 moles/(m3s)
| (16) |
As mentioned earlier, the EBU model assumes that the reaction rate is determined solely by the turbulent mixing rate. There have been attempts in the literature to add the effects of chemical kinetics to the eddy break-up model. Before describing these, we need to explain how chemical reaction rates are obtained from finite-rate kinetics.
The reaction rate of each reaction can be written down (from the point of view of a reactant) as a function of composition and temperature in the modified Arrhenius form:
|
moles/(m3s)
| (16) |
In the above equation, 
, 
and 
are the pre-exponential factor, temperature exponent and activation energy for the 
reaction, respectively, and 
is the universal gas constant. The 
exponents of the reacting species 
are the same as 
when the reactions are elementary, as in the case of full complex chemistry. When a reduced or a global chemical mechanism is used instead of the full known mechanism, the 
exponents will be different from the stoichiometric coefficients.
This model accounts for finite rate effects by assuming that the actual reaction rate 
, used in Eqn. 15, is the minimum of the reaction rates from Eqn. 16, with 
, 
, and 
, in place of 
, 
, and 
, and Eqn. 9 or Eqn. 10, as the case may be. This assumption can be expressed as:
| (17) |
The turbulent mixing time scale, 
, used in the standard EBU model, decreases with decreasing distance from solid surfaces. This leads to over-prediction of reaction rates in near-wall regions. To alleviate this problem, the mixing time scale is augmented by a time scale derived from the chemical reaction rate from finite-rate kinetics, Eqn. 16, defined as:
| (18) |
As a result, the time scale 
used in the standard EBU model (Eqn. 9 or Eqn. 10) can now be modified to:
| (19) |
Clearly, the reaction rate predicted by using this model is smaller than that from the standard EBU model. This may lead to difficulty in sustaining the reaction during the numerical simulation.