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VII.3 Structure of a flame

Some understanding of the structure of a flame is important for discussing the modelling being used. We will start with premixed combustion. The simplest flame will be a flame propagating in a laminar flow : this can be characterised by a laminar flame speed sL and a flame thickness lF . Given the molectular diffusivity DL, dimensional analysis suggests that the thickness of the flame should be

DL lF = ---- sL
and a characteristic chemical reaction time is the time taken for the flame front to pass
t = -lF- L sL

Turbulent flames are of course more complicated. The turbulence itself is characterised by a number of scales : the turbulence intensity u' and the integral and Kolmogorov length scales l I and j. We can define a number of different Reynolds numbers relating to a turbulent flow, but the most useful here is a turbulent Reynolds number relating to the integral length scale

u'lI- ReT = n
The integral and Kolmogorov length scales are related as
lI 3/4 j-= Re T
This of course represents the fact that as the fluid becomes more turbulent, the turbulence spectrum becomes broader (and as mentioned earlier is the reason why DNS, which has to simulate length scales down to j, becomes impractical at large Re). We can also write a characteristic turbulent eddy turnover time as
lI- tT = u'
The ratio of the eddy turnover time to the laminar burning time is called the Damköhler number :
Da = tT-= lIsL tL u'lF
This is (an inverse measure) of the influence of the turbulent flow on the chemical processes. Other ratios of interest include
lF /j
This is a measure of the stretch or local distortion to which a laminar flame is subjected by the turbulence.
u'/s L
This is a measure of the relative strength of turbulence in the flow.

Looking in more detail at the structure of a premixed flame, we can distinguish different regions

  1. a preheat zone, where the gas is heated without reaction occurring
  2. an inner layer of fuel consumption, where the fuel is destroyed
  3. the oxidation layer, where radicals produced by the combustion are mopped up by the O2.

The thickness of the inner layer is a fraction of the whole flame thickness

ld = dlF
For stoichoimetric methane at 1 atmosphere, lF = 0.175 mm and d = 0.1.

In non-premixed combustion there is no characteristic velocity scale. However one can still define a characteristic diffusion thickness lD characteristic of the thickness of the combustion regime. This also can be divided into fuel consumption and oxidation layers : here the oxidation layer

l = el e D
is often of importance.

PIC
Figure 1: Schematic of the flame structure of a premixed flame.

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