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# Eddy Break-Up Model

High Reynolds and Damkohler numbers are assumed in the model. The mean reaction rate is mainly controlled by the turbulent mixing time \tau_t defined as the ratio between turbulent kinetic energy and its dissipation rate (SpaldingDB:1971). In term of progress variable c , the expression of the mean reaction rate that is usually used is:

$\bar{\dot{\omega }}= C_{EBU} \bar{\rho }\frac{\varepsilon }{\kappa } \tilde{c}\left(1-\tilde{c}\right)$

or in term of fuel mass fraction Y_F , assuming excess of oxidizer:

$\bar{\dot{\omega }}=C_{EBU} \bar{\rho }\frac{\varepsilon }{\kappa } \frac{\tilde{Y}_{F} }{Y_{F}^{0} } \left(1-\frac{\tilde{Y}_{F} }{Y_{F}^{0} } \right)$

The eddy-break model (EBU) is available in many CFD commercial codes. The model has been extensively employed in numerical analysis because the reaction rate is simply written as a function of known quantities and therefore its use is convenient from the computational point of view. For turbulent combustion, the EBU model gives generally better results than the simple Arrhenius model. It is known that the EBU model tends to overestimate the reaction rate, especially in highly strained regions where the turbulent mixing time is small such as close to flame holders and walls (PoinsotT:2001). The accuracy of this model can be improved with the introduction in the formulation of the efficiency function of the ITNFS (Intermittent Turbulent Net Flame Stretch) model (Meneveau and Poinsot, 1991).

Other weaknesses of the original EBU model are that the reaction rate does not depend on the chemical properties of the mixture and that the turbulence is assumed to be homogeneous and isotropic. Some modifications of the constant placeCEBU have been proposed by Said and Borghi (1988) to mimic chemical features.

Spalding D.B., Stephenson P.L. and Taylor R.G. (1971) A Calculation Procedure for the Prediction of Laminar Flame Speeds. Combustion and Flame, 17:55-64.(BibTeX)
Poinsot T. and Veynante D. (2001) Theoretical and numerical combustion. Edwards, Philadelphia.(BibTeX)

Meneveau C. and Poinsot T., 1991 Stretching and quenching of flamelets in premixed turbulent combustion. Combust. Flame, 86, 311-332.

Said R. and Borghi R. (1988), A simulation with a cellular automaton for turbulent combustion modelling. 22nd Symposium (Int.) on Combustion, The Combustion Institute, placeCityPittsburgh, 569-577.