Difference between revisions of "Directed Relation Graph with Error Propagation (DRGEP)"

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The DRGEP (Directed Relation Graph with Error Propagation) method calculates the contribution of all species and reactions on the production rate of the targeted species. First, the rate of direct inter-relation between two species A and B is calculated :
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The DRGEP (Directed Relation Graph with Error Propagation<ref name="wazaa"> T. Lu and C. K. Law. A directed relation graph method for mechanism reduction. Proceedings of the Combustion Institute, 30(1):1333–1341, 2005</ref>) method calculates the contribution of all species and reactions on the production rate of the targeted species. We present here a modified method<ref> N. Jaouen. An automated approach to derive and optimise reduced chemical mechanisms for turbulent combustion</ref> from the original one<ref name="wazaa"/>. First, the influence of a species B on the consumption/production of a target species A is calculated :
  
 
<math> r_{A-B} = \frac{\sum_{j=1}^{N_r} |\nu_{Aj} \dot{Q}_j \delta_{B_j}|}{\sum_{j=1}^{N_r} |\nu_{Aj} \dot{Q}_j|} </math>
 
<math> r_{A-B} = \frac{\sum_{j=1}^{N_r} |\nu_{Aj} \dot{Q}_j \delta_{B_j}|}{\sum_{j=1}^{N_r} |\nu_{Aj} \dot{Q}_j|} </math>
  
Then the indirect rate of a species D on A :
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with :
  
<math> r_{AD} =  </math>
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<math>
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\left\{
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\begin{array}{l}
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  \delta_{B_j} = 1  \quad \text{if B is involved in the jth reaction} \\
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  \delta_{B_j} = 0 \quad  \text{otherwise}
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\end{array}
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\right.
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  </math>
  
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and <math>\dot{Q}_j</math> the rate of reaction j. Next, the indirect impact of a species D on A is also considered :
  
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<math> r_{A-D} = max(r_{A-B} \quad \text{x} \quad r_{B-D}, r_{A-D})</math>
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----
  
 
The DRGEP repertory contains two files :
 
The DRGEP repertory contains two files :
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* drgep_species :  
 
* drgep_species :  
Calculates the rate of direct inter-relation between species r_AB and the indirect one r_AD
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Calculates the rate of direct inter-relation between species <math> r_{A-B} </math> and the indirect one <math> r_{A-D}</math>
  
 
* drgep_reaction :  
 
* drgep_reaction :  
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* drgep_1D_reactions :  
 
* drgep_1D_reactions :  
 
Runs the analysis of drgep_reaction for 1D premix regime
 
Runs the analysis of drgep_reaction for 1D premix regime
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=== Bibliography ===

Latest revision as of 21:48, 26 March 2017

The DRGEP (Directed Relation Graph with Error Propagation[1]) method calculates the contribution of all species and reactions on the production rate of the targeted species. We present here a modified method[2] from the original one[1]. First, the influence of a species B on the consumption/production of a target species A is calculated :

with :

and the rate of reaction j. Next, the indirect impact of a species D on A is also considered :



The DRGEP repertory contains two files :

- drgep.cpp

- drgep.h


where the DRGEP analysis of species and reactions is defined through the following functions :

  • drgep_species :

Calculates the rate of direct inter-relation between species and the indirect one

  • drgep_reaction :

Calculates the impact of each reaction on the creation and destruction of the target species

  • drgep_0D_species :

Runs the analysis of drgep_species for 0D auto-ignition or multiple inlet regime

  • drgep_0D_reactions :

Runs the analysis of drgep_reaction for 0D auto-ignition or multiple inlet regime

  • drgep_1D_species :

Runs the analysis of drgep_species for 1D premix regime

  • drgep_1D_reactions :

Runs the analysis of drgep_reaction for 1D premix regime


Bibliography

  1. 1.0 1.1 T. Lu and C. K. Law. A directed relation graph method for mechanism reduction. Proceedings of the Combustion Institute, 30(1):1333–1341, 2005
  2. N. Jaouen. An automated approach to derive and optimise reduced chemical mechanisms for turbulent combustion