Under reacting conditions several flame shapes were encountered. An overview is given by the flame photographs shown in Fig. 4.2. In order to find a parametric description of the flow fields and flame shapes, two simple parameters are introduced. The first parameter is the
4.4 Classification of Flame Shapes 55
Short V-flame Long V-flame
Short detached flame
Trumpet flame
Long detached flame Short hydrogen flame
Figure 4.2: Photographs of the flame shapes. Solid arrows are continuous transitions and dashed arrows indicate sudden transitions. The picture of the short hydrogen flame is a false-colored OH*-chemiluminescence image due to the lack of emitted visible light.
axial location of the center of gravity of the OH*-chemiluminescence intensity xfl:
xfl =
R IOH(x, r)xdV
R dV . (4.1)
Here,IOH is the Abel-deconvoluted OH*-chemiluminescence intensity. The second parameter describes the initial opening angleα of the jet averaged over 0.5< x/Dh <4 with
αx(x) = atan drp
dx
and α= 1
(4−0.5)Dh
Z x/Dh=4
x/Dh=0.5
αxdx. (4.2) The encountered parameter combinations xfl and α are summarized in Fig. 4.3 for a wide range of operating conditions (see Tab. 4.1).
From Fig. 4.3a it is evident that parameters resulting in a decrease of the mixture reactivity, such as steam dilution, shift the flame downstream. An increase of the reactivity, e.g., due to hydrogen addition, causes an upstream shift of the flame. This is even more evident when the combinations of xfl and α are color-coded with the ratio of the laminar burning velocity to the inlet flow velocity, as presented in the Fig. 4.3b. The laminar burning velocity is the dominating parameter for the reactivity of the mixture. It strongly influences if a flame at a given flow velocity, turbulence intensity, and strain rate can be stabilized or is quenched (Williams, 2000). In Fig. 4.3b, the laminar burning velocity is calculated with
Ω= 0 Ω= 0.2 Ω≥0.3 V-flames
Detached flames
Trumpet fl.
Short H2 fl.
0 2 4 6 8 10 12
0 0.1 0.2 0.3 0.4 0.5
xfl/Dh
α(rad)
0 0.2 0.4wH20.6 0.8 1
(a) The size of the marker indicates the rate of steam dilution and the color the mass fraction of hydrogen. Red bold circles indicate the selected operating conditions for the detailed investigation (Tab. 4.2).
V-flames
Detached flames
Trumpet fl.
Short H2 fl.
0 2 4 6 8 10 12
xfl/Dh
1 S2L/U0·1003 4 5
(b) The color of the marker indicates the nor-malized calculated laminar flame speed.
Figure 4.3: Parametric classification of the flame shapes.
Table 4.2: Operating conditions of the selected cases representing the four flame shapes.
Parameter Tin (K) Tad (K) φ Fuel Ω u0 (m/s) SL (m/s)
Detached 620 1850 0.8 CH4 0.2 72.9 0.39
Trumpet 620 1850 0.68 CH4 0.1 69.6 0.48
V-flame 620 1850 0.56 CH4 0 66.1 0.59
Short H2 540 1850 0.5 H2 0 65.8 2.58
one-dimensional simulations employing Cantera (Goodwin, 2003) with the GRI mechanisms (Smith et al., 2000) and the reaction mechanism developed by Burke et al. (2012). Some operating conditions (e.g., very lean hydrogen flames) are outside of the validity range of the reaction mechanisms and are omitted. Details about the calculation can be found in a recent publication by Kr¨uger et al. (2013).
From Fig. 4.3 four separated regions are evident and correspond to the flame shapes pre-sented in Fig. 4.2. The shortest flames occurred at dry conditions with hydrogen fuel. Sub-stituting hydrogen with natural gas leads to a rather sudden change of the flame opening angle. At dry conditions with natural gas fuel, the flame usually showed the typical V-shape.
Leaning out the flame or mildly steam diluting the air, leads to a continuous enlargement of the flame. Further reducing the equivalence ratio or increasing the rate of steam dilution leads to a sudden change of the flame shape into the trumpet shape. At high rates of steam dilution, the flame shape changes again abruptly and shows detached annular shapes of
dif-4.4 Classification of Flame Shapes 57
0.5 2 3.5 5 6.5 8
−4
−2 0 2 4
x/Dh y/Dh
0 0.2 0.4 0.6 0.8 1 IOH/IOH,max
(a) V-flame
0.5 2 3.5 5 6.5 8 x/Dh
0 0.2 0.4 0.6 0.8 1 IOH/IOH,max
(b) Trumpet flame
0.5 2 3.5 5 6.5 8 x/Dh
0 0.2 0.4 0.6 0.8 1 IOH/IOH,max
(c) Detached flame
0.5 2 3.5 5 6.5 8 x/Dh
0 0.2 0.4 0.6 0.8 1 IOH/IOH,max
(d) Short hydrogen flame
Figure 4.4: Streamlines of the time-averaged flow fields superimposed on the normalized Abel-deconvoluted OH*-chemiluminescence intensity distribution. Dashed lines indicate zero axial velocity.
ferent lengths. The flow fields corresponding to the same flame shape are very similar (for details see Terhaar et al., 2011), whereas flow fields of different flame shapes show significant differences. In order to assess the different flame shapes and the corresponding velocity fields, representative examples were chosen and are presented in Figs. 4.4 and 4.5. The first example represents a typical V-shaped flame with a wide opening angle. The second example has a very narrow flame opening angle and features a trumpet like shape. Next, an example of a detached flame located comparably far downstream in the combustor is provided in Fig. 4.3c.
Finally, in Fig. 4.3d a very short hydrogen flame with a small opening angle is depicted. All experiments were conducted at the same flame temperature and all but one at the same inlet temperature. This way, the dilatation over the flame is comparable. The selected operating conditions are presented in Tab. 4.2 and are indicated by red markers in Fig. 4.3.
The typical V-flame (Fig. 4.4a), which is anchored at the centerbody and along the inner shear layer, has a wide jet opening angle and negative axial velocities in the IRZ that are very uniform in radial direction and comparably low (see Fig. 4.5a). This comes along with much lower levels of the local turbulence in the IRZ, compared to the other investigated cases.
Additionally, the radial gradient of the tangential velocity, i.e., the rotational speed of the vortex core, remains very low up to an axial location ofx/Dh = 2. This indicates a very low transport of angular momentum from the annular swirling jet at the combustor inlet into the IRZ. The estimated density distribution of the V-flame case shows that the IRZ is completely filled with hot burned gases. Similarly to the tangential momentum, the fluid interchange between the jet and the IRZ seems to be rather low, causing steep density gradients in radial direction.
a) V-flame
−4
−2 0 2 4
y/Dh
0 0.5 1
|U/U0|
−0.5 0 0.5 W/U0
0.1 0.2 0.3 T u
0.2 0.4 0.6 0.8 ρ∗
b) Trumpet flame
−4
−2 0 2 4
y/Dh
c) Detached flame
−4
−2 0 2 4
y/Dh
d) Short H2 flame
0.5 2 3.5 5 6.5 8
−4
−2 0 2 4
x/Dh;U/U0·1.5 y/Dh
Normalized axial velocity
0.5 2 3.5 5 6.5 8 x/Dh;W/U0·2 Normalized tangen-tial velocity
0.5 2 3.5 5 6.5 8 x/Dh;T u·2 Normalized turbu-lence intensity
0.5 2 3.5 5 6.5 8 x/Dh;ρ∗ Normalized density
Figure 4.5: Flow fields and density fields of the different flame shapes. First row (a): V-flame, second row (b): trumpet V-flame, third row (c): detached V-flame, and fourth row (d):
short hydrogen flame. Streamlines of the time-averaged flow field and radial profiles are superimposed on the corresponding quantity. Dashed lines indicate zero axial velocity.
4.4 Classification of Flame Shapes 59 The flow field shown in Fig. 4.5b corresponds to the region of very narrow flame opening angles (see Fig. 4.3) and, thus, to the trumpet-like flame shown in Fig. 4.4b. This flame, which is denoted as a trumpet flame in the following, is anchored near the centerbody and along the inner shear layer. Compared to the V-flame, the flow field of the trumpet flame has a considerably narrower IRZ with much higher recirculating velocities. The very low jet divergence near the combustor inlet and the small axial decay of the tangential velocities indicate a downstream shift of the onset of vortex breakdown. Consequently, the strong backflow on the centerline is assumed to depend on the recirculation bubble downstream of the centerbody. This assumption is supported by the observation that the trumpet flame is much less prone to appear with higher swirl numbers and smaller centerbody sizes. Compared to the V-flame, the transfer of tangential momentum from the jet to the IRZ is significantly increased, leading to a much higher rotational speed of the solid body vortex core. However, this transfer does not set in before x/Dh = 2 corresponding to a significant increase of the normalized turbulence intensity. The density distribution of the trumpet flame is similar to the V-flame with the IRZ being completely filled with burned gases. Downstream of x/Dh = 2 the higher transfer of angular momentum is accompanied by a smoothing of the density gradients.
Both the V-flame and the trumpet flame anchor at the centerbody. If the flame root is quenched, for instance due to high strain rates near the combustor inlet, it detaches and takes an annular shape (Fig. 4.4c). The density distribution of the detached flame (Fig. 4.5c) shows a large region of cold unburned gases near the combustor inlet. This region includes the jet and the upstream part of the IRZ. The tangential velocity distribution of the detached annular flame shows a considerable amount of angular momentum transfer from the jet into the IRZ. This results in solid body rotational speeds of the vortex core that are similar to the isothermal case. The high radial transport is assumed to be linked to the high turbulence intensity in this region. Consistently, also very low density gradients from the jet to the IRZ are evident.
For very high laminar burning velocities, the flame gets very short and is also able to reside in the inner and outer shear layer (Fig. 4.4d). Interestingly, the flow field of the short hydrogen flame (Fig. 4.5d) features a similar jet opening angle and similar axial and tangential velocity distributions in the IRZ as the flow field of the detached flame. Obviously, the hydrogen flame is much shorter, leading to significantly higher axial velocities close to the combustor inlet.
Only a very small region near the combustor inlet remains at the combustor inlet temperature, while almost the complete combustor is filled with the hot combustion products. Note that the resolution of the used density estimation technique did not allow for the assessment of smaller density gradient in the downstream section of the combustor. Therefore, the profiles forx/Dh >2.5 are set toρ=ρburnt (i.e.,ρ∗= 0). The transfer of angular momentum seems to be slightly lower compared to the detached flame, resulting in lower solid body rotational speeds. However, compared to the V-flame, still considerably more angular momentum is transferred. This is consistent with the much higher turbulence intensities.
10 100 0
2 4 6
8 a) Energy
POD mode j Kjin%
0 0.1 0.2 0.3 0.4 b) Spectra
PVC
St PSD(aj)
a1 a2 a3
0 10 20 30
0
c) Time traces
t·U0/Dh aj
d) POD mode 1
0 2 4 6 8
−4
−2 0 2 4
x/Dh y/Dh
e) POD mode 2
0 2 4 6 8
x/Dh
f) POD mode 3
0 2 4 6 8
x/Dh
−1
−0.5 0 0.5 1
Ωxy/Ωxy,max
Figure 4.6: Results of the POD analysis of the isothermal flow. a) Distribution of the turbulent kinetic energy over the modes. b) Power spectra of the temporal POD coefficients. c) Time traces of the temporal coefficients related to the PVC. d-f) Normalized through-plane vorticity Ωxy of the spatial POD modes.