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

4 Numerical Modeling and Simulation
Conservation of non-vaporizing species n (n≠ m):
(
u g ,n,r − ∂R )∣
∣∣∣R=R(t)
= 0 (4.60)
∂t
Conservation of momentum:
p l = p g (4.61)
Conservation of energy:
∂R
ρ l h v,m
∂t + ρ u 2 g ,r ∂R
l
2 ∂t = ˙q g ,r − ˙q l,r (4.62)
In Equation (4.62), h v,m is the heat of vaporization, which represents the energy
required to transform the species m from the liquid into the vaporous
state. It is derived from the difference of enthalpies with h v,m = h g ,m − h l .
4.5.2 Meshing and Solver Settings
In order to find a good compromise between simulation time and numerical
accuracy, the model configuration was determined by varying the spatial grid
resolution and studying different Cosilab ® solvers. This also included assessing
different discretization schemes for the convective terms. The results were
compared to simulations of the NO x emissions of n-heptane (C 7 H 16 ) droplets
performed by Baessler [31, 175]. A reliable quality criterion can be derived in
this context from the conservation of mass. The converted fuel mass plus the
remaining fuel in the gas phase at the end of simulation has to be equal to the
initial fuel mass of the droplet [298].
Convergence studies were conducted on a simple and easily reproducible
problem. An n-heptane droplet at T = 360K is placed in an atmosphere of
air at 1500 K and 1bar. The initial droplet diameter is set to D 0 = 100µm, and
the associated liquid phase is resolved with 10 grid points. The outer diameter
of the whole numerical domain is D ∞ = 100D 0 . Thus, the grid points in the
gas phase are initially discretized by
( i
D i = D 0 + (D ∞ − D 0 )
N
) 3
, (4.63)
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