Abstract
Modelling premixed turbulent flames is of importance in a variety of technological applications. In many industrial combustors, reactants may not be uniformly mixed and the local equivalence ratio depends on the flame element considered and changes with spatial location, time, degree of reaction,… A way to model premixed turbulent flames in non uniformly mixed reactants is proposed. Our approach is based on the Coherent Flame Model due to Marble and Broadwell (1977). In this model as in various other flamelet descriptions, the reaction zone is viewed as a collection of laminar flame elements (flamelets) embedded in the turbulent flow. A first extension of the Coherent Flame Model is derived and tested but does not account for the reactions that may take place in the burned gases. An improved model is then proposed to deal with more complex situations in which unburned reactants remaining in the burned gases form a diffusion flame inside the hot stream. This configuration arises when rich and lean premixed flames coexist in the same flow. The temperature of combustion products is then sufficiently high to initiate and sustain a diffusion flame. Numerical calculations are provided to illustrate the different models.
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Abbreviations
- s :
-
mass stoichiometric ratio
- u k :
-
velocity component
- V Di :
-
consumption rate per unit flame area
- V F :
-
actual mass consumption of fuel
- V L :
-
laminar flame speed
- W i :
-
consumption rate of reactant i (per unit volume)
- x k :
-
spatial coordinates
- Y f0 :
-
mass fraction of oxidizer in fresh gases
- Y ff :
-
mass fraction of fuel in fresh gases
- Y bo :
-
mass fraction of oxidizer in burned gases
- Y bf :
-
mass fraction of fuel in burned gases
- α :
-
constant
- ß :
-
constant
- ε s :
-
strain rate
- μ t :
-
turbulent viscosity
- v t :
-
kinematic viscosity
- Σ :
-
flame surface density
- Σ d :
-
diffusion flame surface density
- Σ p :
-
premixed flame surface density
- σi :
-
Schmidt number of specie i
- σΣ d :
-
Schmidt number of flame surface density
- ρ :
-
density
- ρ f :
-
density in the fresh gases
- Φ :
-
equivalence ratio
References
Bray, K. N. C., Libby, P. A., Moss, J. B. (1984): Comb. Sci. Tech., 143
Bray, K. N. C. (1986): In Complex Chemical Reaction Systems, J. Warnatz and W. Jaëger, eds., Springer Verlag, Heidelberg, pp. 356–375
Bray, K. N. C., Champion, M., Kostiuk, L. W., Libby, P. A. (1989): Seventh Symposium on Turbulent Shear Flows. Stanford
Buckmaster, J., Matalon, M. (1988): Anomalous Lewis number effects in tribrachial flames. 22nd Int. Symp. on Combustion. The Combustion Institute
Candel, S. M., Darabiha, N., Esposito, E., Giovangigli, V., Lacas, F., Laverdant, A., Maistret, E., Poinsot, T., Trouvé, A., Veynante, D., Zikikout, S. (1988): Internal report, Lab. E.M2.C., C.N.R.S. et Ecole Centrale des Arts et Manufactures. Châtenay Malabry, France
Carrier, G. F., Fendell, F. E., Marble, F. E. (1975): SIAM, J. Appl. Math. 28, 00–00
Clavin, P., Williams, F. A. (1982): J. Fluid Mech. 116, 215
Darabiha, N., Giovangigli, V., Trouvé, A., Candel, S. M., Esposito, E. (1987): Coherent flame description of turbulent premixed ducted flames. In Turbulent Reactive Flows, R. Borghi and S. N. B. Murthy, eds., Springer Verlag, New-York, pp. 591–637
Lacas, F., Zikikout, S., Candel, S. M. (1987): 23rd Joint Propulsion Conference. San Diego, AIAA Paper No 87-1782
Maistret, E., Darabiha, N., Poinsot, T., Veynante, D., Lacas, F., Candel, S., Esposito, E. (1989): Recent developments in the coherent flamelet description of turbulent combustion. Numerical Combustion, A. Dervieux and B. Larrouturou eds., Springer Verlag, Berlin pp. 98–117
Marble, F. E., Broadwell, J. E. (1977): The coherent flame model for turbulent chemical reactions. Project Squid Rep. TRW-9-PU
Marble, F. E., Broadwell, J. E. (1979): A theoretical analysis of nitric oxide production in a methane-air turbulent diffusion flame. EPA Tech. Rep.
Peters, N. (1984) Prog Energy Comb. Sci. 10, 319
Peters, N. (1986): 21st Symp. (International) on Combustion. The Combustion Institute
Phillips, H. (1965): Flame in a buoyant methane layer. 10th Int. Symp. on Combustion. The Combustion Institute
Rogg, B. (1989): Seventh Symposium on Turbulent Shear Flows. Stanford
Spalding, D. B. (1978): Seventeenth Symposium (International) on Combustion. The Combustion Institute
Veynante, D., Candel, S. M., Martin, J. P. (1986): In Complex Chemical Reaction Systems, J. Warnatz and W. Jaëger, eds. Springer Verlag, Heidelberg, pp. 386–398
Veynante, D., Lacas, F., Candel, S. M. (1989): A new flamelet combustion model combining premixed and non premixed turbulent flames. A.I.A.A. 27th Aerospace Sciences Meeting. Reno (Nevada)
Williams, F. A. (1975): AGARD Conf. Proc. 164
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Veynante, D., Lacas, F., Maistret, E., Candel, S.M. (1991). Coherent Flame Model for Non-Uniformly Premixed Turbulent Flames. In: Durst, F., Launder, B.E., Reynolds, W.C., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76087-7_27
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DOI: https://doi.org/10.1007/978-3-642-76087-7_27
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