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| − | == Chemical kinetics ==
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| − | This chapter reports the principles that drive the computation of combustion chemistry in most CFD softwares.
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| − | === Chemkin (.scheme .therm .trans), Cantera (xml) ===
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| − | ...
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| − | === Arrhenius law ===
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| − | <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
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| − |
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| − | <math>
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| − | k_j = \mathcal{A}_j T^{\mathcal{\beta}_j} \exp \left(-\frac{E_{a_j}}{R T}\right)
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| − | </math>
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| − |
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| − | === Three-body reactions ===
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| − | 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 <math>\text{M}</math> 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.
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| − | <math>......</math>
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| − | The third body M can be any inert molecule.
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| − |
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| − | === Falloff reactions ===
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| − | 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.
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| − | ==== Lindemann ====
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| − | 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
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| − | * the low pressure limit
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| − | <math>
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| − | k_0 = \mathcal{A}_0 T^{\mathcal{\beta}_0} \exp\left(-\frac{E_0}{R T}\right)
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| − | </math>
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| − | * and the high pressure limit
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| − | <math>
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| − | k_\infty = \mathcal{A}_\infty T^{\mathcal{\beta}_\infty} \exp\left(-\frac{E_\infty}{R T}\right)
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| − | </math>.
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| − | The expression taken at any pressure is based on a combination of both low and high-pressure Arrhenius expressions. The term <math>P_r</math> is here equivalent to a pressure and <math>\text{M}</math> represents the concentration of the mixture, possibly estimated from third-body efficiencies.
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| − |
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| − | ==== Troe ====
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| − | <code>
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| − | <!-- reaction 0012 -->
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| − | <reaction reversible="yes" type="falloff" id="0012">
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| − | <equation>O + CO (+ M) [=] CO2 (+ M)</equation>
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| − | <rateCoeff>
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| − | <Arrhenius>
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| − | <A>1.800000E+07</A>
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| − | <b>0</b>
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| − | <E units="cal/mol">2385.000000</E>
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| − | </Arrhenius>
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| − | <Arrhenius name="k0">
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| − | <A>6.020000E+08</A>
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| − | <b>0</b>
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| − | <E units="cal/mol">3000.000000</E>
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| − | </Arrhenius>
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| − | <efficiencies default="1.0">AR:0.5 C2H6:3 CH4:2 CO:1.5 CO2:3.5 H2:2 H2O:6 O2:6 </efficiencies>
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| − | <falloff type="Lindemann"/>
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| − | </rateCoeff>
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| − | <reactants>CO:1 O:1.0</reactants>
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| − | <products>CO2:1.0</products>
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| − | </reaction>
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| − | </code>
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| − | === Reaction rates ===
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| − | 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.
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| − | <math>
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| − | \mathcal{Q}_j = \mathcal{Q}_{f,j} - \mathcal{Q}_{r,j}
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| − | </math>
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| − | === Species production/consumption source terms ===
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| − | Species <math>Y_k</math> source terms are deduced from
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| − |
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| − | <math>
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| − | \dot{\omega}_k = W_k \sum_{j=1}^{N_R} \nu_{k,j} \mathcal{Q}_j
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| − | </math>
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| | == Solver to build reference trajectories == | | == Solver to build reference trajectories == |
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