- Email: [email protected]
Application of a dual-grid multiscale CFD-DEM coupling method to model the raceway dynamics in packed bed reactors
Accepted Manuscript Application of a Dual-Grid Multiscale CFD-DEM Coupling Method to Model the Raceway Dynamics in Packed Bed Reactors Edder Rabadan Santana, Gabriele Pozzetti, Bernhard Peters PII: DOI: Reference:
S0009-2509(19)30390-2 https://doi.org/10.1016/j.ces.2019.04.025 CES 14936
To appear in:
Chemical Engineering Science
Received Date: Revised Date: Accepted Date:
17 January 2019 30 March 2019 13 April 2019
Please cite this article as: E.R. Santana, G. Pozzetti, B. Peters, Application of a Dual-Grid Multiscale CFD-DEM Coupling Method to Model the Raceway Dynamics in Packed Bed Reactors, Chemical Engineering Science (2019), doi: https://doi.org/10.1016/j.ces.2019.04.025
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Application of a Dual-Grid Multiscale CFD-DEM Coupling Method to Model the Raceway Dynamics in Packed Bed Reactors Edder Rabadan Santana1,∗, Gabriele Pozzetti1 , Bernhard Peters1 a
Universit du Luxembourg, 6 Avenue de la Fonte, L-4364, Esch-sur-Alzette, Luxembourg
1. ABSTRACT A CFD-DEM coupling model with dual-grid multiscale approach is used to model high-speed injection into a packed bed reactor. The present CFD-DEM coupling uses a separate coarse grid for the discrete phase (DEM model) and a fine grid for the continuum phase (CFD model). This CFD-DEM approach allows high grid resolution for solving the gas phase and preserving the accuracy of the CFD solution at higher Reynolds numbers. The dual-grid multiscale approach is used to model high-speed lateral gas injection in a two-dimensional blast furnace reactor. Blast velocities up to 230 m s−1 , as in real blast furnace operation, are used to investigate the formation and dynamics of the raceway inside the reactor. The effect of the blast velocity on the size and shape of the raceway was investigated using different jet velocities. It is shown how the use of an adequate grid resolution for the continuum phase is needed in order to achieve a grid independent solution and how it influenced on the discrete solution. It was observed that the variation of the blast velocity directly influenced on the size and shape of the cavity. However, the particles and the flow showed the same pattern and behavior at the different investigated blast velocities, with a proportional scaling according to the gas velocity. At the investigated blast velocities the raceway formed very rapidly showing a transition period with lateral periodic oscillations before stabilization was observed. 2. Introduction Lateral air injection into particle beds is widely used in many industrial applications found in the processing, petroleum, and metallurgical industries [1]. When air is injected laterally into a particle bed it causes the formation of a granular circulation region within the bed. The fast stream of blast air entering into the packed bed forces the particles to displace back and upwards forming a circulation region around the injected gas. This is a accompanied by a characteristic high void fraction region around the gas inlet. This blast air induced cavities are termed raceways. Lateral gas injection is preferred in several industrial applications since it increases the interaction between the solid and gas phases, and thus, resulting in a more efficient heat and mass transfer within the reactor. One of the main applications of lateral gas injection is found in blast furnace reactors. Blast furnace ∗ Principal
corresponding author. Email: [email protected] Email address: [email protected] (Edder Rabadan Santana)
Preprint submitted to Elsevier
March 30, 2019
Figure 1: (a) General scheme of a blast furnace [4]; (b) the raceway [5].
reactors are widely used in the ironmaking industry and are one of the largest operational reactors. Typical dimensions of BF are about 40 m high and 15 m wide for a production over 10 000 t/d of pig iron with blast injection velocities larger than 230 m s−1 [2]. One of the main challenges to model and predict the raceway formation in a blast furnace is associated with the very high velocity of the blast gas. The blast gas is injected at very high speed and, as a result, it strongly interacts with the particulate phase affecting the heat and mass transfer and chemical processes occurring in the reactor [2, 3]. An schematic diagram of a blast furnace and the raceway is presented in Fig. 1. Currently, two models are used to investigate the formation of the raceway: i) continuum approach and ii) combined Euler-Lagrange method. In the first approach the geometry/shape of the raceway is fixed and the bed of coke is considered to be a porous media [6, 7, 8]. In such continuum approach the Navier-Stokes equations accounting for porosity are solved over the entire domain [9, 10]. This method is restricted to the dynamics of the gas flow and therefore the formation of the raceway cannot be investigated. As a result, to determine the boundaries of the raceway becomes a complicated task. The second approach, combined Euler-Lagrange method, is used to simulate the interactions between the particulate and the gas phase. In this approach, the solid phase is considered as a discrete part while the flow in the void space between the particles is treated as a continuum phase. The discrete part is solved via the Discrete Element Method (DEM) while the continuum phase is modeled by the Computational Fluid Dynamics (CFD) approach. This coupled CFD-DEM approach, also referred to as a Combined Continuum and Discrete Model (CCDM) [11] allows to study the interaction between particle-fluid without loosing the particles’ information. The capability of the CFD-DEM approach to model the interaction fluid-particle makes it the selected approach to model blast furnace reactors. Since the stability of the blast furnace operation is related to the motion of coke particles in and around the raceway, several studies have been conducted using a coupled CFD-DEM method to investigate its formation. Xu et al. [12] used a coupled CFD-DEM model to simulate lateral gas injection into a twodimensional bed. The particle circulation and the raceway formation were found to be formed near the blast injection point. The effect of the blasting velocity on the behavior of the bed showed to be a critical 2
factor. However, only blasting velocities up 50 m s−1 were investigated. Umekage et al. [13] used DEM for the calculation of the interaction forces between coke particles together with a Finite Difference Method for computing the Navier-Stokes equations to account for the interaction terms between gas and particles. The raceway formation was investigated using the dimensions of an actual commercial blast furnace. However, the computational domain was reduced to a slice of the cylindrical part of the furnace. The study reported an unstable and unsteady motion of the raceway with periodical changes affecting its size and shape. Similar to [12], the raceway formation was investigated only for a maximum blasting velocity of 50 m s−1 . Measurements of the raceway depth in an actual blast furnace have been conducted by Matsui et al. [14] using a microwave reflection gunned through the tuyere. In the study, the measurements of the raceway depth were correlated with the depth of the tap hole. It was assumed that the tap hole depth varies according to the changes of the raceway depth. It was found that the blast velocity and blast flow rate highly affected the size of the raceway and thus the tap hole depth. An increase in the raceway depth resulted in an increase on the tap hole depth. An unsteady behavior of the raceway was also observed. Raceway formation using non-spherical particles was also studied by Adema et al. [15]. In [15] a slice of an experimental reduced-scale geometry reactor with blast velocity of 20 m s−1 was used to investigate the effect of non-spherical particles. It was shown that the blast velocity affects the raceway dynamics especially with non-spherical particles. Similarly, Hilton et al. [16] focused on the investigation of the raceway formation using different particle shapes. The raceway formation and particularly the dynamics of the bed were influenced not only by the shape of the particles but especially by the gas velocity. It was found that the raceway can be formed at lower blast velocities in the presence of non-spherical particles. For spherical particles, larger velocities were required to form a raceway. Inlet gas velocities up to 120 m s−1 were investigated. Three-dimensional geometries, either using a slot or a slice of a cylindric reactor, have been also used to investigate the raceway formation [17, 18, 19, 20]. In such configurations periodic boundary conditions have been used to mimic the circular shape of the reactor [21]. The slice configuration has been reported to provide better description of the particle flow behavior [17], when compared with experimental data from small lab-scale experimental blast furnaces [22, 23]. All these studies have only investigated maximum blast velocities up to 50 m s−1 . Studies including heat and mass transfer between the gas and particulate phases showed that the blast velocity affects the heat exchange and chemical reactions between the gas and particles, thus directly impacting on the raceway formation. Nogami et al. [24] investigated the raceway formation in a small scale blast furnace model considering heat exchange and chemical reactions. It was shown that heat and mass transfer in the reactor and the shape and size of the raceway were highly affected by the blast velocity. Rabadan et al. [25] investigated the raceway formation including chemical reactions in the raceway and the mass reduction of coke particles due to gasification. It was concluded that the raceway dynamics and heat and mass transfer processes were dependent on the blast velocity. However, the study was limited to a maximum blasting velocity of 20 m s−1 . This poses a complex scenario since high blast velocities need to be used first to proper represent the raceway dynamics and account for heat exchange and chemical processes under realistic furnace operating conditions. On the other hand, the use of high gas velocities poses some difficulties when using CFD-DEM coupling methods, mainly due to the restriction of the grid size given by the particulate phase. When the size of the particulate phase is large, such as coke in the blast furnace, this generally results in coarse meshes. A coarse mesh may not necessary have the most 3
appropriate grid resolution to capture the flow physics originated by large blast velocities. In this paper, we propose to address this issue by adopting a dual-grid multiscale approach as proposed in [38]. We show how this approach allows to treat higher blast velocities by ensuring grid-independent solutions for the fluid flow. Furthermore, we show how the usage of a coarser mesh can indeed affects the prediction capability of the raceway shape and dynamics introducing purely numerical error that can and should be avoided. We consider this is a fundamental consistency check that has to be performed before treating more complex physics of the raceway formation such as inter-phase heat transfer and complex combustion models. The following study is structured as follows, first the numerical methodology of the employed CFDDEM dual-grid approach is described in Sec. 3. The general expressions for the CFD and DEM methods are presented within the context of the used in-house solver. Afterwards, the two-dimensional simulation domain for the case study and boundary conditions are presented. The formation of the raceway is investigated by 2D simulations using three different blast velocities. The results and discussion of the findings are presented in Sec. 4. Finally conclusion are drawn in Sec. 5. 3. Model and Numerical Methods The proposed numerical approach is based on the Discrete Element Method (DEM) to model the dynamics of granular matter and the Eulerian Computational Fluid Dynamics (CFD) model for the fluid phase. A coupling between both modeling approaches allows tracking the individual motion of the particles and the dynamics of the fluid phase. For that purposes, the XDEM solver [26] has been coupled with the open source libraries OpenFoam-Extend 3.2. In the following the main governing equations and closure models used in the computational modeling are briefly described. Further detailed information regarding to the XDEM numerical framework can be found in [27]. 3.1. Discrete Element Method In this work, the dynamic module of the XDEM platform [28] was used to evolve a set of discrete entities moving in the presence of a gas phase flow. We here briefly describe the equations solved by this module. The positions and orientations of the particles are updated at every time-step according to d2 xi dt2 d2 Ii 2 φi dt
mi
=
Fcoll + Fdrag + Fg
(1)
=
Mcoll + Mext
(2)
where xi are the positions, mi the masses, and φ the orientations of the entities. The term Fcoll indicates the force arising from collisions Fcoll =
X
Fij (xj , uj , φj , ωj )
(3)
i6=j
with uj the velocity of particle j, and ω the angular velocity. In this contribution, the interactions between particle-particle and particle-wall F~ij are calculated by the non-linear model of Hertz-Mindlin [29, 30]. The term Mcoll represents the torque acting on the particle due to collisions X Mcoll = Mij (xj , uj , φj , ωj ) i6=j
4
(4)
with Mij being the torque imposed from particle j to particle i. The term Fdrag takes into account the force rising from the interaction with the fluid, and Fg corresponds to the gravitational force. For Fdrag a semi empirical model was chosen in the form: Fdrag = β(uf − up )
(5)
β = β(uf − up , ρf , ρp , dp , Ap , µf , )
(6)
with uf , up being the fluid and particle velocity, respectively; ρf , ρp the respective densities, dp , Ap the particle characteristic length and area, µf the fluid viscosity, and the porosity, defined as the ratio between the volume occupied by the fluid and the total volume of the CFD cell. For the sake of simplicity, to simulate the interactions occurring between the porous bed and the fluid β was taken as described in [31]. 3.2. Computational Fluid Dynamics (CFD) In order to better assess the capability of the numerical scheme to tackle high-velocity scenarios, we here focus on the representation of the high-velocity jet and its dynamic interaction with the particle phase. For this reason, we currently neglect the heat-up and combustion process that would make the analysis of the results more delicate. For the fluid solution, we therefore refer to an unsteady incompressible flow through a porous media with forcing terms arising from the particle phase, as described in [32, 34]. Defining the porosity field as =
Vg Vs =1− Vcell Vcell
(7)
the system must fulfill the Navier-Stokes equations in the form, ∇ · uf = −
∂ ∂t
∂uf + ∇ · (uf uf ) = −∇p + TD + Fb + Fdd ∂t TD = ∇ · µf ∇uf + ∇T uf
(8) (9) (10)
with uf being the fluid velocity, p the fluid pressure, µf the fluid viscosity, TD the contribution from the viscous stress tensor, Fb a generic body force, Ffdd the drag force density, that is the counterpart of Fdrag , which is here treated with the semi-implicit algorithm proposed in [35]. The closure problem of the RANS set of equations is solved using the standard k − model [36, 37] with k being the turbulence kinetic energy and the turbulence dissipation rate. Initial values of k and are estimated using a turbulence intensity I = 3 % and turbulence length scale l = 0.1 m. 3.3. Dual-Grid Multiscale CFD-DEM coupling The dual-grid multiscale approach for CFD-DEM coupling was first introduced in [32], and later used in several recent works [33, 38, 39, 40]. As recalled in [38], in this kind of coupling two length-scales are identified within the particle-laden flow: a bulk scale, and a fluid fine-scale. As shown in Fig. 2, this approach adopts a coarse and uniform CFD grid to resolve the fluid-particle interactions at the bulk scale, and a fine CFD grid to solve the fluid flow equations at the fine-scale. An interpolation strategy ensures the communication between the two grids i.e. the two length scales. The dual-grid multiscale approach was originally introduced 5
with reference to the coupling between DEM and VOF, as the fine resolution required by the VOF scheme was found to induce a marked separation between the two scales. In the present contribution, this coupling strategy is applied to a monophase CFD configuration coupled with a particle phase. From a software point of view, the implementation of the dual-grid multiscale approach requires the presence of two computational grids and a routine to interpolate between them, as depicted in Fig. 2. The choice of the coarse grid depends on the selected averaging operation. It is recommended to use a discretization at least 2 to 3 times larger than the particle diameter. The fine grid should be identified as the one at which the results can be considered grid-independent. An illustration of this is provided in section 3.4. In [32] it was underlined how the coarse and fine CFD grids should be independent from each other in order to allow maximum flexibility of the approach. For instance, while an uniform grid is optimal when performing a Eulerian-Lagrangian coupling, a nonuniform, locally refined, computational grid provides several advantages for the solution of complex flows. For this reason the two grids will not, in general, be nested. In this contribution, the inter-scale interpolation is performed with the library described in [38] that allows an efficient parallel implementation of the method.
Figure 2: Dual-Grid multiscale coupling scheme to resolve high velocity gas phase with particle interaction.
3.4. Simulation Domain and Boundary Conditions A two-dimensional rectangular geometry is used to represent a generic reactor. The dimensions of the computational domain are showed in Fig. 3. The computational domain is bounded by two side-walls, an inlet, an outer wall, an outlet (top wall) and a bottom wall. The inlet is located at the outer wall at 0.5 m from the bottom wall. The height of the inlet is 0.03 m. The packed bed is represented by an ensemble of particles with an inhomogeneous void space between them due to their packing. Each 3D sphere has a diameter of 20 mm ± 1 mm and is considered to be a coke particle. The coke particles are at rest and randomly settled at the bottom of the domain. This was done in a preliminary simulation by placing the particles at the center of the domain and let them fall until they reached their random and steady position. 6
The computational domain contains 6520 coke particles. Coke properties are shown in Table 1. The coke particles located in front of the gas injection were removed to avoid numerical instabilities at the initial time step. A nominal blast injection velocity corresponding to a real furnace operation of u = 230 m s−1 is used to investigate the dynamics of the raceway. In order to study the effect of the injection velocity on the prediction of the size and shape of the raceway two additional inlet velocities were also investigated, u = 200 m s−1 and u = 180 m s−1 , Inlet velocities are imposed at the inlet as a Dirichlet boundary condition. The injected air is considered to be in a standard mass fraction composition, YO2 = 0.21 and YN2 = 0.79. For simplicity the inflow profile is considered to be uniform. Side-walls are modeled assuming viscous nonslip conditions with an adaptive wall-functions [37]. At the outlet (top wall),the conservative variables are simply extrapolated from the inside domain. A time step of 1 × 10−6 is used to advance the solution of both discrete and continuum phases. The flow energy equation is not solved, accordingly the temperature of the injected gas is not considered. Table 1: Mechanical properties of coke.
Density [kg/m3 ] Restitution coefficient [-] Rolling friction coefficient [-]
1050 0.6 2.5
Young modulus [GPa] Poisson ratio [-] Friction coefficient [-]
1.0 0.3 1
The two-dimensional computational domain shown in Fig. 3 was spatially discretized using a structured multi-block technique. To asses a grid independent solution three different structured grids with different levels of refinement were investigated: a coarse grid with 3200 cells, a medium grid with 25600 cells, and a fine grid with 102400 cells. Despite that the structure of the coupling does not require an uniform discretization strategy, in this study we adopted an uniformly discretized fine grid for the fluid domain to ensure the results are not effected by the local structure of the refinement. However, local refinement could be an effective technique to reduce computational costs. Table 2 summarizes the grid resolutions used in the present study and the investigated inlet velocities of the blast injection. Figure 4 shows the CFD fine grid imposed on the DEM coarse grid. Convergence was monitored by the decrease of the right-hand side residuals of the Navier-Stokes equations averaged over all cells at each iteration as well as by the evolution of the kinetic energy and the velocity along the inlet central line. All computations achieved a converged solution with residuals dropping between 4 and 6 orders of magnitude. Figure 5a shows the flow field kinetic energy from the initial time t = 0 s until t = 10 s, for the three grid levels of refinement. Figure 5b plots the distribution of the gas velocity along the horizontal axis starting at the center of the inlet and extending until the end of the domain at t = 10 s. Variations lower than 5% were observed between the medium and fine solutions. Table 2: Grid resolutions and blast inlet velocities
Grid size [cells]
Coarse (CFD-DEM coupling) 3200
Inlet velocity [m/s]
230 7
Medium
Fine
25600
102400
200
180
a) Dimensions of the generic reactor.
b) Coarse grid resolution (CFD-DEM coupling).
Figure 3: Dimensions of the computational domain and coarse grid resolution.
Figure 4: Fine grid and particles: (a) complete computational domain, (b) grid refinement around particles, (c) grid resolution around a particle.
Accordingly, for the present study the solution was considered as a grid independent and the fine grid is used for all further calculations. As originally mentioned in [32], the dual-grid multiscale approach is more complex than a standard 8
a) Normalized kinetic energy of the flow.
b) Inlet velocity.
Figure 5: Computations with the three grid levels of refinement: a) normalized kinetic energy of the flow and b) inlet velocity of the incoming jet along the length of the reactor.
CFD-DEM coupling since introduces the additional computational cost associated to the finer CFD grid. Nevertheless, as often the case, the CFD part only represents an aspect of the overall CFD-DEM computational load and, therefore, the global cost of the simulation is only partially affected by the increase of the CFD grid resolution. On the other hand, as proposed in [38], using a dual-grid multiscale approach allows to obtain a significantly better parallel performance compared to the single scale CFD-DEM coupling. This two aspects are shown in Fig. 6, where the computational time of the simulation of the first second is compared by using the dual-grid and the single-grid approach. Similarly to what was observed, with reference to a different test case in [38], the dual-grid approach is slower than the single-grid approach in sequential execution (in this case it takes roughly 50% more time). Nevertheless, the scalability properties of the dual-grid approach are significantly better than the single scale CFD-DEM coupling. In particular when using more than 2 computing cores the dual-grid approach is faster than the single-grid, despite of using a refined grid.
Figure 6: Execution time as a function of the number of computing cores.
4. Results and Discussion 4.1. Single-grid vs dual-grid approach The first set of results shows the predictions obtained using a monoscale and a multiscale approach for a nominal operating blast velocity of u = 230 m s−1 . Accordingly, the inlet velocity u = 230 m s−1 was used 9
in all three grid levels (coarse, medium and fine) to investigate the effect of the mesh refinement on the solution. Since most significant differences were observed between the coarse and fine grids, the following discussion focuses on the findings between these two grids. Figure 7 shows the instantaneous flow field velocity at t = 10 s for the coarse and fine grids. When using the coarse grid the flow field shows a sharp decrease of the inflow velocity (Fig. 7a), even though an inlet velocity of u = 230 m s−1 was prescribed at the inlet boundary. Here, the jet velocity instantly decreases from u = 230 m s−1 at the inlet to u = 134 m s−1 when entering the reactor. This sharp decrease occurs due to the large grid size and increased discretization error, rather than to the loss of gas momentum penetrating the bed. On the other hand, employing the dual-grid approach (with the fine grid resolution for the CFD phase) Fig. 7b shows that the computed flow field velocity conserves the initial momentum prescribed at the inlet boundary and the jet penetrates the bed at the prescribed inlet velocity, u = 230 m s−1 . Figure 7 shows that in both, coarse and fine grids, the gas speed decreases as the gas penetrates into the coke bed and bends upwards towards the top. As the jet penetrates the bed it pushes forward the particles creating a void region adjacent to the inflow.
Figure 8
shows the predicted raceway cavity and the corresponding particle velocities computed with the coarse and fine grids at t = 10 s. The solid flow patterns are assessed through the particle’s velocities. Even though the same inlet velocity is prescribed in both cases (u = 230 m s−1 ), some differences are observed, primarily on the size of the raceway and on the velocity of the particles. A larger raceway size and particle velocities are predicted with the fine grid, mainly due to better transfer of momentum from the gas to the solid phase. A maximum particles’ velocities up to 10 m s−1 are observed for the fine grid, where as for the coarse grid the maximum computed velocity is not larger than 7 m s−1 . In both grid resolutions, particles with larger velocities are located directly in front of the jet injection. This is the result of the jet penetrating the bed and transferring its momentum to the particles located along its trajectory. The particles in the periphery
a) CFD-DEM coupling single grid
b) Dual-grid approach
Figure 7: Instantaneous flow velocity distribution at t = 10 s. Gas injection velocity u = 230 m s−1
10
of the cavity show lower velocities. A stagnant zone with particles showing static behavior is recognized in both cases. For the coarse grid solution the stagnant zone is formed at the bottom part below the injection and towards the end wall, forming an inversed L-shape. Where as for the fine grid solution, the stagnant zone is mainly observed at the bottom part. Even though both solutions predicted a stagnant zone at the bottom, the stagnant zone is larger when computing on the coarse grid. In order to visualize and to asses the different dimensions of the raceway, Fig. 9 shows a highlighted contour of the raceway for each grid resolution. The predicted balloon-shape of the raceway qualitatively agrees with experimental data and observations made in lab-scale blast furnace [24, 13]. To asses the dimension of the raceway, Fig. 10 simultaneously compare both raceway sizes together with its maximum length (L) and hight (h), the subindex c and f stands for the coarse and fine grid dimensions, respectively. From Fig. 10 it is possible to observe the different size predicted with the coarse (CFD-DEM coupling) and fine (CFD) grids. The calculated raceway dimensions with the coarse and fine grids are: Lc = 670 mm, hc = 570 mm and Lf = 880 mm, hf = 820 mm.
This indicates an approximately 25% under-prediction of
the raceway size by using the mono-scale approach where only a coarse grid is used for solving both DEM and CFD methods. The main reason of the observed difference on the size lies in the inaccurate prediction of the inflow velocity with the coarse grid. Due to the large grid cell size, the high inlet velocity is not properly resolved, resulting in lower gas momentum and smaller gas penetration into the bed. On the other hand, the multiscale approach using the fine grid for the CFD solution is able to better capture the blast injection and the incoming jet penetrating through the bed. This jet stream with higher kinetic energy fluidizes the complete bed forcing all particles to move and cover the complete confined space. Conversely, in the coarse grid solution (standard CFD-DEM coupling) the blast jet is not strong enough to fluidize the complete bed.
a) CFD-DEM coupling single grid
d) Dual-grid approach
Figure 8: Instantaneous particle velocity distribution using a standard CFD-DEM coupling (coarse grid: bulk scale, particulate phase) and the dual-grid approach with a fine grid for the fluid scale, at t = 10 s. Gas injection velocity u = 230 m s−1
. 11
a) CFD-DEM coupling single grid
b) Dual-grid approach
Figure 9: Predicted raceway shape with the CFD-DEM standard coupling (coarse grid) and the dual-grid approach (fine grid for the continuum phase).
Figure 10: Definition of the raceway dimensions.
The jet penetration is shorter and after l = 900 mm the particles show a static behavior. However, both solutions coincide on the gas speed decreasing as the jet penetrates the bed and transfers its momentum to the particulate phase. Since more accurate representation of the flow field and solid flow of particles is achieved with the multiscale approach, hereafter all presented results corresponds to the solution computed using this method. 4.2. Raceway formation —nominal inlet velocity Figure 11a shows the velocity distribution for the flow field and the particles at t = 10 s at the nominal inlet velocity u = 230 m s−1 . The streamlines colored by the gas velocity showing the flow path through the coke bed are depicted in Fig. 11b. After gas injection, the coke particles located in front and around the inlet are pushed inwards by the stream traveling to the center. As the jet continues penetrating into the 12
a)
b)
Figure 11: Flow field and particle velocity distributions: a) gas-particulate phase; b) fluid velocity distribution with streamlines. Gas injection velocity u = 230 m s−1 , t = 10 s.
packed bed, particles are further displaced upwards and in the direction to the end wall, leaving a cavity at the center occupied only by the incoming air. Due to the displacement of these particles, and the jet penetrating deeper into the packed bed, more coke particles descend directly to the raceway region to fill the free space. Since air is continuously supplied, the particles descending in front of the jet are trapped by the incoming stream and carried into the raceway region where they move upwards following the gas stream deflected by the surrounding packed bed. The air speed is large enough to penetrate deep through the bed until approximately 900 mm and push the particles further towards the top and end wall. The air injected into the packed bed generates two main recirculating regions with particles moving around. These two main regions, above and below the inlet, can be appreciated with the streamlines showed in Fig. 11b. The main recirculation region is located above the inlet and at the center of the reactor. This region is confined to the raceway cavity where the air, due to the densely pack, is deflected and recirculates towards the center of the domain. The raceway is characterized by a central high void region with a counter-clockwise circulation area. The second recirculation region is located below the inlet where air circulates clock-wise with particles entrained in the gas flow forming an elliptical circulation region. Consistent with experimental observations [41], two anti-directional vortex of solid flows can co-exist inside the raceway. The lower circulation zone appears to be smaller than the upper one, similar flow-particle circulation behavior has been also observed numerically in [16]. Figure 12 shows instantaneous distribution of the coke particles within the bed. The instantaneous snapshots show the evolution of the raceway from t = 0 s until t = 10 s. At the initial time, t = 0 s, the bed is completely static. Right after gas injection stars, t = 0.2 s, the jet rapidly penetrates into the bed pushing the particles inwards and creating a void space. The initial formed cavity growths and elongates until the characteristic balloon-shape is observed, t = 1.3 s. After t = 1.3 s the shape of the raceway is well formed and its boundaries are well defined. The raceway cavity is rapidly formed, however, 13
a) t = 0 s
b) t = 0.20 s
c) t = 0.30 s
d) t = 1.3 s
a) t = 1.7 s
b) t = 2.5 s
c) t = 2.8 s
d) t = 3 s
a) t = 4 s
b) t = 6 s
c) t = 8 s
d) t = 10 s
Figure 12: Dynamic evolution of the raceway at different time instants after gas injection. Gas injection velocity u = 230 m s−1
an alternating lateral oscillations are observed from t = 1.3 s until t = 3 s. This lapse of time corresponds to a transition period where the size of the raceway changes in a periodic contracting and expanding pattern. This transition pattern and period has also been observed in [14]. This transient period provides the necessary time for the jet to fully penetrate and partly fluidized the bed. Before the raceway reaches a stable condition some exchange of particles between the raceway and the surrounding bed is observed. Here, the particles falling back into the gas stream are entrained in the jet and partially dividing the raceway in two cavities, t = 2.5 s. A macroscopically stable raceway is formed after about t = 4 s. The ability to quickly stabilized the raceway boundary has also been reported during experimental studies [42, 43]. After the raceway is stabilized t > 3 s, its size remains nearly unchanged. The corresponding instantaneous velocity field is shown in Fig. 13. Due to the fine grid resolution used for solving the fluid phase in the dual-grid approach the 14
a) t = 0 s
b) t = 3 s
c) t = 5 s
d) t = 10 s
Figure 13: Instantaneous velocity distribution. Gas injection velocity u = 230 m s−1
incoming jet conserves its initial momentum. As it penetrates into the bed the jet velocity decreases. The flow velocity in the bed remains nearly constant after the raceway cavity has stabilized, t > 3 s. The raceway boundary can also been identified by the contour of the flow velocity and its different intensity. 4.3. Influence of the blast velocity on the raceway formation In this subsection the dynamics of the raceway formation at different blasting velocities is investigated. Accordingly, two different velocities were used to further investigate the influence of the injection velocity on the raceway formation: u = 180 m s−1 and u = 200 m s−1 . Figure 14 shows the particle’s velocity distribution for a blast injection u = 200 m s−1 . The case with blast velocity u = 200 m s−1 showed the same pattern and behavior as the case with u = 230 m s−1 . The raceway was rapidly formed right after the jet penetrated the bed. Similarly, a transition period with alternating lateral oscillations was present until the raceway reached a stable condition with a nearly constant boundary at t > 3 s. Recirculation regions were observed at the same locations as with u = 230 m s−1 . However, the maximum particle’s velocity was 8.2 m s−1 and the jet penetration was about 0.66 m, since the magnitude of the blast velocity was 30 m s−1 lower. This resulted in slighter smaller size of the raceway cavity. Notably was that by decreasing the magnitude of the blast velocity by 30 m s−1 , the jet was not able to completely fluidized the bed and filled the confined space with coke particles.
a) t = 0 s
b) t = 2 s
c) t = 3 s
d) t = 4 s
Figure 14: Dynamic evolution of the raceway at different time instants after gas injection. Gas injection velocity u = 200 m s−1
15
a) t = 0 s
b) t = 2 s
c) t = 3 s
d) t = 4 s
Figure 15: Dynamic evolution of the raceway at different time instants after gas injection. Gas injection velocity u = 180 m s−1
To investigate further the dependency of the size of the raceway on the blast velocity, a case with a jet injection of u = 180 m s−1 was computed. Figure 15 shows the particle’s velocity distribution. In general, the same pattern for the particles and flow behavior was observed as in the two previous cases. Similarly, a rapid formation of the raceway accompanied with a short transition period with lateral oscillation before stabilization was observed. The stabilization of the raceway was equally achieved after t > 3 s. However, the lower magnitude of the blast injection resulted in smaller cavity size and shorter jet penetration. Similarly, due to the lower blast velocity, the momentum of the incoming gas was not able to completely fluidized the bed and fill the confined space in the reactor. Differently from the two previous cases was that the jet, after the raceway stabilized, did not penetrate or deflect towards the bottom part, it remained nearly straight until it was deflected only upwards. This produced a flat-bottom shape of the raceway, when compared to the one formed in the other two cases. This can be appreciated in the Fig. 16 where the particle’s velocity distribution and raceway cavity are shown for the three investigated blast velocities. The jet penetration for the three blast velocities is plotted in Fig. 17. The jet penetration depth in Fig. 17 represents the axial
a) 180 m s−1
b) 200 m s−1
c) 230 m s−1
Figure 16: Instantaneous particle velocity distribution for different inlet gas velocities at t = 4 s.
16
Figure 17: Jet penetration at different blast velocities.
length, from the inlet towards the reactor, where the gas velocity is approximately 2 % of the initial blast velocity. The penetration depth shows a nearly lineal correlation with the magnitude of the blast velocity. 5. Conclusions This work intended to present an efficient CFD-DEM coupling strategy to model high-speed gas velocities. The used CFD-DEM coupling method employs a dual-grid multiscale approach where the discrete and continuous phases are solved in a separate grids, allowing the use of a refine meshes for the continuous phase and to achieve a grid independent solution. This coupling technique is integrated into the well validated inhouse solver eXtended Discrete Element Method (XDEM). Accordingly, the CFD-DEM dual-grid multiscale approach was used to simulate lateral gas injection in packed bed reactors. A generic blast furnace reactor, typically used in the iron-making industry, was selected as a test case due to its high operational blast velocities. In particular, the effect of high-speed injection (blast injection) on the formation of the raceway was investigated. In order to investigate the dependency of the size of the raceway on the blast velocity, three different injection velocities were investigated 230 m s−1 , 200 m s−1 and 180 m s−1 . A great dependency of the size of the raceway on the injection velocity was observed. It was observed that the effect of varying the blast velocity on the raceway formation affected the size of the cavity, however the pattern of the particles and the behavior of the gas flow remained nearly the same. In all investigated cases the raceway cavity was formed very rapidly with presence of a transition period with periodic contracting and expanding patterns before it stabilized. Acknowledgments The authors would like to thank to the Luxembourg National Research Fund (FNR) for the financial support of this project and to the HPC Cluster facilities of the University of Luxembourg. References [1] Pilcher K.A and Bridgwater J. (1990) Pinnig in a rectangular moving bed reactor with gas cross-flow. Chemical Engineering Science 45, 2535-2542. Doi: 10.1016/0009-2509(90)80139-6 [2] Adema, A. (2014) DEM-CFD Modelling of the ironmaking blast furnace. PhD Thesis TU Delft, The Netherlands. [3] Peters, B., Dziugys, A., and Navakas, R. (2012) A shrinking model for combustion/gasification of char based on transport and reaction time scales. Mechanika 18(2), 177-185. Doi: 10.5755/j01.mech.18.2.1564
17
[4] Geerdes, M., Toxopeus, H., van der Vliet, C., Chaigneau, R., and Vander, T. (2009) Modern Blast Furnace Ironmaking: An Introduction. IOS Press. [5] Mathieson, J. G., Truelove, J. S., and Rogers, H. (2005) Toward an understanding of coal combustion in blast furnace tuyere injection. Fuel 84(10), 1229-1237. Doi: 10.1016/j.fuel.2004.06.036 [6] Shen, Y., Yu, A., Austin, P., and Zulli, P. (2012) Modelling in-furnace phenomena of pulverized coal injection in ironmaking blast furnace: effect of coke bed porosities Minerals Engineering 33, 54-65. Doi: 10.1016/j.mineng.2011.10.014 [7] Li, Y., Zhang, X., Zhang, J., Zhou, J., and Yan, H. (2014) Numerical simulation and optimization of pulverized coal injection with enriched oxygen into blast furnace Applied Thermal Engineering 67, 72-79. Doi: 10.1016/j.applthermaleng.2014.02.062 [8] Shen, Y.S., Guo, B.Y., Yu, A.B., Austin, P.R., and Zulli, P. (2011) Three-dimensional modelling of in-furnace coal/coke combustion in a blast furnace Fuel 90, 728-738. Doi: 10.1016/j.fuel.2010.08.030 [9] Gidaspow, D. (1994) Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic Press 9780122824708 ISBN: 9780122824708 [10] Kuipers, J. A. M., and van Swaaij W. P. M. (1997) Application of Computational Fluid Dynamics to Chemical Reaction Engineering. Reviews in Chemical Engineering. Doi: 10.1515/REVCE.1997.13.3.1 [11] Xu, B. H., and Yu, A. B. (1998) Comments on the paper numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics - reply. Chemical Engineering Science. 53(14), 2645-2646. Doi: 10.1016/S0009-2509(98)00085-2 [12] Xu, B.H., Yu, A.B., Chew, S.J., and Zulli P. (2000) Numerical simulation of the gas-solid flow in a bed with lateral gas blasting. Powder Technology 109, 13-26. Doi: 10.1016/S0032-5910(99)00223-5 [13] Umekage, T., Yuu, S., and Kadowaki, M. (2005) Numerical simulation of blast furnace raceway depth and height, and effect of wall cohesive matter on gas and coke particle flows ISIJ International 45(10), 14161425. Doi: 10.2355/isijinternational.45.1416 [14] Matsui, Y., Tadai, R., Ito, K., Matsuo, T., Nagai N., and Imai T. (2005) Stabilization of tapping hole length by controlling blast furnace raceway depth SIJ International 45(10), 14391444. Doi: 10.2355/isijinternational.45.1439 [15] Adema, A.T., Yang Y., and Boom, R. (2010) Discrete element method-computational fluid dynamic simulation of the materials flow in an iron-making blast furnace ISIJ International 50(7), 954961. Doi: 10.2355/isijinternational.50.954 [16] Hilton, J. E. and Cleary, P. W. (2012) Raceway formation in laterally gas-driven particle beds. Chemical Engineering Science 80, 306-316. Doi: 10.1016/j.ces.2012.06.044 [17] ang, W.J., Zhou, Z,Y, and Yu, A.B. (2015) Discrete particle simulation of solid flow in a three-dimensional blast furnace sector model Chemical Engineering Journal 278, 339352. Doi: 10.1016/j.cej.2014.11.144 [18] Tang, H., Meng, F., Zhao, Z., and Zhang, L. (2015) Modeling coal/coke combustion behavior in tuyere-raceway-dripping zone in blast furnace Procedia Engineering 102, 1583-1592. Doi: 10.1016/j.proeng.2015.01.294 [19] Umekage, T., Kadowaki, M., and Yuu, S. (2007) Numerical simulation of effect of tuyere angle and wall scaffolding on unsteady gas and particle flows including raceway in blast furnace. ISIJ International 47(5), 659-668. Doi: 10.2355/isijinternational.47.659 [20] Natsui, S., Nogami, H., Ueda, S., Kano, J. Inoue, R., and Ariyama, T. (2011) Simultaneous three-dimensional analysis of gassolid flow in blast furnace by combining discrete element method and computational fluid dynamics. ISIJ International 51(1), 41-50. Doi: 10.2355/isijinternational.51.41 [21] Yang, W., Zhou, Z., Pinson, D., and Yu, A. (2014) Periodic boundary conditions for discrete element method simulation of particle flow in cylindrical vessels. Ind. Eng. Chem. Res. 53(19), 82458256. Doi: 10.1021/ie404158e [22] Wright, B., Zulli, P., Zhou, Z.Y., and Yu, A.B. (2011) Gas-solid flow in an ironmaking blast furnace I: physical modelling. Powder Technology 208, 8697. Doi: 10.1016/j.powtec.2010.12.006 [23] Ho, C.K., Chen, Y.M., Lin, C.I., Jeng, J.R. (1990) On the flow of granular material in a model blast furnace. Powder Technology 63, 1321. Doi: 10.1016/0032-5910(90)80003-H [24] Nogami, H., Yamaoka, H., and Takatani, K. (2004) Raceway Design for the Innovative Blast Furnace. ISIJ International 44, 2150-2158. Doi: 10.2355/isijinternational.44.2150 [25] Rabadan-Santana, E., and Peters, B. (2016) An Euler-Lagrange Approach to Model the Dynamics of Particulate Phase Exposed to Hot Gas Injection into Packed Bed Reactors. Proceedings of the International Conference on Computational Methods 3, 294-306. ISSN 2374-3948 [26] Peters, B. (2013) The extended discrete element method XDEM for multi-physics applications. Scholarly Journal of Engineering Research 2(1), 1-20. [27] Samiei, K., Peters, B., Bolten, M., and Frommer, A. (2013) Assessment of the potentials of implicit integration method in discrete element modelling of granular matter. Computers and Chemical Engineering 49, 183-193. Doi: 10.1016/j.compchemeng.2012.10.009 [28] Peters, B., Baniasadi, Me., Baniasadi, Ma., Besseron, X., Donoso, A., Mohseni, M., and Pozzetti, G. (2018) XDEM multiphysics and multi-scale simulation technology: Review of DEMCFD coupling, methodology and engineering applications. Particuology, in press. Doi: 10.1016/j.partic.2018.04.005 [29] Mindlin, R. (1949) Compliance of elastic bodies in contact. Appl. Mech 16, 259-268. [30] Hertz, H. (1881) Ueber die beruehrung elastischer koerper. J. Reine Angew. Math 92 156-171. [31] Ergun, S., Orning, A. (1949) Fluid flow through randomly packed columns and fluidized beds. Industrial & Engineering Chemistry 41 (6), 11791184. Doi: 10.1021/ie50474a011 [32] Pozzetti, G., and Peters, B. (2018) A multiscale DEM-VOF method for the simulation of three-phase flows. International Journal of Multiphase Flow 99 186-204 . Doi: 10.1016/j.ijmultiphaseflow.2017.10.008 [33] Pozzetti, G., and Peters, B. (2017) On the choice of a phase interchange strategy for a multiscale DEM-VOF method. AIP Conference Proceedings 1863, 1800002. Doi: 10.1063/1.4992362
18
[34] Pozzetti, G., Besseron, X., Rousset, A., and Peters, B. (2018) A co-located partitions strategy for parallel CFD-DEM couplings. Advanced Powder Technology Doi: 10.1016/j.apt.2018.08.025 [35] Xiao, H., and Sun, J. (2011) Algorithms in a Robust Hybrid CFD-DEM Solver for Particle-Laden Flows. Communication Computer Physics 9(2), 297-323. Doi: 10.4208/cicp.260509.230210a [36] Launder, B.E., and Spalding, D.B., (1974) The numerical computation of turbulent flows. Computer methods in applied mechanics and engineering 3(2), 269-289. Doi: 10.1016/0045-7825(74)90029-2 [37] OpenFoam User Guide, V.2.0.0. (2011) [38] Pozzetti, G., Jasak, H., Besseron, X., Rousset, A. and Peters, B. (2019) A parallel dual-grid multiscale approach to CFD–DEM couplings. Journal of Computational Physics 378, 708-722. Doi: 10.1016/j.jcp.2018.11.030 [39] Pozzetti, G., and Peters, B. (2017) Flow characteristics of metallic powder grains for additive manufacturing. EPJ Web Conf. 140, 13001. Doi: 10.1051/epjconf/201714013001 [40] Pozzetti, G., and Peters, B. (2018) A numerical approach for the evaluation of particle-induced erosion in an abrasive waterjet focusing tube. Powder Technology, 333, 229-242. Doi: 10.1016/j.powtec.2018.04.006 [41] Takahashi, H., Komatsu, N. (1993) Cold Model Study on Burden Behaviour in the Lower Part of Blast Furnace. ISIJ International 33(6), 655-663. Doi: 10.2355/isijinternational.33.655 [42] Elliott, J.F., Buchanan, R.A., and Wagstaff, J.B. (1952) Physical Conditions in the Combustion and Smelting Zones of a Blast Furnace The Journal of The Minerals, Metals and Materials Society (TMS) 4(7), 709717. Doi: 10.1007/BF03398129 [43] Flint, P.J., and Burgess, J.M. (1992) A fundamental study of raceway size in two dimensions. Metallurgical and Materials Transactions B 23(3), 267283. Doi: 10.1007/BF02656282
19
A Coupled CFD-DEM Method for Modeling High-Speed Gas Injection in Packed Bed Reactors
Edder Rabadan Santana, Gabriele Pozzetti, Bernhard Peters University of Luxembourg, 6 Avenue de la Fonte, 4364, Esch-sur-Alzette, Luxembourg
HIGHLIGHTS
CFD-DEM coupling with dual-grid multiscale approach to model a high-speed gas phase.
Dual-grid multiscale approach suitable for modeling high flow velocities in a CFD-DEM coupling.
High-speed lateral blast injection is well captured using the dual-grid multiscale approach.
Raceway forms rapidly after a transition period with lateral periodic oscillations.
Size and shape of the raceway are directly influenced by the blast velocity.
S0009-2509(19)30390-2 https://doi.org/10.1016/j.ces.2019.04.025 CES 14936
To appear in:
Chemical Engineering Science
Received Date: Revised Date: Accepted Date:
17 January 2019 30 March 2019 13 April 2019
Please cite this article as: E.R. Santana, G. Pozzetti, B. Peters, Application of a Dual-Grid Multiscale CFD-DEM Coupling Method to Model the Raceway Dynamics in Packed Bed Reactors, Chemical Engineering Science (2019), doi: https://doi.org/10.1016/j.ces.2019.04.025
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Application of a Dual-Grid Multiscale CFD-DEM Coupling Method to Model the Raceway Dynamics in Packed Bed Reactors Edder Rabadan Santana1,∗, Gabriele Pozzetti1 , Bernhard Peters1 a
Universit du Luxembourg, 6 Avenue de la Fonte, L-4364, Esch-sur-Alzette, Luxembourg
1. ABSTRACT A CFD-DEM coupling model with dual-grid multiscale approach is used to model high-speed injection into a packed bed reactor. The present CFD-DEM coupling uses a separate coarse grid for the discrete phase (DEM model) and a fine grid for the continuum phase (CFD model). This CFD-DEM approach allows high grid resolution for solving the gas phase and preserving the accuracy of the CFD solution at higher Reynolds numbers. The dual-grid multiscale approach is used to model high-speed lateral gas injection in a two-dimensional blast furnace reactor. Blast velocities up to 230 m s−1 , as in real blast furnace operation, are used to investigate the formation and dynamics of the raceway inside the reactor. The effect of the blast velocity on the size and shape of the raceway was investigated using different jet velocities. It is shown how the use of an adequate grid resolution for the continuum phase is needed in order to achieve a grid independent solution and how it influenced on the discrete solution. It was observed that the variation of the blast velocity directly influenced on the size and shape of the cavity. However, the particles and the flow showed the same pattern and behavior at the different investigated blast velocities, with a proportional scaling according to the gas velocity. At the investigated blast velocities the raceway formed very rapidly showing a transition period with lateral periodic oscillations before stabilization was observed. 2. Introduction Lateral air injection into particle beds is widely used in many industrial applications found in the processing, petroleum, and metallurgical industries [1]. When air is injected laterally into a particle bed it causes the formation of a granular circulation region within the bed. The fast stream of blast air entering into the packed bed forces the particles to displace back and upwards forming a circulation region around the injected gas. This is a accompanied by a characteristic high void fraction region around the gas inlet. This blast air induced cavities are termed raceways. Lateral gas injection is preferred in several industrial applications since it increases the interaction between the solid and gas phases, and thus, resulting in a more efficient heat and mass transfer within the reactor. One of the main applications of lateral gas injection is found in blast furnace reactors. Blast furnace ∗ Principal
corresponding author. Email: [email protected] Email address: [email protected] (Edder Rabadan Santana)
Preprint submitted to Elsevier
March 30, 2019
Figure 1: (a) General scheme of a blast furnace [4]; (b) the raceway [5].
reactors are widely used in the ironmaking industry and are one of the largest operational reactors. Typical dimensions of BF are about 40 m high and 15 m wide for a production over 10 000 t/d of pig iron with blast injection velocities larger than 230 m s−1 [2]. One of the main challenges to model and predict the raceway formation in a blast furnace is associated with the very high velocity of the blast gas. The blast gas is injected at very high speed and, as a result, it strongly interacts with the particulate phase affecting the heat and mass transfer and chemical processes occurring in the reactor [2, 3]. An schematic diagram of a blast furnace and the raceway is presented in Fig. 1. Currently, two models are used to investigate the formation of the raceway: i) continuum approach and ii) combined Euler-Lagrange method. In the first approach the geometry/shape of the raceway is fixed and the bed of coke is considered to be a porous media [6, 7, 8]. In such continuum approach the Navier-Stokes equations accounting for porosity are solved over the entire domain [9, 10]. This method is restricted to the dynamics of the gas flow and therefore the formation of the raceway cannot be investigated. As a result, to determine the boundaries of the raceway becomes a complicated task. The second approach, combined Euler-Lagrange method, is used to simulate the interactions between the particulate and the gas phase. In this approach, the solid phase is considered as a discrete part while the flow in the void space between the particles is treated as a continuum phase. The discrete part is solved via the Discrete Element Method (DEM) while the continuum phase is modeled by the Computational Fluid Dynamics (CFD) approach. This coupled CFD-DEM approach, also referred to as a Combined Continuum and Discrete Model (CCDM) [11] allows to study the interaction between particle-fluid without loosing the particles’ information. The capability of the CFD-DEM approach to model the interaction fluid-particle makes it the selected approach to model blast furnace reactors. Since the stability of the blast furnace operation is related to the motion of coke particles in and around the raceway, several studies have been conducted using a coupled CFD-DEM method to investigate its formation. Xu et al. [12] used a coupled CFD-DEM model to simulate lateral gas injection into a twodimensional bed. The particle circulation and the raceway formation were found to be formed near the blast injection point. The effect of the blasting velocity on the behavior of the bed showed to be a critical 2
factor. However, only blasting velocities up 50 m s−1 were investigated. Umekage et al. [13] used DEM for the calculation of the interaction forces between coke particles together with a Finite Difference Method for computing the Navier-Stokes equations to account for the interaction terms between gas and particles. The raceway formation was investigated using the dimensions of an actual commercial blast furnace. However, the computational domain was reduced to a slice of the cylindrical part of the furnace. The study reported an unstable and unsteady motion of the raceway with periodical changes affecting its size and shape. Similar to [12], the raceway formation was investigated only for a maximum blasting velocity of 50 m s−1 . Measurements of the raceway depth in an actual blast furnace have been conducted by Matsui et al. [14] using a microwave reflection gunned through the tuyere. In the study, the measurements of the raceway depth were correlated with the depth of the tap hole. It was assumed that the tap hole depth varies according to the changes of the raceway depth. It was found that the blast velocity and blast flow rate highly affected the size of the raceway and thus the tap hole depth. An increase in the raceway depth resulted in an increase on the tap hole depth. An unsteady behavior of the raceway was also observed. Raceway formation using non-spherical particles was also studied by Adema et al. [15]. In [15] a slice of an experimental reduced-scale geometry reactor with blast velocity of 20 m s−1 was used to investigate the effect of non-spherical particles. It was shown that the blast velocity affects the raceway dynamics especially with non-spherical particles. Similarly, Hilton et al. [16] focused on the investigation of the raceway formation using different particle shapes. The raceway formation and particularly the dynamics of the bed were influenced not only by the shape of the particles but especially by the gas velocity. It was found that the raceway can be formed at lower blast velocities in the presence of non-spherical particles. For spherical particles, larger velocities were required to form a raceway. Inlet gas velocities up to 120 m s−1 were investigated. Three-dimensional geometries, either using a slot or a slice of a cylindric reactor, have been also used to investigate the raceway formation [17, 18, 19, 20]. In such configurations periodic boundary conditions have been used to mimic the circular shape of the reactor [21]. The slice configuration has been reported to provide better description of the particle flow behavior [17], when compared with experimental data from small lab-scale experimental blast furnaces [22, 23]. All these studies have only investigated maximum blast velocities up to 50 m s−1 . Studies including heat and mass transfer between the gas and particulate phases showed that the blast velocity affects the heat exchange and chemical reactions between the gas and particles, thus directly impacting on the raceway formation. Nogami et al. [24] investigated the raceway formation in a small scale blast furnace model considering heat exchange and chemical reactions. It was shown that heat and mass transfer in the reactor and the shape and size of the raceway were highly affected by the blast velocity. Rabadan et al. [25] investigated the raceway formation including chemical reactions in the raceway and the mass reduction of coke particles due to gasification. It was concluded that the raceway dynamics and heat and mass transfer processes were dependent on the blast velocity. However, the study was limited to a maximum blasting velocity of 20 m s−1 . This poses a complex scenario since high blast velocities need to be used first to proper represent the raceway dynamics and account for heat exchange and chemical processes under realistic furnace operating conditions. On the other hand, the use of high gas velocities poses some difficulties when using CFD-DEM coupling methods, mainly due to the restriction of the grid size given by the particulate phase. When the size of the particulate phase is large, such as coke in the blast furnace, this generally results in coarse meshes. A coarse mesh may not necessary have the most 3
appropriate grid resolution to capture the flow physics originated by large blast velocities. In this paper, we propose to address this issue by adopting a dual-grid multiscale approach as proposed in [38]. We show how this approach allows to treat higher blast velocities by ensuring grid-independent solutions for the fluid flow. Furthermore, we show how the usage of a coarser mesh can indeed affects the prediction capability of the raceway shape and dynamics introducing purely numerical error that can and should be avoided. We consider this is a fundamental consistency check that has to be performed before treating more complex physics of the raceway formation such as inter-phase heat transfer and complex combustion models. The following study is structured as follows, first the numerical methodology of the employed CFDDEM dual-grid approach is described in Sec. 3. The general expressions for the CFD and DEM methods are presented within the context of the used in-house solver. Afterwards, the two-dimensional simulation domain for the case study and boundary conditions are presented. The formation of the raceway is investigated by 2D simulations using three different blast velocities. The results and discussion of the findings are presented in Sec. 4. Finally conclusion are drawn in Sec. 5. 3. Model and Numerical Methods The proposed numerical approach is based on the Discrete Element Method (DEM) to model the dynamics of granular matter and the Eulerian Computational Fluid Dynamics (CFD) model for the fluid phase. A coupling between both modeling approaches allows tracking the individual motion of the particles and the dynamics of the fluid phase. For that purposes, the XDEM solver [26] has been coupled with the open source libraries OpenFoam-Extend 3.2. In the following the main governing equations and closure models used in the computational modeling are briefly described. Further detailed information regarding to the XDEM numerical framework can be found in [27]. 3.1. Discrete Element Method In this work, the dynamic module of the XDEM platform [28] was used to evolve a set of discrete entities moving in the presence of a gas phase flow. We here briefly describe the equations solved by this module. The positions and orientations of the particles are updated at every time-step according to d2 xi dt2 d2 Ii 2 φi dt
mi
=
Fcoll + Fdrag + Fg
(1)
=
Mcoll + Mext
(2)
where xi are the positions, mi the masses, and φ the orientations of the entities. The term Fcoll indicates the force arising from collisions Fcoll =
X
Fij (xj , uj , φj , ωj )
(3)
i6=j
with uj the velocity of particle j, and ω the angular velocity. In this contribution, the interactions between particle-particle and particle-wall F~ij are calculated by the non-linear model of Hertz-Mindlin [29, 30]. The term Mcoll represents the torque acting on the particle due to collisions X Mcoll = Mij (xj , uj , φj , ωj ) i6=j
4
(4)
with Mij being the torque imposed from particle j to particle i. The term Fdrag takes into account the force rising from the interaction with the fluid, and Fg corresponds to the gravitational force. For Fdrag a semi empirical model was chosen in the form: Fdrag = β(uf − up )
(5)
β = β(uf − up , ρf , ρp , dp , Ap , µf , )
(6)
with uf , up being the fluid and particle velocity, respectively; ρf , ρp the respective densities, dp , Ap the particle characteristic length and area, µf the fluid viscosity, and the porosity, defined as the ratio between the volume occupied by the fluid and the total volume of the CFD cell. For the sake of simplicity, to simulate the interactions occurring between the porous bed and the fluid β was taken as described in [31]. 3.2. Computational Fluid Dynamics (CFD) In order to better assess the capability of the numerical scheme to tackle high-velocity scenarios, we here focus on the representation of the high-velocity jet and its dynamic interaction with the particle phase. For this reason, we currently neglect the heat-up and combustion process that would make the analysis of the results more delicate. For the fluid solution, we therefore refer to an unsteady incompressible flow through a porous media with forcing terms arising from the particle phase, as described in [32, 34]. Defining the porosity field as =
Vg Vs =1− Vcell Vcell
(7)
the system must fulfill the Navier-Stokes equations in the form, ∇ · uf = −
∂ ∂t
∂uf + ∇ · (uf uf ) = −∇p + TD + Fb + Fdd ∂t TD = ∇ · µf ∇uf + ∇T uf
(8) (9) (10)
with uf being the fluid velocity, p the fluid pressure, µf the fluid viscosity, TD the contribution from the viscous stress tensor, Fb a generic body force, Ffdd the drag force density, that is the counterpart of Fdrag , which is here treated with the semi-implicit algorithm proposed in [35]. The closure problem of the RANS set of equations is solved using the standard k − model [36, 37] with k being the turbulence kinetic energy and the turbulence dissipation rate. Initial values of k and are estimated using a turbulence intensity I = 3 % and turbulence length scale l = 0.1 m. 3.3. Dual-Grid Multiscale CFD-DEM coupling The dual-grid multiscale approach for CFD-DEM coupling was first introduced in [32], and later used in several recent works [33, 38, 39, 40]. As recalled in [38], in this kind of coupling two length-scales are identified within the particle-laden flow: a bulk scale, and a fluid fine-scale. As shown in Fig. 2, this approach adopts a coarse and uniform CFD grid to resolve the fluid-particle interactions at the bulk scale, and a fine CFD grid to solve the fluid flow equations at the fine-scale. An interpolation strategy ensures the communication between the two grids i.e. the two length scales. The dual-grid multiscale approach was originally introduced 5
with reference to the coupling between DEM and VOF, as the fine resolution required by the VOF scheme was found to induce a marked separation between the two scales. In the present contribution, this coupling strategy is applied to a monophase CFD configuration coupled with a particle phase. From a software point of view, the implementation of the dual-grid multiscale approach requires the presence of two computational grids and a routine to interpolate between them, as depicted in Fig. 2. The choice of the coarse grid depends on the selected averaging operation. It is recommended to use a discretization at least 2 to 3 times larger than the particle diameter. The fine grid should be identified as the one at which the results can be considered grid-independent. An illustration of this is provided in section 3.4. In [32] it was underlined how the coarse and fine CFD grids should be independent from each other in order to allow maximum flexibility of the approach. For instance, while an uniform grid is optimal when performing a Eulerian-Lagrangian coupling, a nonuniform, locally refined, computational grid provides several advantages for the solution of complex flows. For this reason the two grids will not, in general, be nested. In this contribution, the inter-scale interpolation is performed with the library described in [38] that allows an efficient parallel implementation of the method.
Figure 2: Dual-Grid multiscale coupling scheme to resolve high velocity gas phase with particle interaction.
3.4. Simulation Domain and Boundary Conditions A two-dimensional rectangular geometry is used to represent a generic reactor. The dimensions of the computational domain are showed in Fig. 3. The computational domain is bounded by two side-walls, an inlet, an outer wall, an outlet (top wall) and a bottom wall. The inlet is located at the outer wall at 0.5 m from the bottom wall. The height of the inlet is 0.03 m. The packed bed is represented by an ensemble of particles with an inhomogeneous void space between them due to their packing. Each 3D sphere has a diameter of 20 mm ± 1 mm and is considered to be a coke particle. The coke particles are at rest and randomly settled at the bottom of the domain. This was done in a preliminary simulation by placing the particles at the center of the domain and let them fall until they reached their random and steady position. 6
The computational domain contains 6520 coke particles. Coke properties are shown in Table 1. The coke particles located in front of the gas injection were removed to avoid numerical instabilities at the initial time step. A nominal blast injection velocity corresponding to a real furnace operation of u = 230 m s−1 is used to investigate the dynamics of the raceway. In order to study the effect of the injection velocity on the prediction of the size and shape of the raceway two additional inlet velocities were also investigated, u = 200 m s−1 and u = 180 m s−1 , Inlet velocities are imposed at the inlet as a Dirichlet boundary condition. The injected air is considered to be in a standard mass fraction composition, YO2 = 0.21 and YN2 = 0.79. For simplicity the inflow profile is considered to be uniform. Side-walls are modeled assuming viscous nonslip conditions with an adaptive wall-functions [37]. At the outlet (top wall),the conservative variables are simply extrapolated from the inside domain. A time step of 1 × 10−6 is used to advance the solution of both discrete and continuum phases. The flow energy equation is not solved, accordingly the temperature of the injected gas is not considered. Table 1: Mechanical properties of coke.
Density [kg/m3 ] Restitution coefficient [-] Rolling friction coefficient [-]
1050 0.6 2.5
Young modulus [GPa] Poisson ratio [-] Friction coefficient [-]
1.0 0.3 1
The two-dimensional computational domain shown in Fig. 3 was spatially discretized using a structured multi-block technique. To asses a grid independent solution three different structured grids with different levels of refinement were investigated: a coarse grid with 3200 cells, a medium grid with 25600 cells, and a fine grid with 102400 cells. Despite that the structure of the coupling does not require an uniform discretization strategy, in this study we adopted an uniformly discretized fine grid for the fluid domain to ensure the results are not effected by the local structure of the refinement. However, local refinement could be an effective technique to reduce computational costs. Table 2 summarizes the grid resolutions used in the present study and the investigated inlet velocities of the blast injection. Figure 4 shows the CFD fine grid imposed on the DEM coarse grid. Convergence was monitored by the decrease of the right-hand side residuals of the Navier-Stokes equations averaged over all cells at each iteration as well as by the evolution of the kinetic energy and the velocity along the inlet central line. All computations achieved a converged solution with residuals dropping between 4 and 6 orders of magnitude. Figure 5a shows the flow field kinetic energy from the initial time t = 0 s until t = 10 s, for the three grid levels of refinement. Figure 5b plots the distribution of the gas velocity along the horizontal axis starting at the center of the inlet and extending until the end of the domain at t = 10 s. Variations lower than 5% were observed between the medium and fine solutions. Table 2: Grid resolutions and blast inlet velocities
Grid size [cells]
Coarse (CFD-DEM coupling) 3200
Inlet velocity [m/s]
230 7
Medium
Fine
25600
102400
200
180
a) Dimensions of the generic reactor.
b) Coarse grid resolution (CFD-DEM coupling).
Figure 3: Dimensions of the computational domain and coarse grid resolution.
Figure 4: Fine grid and particles: (a) complete computational domain, (b) grid refinement around particles, (c) grid resolution around a particle.
Accordingly, for the present study the solution was considered as a grid independent and the fine grid is used for all further calculations. As originally mentioned in [32], the dual-grid multiscale approach is more complex than a standard 8
a) Normalized kinetic energy of the flow.
b) Inlet velocity.
Figure 5: Computations with the three grid levels of refinement: a) normalized kinetic energy of the flow and b) inlet velocity of the incoming jet along the length of the reactor.
CFD-DEM coupling since introduces the additional computational cost associated to the finer CFD grid. Nevertheless, as often the case, the CFD part only represents an aspect of the overall CFD-DEM computational load and, therefore, the global cost of the simulation is only partially affected by the increase of the CFD grid resolution. On the other hand, as proposed in [38], using a dual-grid multiscale approach allows to obtain a significantly better parallel performance compared to the single scale CFD-DEM coupling. This two aspects are shown in Fig. 6, where the computational time of the simulation of the first second is compared by using the dual-grid and the single-grid approach. Similarly to what was observed, with reference to a different test case in [38], the dual-grid approach is slower than the single-grid approach in sequential execution (in this case it takes roughly 50% more time). Nevertheless, the scalability properties of the dual-grid approach are significantly better than the single scale CFD-DEM coupling. In particular when using more than 2 computing cores the dual-grid approach is faster than the single-grid, despite of using a refined grid.
Figure 6: Execution time as a function of the number of computing cores.
4. Results and Discussion 4.1. Single-grid vs dual-grid approach The first set of results shows the predictions obtained using a monoscale and a multiscale approach for a nominal operating blast velocity of u = 230 m s−1 . Accordingly, the inlet velocity u = 230 m s−1 was used 9
in all three grid levels (coarse, medium and fine) to investigate the effect of the mesh refinement on the solution. Since most significant differences were observed between the coarse and fine grids, the following discussion focuses on the findings between these two grids. Figure 7 shows the instantaneous flow field velocity at t = 10 s for the coarse and fine grids. When using the coarse grid the flow field shows a sharp decrease of the inflow velocity (Fig. 7a), even though an inlet velocity of u = 230 m s−1 was prescribed at the inlet boundary. Here, the jet velocity instantly decreases from u = 230 m s−1 at the inlet to u = 134 m s−1 when entering the reactor. This sharp decrease occurs due to the large grid size and increased discretization error, rather than to the loss of gas momentum penetrating the bed. On the other hand, employing the dual-grid approach (with the fine grid resolution for the CFD phase) Fig. 7b shows that the computed flow field velocity conserves the initial momentum prescribed at the inlet boundary and the jet penetrates the bed at the prescribed inlet velocity, u = 230 m s−1 . Figure 7 shows that in both, coarse and fine grids, the gas speed decreases as the gas penetrates into the coke bed and bends upwards towards the top. As the jet penetrates the bed it pushes forward the particles creating a void region adjacent to the inflow.
Figure 8
shows the predicted raceway cavity and the corresponding particle velocities computed with the coarse and fine grids at t = 10 s. The solid flow patterns are assessed through the particle’s velocities. Even though the same inlet velocity is prescribed in both cases (u = 230 m s−1 ), some differences are observed, primarily on the size of the raceway and on the velocity of the particles. A larger raceway size and particle velocities are predicted with the fine grid, mainly due to better transfer of momentum from the gas to the solid phase. A maximum particles’ velocities up to 10 m s−1 are observed for the fine grid, where as for the coarse grid the maximum computed velocity is not larger than 7 m s−1 . In both grid resolutions, particles with larger velocities are located directly in front of the jet injection. This is the result of the jet penetrating the bed and transferring its momentum to the particles located along its trajectory. The particles in the periphery
a) CFD-DEM coupling single grid
b) Dual-grid approach
Figure 7: Instantaneous flow velocity distribution at t = 10 s. Gas injection velocity u = 230 m s−1
10
of the cavity show lower velocities. A stagnant zone with particles showing static behavior is recognized in both cases. For the coarse grid solution the stagnant zone is formed at the bottom part below the injection and towards the end wall, forming an inversed L-shape. Where as for the fine grid solution, the stagnant zone is mainly observed at the bottom part. Even though both solutions predicted a stagnant zone at the bottom, the stagnant zone is larger when computing on the coarse grid. In order to visualize and to asses the different dimensions of the raceway, Fig. 9 shows a highlighted contour of the raceway for each grid resolution. The predicted balloon-shape of the raceway qualitatively agrees with experimental data and observations made in lab-scale blast furnace [24, 13]. To asses the dimension of the raceway, Fig. 10 simultaneously compare both raceway sizes together with its maximum length (L) and hight (h), the subindex c and f stands for the coarse and fine grid dimensions, respectively. From Fig. 10 it is possible to observe the different size predicted with the coarse (CFD-DEM coupling) and fine (CFD) grids. The calculated raceway dimensions with the coarse and fine grids are: Lc = 670 mm, hc = 570 mm and Lf = 880 mm, hf = 820 mm.
This indicates an approximately 25% under-prediction of
the raceway size by using the mono-scale approach where only a coarse grid is used for solving both DEM and CFD methods. The main reason of the observed difference on the size lies in the inaccurate prediction of the inflow velocity with the coarse grid. Due to the large grid cell size, the high inlet velocity is not properly resolved, resulting in lower gas momentum and smaller gas penetration into the bed. On the other hand, the multiscale approach using the fine grid for the CFD solution is able to better capture the blast injection and the incoming jet penetrating through the bed. This jet stream with higher kinetic energy fluidizes the complete bed forcing all particles to move and cover the complete confined space. Conversely, in the coarse grid solution (standard CFD-DEM coupling) the blast jet is not strong enough to fluidize the complete bed.
a) CFD-DEM coupling single grid
d) Dual-grid approach
Figure 8: Instantaneous particle velocity distribution using a standard CFD-DEM coupling (coarse grid: bulk scale, particulate phase) and the dual-grid approach with a fine grid for the fluid scale, at t = 10 s. Gas injection velocity u = 230 m s−1
. 11
a) CFD-DEM coupling single grid
b) Dual-grid approach
Figure 9: Predicted raceway shape with the CFD-DEM standard coupling (coarse grid) and the dual-grid approach (fine grid for the continuum phase).
Figure 10: Definition of the raceway dimensions.
The jet penetration is shorter and after l = 900 mm the particles show a static behavior. However, both solutions coincide on the gas speed decreasing as the jet penetrates the bed and transfers its momentum to the particulate phase. Since more accurate representation of the flow field and solid flow of particles is achieved with the multiscale approach, hereafter all presented results corresponds to the solution computed using this method. 4.2. Raceway formation —nominal inlet velocity Figure 11a shows the velocity distribution for the flow field and the particles at t = 10 s at the nominal inlet velocity u = 230 m s−1 . The streamlines colored by the gas velocity showing the flow path through the coke bed are depicted in Fig. 11b. After gas injection, the coke particles located in front and around the inlet are pushed inwards by the stream traveling to the center. As the jet continues penetrating into the 12
a)
b)
Figure 11: Flow field and particle velocity distributions: a) gas-particulate phase; b) fluid velocity distribution with streamlines. Gas injection velocity u = 230 m s−1 , t = 10 s.
packed bed, particles are further displaced upwards and in the direction to the end wall, leaving a cavity at the center occupied only by the incoming air. Due to the displacement of these particles, and the jet penetrating deeper into the packed bed, more coke particles descend directly to the raceway region to fill the free space. Since air is continuously supplied, the particles descending in front of the jet are trapped by the incoming stream and carried into the raceway region where they move upwards following the gas stream deflected by the surrounding packed bed. The air speed is large enough to penetrate deep through the bed until approximately 900 mm and push the particles further towards the top and end wall. The air injected into the packed bed generates two main recirculating regions with particles moving around. These two main regions, above and below the inlet, can be appreciated with the streamlines showed in Fig. 11b. The main recirculation region is located above the inlet and at the center of the reactor. This region is confined to the raceway cavity where the air, due to the densely pack, is deflected and recirculates towards the center of the domain. The raceway is characterized by a central high void region with a counter-clockwise circulation area. The second recirculation region is located below the inlet where air circulates clock-wise with particles entrained in the gas flow forming an elliptical circulation region. Consistent with experimental observations [41], two anti-directional vortex of solid flows can co-exist inside the raceway. The lower circulation zone appears to be smaller than the upper one, similar flow-particle circulation behavior has been also observed numerically in [16]. Figure 12 shows instantaneous distribution of the coke particles within the bed. The instantaneous snapshots show the evolution of the raceway from t = 0 s until t = 10 s. At the initial time, t = 0 s, the bed is completely static. Right after gas injection stars, t = 0.2 s, the jet rapidly penetrates into the bed pushing the particles inwards and creating a void space. The initial formed cavity growths and elongates until the characteristic balloon-shape is observed, t = 1.3 s. After t = 1.3 s the shape of the raceway is well formed and its boundaries are well defined. The raceway cavity is rapidly formed, however, 13
a) t = 0 s
b) t = 0.20 s
c) t = 0.30 s
d) t = 1.3 s
a) t = 1.7 s
b) t = 2.5 s
c) t = 2.8 s
d) t = 3 s
a) t = 4 s
b) t = 6 s
c) t = 8 s
d) t = 10 s
Figure 12: Dynamic evolution of the raceway at different time instants after gas injection. Gas injection velocity u = 230 m s−1
an alternating lateral oscillations are observed from t = 1.3 s until t = 3 s. This lapse of time corresponds to a transition period where the size of the raceway changes in a periodic contracting and expanding pattern. This transition pattern and period has also been observed in [14]. This transient period provides the necessary time for the jet to fully penetrate and partly fluidized the bed. Before the raceway reaches a stable condition some exchange of particles between the raceway and the surrounding bed is observed. Here, the particles falling back into the gas stream are entrained in the jet and partially dividing the raceway in two cavities, t = 2.5 s. A macroscopically stable raceway is formed after about t = 4 s. The ability to quickly stabilized the raceway boundary has also been reported during experimental studies [42, 43]. After the raceway is stabilized t > 3 s, its size remains nearly unchanged. The corresponding instantaneous velocity field is shown in Fig. 13. Due to the fine grid resolution used for solving the fluid phase in the dual-grid approach the 14
a) t = 0 s
b) t = 3 s
c) t = 5 s
d) t = 10 s
Figure 13: Instantaneous velocity distribution. Gas injection velocity u = 230 m s−1
incoming jet conserves its initial momentum. As it penetrates into the bed the jet velocity decreases. The flow velocity in the bed remains nearly constant after the raceway cavity has stabilized, t > 3 s. The raceway boundary can also been identified by the contour of the flow velocity and its different intensity. 4.3. Influence of the blast velocity on the raceway formation In this subsection the dynamics of the raceway formation at different blasting velocities is investigated. Accordingly, two different velocities were used to further investigate the influence of the injection velocity on the raceway formation: u = 180 m s−1 and u = 200 m s−1 . Figure 14 shows the particle’s velocity distribution for a blast injection u = 200 m s−1 . The case with blast velocity u = 200 m s−1 showed the same pattern and behavior as the case with u = 230 m s−1 . The raceway was rapidly formed right after the jet penetrated the bed. Similarly, a transition period with alternating lateral oscillations was present until the raceway reached a stable condition with a nearly constant boundary at t > 3 s. Recirculation regions were observed at the same locations as with u = 230 m s−1 . However, the maximum particle’s velocity was 8.2 m s−1 and the jet penetration was about 0.66 m, since the magnitude of the blast velocity was 30 m s−1 lower. This resulted in slighter smaller size of the raceway cavity. Notably was that by decreasing the magnitude of the blast velocity by 30 m s−1 , the jet was not able to completely fluidized the bed and filled the confined space with coke particles.
a) t = 0 s
b) t = 2 s
c) t = 3 s
d) t = 4 s
Figure 14: Dynamic evolution of the raceway at different time instants after gas injection. Gas injection velocity u = 200 m s−1
15
a) t = 0 s
b) t = 2 s
c) t = 3 s
d) t = 4 s
Figure 15: Dynamic evolution of the raceway at different time instants after gas injection. Gas injection velocity u = 180 m s−1
To investigate further the dependency of the size of the raceway on the blast velocity, a case with a jet injection of u = 180 m s−1 was computed. Figure 15 shows the particle’s velocity distribution. In general, the same pattern for the particles and flow behavior was observed as in the two previous cases. Similarly, a rapid formation of the raceway accompanied with a short transition period with lateral oscillation before stabilization was observed. The stabilization of the raceway was equally achieved after t > 3 s. However, the lower magnitude of the blast injection resulted in smaller cavity size and shorter jet penetration. Similarly, due to the lower blast velocity, the momentum of the incoming gas was not able to completely fluidized the bed and fill the confined space in the reactor. Differently from the two previous cases was that the jet, after the raceway stabilized, did not penetrate or deflect towards the bottom part, it remained nearly straight until it was deflected only upwards. This produced a flat-bottom shape of the raceway, when compared to the one formed in the other two cases. This can be appreciated in the Fig. 16 where the particle’s velocity distribution and raceway cavity are shown for the three investigated blast velocities. The jet penetration for the three blast velocities is plotted in Fig. 17. The jet penetration depth in Fig. 17 represents the axial
a) 180 m s−1
b) 200 m s−1
c) 230 m s−1
Figure 16: Instantaneous particle velocity distribution for different inlet gas velocities at t = 4 s.
16
Figure 17: Jet penetration at different blast velocities.
length, from the inlet towards the reactor, where the gas velocity is approximately 2 % of the initial blast velocity. The penetration depth shows a nearly lineal correlation with the magnitude of the blast velocity. 5. Conclusions This work intended to present an efficient CFD-DEM coupling strategy to model high-speed gas velocities. The used CFD-DEM coupling method employs a dual-grid multiscale approach where the discrete and continuous phases are solved in a separate grids, allowing the use of a refine meshes for the continuous phase and to achieve a grid independent solution. This coupling technique is integrated into the well validated inhouse solver eXtended Discrete Element Method (XDEM). Accordingly, the CFD-DEM dual-grid multiscale approach was used to simulate lateral gas injection in packed bed reactors. A generic blast furnace reactor, typically used in the iron-making industry, was selected as a test case due to its high operational blast velocities. In particular, the effect of high-speed injection (blast injection) on the formation of the raceway was investigated. In order to investigate the dependency of the size of the raceway on the blast velocity, three different injection velocities were investigated 230 m s−1 , 200 m s−1 and 180 m s−1 . A great dependency of the size of the raceway on the injection velocity was observed. It was observed that the effect of varying the blast velocity on the raceway formation affected the size of the cavity, however the pattern of the particles and the behavior of the gas flow remained nearly the same. In all investigated cases the raceway cavity was formed very rapidly with presence of a transition period with periodic contracting and expanding patterns before it stabilized. Acknowledgments The authors would like to thank to the Luxembourg National Research Fund (FNR) for the financial support of this project and to the HPC Cluster facilities of the University of Luxembourg. References [1] Pilcher K.A and Bridgwater J. (1990) Pinnig in a rectangular moving bed reactor with gas cross-flow. Chemical Engineering Science 45, 2535-2542. Doi: 10.1016/0009-2509(90)80139-6 [2] Adema, A. (2014) DEM-CFD Modelling of the ironmaking blast furnace. PhD Thesis TU Delft, The Netherlands. [3] Peters, B., Dziugys, A., and Navakas, R. (2012) A shrinking model for combustion/gasification of char based on transport and reaction time scales. Mechanika 18(2), 177-185. Doi: 10.5755/j01.mech.18.2.1564
17
[4] Geerdes, M., Toxopeus, H., van der Vliet, C., Chaigneau, R., and Vander, T. (2009) Modern Blast Furnace Ironmaking: An Introduction. IOS Press. [5] Mathieson, J. G., Truelove, J. S., and Rogers, H. (2005) Toward an understanding of coal combustion in blast furnace tuyere injection. Fuel 84(10), 1229-1237. Doi: 10.1016/j.fuel.2004.06.036 [6] Shen, Y., Yu, A., Austin, P., and Zulli, P. (2012) Modelling in-furnace phenomena of pulverized coal injection in ironmaking blast furnace: effect of coke bed porosities Minerals Engineering 33, 54-65. Doi: 10.1016/j.mineng.2011.10.014 [7] Li, Y., Zhang, X., Zhang, J., Zhou, J., and Yan, H. (2014) Numerical simulation and optimization of pulverized coal injection with enriched oxygen into blast furnace Applied Thermal Engineering 67, 72-79. Doi: 10.1016/j.applthermaleng.2014.02.062 [8] Shen, Y.S., Guo, B.Y., Yu, A.B., Austin, P.R., and Zulli, P. (2011) Three-dimensional modelling of in-furnace coal/coke combustion in a blast furnace Fuel 90, 728-738. Doi: 10.1016/j.fuel.2010.08.030 [9] Gidaspow, D. (1994) Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic Press 9780122824708 ISBN: 9780122824708 [10] Kuipers, J. A. M., and van Swaaij W. P. M. (1997) Application of Computational Fluid Dynamics to Chemical Reaction Engineering. Reviews in Chemical Engineering. Doi: 10.1515/REVCE.1997.13.3.1 [11] Xu, B. H., and Yu, A. B. (1998) Comments on the paper numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics - reply. Chemical Engineering Science. 53(14), 2645-2646. Doi: 10.1016/S0009-2509(98)00085-2 [12] Xu, B.H., Yu, A.B., Chew, S.J., and Zulli P. (2000) Numerical simulation of the gas-solid flow in a bed with lateral gas blasting. Powder Technology 109, 13-26. Doi: 10.1016/S0032-5910(99)00223-5 [13] Umekage, T., Yuu, S., and Kadowaki, M. (2005) Numerical simulation of blast furnace raceway depth and height, and effect of wall cohesive matter on gas and coke particle flows ISIJ International 45(10), 14161425. Doi: 10.2355/isijinternational.45.1416 [14] Matsui, Y., Tadai, R., Ito, K., Matsuo, T., Nagai N., and Imai T. (2005) Stabilization of tapping hole length by controlling blast furnace raceway depth SIJ International 45(10), 14391444. Doi: 10.2355/isijinternational.45.1439 [15] Adema, A.T., Yang Y., and Boom, R. (2010) Discrete element method-computational fluid dynamic simulation of the materials flow in an iron-making blast furnace ISIJ International 50(7), 954961. Doi: 10.2355/isijinternational.50.954 [16] Hilton, J. E. and Cleary, P. W. (2012) Raceway formation in laterally gas-driven particle beds. Chemical Engineering Science 80, 306-316. Doi: 10.1016/j.ces.2012.06.044 [17] ang, W.J., Zhou, Z,Y, and Yu, A.B. (2015) Discrete particle simulation of solid flow in a three-dimensional blast furnace sector model Chemical Engineering Journal 278, 339352. Doi: 10.1016/j.cej.2014.11.144 [18] Tang, H., Meng, F., Zhao, Z., and Zhang, L. (2015) Modeling coal/coke combustion behavior in tuyere-raceway-dripping zone in blast furnace Procedia Engineering 102, 1583-1592. Doi: 10.1016/j.proeng.2015.01.294 [19] Umekage, T., Kadowaki, M., and Yuu, S. (2007) Numerical simulation of effect of tuyere angle and wall scaffolding on unsteady gas and particle flows including raceway in blast furnace. ISIJ International 47(5), 659-668. Doi: 10.2355/isijinternational.47.659 [20] Natsui, S., Nogami, H., Ueda, S., Kano, J. Inoue, R., and Ariyama, T. (2011) Simultaneous three-dimensional analysis of gassolid flow in blast furnace by combining discrete element method and computational fluid dynamics. ISIJ International 51(1), 41-50. Doi: 10.2355/isijinternational.51.41 [21] Yang, W., Zhou, Z., Pinson, D., and Yu, A. (2014) Periodic boundary conditions for discrete element method simulation of particle flow in cylindrical vessels. Ind. Eng. Chem. Res. 53(19), 82458256. Doi: 10.1021/ie404158e [22] Wright, B., Zulli, P., Zhou, Z.Y., and Yu, A.B. (2011) Gas-solid flow in an ironmaking blast furnace I: physical modelling. Powder Technology 208, 8697. Doi: 10.1016/j.powtec.2010.12.006 [23] Ho, C.K., Chen, Y.M., Lin, C.I., Jeng, J.R. (1990) On the flow of granular material in a model blast furnace. Powder Technology 63, 1321. Doi: 10.1016/0032-5910(90)80003-H [24] Nogami, H., Yamaoka, H., and Takatani, K. (2004) Raceway Design for the Innovative Blast Furnace. ISIJ International 44, 2150-2158. Doi: 10.2355/isijinternational.44.2150 [25] Rabadan-Santana, E., and Peters, B. (2016) An Euler-Lagrange Approach to Model the Dynamics of Particulate Phase Exposed to Hot Gas Injection into Packed Bed Reactors. Proceedings of the International Conference on Computational Methods 3, 294-306. ISSN 2374-3948 [26] Peters, B. (2013) The extended discrete element method XDEM for multi-physics applications. Scholarly Journal of Engineering Research 2(1), 1-20. [27] Samiei, K., Peters, B., Bolten, M., and Frommer, A. (2013) Assessment of the potentials of implicit integration method in discrete element modelling of granular matter. Computers and Chemical Engineering 49, 183-193. Doi: 10.1016/j.compchemeng.2012.10.009 [28] Peters, B., Baniasadi, Me., Baniasadi, Ma., Besseron, X., Donoso, A., Mohseni, M., and Pozzetti, G. (2018) XDEM multiphysics and multi-scale simulation technology: Review of DEMCFD coupling, methodology and engineering applications. Particuology, in press. Doi: 10.1016/j.partic.2018.04.005 [29] Mindlin, R. (1949) Compliance of elastic bodies in contact. Appl. Mech 16, 259-268. [30] Hertz, H. (1881) Ueber die beruehrung elastischer koerper. J. Reine Angew. Math 92 156-171. [31] Ergun, S., Orning, A. (1949) Fluid flow through randomly packed columns and fluidized beds. Industrial & Engineering Chemistry 41 (6), 11791184. Doi: 10.1021/ie50474a011 [32] Pozzetti, G., and Peters, B. (2018) A multiscale DEM-VOF method for the simulation of three-phase flows. International Journal of Multiphase Flow 99 186-204 . Doi: 10.1016/j.ijmultiphaseflow.2017.10.008 [33] Pozzetti, G., and Peters, B. (2017) On the choice of a phase interchange strategy for a multiscale DEM-VOF method. AIP Conference Proceedings 1863, 1800002. Doi: 10.1063/1.4992362
18
[34] Pozzetti, G., Besseron, X., Rousset, A., and Peters, B. (2018) A co-located partitions strategy for parallel CFD-DEM couplings. Advanced Powder Technology Doi: 10.1016/j.apt.2018.08.025 [35] Xiao, H., and Sun, J. (2011) Algorithms in a Robust Hybrid CFD-DEM Solver for Particle-Laden Flows. Communication Computer Physics 9(2), 297-323. Doi: 10.4208/cicp.260509.230210a [36] Launder, B.E., and Spalding, D.B., (1974) The numerical computation of turbulent flows. Computer methods in applied mechanics and engineering 3(2), 269-289. Doi: 10.1016/0045-7825(74)90029-2 [37] OpenFoam User Guide, V.2.0.0. (2011) [38] Pozzetti, G., Jasak, H., Besseron, X., Rousset, A. and Peters, B. (2019) A parallel dual-grid multiscale approach to CFD–DEM couplings. Journal of Computational Physics 378, 708-722. Doi: 10.1016/j.jcp.2018.11.030 [39] Pozzetti, G., and Peters, B. (2017) Flow characteristics of metallic powder grains for additive manufacturing. EPJ Web Conf. 140, 13001. Doi: 10.1051/epjconf/201714013001 [40] Pozzetti, G., and Peters, B. (2018) A numerical approach for the evaluation of particle-induced erosion in an abrasive waterjet focusing tube. Powder Technology, 333, 229-242. Doi: 10.1016/j.powtec.2018.04.006 [41] Takahashi, H., Komatsu, N. (1993) Cold Model Study on Burden Behaviour in the Lower Part of Blast Furnace. ISIJ International 33(6), 655-663. Doi: 10.2355/isijinternational.33.655 [42] Elliott, J.F., Buchanan, R.A., and Wagstaff, J.B. (1952) Physical Conditions in the Combustion and Smelting Zones of a Blast Furnace The Journal of The Minerals, Metals and Materials Society (TMS) 4(7), 709717. Doi: 10.1007/BF03398129 [43] Flint, P.J., and Burgess, J.M. (1992) A fundamental study of raceway size in two dimensions. Metallurgical and Materials Transactions B 23(3), 267283. Doi: 10.1007/BF02656282
19
A Coupled CFD-DEM Method for Modeling High-Speed Gas Injection in Packed Bed Reactors
Edder Rabadan Santana, Gabriele Pozzetti, Bernhard Peters University of Luxembourg, 6 Avenue de la Fonte, 4364, Esch-sur-Alzette, Luxembourg
HIGHLIGHTS
CFD-DEM coupling with dual-grid multiscale approach to model a high-speed gas phase.
Dual-grid multiscale approach suitable for modeling high flow velocities in a CFD-DEM coupling.
High-speed lateral blast injection is well captured using the dual-grid multiscale approach.
Raceway forms rapidly after a transition period with lateral periodic oscillations.
Size and shape of the raceway are directly influenced by the blast velocity.