SANDIA Flame D
Application Challenge AC209 © copyright ERCOFTAC 2023
Comparison of Test Data and CFD
In this section comparisons of the CFD results and test data are
organized as follows:
 Comparisons of two different approaches for modeling the turbulence/combustion interaction, namely: steady flamelet model and simplified Conditional Moment Closure (designated as CMC model in the figures from here on) obtained with the classical Smagorinsky subgrid scale model,
 Comparisons of two subgridscale models, namely: classical Smagorinsky subgrid scale model and dynamic Smagorinsky one using the steady flamelet model of turbulence/combustion interaction.
Fig.6. shows mean velocity axial component and mixture fraction along
the centerline for both steady flamelet and CMC approaches. One can see
quite significant discrepancies between both models. Steady flamelet
shows rapid velocity decay in the near field and then the slope is
quite close to the one measured experimentally. On the other hand the
CMC model leads to much smaller velocity decay. The velocity profile
for CMC is closer to experimental data but the slope at the distance
z/D=10 is underpredicted. At the distance z/D=30 both models predict
good velocity decay. As to the mixture fraction both models predict
quite a long distance z/D ≤ 16 for which the mixture fraction is unity
while the experiment showed much more intense mixing in this region. As
a consequence, at the jet centerline for a distance z/D ≤ 16 the numerical
models do not predict reaction and this is reflected in the temperature
profile and combustion products like CO_{2} shown in Fig.8. However,
further downstream in the fully developed flame the numerical results
are much closer to the experimental data. Especially CMC predicts the
value of temperature maximum and its location with quite high accuracy
(see Fig.7).



Fig. 6. Axial velocity (left) and mixture fraction (right) along the flame axis


Fig. 7. Temperature along the flame axis

The species distributions are shown in Figs 810. As the models
predict the flame too far from the nozzle exit, in all species
distributions similar discrepancies are observed at the distance
z/D = 10 – 20. And again, as was observed for the temperature profile, further in
the developed flame the agreement with experimental data is much
better. The distributions for H_{2}O, O_{2}, CO predicted with CMC are nearly
perfect. A bit worse results were obtained for H_{2}.



Fig. 8. Mean mass fraction of CH_{4} (left) and CO_{2} (right)




Fig. 9. Mean mass fraction of H_{2}O (left) and O_{2} (right)




Fig. 10. Mean mass fraction of CO (left) and H_{2} (right)

Fig.11 shows the fluctuating axial velocity and mixture fraction
components. In the near field the velocity fluctuations predicted by
both models at the distance z/D ≤ 10 are much higher than measured
experimentally which is consistent with much faster velocity decay in
this region shown in Fig.6. Further downstream in the developed flame,
agreement is very good. For the fluctuating component of the mixture
fraction shown in Fig.11 in the near field fluctuations are lower than
observed experimentally and again in the developed flame agreement is
quite good. Maximum value of temperature fluctuations (Fig.12) is
located much closer to the nozzle exit than the maximum value of mean
temperature. CMC leads to higher level of temperature fluctuations.
Fluctuating components of major species are shown in Figs 1315. Both
models predict reasonable levels of species fluctuation in agreement
with experimental results.



Fig. 11. RMS of axial velocity (left) and mixture fraction (right) along the jet flame axis


Fig. 12. RMS of temperature along the jet flame axis




Fig. 13. RMS of mass fraction of CH_{4} (left) and CO_{2} (right)




Fig. 14. RMS of mass fraction of H_{2}O (left) and O_{2} (right)




Fig. 15. RMS of mass fraction of CO (left) and H_{2} (right)

Sample radial profiles of mean and fluctuating velocities are shown in
Figs 16 and 17. Both models predict radial velocity profiles in very good
agreement with experiment in all the cross sections. Fluctuating
components are also in good agreement with experimental data. At the last
cross section at the distance z/D = 45 the flamelet model leads to some
overprediction of fluctuating components far from the flame axis. Mean
mixture fraction shown in Fig.18 is close to experimental data. As to the
mixture fraction fluctuating component shown in Fig. 19 agreement with
experimental data is also reasonable. However, a surprising result was
obtained at the distance z/D = 30 where the radial distribution of
fluctuating component of mixture fraction obtained with the CMC is
qualitatively different from experimental profile and from the result
obtained with steady flamelet. In the profile predicted with CMC a local
maximum is observed on the axis that is not present in experimental data.
At the current stage of the research it seems to be difficult to explain
these discrepancies analyzing physics of turbulence/combustion
interaction.






Fig 16. Mean axial velocity radial profile at the cross sections (a) z/D=15, (b) z/D=30, (c) z/D=45 
Fig 17. Fluctuating axial velocity radial profile at the cross sections (a) z/D=15, (b) z/D=30, (c) z/D=45







Fig 18. Mean mixture fraction radial profile at the cross sections (a) z/D=15, (b) z/D=30, (c) z/D=45 
Fig 19. Fluctuating mixture fraction radial profile at the cross sections (a) z/D=15, (b) z/D=30, (c) z/D=45

LES calculations were also performed to evaluate the importance of the
SGS model with Smagorinsky and dynamic Smagorinsky models using in both
cases the steady flamelet approach. The mean profile of axial velocity
and mean mixture fraction along the flame axis are shown in Fig. 20. Both
SGS models predict very similar velocity profiles especially in the near
field where only mixing appears without combustion. More clear
differences are observed in the region of combustion z/D > 20. A surprising
conclusion is that the simple Smagorinsky model predicts better the mean
velocity profile than the dynamic one. The mean mixture fraction profile
obtained with the Smagorisnky model is also closer to the experimental
results than the profile obtained with the dynamic model. The same
conclusion that Germano model leads to worse results can be derived from
the analysis of the temperature profile shown in Fig. 21.



Fig. 20. Axial velocity (left) and mixture fraction (right) along the flame axis


Fig. 21. Temperature along the flame axis

Figs 2224 show mean mass fraction of major species. In all cases
agreement with experimental data is satisfactory, and in all cases
results are slightly better for the Smagorinsky SGS model.



Fig. 22. Mean mass fraction of CH_{4} (left) and CO_{2} (right)




Fig. 23. Mean mass fraction of H_{2}O (left) and O_{2} (right)




Fig. 24. Mean mass fraction of CO (left) and H_{2} (right)

Fluctuating components of the axial velocity and mixture fraction are
illustrated in Fig. 25 & 26. Smagorinsky subgridscale model leads also to
better prediction of the fluctuating component of axial velocity
especially in the flame region. For mixture fraction fluctuations the SGS
model does not introduce significant differences. As to the temperature
fluctuations, the influence of the SGS model also is not very important.



Fig. 25. RMS of axial velocity (left) and mixture fraction (right) along the jet flame axis


Fig. 26. RMS of temperature along the jet flame axis

The maximum value of the fluctuating component is predicted upstream
with the use of the Smagorinsky model compared to the dynamic one.
Fluctuations of the major species shown in Figs 27 – 29 are similarly
obtained with both SGS models.



Fig. 27. RMS of mass fraction of CH_{4} (left) and CO_{2} (right)




Fig. 28. RMS of mass fraction of H_{2}O (left) and O_{2} (right)




Fig. 29. RMS of mass fraction of CO (left) and H_{2} (right)

Contributed by: Andrzej Boguslawski, Artur Tyliszczak — Częstochowa University of Technology
© copyright ERCOFTAC 2011