Untitled - Aerobib - Universidad Politécnica de Madrid

6.15. FLAME PROPAGATION IN HYDROGEN-BROMINE MIXTURES 189
Expressions for the reaction rates w i are obtained from chemical kinetics. Between
the five chemical components, the following independent chemical reactions
exist [42]
Br 2 + X −→ k1
2Br + X, (6.233)
k
Br + H
2
2 −→ HBr + H, (6.234)
k
H + Br
3
2 −→ HBr + Br, (6.235)
HBr + H k 4
−→ H 2 + Br, (6.236)
2Br + X k 5
−→ Br 2 + X. (6.237)
These equations give the following expressions for the reaction rates w 1 , w 4
and w 5
( ) 2 p
w 1 = M 1 θ −2 (k 2 X 3 X 4 + k 3 X 2 X 5 − k 4 X 1 X 5 ), (6.238)
RT f
( ) p
w 4 = M 4 θ −1 p
(2k 1 X 2 − 2k 5 θ −1 X4 2 ) − M 4
w 5 , (6.239)
RT f RT f M 5
( ) 2 p
w 5 = M 5 θ −2 (k 2 X 3 X 4 − k 3 X 2 X 5 − k 4 X 1 X 5 ). (6.240)
RT f
Energy Equation
The energy equation is
λ dθ (
dx = mc p (θ − 1) +
5∑
i=1
)
(ε i − ε if ) h0 i
. (6.241)
c p T f
Diffusion Equations
Between mole fractions X i the following relation exists
X 1 + X 2 + X 3 + X 4 + X 5 = 1. (6.242)
Consequently, four additional equations are needed in order to complete the determination
of all of the mole fractions. The remaining equations are those for the diffusion
of four of the components, and they are obtained from Eq. (6.119)
dX i
5∑
(
)
dx = mRT f
p
θ 1 ε j ε i
X i − X j , (i = 1, 2, 3, 4). (6.243)
D ij M j M i
j=1