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15.4 FLAMES 335

15.4.4 FLAME GROWTH
While the flame is small it is susceptible to local processes in the vicinity of the plug. Pischinger and
Heywood (1988) show how the initial flame varies over a short period (300 ms) after ignition. The
growth of the flame is ‘laminar’ but the flame is affectedbyheattransfertoits immediatesur-
roundings, the electrodes. While the flame is small the effects of flame curvature also influence its
growth rate (Boulouchos et al. (1994)). As the flame grows it transforms from laminar to turbulent,
and the actual trajectory of the flame is affected by both the local mean velocity and the turbulence
intensity. Turbulence enhances the flame speed by wrinkling the reaction sheet. As the flame gets
bigger than about 10 mm radius it becomes less affected by the mean flow. Pischinger and Heywood
show that the growth of the flame is almost spherical once it has reached a critical size. It has to be
recognised that the relationship between the flame radius and mass fraction burned is not a simple
direct one because the density of the burned gas is about a quarter of that of the unburned mixture.
This means that for a simple disc-shaped combustion chamber the mass fraction burned is less than
10% of the total mixture even when the flame is halfway across the chamber. The effect of com-
bustion chamber shape modifies this relationship further, and it can be modelled by simple geometry
to take some account of the combustion chamber geometry. The flame makes a transition from
laminar to turbulent when it reaches about 5 mm in radius, and this takes between 5 and 10

crankangle at speeds of 1500–3000 rev/min.
The turbulent flame in spark-ignition engines can be characterised by the parameters given in
Table 15.2.
Schlieren photographs of the flame surface show ‘three-dimensional’ wrinkling of the form shown
in Fig. 15.9. This wrinkling has a significant effect on the speed of the flame, which is enhanced by the
turbulence. The turbulent Reynolds number associated with the flame is in the region 100–1000, while
the Damkohler number (which relates the eddy turnover time to the residence time in the flame) is of
the order of 100. This means that the laminar flame is wrinkled by the flame rather than having its
thickness modified. The wrinkling also tends to ‘stretch’ the flame and this will tend to extinguish it.

Table 15.2 Typical Flame Parameters in Spark-Ignition Engines

Turbulence intensity, u 0 2 m/s
Turbulent Reynolds number 300
Damkohler number 20
Karlovitz stretch factor, K 0.2
Integral scale 2 mm
Taylor microscale 0.7 mm
Kolmogorov scale 0.03 mm
Gibson scale 0.2 mm
Laminar flame thickness 0.02 mm
Laminar flame speed 0.5 m/s
Turbulence intensity/laminar flame speed 4
Turbulent flame speed/laminar flame speed 4
Mean flame radius of curvature 2 mm