Page 117 - Introduction to Computational Fluid Dynamics

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CB908/Date
May 25, 2005
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Reaction 4 0 521 85326 5 2D BOUNDARY LAYERS
1
CO + O 2 → CO 2 , H 4 = 10.1 MJ/kg of CO,
2
−1
k 4 = 2.24 × 10 12 exp (−20,137/T )s ,
0.25 0.5

1.75 ω O 2 ω H 2 O
R CO = ρ k 4 ω CO , (4.122)
M H 2 O
M O 2
where ω H 2 O is treated as a parameter of the problem. The steam mass fraction is, of
course, small enough so that it does not take part in other possible reactions. These
rate laws are taken from Smoot and Pratt [68] and Turns [82].
,ω CO , and
The problem thus requires solution of equations for = u,ω O 2 ,ω CO 2
enthalpy h. We define h = C p (T − T ref ) so that the source terms for each of the
variables are
2
S u = ρ C x V, (4.123)
1 M O 2
=− R CO V, (4.124)
S ω O 2
2 M CO
M CO 2
= R CO V, (4.125)
S ω CO 2
M CO
=− R CO V, (4.126)
S ω CO
S h = R CO H 4 V. (4.127)

The total carbon burn rate is given by

˙ m = ˙ m + ˙ m + ˙ m . (4.128)

c c1w c2w c3w
To effect the wall boundary condition for mass fractions, we modify Equa-
tion 4.59 to account for surface reaction:

˙ m = (ω k,w − ω k,T ) −1 ρ D k ∂ω k + ˙ m , (4.129)

c ω k
∂y y=0
where ˙ m is the surface generation rate of species k and ω k,T = 0 for all species.
ω k
After discretisation, the wall mass fractions can be deduced from
ρ D/ y ω O 2 ,nw − ( ˙ m c1w + 0.5 ˙ m c2w ) M O 2 /M C
ω O 2 ,w = , (4.130)
ρ D/ y + ˙ m c
ρ D/ y ω CO 2 ,nw + ( ˙ m c1w − ˙ m c3w ) M CO 2 /M C
ω CO 2 ,w = , (4.131)
ρ D/ y + ˙ m
c
ρ D/ y ω CO,nw + ( ˙ m + 2 ˙ m c3w ) M CO /M C
c2w
ω CO,w = , (4.132)
ρ D/ y + ˙ m c