Page 348 - Advanced thermodynamics for engineers

15.4 FLAMES 337

where
F L ¼ area of laminar flame;
u ¼ turbulence intensity;
0
l T ¼ Taylor microscale;
d L ¼ laminar flame thickness;
S L ¼ laminar flame speed.
Abdel-Gayed et al. (1987) and Bradley et al. (1992) investigated the way in which turbulence
‘stretches’ the flame and causes it to be extinguished. The results are summarised in Fig. 15.10, which
is a graph of the ratio of turbulent to laminar flame speed, i.e. the flame speed factor defined in Section
15.4.5, Eqn (15.14) below, against the ratio of turbulence intensity to laminar flame speed. The ab-
scissa is closely related to the Karlovitz number, K, which is a measure of the flame stretch. Also
shown on Fig. 15.10 are lines of constant KLe, which is the product of Karlovitz and Lewis numbers,
2
and lines of constant Re/Le , which is the ratio of Reynolds number to the square of Lewis number. If
the value of KLe is low (e.g. 0.0013) then the flame is a wrinkled laminar one, while if the value of KLe
is high (e.g. 6) the flame is stretched sufficiently to quench it. This shows that the design of a com-
bustion chamber must be a compromise between a high enough value of turbulence intensity to get a
satisfactory flame speed, and one which does not cause extinction of the flame.
Abdel-Gayed et al. (1987) and Bradley et al. (1992) have shown that the higher the value of the
product of Lewis and Karlovitz numbers (KLe) the more tendency is there for the flame to be
extinguished by stretching. The Lewis number is about 1 for stoichiometric mixtures and remains
about unity for a wide range of mixture strengths. Hence, the term KLe is dominated by the turbulence
intensity (u ) and the laminar flame speed (S L ). This means that lean mixtures, which have a relatively
0
low laminar flame speed (see Fig. 15.6), will experience higher values of Karlovitz number than rich

20
Disrupted, partial 0.43 6000 0.63 1
18
quench region
Ratio (turbulent/laminar) flame speeds 14 8 6 Wrinkled laminar 0.07 0.1 0.14 0.21 0.3 20 50 100 Quench region 6
16
3000
2000
1000
500
region
12
250
10
0.04
0.02
Constant Re/Le
0 4 2 0.0013 0.005 Constant Kle 2
0 2 4 6 8 10 12 14 16 18 20
Ratio (turbulence intensity/laminar flame speed)
FIGURE 15.10
The effect of turbulence on the turbulent flame speed and tendency to quench for a premixed charge.