orch:Solvers

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Chemical kinetics

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

Chemkin (.scheme .therm .trans), Cantera (xml)

...


Arrhenius law

is the pre-exponential factor, is the temperature exponent and the activation energy

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 typical Arrhenius laws are applicable to the reactions that are described. However, if the pressure is in between, an accurate description of the phenomenon requires a more complicated rate expression. In such a case, the reaction is said to be in the ”fall-off” region.

Lindemann

Several formulas (derived from the Lindemann description) are available to smoothly relate the limiting low and high-pressure rate expressions. With the Lindemann approach, Arrhenius parameters need to be given for both

  • the low pressure limit

  • and the high pressure limit

.

The expression taken at any pressure is based on a combination of both low and high-pressure Arrhenius expressions. The term is here equivalent to a pressure and represents the concentration of the mixture, possibly estimated from third-body efficiencies.

Troe

   <reaction reversible="yes" type="falloff" id="0012">
     <equation>O + CO (+ M) [=] CO2 (+ M)</equation>
     <rateCoeff>
       <Arrhenius>
          <A>1.800000E+07</A>
          <b>0</b>
          <E units="cal/mol">2385.000000</E>
       </Arrhenius>
       <Arrhenius name="k0">
          <A>6.020000E+08</A>
          <b>0</b>
          <E units="cal/mol">3000.000000</E>
       </Arrhenius>
       <efficiencies default="1.0">AR:0.5  C2H6:3  CH4:2  CO:1.5  CO2:3.5  H2:2  H2O:6  O2:6 </efficiencies>
       <falloff type="Lindemann"/>
     </rateCoeff>
     <reactants>CO:1 O:1.0</reactants>
     <products>CO2:1.0</products>
   </reaction>

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.


Species production/consumption source terms

Species source terms are deduced from

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