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

4 Numerical Modeling and Simulation
Conservation of mass:
∂ρ g
∂t + ∂ρ g u g ,r
∂r
+ 2 ρ g u g ,r
r
= 0 (4.49)
Conservation of species:
ρ g
∂Y m
∂t
+ ρ g u g ,r
∂Y m
∂r
+ ∂ρ g Y m ∆u g ,m,r
∂r
+ 2 ρ g Y m ∆u g ,m,r
r
= ˙ω m (4.50)
Conservation of momentum:
∂p g
∂r = 0 (4.51)
Conservation of energy:
ρ g
∂ ∑ m Y m
∫ T
T 0
c p,m dT
∂t
=− ∂∑ m ρ g Y m
∫ T
T 0
c p,m dT ∆u g ,m,r
∂r
− ∑ m
˙ω m h 0 g ,m + ∂p g
∂t − ∂ ˙q g ,r
∂r
∂ ∑ ∫ T
m Y m T
+ ρ g u
0
c p,m dT
g ,r
∂r
− 2
− 2 r ˙q g ,r
∑
m ρ g Y m
∫ T
T 0
c p,m dT ∆u g ,m,r
r
(4.52)
Heat flux:
˙q g ,r =−λ g
∂T
∂r
(4.53)
Liquid Phase
In the liquid phase, the physical properties are assumed to be constant [364].
Density ρ l , specific heat c p,l , and thermal conductivity λ l are independent of
space and time as well as heat of vaporization h v and boiling temperature
T boil . There is only one single species in the liquid, the composition is homogeneous,
and no chemical reactions occur ( ˙ω=0). Diffusion of species is
neglected, and no species can be absorbed in the liquid droplet. All gaseous
components are insoluble in the liquid by definition.
The final liquid phase model corresponds to the so-called “conduction limit
model”, as presented for instance in Aggarwal et al. [9] and Sazhin [381]. The
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