
in combustion model.
Coupling: to investigate radiative contribution to
combustion for a reactive gas mixture of hydrogen and
air.
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3. POLITECNICO DI TORINO Combustion 1/2
ASSUMPTIONS:
1. Flow field is incompressible and not affected by chemical reaction.
2. Transport properties are constant.
3. Fick’s law applies to diffusion
4. Viscous energy dissipation is neglected and radiative heat transfer is
discussed next.
Evolution equations for enthalpy and mass concentration of species i are:
H2+Air 9 species ([1], [2]) 9+1 equations to be solved!
[1] J. Li, Z. Zhao, A. Kazakov. F. L. Dryer, Int. J. Chem. Kinet., 2004
[2] K. Yamamoto et al., J. Stat. Phys. 107 (2002) 367–383 3

4. POLITECNICO DI TORINO Combustion 2/2
ISSUES:
• Solution of a large number of conservation equations
• Stiffness: high computational time
REDUCTION TECHNIQUES, FAST-SLOW MOTION DECOMPOSITION ([3],[4])
Primitive variables are re-parameterized
in terms of new slow quantities
The dynamics of is expected to be
slower than
[3] E. Chiavazzo, I. Karlin, A. N. Gorban, K. Boulouchos, JSTAT, 2009
[4] E. Chiavazzo, I. Karlin, A. N. Gorban, K. Boulouchos, Combust. Flame, in press, 2010 4

5. POLITECNICO DI TORINO Radiation 1/3
• SCATTERING
Rayleigh scattering
theory
Participating medium is absorbing and emitting. RTE reduces:
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6. POLITECNICO DI TORINO Radiation 2/3
• ABSORPTION
NARROW BAND MODELS and WIDE BAND MODELS rigorously
describe absorption of gases. Drawback: more time consuming than the
solution of the RTE itself.
PLANCK-MEAN ABSORPTION COEFFICIENT: less sophisticated and
easy to incorporate in the RTE numerical scheme.
H2O
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7. POLITECNICO DI TORINO Radiation 3/3
PSEUDO-TRANSIENT RTE
2-D PSEUDO-TRANSIENT RTE
[5]
[5] P. Asinari, S. C. Mishra, R. Borchiellini, A lattice Boltzmann formulation to the analysis of radiative
heat transfer problems in a participating medium, NHT-B, in press, 2010 7

8. POLITECNICO DI TORINO Coupling 1/2
DISTRIBUTION FUNCTION FOR MIXTURE AVERAGE TOTAL
ENTHALPY
RADIATIVE SOURCE TERM
Radiative heat flux Incident radiation
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9. POLITECNICO DI TORINO Coupling 2/2
REGIONS OF INFLUENCE ([6])
D2Q8
[6]A. F. Di Rienzo, P. Asinari, R. Borchiellini, S. C. Mishra, Improved angular discretization and error
analysis of the lattice Boltzmann method for solving radiative heat transfer in a participating medium,
submitted to JNMH&FF, 2010 9

10. POLITECNICO DI TORINO Example
2-D LAMINAR BURNER
REACTIVE MIXTURE
Premixed hydrogen/air
mixture at Tin=300 K.
DOMAIN SIZE
Lx = 1.4 mm
Ly = 7.3 mm
NUMERICAL RESOLUTION
Nx = 65
Ny = 330
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11. POLITECNICO DI TORINO Case 1- Dry H2
TEMPERATURE FIELD
Time = 1.11 ms Time = 2.22 ms Time = 4.44 ms
Comb. Comb.+ Rad Comb. Comb.+ Rad Comb. Comb.+ Rad
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12. POLITECNICO DI TORINO Case 1- Dry H2
Time = 2.22 ms
TRANSPARENT MEDIUM:
H2+AIR
NO EFFECT OF RADIATIVE
HEAT TRANSFER !!!
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13. POLITECNICO DI TORINO Case 2- Wet H2
FRESH MIXTURE: H2+Air+H2O Non-reactive
Comb. Comb.+ Rad
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14. POLITECNICO DI TORINO Case 2- Wet H2
Even though the fresh mixture (H2+Air+H2O) is opaque,
contribution of radiative heat transfer is so small that it can be
neglected.
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15. POLITECNICO DI TORINO Conclusions
1. Radiative LBM can be effectively coupled with
combustion model, by providing it the enthalpy rate
(radiative source term).
2. For transparent reactive mixture (H2+Air), radiative
contribution is null:
3. For opaque fresh mixture (H2+Air+H2O), radiative
contribution can be neglected as well:
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16. POLITECNICO DI TORINO
THANKS FOR YOUR
ATTENTION!
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