number of 150 modes has no physical meaning and was chosen to agree with the filtering approach used by Boxx et al. (2010b).
7.3 Extraction of the Instantaneous Flame Shape and the Coherent Structures
During the transient measurements three different flame shapes - the same that are presented in detail in Chapter 4 - occurred in the combustor. In the following, a set of parameters will be introduced that are used to extract the instantaneous flow field shape, the occurrence and type of the PVC, the flame shape, and the characteristics of the density field. To characterize the flame shape in terms of being attached or detached, the mean OH*-chemiluminescence intensity in the vicinity of the centerbody (0 < x/Dh < 2 and −0.8 < y/Dh < 0.8) is calculated as:
ROH(x, t) = RR
AIOH(x, t)dA RR
AIOH(x)dA . (7.1)
This parameter indicates if the flame is detached or attached (either as a V-flame or as a trumpet flame). The second parameter describes the estimated density in the upstream part of the IRZ. Its definition is analog to ROH:
Rρ(x, t) = RR
Aρ∗(x, t)dA RR
Aρ∗(x)dA . (7.2)
The third measure is the instantaneous opening angle α of the jet as defined in Eqn. 4.2. It shows very low values for the narrow trumpet flame, high values for the strongly divergent V-flame, and intermediate values for the detached flame.
In Chapter 4 it was demonstrated that the flow field of the detached flame and the flow field of the trumpet flame feature strong self-excited helical coherent structures, which manifest as a PVC. Their occurrence and shape were extracted from the flow fields by means of a POD.
However, for the transient measurement, the POD cannot be used since in the transient phase, the PVC changes its appearance and frequency. Thus, the POD fails to represent the PVC during the transition in two well-defined POD modes. Instead of the POD, a simple approach
1 2 3 4 5 6
−3
−2
−1 0 1 2 3
x/Dh y/Dh
(a) Detached flame
1 2 3 4 5 6 x/Dh
(b) Trumpet flame
1 2 3 4 5 6 x/Dh
0 0.1 0.2 0.3 0.4
¯σ
(c) V-flame
Figure 7.1: Distribution of the time-averaged normalized antisymmetric velocity fluctuation intensity ¯σ. Dashed square indicates integration zone for Σus and dash-dotted square is the integration zone for Σds.
is employed here, which makes use of the fact that the velocity perturbations induced by the PVC are antisymmetric and occur in well-defined regions. To assess this antisymmetry, a measure for its spatial distribution is introduced as:
σ(x, y, t) = 1 U02
h[u(x, y, t)−u(x,−y, t)]2+ [v(x, y, t) +v(x,−y, t)]2i
. (7.3)
The time-averaged spatial distribution of σ is depicted in Fig. 7.1 for the steady state flow field of a detached flame, a trumpet flame, and a V-flame. It is evident that the asymmetry in the flow field reaches the highest levels in very different regions depending on the flame shape.
These regions are closely coupled to the antisymmetric structure of the PVC. Consequently, for the detached flame, strong antisymmetric fluctuations prevail close to the combustor inlet, where also the PVC is strong. For the trumpet flame, the PVC is shifted downstream, leading to a downstream shift of the region of maximum antisymmetric fluctuations. In the case of the V-flame (where the PVC is suppressed), the region in the jet, where the overall turbulence intensity is high, is the only region with considerable levels of antisymmetric fluctuation intensity.
To exploit the different spatial distribution for the identification of the occurrence of the two PVC types, two integration regions are defined, as indicated by the dashed boxes in Fig. 7.1. An integration over these areas yields a measure for the instantaneous magnitude of the flow asymmetry. The integration close to the combustor inlet yields the upstream asymmetry Σus and shows the highest value for the detached flame. For the V-flame, Σus is very low, due to the suppression of the PVC. For the trumpet flame, the integration further downstream (Σds) yields the highest values, since the PVC is also shifted more downstream.
In the case of the detached flame, a small contribution of the PVC is found to Σds, and for the V-flame, again, the level of asymmetry is very low. A summary of the introduced parameters and their expected values for the three flame shapes is provided in Tab. 7.1.
7.3 Extraction of the Instantaneous Flame Shape and the Coherent Structures 119
Table 7.1: Compilation of the parameters for the identification of the flame shapes.
Parameter Symbol V-flame Detached flame Trumpet flame
Upstream OH* intensity ratio ROH High Low High
Upstream density ratio Rρ Low High Low
Initial jet opening angle α High Medium Low
Upstream antisymmetry Σus Low High Medium
Downstream antisymmetry Σds Low Medium High
0.5 1 1.5 2 Rρ
0 1 2
T V D T V D T D T V
ROH
0.2 0.4
α
0 0.2 0.4 Σus
0 2 4 6 8 10 12 14 16 18
0 0.2 0.4
t(s) Σds
Figure 7.2: Flow field and flame parameters for the transient measurement. The dashed lines indicate changes of the flame shape. V: attached V-flame, T: trumpet flame, D: detached flame.
0 2 4 6 8 10 12 14 16 18 0
0.5 1 1.5 2
φmax≈0.7
φmin≈0.5
t (s)
OH/OH
Trumpet V-flame Detached flame
Figure 7.3: Time trace of the normalized integral OH*-chemiluminescence intensity during the periodic variation of the equivalence ratioφ. Solid red line is the low pass filtered normalized integral OH*-chemiluminescence intensity. Symbols indicate the flame shape. Red dashed lines represent the mean OH*-chemiluminescence intensity for the minimum and maximum equivalence ratio, respectively.
The temporal evolution of all five calculated parameters during the complete measurement time is depicted in Fig. 7.2. The instantaneous flame shapes can be deduced from the param-eters. The time traces of Σus and Σds show the expected trends, with high values of Σus for the detached flame and high values of Σds for the trumpet flame. However, the signals are overlaid by a considerable amount of noise, which is caused by the strong turbulence.
The introduced parameters enable to conveniently extract the interesting flame shape tran-sitions from the transient data. Furthermore, they will be used in the following to assess the role of the PVC for the transition processes.
Figure 7.3 shows the integrated OH*-chemiluminescence intensity of the 27,000 samples measured with an intensified camera. The variation of the equivalence ratio between a min-imum value of φ ≈ 0.5 and a maximum value of φ ≈ 0.7 is evident, even though the sig-nal is very noisy because of the intense turbulence. Due to the nonlinear relation of the OH*-chemiluminescence intensity for partially premixed flames, however, the exact temporal evolution of the equivalence ratio cannot be deduced from the OH*-chemiluminescence inten-sity without an extensive calibration. Nevertheless, Fig. 7.3 provides a very good qualitative idea of the instantaneous equivalence ratio. The instantaneous flame shapes, extracted from Fig. 7.2, are indicated by the overlaid symbols.