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

Bibliographic revision
2
( rsr
)
2 ⎛∂s
⎞ 1 ∂
κs
= nr
⎜ + =
⎝ ∂
s
r
g
2
2
r
⎟
⎠ r ∂r ru
2
( r nr
)
1 ∂
s
κc = un = 2n
2
r
r ∂r
r
u
u
(2.27)
(2.28)
and the total stretch rate is:
s
κ = (2.29)
2 n ru
The outwardly propagating flame, ignited from a central ignition point, is the most
common spherical flame and because the stretch rates to which it is subjected are well
defined, it is well suited to burning velocity measurements.
tel-00623090, version 1 - 13 Sep 2011
2.5.1.1 Karlovitz number
The Karlovitz number (Ka) is defined as the nondimensional stretch factor, using the
thickness of the unstretched flame (δ u0 ) and the normal unstretched laminar flame
velocity (S u0 ) to form a reference time (Kuo, 2005):
Ka
δ
u0
= = (2.30)
S
u0
κ
Residence time for crossing an unstretched flame
Characteristic time for flame stretching
For convenience, the Karlovitz number can be written as a sum of two parts due to the
contribution from strain and curvature as follows:
Ka = Ka + Ka
(2.31)
s
c
Where
δ δ δ
Ka = SS + : ∇ S ; Ka = S ∇ n =
( ηη)
u 0 u 0 u 0 u
s c u
Su0 Su0 R Su0
S
(2.32)
2.5.1.2 Markstein number
Flame stretch can change the burning velocity of premixed flames significantly. It is
important to know the relation between these two parameters, because the burning
velocity is a crucial parameter in premixed combustion processes. Markstein, (1964)
was the first to propose a phenomenological relation between the laminar burning
velocity and the curvature of the flame front. Notice that the straining of the flow is not
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