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 | + | 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> | ||
| − | + | with : | |
| − | <math> | + | <math> |
| + | \left\{ | ||
| + | \begin{array}{l} | ||
| + | \delta_{B_j} = 1 \quad \text{if B is involved in the jth reaction} \\ | ||
| + | \delta_{B_j} = 0 \quad \text{otherwise} | ||
| + | \end{array} | ||
| + | \right. | ||
| + | </math> | ||
| + | and <math>\dot{Q}_j</math> the rate of reaction j. Next, the indirect impact of a species D on A is also considered : | ||
| + | <math> r_{A-D} = max(r_{A-B} \quad \text{x} \quad r_{B-D}, r_{A-D})</math> | ||
| + | |||
| + | |||
| + | |||
| + | ---- | ||
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 | + | 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 | ||
| + | |||
| + | |||
| + | === 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
