Benevolencia Universalismo
Anexo 2 Modelo de Ficha de aportaciones del grupo de trabajo al Manifiesto al Parlamento
in-cluded in the calculations with the EDC since the importance of differential diffusion on flame stabilization is noted in an earlier study [4]. As the fuel considered in this work can have a high proportion of H2, differential diffusion effects could be important to capture stabilization in turbulent flames. In addition, the assumption of constant Lewis numbers in the SLFM may not be acceptable when species with largely differing molec-ular weights are present, such as H2 and CO in the fuel stream. An accurate mixture fraction prediction is important if the resulting scalar fields are to be correct, as will be discussed later.
In the present study, the realizable k-ε closure with the EDC is able to predict the flow without experiencing blow-off, unlike previously reported results using the stan-dard k-ε closure [48]. This is likely to be due to the more accurate prediction of the physical attributes of the recirculation zone, thus giving the correct mixing of the fuel, air and hot product streams. Standard model constants, given in Table5.4, are used for the current calculations. However, for the RS closure, modifications to the model con-stants made in Gran and Magnussen [47] could not be tested as blow-off occurred. The reason for this behaviour is unclear and it may, perhaps, be due to different numerical implementations of the models in their work [47].
the difference in locations of flame stabilization. The SLFM predicts an attached flame, whereas the EDC predicts a lifted flame stabilizing at x/d ≈ 2. A similar observation is made using the RS turbulence closure (Cases B and D) by comparing the left sides of Figures5.7b and5.7d. The predicted ˜YOH fields (shown on the right side of Figures 5.7a–5.7d) follow the ˜T fields closely, but are more pronounced.
Predictions of the EDC with the realizable k-ε closure show an initial temperature rise slightly closer to the bluff-body than the RS closure; compare the left sides of Fig-ures5.7a and5.7b at x/d <2. The region of higher temperature observed in the real-izable k-ε closure (Case A) implies that there is a weaker recirculation of the cold air stream to the flame base than that predicted with the RS closure, where the predicted temperatures are lower in the same region. The location of the maximum tempera-ture region is predicted at a similar location for Cases A and B; x/d ≈ 3.6. Case B shows a larger high temperature region than Case A. Comparing the turbulence closure methods for the SLFM (Cases C and D) shows little difference in temperature fields.
Comparing the combustion submodels using the realizable k-ε closure one can clearly see that the EDC approach predicts higher peak temperatures ( ˜T ≈ 1800 K) than the SLFM ( ˜T ≈1500 K); compare Cases A and C. A similar observation is made for the RS closure.
Predictions of ˜YOH using the EDC and the realizablek-εclosure show slightly lower peak values ( ˜YOH ≈0.0038) at the downstream extent than for Case B ( ˜YOH ≈0.0042) using the RS closure; shown in the right side of Figures5.7aand5.7b, respectively. The same comparison for the SLFM shows that both turbulence closures give very similar predictions. By comparing the combustion submodels a clear difference is again seen.
The EDC predicts higher values of ˜YOH (Cases A and B) than the SLFM (Cases C and D). In addition, the SLFM shows a greater spread of ˜YOH than the EDC. The major difference between flame stabilization locations predicted by the EDC and SLFM could
0.0050.0040.0030.0020.0010
6 4 2 0
Y˜OH
r/d
180015001200900600300
16 14 12 10 8 6 4 2 0
0 -2 -4 -6 T˜ [K]
x/d
(a) Case A
0.0050.0040.0030.0020.0010
6 4 2 0
Y˜OH
r/d
180015001200900600300
16 14 12 10 8 6 4 2 0
0 -2 -4 -6 T˜ [K]
x/d
(b) Case B
0.0050.0040.0030.0020.0010
6 4 2 0
Y˜OH
r/d
180015001200900600300
16 14 12 10 8 6 4 2 0
0 -2 -4 -6 T˜ [K]
x/d
(c) Case C
0.0050.0040.0030.0020.0010
6 4 2 0
Y˜OH
r/d
180015001200900600300
16 14 12 10 8 6 4 2 0
0 -2 -4 -6 T˜ [K]
x/d
(d) Case D
Figure 5.7:Contours of predicted temperature and OH mass fractions for the bluff-body flame; the bluff-body extends fromr/d =0.5 tor/d =6. (a)and(b)are for the EDC,(c) and(d)are for the SLFM.
be explained by the lack of an extinguished flamelet in the library used in the SLFM or an incorrect prediction of the mixture fraction variance in the highly-strained region at the nozzle outlet. The EDC model could be affected by the turbulence field in the near-nozzle region. A comparison of the ˜YOH fields to the ˜k fields given in Figure 5.5 shows that the SLFM gives a consistent pattern in values. The EDC predicts an increase in ˜YOH (and hence temperature) just downstream of the initial peak in ˜k. This initial peak could act as a trigger for the reaction through Equations (3.47) and (3.46). Un-fortunately, experimental evidence is not available for this flame to compare where the flame stabilization actually occurs.
The effect of turbulence closures using the EDC approach is shown in Figure 5.8.
Radial profiles of major species mean mass fractions, ˜Yα, mean mixture fraction, ˜Z, and mean temperature, ˜T, calculated for Cases A and B at two downstream locations (x/d =10 andx/d =20) are given. Comparison is made with experimental results [28].
In general, the effect of the incorrect prediction of the mixing field at x/d =20 can be seen in Figures5.8a,5.8cand5.8ewhereby it affects the products of the reaction and the flame temperature. Small differences exist between the predictions using the realizable k-ε and RS closures. The RS closure suggests slightly enhanced radial diffusion as in Figures5.8a,5.8cand5.8e. The present work over-predicts the reported value of ˜YCO
2
by nearly 100%. It is surprising to note that comparison to the previous simulations using the EDC with detailed chemistry was not possible due to the lack of published computational data [48]. However, previous results using simplified chemistry and the transported-PDF model also show a large (≈ 100%) departure from the experimental values [29]. Indeed, the presented results for ˜YCO
2 are in general agreement with those reported by Correa and Pope [29]. This suggests that the experimental data may be inaccurate, as it is known that measuring CO2using the Raman method is difficult [28].
However, it can be seen that the RS closure predicts a higher peak value compared to
x/d=20 x/d=10
Y˜H
2
r/d 6 4 2 0 -2 -4 -6 0.03 0.025 0.02 0.015 0.01 0.005 0
(a) ˜YH2
x/d=20 x/d=10
Y˜H
2O
r/d 6 4 2 0 -2 -4 -6 0.1 0.08 0.06 0.04 0.02 0
(b) ˜YH2O
x/d=20 x/d=10
Y˜CO
r/d 6 4 2 0 -2 -4 -6 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
(c) ˜YCO
x/d=20 x/d=10
Y˜CO
2
r/d 6 4 2 0 -2 -4 -6 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0
(d) ˜YCO2
x/d=20 x/d=10
Z˜
r/d 4 6
0 2 -2 -6 -4
1 0.8 0.6
0.4 0.2
0
(e) ˜Z
x/d=20 x/d=10
T˜ [K]
r/d 4 6
0 2 -2 -6 -4
1900 1700 1500 1300 1100 900 700 500 300
(f) ˜T
Figure 5.8: Radial profiles of mass fractions, ˜Yα, mixture fraction, ˜Z, and temperature, T˜, using the EDC (Cases A & B) for the bluff-body flame at two downstream locations:
●experimental data [28], realizablek-ε model and RS model predictions with 6-step reduced mechanism.
the realizablek-ε closure; consistent with a higher rate of reaction.
Differences between turbulence closures become apparent by viewing the peak radial temperatures, Figure 5.8f. The realizable k-ε closure gives a slightly better prediction than the RS closure at both locations relative to experiments. At x/d = 10 the realiz-able k-εand RS closures over-predict by 10% and 15%, respectively. At downstream locations, the difference is lower but still significant; 4% and 8%. These differences can again be attributed to variations in mixing, and hence reaction. In addition, the lack of heat loss due to radiation in the simulations necessarily results in an over prediction of temperature. It is known that the temperature can decrease due to radiation of H2O and CO2by about 50 K in these flames [5].