Reaction models#
Eddy break-up model#
Assumptions:
for the assumptions of the RANS EBU model the interested reader is kindly referred to Poinsot & Veynante 2005
Example use case:
reacting turbulent jet flame: Input-output analysis
References:
Nomenclature:
\(\dot{\Omega}\): chemical reaction rate
\(C_\textrm{EBU}\): model constant
\(A_\textrm{EBU}\): model constant lumped together turbulent time scale \(\overline{\varepsilon}/\overline{k}\)
\(k\): turbulent kinetic energy
\(\varepsilon\): turbulent dissipation
\(\rho\): density
\(c\): progress variable
The mean reaction rate is
\[
\overline{\dot{\Omega}} = C_{EBU} \frac{\overline{\varepsilon}}{\overline{k}} \overline{\rho} \, \overline{c} (1-\overline{c}) = A_{EBU} \overline{\rho} \, \overline{c} (1-\overline{c})
\]
where \(A_\textrm{EBU}=C_{EBU} \frac{\overline{\varepsilon}}{\overline{k}}\) is constant in time, but may vary in space. It can be determined by inserting the temporal mean state, obtained by e.g. LES, into the equation above.
Linearized eddy break-up model#
The reaction rate of the linearized eddy break-up model is
\[
\dot{\Omega}' = A_{EBU} (\rho' (\overline{c} - \overline{c}^2) + \overline{\rho}(c'-2\overline{c}c'))
\]
with the same model constant \(A_\textrm{EBU}\) as for the mean reaction rate.