Environmental Engineering Reference
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and combustion reactions. Accordingly, a chemically controlled reaction
model seems suitable.
2. When we use a one-step global reaction model or a reduced mechanism
without reverse reactions, it should be combined with virtual specific heat
taking into account the influences of thermal dissociation.
3. To raise the accuracy of temperature predicted for any equivalence ratio,
the reaction mechanism should at least include reduced reactions relevant
to CO and H
2
.
4. The influence of turbulence on the reaction rate seems less significant in
HiTAC, because the fluctuations of temperature and species concentration
in HiTAC are much smaller than in ordinary combustion. So, we may use
Arrhenius rate expressions without introducing any influences of turbu-
lence.
3.3 HEAT TRANSFER MODEL FOR HIGH TEMPERATURE
AIR COMBUSTION
A large volume reaction zone associated with a mild temperature rise having low
luminosity is a typical feature of HiTAC, which is completely different from ordinary
combustion observed with luminous flames. When considering the numerical sim-
ulation of heat transfer in HiTAC furnaces, we must take this low-luminosity flame
into account. In addition, most of the heat transferred to the material to be heated
is dominated by radiative heat transfer from the walls, which have been heated by
the convective heat transfer of the nonluminous combustion gas. Therefore, we need
an appropriate heat transfer model for HiTAC that can deal with heat transfer from
both gaseous and solid media to the materials to be heated.
3.3.1 H
EAT
T
RANSFER
M
ODELS
3.3.1.1 Gray Model
If the furnace wall material is a blackbody, radiation in all wavelengths is emitted
from its surface at any temperature. The dependency of monochromatic emissive
power of a blackbody,
E
b
λ
, on temperature is shown in
Figure 3.10
.
As shown in
the figure, the dominant wavelength of radiation emitted from a blackbody moves
to the short wavelength range as the temperature of the blackbody rises. The emissive
power,
E
b
, from unit area of the blackbody surface during unit time can be expressed
as follows.
4
E
=
E
=
σ
T
(3.16)
b
b
λ
0
where σ is the Stefan-Boltzmann constant and
T
is surface temperature.
Fractions of the incident radiant energy on a surface are absorbed, reflected, and
transmitted, respectively, and the ratio of respective energy against the incident
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