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Coal and biomass cofiring: CFD modeling 107

the freeboard in modern grate-fired boilers or fluidized bed combustors, the effect of
the dense bed conversion models may be virtually restricted to the vicinity of the
fuel bed.

4.6 Coal and biomass cofiring under oxy-fuel conditions:
special modeling issues

Oxy-fuel combustion has gained many concerns worldwide in the past years. More
recently, oxy-fuel cofiring of coal and biomass also gains much attention, considering
that a below-zero CO 2 emission may be achieved by combining the advantages of both
oxy-fuel combustion and biomass cofiring. The use of CO 2 or the mixture of CO 2 and
H 2 O vapor as the diluent in oxy-fuel combustion, instead of N 2 in air-fuel combustion,
induces significant changes to the combustion fundamentals, particularly to radiative
heat transfer and combustion chemistry, as reviewed in (Yin and Yan, 2016).
Coal and biomass cofiring under oxy-fuel conditions has been numerically investi-

gated in the literature, for example (Alvarez et al., 2013, 2014; Bhuiyan and Naser,
2015, 2016; Black et al., 2013). The overall modeling strategy of oxy-fuel cofiring
is the same as that of air-fuel cofiring. Although the majority of the impacts of the com-
bustion atmospheres can be accommodated in modeling naturally, efforts are still
needed to refine the existing models or mechanisms for radiative heat transfer and
gas-phase combustion chemistry to make them applicable to oxy-fuel combustion
(Yin and Yan, 2016).

4.6.1 Modeling of gaseous radiative properties under oxy-fuel
conditions

The radiative transfer equation to be solved under a typical solid fuel combustor is pre-
sented in Eq. (4.2), in which the gas and particle radiative properties are evaluated by
Eq. (4.3)e(4.5), respectively. The total gas emissivity of a local gas mixture to be used
in Eq. (4.3), ε, is commonly evaluated by a WSGGM in combustion CFD because it is
a good compromise between computational efficiency and accuracy. The WSGGM
postulates that the total emissivity may be represented by the sum of the emissivities
of several hypothetical gray gases and one clear gas, weighted by temperature-
dependent factors (Hottel and Sarofim, 1967). In the model, each of the I gray gases
has a constant pressure absorption coefficient k i , and the clear gas has k 0 ¼ 0.

I
X k i PL
ε ¼ a ε;i ðT g Þ 1 e
i¼0
(4.18)
J I
X X
where a ε;i ¼ b ε;i;j T g j 1 ði ¼ 1; /IÞ and a ε;0 ¼ 1 a ε;i
j¼1 i¼1