Measurement and Simulation of Ash Deposit Microstructure

Energy & Fuels 2003, 17, 1311-1323

1311

Measurement and Simulation of Ash Deposit Microstructure Soon C. Kweon,† Everett Ramer,‡ and Allen L. Robinson*,† Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, and Cellomics, Inc., Pittsburgh, Pennsylvania 15219 Received November 19, 2002

Critical deposit properties such as thermal conductivity and strength are thought to be strongly dependent on deposit microstructure. Image analysis techniques were applied to scanning electron microscopy images of ash deposit cross sections to measure quantitatively the microstructure of two ash deposits formed while firing sub-bituminous coal in a pilot-scale combustor under different temperature conditions. The measurements indicate that the high-temperature deposit has a more interconnected and coarser structure than the low-temperature deposit. Little spatial variability of the structural parameters was observed, except for a significant gradient in the contiguity (a measure of particle interconnectedness) across the high-temperature deposit. The measurements are compared to predictions of a ballistic deposition model. Both sampled and simulated deposits are coincident in terms of the measured structural parameters. The results suggest that temperature and composition can be used to predict the effects of coal quality and combustion conditions on the initial microstructure of an ash deposit. Higher-temperature conditions create a deposit with a more porous structure but whose particles are more interconnected because of deformation.

1. Introduction Ash deposition frequently has a dominant role in the design and operation of power generation systems that operate on coal, biomass, black liquor, and other ashforming fuels. Ash deposits form from fly ash, inorganic vapors, and some gas species that deposit or react on boiler surfaces through a variety of mechanisms. Ash deposits are a complex, heterogeneous, multiphase, porous material. Similar to other porous materials, critical deposit properties such as a thermal conductivity and strength are thought to be determined primarily by the deposit structure.1-9 However, relatively little is known about deposit microstructure and the relationship between deposit properties and microstructure. Few quantitative measurements of deposit microstructure have been reported in the literature. The large * Author to whom correspondence should be addressed. E-mail: [email protected]. † Carnegie Mellon University. ‡ Cellomics, Inc. (1) Robinson, A. L.; Buckley, S. G.; Yang, N.; Baxter, L. L. Energy Fuels 2001, 15, 75-84. (2) Gupta, R. P.; Wall, T. F.; Baxter, L. L. In Impact of Mineral Impurities in Solid Fuel Combustion; Gupta, R., Wall, T., Baxter, L., Eds.; Kluwer Academic Publishers/Plenum Publishers: New York, 1999; pp 65-84. (3) Nowok, J. W.; Benson, S. A.; Jones, M. L.; Kalmanovitch, D. P. Fuel 1990, 69, 1021-2027. (4) Nowok, J. W. J. Inst. Energy 1996, 69, 9-11. (5) Torquato, S. Appl. Mech. Rev. 1991, 44, 37-76. (6) Kunii, D.; Smith, J. M. AIChE J. 1960, 6, 71-78. (7) Kurashige, M.; Mishima, M.; Imai, K. J. Therm. Stresses 1999, 22, 713-733. (8) Rezaei, H. R.; Gupta, R. P.; Bryant, G. W.; Hart, J. T.; Liu, G. S.; Bailey, C. W.; Wall, T. F.; Miyamae, S.; Makino, K.; Endo, Y. Fuel 2000, 79, 1697-1710. (9) Slavin, A. J.; Londry, F. A.; Harrison, J. Int. J. Heat Mass Transfer 2001, 44, 891-891.

number of particles, small length scale, and highly three-dimensional structure make deposit microstructural analysis challenging. Ramer and Martello10 measured a variety of structural parameters using image analysis techniques applied to scanning electron microscopy (SEM) images of deposit cross sections. Using the principles of stereology, they quantitatively measured a variety of two- and three-dimensional structural parameters. Wang et al.11 performed detailed analysis of coal ash deposits using SEM, X-ray, and image analysis to investigate local deposit properties as a function of position. Using cluster analysis, they found that the deposit microstructure varied with distance from the heat-transfer surface. Researchers in other fields have used image analysis techniques to investigate the structure and properties of porous materials.12-14 Currently available microtomographic techniques, such as X-ray tomography, do not have the spatial resolution necessary to examine ash deposit structure. Ballistic deposition models are one class of models used to simulate the complex three-dimensional microstructure of porous materials.15,16 Several investigators (10) Ramer, E. R.; Martello, D. V. In Applications of Advanced Technology to Ash-Related Problems in Boilers; Baxter, L. L., DeSollar, R., Eds.; Plenum Press: New York, 1996; pp 309-323. (11) Wang, H.; West, H.; Harb, J. N. Energy Fuels 1999, 13, 570578. (12) Berryman, J. G.; Blair, S. C. J. Appl. Phys. 1986, 60, 19301938. (13) Masad, E.; Muhunthan, B.; Shashidhar, N.; Harman, T. J. Comput. Civ. Eng. 1999, 88-95. (14) Levitz, P.; Ehret, G.; Sinha, S. K.; Drake, J. M. J. Chem. Phys. 1991, 95, 6151-6161. (15) Visscher, W. M.; Bolsterl, M. Nature 1972, 239, 504-&. (16) Tory, E. M.; Church, B. H.; Tam, M. K.; Ratner, M. Can. J. Chem. Eng. 1973, 51, 484-493.

10.1021/ef020277f CCC: $25.00 © 2003 American Chemical Society Published on Web 08/14/2003

1312 Energy & Fuels, Vol. 17, No. 5, 2003

have used this approach to simulate ash deposit microstructure.17-19 Tassopoulos and Rosner19 examined the relationship between model input parameters and the simulated microstructure. Rezaei et al.17 extended the approach to account for particle size, viscosity, and surface tension. Although a ballistic deposition model seems to create realistic microstructures, predictions of the model have not been compared to measurements of microstructure. In this paper, we present quantitative measurements of ash deposit microstructure and compare the measurements to predictions of a ballistic deposition model. Measurements of microstructure were made on two deposits collected while firing a sub-bituminous coal in a pilot-scale combustor under different temperature conditions. A large number of microstructural parameters were determined by analyzing SEM images of the deposit cross section. A modified version of the ballistic deposition model by Tassopolous and Rosner19 was used to simulate the deposit microstructure. The inputs for the simulations were determined using information on coal quality and combustion conditions. 2. Methods Ash deposits were generated by firing a western subbituminous coal in the multi-fuel combustor (MFC) at Sandia National Laboratories. The MFC is a pilot-scale, 4.2-m-high, down-fired, turbulent-flow reactor that simulates gas temperature and composition histories experienced by particles in commercial combustion systems.20 The conditions of the experiment are designed to simulate ash deposition onto a heat exchanger tube in a full-scale boiler.21 The deposits were collected on a 17-mm-diameter stainless-steel tube placed across the flow at the MFC exit. Air cooling was used to maintain a constant deposition probe surface temperature of 500 °C. Large deposits are formed on the upstream face of the probe, with a relatively thin layer of material extending around to the downstream side of the probe. Two deposits were collected at different furnace wall temperatures. One deposit was collected using a furnace wall temperature of 1300 °C, which creates gas temperatures of 850-900 °C near the deposition probe. A second deposit was collected using a furnace wall temperature of 900 °C, which creates gas temperatures of 700-750 °C near the deposition probe. We refer to the two deposits as the high-temperature deposit and low-temperature deposit, respectively. More details on these experiments can be found in the literature.21,22 Deposits were collected for 3 h at a constant firing rate of ∼2 kg/h. The combination of the short duration and the temperature conditions means that insufficient time is available for extensive sintering to occur. Therefore, the microstructure of these deposits should be representative of the initial structure ash deposits formed in different regions of the convective pass of utility boilers. The high-temperature deposit is characteristic of deposits formed in the superheater section of the boiler, whereas the low-temperature deposit is representative of deposits found in the boiler backpass. (17) Rezaei, H. R.; Gupta, R. P.; Wall, T. F.; Miyamae, S.; Makino, K. In Impacts of Mineral Impurities in Solid Fuel Combustion; Gupta, R., Wall, T., Baxter, L., Eds.; Kluwer Academic Publishers/Plenum Publishers: New York, 1999. (18) Tassopoulos, M.; O’Brien, J. A.; Rosner, D. E. AIChE J. 1989, 35, 967-980. (19) Tassopoulos, M.; Rosner, D. E. AIChE J. 1992, 38, 15-25. (20) Baxter, L. L. Combust. Flame 1992, 90, 174-184. (21) Richards, G. R.; Harb, J. N.; Baxter, L. L. In Applications of Advanced Technology to Ash-Related Problems in Boilers; Baxter, L. L., Desollar, R., Eds.; Plenum Press: New York, 1996. (22) Richards, G. H. Ph.D. Thesis. Brigham Young University, Provo, UT, 1994.

Kweon et al. After the deposit specimens were collected, each was impregnated with epoxy, sectioned perpendicular to the axis of the tube, and polished. An SEM was used to collect backscattered electron images of the sectioned deposit at a resolution of 1.34 µm per pixel. A set of slightly overlapping images was taken to cover the entire deposit cross section; these images were then montaged to create one image of the entire deposit cross section (see Figure 1). This procedure was performed on one cross section of each deposit. In this paper, we focus on the microstructure of the large mass of the deposit collected on the upstream face of the probe. Figure 1 shows the montaged SEM image of this region of the high-temperature deposit. The two deposits had approximately the same width, which was determined by the tube diameter, but different heights. Initially, measurements were performed both parallel and perpendicular to the probe surface to examine the spatial variability of the deposit microstructure. However, no significant spatial variation in deposit properties was observed parallel to the probe surface. Therefore, structural parameters are averaged across the entire deposit width and reported only as a function of the normalized deposit height (see Figure 1). To compare the structure of the two deposits, we normalized the vertical location of a measurement by the total height of the deposit. The heights of the high- and low-temperature deposits were 13.0 and 4.3 mm, respectively. The spatial resolution of the measurements as a function of deposit height was determined on the basis of uncertainty analysis.23,24 To achieve relative uncertainties in the measured parameters of ∼10%, the high-temperature deposit was divided into four equally sized layers (see Figure 1) and the lowtemperature deposit was divided into three equally sized layers. 2.1. Measurement of Ash Deposit Microstructure. Image analysis procedures were applied to the montaged SEM images to determine a set of microstructural parameters. The procedures are largely based on previous work of Ramer and Martello.10 Several steps were performed to prepare the deposits for analysis. The sequence of steps is illustrated in Figure 2. Figure 2a shows a raw unprocessed region of the SEM image. The first step is the creation of a binary image to define solid and void spaces (Figure 2b); the pore space within the particles is then filled (Figure 2c), and, finally, the particles are split for calculation of the particle size distribution (Figure 2d). Each of these steps is discussed in detail below. The first step in the analysis procedure is to differentiate solid and void spaces by reducing the original 8-bit gray scale image to a binary image. Figure 2a shows the raw SEM image of a small region of the deposit cross section. The luminance values of the pixels span from 0 (black) to 255 (white) with the darker pixels corresponding to void space and the lighter pixels corresponding to particles. A threshold within this range must be defined to differentiate between solid and void space. This threshold was defined using the histogram minimization method.25 This method is applied using a luminance histogram, such as that shown in Figure 3. A threshold between the solid and void space is defined using a third-order polynomial fit between the first and second peak of the luminance histogram. The minimum value of the polynomial is used to locate the threshold. The area to the left of the threshold represents the void space, and the area to the right accounts for the particles. This approach was used to determine a threshold value for each SEM image. (23) Goldstein, J. I.; Newbury, D. E.; Echlin, P.; Joy, D. C.; Roming, A. D.; Lyman, C. E.; Fiori, C.; Lifshin, E. Scanning Electron Microscopy and X-ray Microanalysis: A Text for Biologists, Material Scientists, and Geologists, 2nd ed.; Plenum Press: New York, 1992. (24) Taylor, J. R. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, 2nd ed.; University Science Books: Sausalito, CA, 1997. (25) Russ, J. C. Computer-Assisted Microscopy. The Measurement and Analysis of Images; Plenum Press: New York, 1990.

Ash Deposit Microstructure

Energy & Fuels, Vol. 17, No. 5, 2003 1313

Figure 1. Montaged image of the entire cross section of the high-temperature deposit collected on the upstream surface of the deposition probe. The deposit was divided into the four regions indicated by the white rectangles to examine the variation of the structural parameters with deposit height. Certain regions of an ash deposit consist of highly porous particles. Most particles contain limited internal pore space; however, at the extreme, a particle can be a cenosphere. Treatment of the internal pore spaces is dependent on the precise definition of particle and void used for the analysis. The structure of an ash deposit can be viewed on several different levels of increasing complexity, as shown in Figure 4. At the simplest level, a deposit consists of solid particles and void spaces between particles. A more complex view accounts for internal structure within the particles by dividing the particles into solid and pore space. Finally, the solid can be differentiated into its component chemical species. In this study, ash deposit structure is considered at the highest level, differentiating between particles and void spaces. Therefore, particles are defined as a homogeneous solid material, and all the pores within the particles are filled. The filled pore area was 2% of the total solid area in the low-temperature deposit and 0.8% in the high-temperature deposit. For calculation of the particle size distribution and particle number density of the deposit, clustered particles were cut apart into individual particles as illustrated in Figure 2d. This splitting was manually performed and was based on the geometry and the different phases within a cluster. 2.1.1. Particle Volume Fraction. The particle volume fraction, or solid fraction, is the fraction of the deposit occupied by the solid phase. For a random material, the solid fraction is equal to the area fraction in a planar section:26

φ)

As AT

(1)

where As is the area sum of the solid phase on the planar (26) Weibel, E. R. Stereological Methods; Academic Press: New York, 1980.

section and AT is the total area of the planar section. The fraction of deposit volume that is occupied by the void phase (the porosity) is simply 1 - φ. 2.1.2. Particle Number Density. Particle number density is defined as the number of particles per unit deposit volume. It can be determined from the particle number density on the section and volume fraction measurements:26

Np )

( )

1.5 1 Ns λ φ0.5

(2)

where Ns is the total number of the sectioned particles per unit section area and λ is the shape coefficient, which has a value of 1.38 for spherical particles. For calculation of Np, clustered particles were cut apart into individual particles, as illustrated in Figure 2d. 2.1.3. Particle Size Distribution. The three-dimensional size distribution of ash particles in the deposit is determined from the two-dimensional profiles of the sectioned particles, assuming that the ash particles are spherical. The profile size is expressed as an area-equivalent diameter. Measured size profiles are divided into 15 equally sized bins and then the method of Saltykov26 is used to convert the two-dimensional profile distribution to a three-dimensional size distribution:

np(j) )

1 ∆

15

∑ R n (i) ij s

(3)

i)j

where np(j) is the particle number density in the jth size bin, ns(i) is the number of the sectioned particles per unit section area in the ith size class, ∆ is the uniform interval of a size class (15 µm), and Rij is the element of the Saltykov coefficient. 2.1.4. Particle Specific Surface Area. The specific surface area is the surface area of the particles per unit volume of deposit. This parameter describes the fineness of the deposit


Kweon et al.

Figure 2. Sequence of steps used to prepare the SEM images for quantitative analysis, as illustrated using a small region of a deposit cross section: (a) raw SEM image, (b) binary image, (c) pores that have been filled within the particles, and (d) particles that have been split for analysis of particle size distribution. Dark regions correspond to the void space and light regions correspond to the solid phase.

Figure 3. Luminance histogram used for determination of the threshold between the solid and void spaces. Dashed line is a third-order polynomial fit whose minimum value defines the threshold. and has a dominant effect on its optical properties, such as reflectivity. The specific surface area, S, can be calculated as26

S)

4B π φ

()

(4)

where B is the total boundary length between the solid and void phases in the section plane. Note that the specific

surface area is not equivalent to the total particle perimeter because B does not include the boundaries between particles. 2.1.5. Particle Contiguity. The contiguity is the average fraction of area that a particle shares with its neighbors.26 The contiguity measures particle interconnectedness and, therefore, provides insight into particle sintering, which is an



Figure 4. Hierarchal framework of the ash deposit microstructure. In this paper, the ash deposit structure is characterized at the simplest level, differentiating between particles and void spaces. important mechanism of strength development in ash deposits. It can be expressed as

C)

Sp Sp + S

(5)

where Sp is the particle contact area per unit volume of deposit, which is determined from the length of lines that are drawn to separate the particles (see Figure 2d). 2.1.6. Solid Mean Chord Length and Void Mean Free Path Length. The mean chord and mean free path lengths are characteristic dimensions of the solid and void regions within the deposit. The solid is a continuous network of particles that provides the framework for the deposit. Interpenetrating this framework is a second continuous network of empty space. A random line that is passed through the deposit intersects the solid and void structures in chords and free paths, respectively. The mean chord length and mean free path are averages of these line segments. Both quantities are three-dimensional attributes that have been determined from measurements made in the plane of the section. The mean chord length of the solid phase is26

Ls ) 4

(Sφ)

(6)

and the mean path length of the void space is

Lv ) 4

(1 -S φ)

(7)

2.1.7. Particle Density-Density Correlation Function. The density-density correlation function describes the average variation in the density of a material. This parameter can be used to evaluate whether the material is homogeneous or heterogeneous, whether the structure is periodic or random, and whether the structure has a preferred orientation.12,27 The normalized density-density correlation is defined as28

γ(r) )

Γ(r) - φ2 φ - φ2

(8)

where Γ(r) is the two-point probability function, which is evaluated using the two-dimensional fast Fourier transform (FFT),28

Γ(r) ) FFT-1(|FFT(ROI)|2)

(9)

(27) Lange, D. A.; Jennings, H. M.; Shah, S. P. Cem. Concr. Res. 1994, 24, 841-853.

where ROI is the region of interest. An ROI of 1024 × 1024 pixels was used for the low-temperature deposit and an ROI of 2048 × 2048 pixels was used for the high-temperature deposit. 2.2. Model for Ash Deposit Microstructure. A ballistic deposition model was used to simulate the microstructure of the two deposits. This approach has previously been used to simulate ash deposits.17-19 A ballistic deposition model uses a simple set of rules to create complex three-dimensional microstructures. We use the ballistic deposition model of Tassopoulos and Rosner,19 with minor modifications to vary the degree of particle swelling within the deposit and to control particle rolling with a probability distribution function. Briefly, particles are dropped from random positions above a target surface (heat-transfer surface) and are assumed to travel in straight lines normal to the target. The particles are hard spheres with a polydisperse size distribution. It is assumed that particles in the deposit cannot be displaced by subsequent particle arrivals. A particle that hits the target surface sticks immediately. If a particle hits another particle, as is likely after the initial layer of the deposit has accumulated, it can roll in the direction of steepest descent. The rolling motion is continued until contact is established with another particle, in which case it can continue to move toward the target while maintaining contact with both fixed particles. Each new contact between the rolling particle and another fixed particle is considered to be a new rolling event. Rolling is continued until a specified number of rolling events are completed, the particle reaches a position of local minimum potential energy, or the original target surface is reached. At rest, point contacts exist between particles and their adjacent neighbors. To increase the contact area between particles, the size of the particles is increased; this process is called swelling. The deposition model requires three inputs: (1) particle size distribution, (2) the number of rolling events per particle, and (3) particle swelling. To simulate the two experimental deposits, these inputs were determined using a combination of parameterizations based on MFC combustion conditions and coal quality, and data from the microstructure measurements. Sensitivity analysis of the model predictions to the input parameters is examined below. The size distribution of the impacting particles was determined using an inertial impaction model:29

ni(dp) ) η(dp)nfa(dp)

(10)

where nfa(dp) is the fly ash size distribution and η(dp) is the fly ash capture efficiency (the probability that a fly ash particle will collide and stick to the deposit). Richards22 reported measurements of the fly ash size distribution for these experiments (see Figure 5); a log-normal distribution was fit to these data. We assume that fly ash deposition is dominated by inertial impaction and use the expression from Israel and Rosner30 to predict the particle capture efficiency as a function of particle size. The expression of Israel and Rosner30 predicts when particles will impact the deposit via inertial impaction; it does not account for the probability that the impacting particle will actually stick. Particle sticking is governed by many complex factors;31,32 for simplicity, we assume that all particles that strike the deposit contribute to the deposit. Upon impact, particles may roll to their final location, as discussed below. The calculations do not account for particles shedding (28) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing; Cambridge University Press: Cambridge, England, 1992. (29) Baxter, L. L.; DeSollar, R. W. Fuel 1993, 72, 1411-1418. (30) Israel, R.; Rosner, D. E. Aerosol Sci. Technol. 1983, 2, 45-51. (31) Walsh, P. M.; Sayre, A. N.; Loehden, D. O.; Monroe, L. S.; Beer, J. M.; Sarofim, A. F. Prog. Energy Combust. Sci. 1990, 16, 327-346. (32) Richards, G. H.; Slater, P. N.; Harb, J. N. Energy Fuels 1993, 7, 774-781.


Kweon et al. Table 1. Fly Ash Composition of Sub-bituminous Coala

a

species

content (wt%)

SiO2 Al2O3 Fe2O3 TiO2 CaO MgO Na2O K2O P2O5 SO3 C

27.4 16.3 10.5 0.9 33.9 6.5 2.4 0.8 1.6 4.1 2.1

From Richards.22

Figure 5. Measured fly ash size distribution and predicted deposit particle size distribution calculated using eq 10. Measured fly ash size distribution from Richards.22 or eroding after the initial impaction on the pile of the ash particles. We use an average particle density of 2 g/cm3 and a mean particle velocity of 5 m/s to calculate the particle Stokes number. Figure 5 shows the predicted size distribution of the impacting particles calculated using eq 10 and the measured fly ash size distribution for the high-temperature case. The predictions of the low- and high-temperature cases are essentially identical. The predicted size distribution of the impacting particles spans a range of 9-100 µm. The capture efficiency of particles with a diameter µcr)

(for µ e µcr)

(11a) (11b)

where µ(Tp) is the particle viscosity as a function of the particle temperature Tp, and µcr is the critical viscosity at which the ash particles are perfectly sticky. The particle viscosity is evaluated using the PSI model,34 which parametrizes the particle viscosity as a function of Tp and composition. The composition of the fly ash is shown in Table 1.22 An energy balance that accounts for the fly ash composition and convective and radiative heat transfer is used to estimate the particle temperature. A critical viscosity of 750 P (Poise) was used to calculate the rolling probability. This value was chosen to provide reasonable agreement with the measured microstructure. A wide range of critical viscosities (103-108 P) have been used by previous work.31-34 The value used here is at the lower end of this range, which is consistent with our slightly dif(33) Srinivasachar, S.; Helble, J. J.; Boni, A. A. Twenty-Third Symposium (International) on Combustion; The Combustion Institute; Pittsburgh, 1990; pp 1305-1312. (34) Senior, C. L.; Srinivasachar, S. Energy Fuels 1995, 9, 277283.

Figure 6. Particle rolling probability (Proll) as a function of particle temperature calculated using eq 11 and the fly ash properties listed in Table 1. Open circles indicate the rolling probability of the two experimental conditions considered here. ferent definition of critical viscosity. The critical viscosity used in eq 11 is the viscosity at which the particles will impact the deposit and not roll; previous work has used the critical viscosity to indicate the viscosity at which the impacting particle will stick to the deposit (but potentially roll). The requirement that particles both stick and not roll is more stringent than only requiring the particles to stick and, therefore, will require a lower value of the critical viscosity. Figure 6 shows the change in rolling probability as a function of Tp, calculated using eq 11. The particle rolling probability Proll decreases as Tp increases (the particles become stickier); the particles are perfectly sticky (no rolling) at a temperature of 1525 K, at which point the particle viscosity corresponds to the critical viscosity (750 P). For the conditions of the low- and high-temperature experiments, eq 11 predicts that 92% and 20% of the particles roll once, respectively. Initially, point contacts exist between the particles. The deposition model then uses a parameter called particle swelling to increase the interconnectedness of the particles. We have defined the amount of particle swelling to match the measurement of deposit contiguity. To account for the effects of swelling on the deposit particle size distribution, the size distribution of the impacting particles is shrunk so that after swelling the final size distribution of the particles matches that which is calculated using eq 10. The microstructure of the simulated deposits was determined by cross-sectioning the simulated deposit parallel to the direction of deposition. The same image analysis procedures as those applied to the actual deposit cross sections were then performed to determine the microstructure of the simulated deposits.



Figure 7. Images of deposit cross sections. Panels a and b are SEM images of the high- and low-temperature deposits, respectively. Panels c-f are images of the simulated microstructure for the high- and low-temperature conditions. The images shown in panels c and d use the predicted deposit particle size distribution (eq 10, Figure 5) as a model input. The images shown in panels e and f use the deposit particle size distribution measured from the SEM images as a model input. The left- and right-hand columns of images correspond to the high- and low-temperature experiments, respectively.

3. Results and Discussion This section first presents results from the quantitative analysis of the microstructure of the two ash deposits. Predictions of the ballistic deposition model are then compared to the measurements. Finally, results from both the measurements and the calculations are used to discuss the effects of temperature on deposit microstructure. 3.1. Measurements of Ash Deposit Structure. Panels a and b in Figure 7 show SEM images of an approximately 1 mm × 1 mm region of each crosssectioned deposit. The direction of the bulk gas flow and

the trajectories of the incoming particles are from top to bottom in the images. Although the solid regions seem to be isolated in the two-dimensional cross section, the solid phase forms a continuous structure in three dimensions. The particles that seem to be isolated are connected on a plane that is not resolved by the twodimensional image. To illustrate the complex threedimensional structure of an ash deposit, two images of a simulated deposit are shown in Figure 8. Figure 8a is a two-dimensional cross section of the simulated microstructure that contains apparently isolated particles and isolated clusters of particles. A three-dimensional pro-


Figure 8. Simulated microstructure of (a) a two-dimensional cross section and (b) a three-dimensional perspective of the high-temperature deposit illustrating the complex threedimensional ash deposit microstructure.

jection of the same simulated microstructure (Figure 8b) reveals the complicated three-dimensional connections between these particles and clusters. Significant qualitative differences between the two deposit microstructures can clearly be observed in the SEM images of the two deposits. For example, the hightemperature deposit (Figure 7a) seems to have larger void space and fewer particles, whereas the low-temperature deposit has more densely packed particles (Figure 7b). The results from the microstructure analysis quantify these and other differences in the deposit structures. Figure 9a plots the deposit solid fraction as a function of the normalized distance from the tube surface. Both deposits are relatively porous, with solid fractions of ∼0.25-0.3. The error bars in the figure indicate an estimated relative uncertainty of 13%-18% at the 95% confidence level. Given these uncertainties, the solid fractions of the two deposits are not significantly different, and both deposits have comparable mass densities. There is no spatial gradient of the solid fraction within either deposit. The comparable mass densities of the two deposits in combination with the significant differences in deposit heights (13 mm for the hightemperature deposit versus 4.3 mm for the low-temperature deposit) indicate a much higher deposition rate for the high-temperature experiment (the firing rate and duration of both experiments was the same).

Kweon et al.

Figure 9b presents the particle number density as a function of the normalized distance from the tube surface. The particle number density of the low-temperature deposit is greater than that of the hightemperature deposit. The solid fractions of both deposits are the same (Figure 9a); therefore, the difference in particle number density is due to differences in the particle size distribution within both deposits. Figure 10 compares the measured size distributions of the particles of the high- and low-temperature deposits on both a number and volume basis. The lowtemperature deposit contains a larger fraction of small particles than the high-temperature deposit (Figure 10a). On a volume basis, this difference is not very significant, because the volume size distribution is dominated by larger particles. The measured size distributions are somewhat more uncertain than other measurements because of the required local image adjustments, such as the splitting of the clustered particles and the filling of the holes inside the particles. Measurements of particle specific surface area are shown in Figure 9c. The results indicate that the lowtemperature deposit has a much larger specific surface area than the high-temperature deposit, which is consistent with the smaller particle size distribution of the low-temperature deposit and with the larger clustering of particles in the high-temperature deposit. Note that this measurement is independent of the particle number density and is not based on the identification and measurement of individual particles. Particle contiguity is a measure of the interparticle contact area per unit volume of deposit. Large differences in the contiguity of the two deposits are shown in Figure 9d. The contiguity of the low-temperature deposit is

Measurement and Simulation of Ash Deposit Microstructure

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