Difference between revisions of "orch:Solvers"

From orch
Jump to: navigation, search
(Lindemann)
(Chemical kinetics)
 
(7 intermediate revisions by the same user not shown)
Line 1: Line 1:
== 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 ===
 
 
<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>
 
 
=== 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.
 
 
 
=== 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 $k_0$ and the high pressure limit <math>k_\infty</math>.
 
 
<math>
 
  k_0 = \mathcal{A}_0 T^{\mathcal{\beta}_0} \exp\left(-\frac{E_0}{R T}\right)
 
</math>
 
 
==== Troe ====
 
 
 
 
 
 
<code>
 
    <!-- reaction 0012    -->
 
    <reaction reversible="yes" type="falloff" id="0012">
 
      <equation>O + CO (+ M) [=] CO2 (+ M)</equation>
 
      <rateCoeff>
 
        <Arrhenius>
 
          <A>1.800000E+07</A>
 
          &lt;b>0&lt;/b>
 
          <E units="cal/mol">2385.000000</E>
 
        </Arrhenius>
 
        <Arrhenius name="k0">
 
          <A>6.020000E+08</A>
 
          &lt;b>0&lt;/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>
 
</code>
 
 
=== 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>
 
 
 
=== Species 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>
 
 
 
== Solver to build reference trajectories ==
 
== Solver to build reference trajectories ==
  

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