orch:Solvers

Chemical kinetics

This chapter reports the principles that drive the computation of combustion chemistry in most CFD softwares.

• Arrhenius law

${\mathcal {A}}_{j}$ is the pre-exponential factor, ${\mathcal {\beta }}_{j}$ is the temperature exponent and $E_{a_{j}}$ the activation energy

$k_{j}={\mathcal {A}}_{j}T^{{\mathcal {\beta }}_{j}}\exp \left(-{\frac {E_{a_{j}}}{RT}}\right)$

• Three-body reactions

In the forward direction, three-body reactions involve two species A and B as reactants and yield a single product AB. In that case, the third body M is used to stabilize the excited product AB*. On the contrary, in the reverse direction, heat provides the energy necessary to break the link between A and B.

$......$

The third body M can be any inert molecule.

• Falloff reactions

Under specific conditions, some reaction rate expressions are dependent on pressure and temperature. This is especially true for the rate associated to unimolecular/recombination fall-off reactions which increases with pressure. In such cases, if the chemical process takes place in a high or low pressure limit

• Reaction rates

The global rate of a reaction j (evolution in concentration per unit of time) varies depending on the proportion of the rates associated to the forward and backward directions.

${\mathcal {Q}}_{j}={\mathcal {Q}}_{f,j}-{\mathcal {Q}}_{r,j}$

• Production/Consumption source terms

Species $Y_{k}$ source terms are deduced from

${\dot {\omega }}_{k}=W_{k}\sum _{j=1}^{N_{R}}\nu _{k,j}{\mathcal {Q}}_{j}$

DRGEP solver for species reduction

• Compute species direct inter-relations

• Compute species relations through indirect paths

• Compute relations between targets and

QSS solver

• Solve for thermodynamic

$h_{k}=\Delta h_{f,k}^{0}+h_{sk}$

$h_{sk}=\int _{T_{0}}^{T}Cp_{k}dT$

Get Gibbs Free Energy

Get Equilibrium constants