[Law_C.K.] Combustion physics

498 Combustion in Turbulent Flows
Unburned
mixture sL
Burned
product
u'
o
s L
u'
o
s L
u' o
(a) (b) (c)
Figure 11.3.2. (a) Weak flame-vortex interaction (u ′ o < s L) resulting in a wrinkled flamelet.
(b) Strong flame-vortex interaction (u ′ o > s L) resulting in a corrugated flamelet. (c) Strong flamevortex
interaction with the smaller eddies penetrating into and broadening the preheat zone of the
flame (Peters 2000).
Laminar Flame Regime (Re o < 1): In this regime the turbulence intensity is weak
and the turbulence scale is small. The flow is laminar and there is minimum extent
of flame wrinkling.
Wrinkled Flamelet Regime (Re o > 1, Ka L < 1, u ′ o /s L < 1): Since Ka L < 1, the flame
thickness is much smaller than the Kolmogorov scale. As such, the fundamental flame
element retains the laminar flame structure within the turbulent flow field, hence the
name laminar flamelet. Since u ′ o can be interpreted as the turnover velocity of the
large eddies, u ′ o < s L implies that the flamelet surface is only slightly wrinkled as it
passes through these eddies (Figure 11.3.2a).
Corrugated Flamelet Regime (Re > 1, Ka L < 1, u ′ o /s L > 1): Since Ka L < 1, the
flame element still retains its laminar flame structure. However, since u ′ o > s L, the
flamelet becomes highly convoluted upon traversing the eddy (Figure 11.3.2b), with
the extent of distortion being of the same order as the size of the eddy and folding
of the flamelet is expected. The characteristic eddy size that separates the behaviors
of wrinkled and corrugated flames can be assessed by equating the turnover velocity
with the laminar flame speed. By calling this eddy size as the Gibson scale, l G , and
from the general relation (11.1.25), we have
l G
l o
≈
(
sL
u ′ o
) 3
. (11.3.6)
It is reasonable to expect that folding of the flamelet can lead to pockets of unburned
and burned mixtures. The unburned pocket will burn out by itself as the
enclosing flame propagates inward, provided it does not extinguish due to curvatureinduced
stretch effects. The burned pocket, however, will grow as the enclosing flame
propagates outward. Such a growth will be limited by the continuous interaction with