Generation

To generate the species Lewis numbers, the physical configuration should be Flame is Counterflow Diffusion in Mixture Fraction Space.

(0) Set #define MOLARDIFF, #define MOLARDIFFUSION, #define CONVECTION, #define COOLTRANSPORT, and #undef SIMPLEMIXING, and then recompile the code. See more details in the next section.

(1) First run FlameMaster with ConstLewisNumber is FALSE (i.e. use the unsteady solver).

(2) Once the solution is generated at a moderate chi_st (probably 10 1/s, please run several ones to check the sensitivity!) adiabatic upper branch (i.e., no radiation) case, copy the species/Le pairs at the end of the file to a new file like upper-Le_i.txt. For more details about radiation settings, see here.

(3) You can also modify Le values in that file (i.e., upper-Le_i.txt), although you might need to step to the values you want to enable convergence.

Then you can run FlameMaster again with ConstLewisNumber is TRUE and LewisNumberFile is upper-Le_i.txt. The same file or constant Lewis numbers can be used for NGA.

Detailed settings for different transport models

The following settings are to guarantee mass conservation and avoid the summation of mass fractions to be greater than 1.

(1) Full transport: #define MOLARDIFF, #define MOLARDIFFUSION, #define CONVECTION, #define COOLTRANSPORT, #undef SIMPLEMIXING.

(2) Constant but non-unity Lewis numbers: #define MOLARDIFF, #define MOLARDIFFUSION, #define CONVECTION, #undef COOLTRANSPORT, #undef SIMPLEMIXING.

(3) Unity Lewis number: #undef MOLARDIFF, #undef MOLARDIFFUSION, #undef CONVECTION, #undef COOLTRANSPORT, #define SIMPLEMIXING.

Remark:

• Both MOLARDIFF and CONVECTION appear in TCountDiffFlameMix.C and TTransFlameSolver.C, but COOLTRANSPORT only appears in TCountDiffFlameMix.C. MOLARDIFFUSION appear in TCountDiffFlameCont.C, TCountDiffFlameSim.C and TUnstrPremFlamePhys.C.
• In TCountDiffPhysEigen.C, when you use full transport or constant but non-unity Lewis numbers, remember to #undef SIMPLEMIXING because defining it will #undef MOLARDIFFUSION. When you use unity Lewis number, remember to #define SIMPLEMIXING and #undef MOLARDIFFUSION.
• Unity Lewis number is much easier to converge than the other two. So a good strategy is to make the unity Lewis number case converge, and start from there to get converged solutions for the other two cases.

Sensitivity

About the sensitivity of these constant Lewis numbers to conditions:

(0) Prefer to re-generate a set of constant Lewis numbers for the specific fuel mixture to encourage the convergence of flamelet solutions, although this may not be necessary sometimes.

(1) I think changing those parameters could make a difference, although I am not 100% sure.

(2) I usually set the fuel/oxidizer temperatures and pressures to whatever was in the experiment (e.g., T = 298 K and atmospheric pressure 1.013e5 Pa).

(3) I don’t think I have ever used a non-atmospheric pressure, but you should try to see the pressure effect (for our high pressure soot formation paper).

(4) Changing the scalar dissipation rate matters the most, since this parameter is chi_st and gives you the flamelets along the S-curve – you can specify multiple values in the .input file to let FlameMaster generate solutions in succession. However, generating a set of Lewis numbers at each chi_st with the detailed transport solver would take a very long time. We did investigate the Le at various chi_st values (10, 20, and maybe a few more), and we don’t think there were huge differences.

Knowledge

(1) The value of stoichiometric mixture fraction Zst changes when the major species have differential diffusion: with differential diffusion, the peak temperature occurs at stoichiometric Bilger mixture fraction, not the conserved mixture fraction.

(2) When there is no differential diffusion (e.g., unity Lewis number), Bilger mixture fraction is exactly the same as the conserved mixture fraction.

(3) When SSTA is used, Bilger mixture fraction is almost the same as the conserved mixture fraction, and their difference is negligible. This is because most of the major species are identified as strain-insensitive by SSTA and unity Lewis number is used for these species.