Difference between revisions of "orch:Solvers"

Revision as of 15:07, 7 March 2016

Chemical kinetics

• Arrhenius law

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

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

• 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.

${\displaystyle ......}$

The third body M can be any inert molecule.

• 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.

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

• Production/Consumption source terms

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

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

Solver to build reference trajectories

DRGEP solver for species reduction

• Compute species direct inter-relations

• Compute species relations through indirect paths

• Compute relations between targets and

DRGEP solver for reactions reduction

QSS solver

• Solve for thermodynamic

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

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

Get Gibbs Free Energy

Get Equilibrium constants