View source for Premix CH 4/Air flame with scheme GRI12

== '''Objectives''' ==

The Stochastic_GRI12 test case describes a reduction of the GRI1.2 scheme for a 1D premixed flame. Starting with 32 species and 177 reactions, we reduce to 14 species and 26 reactions.

== '''Key parameters''' ==


The target species considered for this test case are O2, CO and CO2. The characteristics of the premixed flame are displayed below (part of the input_file.ini) :

 //------Flame parameters------//
 //Flame 0
  Tf = 300
  To = 300 
  Pressure = 1E+05
  Equivalence_ratio = 0.75 
  Xf = CH4:1.0               
  Xo = O2:0.21, N2:0.79
 // the composition can also be added with mass fractions, for that replace "Xf" by "Yf" and "Xo" by "Yo"  
  Initial_flame = flames/flame__Phi_0_75__P_100000__T_300.cantera
  Final_flame = flames/flame
 //End

== '''Results''' ==

=== DRGEP step === 

While running the DRGEP species step (with <code>step = DRGEP_Species</code> in the "input_file.ini"), your terminal should display the following information :

 MECHANISM:------------------------------------------------------------------------------------------------------
            Reading initial mechanism "mechanisms/gri12.xml" with description "gri12" ----------> OK
               Number of species: 32
               Number of reactions: 177

 PREMIXED FLAME:--------------------------------------------------------------
  Reading initial flame "flames/flame__Phi_0_75__P_100000__T_300.cantera" with description "st_flame" ----------> description: test flame
 OK
               Pressure: 100000
               Equivalence ratio: 0.75
               Composition (mass fractions): 
                                    <O2:0.223145>
                                    <CH4:0.0419532>
                                    <N2:0.734901>



followed by the the species associated with their rank :

 -------DRGEP coefficients-------
 --------------------------------
 1.37642e-15  AR
 2.12795e-06  HCCOH
 4.32935e-05  C2H
 0.000157543  CH2CO
 0.000362521  C
 0.000444401  C2H2
 0.00101888  HCCO
 0.00357515  C2H3
 0.00398744  CH3OH
 0.00409277  CH
 0.00543294  CH2OH
 0.0126485  C2H4
 0.0126485  C2H5
 0.0170844  CH2(S)
 0.0190984  C2H6
 0.0314311  CH2
 0.0362943  H2O2
 0.0844714  H2
 0.0862782  CH3
 0.105794  CH2O
 0.110349  HCO
 0.141159  H2O
 0.150828  CH3O
 0.218864  O
 0.294638  HO2
 0.48461  OH
 0.48475  H
 1  O2
 1  CH4
 1  CO
 1  CO2
 1  N2




From a detailed 32 species scheme, we obtain reduced schemes (31 to 14 species). and we choose the one with 14 species for the next step because the shape of the velocity and species are conserved (and Cantera is unable to converge the 13-species scheme. The code will therefore end with an error message. But it is fine). The following Figure 1 is available in the directory <code>outputs/Premixed/</code> with the file format of EPS.

[[File:DRGEPSpec_14Sp_42R_Premixed.png|900px|center]]

Fig1 : Comparison between the reference trajectories of the target species, the temperature and the flame speed  (in black), and the trajectories computed with the reduced mechanism with 14 transported species and 42 reactions, after a DRGEP species reduction  (in red).



From the reduced scheme with 14 species, we then perform the next DRGEP Reactions step by manually change the value of the "step" keyword in the "input_file.ini" as <code>step = DRGEP_Reactions</code>. Make sure the reference mechanism and trajectory are correctly set up (i.e., <code>mech_ref = mechanisms/gri12.xml; trajectory_ref = Ref_DRGEP_Species32</code>). The DRGEP Reactions step displays the associated 42 reactions (forward, reverse and global) with their rank : 


 Reaction 22  9.23227e-06
 Reaction 1  2.08238e-05
 Reaction 11  2.29985e-05
 Reaction 2  5.30076e-05
 Reaction 12  0.00029274
 Reaction 18  0.00191785
 Reaction 6  0.00198407
 Reaction 36  0.00293471
 Reaction 38  0.00420356
 Reaction 31  0.00462285
 Reaction 34  0.00611017
 Reaction 7  0.00905302
 Reaction 10  0.00921383
 Reaction 32  0.0106164
 Reaction 37  0.0133867
 Reaction 8  0.0136681
 Reaction 25  0.0237175
 Reaction 24  0.0277978
 Reaction 29  0.0305413
 Reaction 13  0.0329515
 Reaction 9  0.0342601
 Reaction 3  0.0398655
 Reaction 5  0.0422524
 Reaction 14  0.0442348
 Reaction 19  0.0493222
 Reaction 35  0.102885
 Reaction 40  0.103946
 Reaction 26  0.111933
 Reaction 30  0.131232
 Reaction 23  0.159996
 Reaction 21  0.161005
 Reaction 20  0.180048
 Reaction 39  0.18465
 Reaction 42  0.19675
 Reaction 4  0.208145
 Reaction 15  0.215404
 Reaction 16  0.222982
 Reaction 27  0.274358
 Reaction 17  0.274617
 Reaction 33  0.403162
 Reaction 41  0.437888
 Reaction 28  0.438952


After this step, by comparing the reference trajectories with the new ones, we choose to delete 16 reactions because after 17 reactions removed, the CO2 profile loose its initial shape.
The next step is performed with 14 species and 26 reactions.

[[File:DRGEPR_14sp_26R_Premixed.png|900px|center]]

Fig2 : Comparison between the trajectories of the target species, the temperature and the flame speed computed with the reduced 14-species 42-reaction mechanism (in black) , and the trajectories computed with the reduced mechanism with 14 transported species and 26 reactions after a DRGEP reaction reduction (in red).

=== QSS step ===


The '''computeQSSCriteria''' step provides the QSS criteria of each species and the different links with the others species : 

 Species H  0.0752034
 Species O  0.0211171
 Species O2  0.33194
 Species OH  0.019287
 Species H2O  0.379235
 Species HO2  0.0113201
 Species CH3  0.107792
 Species CH4  0.79541
 Species CO  0.693792
 Species CO2  0.720209
 Species HCO  0.00321461
 Species CH2O  0.0817911
 Species CH3O  0.0360026
 Species N2  0


 Interactions with species H  with QSS Criteria 0.0752034
 HO2:2  CH3:1  CH2O:2  CH3O:1  N2:1  

 Interactions with species O  with QSS Criteria 0.0211171
 OH:1  HO2:1  CH3:1  CH2O:1  CH3O:1  

 Interactions with species OH  with QSS Criteria 0.019287
 O:1  OH:2  HO2:1  CH3:2  HCO:2  CH2O:1  CH3O:1  

 Interactions with species HO2  with QSS Criteria 0.0113201
 H:2  O:1  OH:1  CH3:1  CH2O:1  N2:1  

 Interactions with species CH3  with QSS Criteria 0.107792
 H:1  O:1  OH:2  HO2:1  

 Interactions with species HCO  with QSS Criteria 0.00321461
 OH:2  

 Interactions with species CH2O  with QSS Criteria 0.0817911
 H:2  O:1  OH:1  HO2:1  

 Interactions with species CH3O  with QSS Criteria 0.0360026
 H:1  O:1  OH:1  

 Interactions with species N2  with QSS Criteria 0
 H:1  HO2:1  



We choose to put the species CH3O and HCO in QSS hypothesis due to their low QSS coefficient. The species HO2 could have been a good candidate too but it is linked to himself (non linearity).

In order to obtain the trajectories of the 14-species 26-reaction reduced scheme with these 2 species in QSS hypothesis, we run the '''getQSSfile''' step and we obtain the following graphs.We observe that the final state and the shape of the trajectories are conserved. It is under these conditions that the optimisation step will be efficient.

We can note that the main target profiles are not impacted by the QSS hypothesis, nevertheless the fitness seems better. This is due to errors compensations by the other species not shown here (remind that the fitness is calculated for all species, velocity and temperature, the target just have a larger impact coefficient on the fitness). 

[[File:QSS_12sp_Premixed.png|900px|center]]

Fig3 : Comparison between the reference trajectories of the target species, the temperature and the flame speed (in black), and the trajectories computed with the reduced mechanism with 12 transported species and 26 reactions after a DRGEp reaction reduction (in red).

=== Optimisation ===

The final step of the ORCh method, the genetic algorithm, enables to recover the trajectories of the target species. Firstly, we allowed a 10 % variation on the pre exponential factor, the temperature exposant and 6 % on the energy activation in order to find their optimal values (i.e., <code>AllowedVariation_A = 0.10; AllowedVariation_b = 0.10; AllowedVariation_E = 0.06</code>). 

A population of 40 elements was used during 50 generations. The optimisation step supports running in parallel. For example, we can use 20 processors via <code>mpirun -np 20 mainprogram</code>. Just make sure that PopSize divided by the number of processes is an integer. This step may take a long time, like several hours, depending on how many processors are used. The optimised scheme is in <code>analytic_schemes/Ref/</code> while the corresponding EPS figures can be found in <code>analytic_schemes/PLOTS/</code>.


The following trajectories of the temperature, the flame speed and the target species match perfectly the ones of the reference detailed scheme with only 12 transported species and 26 reactions.
 
[[File:Optim_PremixGRI12.png|900px|center]]

Fig4 : Comparison between the reference trajectories of the target species, the temperature and the flame speed (in black), and the trajectories computed with the reduced mechanism with 12 transported species and 26 reactions after optimisation (in red).

== '''Bibliography''' ==