Influence of Operating Parameters on Raceway Properties in a Model

In the lower part of an ironmaking blast furnace, a hot air jet is injected horizontally into a bed of coke particles, forming a void zone, called a â...
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Influence of Operating Parameters on Raceway Properties in a Model Blast Furnace Using a Two-Fluid Model Deepak Rangarajan,†,* Tomo Shiozawa,‡ Yansong Shen,‡ Jennifer S. Curtis,† and Aibing Yu‡ †

Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, United States Lab for Simulation and Modelling of Particulate Systems, School of Material Science & Engineering, University of New South Wales, Sydney, NSW, 2052, Australia

‡

S Supporting Information *

ABSTRACT: In the lower part of an ironmaking blast furnace, a hot air jet is injected horizontally into a bed of coke particles, forming a void zone, called a “raceway”. In this paper, two-fluid gas−solid modeling is used to study the influence of various operational parameters on the size and shape of the raceway (void zone). The model employs state-of-the-art closure relations to describe solid-phase stress, which then incorporates frictional forces based on soil mechanics, and k-epsilon equations to describe gas-phase stress. The results show that raceway size and shape depend on jet velocity, outlet pressure, particle size, bed height, height of the jet inlet and the particle downward extraction rate. The influence of jet injection angle, domain geometry, and initial porosity on the raceway properties are found to be insignificant for the investigated range, although changing initial porosity suggests a small degree of hysteresis.

1. INTRODUCTION The ironmaking blast furnace is the dominant route to produce iron. In the lower part of a typical ironmaking blast furnace operation, a hot gas jet at high velocity is injected into a high pressure bed of primarily coke particles forming a cavity in the bed referred to as “raceway”. The extent of various smelting and reduction reactions that follow is largely determined by the mixing between coke particles and the injected gas, which in turn is related to the size and shape of the raceway formed.1,2 Hence, it is important to recognize the key parameters that govern the size and shape of the raceway in order to better understand and predict blast furnace operation. In-situ experimental investigation is difficult because of the high temperature and harsh nature of the flow. For this reason, physical modeling is widely preferred.3 A large number of mathematical modeling studies involving prediction of raceway size and shape can be found in the literature.3−13 Early works describe raceway properties using empirical or semiempirical correlations3−6 while, more recently, computational modeling has been the norm.7−13 In general, the computational modeling studies on raceway formation can be classified into two categories: combined continuum and discrete modeling (CCDM) and two-fluid modeling (TFM). In CCDM, the coke particles are treated as discrete entities and their motion is combined with Navier−Stokes equations that describe the continuum flow of the gas phase. CCDM enables one to obtain microscopic information which helps in the understanding of the physics of the flow, but is computationally expensive. Earlier CCDM studies used small-scale two-dimensional geometries where the particle number is on the order of 104.7,11 On the other hand, in TFM, the gas and particles are considered as interpenetrating continua and conservation equations are solved by means of the conventional computational fluid dynamics techniques.13 But its effective use depends on the appropriate description of the closure relations, which will be © 2013 American Chemical Society

part of the present study. One of the advantages is that TFM is more feasible for large scale computations. This is important for raceway studies, particularly when the aim is to produce results that can be directly used in blast furnace operations. While CCDM has been used to study raceway properties in a laboratory scale blast furnace,7−11 TFM is relatively less commonly encountered.12,13 The most recent work based on TFM is that of Mondal et al.,13 who studied the influences of three parameters: jet velocity, initial porosity of the coke bed, and the bed height on the shape and size of the raceway zone. The closure for the solid stress in their work included both instantaneous particle−particle interactions (kinetic and collisional regimes) as well as particle−particle interactions due to enduring contacts (frictional regime), which are important in dense regions of the coke bed. A k-epsilon model for the turbulent gas-phase stress was modified to account for the presence of particles. The kinetic and collisional solid stress was described using granular kinetic theory. The frictional shear stress was taken to be proportional to the solids pressure, given by kinetic theory. Such a description for the frictional stress has no conceptual basis, where the frictional shear stress is proportional to the kinetic and collisional pressure, and is not commonly found in published two-fluid, gas−solid flow models. Instead, the frictional stresses, that are significant in dense regions, are commonly described using concepts from soil mechanics as explained in Benyahia.14 In the present study, the TFM approach adopted by Mondal et al.13 is modified by including an improved description for the Special Issue: David Himmelblau and Gary Powers Memorial Received: Revised: Accepted: Published: 4983

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frictional stress. The improved friction model is taken from a widely used expression for frictional pressure based on soil mechanics as proposed by Johnson et al.,15 combined with a frictional viscosity that depends on the fluctuations in the solid strain rate as developed by Savage.16 The influence of six new parameters on raceway predictions are investigated, that is, particle diameter, outlet pressure, jet location, solids extraction rate, jet angle, and domain geometry, in addition to the parameters already investigated by Mondal et al.13

cally in this aspect,13,24 where the raceway formation and properties can be examined. At least, the trend with respect to the flow-related operating parameters can be generated by use of such a cold model. In fact, considering the thermal-chemical behavior including the melting and flow of liquid iron and slag will complicate the physics considerably and is beyond the scope of this work. Therefore, in this study, the 3D TFM model of gas−solid flow in a cold model blast furnace is used to investigate the effects of variables on raceway properties.

2. MODEL DESCRIPTION The gas and particle (solid) phases are assumed to behave as interpenetrating continua, as originally proposed by Anderson and Jackson.17 The governing equations solved in the present study are mass, momentum, granular energy, turbulent kinetic energy, and turbulent energy dissipation balances. The closure for the gas−solid drag force is obtained from the drag correlation of Syamlal et al.18 while a standard k-epsilon model is adopted to describe the gas-phase stress. Turbulent gas-particle interaction terms have been neglected in the turbulence equations since including these terms of the form proposed by Simonin19 produced no significant change in raceway size and shape for the base set of operating parameters tested. The solid stress is assumed to be a sum of kinetic, collisional, and frictional contributions, the latter activated above an intermediate solids fraction of 0.5. The kinetic and collsional solid stress is described using granular kinetic theory, which was derived for frictionless spherical particles in a vacuum by Lun et al.20 and slightly modified to account for interstitial gas effects by Agrawal et al.21 The frictional solid stress is described using soil mechanics concepts with an empirical expression for pressure proposed by Johnson et al.15 and a shear viscosity that depends on the fluctuations in the strain rate, μsf ≈ Dp/√θ, as recognized by Savage16 and modified to blend with the granular kinetic theory implemented in the present study. The granular assembly has been assumed to deform without any volume change, that is, at critical state, which has been shown to be an accurate simplification in many dense flows.22 The boundary conditions for particle velocity and granular temperature at the wall are taken from Johnson and Jackson23 who considered partial slip arising from collisional momentum loss at the wall. Standard wall functions are imposed for the gas phase. No reaction or thermal energy transfer is considered in this study for simplicity. The TFM model equations used in the present study are summarized in the Supporting Information and the model parameters specified are shown in Table 1. The raceway size and shape can be affected by a number of factors such as blast dynamics, coke bed propertie,s and liquid flow inside the coke bed. Cold models under simplified conditions have been widely used experimentally and numeri-

3. METHOD OF SOLUTION The TFM equations are solved by a finite volume approach in a compressible fashion following the ideal gas law, using an open source codeMultiphase Flows with Interphase Exchanges (MFIX). The details of the numerical technique can be found in Syamlal et al.18 The maximum residual at convergence is set to 1 × 10−3 for the continuity and momentum equations combined and 1 × 10−4 for the granular energy, turbulent kinetic energy, and turbulent dissipation equations, respectively. The simulation domain is chosen to represent a typical subsection of an industrial scale blast furnacea cuboid of length 3.7 m, width 1 m, and height 5 m (Figure 1). Gravity

Figure 1. Simulation domain for the lower part of ironmaking blast furnace.

acts in the negative z direction. The jet orifice is a square of side Dj = 0.15 m, located at a height Hj from the bottom. Initially a stagnant, uniform solid phase of porosity εi is specified to occupy the space from the bottom to a bed height of Hi. The boundary conditions imposed are a constant gas mass inflow corresponding to a horizontal velocity, Uj, and gas density, 1.1 kg/m3 at the orifice, and a constant pressure outflow corresponding to a pressure of Po at the top boundary (z = 5 m). Wall conditions are specified on all other boundaries. The physical properties of gas and particles specified in the present study are summarized in Table 2. The operating parameters that were varied are shown in Table 3. The inlet values of turbulent kinetic energy and turbulence dissipation at the orifice are fixed at 39 m2/s2 and 2692 m2/s3, respectively. These values have been estimated using standard CFD guidelines corresponding to a jet velocity of Uj = 165 m/s. 3 −1/8 2 k j = (0.16URe ) j j (1) 2

Table 1. Model Parameters Specified parameter

description

σk, σε, C1ε, C2ε, Cμ E, κv

constants in k−ε gas turbulence model constants in standard wall functions for gas constant in granular theory constants in frictional pressure expression specularity coefficient

ά Fr, r, s, εsmin, εsmax φ

value 1.0, 1.3, 1.44, 1.92, 0.09 9.81, 0.42 1.6 0.05 N/m2, 2, 5, 0.5, 0.65 0.002 4984

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Table 2. Physical Properties Specified parameter MW T μg ρs e ew δ δw

description molecular weight of gas temperature of gas gas viscosity particle density particle−particle coefficient of restitution particle-wall coefficient of restitution angle of internal friction angle of wall friction

value 29 1473 K 5.37 × 10−5 kg/(m s) 900 kg/m3 0.8 0.8 27 deg 27 deg

Table 3. Operating Parameters That Were Varied (Base Parameters Are in Bold) parameter

description

Dj Uj

jet orifice diameter inlet jet horizontal (x) velocity

α Hj Po

angle made by jet inlet with the horizontal plane in the downward (−z) direction height of jet orifice from the bottom outlet pressure

εi Hi Dp ms

initial porosity of the bed initial bed height particle diameter solids downward extraction rate

⎛ k 1.5 ⎞ j ⎟ εj = 0.1643⎜⎜ ⎟ l ⎝ e ⎠

Figure 2. Time evolution of raceway size and shape for the base case.

value 0.15 m 165, 195, 220, 250, 280 m/s 0, 5, 15 degrees

To visualize the general nature of flow that occurs after a stable raceway is formed, vector plots of mean gas and particle velocities and the dense phase porosity distribution along the central y slice at t = 2 s are shown in Figure 3. From Figure 3a it can be observed that a majority of the region beyond the raceway, except very close to the boundary, is a packed bed where the particles do not move to a significant extent, but the gas penetrates through the voids of the packed bed. The gas velocities show that gas enters horizontally from

0.3, 1.2, 2.5 m 2.61, 4.61, 7.61 atm 0.4, 0.5, 0.6 1.8, 3, 4.5, 6 m 2, 4, 6 cm 0, 0.82, 16.4 kg/s

(2)

where, k is turbulent kinetic energy at inlet; ε is turbulent dissipation at inlet; Rej is Reynolds number at the inlet; le is turbulence length scale approximated as 0.1 times the jet diameter Dj. The sensitivity of the inlet turbulence values on the raceway results was found to be negligible. A structured but nonuniform mesh of ∼132 000 grids with more grids close to the jet orifice was chosen after ensuring that the mesh produced grid insensitive results. Starting from t = 0, the simulations took approximately 2 s of real time to reach a steady state after which there was negligible change in raceway size or shape. All results are analyzed after such a stable state was reached. The simulations were run in parallel using 2 processors (quad-core 2.93 GHz Intel Nehalem) at National Computational Infrastructure (NCI) Facility in Australia.

4. RESULTS AND DISCUSSION The boundary of the raceway region is characterized by a contour of constant porosity equal to 0.5 for all cases considered in this paper. The physical basis for choosing this value comes from the continuum model description which estimates that enduring particles are significant only below a porosity of 0.5, above which the particle movement is governed by instantaneous collisions. The time evolution of raceway formation is shown in Figure 2 for the base set of parameters. Since the base conditions correspond to a loosely packed bed, the time evolution shows that as the bed compacts, the raceway size becomes smaller until a steady raceway is formed after roughly 2 s of real time.

Figure 3. (a) Vector plot of mean gas and mean particle velocity along the plane y = 0.5 m at t = 2 s for the base case. The magnitude of the gas velocity has been reduced by a factor of 30 compared to the solid velocity. (b) The dense phase porosity distribution in the packed region beyond the raceway, along the plane y = 0.5 m at t = 2 s for the base case. 4985

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This trend agrees well with the findings of other authors.11,13,25,26 2. Particle Diameter. Increasing particle diameter from Dp = 2 cm through Dp = 6 cm reduces the raceway size, accompanied by a narrowing of raceway shape (Figure 5). This

the jet orifice, loses velocity through the raceway, and escapes out of the voids in the packed bed. Two-patterns can be observeda high-speed central jet and recirculation. That is, there is entrainment of gas toward the jet axis from the top and bottom regions of the raceway very near the orifice; otherwise, the gas flow is predominantly outward of the jet axis. The particle velocities show that while in the region beyond the raceway boundary particles hardly move, inside the raceway there is significant particle movement. Particles move toward the jet axis from the top and bottom regions of the raceway close to the orifice (entrainment zone). Some of the particles are transported horizontally along the jet axis until they can no longer move upon hitting the boundary of the packed bed, and the rest of the particles are recirculated back toward the orifice along the top and bottom boundaries (recirculation zone). This particle motion is more significant in the top part of the raceway than the bottom. With regard to the forces that govern particle motion inside the raceway, the particle velocity tends to follow the gas velocity along the jet axis. Therefore, the horizontal acceleration near the orifice can be attributed to the gas−solid drag force. Further downstream, particles retard due to collision with the packed bed region. The entrainment of particles near the jet orifice is caused primarily by drag. The weight of the particles enhances entrainment from the top and opposes entrainment from the bottom. The particle recirculation along the top and bottom boundaries away from the orifice is driven by particle−particle interactions. Figure 3b illustrates the porosity distribution in the packed bed region of the furnace for the base case. It can be seen that the porosity in the dense-phase region, as predicted by the frictional model, decreases rapidly close to the surface and slower toward the bottom of the particle bed. The effects of the key parameters on raceway size and shape are discussed comprehensively in the next sections. The effect of each parameter on the raceway size, defined as the penetration depth in the horizontal direction, and shape of the raceway is investigated one at a time, keeping all other parameters fixed at their base values. 1. Jet Inlet Velocity. Jet inlet velocities of Uj = 165, 195, 220, and 250 m/s were simulated. It is found that increasing the horizontal jet velocity increases the raceway size. However, there is only a small change in raceway shape (Figure 4). This can be explained by the increase in horizontal momentum of the gas which is transferred to the particles. The particles are dragged further into the bed before the retardation caused by the packed bed prevents any further horizontal penetration.

Figure 5. Effect of particle diameter on raceway size and shape.

behavior is due to a combination of a decrease in the drag force and increase in the particle resistance (solids frictional viscosity) with increase in particle size. The particles are not dragged sufficiently far horizontally, and higher particle resistance to flow prevents a larger region of particles from taking part in the entrainment and recirculation process. This qualitative behavior with respect to particle size is also in agreement with other works.9,26 3. Outlet Pressure. In the ironmaking blast furnace, high top pressure is usually adopted and the top pressure varies with operating conditions. In this study, outlet pressures of Po = 2.61, 4.61, and 7.61 atm were simulated. From Figure 6, it can

Figure 6. Effect of outlet pressure on raceway size and shape.

be seen that increasing the outlet pressure decreases the raceway size accompanied by some change in the raceway shape as well. The outlet pressure controls the gas pressure inside the bed, which in turn is directly proportional to the gas density. Hence, for the same mass inflow, the gas velocities decrease with increase in outlet pressure resulting in lower gas− solid drag and shorter, narrower raceways. 4. Initial Bed Height. In the ironmaking blast furnace, the solid loading above the raceway varies with the furnace shape and operating conditions. In this study, the computational domain does not describe the entire furnace but only the lower

Figure 4. Effect of inlet jet velocity on raceway size and shape. 4986

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so as to keep the total mass of particles a constant. The results (Figure 9) show only a small change in the size and shape of

part of the furnace. For this reason, it is necessary to investigate the initial bed height. The initial bed height determines the weight of particles in the bed. Figure 7 shows that increasing

Figure 9. Effect of initial porosity on raceway size and shape. Figure 7. Effect of initial bed height on raceway size and shape.

the raceway with change in porosity. A loosely packed bed of particles simply falls to its randomly packed state (ε ≈ 0.4) resulting in a similar steady state configuration for all the three porosities. Narrowing of the raceway at εi = 0.6 can be attributed to a small dependence of the steady state solution on initial conditions, a hysteresis phenomenon in raceway formation which has been noted in literature.7 The maximum porosity case (εi = 0.6) was simulated in a computational domain of height z = 6 m to accommodate the increased bed height. The results presented here with regards to the effect of the initial porosity do not agree with Mondal et al.,13 who found that increasing initial porosity from εi = 0.4 to 0.5 significantly narrows the raceway shape, accompanied by a decrease in size. It is to be noted that the other porosities considered by Mondal et al., εi = 0.2 and 0.3, correspond to unphysical conditions of spherical packing densities greater than 0.65 and hence have been neglected in the present comparison. It is also unclear what maximum packing value was used in their work. Hence, the reason for the disagreement in the effect of initial porosity is due to the lack of frictional pressure in the gas−solid flow modeling of Mondal et al.13 The frictional pressure prevents the bed from reaching packing fractions higher than maximum random packing, without which unphysical porosity distribution may result depending on the initial state, since the dense bed porosity distribution is then governed by the radial distribution function. 7. Particle Downward Extraction. To describe the slow particle extraction that mimics the solid loss due to coke combustion or carbon dissolution in the lower part of a blast furnace, a constant solids mass outflow condition was specified at the bottom boundary (z = 0). Such a method to approximate the effect of loss in solids has been successfully applied in the experimental study of Pinson et al.27 Solids mass flow rates of ms = 0.82 kg/s and 16.4 kg/s were simulated for a jet velocity of Uj = 165 m/s. To compensate for the loss in solids with time, the initial bed height was increased from Hi = 4.5 m to Hi = 6 m, which is above the critical height and hence should not affect the raceway (Figure 7). The domain height was increased to z = 6.5 m to accommodate the increased bed height. The time to predict a stable raceway formation was longer, 10 s of real time, at the highest solids extraction rate. While there is no change in raceway size or shape at a small rate of extraction of ms = 0.82 kg/s, a significant increase in size and change in shape is

the initial height of the bed decreases the raceway size and narrows the shape at small heights. However, above height Hi = 4.5 m of solids, the size or shape of the raceway does not change with a further increase in bed height. This behavior is attributed to the variation in local porosity in a packed bed assembly as a function of the height of the bed. At small heights, the porosity decreases significantly with bed height causing smaller raceways, but after a sufficiently large bed height, there is negligible change in porosity upon increasing height. The maximum bed height (Hi = 6 m) was simulated in a domain of height z = 6.5 m. This behavior with respect to bed height is comparable with the findings of other authors.13,26 5. Jet Location. The jet orifice was located at different heights of Hj = 2.5, 1.2, and 0.3 m (Figure 8). All the three

Figure 8. Effect of jet location on raceway size and shape.

heights have been plotted in the same figure to enable easier comparison. While there is significant change in raceway size and shape when inlet height is decreased from Hj = 2.5 to 1.2 m, negligible influence on raceway size and shape is observed below height Hj = 1.2 m. The reason for such a behavior with change in jet location is because there is no significant change in the packed bed porosity in the region where the jet penetration occurs with further decrease in inlet height. This is the same trend that was seen when increasing the initial height of the bed. 6. Initial Porosity. Three different initial porosities of εi = 0.6, 0.5, and 0.4 were simulated with varying initial bed heights, 4987

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observed at a downward solids extraction rate of ms = 16.4 kg/s (Figure 10). This behavior with respect to solids extraction is

Figure 10. Effect of solids downward extraction on raceway size and shape.

attributed to the increase in porosity of the packed bed assembly as solids are extracted downward at high rates. Such a trend with particle extraction was also found in the CCDM work of Feng et al.11 8. Jet Angle. To simulate the condition where the jet inlet pipe makes an angle -α with the horizontal plane, the inlet boundary conditions were specified as Uj′ = Uj cos α, Vj′ = −Uj sin α, and the orifice length in the z direction changed correspondingly to Dj/cos α. No significant effect on the raceway size or shape was observed when changing the inlet jet angle from 0 to 15 degrees. 9. Domain Geometry. In the present study a simplified Cartesian geometry has been assumed, but real blast furnace subsections have slanting edges at the sides.28 To test the effect this could have on raceway properties while still using staircase mesh implementation, the simulation domain was changed as shown in Figure 11, top. The jet enters the bed of particles via an inlet pipe and there is a cut in the bed at a height of 1.05 m from the bottom. A simulation with base parameters was performed using this domain and no significant difference was found in the resulting raceway size or shape when compared to the corresponding simulation run using the original domain (Figure 11, bottom). This suggests that a simple Cartesian geometry captures the stresses in the coke bed quite accurately.

Figure 11. (Top) Modified simulation domain. (Bottom) Effect of simulation domain on raceway size and shape.

certain height. The same trend is observed when decreasing the height at which the jet is located. Varying the initial bed porosity has no significant effect since a loosely packed bed tends to fall to its random packing state. However, the narrowing of the raceway at high porosity suggests some hysteresis effect. Extracting solids from the bottom has the tendency to increase raceway size and change the raceway shape as the bed becomes more porous. Small changes in the jet injection angle and geometry of the domain were found to have negligible effect on the raceway properties. Research that employs the details of these simulation results, in particular the porosity distribution of coke inside the raceway,29 to quantitatively predict the reaction efficiencies in the lower part of a blast furnace, is currently under progress.

5. CONCLUSIONS There is a lack of two-fluid modeling studies with appropriate closure relations that explore raceway properties in a large-scale blast furnace operation. To address this issue, a TFM approach has been undertaken to understand the flow behavior and investigate the influences of various operating parameters on the size and shape of a raceway. The model uses soil mechanics concepts to include the effect of enduring contacts (friction) between particles while describing the solid-phase stress, and employs k-epsilon turbulence equations to describe the gasphase stress. Simulation results show that increasing jet velocity increases raceway size without considerable change in shape, whereas changing particle size and outlet pressure affects both raceway size and shape considerably. Increasing the height of coke particles in the bed decreases raceway size and narrows the raceway at small heights but produces no change beyond a

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ASSOCIATED CONTENT

S Supporting Information *

This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: deepakrangarajan@ufl.edu. 4988

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Notes

Subscript

The authors declare no competing financial interest.

j = inlet jet conditions g = gas phase s = solid phase

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ACKNOWLEDGMENTS The funding for this work was sponsored by Department of Energy’s Office of Fossil Energy’s University Research Program under Project No. DE-NT0007649. This computation work was supported by NCI National Facility in Australia. The authors would like to thank the MFIX development team for their help in using the code.

Superscript

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NOTATION C1ε, C2ε, Cμ, σk, σε = constants in k-epsilon gas turbulence model CD = drag coefficient Dj = inlet jet diameter [L] Dp = particle diameter [L] e = particle−particle restitution coefficient E = constant in wall function formulation ew = particle-wall restitution coefficient FD = interphase drag force per unit volume [ML−2 T−2] Fr = constant in frictional pressure expression [ML−1 T−2] g = acceleration due to gravity [L T−2] g0 = radial distribution function at contact Hi = initial bed height [L] Hj = inlet jet height from the bottom [L] I = identity tensor Js = granular energy dissipation due to inelastic collisions [L2 T−3] k = gas-phase turbulent kinetic energy [L2 T−2] ms = solids downward extraction rate [MT−1] MW = molecular weight of gas p = pressure [ML−1 T−2] Po = outlet pressure [ML−1 T−2] r = constant in frictional pressure expression s = constant in frictional pressure expression T = temperature of gas [K] u = velocity [LT−1] Uj = inlet horizontal jet velocity [L T−1] Vj = vertical inlet jet velocity [L T−1] x, y, z = horizontal, spanwise, and vertical corrdinates

kc = kinetic and collisional f = frictional max = maximum packing min = intermediate packing

REFERENCES

(1) Dong, X. F.; Yu, A. B.; Yagi, J. I.; Zulli, P. Modelling of multiphase flow in a blast furnace: Recent developments and future work. ISIJ Int. 2007, 47 (11), 1553−1570. (2) Shen, Y. S.; Guo, B. Y.; Yu, A. B.; Austin, P. R.; Zulli, P. Threedimensional modelling of in-furnace coal/coke combustion in a blast furnace. Fuel 2011, 90 (2), 728−738. (3) Rajneesh, S.; Sarkar, S.; Gupta, G. S. Prediction of raceway size in blast furnace from two dimensional experimental correlations. ISIJ Int. 2004, 44 (8), 1298−1307. (4) Flint, P. J.; Burgess, J. M. A fundamental-study of raceway size in 2 dimensions. Metall. Trans. B 1992, 23 (3), 267−283. (5) Gupta, G. S.; Rajneesh, S.; Rudolph, V.; Singh, V.; Sarkar, S.; Litster, J. D. Mechanics of raceway hysteresis in a packed bed. Metall. Mater. Trans. B 2005, 36 (6), 755−764. (6) Sastry, G.; Gupta, G. S.; Lahiri, A. K. Void formation and breaking in a packed bed. ISIJ Int. 2003, 43 (2), 153−160. (7) Xu, B. H.; Yu, A. B.; Chew, S. J.; Zulli, P. Numerical simulation of the gas-solid flow in a bed with lateral gas blasting. Powder Technol. 2000, 109 (1−3), 13−26. (8) Yu, A. B.; Xu, B. H. Particle-scale modelling of gas-solid flow in fluidisation. J. Chem. Technol. Biotechnol. 2003, 78, 111. (9) Nogami, H.; Yamaoka, H.; Takatani, K. Raceway design for the innovative blast furnace. ISIJ Int. 2004, 44 (12), 2150−2158. (10) Yuu, S.; Umekage, T.; Miyahara, T. Predicition of stable and unstable flows in blast furnace raceway using numerical simulation methods for gas and particles. ISIJ Int. 2005, 45 (10), 1406−1415. (11) Feng, Y. Q.; Pinson, D.; Yu, A. B.; Chew, S. J.; Zulli, P. Numerical study of gas-solid flow in the raceway of a blast furnace. Steel Res. Int. 2003, 74 (9), 523−530. (12) Aoki, H.; Nogami, H.; Tsuge, H.; Miura, T.; Furukawa, T. Simulation of transport phenomena around the raceway zone in the blast-furnace with and without pulverized coal injection. ISIJ Int. 1993, 33 (6), 646−654. (13) Mondal, S. S.; Som, S. K.; Dash, S. K. Numerical predictions on the influences of the air blast velocity, initial bed porosity and bed height on the shape and size of raceway zone in a blast furnace. J. Phys. D: Appl. Phys. 2005, 38 (8), 1301−1307. (14) Benyahia, S. Validation study of two continuum granular frictional flow theories. Ind. Eng. Chem. Res. 2008, 47 (22), 8926− 8932. (15) Johnson, P. C.; Nott, P.; Jackson, R. Frictional collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 1990, 210, 501−535. (16) Savage, S. B. Analyses of slow high-concentration flows of granular materials. J. Fluid Mech. 1998, 377, 1−26. (17) Anderson, T. B.; Jackson, R. A fluid mechanical description of fluidized beds. Ind. Eng. Chem. Fundam. 1967, 6 (4), 527. (18) Syamlal, M.; Rogers, W.; O’Brien, T. J. MFIX Documentation: Theory Guide; U.S. Department of Energy: Washington, DC, 1993. (19) Simonin, O. Continuum modeling of dispersed two-phase flows in combustion and turbulence in two-phase flows. Von Karman Inst. Fluid Dyn., Lect. Ser. 1996, 29. (20) Lun, C. K. K.; Savage, S. B.; Jeffrey, D. J.; Chepurniy, N. Kinetic theories for granular flowInelastic particles in couette-flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 1984, 140 (MAR), 223−256.

Greek Letters

Δx = width of computational cell next to wall [L] α = angle of jet with the horizontal ά = constant in granular theory β = gas−solids drag force coefficient [ML−3 T−1] δ = angle of internal friction δw = angle of wall friction ε = gas turbulent energy dissipation [L2 T−3] εi = initial gas volume fraction εm = volume fraction of phase m η = constant depending on particle restitution coefficient θ = granular temperature [L2 T−2] κs = solids granular conductivity [ML−1 T−1] κv = von Karmen constant μ = viscosity [ML−1 T−1] πθ = granular energy enhancement due to turbulence exchange [ML T−3] ρ = density [ML−3] σ = stress tensor [ML−1 T−2] τ = shear stress tensor [ML−1 T−2] φ = specularity coefficient 4989

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(21) Agrawal, K.; Loezos, P. N.; Syamlal, M.; Sundaresan, S. The role of meso-scale structures in rapid gas-solid flows. J. Fluid Mech. 2001, 445, 151−185. (22) Srivastava, A.; Sundaresan, S. Analysis of a fractional-kinetic model for gas-particle flow. Powder Technol. 2003, 129 (1−3), 72−85. (23) Johnson, P. C.; Jackson, R. Frictional collisional constitutive relations for antigranulocytes-materials, with application to plane shearing. J. Fluid Mech. 1987, 176, 67−93. (24) Burgess, J. M. Fuel combustion in the blast-furnace raceway zone. Prog. Energy Combust. Sci. 1985, 11, 61−82. (25) Sarkar, S.; Gupta, G. S.; Kitamura, S.-y. Prediction of raceway shape and size. ISIJ Int. 2007, 47 (12), 1738−1744. (26) Gupta, G.; Rudolph, V. Comparison of blast furnace raceway size with theory. ISIJ Int. 2006, 46 (2), 195−201. (27) Pinson, D.; Shaw, J.; Yu, A. B.; McCarthy, M.; Zulli, P. An experimental study of gas-solid flow in the blast furnace raceway. Chem. 99 Newcastle 1999, 192−197. (28) Shen, Y. S.; Maldonado, D.; Guo, B. Y.; Yu, A. B.; Austin, P.; Zulli, P. Computational fluid dynamics study of pulverized coal combustion in blast furnace raceway. Ind. Eng. Chem. Res. 2009, 48 (23), 10314−10323. (29) Shen, Y. S.; Yu, A. B.; Austin, P. R.; Zulli, P. CFD study of infurnace phenomena of pulverised coal injection in blast furnace: Effects of operating conditions. Powder Technol. 2012, 223 (0), 27−38.

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dx.doi.org/10.1021/ie301936r | Ind. Eng. Chem. Res. 2014, 53, 4983−4990