Difference between revisions of "orch:Solvers"

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(Chemical kinetics)
(Chemical kinetics)
 
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== Solver to build reference trajectories ==
 
== Solver to build reference trajectories ==
  
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Get Equilibrium constants
 
Get Equilibrium constants
 
 
 
 
 
== Chemical kinetics ==
 
 
* Arrhenius law
 
 
<math>\mathcal{A}_j</math> is the pre-exponential factor, <math>\mathcal{\beta}_j</math> is the temperature exponent and <math>E_{a_j}</math> the activation energy
 
 
<math>
 
k_j = \mathcal{A}_j T^{\mathcal{\beta}_j} \exp \left(-\frac{E_{a_j}}{R T}\right)
 
</math>
 
 
 
* 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.
 
 
<math>
 
\mathcal{Q}_j = \mathcal{Q}_{f,j} - \mathcal{Q}_{r,j}
 
</math>
 
 
 
* Production/Consumption source terms
 
 
species <math>Y_k</math> source terms are deduced from
 
 
<math>
 
\dot{\omega}_k = W_k \sum_{j=1}^{N_R} \nu_{k,j} \mathcal{Q}_j
 
</math>
 
 
* 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.
 
 
<math>......</math>
 
 
The third body M can be any inert molecule.
 

Latest revision as of 19:33, 7 March 2016

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

Get Gibbs Free Energy

Get Equilibrium constants