Etude de la combustion de gaz de synthèse issus d'un processus de ...

Bibliographic revision
1 d( δ A)
1 dA
κ = = (2.2)
δ A dt A dt
The effect of stretch on the flame is to reduce the thickness of the flame front and
hence the flame speed and influence the flame structure through its coupled effect with
mass and heat diffusion. The concept of flame stretch can be applied to laminar flame
speed; flame stabilization; flammability limits; and modeling of turbulent flames.
Let’s first derive the basic relationship between the stretch rate and the strain rate,
dilatation of the fluid element, and curvature of the flame surface. The three
perpendicular coordinates on a curved flame surface are shown in Fig. 2.7, which has
two unit vectors (ν and η ) tangent to the flame surface and an outward normal unit
vector n , at the spatial point r( νη , , n)
as a function of the three independent coordinates.
tel-00623090, version 1 - 13 Sep 2011
Figure 2.7 - Curved laminar flame front with three perpendicular curvilinear coordinates.
The elemental arc ( ds ) ν
are given by:
in the directionν and the elemental arc ( )
⎛δr
⎞
⎛δr
⎞
ds = d ds = dη
ν ⎜
η ⎜ ⎟
δν ⎟
⎝ ⎠ ⎝δη
⎠
( ) ν , ( )
n
η ν
ds η
in the direction η
(2.3)
The elemental flame surface can be calculated by:
⎛δr
δr
⎞
dA t ⎜ ⎟ n d d
⎝δν
δη ⎠
() = × ⋅ ( ν )( η )
(2.4)
In the orthogonal curvilinear coordinates system, the two unit vectors e , e can be
given by:
δr
δν δr
δη
e = , e and e e n
ν = × =
δr
δν η
δr
δη
ν η
(2.5)
ν
η
Thus:
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