On the Formation of Nitrogen Oxides During the Combustion of ...

4 Numerical Modeling and Simulation
estimate. Consequently, the model would be limited to configurations where
diffusive transport between two neighboring droplets τ d takes more time than
the vaporization and combustion τ v of one single droplet:
τ v ≪ τ d . (4.69)
The diffusive transport of mass is characterized by the time scale
The respective transport of heat is
where the thermal diffusivity α in m 2 s −1 is
τ d,m = L2
D O2
. (4.70)
τ d,h = L2
α , (4.71)
α= λ
ρ c p
.
The half distance between two droplets is denoted L, and D O2 is the diffusion
coefficient of oxygen (Eq. (4.70)). As a consequence of Equation (4.69), the half
distance L has to fulfill the conditions
L≫ √ D O2 τ v and (4.72)
L≫ a τ v . (4.73)
Using the thermophysical properties of exhaust gas at an equivalence ratio of
φ= 0.8 as an example, the thermal diffusivity and the diffusion coefficient of
oxygen can be retrieved as α= 0.58×10 −3 m 2 s −1 and D O2 = 0.56×10 −3 m 2 s −1 ,
respectively. Estimating the vaporization time τ v from numerical results and
the D² law,
yields the condition
τ v = D 2 0
k = D 2 0· 0.94×106 s m −2 (4.74)
L≫ 25D 0 . (4.75)
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