Environmental Engineering Reference
In-Depth Information
The NO source term due to the formation/destruction of the thermal NO, prompt
NO, and NO reburning can be calculated by
[
]
[
]
[
]
M
d
NO
d
NO
d
NO
T
P
R
S
=
+
(3.31)
!
NO
NO
dt
dt
dt
To calculate the mean NO formation rate,
S
NO
, which is required in the mean
NO concentration equation, a PDF is employed to take into account temperature
and composition fluctuations. NO is formed mainly by the thermal mechanism in
gas-fired furnaces. The rate of thermal NO formation depends on the temperature
and oxygen concentration. Therefore, a joint two-variable PDF in terms of temper-
ature and oxygen concentrations was used. The mean formation rate,
S
NO
, can be
determined by
(
)
()
(
)
˜
S
=
S
TY
,
PTPY dTdY
(3.32)
NO
NO
O
1
2
O
O
2
2
2
The shape of
P
1
(
T
) and
P
2
(
Y
O2
) is approximated by a β -function since the β -
PDF is widely used in turbulent combustion simulations.
The governing equations for turbulent non-premixed combustion include the
conservation equations of mass, momentum, energy, turbulence kinetic energy, dis-
sipation rate of turbulent kinetic energy, mixture fraction, and its variance. Density-
weighted (Favre) averaging was utilized to account for the effects of density change.
The steady three-dimensional Favre-averaged conservation equations in Carte-
sian coordinates were solved. The numerical simulations were carried out on a
nonuniform grid of 89 × 25 × 31 nodes along the
x
-,
y
-, and
z
-coordinates to
accommodate the locations and sizes of the slab, air, and fuel injection nozzles, and
auxiliary exhaust tube of the experimental furnace. The furnace had inner dimensions
of 8 × 4 × 3 m. The grid dependence test in the former work
23
indicated that the
grid arrangement described above can yield essentially grid-independent results.
The turbulent combustion model adopted in the simulation was the mixed-is-
reacted model combined with the prescribed PDF (β -function) of mixture fraction
fluctuations. The radiative heat transfer model used to estimate the source term in
the energy conservation equation was the P-1 model by Cheng
24
associated with the
weighted sum of gray-gas model. In the numerical simulations, the top and side
refractory walls of the furnace were treated as convection/radiation walls with an
overall external heat transfer coefficient of 0.58 J/m
2
sK, which was based on the
thickness and thermal properties of refractory walls as well as the surrounding
conditions. The bottom wall of the furnace was considered as a wall with a constant
heat flux of 8.47 kW/m
2
. This value was estimated from the heat-extraction rate by
the cooling water flowing through the bottom of the furnace.
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