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

3 Experiments on Droplet Array Combustion
Q 2
Q 1
D(t)
r 1
r 2
A
B
Figure 3.21: Model of Heat Transfer to Droplet Surface. The diameter D(t) of the fuel source
is a function of time and part of the numerical solution. The two spheres of the
constant radii r 1 and r 2 are employed for the calculation of the heat transfer to
the imaginary droplet. A: area of heat release, B: spherical volumetric source of
vaporized fuel (i.e. extension of “imaginary” droplet).
fuel mass m n−1 of the previous time step (n−1). In contrast to user CEL (CFX ®
expression language) functions, user junction box routines allow a defined execution
of user-specified routines and are chosen here on this account. The
mass m of each droplet is stored as a single, integral value in an additional
variable managed by the CFX ® memory management system (MMS).
m n = m n−1 − ∆m n v (3.11)
The fuel amount ∆m n v is determined from the averaged mass flow ṁ v due to
vaporization, which is based on Fourier’s law and the given heat of vaporization
∆h v . Equation (3.12) is valid, implying the absence of any heat sources as
well as a negligible variation of heat capacity c p between the two end points
of the temperature gradient ∆T
∆r , r 1 and r 2 (Fig. 3.21) [443]:
λA ∆T
∆r ≡ ṁ v∆h v = ˙ Q v . (3.12)
A single-step reaction scheme of Westbrook and Dryer [459] for
C 10 H 22 is employed to model combustion (Eq. (3.13)), where the reaction
rate is expressed in mol cm −3 s −1 . It is comprised of an activation
energy of E a = 1.255×10 5 J mol −1 , a pre-exponential factor of
A = 3.8×10 11 (mol/cm 3 ) (1-m-n) /s, and the concentration exponents m = 0.25
and n=1.5:
(
d [C 10 H 22 ]
= A exp − E )
a
[X C10 H
dt
R T
22
] m [X O2 ] n . (3.13)
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