Page 136 - New Trends In Coal Conversion

Coal and biomass cofiring: CFD modeling 99

• For fly ash particles, the deposit is formed mainly by inertial impaction, while turbulent and
thermophoretic mechanisms also contribute to some extent.

The deposition velocity u d ¼ _ m 00 d C 0 is often normalized by the friction velocity or
þ
shear velocity u s to yield a dimensionless deposition velocity u ,
d

u d _ m 00 d C 0
þ
u ¼ ffiffiffiffiffiffiffiffiffiffiffiffi (4.12)
d ¼ q
u s
s w r g
2
where _ m , C 0 , s w , and r g represent particle deposition flux (kg/(m $s)), near-wall
00
d
3
droplet/particle mass concentration (kg/m ), wall shear stress (Pa), and gas density
3
at wall temperature (kg/m ), respectively. Empirical correlations for the dimensionless
deposition velocity exist in the literature.
For submicron salt vapor droplets/particles, the dimensionless deposition velocities
due to diffusion, turbulent eddy impaction, and thermophoretic mechanisms are
8
> u ¼ 0:057 Sc 2=3
> þ
> d;Diff p
>
>
>
< 2
u þ ¼ min 4:5 10 4 s þ ; 0:14 (4.13)
d;Turb p
>
>
>
>
>
> þ
: u ¼ðF therm $s p Þ=ðm p $u s Þ
d;Therm
where Sc p , s , F therm , s p , and m p are the particle Schmidt number, dimensionless
þ
p
particle relaxation time, thermophoretic force, particle relaxation time, and particle
mass, respectively. Based on the above empirical equations, the deposition rate of a
given salt vapor, i, can be calculated as,

_ m 00 ¼ u þ þ u þ þ u þ (4.14)
g
d;vapor i d;Diff d;Turb d;Therm $u s $ r Y vapor i
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
total dimensionless deposition velocity mass concentration
in which the mass fraction of vapor i, Y vapor i , is calculated from its transport equation.
For fly ash particles, the deposition rate is calculated as,

_ m 00 d;flyash ¼ _ m p $h stick =A þ u þ þ u þ $u s $Conc p $h stick (4.15)
d;Therm
d;Turb
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
00 _ m 00 þ _ m 00
_ m d;Inert d;Turb d;Therm
where _ m p , A, h stick , and Conc p represent the mass flow rate of fly ash particles being
tracked that is currently hitting a wall, area of the reflecting surface that the particle is
hitting, net fraction of particles contributing to deposit growth which is dependent on
both the particle and wall surface conditions (e.g., particle and wall temperatures), and
particle mass concentration, respectively.