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Combustion
Radiative Properties of Coal Ash Deposits with Sintering Effects
John Parra-Alvarez, Benjamin Isaac, Minmin Zhou, Sean
T. Smith, Terry A Ring, Stan Harding, and Philip J. Smith
Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b04206 • Publication Date (Web): 29 Jan 2019
Downloaded from http://pubs.acs.org on January 30, 2019
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Energy & Fuels
Radiative Properties of Coal Ash Deposits with
Sintering Effects
John Parra-Álvarez,∗,†,‡ Benjamin Isaac,†,‡ Minmin Zhou,†,‡ Sean Smith,†,‡ Terry
Ring,†,‡ Stan Harding,‡ and Philip Smith†,‡
†Chemical Engineering Department, University of Utah, Salt Lake City
‡Institute for Clean and Secure Energy, University of Utah, Salt Lake City
E-mail: jcparraa@gmail.com
Phone: +1 801 581 5688
Abstract
The heat-transfer characteristics in the the fireside of a pulverized-coal furnace are
affected, among other factors, by the physical and chemical characteristics of the ash
deposits. Indeed, the physical state of the ash deposits and their chemical composition
determine the radiative and conductive properties of the furnace walls. Particularly,
several complex mechanisms are involved in the radiative heat-transfer process at the
walls that restricts the absorption of the incident radiation of the flame, particles and
hot gases. These mechanisms involve dependencies on the radiation spectrum due
to the ash chemical composition and ash-sintering effects that enhance or hinder the
overall heat transfer. In this paper, we discuss the complex mechanisms that describe
the heat exchange in presence of ash deposits and their impact on the prediction of the
wall emissivity and ultimately the wall heat transfer in a real system.
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Introduction
Pulverized coal boiler efficiency is generally compromised due to deposition of material on
the steam tubes and superheaters, it not only affects the overall heat transfer rates but also
affects the structural integrity of the boiler through corrosion and erosion. 1 If the problem
cannot be controlled by a proper soot-blow schedule, it can increase the overall internal
temperature and lead to undesired downtimes. Ash deposition is a complex phenomena that
involves both physical and chemical processes starting even before the particle is deposited
on the walls. The state of the particles and their interactions with the gas phase determines
the specific mechanisms for particle deposition and ultimately the fate of the particles. 2
The heterogeneous composition of coal and ash particles make these phenomena even more
difficult to understand, since these differences affect how the particle sticks to walls, sinters
and/or aggregates to other particles, and how the layers of particles are formed. 3 There is
enough motivation (financial and otherwise) to understand the mechanisms and characteristics that control deposition phenomena, as reflected by literature dating 30+ years back. 4–7
The general consensus agrees that deposition affects two main heat-transfer properties that
influence the overall behavior of a pulverized-coal combustion system: emissivity and thermal conductivity. In this paper, we briefly mention the role of the thermal conductivity but
the main focus is emissivity and in the ways to predict this property in the presence of ash
deposits on the boiler walls.
Heat-transfer impact of deposits
Physical and chemical properties of the fly, and deposited ash are crucial to determine the
likelihood of particles sticking to the walls and forming deposits that ultimately affect the
performance of the boiler in terms of heat-transfer efficiency. Figure 1 shows a qualitative
description of the deposits that can form on walls and tubes. A mathematical description of
the heat transfer to the walls presented in Figure 1 is given as a steady state heat balance
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Inner layer, mostly made up
of very small particles, rich
in alkali metals
Powdery layer, with particles
Between 10um and 100um
Fire side
Sintered particles made up
of molten slags
Qin + Qconv
Qcond
Qrad
Tf
Steam side
Ts
Tt
Tw
5
4
3
2
1
Figure 1: Qualitative description of the heat flux through the walls and the physical structure
of the deposits. The numbers 1 to 5 represent the specific stages of the energy transfer: 1)
flue gas to surface 2) surface to sintered and powdery deposits (outer deposits) 3) outer
deposits to inner deposits (enamel) 4) enamel to steel tubes and 5) steel tube to steam side.
that can be written as:
Qcond = Qin − Qrad + Qcon
(1)
Ts − Tt
= ε(Ts )σ(Tf4 − Ts4 ) + hconv (Tf − Ts )
δw /kw + δdep /kdep
where δi are the thickness of the deposits and the steel tubes and ki are the thermal conductivity of the deposits and steel tubes. Two of the most important quantities in Equation (1)
are: kdep and ε(Ts ). These two properties are determinant to characterize heat transfer; while
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thermal conductivity will be briefly explained, emissivity will be the focus of this paper.
Thermal Conductivity
Complex structures are formed onto surfaces when particles are deposited. Porous and plastic deposits continuously reshape the surfaces making it one of the most difficult quantities
to predict. Particle size and surface temperature, porosity and chemical composition, play
a fundamental role as parameters for thermal conductivity models. The literature has reported 8,9 a reduction up to 25% in the heat-transfer coefficients in the economizer due to
formation of thin layers of powdery deposits, where hot particles impacting the surfaces,
solidify due to the low temperatures of the gas (400 ◦C to 600 ◦C) and tubes, around 300 ◦C.
Thermal conductivity is reduced up to an order of magnitudea leading to degraded heattransfer rates from the fire-side to the steam-side. Different modeling methodologies have
been developed to represent the thermal conductivity in porous deposits; 1,10 in our computational approach we have chosen a model proposed by Hadley 11 to represent the thermal
conductivity through porous media. The model is developed based on volume averages of a
finite number of spatially distributed phases. The effective thermal conductivity in relation
with the fluid thermal conductivity can be written as 11
pf0 + (1 − pf0 )κ
kef f
= (1 − α)
kf luid
1 − p(1 − f0 ) + p(1 − f0 )κ
2(1 − p)κ2 + (1 + 2p)κ
+α
(2 + p)κ + 1 − p
(2)
here, p is the porosity and κ is the ratio ks /kg where ks is the thermal conductivity of the
solids and kg is the thermal conductivity of the gases. 1 α is an empirical mixing parameter that measures the degree of consolidation of particulate metals 1 and is given by the
a
0.2 W/(m K) < kdep < 3.0 W/(m K) compared to 15 W/(m K) < ktube < 57 W/(m K)
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expressions:
0.7079(1 − p)6.3051
α=
1.5266(1 − p)8.7381
for 0.0975 ≤ p < 0.3
(3)
for 0.3 ≤ p < 0.572
f0 is an semi-empirical parameter for solid structures that correlates with the volume fraction
and ranges between 0.8 to 0.9. 1 In the simulation, this parameter takes a value of f0 = 0.85
Emissivity
Thermal radiation is responsible for a large percentage (>80 %) of the heat transfer inside
the furnace section of the boiler and the characteristic properties that govern the emissivity,
absorptivity and reflectivity are fundamental to predict radiative heat transfer. The radiation
coming from deposited surfaces is spectral in nature and is affected by the index of refraction,
the temperature, the physical structure and the chemical composition of the deposits. The
spectral emissivity is related to the intensity (radiant flux per unit area) corresponding to
each wavelength in the spectral distribution. The total emissivity, defined in terms of the
spectral emissivity can be written as:
εt (Ts ) =
1 Z∞
ελ (λ, Ts )IB (λ, Ts )dλ
σTs4 λ=0
(4)
where IB (λ, Ts ) is the spectral black-body flux density and corresponds to the upper limit
of emission by any body. The expression is given by:
IB (λ, Ts ) =
2hc2
1
5
λ exp(hc/λkB T ) − 1
(5)
where c is the speed of light, kB is the Boltzmann constant and h is the Planck constant.
The underlying assumptions in Equation (4) are discussed by Wall and Becker 12 and Wall
et al. 13 . Compared to clean surfaces, ash deposit surfaces present a greater variability
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in total emissivity. For instance, surfaces with a thin, particulate layer of deposit can have
emissivities in the range 0.2 to 0.5 heavily influenced by the wavelength, while heavily sintered
slags can have emissivities in the range 0.8 to 0.9. This morphology plays an important role
as pointed out by Markham et al. 14 , since it increases the scattering efficiency by increasing
the surface available. Also, as molten deposits solidify, they become glassy and increase
the overall emissivity of the surface with typical values >0.85. Boow and Goard 15 studied
the characteristic trends of emissivity in ash deposits; their findings can be summarized as
follows: i) emissivity decreases with temperature, ii) emissivity increases with particle size,
iii) emissivity tends to increase upon sintering, iv) emissivity increases with iron content.
One of the purposes of this paper is to put some of this findings into a model that can predict
the total emissivity of a deposit. In the next section, we review the steps necessary to model
ελ (Ts ), including Mie theory and the determination of the optical properties related to the
complex index of refraction.
Thermal Radiation
As incident radiation hits the deposits on the walls, it is scattered in all possible directions
and it is measured as reflected radiation. The materials on the walls can also absorb the
incident radiation and emit it back depending on the physical and chemical composition
of the participating media. One of the appropriate framework to approach the problem of
predicting the spectral emissivity of coal ashes is given by Mie theory. For isotropic, homogeneous, spherical particles, Mie theory calculates the scattering and absorption properties
of the material and ultimately the emissivity, given the complex index of refraction and the
particle size distribution. The complex index of refraction, defined as: m(λ) = nλ − ikλ is
an indicator of the attenuation that a electromagnetic wave (thermal radiation) undergoes
when passing through a medium, here nλ = n(λ) is the real refractive index and kλ = k(λ)
is the imaginary absorption index; their characteristics have been thoroughly discussed by
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Goodwin 16 and Ebert 17 . In the following, we describe a methodology proposed by Ebert 17
to predict n and k for coal ashes based on composition and other physical properties; these
quantities will be used in Mie theory to calculate the spectral emissivity which will help us
calculate the total emissivity through Equation (4). Based on the data described by Boow
and Goard 15 , we add sintering effects that directly affect the particle size and change the
trends of emissivity.
Complex index of refraction
Besides temperature and chemical composition, the complex index of refraction depends on
the wavelength, so given an appropriate range of these three parameters, correlations can be
proposed to represent a wide range of coal ashes, whose physical and chemical complexity
make it difficult to develop universal formulas to compute radiative properties.
Real refractive index
The calculation for nλ requires correlations for short wavelengths and long wavelength. For
wavelengths in the range 1 µm to 8 µm a correlation to calculate the refractive index is given
by the following mixture rule
X xm,i n2i,λ − 1
n2λ − 1
=ρ
n2λ + 2
ρi n2i,λ + 2
i
(6)
where xm,i is the mass fraction, ρi is the density, and ni,λ is the refractive index of the
corresponding species i. The density and the species refractive index can be calculated as:
1 X xi
≃
ρ
i ρi
ni,λ − 1 ≃ Ci −
7
(7)
Bi λ2
λ2o,i − λ2
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and the values for the parameters C, B and λ0 can be found in Ebert 17 . For wavelengths
in the range 8 µm to 13 µm, the absorption band is mainly due to vibrational absorption of
glassy slags composed by structural bounds of the type Si O Si and Si O–; this portion of
the spectra can be modeled using a solution to the Lorentz harmonic oscillator:
(n + ik)2 = n2∞ +
ωp2
ω02 − ω 2 − iγω
(8)
ω0 ≃ 755 + 355x̂SiO2
γ
≃ 0.404 − 0.724[Si]
ω0
ωp
ω0
≃ 0.747 − 0.740[Si]
n2∞ ≃ 1.41 + 0.21ρ
where the absorption frequencies (ω = c/λ) have been correlated to the SiO2 composition
from 10 different slags; [Si] = ρxSiO2 /M̂SiO2 is the molar concentration of Si atoms in units
of mol L−1 , ρ is the density in g cm−3 , xSiO2 is the mass fraction of SiO2 and M̂SiO2 is the
molecular weight of SiO2. To preserve continuity at the different wavelengths, it is necessary
to identify the point where the mixture rule yield values of nλ that are smaller than the single
oscillator model; generally, this point happens around 7 µm. Assuming that the wavelength
at which nmix = nosc is λeq , then for λ < λeq the mixture rule should be used and for λ > λeq
the single oscillator model should be used.
Imaginary absorption index
According to available research, 14,16–18 absorption in slags at short wavelengths (1 µm to
4.5 µm) is mainly due to the presence of iron and depends on its concentration and valence
state. Goodwin 16 has developed correlations for k that depend on the valence of the iron
which is affected by the conditions in which the slag was produced (reducing or oxidizing
environments). Without valence information for slags, the correlations are difficult to use;
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instead a simpler solution has been proposed. Assuming that kλ is constant in this range;
the trends show that increasing Fe2O3 concentration increases the average value of kλ over
this range. The correlation presented in Ebert 17 was obtained as a quadratic fit over many
different samples of slags, and reads as:
k̄ ≃ (4.02x + 16.9x2 ) × 10−3
(9)
where x is the iron mass fraction in the slag. For the range of wavelengths 4.5 µm to
8.5 µm the two-phonon model gives reasonable results, considering that in this region the
absorption index varies from transparent (kλ < 10−4 ) to highly absorbing (kλ > 10−1 ) having
an exponential form. 19,20 The underlying assumption of the model is that the contribution
to the absorption at a specific frequency ω is the result of the combination of two single
absorption events at half of the frequency ω/2
2
kλ = k0 + kb 1 +
C2
)−1
exp( 2λT
ω − Bk0 2
k0 ≃ Ak0 exp −
Ck0
kb =
ω∗ =
Aω0 exp(−ω/B0 )
A1 exp(−ω/B1 )
ω
(10)
for ω < ω ∗
for ω > ω ∗
ln(A1 /A0 )
.
1
− B10
B1
The values for the parameters of Equation (10) are listed in Table 1. For the range of waveTable 1: Parameter for the 2-phonon model at short wavelengths
k0
Parameter
Ak 0
Bk0
Ck0
Value
0.0015
1800 cm−1
110 cm−1
Parameter
A0
B0
–
Value
295 cm−1
443 cm−1
–
9
kb
Parameter
A1
B1
–
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Value
51 370 cm−1
200 cm−1
–
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lengths >8.5 µm, the absorption is mainly due to the contribution of vibrational absorption
of silica, and the single oscillator model presented previously would yield acceptable results.
To account for the transitions, the absorption index can be computed as: kλ = k1 + k2 ,
with k1 given by:
k1 =
k̄(xFe2O3 )
for λ < 4.5 µm
k̄(xFe2O3 ) exp(4.5 − λ)
0
for 4.5 ≤ λ < 8.5 µm
(11)
for λ ≥ 8.5 µm
and the expression for the range <4.5 µm given by Equation (9). The second term k2 is
either the 2-phonon model or the single oscillator model, depending on the wavelength where
k from the two models intercept. Further details can be found in Ebert 17 . Applying the set
of Equations (6)–(11) it is possible to represent both, the complex index of refraction and
the imaginary absorption index.
Particle Scattering
Once we have estimated nλ and kλ , the complex index of refraction can be calculated as:
m(λ) = nλ + ikλ which will be used in Mie theory in order to obtain the scattering and
absorption properties of the particles. The scattering efficiency Qsca and the absorption
efficiency Qabs for a single particle are defined as the scattered and absorbed power by the
particle, normalized by incident power and the particle’s projected area. The size parameter
corresponds to the size of the particle relative to the wavelength of the incident monochromatic light and is defined as: x = πD/λ. In addition, it is necessary to define the asymmetry
parameter g, that describes the direction of the scattering, ranging from completely forward
(g = 1) to completely backward (g = −1) including symmetric forward and backward scattering and isotropic scattering (g = 0). From Bohren and Huffman 21 , the efficiencies and
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asymmetry parameters are given by:
Qsca =
∞
2 X
2
2
(2j
+
1)(|a
(x,
m)|
+
|b
(x,
j)|
)
j
j
x2 j=1
Qext =
∞
2 X
(2j
+
1)Re{a
(x,
m)
+
b
(x,
j)}
j
j
x2 j=1
(12)
Qabs = Qext − Qsca
g=
+
X
∞
4
j(j + 2)
Re{aj a∗j+1 + bj b∗j+1 }
2
x Qsca j=1 j + 1
∞
X
2j + 1
j=1
j(j + 1)
Re{aj b∗j }
where aj = aj (x, m), bj = bj (x, m) correspond to the complex Mie amplitudes and are
computed from relationships derived based on the Riccati-Bessel functions; the asterisks in
aj and bj represent complex conjugates. Details about underlying assumptions and validity,
can be found in Bohren and Huffman 21 . In general, scattering and absorption characteristics
involve multiple particles and the radiation effects between them depend on their proximity
and their number, this multiple and dependent scatter effect usually increase the absorption
and emission relative to the predictions from Mie theory. Drolen and Tien 22 have found a
discrepancy up to 5% between dependent and independent scatter effects for big particles
(>50 µm), which makes it easier to use Mie theory for far field, single scatter particles in
order to determine the different efficiencies. The physical structure of the deposits plays
a fundamental role on how the surface emissivity of the deposits is treated. For instance,
the spectral emissivity of homogeneous slabs having optically smooth surface (glassy and
melting deposits) is given by the Fresnel relations:
ελ = 1 −
(nλ − 1)2 + kλ2
(nλ + 1)2 + kλ2
(13)
This emissivity is specially valid for particles in sintered structures that have grown bigger
than >300 µm. For a slab of particles (sintered structures on the wall with <300 µm) multiple
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scattering considerations are necessary; Bohren 23 has proposed a special solution to the
discrete ordinates equations in which only two scattering directions are used: backward and
forward scattering. This approximation was coined two-flux model and is used to calculate
the spectral emissivity as:
√
√
( 1 − ϕg − 1 − ϕs )
√
ελ = 1 − √
( 1 − ϕg + 1 − ϕs )
(14)
where ϕ is the albedo of scatter defined as: ϕs = Qsca /Qext and g is the asymmetry parameter. The total emissivity, obtained from the integration of Equation (4) using the functions
in Equations (13) (Fresnel emissivity) and (14) (two-flux emissivity); is presented in Figure 2. Figure 2a compares the measured emissivity of a sub-bituminous coal ashes (Lidell
ash) taken from Wall and Becker 12 . Figure 2b presents the comparison of total emissivity
data from Boow and Goard 15 including particle sintering effects, which will be explained in
the next subsection.
Particle Sintering
As particles coalesce together, the physical structure of the deposit changes, changing in turn,
the mechanisms of absorption and scattering and overall; increasing the total emissivity.
This effect is called onset sintering and can be spotted in Figure 2 a and b where the
total emissivity stops decreasing and starts increasing. In this work, we have attempted to
implement a sintering model that represent these effects.
One of the first attempt to describe sintering goes back to Frenkel 24 who introduced the
concept as an energy balance: the total energy produced by dissipation of the flow is equal
to the work done by the surface tension in decreasing the total surface area. This concept
is used in almost all mathematical models describing viscous sintering, which is the most
common mechanism for which particles form compact structures in combustion systems.
Review of the most common models can be found elsewhere. 25,26 The sintering model used
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in this work was proposed by Pokluda et al. 27 which is also based on a balance between the
work of surface tension and viscous dissipation. This model measures the degree of sintering
by calculating the angleb between the center of the neck formation and its edge, which can
be easily translated into the more familiar ratio x/r: length of the sintering neck to the
particle radius. These expressions are given by:
Γ 2−5/3 cos(θ) sin(θ)(2 − cos(θ))1/3
dθ
=
dt
r0 µ
(1 − cos(θ))(1 + cos(θ))1/3
x
= sin(θ)
r
1/3
4
x
= sin(θ)
r0
(1 + cos(θ))2 (2 − cos(θ))
1/3
4
r = r0
(1 + cos(θ))2 (2 − cos(θ))
(15)
The previous equations describe the sintering process for 2 particles. The effect of several
particles can be added by noting that τ = Γ/r0 µ is a sintering time scale; where Γ is the
surface tension and µ is the particle viscosity. If N particles are sintering simultaneously,
the sintering time scale is given by: τ = Γ/r0 µ(N/2)1/3 . For N particles from a ballistic
dense cluster the sintering time scale is given by τ = Γ/r0 µ(N/2)(1/2−Df /6) ; where Df is
the fractal dimension for the cluster varying between 1 and 3, and N is the coordination
number with a value that varies between 2 and 8. The effects of particle sintering are
taken into account when the size parameter for the Mie theory is calculated. Given a
time scale for particle deposition on the walls, the method calculates sintering within this
timescale and then recalculates the optical constants for the complex index of refraction
m(λ), which in turn, is used to calculate the spectral emissivity and subsequently, the total
emissivity. The sintering effects can be seen in Figure 2b reflecting the dips consistent
with the observations of Boow and Goard 15 . The sizes are given in terms of ranges from a
particle size distribution of a sample of crushed ash. These experimental ranges were fitted
to a Rossim-Ramble distribution and an inverse problem was solved in each range in order
b
This angle varies between 0° for no sintering and 90° for complete sintering
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to find weights that described the importance of the different sizes within the range. The
fitting within each particle size range was done via quadrature approximations as proposed
by Marchisio et al. 28 . We have hypothesized that the smooth transition at the onset sintering
(lowest emissivity values for the experiments presented in figure 2) that increases emissivity
with temperature is due to not-yet-understood particle sintering effects. Our simplistic model
transitions rather quickly from the emissivity at the onset point to the emissivity given by
the Fresnel relationships and produces a sharp transition between the emissivity estimated
with Equation (14) and the emissivity calculated with Equation (13). Once the structure
has melted or turned into a glassy slag, the spectral emissivity is calculated from the Fresnel
relation. One way to make a smooth transition between the calculated emissivities, is to
propose an additional model for the coordination number (the effective number of particles
that surround a given particle in the sintering structure) that takes into account the time
scale of deposition and effective particle size of the sintered structure. Currently we are
considering to iteratively growing the structure by sintering pairs of particles that enter the
computational domain of the wall. The effects of this sharp transition can be visualized in
Figure 3 where there is a clear, defined region of high emissivity (> 0.90) surrounded by
regions of moderate emissivity (< 0.7). This methodology to predict wall emissivity was
applied to the prediction of the wall heat flux in a real combustion system as it is described
in the next section.
Application in Heat-Flux Prediction
The results obtained in the previous section were applied to the prediction of heat flux in a
15 MW capacity pilot unit, the boiler simulator facility (BSF) formerly located at ALSTOMGE. This unit is an oxy-combustion boiler-simulator facility which is an atmospheric-pressure,
balanced-draft, combustion facility designed to simulate the temperature-stoichiometry history of typical utility boilers. 29,30 The furnace is fired from 4 corners with 2 levels of separated
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1
Composition
Oxide
SiO2
Al2O3
Fe2O3
%wt
51.4
29.3
6.1
0.9
CaO
MgO
Na2O
1.4
0.8
0.8
0.8
K2O
TiO2
SO3
0.7
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0.14
sim results - SA05 < 44 microns, 360 [s]
sim results - SA05 53-104 microns, 360 [s]
sim results - SA05 - 104-211 microns, 360 [s]
sim results - SA05 - 211-422 microns, 360 [s]
sim results - SA05 < 44 microns, 3600 [s]
sim results - SA05 53-104 microns, 3600 [s]
sim results - SA05 - 104-211 microns, 3600 [s]
sim results - SA05 - 211-422 microns, 3600 [s]
sim results - SA05 < 44 microns, 20000 [s]
sim results - SA05 53-104 microns, 20000 [s]
sim results - SA05 - 104-211 microns, 20000 [s]
sim results - SA05 - 211-422 microns, 20000 [s]
sim results - Fresnel reln.
SA05 < 44 microns
SA05 53-104 microns
SA05 - 104-211 microns
SA05 - 211-422 microns
SA05 slag
0.7
Mass mean size: 17 um
0.6
0.5
0.4
0.3
400
600
800
1000
1200
Temperature [K]
1400
1600
1800
Figure 2: Comparison of measured values of total emissivity against model predictions. a)
Lidell coal ashes Wall and Becker 12 without sintering effects. b) Synthetic ashes from Boow
and Goard 15 with sintering effects
overfired air and three levels of coal injectors in which mixing occurs mainly throughout the
boiler instead of near the burner nozzle. The heat-transfer surfaces are cooled by a surrounding water jacket and the steam generated is vented off at atmospheric pressure with
a constant sink temperature of 212 F. The BSF was simulated with a computational fluid
dynamics (CFD) simulation tool used to represent the complex physical processes occurring inside the oxy-coal system; this tool is ARCHES, which is a component of the UINTAH
computational framework, 31–33 developed to solve partial-differential equations on structured
grids using hundreds of thousand of processors. ARCHES solves conservation equations for
mass, momentum, energy and solid phases using a low-Mac, pressure-projected, variabledensity code. Turbulence is modeled using the Large-Eddy Simulation (LES) approach with
the dynamic-Smagorinsky closure model for the random fluctuations in the momentum equation. The solid phase (coal and ash particles) is represented in an Eulerian framework through
the direct quadrature method of moments (DQMOM), 34 introducing evolution equations for
particle variables such as: velocity, size, raw coal mass, char mass, enthalpy, maximum
temperature; that ultimately describe the high dimensional particle property distribution
through their moments. Gas-phase reactions were modeled using a mixture fraction approach with three streams: a primary stream, a secondary stream and a coal off stream.
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Figure 3: Emissivity and heat-flux distribution values from simulation results
These mixture fractions relate the products of devolatilization and char oxidation from the
coal particles to the gas phase. Radiation is solved using discrete ordinates with 8 ordinates
and 80 directions. A more detailed explanation of the models used in this simulation can
be found elsewhere. 35,36 One simulation of the BSF costs 740,000 CPU-hours on 3,000 cores
with a resolution of 2 cm and a total number of cells around 17,000,000. The simulations
run 28 seconds of computational time achieving steady state at approximately 20 seconds.
Figure 3 show results for the wall emissivity and the heat flux to the wall for the BSF.
The BSF is equipped with four water-wall panels that simulate heat transfer pickup in the
radiant section of the furnace. There is a system of air-lances in place in order to clean-up the
panels (soot-blow) and control the impact of ash deposition. Twenty-four experimental heatflux measurements to these panels are available for comparison with simulation results. The
comparison is done via verification and uncertainty quantification (V/UQ), which employ an
overall validation approach that includes uncertainty propagation across multiple scales and
simultaneous validation across different sets of experimental and simulation data for air and
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oxy-combustion systems. The key physics components for these kinds of systems, include
particle combustion, ash transformations, multiphase flow radiation and LES turbulence. 35,37
The analysis uses Bayesian inference and bound-to-bound data collaboration 38,39 in order
to estimate the regions of uncertainty of the simulation data and the region of consistency
between the experimental data and the simulation data. Figure 4 shows the estimation of the
uncertainty as error bars. The blue and red error bars are calculated using Bayesian inference,
and describe the region for which the simulation models, can be used to represent the system,
given a body of evidence for these constitutive models 35,37 . The green error bars correspond
to region of consistency between the experiments and the simulation results. 35,38,40 As in most
V/UQ methodologies, one of the main objectives is to find the values of model parameters
that produce predictions that lie within the regions of consistency. Figure 4 also shows
a black line representing a simulation obtained with the predicted model parameters from
the V/UQ methodology. For most of the measurements, the black line lies in the accepted
region of uncertainty (blue and red bars); better predictions will be obtained when the black
line lies also within the green region. For most of the predictions this is true, but some of
them lie outside the green region. Subsequent analysis to diagnose the discrepancy issues for
these specific locations, would require to revisit the assumptions on the different models used
in the simulation, for instance, emissivity and thermal conductivity. Future work includes
improvements on the emissivity model by revisiting the effect of the structure (coordination
number) and the sharp transition between Equations (13) and (14)
Summary and Future Work
In this paper, we have described a methodology to model optical constants and spectral
emissivity of coal ashes. The determination of these properties is extremely important in
order to assess the heat-transfer efficiency to the walls. The complex index of refraction
m, was determined using the methodology proposed by Ebert 17 and the spectral emissivity
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Figure 4: Heat-flux prediction with uncertainty bars. The horizontal axis correspond to the
locations were the heat flux probe was introduced to take a measurement
was determined using Mie theory and particular solutions to the intensity transport equations. 12,14,23 The particle-size effects and onset sintering observed by Boow and Goard 15
were incorporated using a sintering model proposed by Pokluda et al. 27 ; direct comparison
of the total emissivity against measured values was reported. 12,15 it is possible to improve
the sintering model by adding coordination number effects that depend on the time scale
of particle deposition and the effective size of the deposited structure, this will be left for
future work. The proposed emissivity model, was used in the prediction of the heat flux
to the wall of a 15MW oxy-coal boiler at ALSTOM-GE, the results were validated using
V/UQ as explained in Parra-Alvarez et al. 37 and Diaz-Ibarra et al. 35 . In general the prediction is accurate within the uncertainty ranges given by the V/UQ methodology, which, for
engineering purposes is the desired result.
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Acknowledgement
This material is based upon work supported by the Department of Energy, National Nuclear
Security Administration, under Award Number DE-NA0002375
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