Simulation of Coal Ash Particle Deposition Experiments - Energy

The kinetic theory has been used to compute Cu.(8) ... temperature-controlled particle impact probe oriented at a 30° angle to the atmospheric pressu...
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Energy Fuels 2011, 25, 708–718 Published on Web 01/20/2011

: DOI:10.1021/ef101294f

Simulation of Coal Ash Particle Deposition Experiments† Weiguo Ai‡,§ and John M. Kuhlman*,‡,§ ‡

National Energy Technology Laboratory, Morgantown, West Virginia 26507-0880, United States, and § Mechanical and Aerospace Engineering Department, West Virginia University, Morgantown, West Virginia 26506-6106, United States Received September 24, 2010. Revised Manuscript Received January 3, 2011

Existing experimental ash particle deposition measurements from the literature have been simulated using the computational fluid dynamics (CFD) discrete phase model (DPM) Lagrangian particle tracking method and an existing ash particle deposition model based on the Johnson-Kendall-Roberts (JKR) theory, in the Fluent commercial CFD code. The experimental heating tube was developed to simulate ash temperature histories in a gasifier; ash-heating temperatures ranged from 1873 to 1573 K, spanning the ash-melting temperature. The present simulations used the realizable k-ε turbulence model to compute the gas flow field and the heat transfer to a cooled steel particle impact probe and DPM particle tracking for the particle trajectories and temperatures. A user-defined function (UDF) was developed to describe particle sticking/ rebounding and particle detachment on the impinged wall surface. Expressions for the ash particle Young’s modulus in the model, E, versus the particle temperature and diameter were developed by fitting to the E values that were required to match the experimental ash sticking efficiencies from several particle size cuts and ash-heating temperatures for a Japanese bituminous coal. A UDF that implemented the developed stiffness parameter equations was then used to predict the particle sticking efficiency, impact efficiency, and capture efficiency for the entire ash-heating temperature range. Frequency histogram comparisons of adhesion and rebound behavior by particle size between model and experiments showed good agreement for each of the four ash-heating temperatures. However, to apply the present particle deposition model to other coals, a similar validation process would be necessary to develop the effective Young’s modulus versus the particle diameter and temperature correlation for each new coal.

current particle deposition wall boundary condition, along with the ash chemical and physical characteristics, will be specified to determine ash particle acceptance or rejection and their subsequent trajectories. The probability of a particle sticking to a surface depends upon several parameters, including particle size, composition, and temperature, target material properties, particle impact velocity and angle of incidence, and gas and surface temperatures. The most common sticking forces (Figure 1) are the van der Waals force, electrostatic force, and liquid bridge force. The liquid bridge force is important under wet surface (slagging) conditions, while for dry surfaces, the van der Waals force generally dominates the sticking process. Other forces can include electrostatic or thermophoretic effects. A number of particle deposition models have been developed for dry particle deposition1,2 and particle deposition under slagging conditions.3-5 In the present work, the dry particle deposition model previously implemented by Ai6 has been evaluated

1. Introduction Inorganic component partitioning, mineral transformations, fly ash size evolution at temperature and pressure, particle fragmentation, and conversion in gasification all influence the propensity for slagging and fly ash formation. The development of a computer model to predict the effects of the particle size and density partitioning on slagging is an essential tool that will enable one evaluation of potential modifications to mineral preparation procedures for the mitigation of slagging and fouling and improvement of gasifier availability. The goal of the present work is the initial development and evaluation of a computer model describing coal mineral deposition behavior in an entrained gasifier for incorporation into a computational fluid dynamics (CFD) gasification model to determine the impact of slagging and fly ash formation for coal gasification. Ash particles are categorized by coal size and density fractions as one of the inputs to CFD modeling. The † Disclaimer: Neither the United States Government nor any agency thereof, nor any of their employees, nor URS Energy and Construction, Inc., nor any of their employees, makes any warranty, expressed or implied, assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe upon privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. *To whom correspondence should be addressed. Telephone: 304-2933180. Fax: 304-293-6689. E-mail: [email protected].

r 2011 American Chemical Society

(1) Johnson, K. L.; Kendall, K.; Roberts, A. D. Surface energy and the contact of elastic solids. Proc. R. Soc. London, Ser. A 1971, 324, 301– 313. (2) Brach, R.; Dunn, P. A mathematical model of the impact and adhesion of microspheres. Aerosol Sci. Technol. 1992, 16, 51–64. (3) Urbain, G.; Cambier, F.; Deletter, M.; Anseau, M. R. Viscosity of silicate melts. Trans. J. Br. Ceram. Soc. 1981, 80, 139–141. (4) Kalmanovitch, D. P.; Frank, M. An effective model of viscosity for ash deposition phenomena. Proceedings of the Engineering Foundation Conference on Mineral Matter and Ash Deposition from Coal; United Engineering Trustees, Inc., Santa Barbara, CA, 1988. (5) Browning, G. J.; Bryant, G. W.; Hurst, H. J.; Lucas, J. A.; Wall, T. F. An empirical method for the prediction of coal ash slag viscosity. Energy Fuels 2003, 17, 731–737.

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kinematic restitution coefficient, defined as the ratio of rebound/approach deformation impulses.2 Note that, as either R or Young’s moduli become small, the critical velocity increases, resulting in a predicted increase in particle adhesion. Here, a fixed value of R = 0.9 for low velocity normal impacts has been used.2 The above model was developed by Brach and Dunn2 based on the Johnson-Kendall-Roberts (JKR) theory of ref 1. The particle normal impact velocity is compared to the particle critical velocity from eq 2, and if the particle normal impact velocity is smaller than the critical velocity, the particle sticks to the surface. Otherwise, the particle rebounds with a velocity computed from a restitution coefficient and continues the trajectory until it leaves the domain or impacts the surface at another location. Note that this method was originally developed as a model for particle deposition to a dry surface1,2 based on effects of the van der Waals force. In the present work, K has been determined on the basis of empirical Es and Ep values that have been curve-fit versus the particle diameter and impact temperature. The critical moment theory has been applied by Soltani and Ahmadi8 in the detachment process. Particles that are predicted to adhere to the surface based on eq 2 will be removed from the surface if the turbulent flow has a local wall friction velocity, vw, which is larger than uτc, which is given by !1=3 Cu WA WA 2 uτc ¼ ð6Þ Fdp dp E

Figure 1. Schematic of forces acting on a particle impacting a surface.

against experimental data by Ichikawa et al.7 for the deposition of coal ash onto a test probe that was maintained at a temperature that was below the ash fusion temperature. The Ai deposition model6 uses the deposition model that was originally developed by Brach and Dunn2 for dry particle deposition that includes the effects of the van der Waals force to predict a critical particle impact velocity, below which the particle is assumed to stick to the impact surface. 2. Summary of the Present Particle Deposition Model The sticking force, Fs, in the present macroscopic approach1,6,8 is given by Fs ¼ ð3π=4ÞWA dp

ð1Þ

where WA, called the adhesion work, depends upon particle and surface material properties. Herein, a constant value of WA = 0.039 J/m2 has been used, from Soltani and Ahmadi,8 for silcon particle impacts onto a silicon surface. On the basis of work by Brach and Dunn,2 the critical velocity below which a particle will stick to the surface is given by " #10=7 2K ð2Þ Vcr ¼ dp R2

where uτc is the critical wall shear velocity, Cu is the Cunningham correction factor, F is the gas density, and E is composite Young’s modulus. The wall friction velocity is defined as pffiffiffiffiffiffiffiffiffiffi ð7Þ vw ¼ τω =F where τw is the wall shear stress, τw = μ(du/dy)yw. The kinetic theory has been used to compute Cu.8 3. Validation Model Setup

where K, an effective stiffness parameter, is computed from " #2=5 5π2 ðks þ kp Þ K ¼ 0:51 ð3Þ 4Fp 3=2

3.1. Geometry and Boundary Conditions. Ichikawa et al.7 measured deposition behavior for ash particles from ashing tests for a series of five coals, using a nominally 1 m tall  60 mm diameter ash-heating tube that was fitted with a cooled, temperature-controlled particle impact probe oriented at a 30° angle to the atmospheric pressure air flow. Individual particle diameters, velocities, and temperatures were recorded just prior to particle impact using a high-speed video camera and a two-color optical pyrometer. Particle diameters were determined by pixel counting, while particle velocities were determined by particle tracking. They determined that the overall particle deposition correlated well with the ash liquid fraction for all five coal ash compositions, where the ash liquid fraction was determined from a combination of mechanical and thermal measurements [thermomechanical analysis (TMA) and differential thermal analysis (DTA)]. For one coal ash (TJ coal), they presented details of particle deposition and rebound behavior for 14 individual particle size cuts from 38 to 356 μm. It is this detailed data set for the TJ coal ash that has been simulated in the present study. This TJ coal is a Japanese bituminous coal. There are, however, three details about experimental conditions that were lacking in ref 7 that had to be approximated in the present simulations. First, the particle size distribution of the ash after injection into the heating tube was not specified in the reference. Also, the air mass flow rate was not specified; instead, the air velocity in the ash-heating tube above the particle impact probe was listed as “approximately 1 m/s”. Also, the precise location of

with ks ¼

1 - νs 2 πEs

ð4Þ

kp ¼

1 - νp 2 πEp

ð5Þ

where Vcr is the particle critical velocity, Es and Ep are Young’s moduli of the surface and particle, respectively, vs and vp are Poisson’s ratios of the surface and particle, respectively, dp is the particle diameter, Fp is the particle density, and R is the (6) Ai, W. G. Deposition of particulate from coal-derived syngas on gas turbine blades near film cooling holes. Ph.D. Dissertation, Chemical Engineering Department, Brigham Young University, Provo, UT, 2009. (7) Ichikawa, K.; Oki, Y.; Inumaru, J. Study on the mechanism of the coal ash deposit and the growth in the gasifier;Analysis of ash particles sticking tendencies on a particle by particle basis. Proceedings of the Effects of Coal Quality on Power Plant Performance: Ash Problems, Management and Solutions; Park City, UT, March, 2001; Paper 2000-4. (8) Soltani, M.; Ahmadi, G. On particle adhesion and removal mechanisms in turbulent flows. J. Adhes. Sci. Technol. 1994, 8, 763–785.

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Table 1. Summary of Boundary Conditions for the CFD Model setup conditions

case 1

case 2

case 3

case 4

first-third stage wall T (K) fourth stage wall T (K) probe surface T (K) turbulent intensity (%) hydraulic diameter (mm) density (kg/m3) thermal conductivity (W m-1 K-1)a dynamic viscosity (kg m-1 s-1)a

1873 1473 1273

1773 1473 1273

1673 1473 1273

1573 1473 1273

a

10 6 Fluent “incompressible ideal gas” model 2  10-10T3 - 6  10-7T2 þ 0.001116T - 0.020004 2  10-15T3 - 2  10-11T2 þ 5.48  10-8T - 3.2984  10-6

T = air temperature (K).

Figure 2. (a) Schematic of the 2D validation model and (b) 2D validation model boundary conditions for case 1 from Table 1.

a combustion zone. Note, however, that no combustion occurred in their experiments, because only ash particles were injected into their heating tube. The probe surface temperature was set at a constant 1273 K in the four cases. The outlet was set as a pressure outlet at an outlet backflow temperature of 300 K. The fluid model used was an incompressible ideal gas. The realizable k-ε turbulence model with standard wall functions was employed to calculate the gas flow field. The wall temperature and inlet turbulence intensity boundary conditions have been listed in Table 1. 3.2. Particle Size Distribution. The size distribution of the ash particles that impacted the 45 mm diameter impact surface or “probe” was measured by Ichikawa et al. and provided in ref 7. However, the overall ash particle size distribution of the injected ash was not specified in their paper. A measured ash particle size distribution obtained from the authors9 was inconsistent with the measured size distribution of the impacting particles, having an average diameter between 10 and 20 μm, a value that was smaller than any of the measured diameters of the impacting ash particles. This indicates that there was significant agglomeration

the particle impact probe along the centerline of the heating tube was not specified. All of these have had to be approximated as accurately as possible in the present work. To establish the variation of the effective stiffness parameter, K, versus the particle size and temperature, a two-dimensional (2D) geometry verification model and CFD mesh were developed on the basis of the Ichikawa et al.7 facility. Four experimental cases have been simulated using the developed CFD model for the TJ coal ash for conditions shown in Table 1, to verify the values of particle Young’s modulus versus the temperature and diameter that are required for the present particle deposition model. These simulations have been performed using FLUENT, version 13.1. A schematic of the experimental facility, and the applied wall boundary conditions for case 1 of the CFD model are presented in Figure 2. The CFD model geometry included 13 014 cells. The air inlet velocity was set to 4 m/s to achieve the gas velocity of approximately 1 m/s inside the tube just above the impingement surface that was specified by Ichikawa et al.7 The wall temperature of the first three stages from the top has been varied from 1873 to 1573 K in 100 K increments, as was performed in the experiments. The bottom stage wall temperature was fixed at 1473 K; this region is to represent a gasification region, while the upper region represents

(9) Ichikawa, K. Personal communication. Central Research Institute of Electric Power Industry (CRIEPI), Kenagawa-ken, Japan, 2009.

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7

Ichikawa et al. Ichikawa et al. did not specify the injected air flow rate but, instead, stated that the average gas velocity above the impact probe was approximately 1 m/s; the assumed inlet gas velocity of 4 m/s resulted in a computed average gas velocity in the simulations that is very close to the specified velocity of 1 m/s. Particle trajectories and temperatures and velocities at impact were modeled using the Fluent discrete phase model (DPM), on a particle-by-particle basis in the stochastic randomwalk model. This Lagrangian particle tracking model assumes that particles do not interact or collide with one another and the particle volume is ignored. The Runge-Kutta method was used to integrate the particle trajectories. For each of the four ash-heating temperatures, the simulation starts with continuous-phase computation iteration until the gas flow field has converged. After this, the discrete ash particles are then injected in a post-processing step and the current particle deposition model is used to predict whether or not each of the impacting particles adhere to the impact probe surface (Because the particles herein consist entirely of ash, no chemistry has been implemented in the simulations and no mass transfer occurs). The SIMPLE algorithm was used to couple the pressure and velocity in the continuous phase. The discretization of the convection terms in the energy-governing equation, momentum equations, and k-ε equations was performed using the firstorder upwind scheme. Convergence of the flow field was determined by reduction in the residuals by the following orders of magnitude for the listed quantities: 10-5 for continuity, 10-6 for velocity, 10-7 for energy, and 10-6 for turbulence.

of the ash either prior to or after the injection of the particles into the heating tube. Because it was known that the average impacting ash particle diameter had to be somewhat larger than the average diameter of the injected ash (i.e., smaller particles were less likely to strike the impact probe), then in the present simulations, it has been assumed that the injected coal ash had the profile illustrated in Figure 3; this profile was obtained from the data obtained from Ichikawa but was rescaled to an average particle diameter of 100 μm. The particle size distribution in the computational model has been modeled using a Rosin-Rammler distribution to match the assumed distribution of the impacting particles from the experiment7 (Figure 3). The mean diameter has been assumed to be 100 μm, with a spread parameter, n, of 1.76. The density of ash particles has been set to a constant value of 990 kg/m3; this is a bulk density, which, because of agglomeration, is lower than the individual particle density of 1980 kg/ m3. Table 2 shows other assumed physical properties of the ash particles. A total of 5000 particle tracks with a size distribution matching that shown in Figure 3 were injected from the center of the top inlet surface at the velocity of 0.1 m/s. The total ash particle injection rate was set to 300 mg/min, to match the value given by

4. Validation Model Results and Discussion The flow field mean velocity results for ash-heating temperatures of 1873, 1773, 1673, and 1573 K are shown in Figure 4. As can be seen, velocity gradients are large near the inlet because of the abrupt increase of the flow cross-sectional area at the tube inlet. Also, there are significant velocity variations in the wake downstream of the probe. The flow field has become relatively uniform with a velocity magnitude close to 1 m/s in the region above the probe, consistent with the value given by Ichikawa et al. Variation of the velocity profile in the tube with the ash-heating/wall temperature is not apparent in the four cases. The temperature contours shown in Figure 5 show that the air temperature in much of the top three heating stages is very close to the specified wall temperature (called the “ash-heating

Figure 3. Assumed cumulative size distribution of particles. Table 2. Assumed Ash Particle Properties Cp k T maximum minimum mean F d (μm) d (μm) d (μm) (kg/m3) (J kg-1 K-1) (W m-1 K-1) (K) 355

27

100

990

984

0.5

800

Figure 4. Air velocity magnitude contour (m/s) at an ash-heating temperature of (a) 1873 K, (b) 1773 K, (c) 1673 K, and (d) 1573 K.

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Figure 5. Air temperature contours at an ash-heating temperature of (a) 1873 K, (b) 1773 K, (c) 1673 K, and (d) 1573 K. Table 3. TJ Coal Ash Composition oxide

SiO2

Al2O3

Fe2O3

CaO

TiO2

MgO

SO3

P2O5

Na2O

K2O

percentage (%)

48.82

22.47

5.15

8.03

0.94

1.71

2.9

0.59

1.14

1.12

Figure 6. Particle Young’s modulus versus the temperature (in K).

temperature” by Ichikawa et al.) in the top three stages and varies from 1873 to 1573 K. Large temperature gradients are observed in the region near the probe because of the much lower temperature setting of its front surface compared to the tube wall, which then leads to the ash particles cooling significantly as they approach the probe surface. Once the CFD flow field calculation had been converged, the particles were then injected into the computed flow field in a post-processing step, to perform the particle deposition calculations. As ash particles arrived at the probe surface, a userdefined function (UDF) that was developed to enforce the specified particle deposition boundary condition on the front probe surface was called to record the mass of particles that impacted the surface, particle temperature, and velocity at impact and also the mass that was predicted to stick to the test probe. Any of the ash particles that impacted the back side of the probe surface or the heating tube walls themselves were not tracked in the UDF; this is entirely consistent with the experimental procedures of Ichikawa et al.,7 where they recorded particle deposition only for the front surface of their deposition probe, using high-speed video imaging of each individual particle trajectory versus time. It was noted that the computed particle residence times were on the order of 1 s, consistent with the dimensions of the ash-heating tube and average air velocity. The predicted times for particles to

heat to the gas temperature were nominally 50 ms, while the corresponding cooling times for particles to cool to the impact probe temperature as they entered the thermal boundary layer above the impact probe were only slightly larger, on the order of 50-80 ms. To obtain the correlation of particle Young’s modulus with the particle temperature and diameter, the model was applied to the TJ coal ash7 at ash-heating temperatures between 1873 and 1573 K. The measured TJ coal ash composition reported by Ichikawa et al.7 is shown in Table 3. In the case with an ashheating temperature of 1873 K, different particle cuts falling within the experimental particle size range shown in Table 2 were each separately injected into the converged flow field and tracked. The critical velocities were calculated by a certain particle Young’s modulus value that was computed using the known ash particle temperature at the time of its impact with the surface. Wall material Young’s modulus was assumed to be equal to the particle value for each impact. The particles with normal velocities less than the critical capture velocity were assumed to stick to the surface. The sticking ratio was computed, defined as the ratio of the mass of the adhered particles to the total mass of particles impacting the probe. This process was iterated by adjusting the values of Ep until the sticking ratio predicted by the model was in agreement with the experimental results for each particle size cut (Figure 6 712

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of Ichikawa et al.). The dependence of Young’s modulus versus the particle impact temperature was then fit to three different exponential functions over three different particle size ranges, as shown in eq 8 and Figure 6. These curve fit equations for E were then used in eqs 2-5 to compute the particle critical impact velocity. Figure 7 shows the calculated overall sticking efficiency from the CFD model using eqs 2-8, as compared to the experimental data by Ichikawa et al. for their TJ coal. A good agreement is seen.

particle sticking behavior. At each ash-heating temperature, a total of 5000 particle streams were injected into the converged flow field. The particle size distribution was modeled using the Rosin-Rammler distribution as described above (Figure 3). Particle effective Young’s modulus curve fit equations obtained above were implemented in the post-processing UDF to calculate the critical velocity for each individual impinging particle. The impacting particle temperatures from the CFD model versus the particle diameter are shown for each of the four ash-heating temperatures in Figure 8. It is seen that the smaller impacting particles are cooler and have a more nearly uniform temperature upon impact, while the larger particles have a wide temperature distribution at impact, as much as a 300 K variation for the highest ash-heating temperature. The wide variations in particle impact temperatures are due to variations in the particle trajectories, as well as the stochastic nature of the turbulence. The model predicts that the particle temperature at impact decreases with a decreasing particle size because of the fact that small particles cool much more quickly as they approach the cooled probe surface; this is likely due to their much larger surface area/volume ratio. This trend is more pronounced for the higher ash-heating (i.e., maximum) temperatures. Ichikawa et al. reported data for the impacting TJ coal particle temperatures; these data have been compared to the current CFD simulation results, as follows. At an ashheating temperature of 1873 K, the experimental average temperature of the impacting particles was 1622 versus 1513 K for the CFD simulation. At the 1773 K ash-heating temperature, the experimental average temperature was 1499 K versus 1474 K for CFD. The average impacting ash temperature results for the other two ash-heating temperatures were 1418 K for the experiment versus 1416 K for the CFD simulation at Tash = 1673 K and 1348 K for the experiment versus 1378 K for CFD at Tash = 1573 K. These are judged to be in reasonable agreement. These average temperatures for the CFD simulations have been computed as mass weighted averages;

E ¼ 3  1081 expð- 0:1302TÞ, d < 110 μm E ¼ 9  1019 expð- 0:02255TÞ, 110 < d < 200 μm ð8Þ E ¼ 5  1013 expð- 0:01208TÞ, d > 200 μm For each of the CFD simulations shown in Figures 4 and 5 above for TJ coal ash at ash-heating temperatures varying between 1873 and 1573 K, the particle deposition model described above has also been used to predict the detailed

Figure 7. Calculated overall capture efficiencies from the 2D CFD model compared to the experiment.

Figure 8. Temperature of particles impacting the probe surface versus the particle size at ash-heating temperatures of (a) 1873 K, (b) 1773 K, (c) 1673 K, and (d) 1573 K.

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Figure 9. Particle critical velocity and normal impact velocity versus the particle size at ash-heating temperatures of (a) 1873 K, (b) 1773 K, (c) 1673 K, and (d) 1573 K.

Figure 10. CFD calculations of impact efficiency, sticking efficiency, and capture efficiency versus the particle size at ash-heating temperatures of (a) 1873 K, (b) 1773 K, (c) 1673 K, and (d) 1573 K.

Niksa et al.10 developed optical instrumentation similar to that used by Ichikawa and reported an accuracy for their carbon particle temperature measurements within (50 K; therefore, some disagreement is to be expected. Figure 9 compares the normal velocity at impact from the CFD simulations for each impacting particle with the corresponding computed critical velocity using the impact temperature for each particle (Figure 8) from the Fluent simulation in the present particle deposition model. These two

the authors believe that those reported by Ichikawa et al. are also on a mass weighted basis. While it would be more comforting if the agreement between the average particle temperatures was closer at the highest ash-heating temperature, (10) Niksa, S.; Mitchell, R. E.; Hencken, K. R.; Tichenor, D. A. Optically determined temperatures, sizes, and velocities of individual carbon particles under typical combustion conditions. Combust. Flame 1984, 60, 183–193.

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Figure 11. Comparsion of the size histogram of rebound and sticking particles between the (top) CFD model result and (bottom) experimental result.7 Tash = 1873 K; TJ coal.

Figure 12. Comparsion of the size histogram of rebound and sticking particles between the (top) CFD model result and (bottom) experimental result.7 Tash = 1773 K; TJ coal.

velocities are of the same order of magnitude for all four ashheating temperatures, but there is a clear trend for the range of critical velocities becoming lower than the particle impact velocity as the ash-heating temperature is reduced. For each ash-heating temperature, it is seen that the smaller particles have higher critical velocities below which sticking occurs, so that they are more likely to adhere to the target surface. The maximum predicted critical velocities are reduced as the ashheating temperature is reduced (Note the smaller vertical axis scales as the ash-heating temperature is reduced). The three bands of predicted critical velocity that can be seen for the two lower ash-heating temperatures are an artifact of using three different curve fits for the effective stiffness parameter versus the temperature over three different particle diameter ranges (eq 8). A better curve fit of Young’s modulus versus the particle diameter likely would have eliminated this. While particles are delivered by inertial forces onto the target surface, the actual deposition that occurs depends upon whether particles stick upon arrival at that surface. This will depend upon whether or not the forces that tend to make the particles adhere to the wall are large enough to overcome the tendency of the particle to rebound from the surface. The impact efficiency is defined as the ratio of the mass of particles impacting the surface to the total particle mass flowing into the system. The sticking efficiency is defined as the ratio of the total mass of particles that adhere to the surface to the total mass of all impacting particles. The impact efficiency and sticking efficiency specify the effects of delivery and attachment on surface deposition, respectively. The overall particle capture efficiency is defined as the product of the impact

efficiency and sticking efficiency and represents the fraction of particles entering the system that stick to the surface. Figure 10 presents the model predictions for all three of these efficiencies versus the particle diameter for the TJ coal ash, for each of the four ash-heating temperatures. The impact efficiency increases from nearly 0% for the smallest particles to 100% for the largest particles, because of the large Stokes number, which enables these particles to maintain their trajectories and impact the target surface. Sticking efficiency decreases with an increasing particle diameter for each ash-heating temperature. Also, the sticking efficiency decreases significantly as the ashheating temperature (and the resulting particle temperature at impact; see Figure 8) is decreased. Capture efficiency increases with the particle size at ash-heating temperatures of 1873 and 1773 K, which likely is due to the higher temperature of the large particles resulting in non-zero sticking efficiencies for some of the largest particles, which would tend to outweigh the influence of particle size on the tendency to rebound. A peak in capture efficiency appears in the size range of 150 μm for the lower ash-heating temperatures of 1673 and 1573 K. To further assess the accuracy of the developed particle deposition model, the frequency histograms of adhesion and rebound behavior versus the particle size for the TJ coal have been computed using the present deposition model and are compared to the experimental measurements7 in Figures 11-14 for each of the ash-heating temperatures of 1873, 1773, 1673, and 1573 K, respectively. The frequencies have been normalized by the total weight of particles colliding with the probe, as performed by Ichikawa et al.7 As a result, the sum of all of the 715

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Figure 14. Comparsion of the size histogram of rebound and sticking particles between the (top) CFD model result and (bottom) experimental result.7 Tash = 1573 K; TJ coal.

Figure 13. Comparsion of the size histogram of rebound and sticking particles between the (top) CFD model result and (bottom) experimental result.7 Tash = 1673 K; TJ coal.

individual frequencies over all of the different particle diameters is equal to 1. As seen, the results are in reasonably good agreement for all four ash-heating temperatures. Variability in the percentages of the smaller particles that impact the surface out of the total mass are likely the result of the decrease in the impact efficiency as particle size decreases (Figure 10) (That is, of the 5000 particle streams that were injected in the postprocessing to generate each of the cases shown in Figures 11-14, only a relatively few of the smaller particles actually impact the surface, leading to poorly converged statistics for the smaller particle diameters). Ichikawa et al. present data for the particle sticking efficiency versus the particle temperature at impact for all four ash-heating temperatures that impact their test probe; these data have been replotted from ref 7, as shown in Figure 15. These results give some support to the present findings that it was necessary to use different correlation equations for particle Young’s modulus, E, for different particle size classes (eq 8). In Figure 15, it is seen that, for particle impact temperatures above nominally 1573 K, the ash-heating temperature does not influence the particle sticking efficiency significantly, while for particle impact temperatures at or below 1573 K, there is significant variation. Assuming this categorization is correct, then the variations in sticking efficiency at particle impact temperatures above 1573 K are interpreted as a measure of experimental accuracy or repeatability, estimated as (5-10%. We observe that the ash particles that impacted the test probe at measured impact temperatures

Figure 15. Measured ash particle sticking probability versus the particle temperature at impact. Data were replotted from Ichikawa et al.7

between 1400 and 1500 K had a sticking efficiency of about 40% if they were subjected to an ash-heating temperature of 1873 K, but the sticking efficiency fell to nominally 20% for an ash-heating temperature of 1773 K and to below 10% for an ash-heating temperature of 1673 K. This indicates that the ash particle surface temperatures at impact measured by Ichikawa et al. were not an adequate indicator of the sticking tendencies of the ash particles if they were heated above the final ashmelting temperature between 1573 and 1673 K but impacted the test probe at measured surface temperatures below this temperature. This could be explained if the time required for 716

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the larger molten ash particles to completely solidify was longer than the particle transit time through the cool thermal boundary layer adjacent to the test probe, at least for some of the particles. This hypothesis would result in the core of the larger impacting particles remaining molten, while a solidified outer surface layer would have sufficient time to form prior to impact. Individual particle temperature-time histories for the simulation for Tash = 1873 K indicated that the times for the particles to cool from the ash-heating temperature to the temperature of the cooled impact probe ranged from approximately 50 ms for smaller particles to 80 ms for the larger particles; these times were the same order of magnitude as the predicted times for the particles to heat to the ash-heating temperature. In the present work, it was noted that, if a single curve fit of particle Young’s modulus, Ep, versus the temperature was used for all particle size classes and if the model Ep was adjusted to yield the measured overall particle sticking efficiency for the ash-heating temperature of 1873 K, then the sticking efficiencies predicted by the model for the various particle size cuts did not match the experiemental data (bottom plot in Figure 11). For example, this preliminary model formulation predicted 100% sticking efficiency for all particles below d = 200 μm and 20% sticking efficiency for all particles larger than d = 300 μm. Although this was consistent with the experimental trend of greater sticking efficiencies for the smaller particles,7 it did not yield a quantitative match with the Ichikawa et al. sticking efficiency data, where between 60 and 70% sticking efficiency was observed for particles between 45 and 250 μm. A somewhat similar behavior was observed by Richards et al.11 in their experiments on coal particle deposition onto gas turbine blades. Two bituminous coals were combusted under controlled conditions in a drop-tube reactor with residence times that were similar to those of the apparatus of Ichikawa et al., and the exiting particles were accelerated through a nozzle to achieve higher velocities (order of 50 m/s), representative of those in gas turbines. The exiting particles were then impacted onto a colder deposition target, and the resulting ash deposits were analyzed. They observed that lower temperature combustion increased the particle sticking coefficients. An axisymmetric analytical model based on the boundary layer theory predicted that smaller particles more nearly followed the gas flow, resulting in longer residence times in the colder boundary layer flow adjacent to the deposition target, while the larger particles more nearly followed ballistic trajectories, impacting the target more nearly normal to the surface and at higher temperatures. Richards et al. reasoned that the smaller particles would have sufficient time to cool and solidify, while the larger particles would not have sufficient time. Thus, they concluded that this cooling of the smaller particles could lead to reduced particle deposition, at least for the smaller particles, but that larger particles were formed at the lower temperatures. Critical viscosity particle deposition models5,12 would yield predictions that would be opposite the experimental trends.7 That is, because for the experiments of Ichikawa et al., the smaller particles are always cooler than the large particles when they impact the test probe, then these models would predict that only the larger particles would tend to stick, while

the cooler small particles would tend to rebound. This trend is inconsistent with the experimental observations. Further, if the Browning et al. critical viscosity model5 is adjusted to yield the correct overall particle sticking efficiency for the highest ash-heating temperature of 1873 K, then it predicts a sticking efficiency at 1573 K that is more than 3 times too high. Therefore, it is clear that traditional critical viscosity models are not able to reliably predict either the overall or detailed particle deposition behavior for situations such as in the Ichikawa et al. work, where the particles have been heated above the ashmelting temperatures and are deposited onto surfaces that are considerably cooler than the ash-melting temperature. The present model does not include the effects of either electrostatic or thermophoretic forces;13,14 these forces could have significant effects, at least for the smallest ash particles (typically on the order of 1 μm). However, Ichikawa et al. do not report any particle deposition of particles this small, because of either limited resolution of their high-speed video imaging system or the agglomeration. However, thermophoresis can also cause agglomeration of aerosol particles,15 which may be at least a partial explanation for the order of magnitude difference between the ash particle average diameter measured prior to the experiments of around 15 μm9 versus the measured average diameter for the ash particle deposits of somewhat above 100 μm.7 The present particle deposition model is similar to the work by Losurdo.16 However, the present comparisons to the Ichikawa et al. experiments7 present a much more detailed evaluation of the model capabilities or limitations to correctly match the observed particle sticking efficiency behavior versus the particle size as well as temperature. 5. Summary and Conclusions An ash particle deposition model based on existing work has been implemented in a 2D Fluent CFD DPM numerical simulation of the ash behavior measured experimentally in a heating tube that was developed to simulate ash temperature histories in a gasifier. Ash-heating temperatures ranged from 1873 to 1573 K. The present simulations used CFD and the realizable k-ε turbulence model to compute the gas flow field and the heat transfer to a steel probe and DPM particle tracking for the particle trajectories and temperatures. A UDF was developed to describe particle sticking/rebounding and particle detachment on the impinged wall surface. Expressions for ash particle Young’s modulus versus the particle temperature and diameter were developed by fitting to the required Young’s modulus values in the model that matched the experimental ash sticking efficiencies from several particle size cuts and ash-heating temperatures for a TJ coal. A UDF that implemented the developed Young’s modulus curve fit equations versus the particle temperature and diameter was used to predict the particle sticking efficiency, impact efficiency, and capture efficiency. The frequency histogram comparisons of adhesion and rebound behavior by particle size between (13) Batchelor, G. K.; Shen, C. Thermophoretic deposition of particles in gas flowing over cold surfaces. J. Colloid Interface Sci. 1985, 107, 21–37. (14) Tsai, R.; Liang, L. J. Correlation for thermophoretic deposition of aerosol particles onto cold plates. Aerosol Sci. 2001, 32, 473–487. (15) Jung, H.; Lee, S. Y.; Kim, J. H. Numerical analysis for the thermophoretic coagulation of monodisperse particles at continuum regime. J. Colloid Interface Sci. 2010, 349, 438–441. (16) Losurdo, M. Particle tracking and deposition from CFD simulations using a viscoelastic particle model. Ph.D. Dissertation, Delft University of Technology, Delft, The Netherlands, 2009.

(11) Richards, G. A.; Logan, R. G.; Meyer, C. T.; Anderson, R. J. Ash deposition at coal-fired gas turbine conditions: Surface and combustion temperature effects. J. Eng. Gas Turbines Power 1992, 114, 132–138. (12) van Dyk, J. C.; Waanders, F. B.; Benson, S. A.; Laumb, M. I.; Hack, K. Viscosity predictions of the slag composition of gasified coal, utilizing FactSage equilibrium modeling. Fuel 2009, 88, 67–74.

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Energy Fuels 2011, 25, 708–718

: DOI:10.1021/ef101294f

Ai and Kuhlman

model and experiments showed reasonably good agreement for each of the four ash-heating temperatures. The developed particle deposition model and the Young’s modulus correlation with temperature can now be applied in predicting the deposition behavior of ash particles for the TJ coal in a gasifier. However, to apply the present particle deposition model to other coals, a similar validation process would have to first be conducted to develop the necessary effective Young’s modulus temperature correlation for each new coal.

dp = particle diameter (m) Ep = Young’s modulus of the particle (Pa) Es = Young’s modulus of the impact surface (Pa) E = composite Young’s modulus (Pa) Fs = particle sticking force (N) k = ash thermal conductivity (W m-1 K-1) kp = factor in effective stiffness parameter for particle; see eq 5 (m2/N) ks = factor in effective stiffness parameter for surface; see eq 4 (m2/N) K = effective stiffness parameter from Brach and Dunn empirical curve fit; see eq 3 R = kinematic restitution coefficient T = gas or particle temperature (K) Tash = ash-heating temperature (K) uτc = critical wall shear velocity (m/s) Vcr = particle critical velocity (m/s) WA = adhesion work (J/m2) vp = Poisson’s ratio of the particle (equal to 0.27) vs = Poisson’s ratio of the impact surface (equal to 0.27) vw = wall friction velocity (m/s) Fp = particle density (kg/m3) F = gas density (kg/m3) τw = wall shear stress (Pa)

Acknowledgment. This work has been supported under the Department of Energy (DOE) Gasification Technology Program, funded by the National Energy Technology Laboratory in Morgantown, WV, as part of the University Research Initiative, through the “Collaboratory for Multiphase Flow Research”, RDS Contracts 41817M2318 and 41817M2100, and URS Energy and Construction, Inc. Subcontract 2010-SC-RES-30033-023/04. The authors thank Dr. S. Niksa for making us aware of the experiments by Ichikawa et al.

Nomenclature Cu = Cunningham correction factor Cp = ash specific heat (J kg-1 K-1)

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