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3D numerical study of particle flow behavior in the impinging zone of an Opposed Multi-Burner gasifier
Powder Technology 225 (2012) 118–123
Contents lists available at SciVerse ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
3D numerical study of particle flow behavior in the impinging zone of an Opposed Multi-Burner gasifier Chao Li, Zhenghua Dai ⁎, Weifeng Li, Jianliang Xu, Fuchen Wang Key Laboratory of Coal Gasification of Ministry of Education, East China University of Science and Technology, Shanghai 200237, PR China
a r t i c l e
i n f o
Article history: Received 30 November 2011 Received in revised form 21 February 2012 Accepted 26 March 2012 Available online 1 April 2012 Keywords: Coal gasifier Impinging flow Hard-sphere model DSMC method Particle flow behavior
a b s t r a c t A 3D model of the impinging zone of a commercial scale Opposed Multi-Burner (OMB) gasifier is established in this article, in which the gas flow and particle motion are simulated by the Eulerian–Lagrangian approach, and the gas turbulence is calculated using the realizable k-ε model. The particle collision is determined by the Direct Simulation Monte Carlo (DSMC) method and the modified Nanbu method, with the presumption that the particle is hard sphere. The model is validated with reference to the experimental result obtained on a laboratory device equipped with two opposed jets. The model reveals the concentration and mean velocity profiles of particles in the impinging zone. It is quantitatively observed that particles move at an accelerated speed from the jet and then at a rapidly decelerated speed near to the central impinging zone; particles are concentrated in the central impinging zone due to collision. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Entrained flow coal gasification is an advanced gasification technology, which has widely found commercial applications for the production of coal-based chemicals such as methanol, ammonia, DME, and hydrogen. OMB gasifier is an entrained flow gasifier developed in China, and it has been successfully applied in several plants [1]. One of the patented designs of OMB gasifier is to strengthen the mass and heat transfer and prolong the particle residence time via the formation of an impinging flow field. This study is focused on a model study of particle flow behavior in the impinging zone. There are two classical methods in simulation of gas–particle flow, the Eulerian–Eulerian method which treats particles as a continuous phase and the Eulerian–Lagrangian which tracks individual particles. The latter method is used in this study to calculate the gas turbulence and the motion of individual particle. Considering that inter-particle collision is an important physical phenomenon in the impinging zone of an OMB gasifier, we combine the Eulerian–Lagrangian method with particle collision in this study. Particle collision is generally simulated by the soft-sphere model and the hard-sphere model in terms of interactions between particles. Cundall and Strack [2] proposed a discrete element method (DEM) in treatment of soft-sphere collision in 1979. Tsuji [3] and Xu
⁎ Corresponding author. Tel.: + 86 021 64250784; fax: + 86 021 64251312. E-mail address: [email protected] (Z. Dai). 0032-5910/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2012.03.044
[4] simulated a fluidized bed using the soft-sphere model. In recent years, DEM has been used frequently by coupling with LES [5] or commercial CFD software [6]. With respect to the hard-sphere model, inter-particle collision is treated generally as a binary and instantaneous process and simulated by solving the conservation equation of momentum. Many researches verified the application of the hardsphere model to Couette shear-flow [7], horizontal channel [8] and gas-fluidized bed [9,10]. The hard-sphere model has also widely been used to investigate the formation and structure of bubbles and clusters in fluidized bed [11,12] and riser [13]. Direct Simulation Monte Carlo (DSMC) method is commonly used to deal with the hard-sphere collision. In DSMC method, a particle collision probability is assessed from a representative amount of tracked particles instead of all particles; therefore, it is advantageous in saving computing time. Tsuji [14] and Wang [15] coupled the DSMC method and the hard-sphere model to study the clustering behavior in a circulating fluidized bed and the gas-particle flow behavior in a riser, respectively. Many studies have been reported on the impinging flow. An early study by Kitron [16] used a stochastic model based on Boltzmann transport equation for description of gas–solid impinging streams. Guo [17] and Ni [18] in our research group developed a Markov chain stochastic model to predict the residence time distribution of gas and particle in an OMB gasifier. Ni [19] further studied the flow behavior of particle and slag in an OMB gasifier by treating particles as liquid drops. In this work, emphasis is placed on the modeling of inter-particle collision and interaction between solid particle and fluid associated with the gas–solid impinging flow in a commercial OMB gasifier by coupling the DSMC method with the hard-sphere model.
C. Li et al. / Powder Technology 225 (2012) 118–123
2. Model description Realistic processes in an entrained flow gasifier are very complex, which include multiphase flow, heterogeneous and homogeneous reactions, and heat transfer. For simplifying the issue, the following assumptions are made in the modeling: (1) no chemical reactions and heat transfer are considered; (2) particle is treated as rigid hard sphere; (3) particle collision is treated as a binary and instantaneous contact; (4) effects of particle rotation on fluid field are neglected. 2.1. Fluid motion Fluid motion is solved by the Reynolds Averaged Navier–Stokes (RANS) equations. The unknown terms of Reynolds stresses in RANS are dealt with using the eddy viscosity model based on Boussinesq hypothesis. The impinging flow is calculated using the typical Realizable k-ε model [20,21]: ∂ ρg kt ∂t ∂ ρg ε t ∂t
þ
þ
∂ ρg kt ug;j ∂xi ∂ ρg εt ug;j ∂xj
¼
" # ∂ μ ∂kt μg þ t þ Gk −ρg εt þ Gb −Y M σ k ∂xj ∂xi þ Sk ð1Þ
∂ ¼ ∂xj
"
# μ t ∂εt μg þ σ ε ∂xj 2
εt ð2Þ þ ρg C 1 Sεt −ρg C 2 pffiffiffiffiffiffiffi þ Sε kt þ vεt η , and η is a where σk = 1.0, σε = 1.2, C2 = 1.9, C 1 ¼ max 0:43; ηþ5 function of k, ε and gradient of velocity. 2.2. Particle suspension Particle motion is solved by the hard-sphere model, in which total particle motion is divided into two independent motions, suspension and collision. Suspension is determined by Newton's law expressed by the equation of translational motion of a particle: mp
dup ¼ f d þ V p g ρp −ρg þ f x dt
119
In addition, taking into account the effect of fluid motion on particle angular velocity, the following torque equation of a particle is adopted [23]: 3 1=2 T ¼ 2μ g dp ωg =2−ωp 1 þ 0:20Rep
20bRep b1000:
2.3. Particle collision Following assumptions are made to solve the particle collision in dispersed gas–particle flow: (1) inter-particle collision is assumed to be binary and instantaneous; (2) during collision process, the distance between the centers of particles is sum of their radius from the negligible deformation of particles; (3) the friction between particles obeys Coulomb's friction law when they keep sliding; (4) sliding occurs no longer once it stops. Fig. 1 illustrates the collision of two hard spheres and some relevant physical variables. Postcollision velocities of particles are derived from the following impulse equations [14]: ð0Þ m1 v1 −v1 ¼ J
ð9aÞ
ð0Þ m2 v2 −v2 ¼ −J
ð9bÞ
ð0Þ I1 ω1 −ω1 ¼ r 1 n J
ð10aÞ
ð0Þ I2 ω2 −ω2 ¼ r 2 n J:
ð10bÞ
The solution of Eqs. (9a), (9b), (10a) and (10b) differs depending on whether two particles keep sliding during collision process or not. 2.4. DSMC method Since there are an enormous amount of particles involved in our simulation, the computation of a common hard-sphere model for particle collision is time-consuming. The DSMC method is therefore coupled with the hard-sphere model to solve this problem. In this
ð3Þ
where fd is the drag force, g represents the acceleration of gravity, and fx means the additional forces. Virtual mass force and pressure gradient force are incorporated in this model. Drag force on particle is calculated according to the following equation [22]: fd ¼
1 2 2 −ðχþ1Þ dp C d ρg πug −up ug −up ε ε 8
ð4Þ
where ε is the voidage of cell where particle is located. The drag coefficient Cd of a particle and the equation coefficient χ are obtained from the equations [22]: Cd ¼
4:8 0:63 þ 0:5 Rep
!2 ð5Þ
2 3 1:5− log10 Rep 7 6 χ ¼ 3:7−0:65 exp4− 5 2
2
ð6Þ
where Rep is the particle Reynolds number, which is defined as:
Rep ¼
ερg dp ug −up μg
:
ð8Þ
ð7Þ Fig. 1. Collision of two hard spheres.
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C. Li et al. / Powder Technology 225 (2012) 118–123 Table 1 Parameters used for model validation.
Fig. 2. Schematic diagram of two opposed jets experiment.
method, a certain number of tracked particles are taken as representatives. The collision probability between tracked particles i and j in a time step is calculated by [14]: di þ dj 2 n P^ ij ¼ π Gij ⋅Δt : N 2
N X
P^ ij :
ð12Þ
j¼1
1 Here, the collision probability is limited to 0 b P^ ij b , so that the N total collision probability of particle i is a value between 0 and 1. The modified Nanbu method [24] is used to decide which particles collide. In this method, every tracked particle in cell is assumed to have the same probability to collide with particle i, so one particle taken randomly can be used as a candidate, expressed as: h i ^ þ 1 k≠i: k ¼ int RN
ð13Þ
From Eqs. (11) and (13), the occurrence of particle collision is made sure if the following criterion is satisfied: ^ > k −P^ : R ik N
Value
Parameter
Value
Temperature Pressure Gas component Length of nozzle Inner diameter of nozzle Distance between nozzles Inlet gas velocity
298 (K) 1 (atm) Air 20 (mm) 8 (mm) 140 (mm)
Mass ratio of gas–solid Particle shape Particle density Particle spray angle Time step Restitution coefficient
1 Sphere 2500 (kg·m− 3) 14° 5 × 10− 5 (s) 0.9
100 (m·s− 1) Friction coefficient
0.2
Parameter
Case 1
Case 2
Particle diameter Particle tracked Inlet particle velocity
77 (μm) ~ 13,400 25 (m·s− 1)
33 (μm) ~ 18,000 55 (m·s− 1)
ð11Þ
Thus, the total collision probability of particle i with all other particles in a time step is given: P^ i ¼
Parameter
consisting of two opposed nozzles. The inner diameter of either nozzle was 8 mm. The distance between two nozzles was 140 mm. Particles were conveyed by air into the nozzles. Fig. 3 shows the calculation domain and the grid meshing with about 60,000 hexahedral cells. Table 1 lists the parameters used for the model validation. Fig. 4 shows the image of particle flow taken by a high-speed camera and the simulation results, both obtained under the same conditions (case 1 in Table 1). Fig. 5 shows the experimentally measured and simulated profiles of the particle concentration along the axis of the nozzle, in which C0 is the particle concentration at the outlet of the nozzle, and L is the total length between the two nozzles. It is found that the simulation result is essentially consistent with experimental result. This validates the model. Moreover, the particle concentration drops sharply with the particle being away from the outlet of nozzle along x-axial direction because of dispersion, but it increases to some degree near to the center and appears with a smaller peak around the center.
ð14Þ 4. Results and discussion
Moreover, the particle collision only leads to a change in the velocity of a particle but no change in the position. 3. Model validation Model validation is conducted by comparing with the experimental results obtained by our colleague [25] using two opposed jets. Fig. 2 shows the schematic diagram of the experimental apparatus
Fig. 3. Simulation domain and grid meshing (another nozzle, inlet #2, is located on the opposed side).
4.1. Snapshots of particle motion The following part of work is targeted to model in the impinging zone of a commercial scale OMB gasifier. Fig. 6 shows the sketch of a commercial scale OMB gasifier, which was surrounded by four opposed burners that are horizontally mounted. The relevant parameters used for calculation are listed in Table 2 with reference to the parameters used practically, although few of them are changed slightly for simplicity. The simulation domain is meshed into about 1 160,000 hexahedral cells. No collision between particles and the
Fig. 4. Comparison of experimental image and snapshot of simulation results of particle flow. (a): experimental image; (b): simulation results.
C. Li et al. / Powder Technology 225 (2012) 118–123
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Table 2 Parameters used in simulation of particle flow behavior in impinging zone. Parameter
Value
Parameter
Value
Temperature Pressure Gas component Gas flow rate Particle flow rate Inlet gas velocity Inlet particle velocity Particle shape
1523 (K) 5.0 (MPa) H2, CO, CO2, H2O 8.95 × 4 (kg·s− 1) 3.60 × 4 (kg·s− 1) 130 (m·s− 1) 15 (m·s− 1) Sphere
Particle diameter Particle density Particle spray angle Particle tracked Time step Restitution coefficient Friction coefficient
120 (μm) 1500 (kg·m− 3) 20° ~ 700,000 5 × 10− 5 (s) 0.9 0.2
flow. In view of the YZ plane, more particles move axially at a higher speed after leaving the central region of the impinging zone in the case of having collision than in the case of no collision due to the concentrated particles caused by the particle collision in this region. 4.2. Particle concentration distribution Particle concentration distribution is important for gasification because high particle concentration readily causes the cohesion and agglomeration of char and ash particles. Fig. 8 shows the profiles of particle concentration along the axes of opposed burner (direction x) and gasifier (direction z). From direction x, the particle concentration has a maximum of 120 kg·m − 3 at the center for the case of collision, which is larger than that at the outlets of the burners. A similar result is observed for the case of no collision, but the particle concentration at the center is smaller than that at the outlets of the burners. From direction z, a sharp decrease of the particle concentration occurs as particles are away from the cross section of the burners (z = 0). 4.3. Particle velocity Fig. 5. Comparison of dimensionless particle concentration profile of experimental and simulation results. (□): experimental results; (■): simulation results. (a): case 1; (b): case 2.
wall of reactor is involved in calculation because it can be almost neglected in this zone. Fig. 7 shows the snapshot of particle motion on horizontal plane (i.e., XY plane) and axial plane (i.e., YZ plane), in which the result obtained with no consideration of collision is also presented for contrast. In both cases, particle is accelerated by the gas stream after introduced into the gasifier. The velocity of particle increased near to the central region of the jet. In view of the XY plane, particles are dispersed in a larger region for the case of no collision because particles pneumatically move to and fro more freely across the central region of the impinging zone, whereas for the case of having collision, collision strongly resists the particles motion in the central region, resulting in a concentration of particles in this region. Also, the collision leads to a slight enhancement in particle dispersion in the jet
Fig. 6. Sketch of a commercial scale OMB gasifier and grid meshing of impinging zone.
Fig. 9 shows the mean horizontal velocity of particle along the axis of burner (direction x) and the mean axial velocity along the axis of gasifier (direction z). In both directions of x and z, only slight differences occur between the case of no collision and the case of having collision. From direction x, it is clearly seen that the mean horizontal velocity of particles increases from 40 m·s − 1 at the outlets of the burners to about 100 m·s − 1, and then sharply decreases near to a central region because of the drag force and particle collision. Comparison of the gas velocity with the mean horizontal velocity of particle exhibits a reduction followed by an increase in their difference with the particles approaching the center. As an advantage of impinging flow, the increment of relative velocity between gas and solid phases enhances inter-phase mass and heat transfer in central region of impinging zone. From direction z, both the gas velocity and
Fig. 7. Snapshot of particle motion in horizontal plane (XY plane) and axial plane (YZ plane). (a): no collision; (b): with collision.
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C. Li et al. / Powder Technology 225 (2012) 118–123
Fig. 8. Particle concentration distribution profiles. (—): no collision; (―): with collision. (a): along the axis of burner; (b): along the axis of gasifier.
Fig. 9. Mean particle velocity profiles. (■): particle velocity (no collision); (□): particle velocity (with collision); (—): gas velocity (no collision); (―): gas velocity (with collision). (a): mean horizontal velocity along axis of burner; (b): mean axial velocity along axis of gasifier.
the mean axial velocity of particle at the center (z = 0) are about zero; with the particle being distant from the center, the gas velocity becomes larger than the mean axial velocity of the particle.
I1, I2 J k m1, m2 mp n n N p P^ ij P^ i
5. Conclusion A 3D model of the impinging zone of a commercial scale OMB gasifier has been established and validated to study particle flow behavior. The following conclusions have been drawn: (1) interparticle collision strongly resists the particles motion, concentrates particles in the central region of impinging zone and slightly enhances particle dispersion in the jet flow; (2) in the center of impinging zone, collision increases the chance of particle cohesion and agglomeration by resulting a high particle concentration region, in which, particle concentration is larger than that at the outlets of burners; (3) high relative velocity between gas–solid phases caused by the rapid deceleration of particles is observed near the center of impinging zone, which improves the performance of gasifier in terms of heat and mass transfer. Nomenclature Cd drag coefficient dp diameter of particle e coefficient of restitution fd vector of drag fx total force of other forces g vector of gravitational acceleration
r1, r2 Rep t Δt T up ug v1, v2 v1(0), v2(0)
moment of inertia of particles 1 and 2 vector of collision impulse turbulence kinetic energy; index of candidate particle mass of particles 1 and 2 mass of particle unit normal vector of contact point of particle collision number density of real particle in cell number of track particle in cell pressure of gas phase collision probability of particles i and j total probability of particle i and other particles in a single time step radius of particles 1 and 2 Reynolds number of particle unit tangential vector of contact point of particle collision time step of DSMC method vector of torque of particle vector of particle velocity vector of gas velocity velocity vector of particles 1 and 2 after collision velocity vector of particles 1 and 2 before collision
Greek letters χ equation coefficient of drag force ε voidage; dissipation rate of turbulence kinetic energy μ viscosity of gas
C. Li et al. / Powder Technology 225 (2012) 118–123
ρp density of particle ρg density of gas ωg vector of angular velocity of gas ωp vector of angular velocity of particle ω1, ω2 angular velocity vector of particles 1 and 2 after collision ω1(0), ω2(0) angular velocity vector of particles 1 and 2 before collision ξ coefficient of friction
Subscript g gas phase p particle phase i, j index of particle, index of component of gas velocity
Acknowledgments This work is supported by the National High Technology Research and Development Program of China (no. 2008AA050301), the National Basic Research Program of China (no. 2010CB227000) and the Fundamental Research Funds for the Ministry of Education (no. WB1014037). Thanks are due to our colleagues Prof. Haifeng Liu and Dr. Zhigang Sun for providing experimental data in model validation. We also wish to acknowledge Prof. Jie Wang for his revision of this paper. References [1] Institute of Clean Coal Technology, Commercial Plants of OMB Coal–Water Slurry Gasification, 2011 http://icct.ecust.edu.cn. [2] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 (1979) 47–65. [3] Y. Tsuji, T. Kawaguchi, T. Tanaka, Discrete particle simulation of two dimensional fluidized bed, Powder Technology 77 (1993) 79–87. [4] B.H. Xu, A.B. Yu, Numerical simulation of the gas–solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics, Chemical Engineering Science 52 (1997) 2785–2809. [5] N. Gui, J.R. Fan, Numerical study of particle mixing in bubbling fluidized beds based on fractal and entropy analysis, Chemical Engineering Science 66 (2011) 2788–2797. [6] K.W. Chu, A.B. Yu, Numerical simulation of complex particle–fluid flows, Powder Technology 179 (2008) 104–114.
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[7] C.S. Campbell, C.E. Brennen, Computer simulations of granular shear flows, Journal of Fluid Mechanics 151 (1985) 167–188. [8] Y. Tsuji, Y. Morikawa, T. Tanaka, et al., Numerical simulation of gas–solid twophase flow in a two-dimensional horizontal channel, International Journal of Multiphase Flow 13 (1987) 671–684. [9] B.P.B. Hoomans, J.A.M. Kuipers, W.J. Briels, et al., Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: a hard-sphere approach, Chemical Engineering Science 51 (1996) 99–118. [10] J. Ouyang, J.H. Li, Discrete simulations of heterogeneous structure and dynamic behavior in gas–solid fluidization, Chemical Engineering Science 54 (1999) 5427–5440. [11] E. Helland, R. Occelli, L. Tadrist, Computational study of fluctuating motions and cluster structures in gas–particle flows, International Journal of Multiphase Flow 28 (2002) 199–223. [12] H.L. Lu, S.Y. Wang, Y.H. Zhao, et al., Prediction of particle motion in a twodimensional bubbling fluidized bed using discrete hard-sphere model, Chemical Engineering Science 60 (2005) 3217–3231. [13] S.Y. Wang, X. Li, H.L. Lu, et al., DSMC prediction of granular temperatures of clusters and dispersed particles in a riser, Powder Technology 192 (2009) 225–233. [14] Y. Tsuji, T. Tanaka, S. Yonemura, Cluster patterns in circulating fluidized beds predicted by numerical simulation (discrete particle model versus two-fluid model), Powder Technology 95 (1998) 254–264. [15] S.Y. Wang, H.P. Liu, H.L. Lu, et al., Flow behavior of clusters in a riser simulated by direct simulation Monte Carlo method, Chemical Engineering Journal 106 (2005) 197–211. [16] A. Kitron, T. Elperin, A. Tamir, Monte Carlo simulation of gas–solids suspension flows in impinging streams reactors, International Journal of Multiphase Flow 16 (1990) 1–17. [17] Q.H. Guo, Q.F. Liang, J.J. Ni, et al., Markov chain model of residence time distribution in a new type entrained-flow gasifier, Chemical Engineering and Processing 47 (2008) 2061–2065. [18] J.J. Ni, Q.F. Liang, Q.H. Guo, et al., Stochastic modeling of the particle residence time distribution in an opposed multi-burner gasifier, Chemical Engineering and Technology 31 (2008) 1487–1493. [19] J.J. Ni, Q.F. Liang, Z.J. Zhou, et al., Numerical and experimental investigations on gas– particle flow behaviors of the Opposed Multi-Burner gasifier, Energy Conversion and Management 50 (2009) 3035–3044. [20] T.H. Shih, W.W. Liou, A. Shabbir, et al., A new k-ε eddy viscosity model for high Reynolds number turbulent flows, Computers & Fluids 24 (1995) 227–238. [21] Z H Dai, The studies of the multiphase reaction flow in entrained flow gasifier and the coal gasification process system, PhD thesis. 2008. [22] B.H. Xu, A.B. Yu, S.J. Chew, et al., Numerical simulation of the gas–solid flow in a bed with lateral gas blasting, Powder Technology 109 (2000) 13–26. [23] E. Loth, Numerical approaches for motion of dispersed particles, droplets and bubbles, Progress in Energy and Combustion Science 26 (2000) 161–223. [24] R. Illner, H. Neunzert, On simulation methods for the Boltzmann equation, Transport Theory and Statistical Physics 16 (1987) 141–154. [25] Z G Sun, Study on multiphase opposed jets and dense gas–solid two-phase coaxial jets, PhD Thesis. 2009.
Contents lists available at SciVerse ScienceDirect
Powder Technology journal homepage: www.elsevier.com/locate/powtec
3D numerical study of particle flow behavior in the impinging zone of an Opposed Multi-Burner gasifier Chao Li, Zhenghua Dai ⁎, Weifeng Li, Jianliang Xu, Fuchen Wang Key Laboratory of Coal Gasification of Ministry of Education, East China University of Science and Technology, Shanghai 200237, PR China
a r t i c l e
i n f o
Article history: Received 30 November 2011 Received in revised form 21 February 2012 Accepted 26 March 2012 Available online 1 April 2012 Keywords: Coal gasifier Impinging flow Hard-sphere model DSMC method Particle flow behavior
a b s t r a c t A 3D model of the impinging zone of a commercial scale Opposed Multi-Burner (OMB) gasifier is established in this article, in which the gas flow and particle motion are simulated by the Eulerian–Lagrangian approach, and the gas turbulence is calculated using the realizable k-ε model. The particle collision is determined by the Direct Simulation Monte Carlo (DSMC) method and the modified Nanbu method, with the presumption that the particle is hard sphere. The model is validated with reference to the experimental result obtained on a laboratory device equipped with two opposed jets. The model reveals the concentration and mean velocity profiles of particles in the impinging zone. It is quantitatively observed that particles move at an accelerated speed from the jet and then at a rapidly decelerated speed near to the central impinging zone; particles are concentrated in the central impinging zone due to collision. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Entrained flow coal gasification is an advanced gasification technology, which has widely found commercial applications for the production of coal-based chemicals such as methanol, ammonia, DME, and hydrogen. OMB gasifier is an entrained flow gasifier developed in China, and it has been successfully applied in several plants [1]. One of the patented designs of OMB gasifier is to strengthen the mass and heat transfer and prolong the particle residence time via the formation of an impinging flow field. This study is focused on a model study of particle flow behavior in the impinging zone. There are two classical methods in simulation of gas–particle flow, the Eulerian–Eulerian method which treats particles as a continuous phase and the Eulerian–Lagrangian which tracks individual particles. The latter method is used in this study to calculate the gas turbulence and the motion of individual particle. Considering that inter-particle collision is an important physical phenomenon in the impinging zone of an OMB gasifier, we combine the Eulerian–Lagrangian method with particle collision in this study. Particle collision is generally simulated by the soft-sphere model and the hard-sphere model in terms of interactions between particles. Cundall and Strack [2] proposed a discrete element method (DEM) in treatment of soft-sphere collision in 1979. Tsuji [3] and Xu
⁎ Corresponding author. Tel.: + 86 021 64250784; fax: + 86 021 64251312. E-mail address: [email protected] (Z. Dai). 0032-5910/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2012.03.044
[4] simulated a fluidized bed using the soft-sphere model. In recent years, DEM has been used frequently by coupling with LES [5] or commercial CFD software [6]. With respect to the hard-sphere model, inter-particle collision is treated generally as a binary and instantaneous process and simulated by solving the conservation equation of momentum. Many researches verified the application of the hardsphere model to Couette shear-flow [7], horizontal channel [8] and gas-fluidized bed [9,10]. The hard-sphere model has also widely been used to investigate the formation and structure of bubbles and clusters in fluidized bed [11,12] and riser [13]. Direct Simulation Monte Carlo (DSMC) method is commonly used to deal with the hard-sphere collision. In DSMC method, a particle collision probability is assessed from a representative amount of tracked particles instead of all particles; therefore, it is advantageous in saving computing time. Tsuji [14] and Wang [15] coupled the DSMC method and the hard-sphere model to study the clustering behavior in a circulating fluidized bed and the gas-particle flow behavior in a riser, respectively. Many studies have been reported on the impinging flow. An early study by Kitron [16] used a stochastic model based on Boltzmann transport equation for description of gas–solid impinging streams. Guo [17] and Ni [18] in our research group developed a Markov chain stochastic model to predict the residence time distribution of gas and particle in an OMB gasifier. Ni [19] further studied the flow behavior of particle and slag in an OMB gasifier by treating particles as liquid drops. In this work, emphasis is placed on the modeling of inter-particle collision and interaction between solid particle and fluid associated with the gas–solid impinging flow in a commercial OMB gasifier by coupling the DSMC method with the hard-sphere model.
C. Li et al. / Powder Technology 225 (2012) 118–123
2. Model description Realistic processes in an entrained flow gasifier are very complex, which include multiphase flow, heterogeneous and homogeneous reactions, and heat transfer. For simplifying the issue, the following assumptions are made in the modeling: (1) no chemical reactions and heat transfer are considered; (2) particle is treated as rigid hard sphere; (3) particle collision is treated as a binary and instantaneous contact; (4) effects of particle rotation on fluid field are neglected. 2.1. Fluid motion Fluid motion is solved by the Reynolds Averaged Navier–Stokes (RANS) equations. The unknown terms of Reynolds stresses in RANS are dealt with using the eddy viscosity model based on Boussinesq hypothesis. The impinging flow is calculated using the typical Realizable k-ε model [20,21]: ∂ ρg kt ∂t ∂ ρg ε t ∂t
þ
þ
∂ ρg kt ug;j ∂xi ∂ ρg εt ug;j ∂xj
¼
" # ∂ μ ∂kt μg þ t þ Gk −ρg εt þ Gb −Y M σ k ∂xj ∂xi þ Sk ð1Þ
∂ ¼ ∂xj
"
# μ t ∂εt μg þ σ ε ∂xj 2
εt ð2Þ þ ρg C 1 Sεt −ρg C 2 pffiffiffiffiffiffiffi þ Sε kt þ vεt η , and η is a where σk = 1.0, σε = 1.2, C2 = 1.9, C 1 ¼ max 0:43; ηþ5 function of k, ε and gradient of velocity. 2.2. Particle suspension Particle motion is solved by the hard-sphere model, in which total particle motion is divided into two independent motions, suspension and collision. Suspension is determined by Newton's law expressed by the equation of translational motion of a particle: mp
dup ¼ f d þ V p g ρp −ρg þ f x dt
119
In addition, taking into account the effect of fluid motion on particle angular velocity, the following torque equation of a particle is adopted [23]: 3 1=2 T ¼ 2μ g dp ωg =2−ωp 1 þ 0:20Rep
20bRep b1000:
2.3. Particle collision Following assumptions are made to solve the particle collision in dispersed gas–particle flow: (1) inter-particle collision is assumed to be binary and instantaneous; (2) during collision process, the distance between the centers of particles is sum of their radius from the negligible deformation of particles; (3) the friction between particles obeys Coulomb's friction law when they keep sliding; (4) sliding occurs no longer once it stops. Fig. 1 illustrates the collision of two hard spheres and some relevant physical variables. Postcollision velocities of particles are derived from the following impulse equations [14]: ð0Þ m1 v1 −v1 ¼ J
ð9aÞ
ð0Þ m2 v2 −v2 ¼ −J
ð9bÞ
ð0Þ I1 ω1 −ω1 ¼ r 1 n J
ð10aÞ
ð0Þ I2 ω2 −ω2 ¼ r 2 n J:
ð10bÞ
The solution of Eqs. (9a), (9b), (10a) and (10b) differs depending on whether two particles keep sliding during collision process or not. 2.4. DSMC method Since there are an enormous amount of particles involved in our simulation, the computation of a common hard-sphere model for particle collision is time-consuming. The DSMC method is therefore coupled with the hard-sphere model to solve this problem. In this
ð3Þ
where fd is the drag force, g represents the acceleration of gravity, and fx means the additional forces. Virtual mass force and pressure gradient force are incorporated in this model. Drag force on particle is calculated according to the following equation [22]: fd ¼
1 2 2 −ðχþ1Þ dp C d ρg πug −up ug −up ε ε 8
ð4Þ
where ε is the voidage of cell where particle is located. The drag coefficient Cd of a particle and the equation coefficient χ are obtained from the equations [22]: Cd ¼
4:8 0:63 þ 0:5 Rep
!2 ð5Þ
2 3 1:5− log10 Rep 7 6 χ ¼ 3:7−0:65 exp4− 5 2
2
ð6Þ
where Rep is the particle Reynolds number, which is defined as:
Rep ¼
ερg dp ug −up μg
:
ð8Þ
ð7Þ Fig. 1. Collision of two hard spheres.
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C. Li et al. / Powder Technology 225 (2012) 118–123 Table 1 Parameters used for model validation.
Fig. 2. Schematic diagram of two opposed jets experiment.
method, a certain number of tracked particles are taken as representatives. The collision probability between tracked particles i and j in a time step is calculated by [14]: di þ dj 2 n P^ ij ¼ π Gij ⋅Δt : N 2
N X
P^ ij :
ð12Þ
j¼1
1 Here, the collision probability is limited to 0 b P^ ij b , so that the N total collision probability of particle i is a value between 0 and 1. The modified Nanbu method [24] is used to decide which particles collide. In this method, every tracked particle in cell is assumed to have the same probability to collide with particle i, so one particle taken randomly can be used as a candidate, expressed as: h i ^ þ 1 k≠i: k ¼ int RN
ð13Þ
From Eqs. (11) and (13), the occurrence of particle collision is made sure if the following criterion is satisfied: ^ > k −P^ : R ik N
Value
Parameter
Value
Temperature Pressure Gas component Length of nozzle Inner diameter of nozzle Distance between nozzles Inlet gas velocity
298 (K) 1 (atm) Air 20 (mm) 8 (mm) 140 (mm)
Mass ratio of gas–solid Particle shape Particle density Particle spray angle Time step Restitution coefficient
1 Sphere 2500 (kg·m− 3) 14° 5 × 10− 5 (s) 0.9
100 (m·s− 1) Friction coefficient
0.2
Parameter
Case 1
Case 2
Particle diameter Particle tracked Inlet particle velocity
77 (μm) ~ 13,400 25 (m·s− 1)
33 (μm) ~ 18,000 55 (m·s− 1)
ð11Þ
Thus, the total collision probability of particle i with all other particles in a time step is given: P^ i ¼
Parameter
consisting of two opposed nozzles. The inner diameter of either nozzle was 8 mm. The distance between two nozzles was 140 mm. Particles were conveyed by air into the nozzles. Fig. 3 shows the calculation domain and the grid meshing with about 60,000 hexahedral cells. Table 1 lists the parameters used for the model validation. Fig. 4 shows the image of particle flow taken by a high-speed camera and the simulation results, both obtained under the same conditions (case 1 in Table 1). Fig. 5 shows the experimentally measured and simulated profiles of the particle concentration along the axis of the nozzle, in which C0 is the particle concentration at the outlet of the nozzle, and L is the total length between the two nozzles. It is found that the simulation result is essentially consistent with experimental result. This validates the model. Moreover, the particle concentration drops sharply with the particle being away from the outlet of nozzle along x-axial direction because of dispersion, but it increases to some degree near to the center and appears with a smaller peak around the center.
ð14Þ 4. Results and discussion
Moreover, the particle collision only leads to a change in the velocity of a particle but no change in the position. 3. Model validation Model validation is conducted by comparing with the experimental results obtained by our colleague [25] using two opposed jets. Fig. 2 shows the schematic diagram of the experimental apparatus
Fig. 3. Simulation domain and grid meshing (another nozzle, inlet #2, is located on the opposed side).
4.1. Snapshots of particle motion The following part of work is targeted to model in the impinging zone of a commercial scale OMB gasifier. Fig. 6 shows the sketch of a commercial scale OMB gasifier, which was surrounded by four opposed burners that are horizontally mounted. The relevant parameters used for calculation are listed in Table 2 with reference to the parameters used practically, although few of them are changed slightly for simplicity. The simulation domain is meshed into about 1 160,000 hexahedral cells. No collision between particles and the
Fig. 4. Comparison of experimental image and snapshot of simulation results of particle flow. (a): experimental image; (b): simulation results.
C. Li et al. / Powder Technology 225 (2012) 118–123
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Table 2 Parameters used in simulation of particle flow behavior in impinging zone. Parameter
Value
Parameter
Value
Temperature Pressure Gas component Gas flow rate Particle flow rate Inlet gas velocity Inlet particle velocity Particle shape
1523 (K) 5.0 (MPa) H2, CO, CO2, H2O 8.95 × 4 (kg·s− 1) 3.60 × 4 (kg·s− 1) 130 (m·s− 1) 15 (m·s− 1) Sphere
Particle diameter Particle density Particle spray angle Particle tracked Time step Restitution coefficient Friction coefficient
120 (μm) 1500 (kg·m− 3) 20° ~ 700,000 5 × 10− 5 (s) 0.9 0.2
flow. In view of the YZ plane, more particles move axially at a higher speed after leaving the central region of the impinging zone in the case of having collision than in the case of no collision due to the concentrated particles caused by the particle collision in this region. 4.2. Particle concentration distribution Particle concentration distribution is important for gasification because high particle concentration readily causes the cohesion and agglomeration of char and ash particles. Fig. 8 shows the profiles of particle concentration along the axes of opposed burner (direction x) and gasifier (direction z). From direction x, the particle concentration has a maximum of 120 kg·m − 3 at the center for the case of collision, which is larger than that at the outlets of the burners. A similar result is observed for the case of no collision, but the particle concentration at the center is smaller than that at the outlets of the burners. From direction z, a sharp decrease of the particle concentration occurs as particles are away from the cross section of the burners (z = 0). 4.3. Particle velocity Fig. 5. Comparison of dimensionless particle concentration profile of experimental and simulation results. (□): experimental results; (■): simulation results. (a): case 1; (b): case 2.
wall of reactor is involved in calculation because it can be almost neglected in this zone. Fig. 7 shows the snapshot of particle motion on horizontal plane (i.e., XY plane) and axial plane (i.e., YZ plane), in which the result obtained with no consideration of collision is also presented for contrast. In both cases, particle is accelerated by the gas stream after introduced into the gasifier. The velocity of particle increased near to the central region of the jet. In view of the XY plane, particles are dispersed in a larger region for the case of no collision because particles pneumatically move to and fro more freely across the central region of the impinging zone, whereas for the case of having collision, collision strongly resists the particles motion in the central region, resulting in a concentration of particles in this region. Also, the collision leads to a slight enhancement in particle dispersion in the jet
Fig. 6. Sketch of a commercial scale OMB gasifier and grid meshing of impinging zone.
Fig. 9 shows the mean horizontal velocity of particle along the axis of burner (direction x) and the mean axial velocity along the axis of gasifier (direction z). In both directions of x and z, only slight differences occur between the case of no collision and the case of having collision. From direction x, it is clearly seen that the mean horizontal velocity of particles increases from 40 m·s − 1 at the outlets of the burners to about 100 m·s − 1, and then sharply decreases near to a central region because of the drag force and particle collision. Comparison of the gas velocity with the mean horizontal velocity of particle exhibits a reduction followed by an increase in their difference with the particles approaching the center. As an advantage of impinging flow, the increment of relative velocity between gas and solid phases enhances inter-phase mass and heat transfer in central region of impinging zone. From direction z, both the gas velocity and
Fig. 7. Snapshot of particle motion in horizontal plane (XY plane) and axial plane (YZ plane). (a): no collision; (b): with collision.
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Fig. 8. Particle concentration distribution profiles. (—): no collision; (―): with collision. (a): along the axis of burner; (b): along the axis of gasifier.
Fig. 9. Mean particle velocity profiles. (■): particle velocity (no collision); (□): particle velocity (with collision); (—): gas velocity (no collision); (―): gas velocity (with collision). (a): mean horizontal velocity along axis of burner; (b): mean axial velocity along axis of gasifier.
the mean axial velocity of particle at the center (z = 0) are about zero; with the particle being distant from the center, the gas velocity becomes larger than the mean axial velocity of the particle.
I1, I2 J k m1, m2 mp n n N p P^ ij P^ i
5. Conclusion A 3D model of the impinging zone of a commercial scale OMB gasifier has been established and validated to study particle flow behavior. The following conclusions have been drawn: (1) interparticle collision strongly resists the particles motion, concentrates particles in the central region of impinging zone and slightly enhances particle dispersion in the jet flow; (2) in the center of impinging zone, collision increases the chance of particle cohesion and agglomeration by resulting a high particle concentration region, in which, particle concentration is larger than that at the outlets of burners; (3) high relative velocity between gas–solid phases caused by the rapid deceleration of particles is observed near the center of impinging zone, which improves the performance of gasifier in terms of heat and mass transfer. Nomenclature Cd drag coefficient dp diameter of particle e coefficient of restitution fd vector of drag fx total force of other forces g vector of gravitational acceleration
r1, r2 Rep t Δt T up ug v1, v2 v1(0), v2(0)
moment of inertia of particles 1 and 2 vector of collision impulse turbulence kinetic energy; index of candidate particle mass of particles 1 and 2 mass of particle unit normal vector of contact point of particle collision number density of real particle in cell number of track particle in cell pressure of gas phase collision probability of particles i and j total probability of particle i and other particles in a single time step radius of particles 1 and 2 Reynolds number of particle unit tangential vector of contact point of particle collision time step of DSMC method vector of torque of particle vector of particle velocity vector of gas velocity velocity vector of particles 1 and 2 after collision velocity vector of particles 1 and 2 before collision
Greek letters χ equation coefficient of drag force ε voidage; dissipation rate of turbulence kinetic energy μ viscosity of gas
C. Li et al. / Powder Technology 225 (2012) 118–123
ρp density of particle ρg density of gas ωg vector of angular velocity of gas ωp vector of angular velocity of particle ω1, ω2 angular velocity vector of particles 1 and 2 after collision ω1(0), ω2(0) angular velocity vector of particles 1 and 2 before collision ξ coefficient of friction
Subscript g gas phase p particle phase i, j index of particle, index of component of gas velocity
Acknowledgments This work is supported by the National High Technology Research and Development Program of China (no. 2008AA050301), the National Basic Research Program of China (no. 2010CB227000) and the Fundamental Research Funds for the Ministry of Education (no. WB1014037). Thanks are due to our colleagues Prof. Haifeng Liu and Dr. Zhigang Sun for providing experimental data in model validation. We also wish to acknowledge Prof. Jie Wang for his revision of this paper. References [1] Institute of Clean Coal Technology, Commercial Plants of OMB Coal–Water Slurry Gasification, 2011 http://icct.ecust.edu.cn. [2] P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies, Geotechnique 29 (1979) 47–65. [3] Y. Tsuji, T. Kawaguchi, T. Tanaka, Discrete particle simulation of two dimensional fluidized bed, Powder Technology 77 (1993) 79–87. [4] B.H. Xu, A.B. Yu, Numerical simulation of the gas–solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics, Chemical Engineering Science 52 (1997) 2785–2809. [5] N. Gui, J.R. Fan, Numerical study of particle mixing in bubbling fluidized beds based on fractal and entropy analysis, Chemical Engineering Science 66 (2011) 2788–2797. [6] K.W. Chu, A.B. Yu, Numerical simulation of complex particle–fluid flows, Powder Technology 179 (2008) 104–114.
123
[7] C.S. Campbell, C.E. Brennen, Computer simulations of granular shear flows, Journal of Fluid Mechanics 151 (1985) 167–188. [8] Y. Tsuji, Y. Morikawa, T. Tanaka, et al., Numerical simulation of gas–solid twophase flow in a two-dimensional horizontal channel, International Journal of Multiphase Flow 13 (1987) 671–684. [9] B.P.B. Hoomans, J.A.M. Kuipers, W.J. Briels, et al., Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: a hard-sphere approach, Chemical Engineering Science 51 (1996) 99–118. [10] J. Ouyang, J.H. Li, Discrete simulations of heterogeneous structure and dynamic behavior in gas–solid fluidization, Chemical Engineering Science 54 (1999) 5427–5440. [11] E. Helland, R. Occelli, L. Tadrist, Computational study of fluctuating motions and cluster structures in gas–particle flows, International Journal of Multiphase Flow 28 (2002) 199–223. [12] H.L. Lu, S.Y. Wang, Y.H. Zhao, et al., Prediction of particle motion in a twodimensional bubbling fluidized bed using discrete hard-sphere model, Chemical Engineering Science 60 (2005) 3217–3231. [13] S.Y. Wang, X. Li, H.L. Lu, et al., DSMC prediction of granular temperatures of clusters and dispersed particles in a riser, Powder Technology 192 (2009) 225–233. [14] Y. Tsuji, T. Tanaka, S. Yonemura, Cluster patterns in circulating fluidized beds predicted by numerical simulation (discrete particle model versus two-fluid model), Powder Technology 95 (1998) 254–264. [15] S.Y. Wang, H.P. Liu, H.L. Lu, et al., Flow behavior of clusters in a riser simulated by direct simulation Monte Carlo method, Chemical Engineering Journal 106 (2005) 197–211. [16] A. Kitron, T. Elperin, A. Tamir, Monte Carlo simulation of gas–solids suspension flows in impinging streams reactors, International Journal of Multiphase Flow 16 (1990) 1–17. [17] Q.H. Guo, Q.F. Liang, J.J. Ni, et al., Markov chain model of residence time distribution in a new type entrained-flow gasifier, Chemical Engineering and Processing 47 (2008) 2061–2065. [18] J.J. Ni, Q.F. Liang, Q.H. Guo, et al., Stochastic modeling of the particle residence time distribution in an opposed multi-burner gasifier, Chemical Engineering and Technology 31 (2008) 1487–1493. [19] J.J. Ni, Q.F. Liang, Z.J. Zhou, et al., Numerical and experimental investigations on gas– particle flow behaviors of the Opposed Multi-Burner gasifier, Energy Conversion and Management 50 (2009) 3035–3044. [20] T.H. Shih, W.W. Liou, A. Shabbir, et al., A new k-ε eddy viscosity model for high Reynolds number turbulent flows, Computers & Fluids 24 (1995) 227–238. [21] Z H Dai, The studies of the multiphase reaction flow in entrained flow gasifier and the coal gasification process system, PhD thesis. 2008. [22] B.H. Xu, A.B. Yu, S.J. Chew, et al., Numerical simulation of the gas–solid flow in a bed with lateral gas blasting, Powder Technology 109 (2000) 13–26. [23] E. Loth, Numerical approaches for motion of dispersed particles, droplets and bubbles, Progress in Energy and Combustion Science 26 (2000) 161–223. [24] R. Illner, H. Neunzert, On simulation methods for the Boltzmann equation, Transport Theory and Statistical Physics 16 (1987) 141–154. [25] Z G Sun, Study on multiphase opposed jets and dense gas–solid two-phase coaxial jets, PhD Thesis. 2009.