code_saturne User's Forum

Hello
 
I want to use the Libby-Williams model for a partially premixed flame. And I have two points:
 
First I examend the sbr. pdflwc.
This sbr uses the combination (fmin,hmax) and (fmax,hmin). which leads to the programmed form for h(f):
h(idirac) = ((hmax-hmin)*f(idirac) + hmin*fmin - hmax*fmax)  / (fmin-fmax)
 
However sbr. lwctcl combines (fmin,hmin) and (fmax,hmax) This leads to the form:
h(idirac) = ((hmin-hmax)*f(idirac) + hmax*fmin - hmin*fmax) / (fmin-fmax)
 
The second point concerns the calculated temperature level: For all
inflows with 500 K the calculated temperatures do not exceed 1250K. The
maximal temperatures however should reach values of about 2200 to 2300
K.(Used the EBU model to get this temperatures) Only decreasing the
activation temperature in sbr uslwc1 from 0.2 d05 (which seems to be
realistic?) to 2.5 d00 and chancing tstar from 0.12 d04 to 0.12 d06,
which effectively diminished its influence,leaded to the expected temperature level (including the correted calculation of h(idirac)).
Does anybody have any experience with the Libby-Williams model?
Can you tell me in which literature the uprogrammed reaction rate form is mentioned?
 
Thanks
Johannes Koopman
 
part2:
I figured out that the 4 pic  sbr: pdfpp4.f90 has the "correct" form.
Morover I noticed that somtimes massfractions < 0 are calculated. Replacing them by for instance: yfuel = min(max(yfuel,0.d0),1.d0) improved the results a lot. (I could enlarge the mentioned value of the activation temperature to 0.2d04. Which is nearer, but "only" one size of magnitude below the advised value)
 
Nevertheless I am very interested in any comments on this subject.
 
regards
Johannes Kopman
 

The original Libby - Williams model have been developped to describe combustion in gas-turbine using Lean Premix. First ref. is :
Libby P.A. a Williams F. A. , "Presumed pdf analysisof partially premixed turbulent combustion" Combustion Science & Technology 161 : 351-390 (2000)
the model assume a joint pdf (in the mixture ratio - fuel mass fraction space) done of two Dirac's peaks. A budget equation is proposed for the covariance <f"Y"> but not extensively used (two Dirac's peaks => linear relationship and the correlation between variances is complete). Libby - Williams @ Poitiers models are issued from a collaboration between M. Champion at LCD (Poitiers) and EDF R&D. The most documented one include a PDF done of four Dirac's peaks. A first Curl distribution is assumed on the mixture fraction and progress variables conditionned by the mixture fraction are determined. Then Curl assumption is done again to split each mixture fraction peak in two fuel mass fraction peaks. The chemical source term is computed in the same way than for the standard Libby-Williams model. The source term for the covariance is used and new behaviour are enligthened (the mixture ratio don't have any reactive source term but the closer the stoechimoetry, the faster the reaction). With Oracle test bench (symmetric enlargement with two stream of different fuel air ratio)  in the mixture zone (splitter's wake) the correlation (between mixture fraction fluctuations and fuel mass fraction fluctuations) is +1 and, after the flamme it possibly  (depending on the two fuel air ratio) become negative. This version of model and it's capabilities are extensively documented in :
 G. Ribert & al. , "Modeling turbulent reactive flow with variable equivalence ratio : appications to the calculation of a reactive shear layer" Combustion Science & Technology , 176 : 907-923 (2004)
 
V. Robin & al., "Relevance of approximated PDF shapes for turbulent combsution modeling with variable equivalence ratio" Icders 2007 . The form for the kinetic parameters is from asymptotic analysis, free to tune. Some clipping on temperature is allowed (solution of a state equation, only the enthalpy is transported) but caution is needed for fuel mass fraction clipping (conservativity no more guaranteed ). Extensive use in industrial situation enlight limitiations of the original presumed pdf (when reactivity is strong, Dirac's peak are too close to the complete reaction limit) ; some modifications have been proposed, with a pdf done of Curl distribution for mixture fraction but with two Beta distributions for fuel mass fraction ; specially useful when the reaction kinetic can be fitted by a Beta function (use of a "free enthalpy" progress variable) see V. Fichet (chap 7 of the PhD thesis - in french - "Modelisation de la combustion du gaz naturel  ..." 2008 @ Ecole Centrale de Paris) and V. Robin & al. ... to be published. This model is still in progress, any collaboration and feedback are welcome.
 
Regards