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

3.3 Numerical Study of the Fluid Dynamics Within the Combustion Chamber
As exhaust gas sampling is not yet relevant in this first part of the CFD study
(cf. Chap. 3.3.2), the sample probes are implemented as a wall with an isothermal,
no-slip boundary condition, similar to the regular combustion chamber
walls. The open area at the bottom of the combustion chamber is modeled
by an opening in order to allow a bidirectional gas exchange with the environment.
Special subdomains are created for the fuel sources (droplets) and
the area of heat release (ignition wire). The area of the fuel sources and their
surroundings is meshed by spheres, using multiple nested O-grids for each
fuel source. The O-grids provide a refined mesh, and thus improved heat and
mass transfer. The innermost O-grid in each case matches the inner sphere
of Figure 3.21, has the radius of r 1 = 0.75 mm, and is discretized by 17 cells.
Accordingly, r 2 allocates the second O-grid. It is separated only one cell and
0.05mm from the inner sphere. The zone of heat release (ignition) is schematically
included in Figure 3.21 and colored orange (A). Both fuel sources and
zone of heat release are realized by step functions within their particular subdomain
using CEL, which allows temporal, spatial, and conditional control.
Each fuel source is patched with a spatially uniform temperature that is the
wet-bulb temperature of C 10 H 22 associated with the actual temperature T r1 (t )
at the respective inner sphere. The relevant correlation was assessed beforehand
by the heat and mass transfer model of Spalding [418] for ambient temperatures
in the range of 300 to 1000 K and is provided as a polynomial fit function
within a separate CEL expression for each fuel source [418, 453]. Thus, the
model is also capable of reproducing the transient heating process of each fuel
source, i.e. fuel droplet. In summary, the final computational domain of this
combustion simulation consists of a structured hexahedral mesh of 1353992
elements. Parallel computing with up to 8 CPUs was performed to reduce the
overall simulation time. Time-stepping was optimized, obtaining a final time
step size of 3×10 −5 s and convergence within the seventh coefficient loop in
approximately 90 % of the time steps.
Since the software package CFX ® 11.0 does not include the thermophysical
properties of C 10 H 22 by default, a new data set for gas-phase combustion was
integrated in the software libraries. Data sources were the NIST Chemistry
WebBook [311] and the VDI Wärmeatlas [453]. Particularly the VDI Wärmeatlas
provides instructions for the calculation of the dynamic viscosity η in
Pa s, specific heat capacity c p in J kg −1 K −1 , and thermal conductivity λ in
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