Untitled - Aerobib - Universidad Politécnica de Madrid

218 CHAPTER 7. TURBULENT FLAMES
7.3 Turbulence generated by the flame
Markstein [21] has shown that the disturbances originated at a certain point of an incline
flame propagate and amplify along the same and eventually generate turbulence.
In their studies of turbulent flames stabilized in tubes, Willians, Hottel and Scurlock
[5] recognized the existence of turbulence originated by the flame. They considered
this turbulence as a consequence of the strong gradients of velocity which originate
through the flame in this case. 3
Scurlock and Grove have given a formula for the
maximum intensity v ′ of the possible turbulence. Such formula was deduced from elementary
considerations on mass and momentum conservation across the flame before
and after the mixing of burnt gases. This formula is
√
( )
v m ′ K m ρ u
= (vu 3 ρ 2 − u 2 l ) ρu
− 1 . (7.27)
b ρ b
Here, K m = ∆p ∆p
−1, where is the relation between pressure jumps across
∆p
′
∆p
′
the flames before and after the turbulent mixing, v u is the velocity of the unburnt gases
normal to the mean flame front and ρ u /ρ b is the ratio between densities of unburnt and
burnt gases. Formula (7.27) gives a maximum limit to the turbulence that could be
originated in the flame but does not allow the computation of the possible turbulence
for each case. This arises the problem of introducing an additional undetermined
element in the theory which adds difficulties to the comparison between theoretical
and experimental results. In practice v ′ m can be considerably larger than the turbulence
of the incident stream.
Karlovitz [16] when comparing the values for u t predicted by his theory with
those obtained from experimenting with flames stabilized in bunsen burner verified
that experimental velocities were much larger than those calculated and he considered
this discrepancy to be due to the influence of the turbulence originated by the flame.
Karlovitz explains the production of turbulence as follows: through the laminar front
an increase in velocity takes place of the order of magnitude of ρ u
ρ b
− 1. In a laminar
flame this increase has a constant direction but in a turbulent flame it oscillates since
it must be normal to the temporary position of the flame front at all instants which is
variable. The statistic oscillations of this increase are the source of the turbulence.
Through a not too legitimate calculation Karlovitz deduces the following expression
for the maximum intensity of turbulence produced by the flame
v m ′ = √ 1 ( )
ρu
− 1 u l . (7.28)
3 ρ b
3 See chapter 10.