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Entrainment of particles and gas induced by draft fan over the particles bed
Advanced Powder Technology xxx (xxxx) xxx
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Original Research Paper
Entrainment of particles and gas induced by draft fan over the particles bed Xiaoxue Jiang a, Yingqiao Xu b, Yan Geng b, Chuang Wang b, M. Hassan a, Linzhi Meng b, Huilin Lu a,⇑ a b
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China China Aerospace Science and Technology Corporation Fifth Research Institute, Beijing 100081, China
a r t i c l e
i n f o
Article history: Received 22 November 2018 Received in revised form 6 July 2019 Accepted 10 October 2019 Available online xxxx Keywords: Entrainment Kinetic theory of granular flow Draft fan Hovering height Particles bed
a b s t r a c t The draft fan is used to generate a controlled transportation of particles to enhance entrainment of gas and particles from the particles bed. Present investigations show the entrainment behavior of particles induced by an axial 4-blade draft fan hovering over the particles bed. The distributions of velocities and volume fractions of gas and particles are simulated using Euler-Euler two-fluid model (TFM) with kinetic theory of granular flow (KTGF) at different hovering heights and rotational speeds of the draft fan. The dense region with high solids volume fraction and low particles velocity and the dilute region with low solids volume fraction and high particles velocity exist beneath the draft fan along hovering heights. The entrainment of particles increases with the decrease of hovering height and increase of rotational speed of the draft fan. Present numerical simulations confirm that the gas-solid TFM with the kinetic theory of granular flow and multiple reference frame model can be effectively applied to analysis for entrainment of particles induced by draft fan. Ó 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
1. Introduction Entrainment of particles by an air stream is a process which occurs in industrial applications including clean technology, spread of radioactive particles, handling of toxic powders and dust storms in desert areas [1–3]. Furthermore, the entrainment of particles is very important processes to avoid the reduction of particles from gas-particles fluidized bed reactors [4–6]. Hence, the entrainment rate of particles has to be known for the design of an appropriate gas-solid system. The entrainment in gas-particles fluidized beds refers to the removal of solids from a fluidized bed by fluidizing gas from the bottom to the exit. The flow behavior of fine particles entrained by the ascending gas flow was measured in a fluidized bed riser [7]. The entrainment of fluid catalytic cracking (FCC) particles from the spheres packed bed was tested, and the empirical equations of dynamic and static volume fractions of particles were correlated as a function of fluidizing gas velocity and particles properties. The discrete particle model was used to study the effects of gas turbulence on particle entrainment [8]. Simulated results showed the entrainment of particles depends on forces acting on particles.
⇑ Corresponding author. E-mail address: [email protected] (H. Lu).
The entrainment of particles in fluidized beds was acknowledged by up-flow gas from the bed surface [9,10]. The entrainment of particles was reviewed by Chew et al. [11] in gas–particles fluidization. The comparisons of the predicted entrainments using different empirical elutriation rate correlations were analyzed in gas-particles fluidized beds. On the other hand, the ceiling fan is widely used to generate a controlled gas and particles flow in the air-conditioned space, cooling scenarios and residential and commercial buildings because it has inherently diverse merits, including a compact structure, a wide operating scope and high efficiency [12]. The hydrodynamics of gas induced by the ceiling fan rotation were investigated by numerical simulations and experiments [13]. The distributions of velocity, temperature and humidity using a ceiling fan were predicted in an air-conditioned room. A parametric analysis on the effect of the ceiling fan was conducted using numerical simulations. The air movement in the indoor environmental room with ceiling fan was simulated using the commercial CFD software Star-CCM [14]. The air flow created by the rotation of the ceiling fan was predicted by means of the rotating reference frame method to model the rotation of fan blades. The simulated average vertical speeds were validated against experimental results. The velocity profiles by ceiling fan were simulated using a commercial CFD FLUENT code with k-e turbulent models [15]. The local free shear layers generated by the ceiling fan were predicted and
https://doi.org/10.1016/j.apt.2019.10.011 0921-8831/Ó 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
Please cite this article as: X. Jiang, Y. Xu, Y. Geng et al., Entrainment of particles and gas induced by draft fan over the particles bed, Advanced Powder Technology, https://doi.org/10.1016/j.apt.2019.10.011
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Nomenclature CD ds D Gkg Gs gi go h H I I2D kg ks ps psc psf Res S Ss u ur ut x
drag coefficient [–] particle diameter [m] width of particles bed [m] turbulent kinetic energy generation [kgm1s3] solid mass flux rate [kgs1] gravitational acceleration [ms2] radial distribution function [–] height from the particle bed [m] hovering height [m] identity matrix [–] second invariant of the deviatoric stress tensor [–] turbulent kinetic energy [m2s2] conductivity of fluctuating energy [kgm1s1] solid phase pressure [Pa] collisional and kinetic part of solid phase pressure [Pa] frictional part of solid phase pressure [Pa] particle Reynolds number [–] mean strain rate [s1] solid strain rate tensor [–] absolute velocity (the velocity viewed from the stationary frame) [m/s] relative velocity (the velocity viewed from the moving frame) [m/s] translational frame velocity [m/s] radial position [m]
compared to experimental results in the environmental chamber. The effect of ceiling fan rotational speed and ceiling height on air velocity and temperature was analyzed [16]. Two zones were identified, including the cylindrical domain beneath the blades and remaining zone. The jet impingement formed by the ceiling fan generated a radial flow on the floor. Numerical results mentioned above show that the CFD provides a convenient and affordable alternative to model the performance of ceiling fans. Despite there are a number of numerical simulations and experimental measurements of gas flow induced by the rotation of ceiling fan, the knowledge of particles entrainment induced by fan rotation is very limited. The present study attempts to simulate the flow field of gas and particles induced by the draft fan hovering over the particles bed by means of Euler-Euler two-fluid model (TFM). To accurately simulate the flow field of particles when the draft fan rotates at the specific rotational speed, the interactions between the particles and the blade surface and the interactions of particles are modeled by means of kinetic theory of granular flow (KTGF). The flow field around the rotor blade is numerically calculated using the multiple reference frame (MRF) method to model the revolving movement of the rotor. The effect of hovering heights on volume fractions and velocities of gas and particles is simulated, and the distributions of volume fraction and velocity of particles are analyzed along the surface of the particles bed. Present numerical simulations will be available for a parametric investigation of hydrodynamics of gas and particles induced by fan rotation in gas-solid processes.
2. Euler-Euler TFM of gas-particles flow induced by draft fan rotation The flow characteristics of gas and particles induced by the rotation of draft fan are obviously very complex because of the contribution of interactions of collisions between the blades and
Symbols
a as;max as;f ;max
b
eg
/ /gs
cs
ks
lg lgt ls lsc lsf
h
q s
X
volume fraction [–] maximum solid packing limit [–] frictional stress threshold [–] drag coefficient of gas–solids phase [kgm3s1] dissipation rate of turbulent kinetic energy [kgm3s1] internal friction angle of particles [°] switch function [–] collisional dissipation of solid fluctuating energy [m2s2] solid bulk viscosity [Pas] gas dynamic viscosity [Pas] gas turbulent viscosity [Pas] solid phase shear viscosity [Pas] collisional and kinetic part of shear viscosity [Pas] frictional part of shear viscosity [Pas] granular temperature [m2s2] density [kgm3] stress tensor [Pa] rotational speed [rpm]
Subscripts g gas phase s solid phase
particles. The entrainment of particles varies with the change of solids volume fractions from the particles bed. Thus, the present numerical simulations will focus on the entrainment of particles induced by the rotation of the draft fan hovering over the particles bed. The schematic diagram used in numerical simulations is showed in Fig. 1, where the particles bed is arranged at the bottom of the closed vessel. An axial 4-blade draft fan is installed over the bed at the upper part of the computational domain which consists of the internal region and the external region. The revolving center is the axis of the draft fan. The draft fan measures 2.3 m in diameter with blades that are 1.06 m long and 5 mm thick. The chord is 0.2 m. The pitch angle of the blades is 15 degree. The diameter of the hub is 0.18 m. The elastic deformation of blades is ignored. The mono-sized particles are filled into a box container forming a particles bed. The diameter and density of particles are 50 lm and 2000 kg/m3 in the particles bed. 2.1. Models of gas-particles flow induced by rotation of draft fan The present numerical simulations aim to study the entrainment of gas and particles induced by the blade rotation of the draft fan from the particles bed, therefore, the formula used in the models must be able to describe the gas and particles movement induced by the draft fan and capture the distributions of gas and particles from the bed. As a result, the flow field of a revolving rotor is modeled using the multiple reference frame (MRF) model [17], and the kg-eg turbulence model is selected to model turbulence of gas phase by the rotation of blades. The KTGF is used to model interactions between the blades and particles. The equations of mass balance for gas phase and solid phase are expressed as follows [18].
@ ag q urgj @ g ag qg þ ¼0 @t @xj
ð1Þ
Please cite this article as: X. Jiang, Y. Xu, Y. Geng et al., Entrainment of particles and gas induced by draft fan over the particles bed, Advanced Powder Technology, https://doi.org/10.1016/j.apt.2019.10.011
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Fig. 1. Schematic diagram of draft fan system used in numerical simulations.
@ @ as qs ursj ðas qs Þ þ ¼0 @t @xj
ð2Þ
The equation of gas momentum conservation in the moving reference frame is: @s @p a qg urgi Þ þ @x@ j ðag qg urgi urgj Þ ¼ ag @x þ @xgij þ ag qg g i bðursi urgi Þ i j 2ag qg Xgj urgi ag qg Xgi Xgj Ri
@ ð g @t
ð3Þ where X and R are the angular spin rate and the radius of rotating. The gas stress tensor sg is shown in Table 1 [17]. The effective gas viscosity is predicted using a kg–eg turbulence model [16]. The forth term of the right-hand side is the interfacial momentum transfer between the gas phase and the solid phase. The fifth and sixth terms are due to the unsteady change of the rotational speed and linear velocity of gas phase, respectively. They represent the gas Coriolis acceleration and centrifugal acceleration [16]. Similarly for the solid phase, the equation of momentum conservation is: @s @p s a qs ursi Þ þ @x@ j ðas qs ursi ursj Þ ¼ as @x þ @p þ @xsijj þ as qs g i þ bðurgi ursi Þ @xi i 2as qs Xsj ursi as qs Xsi Xsj Ri
@ ð s @t
ð4Þ where the fifth and sixth terms are due to the unsteady change of the rotational speed and linear velocity of solid phase, and relate to angular spin rate of particles. The stress tensor of solid phase is shown in Table 1 [17] according to solid pressure ps and viscosity ls. The pressure and viscosity of particles are simulated as a function of granular temperature h by solving a fluctuating kinetic energy equation of particles using KTGF [18,19]. In order to solve the fluctuating energy equation, we need to specify the collisional energy dissipation cs due to inelastic collisions of particles and the granular conductivity ks as a function of restitution coefficient of particles e. To simulate a gas–particles flow induced by the draft fan from the particles bed, a relation of frictional stresses is needed to solve the momentum equation. The frictional components of pressure psf and viscosity lsf are modeled using Eq. (T10) and (T13). The interface momentum transfer coefficient is modeled using Huilin-Gidaspow drag model in ANSYS [17,20].
2.2. Boundary conditions and simulation strategy To predict entrainment of gas and particles induced by the rotation of the draft fan from the particles bed, the computational domain assigns a cube with the length of 10 m, the width of 10 m and the height of 4 m, as shown in Fig. 1, with the axial draft fan at the center and the bed at the bottom. The blades are connected by the rotor hub. The draft fan is modeled by MRF model in the internal region. The radius of the internal region is 1.2 m which is large enough to contain the intersecting rotational surfaces. In the MRF model, it is possible to transform the equations of fluid motion to the moving frame such that the steady-state solutions are possible for a steadily moving frame [21]. The unsteady simulation can be run in a moving reference frame with constant rotational speed. The coupling between the rotating reference frame and the stationary reference frame is shown in Fig. 2 [17]. The rotating axis of the rotating system corresponds with the z axes. The velocities of gas phase and solid phase are transformed from the stationary reference frame to the rotating frame using the following relation [17,21,22]:
! ! ! ! ! u ¼ ur þðut þ X RÞ
ð5Þ
The particles bed is located at the bottom of the computational domain. Initially, the static height Ho of the bed is 0.5 m with the initial volume fraction of particles of 0.6. The initial velocities of particles and gas are zero. The inlet is assigned with the pressure inlet boundary condition, and the exit is assigned with the pressure outlet boundary condition. The bottom of the bed is the wall boundary condition. During the rotation of the blades, the non-slip boundary condition is used for gas phase at the walls of the blades. The gas velocity along the boundary is equal to the moving velocity of the blades. For solid phase, the slip wall boundary condition is used at the blade surface [23]. The computational domain divides into the internal region with the rotational blades and the external region. The blades rotate at the rotational speed in the rotating reference frame and the MRF model is used in the internal region. The denser unstructured grids are deployed on the blades, including the hub surface and the rounding at the tips of the draft fan. The rest space in the
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Table 1 A summary of the constitutive equations. A. Constitutive equations of gas phase (a) Gas phase stress " T # * * * 2a sg ¼ ag lge r u rg þ r u rg 3 g lge r u rg
(T1)
(b) Effective gas viscosity (T2)
2
lge ¼ lg þ lgt ¼ lg þ C l qg kegg
(c) Gas kg-eg model l pffiffiffiffiffiffiffiffipffiffiffiffiffiffi * ag qg kg þ r ag qg u rg kg ¼ r ag rgtk rkg þ ag Gkg ag qg eg kgs 2kg 2kg 3h * @ ¼ @t ag qg eg þ r ag qg u rg eg l pffiffiffiffiffiffiffiffipffiffiffiffiffiffi eg gt r ag re reg þ ag kg C 1 Gkg C 2 qg eg C 2 kegg kgs 2kg 2kg 3h pffiffiffiffiffiffiffiffiffiffiffiffi * * Gkg ¼ lgt S2 , S ¼ 2Sg Sg and Sg ¼ 12 r u rg þ rT u rg
@ @t
(T3) (T4)
(T5)
C1 = 1.44, C2 = 1.92, Cl = 0.09, rk = 1.0 and re = 1.3 B. Constitutive equations of solids phase (a) Conservation of solid phase fluctuating energy * * 3 @ ¼ ps I þ ss r u rs þ r ðks rhÞ cs 2 @t ðas qs hÞ þ r as qs u rs h
(T6)
(b) Solid phase stress " #
* * T * ss ¼ as ls r u rs þ r u rs þ as ks 23 ls r u rs I
(T7)
(c) Solid phase pressure ps ¼ psc þ psf psc ¼ ½1 þ 2ð1 þ eÞas g o as qs h (
10 25 as > as;f ;max psf ¼ 10 as as;f ;max 0 as 6 as;f ;max
(T8) (T9) (T10)
(d) Solid phase shear viscosity
ls ¼ lsc þ lsf
pffiffiffiffi
qffiffiffi
2 ph 4 lsc ¼ 9610aqs sgdosð1þe þ 45 as qs ds g o ð1 þ eÞ Þ 1 þ 5 as g o ð1 þ eÞ
ffiffiffiffiffi lsf ¼ p2sfpsin/ I
h
p
(T11) (T12) (T13)
2D
I2D ¼ SS : SS and SS ¼ 12
* * r u rs þ rT u rs
(T14)
(e) Solid phase bulk viscosity qffiffiffi ks ¼ 43 as qs ds g o ð1 þ eÞ ph
(T15)
cs ¼ 3 1 e2 g o qs a2s
(f) Collisional dissipation of solid fluctuating energy h qffiffiffi i
! 4 h p r u rs ds
(T16)
(g) Conductivity of the fluctuating energy qffiffiffi pffiffiffiffi 2 qs ds p h 1 þ 65 as g o ð1 þ eÞ þ 2a2s qs ds g o ð1 þ eÞ ph ks ¼ 150 384ð1þeÞg
(T17)
(h) Radial distribution function h i1 as Þ1=3 g 0 ¼ 1 ðas;max
(T18)
(i) Gas–solid phase interphase exchange coefficient
0
* * 1
* * 1:75as qg u rs u rg 3C D as ag qg u rs u rg 150as ð1ag Þla @ A þ a2:65 b ¼ /gs þ ð1 /gs Þ 2 g ds 4ds
(T19)
o
a g ds
as Þ /gs ¼ arctan½1501:75ð0:2 þ 0:5 ( h p
0:687 i 24 1 þ 0:15 a Re g s C D ¼ ag Res 0:44
* * qg ds u rs u rg Res ¼ l
(T20) for Res 6 1000
(T21)
for Res > 1000 (T22)
g
computational domain is the external region which is fixed in the stationary reference frame. The internal grids revolve when the hub rotates along its axis. The discontinuity of the nodes arises from between the internal grids and the external grids. Thus, the interface boundary condition is assigned, and the physical quantities of the block are transferred using interpolation through the boundary. To confirm that the results are independent of grid size, the increments of grid numbers are performed. Fig. 3 shows the computed time-averaged velocity of particle and gas pressure along the radial position at
three different grid numbers. The computational domains consist of 120,000, 210,000 and 330,000 non-uniform grids. The computed values are approximately same for all the grid number cases. The minimum and maximum velocity and pressure error percentages as compared with the lowest grid number case are only 0.15% and 12.4%, respectively. This indicates that all the grid number cases are sufficiently fine for providing reasonably grid independence results. However, the computational time is still a significant restriction when using a finer grid. In this study, the computational domain consisting of 210,000 non-uniform grids is selected to use.
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X. Jiang et al. / Advanced Powder Technology xxx (xxxx) xxx Table 2 Simulation conditions and model parameters. Particle diameter Height of particles bed Gas viscosity Particles restitution coefficient (e) Initial particle concentration
Fig. 2. Schematic of the coupling between the rotating and the absolute reference frames.
Therefore, the interface between the internal grids and the external grids avoids discontinuities of physical quantities across the bordering nodes. The 3D simulation parameters are shown in Table 2. The value of restitution coefficient of particles of 0.9 is suggested to study the distribution of particle velocities in the circulating spout- fluid bed with the draft tube [24]. On the other hand, the value of wall restitution coefficient of 0.25–0.75 is suggested [25,26]. The pressure– velocity coupling scheme is used with the standard pressure discretization scheme, and the volume fraction is discretized with a QUICK scheme. The other terms of the governing equations are discretized with second order upwind schemes. The values of the under-relaxation factors of pressure and volume fraction are 0.15 and 0.4, respectively. The numerical simulations are conducted using ANSYS Fluent code [17] at the computational time step of 1.0 104 s.
3. Simulations and discussions 3.1. Instantaneous entrainment of gas and particles The flow structure of gas and particles induced by the rotation of the draft fan is studied with the change of hovering heights over the particles bed. The gas velocity contours are shown in Fig. 4 at four hovering heights, where H is the distance from the surface of the bed to the blade plane. The vortexes are generated when the rotor rotates anticlockwise. A draft fan entrains gas, and
50 (lm) 0.5 (m)
Particle density Gas density
2000 (kg/m3) 1.225 (kg/m3)
1.789 105 (kg/ms) 0.9
Rotational speed
700, 1000, 1300, 1600 (rpm) 0.4
0.6
Wall restitution coefficient (ew) Hovering height
0.5, 0.625, 0.75, 1.0 (m)
produces negative gas pressure beneath the blades. This negative pressure drives as a swirling gas jet that impinges on the surface of the bed. The differences among four gas stream lines are attributed to the hovering height difference over the bed. When the hovering height is at 0.5 m, the gas vortexes are formed at the tip of the blades. At the hub, gas flow from the top to the blade plane with the negative gas velocity, and then enters into the vortex. Gas and particles are sucked from the surface of the bed, and enter into the blade plane. At the same time, gas flows horizontally along the surface of the bed. When the draft fan is raised at 0.625 m and 0.75 m, the double anti-symmetric vortexes are formed at the tip of the blades. At the hovering height of 1.0 m, the gas vortex moves away from the tip into the external zone. The volume fraction contours and velocity vectors of particles are shown in Fig. 5 at four hovering heights. The sectional views of flow of particles created by the draft fan illustrate similar flow patterns of particles. When the hovering height is small, the space between the blade plane and the surface of the particles bed is small, and the flow resistance in this space will be increased. This leads to increase air flow rate. Numerical simulations further illustrate that the velocity of particles located at the surface of the bed is reduced with the increase of heights from the bed. The draft fan revolves to generate gas pressures both above and under the blades. The gas pressure contour is shown in Fig. 6 at four hovering heights. The simulated gas pressures show the negative gas pressure beneath the blades and positive gas pressure above the blades. The large gas pressure difference is found at the hovering height of 0.5 m and 0.625 m, and resulting in forces which enable to move particles at the surface of the bed. The gas pressure difference is reduced at the high hovering height, indicating a major influence of hovering height on gas pressure. The pressure difference indicates that the draft fan revolves to generate the negative gas pressure beneath the blades and positive gas pressure above the blades.
Fig. 3. Comparison of particles velocity and gas pressure for different mesh resolutions.
Please cite this article as: X. Jiang, Y. Xu, Y. Geng et al., Entrainment of particles and gas induced by draft fan over the particles bed, Advanced Powder Technology, https://doi.org/10.1016/j.apt.2019.10.011
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Fig. 4. Gas velocity streamlines and contours at different hovering heights.
Fig. 5. Volume fraction contour and velocity vector of particles at different hovering heights.
The solids volume fraction contours are shown in Fig. 7 at four hovering heights. The solids volume fraction is high beneath the blade plane and low at the upper blade plane because particles located at the surface of the bed are entrained by gas induced by the rotation of the blades. The solids volume fraction is reduced with the increase of hovering heights. From simulated solids volume fractions, the flow field can be divided into four parts except for the bed, and shown in Fig. 8. The first part I is the one surrounding the rotor, composed of a cylindrical domain with the width same as the fan diameter. Gas and particles are carried from the surface of the bed to the blade plane. The gas pressure is negative in the cylindrical domain of part I. The vortex formed at the tip of the blades is known as the part II. The region of part II is increased
with the increase of hovering height of the draft fan. The third part III is the transition over the bed. Particles carried by gas move horizontally towards part I. The rest region becomes the part IV in the computational domain. With the decrease of hovering height of the draft fan, the solids volume fractions in part I and II are increased, indicating more particles are entrained by the draft fan. Similarly different flow regions were also observed in a room using ceiling fan in the experiment [27]. The main flow region was the area below the fan with high gas velocity, forming a transport zone. The diameter of the flow region immediately below the ceiling fan is close to the diameter of the ceiling fan. The simulated results confirm that the model used is able to predict the flow of gas and particles generated by a fan hovering over the bed.
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Fig. 6. Gas pressure contour at four hovering heights.
Fig. 7. Solid volume fraction contour at four hovering heights.
3.2. Distributions of volume fractions and velocities
Fig. 8. Flow regions of particles and gas induced by draft fan.
To describe entrainment characteristics of particles induced by the draft fan, the velocity and volume fraction are calculated in the cylindrical domain with the same diameter as the fan blades. The distributions of axial and lateral velocities of gas and particles are shown in Figs. 9 and 10 at four hovering heights, where H is the hovering height of the draft fan. The simulated axial velocities of gas and particles are positive because gas passes from the bed to the blade plane. The negative lateral velocities of gas and particles
Please cite this article as: X. Jiang, Y. Xu, Y. Geng et al., Entrainment of particles and gas induced by draft fan over the particles bed, Advanced Powder Technology, https://doi.org/10.1016/j.apt.2019.10.011
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Fig. 9. Simulated axial and lateral velocities of gas as a function of hovering heights.
the tip of the blades, and particles are entrained by the swirling flow induced by the draft fan. Fig. 11 shows the velocity vectors of gas and particles at two dimensionless heights h/H, where h is the height from the surface of the bed. At the dimensionless height of 0.9 near the blade plane, the high tangential velocities of gas and particles are formed by the rotation of blades. However, the tangential velocities of gas and particles are reduced at the dimensionless height of 0.2 near the surface of the bed. It can be found that the directions of gas and particles are the same at two dimensionless heights. The tangential velocities form a swirling flow, and enhance shear forces which overcome the contact forces between particles. Particles detach from the surface of the bed, and are entrained by gas flow induced by the draft fan. The averaged cross-sectional area solids volume fraction is calculated in the cylindrical domain. The distributions of averaged cross-sectional area solids volume fractions are shown in Fig. 12 at four hovering heights. The solids volume fraction decays along dimensionless heights. The transport zone of the cylindrical domain is characterized by a solids volume fraction corresponding to the value of the exit solids concentration extrapolated to the surface of the bed. There is a relatively dense region (DE) with high volume fraction of particles at the low height h. While a dilute region (DI) with low volume fraction of particles exists at the high height h. The transition (TR) is formed from the dense region to the dilute region. The transition region is shortened, and the dilute region is enlarged with the increase of hovering height of the draft fan. The mean solids volume fraction is calculated. The value of mean solids volume fraction is 0.0798 at the hovering height of 0.5 m, and it is 0.003 at the hovering height of 1.0 m. This indicates that the mean solids volume fraction increases with the decrease of hovering height of the draft fan. Fig. 13 shows the distribution of bulk density along height at two hovering heights. The DE region exists near the surface of the bed, and the DI region locates at the high height h. The TR region fall in them. The intersection of the two curves of the TR region and the DE region is expressed by the point C, and its dimensionless height is hc. The vertical profile of bulk density of particles along the height within the transition (TR) and the dilute region (DI) can be described by means of an equation containing two parameters
qb ¼ qb0 eaðh=Hhc Þ Fig. 10. Simulated axial and lateral velocities of particles as a function of hovering heights.
mean that gas enters from the outside into the inside of the cylindrical domain. The axial and lateral velocities are low at the hub and large at the tip of the blades because of the Coriolis force and centrifugal force induced by the blades rotation. At the low hovering height of 0.5 m and 0.625 m, the axial velocities of gas and particles increase toward the outside. However, both velocities of gas and particles increase, reach maximum at the dimensionless distance x/R of 0.75, and then decrease at the hovering heights of 0.75 m and 1.0 m. The axial and lateral velocities of gas and particles are reduced with the decrease of hovering height. It is also found that the lateral velocities are larger than the axial velocity because of the rotation of the rotor blades. From simulated axial and lateral velocities of gas and particles, it is found that the velocity profiles are similar. Because the axial velocity component pushes upward gas flow, while the lateral velocity component blows particles located at the surface of the bed toward the draft fan, the flow field of gas and particles is driven by the fan blades, and generates rotational motion of gas and particles. The recirculation flow of gas and particles is formed at
ð6Þ
where a is the decay constant, and qb0 is the maximum bulk density at the point C. The bulk density of particles falls off exponentially from the transition to the dilute region. The decay constant represents the characteristics of particles entrainment. The value of the decay constant decreases and the maximum bulk density increases with the decrease of hovering height, indicating more and more particles are entrained by the draft fan. The averaged cross-sectional area axial and lateral velocities of gas and particles are shown in Fig. 14 at four hovering heights of the draft fan. The lateral velocities of gas and particles increase, reach maximum, and then decrease with the increase of dimensionless height. However, the axial velocities of gas and particles increase with the increase of dimensionless heights. The flow fields of gas and particles are characterized by the hovering heights of the draft fan. The instantaneous mass flux rate of entrained particles is calculated at the exit of the draft fan, and shown in Fig. 15 at two hovering heights of the draft fan. The mass flux rate is larger at the hovering height of 0.5 m than that at the hovering height of 1.0 m because the tangential flow velocity is large at the low hovering height. This leads to a large pressure drop Dp (Dp = p0 pc) along the cylindrical domain, as shown in Fig. 13, where po and pc are the pressures at the surface of the particles
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Fig. 11. Velocity vectors (m/s) of gas and particles at two dimensionless heights h/H.
Because a high negative gas pressure exists at the surface of the bed, the large ‘‘pressure gradient effect” causes a large entrainment of particles. Hence, the large gas velocity and high negative gas pressure by the draft fan enhance entrainment of particles. 3.3. Effect of rotational speed of the draft fan
Fig. 12. Profile of solid volume fraction at four hovering heights.
Fig. 13. Profile of bulk density of particles and gas pressure along dimensionless heights.
bed and the blade plane in the cylindrical domain. Greeley and Iversen [28] found that the entrainment of particles from the fixed bed by means of the vortex motion is more efficient that the boundary layer gas shear. There are at least two controlling forces by which particles are lifted from the particles bed [29]. The first is the drag force which lifts particles from the bed. The lifting effect by the drag force relates to the slip velocity between the gas phase and the solid phase. The second mechanism is known as the ‘‘pressure gradient Dp effect” which leads to a lift on the particles [30].
The simulated gas velocity streamlines and contours are shown in Fig. 16 at two rotational speeds at the hovering height of 1.0 m. Both cases show that gas goes horizontally toward the cylindrical domain, and passes through the blade plane, and then spreads after the draft fan. The symmetrical gas vortexes are formed, and the gas circulations are generated at the tip of the blades. Furthermore, the gas vortexes move away from the tip of the blades at the rotational speed of 1300 rpm. These draft fan-induced gas circulations could contribute to the entrainment of particles from the bed. The distributions of particle velocity vectors and solids volume fractions contour are shown in Fig. 17 at two rotational speeds at the hovering height of 1.0 m. Both cases show that particles located at the surface of the bed move horizontally toward the cylindrical domain, and then pass through the blade plane of the draft fan. With the increase of rotational speed, more particles are entrained because of more energy transfer from the blades to particles. The simulated results indicate that the rotational speed of the rotor effects on the entrainment of particles from the bed. The distributions of axial and lateral velocities of gas and particles are shown in Fig. 18 at three rotational speeds along lateral direction x/R. The lateral velocities of gas and particles are large at the x/R = 1.0 and small at the x/R = 0 along lateral direction, indicating gas and particles move horizontally toward the cylindrical domain along the surafce of the bed. The axial velocities of gas and particles increase from x/R = 0, reach maximum and then decrease at x/R = 1.0. Simulated results show that the axial and lateral gas velocities are larger than those of particles, indicating particles located at the surface of the bed are carried by gas flow induced by the rotation of the draft fan. Both velocities of gas and particles are increased with the increase of rotational speeds, indicating more particles are entrained from the bed. The distributions of averaged cross-sectional area volume fraction of particles are shown in Fig. 19 at three rotational speeds of the draft fan. The solids volume fraction increases with the increase of rotational speeds. Numerical simulations further illustrate that the vertical profile of solids volume fraction decay along the height from the surface of the particles bed in the cylindrical domain. The inflection of solids volume fraction profile stands for an interface between the dense and dilute regions, and the solids volume fraction drops rapidly. The variations of solids volume fraction are similar at three rotational speeds, indicating that the rotation speed of the draft fan does not affect the trends of overall
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Fig. 14. Profile of axial and lateral velocities of gas and particles at four hovering heights.
Fig. 15. Distribution of mass flux rate of entrained particles.
distribution of solids volume fraction, but their local solids volume fractions along dimensionless height and mean solids volume fractions in the cylindrical domain. The distributions of averaged cross-sectional area axial and lateral velocities of gas and particles are shown in Fig. 20 at three rotational speeds. Both velocities of gas and particles increase with the increase of rotational speed of the draft fan because more energy from the draft fan is transferred to gas and particles. Both
lateral velocities of gas and particles are reduced at the dimensionless height larger than 0.9 because of the effect of the hub of the draft fan. The distribution of instantaneous mass flux rate Gs of particles is shown in Fig. 21 at two different rotational speeds of the draft fan. The mass flux rates are larger at the rotational speed of 1300 rpm than that at the rotational speed of 700 rpm because the high rotational speed of the draft fan produces a large gas velocity at the surface of the bed. The pickup velocity is defined as the gas velocity necessary to suspend the particles initially at rest at the bottom of the pipeline or it may be defined as the gas velocity required to initiate sliding motion, rolling and suspension of particles. To determine the pickup velocity of particles, the empirical correlations are proposed in the axial flow field [31,32]. The diameter and density of particles and particle shape are the crucial factors in the determination of pickup velocity of particles [33]. Fig. 22 shows the calculated pickup velocities using Cabrejos and Klinzing [31] and Kalman et al. [32]. From numerical simulations, the radial and tangential velocities of gas at the surface of the bed is obtained, and the gas velocities ug,cd entering the cylindrical domain is determined at the cylindrical domain x/R = 1.0. The simulated radial and tangential velocities are shown in Fig. 22 as a function of rotational speeds and hovering heights. The gas radial and tangential velocities increase with the increase of rotational speed and the decrease of hovering height. We see that the simulated radial velocities entering the cylindrical domain are smaller than the calculated pickup velocities. From the momentum balance in the shear flow under the axial flow [34], the mechanism of the initial movement
Fig. 16. Gas velocity streamlines and contours at different rotational speeds of the draft fan.
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Fig. 17. Velocity vector and volume fraction contour of particles at two rotational speeds.
Fig. 18. Profile of axial and laterial velocities of gas and particles at three rotational speeds.
Fig. 19. Profile of solid volume fraction at three rotational speeds.
of dry particles occurs when the moment caused by the lift and drag forces is superior to those from the gravitational and adhesion forces. The draft fan-generated flow can be characterized as a swirling flow. The pickup velocity is different in the axial swirling flow fields. The swirl component gives rise to a significant enhancement of lift force acting on particles. The pickup velocity of coal particles was measured in the swirling flow field [35]. The pickup velocity of
particles was decreased when the tangential flow rate was sufficient to disturb particles. The measured pickup velocity demonstrated that the swirling flow with appropriate swirling intensity is beneficial to particle pickup. It anticipates that the entrainment of particles by the draft fan over the bed contributes to the additional disturbance induced by swirling flow. Fig. 23 shows the distribution of solid mass flux rate as a function of rotational speed and hovering height of the draft fan. The solid mass flux rates increase with the increase of rotational speeds and decrease of hovering height. This indicates that particles at the surface of the bed are entrained by gas induced by the draft fan, indicating that the transportation of particles from the bed is controlled by the rotation speed and hovering height of the draft fan. The sediment pickup rates were measured at the unobstructed and obstructed open channel flow [36]. The measured results showed that the pickup rate increased exponentially in the presence of vortices generated by a cross-flow cylinder. The pickup rate with the obstructed flow was larger than that at the unobstructed channel flow. This indicates the swirling flow generated by the draft fan is beneficial to particle pickup from the particle bed.
4. Conclusions In this study, the Euler-Euler TFM is applied to assess entrainment of gas and particles induced by an axial 4-blade draft fan hovering over the particles bed. The interactions of collisions between particles and blade wall-particles are modeled using
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Fig. 20. Profile of axial and lateral velocities of gas and particles at three rotational speeds.
Fig. 21. Profile of mass flux rate of entrained particles at two rotational speeds. Fig. 23. Distribution of solid mass flux rate as a function of rotational speeds and hovering heights.
Fig. 22. Profile of calculated pickup velocity and simulated gas radial and tangential velocities.
KTGF. The multiple reference frame model is used to simulate the rotating reference frame of the blades of the draft fan. With this method, the entrainment of particles is simulated to reproduce flow behavior of gas and particles induced by the draft fan.
Simulated velocity and volume fraction of particles show that the dense region with high solids volume fraction and low particles velocity near the surface of the bed and the dilute region with low solids volume fraction and large particles velocity exist along dimensionless height. The bulk density of particles falls off exponentially from the transition to the dilute region in the cylindrical domain. The gas radial and tangential velocities entering the cylindrical domain increase with the increase of rotational speed and decrease of hovering height. Simulated results indicate that the swirling flow induced by the draft fan generates an additional disturbance and is beneficial to particle entrainment from the bed. Present simulations show that this model is able to predict flow behavior of gas and particles using axial draft fan to control entrainment of particles. In the future, this modeling method will be applied to conduct parametric investigation of entrainment of particles induced by draft fan and to improve transport performance of particles from the bed. The numerical simulations and experimental measurements are needed to investigate the effect of rotational speeds and blade geometrical arrangements on entrainment of particles and particle pickup velocity by the draft fan for further study.
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Acknowledgments This research is financially supported by the National Natural Science Foundation of China via the grants Nos. 91752115 and 51776059, and by the Key Laboratory of Aerospace Thermophysics, Ministry of Industry and Information Technology. The authors express their gratitude for this support. References [1] G. Ziskind, M. Fichman, C. Gutfinger, Resuspension of particulates from surfaces to turbulent flows-review and analysis, J. Aerosol Sci. 26 (1995) 613–644. [2] G.A. Sehmel, Particle resuspension: a review, Environ. Int. 4 (1980) 107–127. [3] W.C. Hinds, Aerosol Technology: Properties, Behavior and Measurement of Airborne Particles, Wiley, Los Angeles, 1999. [4] T. Miyahara, K. Tsuchiya, L.S. Fan, Mechanism of particle entrainment in a gasliquid-solid fluidized bed, AIChE J. 35 (1989) 1195–1198. [5] J.H. Choi, S.D. Kim, J.R. Grace, Entrainment rate of coarse particles at different temperatures in gas fluidized beds, Can. J. Chem. Eng. 85 (2007) 15–17. [6] J.W. Chew, D.M. Parker, C.M. Hrenya, Elutriation and species segregation characteristics of polydisperse mixtures of group B particles in a dilute CFB riser, AIChE J. 59 (2013) 84–95. [7] N. Hidaka, J. Iyama, T. Matsumoto, K. Kusakabe, S. Morooka, Entrainment of fine particles with upward gas flow in a packed bed of coarse particles, Powder Technol. 95 (1998) 265–271. [8] V. Manousos, B.A. Roger, Entrainment of coarse grains using a discrete particle model, AIP Conf. Proc. 1618 (2014) 870–873. [9] H.T. Do, R. Clift, J.R. Grace, Particle ejection and entrainment from fluidized beds, Powder Technol. 6 (1972) 195–200. [10] S.M. Tasirin, D. Geldart, Entrainment of FCC from fluidized beds – a new correlation for the elutriation rate constants K-infinity, Powder Technol. 95 (1998) 240–247. [11] J.W. Chew, A. Cahyadi, C.M. Hrenya, R. Karri, R.A. Cocco, Review of entrainment correlations in gas–solid fluidization, Chen. Eng. J. 260 (2015) 152–171. [12] F.H. Rohles, S.A. Konz, B.W. Jones, Ceiling fans as extenders of the summer comfort envelope, ASHRAE Trans. 89 (1A) (1983) 245–263. [13] S.H. Ho, L. Rosario, M.M. Rahman, Thermal comfort enhancement by using a ceiling fan, Appl. Therm. Eng. 29 (2009) 1648–1656. [14] Z. Shengwei, J. Srebric, S.N. Rudnick, R.L. Vincent, E.A. Nardell, Numerical modeling of indoor environment with a ceiling fan and an upper-room ultraviolet germicidal irradiation system, Build. Environ. 72 (2014) 116–124. [15] F. Babich, M. Cook, D. Loveday, R. Rawal, Y. Shukla, Transient threedimensional CFD modeling of ceiling fans, Build. Environ. 123 (2017) 37–49. [16] C. Wenhua, L. Shichao, G. Yunfei, Z. Hui, E. Arens, L. Zhao, Experimental and numerical investigations of indoor air movement distribution with an office ceiling fan, Build. Environ. 130 (2018) 14–26. [17] ANSYS Fluent Inc., FLUENT 6.2 User’s Guide, 2012.
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Advanced Powder Technology journal homepage: www.elsevier.com/locate/apt
Original Research Paper
Entrainment of particles and gas induced by draft fan over the particles bed Xiaoxue Jiang a, Yingqiao Xu b, Yan Geng b, Chuang Wang b, M. Hassan a, Linzhi Meng b, Huilin Lu a,⇑ a b
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China China Aerospace Science and Technology Corporation Fifth Research Institute, Beijing 100081, China
a r t i c l e
i n f o
Article history: Received 22 November 2018 Received in revised form 6 July 2019 Accepted 10 October 2019 Available online xxxx Keywords: Entrainment Kinetic theory of granular flow Draft fan Hovering height Particles bed
a b s t r a c t The draft fan is used to generate a controlled transportation of particles to enhance entrainment of gas and particles from the particles bed. Present investigations show the entrainment behavior of particles induced by an axial 4-blade draft fan hovering over the particles bed. The distributions of velocities and volume fractions of gas and particles are simulated using Euler-Euler two-fluid model (TFM) with kinetic theory of granular flow (KTGF) at different hovering heights and rotational speeds of the draft fan. The dense region with high solids volume fraction and low particles velocity and the dilute region with low solids volume fraction and high particles velocity exist beneath the draft fan along hovering heights. The entrainment of particles increases with the decrease of hovering height and increase of rotational speed of the draft fan. Present numerical simulations confirm that the gas-solid TFM with the kinetic theory of granular flow and multiple reference frame model can be effectively applied to analysis for entrainment of particles induced by draft fan. Ó 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
1. Introduction Entrainment of particles by an air stream is a process which occurs in industrial applications including clean technology, spread of radioactive particles, handling of toxic powders and dust storms in desert areas [1–3]. Furthermore, the entrainment of particles is very important processes to avoid the reduction of particles from gas-particles fluidized bed reactors [4–6]. Hence, the entrainment rate of particles has to be known for the design of an appropriate gas-solid system. The entrainment in gas-particles fluidized beds refers to the removal of solids from a fluidized bed by fluidizing gas from the bottom to the exit. The flow behavior of fine particles entrained by the ascending gas flow was measured in a fluidized bed riser [7]. The entrainment of fluid catalytic cracking (FCC) particles from the spheres packed bed was tested, and the empirical equations of dynamic and static volume fractions of particles were correlated as a function of fluidizing gas velocity and particles properties. The discrete particle model was used to study the effects of gas turbulence on particle entrainment [8]. Simulated results showed the entrainment of particles depends on forces acting on particles.
⇑ Corresponding author. E-mail address: [email protected] (H. Lu).
The entrainment of particles in fluidized beds was acknowledged by up-flow gas from the bed surface [9,10]. The entrainment of particles was reviewed by Chew et al. [11] in gas–particles fluidization. The comparisons of the predicted entrainments using different empirical elutriation rate correlations were analyzed in gas-particles fluidized beds. On the other hand, the ceiling fan is widely used to generate a controlled gas and particles flow in the air-conditioned space, cooling scenarios and residential and commercial buildings because it has inherently diverse merits, including a compact structure, a wide operating scope and high efficiency [12]. The hydrodynamics of gas induced by the ceiling fan rotation were investigated by numerical simulations and experiments [13]. The distributions of velocity, temperature and humidity using a ceiling fan were predicted in an air-conditioned room. A parametric analysis on the effect of the ceiling fan was conducted using numerical simulations. The air movement in the indoor environmental room with ceiling fan was simulated using the commercial CFD software Star-CCM [14]. The air flow created by the rotation of the ceiling fan was predicted by means of the rotating reference frame method to model the rotation of fan blades. The simulated average vertical speeds were validated against experimental results. The velocity profiles by ceiling fan were simulated using a commercial CFD FLUENT code with k-e turbulent models [15]. The local free shear layers generated by the ceiling fan were predicted and
https://doi.org/10.1016/j.apt.2019.10.011 0921-8831/Ó 2019 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
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Nomenclature CD ds D Gkg Gs gi go h H I I2D kg ks ps psc psf Res S Ss u ur ut x
drag coefficient [–] particle diameter [m] width of particles bed [m] turbulent kinetic energy generation [kgm1s3] solid mass flux rate [kgs1] gravitational acceleration [ms2] radial distribution function [–] height from the particle bed [m] hovering height [m] identity matrix [–] second invariant of the deviatoric stress tensor [–] turbulent kinetic energy [m2s2] conductivity of fluctuating energy [kgm1s1] solid phase pressure [Pa] collisional and kinetic part of solid phase pressure [Pa] frictional part of solid phase pressure [Pa] particle Reynolds number [–] mean strain rate [s1] solid strain rate tensor [–] absolute velocity (the velocity viewed from the stationary frame) [m/s] relative velocity (the velocity viewed from the moving frame) [m/s] translational frame velocity [m/s] radial position [m]
compared to experimental results in the environmental chamber. The effect of ceiling fan rotational speed and ceiling height on air velocity and temperature was analyzed [16]. Two zones were identified, including the cylindrical domain beneath the blades and remaining zone. The jet impingement formed by the ceiling fan generated a radial flow on the floor. Numerical results mentioned above show that the CFD provides a convenient and affordable alternative to model the performance of ceiling fans. Despite there are a number of numerical simulations and experimental measurements of gas flow induced by the rotation of ceiling fan, the knowledge of particles entrainment induced by fan rotation is very limited. The present study attempts to simulate the flow field of gas and particles induced by the draft fan hovering over the particles bed by means of Euler-Euler two-fluid model (TFM). To accurately simulate the flow field of particles when the draft fan rotates at the specific rotational speed, the interactions between the particles and the blade surface and the interactions of particles are modeled by means of kinetic theory of granular flow (KTGF). The flow field around the rotor blade is numerically calculated using the multiple reference frame (MRF) method to model the revolving movement of the rotor. The effect of hovering heights on volume fractions and velocities of gas and particles is simulated, and the distributions of volume fraction and velocity of particles are analyzed along the surface of the particles bed. Present numerical simulations will be available for a parametric investigation of hydrodynamics of gas and particles induced by fan rotation in gas-solid processes.
2. Euler-Euler TFM of gas-particles flow induced by draft fan rotation The flow characteristics of gas and particles induced by the rotation of draft fan are obviously very complex because of the contribution of interactions of collisions between the blades and
Symbols
a as;max as;f ;max
b
eg
/ /gs
cs
ks
lg lgt ls lsc lsf
h
q s
X
volume fraction [–] maximum solid packing limit [–] frictional stress threshold [–] drag coefficient of gas–solids phase [kgm3s1] dissipation rate of turbulent kinetic energy [kgm3s1] internal friction angle of particles [°] switch function [–] collisional dissipation of solid fluctuating energy [m2s2] solid bulk viscosity [Pas] gas dynamic viscosity [Pas] gas turbulent viscosity [Pas] solid phase shear viscosity [Pas] collisional and kinetic part of shear viscosity [Pas] frictional part of shear viscosity [Pas] granular temperature [m2s2] density [kgm3] stress tensor [Pa] rotational speed [rpm]
Subscripts g gas phase s solid phase
particles. The entrainment of particles varies with the change of solids volume fractions from the particles bed. Thus, the present numerical simulations will focus on the entrainment of particles induced by the rotation of the draft fan hovering over the particles bed. The schematic diagram used in numerical simulations is showed in Fig. 1, where the particles bed is arranged at the bottom of the closed vessel. An axial 4-blade draft fan is installed over the bed at the upper part of the computational domain which consists of the internal region and the external region. The revolving center is the axis of the draft fan. The draft fan measures 2.3 m in diameter with blades that are 1.06 m long and 5 mm thick. The chord is 0.2 m. The pitch angle of the blades is 15 degree. The diameter of the hub is 0.18 m. The elastic deformation of blades is ignored. The mono-sized particles are filled into a box container forming a particles bed. The diameter and density of particles are 50 lm and 2000 kg/m3 in the particles bed. 2.1. Models of gas-particles flow induced by rotation of draft fan The present numerical simulations aim to study the entrainment of gas and particles induced by the blade rotation of the draft fan from the particles bed, therefore, the formula used in the models must be able to describe the gas and particles movement induced by the draft fan and capture the distributions of gas and particles from the bed. As a result, the flow field of a revolving rotor is modeled using the multiple reference frame (MRF) model [17], and the kg-eg turbulence model is selected to model turbulence of gas phase by the rotation of blades. The KTGF is used to model interactions between the blades and particles. The equations of mass balance for gas phase and solid phase are expressed as follows [18].
@ ag q urgj @ g ag qg þ ¼0 @t @xj
ð1Þ
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Fig. 1. Schematic diagram of draft fan system used in numerical simulations.
@ @ as qs ursj ðas qs Þ þ ¼0 @t @xj
ð2Þ
The equation of gas momentum conservation in the moving reference frame is: @s @p a qg urgi Þ þ @x@ j ðag qg urgi urgj Þ ¼ ag @x þ @xgij þ ag qg g i bðursi urgi Þ i j 2ag qg Xgj urgi ag qg Xgi Xgj Ri
@ ð g @t
ð3Þ where X and R are the angular spin rate and the radius of rotating. The gas stress tensor sg is shown in Table 1 [17]. The effective gas viscosity is predicted using a kg–eg turbulence model [16]. The forth term of the right-hand side is the interfacial momentum transfer between the gas phase and the solid phase. The fifth and sixth terms are due to the unsteady change of the rotational speed and linear velocity of gas phase, respectively. They represent the gas Coriolis acceleration and centrifugal acceleration [16]. Similarly for the solid phase, the equation of momentum conservation is: @s @p s a qs ursi Þ þ @x@ j ðas qs ursi ursj Þ ¼ as @x þ @p þ @xsijj þ as qs g i þ bðurgi ursi Þ @xi i 2as qs Xsj ursi as qs Xsi Xsj Ri
@ ð s @t
ð4Þ where the fifth and sixth terms are due to the unsteady change of the rotational speed and linear velocity of solid phase, and relate to angular spin rate of particles. The stress tensor of solid phase is shown in Table 1 [17] according to solid pressure ps and viscosity ls. The pressure and viscosity of particles are simulated as a function of granular temperature h by solving a fluctuating kinetic energy equation of particles using KTGF [18,19]. In order to solve the fluctuating energy equation, we need to specify the collisional energy dissipation cs due to inelastic collisions of particles and the granular conductivity ks as a function of restitution coefficient of particles e. To simulate a gas–particles flow induced by the draft fan from the particles bed, a relation of frictional stresses is needed to solve the momentum equation. The frictional components of pressure psf and viscosity lsf are modeled using Eq. (T10) and (T13). The interface momentum transfer coefficient is modeled using Huilin-Gidaspow drag model in ANSYS [17,20].
2.2. Boundary conditions and simulation strategy To predict entrainment of gas and particles induced by the rotation of the draft fan from the particles bed, the computational domain assigns a cube with the length of 10 m, the width of 10 m and the height of 4 m, as shown in Fig. 1, with the axial draft fan at the center and the bed at the bottom. The blades are connected by the rotor hub. The draft fan is modeled by MRF model in the internal region. The radius of the internal region is 1.2 m which is large enough to contain the intersecting rotational surfaces. In the MRF model, it is possible to transform the equations of fluid motion to the moving frame such that the steady-state solutions are possible for a steadily moving frame [21]. The unsteady simulation can be run in a moving reference frame with constant rotational speed. The coupling between the rotating reference frame and the stationary reference frame is shown in Fig. 2 [17]. The rotating axis of the rotating system corresponds with the z axes. The velocities of gas phase and solid phase are transformed from the stationary reference frame to the rotating frame using the following relation [17,21,22]:
! ! ! ! ! u ¼ ur þðut þ X RÞ
ð5Þ
The particles bed is located at the bottom of the computational domain. Initially, the static height Ho of the bed is 0.5 m with the initial volume fraction of particles of 0.6. The initial velocities of particles and gas are zero. The inlet is assigned with the pressure inlet boundary condition, and the exit is assigned with the pressure outlet boundary condition. The bottom of the bed is the wall boundary condition. During the rotation of the blades, the non-slip boundary condition is used for gas phase at the walls of the blades. The gas velocity along the boundary is equal to the moving velocity of the blades. For solid phase, the slip wall boundary condition is used at the blade surface [23]. The computational domain divides into the internal region with the rotational blades and the external region. The blades rotate at the rotational speed in the rotating reference frame and the MRF model is used in the internal region. The denser unstructured grids are deployed on the blades, including the hub surface and the rounding at the tips of the draft fan. The rest space in the
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Table 1 A summary of the constitutive equations. A. Constitutive equations of gas phase (a) Gas phase stress " T # * * * 2a sg ¼ ag lge r u rg þ r u rg 3 g lge r u rg
(T1)
(b) Effective gas viscosity (T2)
2
lge ¼ lg þ lgt ¼ lg þ C l qg kegg
(c) Gas kg-eg model l pffiffiffiffiffiffiffiffipffiffiffiffiffiffi * ag qg kg þ r ag qg u rg kg ¼ r ag rgtk rkg þ ag Gkg ag qg eg kgs 2kg 2kg 3h * @ ¼ @t ag qg eg þ r ag qg u rg eg l pffiffiffiffiffiffiffiffipffiffiffiffiffiffi eg gt r ag re reg þ ag kg C 1 Gkg C 2 qg eg C 2 kegg kgs 2kg 2kg 3h pffiffiffiffiffiffiffiffiffiffiffiffi * * Gkg ¼ lgt S2 , S ¼ 2Sg Sg and Sg ¼ 12 r u rg þ rT u rg
@ @t
(T3) (T4)
(T5)
C1 = 1.44, C2 = 1.92, Cl = 0.09, rk = 1.0 and re = 1.3 B. Constitutive equations of solids phase (a) Conservation of solid phase fluctuating energy * * 3 @ ¼ ps I þ ss r u rs þ r ðks rhÞ cs 2 @t ðas qs hÞ þ r as qs u rs h
(T6)
(b) Solid phase stress " #
* * T * ss ¼ as ls r u rs þ r u rs þ as ks 23 ls r u rs I
(T7)
(c) Solid phase pressure ps ¼ psc þ psf psc ¼ ½1 þ 2ð1 þ eÞas g o as qs h (
10 25 as > as;f ;max psf ¼ 10 as as;f ;max 0 as 6 as;f ;max
(T8) (T9) (T10)
(d) Solid phase shear viscosity
ls ¼ lsc þ lsf
pffiffiffiffi
qffiffiffi
2 ph 4 lsc ¼ 9610aqs sgdosð1þe þ 45 as qs ds g o ð1 þ eÞ Þ 1 þ 5 as g o ð1 þ eÞ
ffiffiffiffiffi lsf ¼ p2sfpsin/ I
h
p
(T11) (T12) (T13)
2D
I2D ¼ SS : SS and SS ¼ 12
* * r u rs þ rT u rs
(T14)
(e) Solid phase bulk viscosity qffiffiffi ks ¼ 43 as qs ds g o ð1 þ eÞ ph
(T15)
cs ¼ 3 1 e2 g o qs a2s
(f) Collisional dissipation of solid fluctuating energy h qffiffiffi i
! 4 h p r u rs ds
(T16)
(g) Conductivity of the fluctuating energy qffiffiffi pffiffiffiffi 2 qs ds p h 1 þ 65 as g o ð1 þ eÞ þ 2a2s qs ds g o ð1 þ eÞ ph ks ¼ 150 384ð1þeÞg
(T17)
(h) Radial distribution function h i1 as Þ1=3 g 0 ¼ 1 ðas;max
(T18)
(i) Gas–solid phase interphase exchange coefficient
0
* * 1
* * 1:75as qg u rs u rg 3C D as ag qg u rs u rg 150as ð1ag Þla @ A þ a2:65 b ¼ /gs þ ð1 /gs Þ 2 g ds 4ds
(T19)
o
a g ds
as Þ /gs ¼ arctan½1501:75ð0:2 þ 0:5 ( h p
0:687 i 24 1 þ 0:15 a Re g s C D ¼ ag Res 0:44
* * qg ds u rs u rg Res ¼ l
(T20) for Res 6 1000
(T21)
for Res > 1000 (T22)
g
computational domain is the external region which is fixed in the stationary reference frame. The internal grids revolve when the hub rotates along its axis. The discontinuity of the nodes arises from between the internal grids and the external grids. Thus, the interface boundary condition is assigned, and the physical quantities of the block are transferred using interpolation through the boundary. To confirm that the results are independent of grid size, the increments of grid numbers are performed. Fig. 3 shows the computed time-averaged velocity of particle and gas pressure along the radial position at
three different grid numbers. The computational domains consist of 120,000, 210,000 and 330,000 non-uniform grids. The computed values are approximately same for all the grid number cases. The minimum and maximum velocity and pressure error percentages as compared with the lowest grid number case are only 0.15% and 12.4%, respectively. This indicates that all the grid number cases are sufficiently fine for providing reasonably grid independence results. However, the computational time is still a significant restriction when using a finer grid. In this study, the computational domain consisting of 210,000 non-uniform grids is selected to use.
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X. Jiang et al. / Advanced Powder Technology xxx (xxxx) xxx Table 2 Simulation conditions and model parameters. Particle diameter Height of particles bed Gas viscosity Particles restitution coefficient (e) Initial particle concentration
Fig. 2. Schematic of the coupling between the rotating and the absolute reference frames.
Therefore, the interface between the internal grids and the external grids avoids discontinuities of physical quantities across the bordering nodes. The 3D simulation parameters are shown in Table 2. The value of restitution coefficient of particles of 0.9 is suggested to study the distribution of particle velocities in the circulating spout- fluid bed with the draft tube [24]. On the other hand, the value of wall restitution coefficient of 0.25–0.75 is suggested [25,26]. The pressure– velocity coupling scheme is used with the standard pressure discretization scheme, and the volume fraction is discretized with a QUICK scheme. The other terms of the governing equations are discretized with second order upwind schemes. The values of the under-relaxation factors of pressure and volume fraction are 0.15 and 0.4, respectively. The numerical simulations are conducted using ANSYS Fluent code [17] at the computational time step of 1.0 104 s.
3. Simulations and discussions 3.1. Instantaneous entrainment of gas and particles The flow structure of gas and particles induced by the rotation of the draft fan is studied with the change of hovering heights over the particles bed. The gas velocity contours are shown in Fig. 4 at four hovering heights, where H is the distance from the surface of the bed to the blade plane. The vortexes are generated when the rotor rotates anticlockwise. A draft fan entrains gas, and
50 (lm) 0.5 (m)
Particle density Gas density
2000 (kg/m3) 1.225 (kg/m3)
1.789 105 (kg/ms) 0.9
Rotational speed
700, 1000, 1300, 1600 (rpm) 0.4
0.6
Wall restitution coefficient (ew) Hovering height
0.5, 0.625, 0.75, 1.0 (m)
produces negative gas pressure beneath the blades. This negative pressure drives as a swirling gas jet that impinges on the surface of the bed. The differences among four gas stream lines are attributed to the hovering height difference over the bed. When the hovering height is at 0.5 m, the gas vortexes are formed at the tip of the blades. At the hub, gas flow from the top to the blade plane with the negative gas velocity, and then enters into the vortex. Gas and particles are sucked from the surface of the bed, and enter into the blade plane. At the same time, gas flows horizontally along the surface of the bed. When the draft fan is raised at 0.625 m and 0.75 m, the double anti-symmetric vortexes are formed at the tip of the blades. At the hovering height of 1.0 m, the gas vortex moves away from the tip into the external zone. The volume fraction contours and velocity vectors of particles are shown in Fig. 5 at four hovering heights. The sectional views of flow of particles created by the draft fan illustrate similar flow patterns of particles. When the hovering height is small, the space between the blade plane and the surface of the particles bed is small, and the flow resistance in this space will be increased. This leads to increase air flow rate. Numerical simulations further illustrate that the velocity of particles located at the surface of the bed is reduced with the increase of heights from the bed. The draft fan revolves to generate gas pressures both above and under the blades. The gas pressure contour is shown in Fig. 6 at four hovering heights. The simulated gas pressures show the negative gas pressure beneath the blades and positive gas pressure above the blades. The large gas pressure difference is found at the hovering height of 0.5 m and 0.625 m, and resulting in forces which enable to move particles at the surface of the bed. The gas pressure difference is reduced at the high hovering height, indicating a major influence of hovering height on gas pressure. The pressure difference indicates that the draft fan revolves to generate the negative gas pressure beneath the blades and positive gas pressure above the blades.
Fig. 3. Comparison of particles velocity and gas pressure for different mesh resolutions.
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Fig. 4. Gas velocity streamlines and contours at different hovering heights.
Fig. 5. Volume fraction contour and velocity vector of particles at different hovering heights.
The solids volume fraction contours are shown in Fig. 7 at four hovering heights. The solids volume fraction is high beneath the blade plane and low at the upper blade plane because particles located at the surface of the bed are entrained by gas induced by the rotation of the blades. The solids volume fraction is reduced with the increase of hovering heights. From simulated solids volume fractions, the flow field can be divided into four parts except for the bed, and shown in Fig. 8. The first part I is the one surrounding the rotor, composed of a cylindrical domain with the width same as the fan diameter. Gas and particles are carried from the surface of the bed to the blade plane. The gas pressure is negative in the cylindrical domain of part I. The vortex formed at the tip of the blades is known as the part II. The region of part II is increased
with the increase of hovering height of the draft fan. The third part III is the transition over the bed. Particles carried by gas move horizontally towards part I. The rest region becomes the part IV in the computational domain. With the decrease of hovering height of the draft fan, the solids volume fractions in part I and II are increased, indicating more particles are entrained by the draft fan. Similarly different flow regions were also observed in a room using ceiling fan in the experiment [27]. The main flow region was the area below the fan with high gas velocity, forming a transport zone. The diameter of the flow region immediately below the ceiling fan is close to the diameter of the ceiling fan. The simulated results confirm that the model used is able to predict the flow of gas and particles generated by a fan hovering over the bed.
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Fig. 6. Gas pressure contour at four hovering heights.
Fig. 7. Solid volume fraction contour at four hovering heights.
3.2. Distributions of volume fractions and velocities
Fig. 8. Flow regions of particles and gas induced by draft fan.
To describe entrainment characteristics of particles induced by the draft fan, the velocity and volume fraction are calculated in the cylindrical domain with the same diameter as the fan blades. The distributions of axial and lateral velocities of gas and particles are shown in Figs. 9 and 10 at four hovering heights, where H is the hovering height of the draft fan. The simulated axial velocities of gas and particles are positive because gas passes from the bed to the blade plane. The negative lateral velocities of gas and particles
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Fig. 9. Simulated axial and lateral velocities of gas as a function of hovering heights.
the tip of the blades, and particles are entrained by the swirling flow induced by the draft fan. Fig. 11 shows the velocity vectors of gas and particles at two dimensionless heights h/H, where h is the height from the surface of the bed. At the dimensionless height of 0.9 near the blade plane, the high tangential velocities of gas and particles are formed by the rotation of blades. However, the tangential velocities of gas and particles are reduced at the dimensionless height of 0.2 near the surface of the bed. It can be found that the directions of gas and particles are the same at two dimensionless heights. The tangential velocities form a swirling flow, and enhance shear forces which overcome the contact forces between particles. Particles detach from the surface of the bed, and are entrained by gas flow induced by the draft fan. The averaged cross-sectional area solids volume fraction is calculated in the cylindrical domain. The distributions of averaged cross-sectional area solids volume fractions are shown in Fig. 12 at four hovering heights. The solids volume fraction decays along dimensionless heights. The transport zone of the cylindrical domain is characterized by a solids volume fraction corresponding to the value of the exit solids concentration extrapolated to the surface of the bed. There is a relatively dense region (DE) with high volume fraction of particles at the low height h. While a dilute region (DI) with low volume fraction of particles exists at the high height h. The transition (TR) is formed from the dense region to the dilute region. The transition region is shortened, and the dilute region is enlarged with the increase of hovering height of the draft fan. The mean solids volume fraction is calculated. The value of mean solids volume fraction is 0.0798 at the hovering height of 0.5 m, and it is 0.003 at the hovering height of 1.0 m. This indicates that the mean solids volume fraction increases with the decrease of hovering height of the draft fan. Fig. 13 shows the distribution of bulk density along height at two hovering heights. The DE region exists near the surface of the bed, and the DI region locates at the high height h. The TR region fall in them. The intersection of the two curves of the TR region and the DE region is expressed by the point C, and its dimensionless height is hc. The vertical profile of bulk density of particles along the height within the transition (TR) and the dilute region (DI) can be described by means of an equation containing two parameters
qb ¼ qb0 eaðh=Hhc Þ Fig. 10. Simulated axial and lateral velocities of particles as a function of hovering heights.
mean that gas enters from the outside into the inside of the cylindrical domain. The axial and lateral velocities are low at the hub and large at the tip of the blades because of the Coriolis force and centrifugal force induced by the blades rotation. At the low hovering height of 0.5 m and 0.625 m, the axial velocities of gas and particles increase toward the outside. However, both velocities of gas and particles increase, reach maximum at the dimensionless distance x/R of 0.75, and then decrease at the hovering heights of 0.75 m and 1.0 m. The axial and lateral velocities of gas and particles are reduced with the decrease of hovering height. It is also found that the lateral velocities are larger than the axial velocity because of the rotation of the rotor blades. From simulated axial and lateral velocities of gas and particles, it is found that the velocity profiles are similar. Because the axial velocity component pushes upward gas flow, while the lateral velocity component blows particles located at the surface of the bed toward the draft fan, the flow field of gas and particles is driven by the fan blades, and generates rotational motion of gas and particles. The recirculation flow of gas and particles is formed at
ð6Þ
where a is the decay constant, and qb0 is the maximum bulk density at the point C. The bulk density of particles falls off exponentially from the transition to the dilute region. The decay constant represents the characteristics of particles entrainment. The value of the decay constant decreases and the maximum bulk density increases with the decrease of hovering height, indicating more and more particles are entrained by the draft fan. The averaged cross-sectional area axial and lateral velocities of gas and particles are shown in Fig. 14 at four hovering heights of the draft fan. The lateral velocities of gas and particles increase, reach maximum, and then decrease with the increase of dimensionless height. However, the axial velocities of gas and particles increase with the increase of dimensionless heights. The flow fields of gas and particles are characterized by the hovering heights of the draft fan. The instantaneous mass flux rate of entrained particles is calculated at the exit of the draft fan, and shown in Fig. 15 at two hovering heights of the draft fan. The mass flux rate is larger at the hovering height of 0.5 m than that at the hovering height of 1.0 m because the tangential flow velocity is large at the low hovering height. This leads to a large pressure drop Dp (Dp = p0 pc) along the cylindrical domain, as shown in Fig. 13, where po and pc are the pressures at the surface of the particles
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Fig. 11. Velocity vectors (m/s) of gas and particles at two dimensionless heights h/H.
Because a high negative gas pressure exists at the surface of the bed, the large ‘‘pressure gradient effect” causes a large entrainment of particles. Hence, the large gas velocity and high negative gas pressure by the draft fan enhance entrainment of particles. 3.3. Effect of rotational speed of the draft fan
Fig. 12. Profile of solid volume fraction at four hovering heights.
Fig. 13. Profile of bulk density of particles and gas pressure along dimensionless heights.
bed and the blade plane in the cylindrical domain. Greeley and Iversen [28] found that the entrainment of particles from the fixed bed by means of the vortex motion is more efficient that the boundary layer gas shear. There are at least two controlling forces by which particles are lifted from the particles bed [29]. The first is the drag force which lifts particles from the bed. The lifting effect by the drag force relates to the slip velocity between the gas phase and the solid phase. The second mechanism is known as the ‘‘pressure gradient Dp effect” which leads to a lift on the particles [30].
The simulated gas velocity streamlines and contours are shown in Fig. 16 at two rotational speeds at the hovering height of 1.0 m. Both cases show that gas goes horizontally toward the cylindrical domain, and passes through the blade plane, and then spreads after the draft fan. The symmetrical gas vortexes are formed, and the gas circulations are generated at the tip of the blades. Furthermore, the gas vortexes move away from the tip of the blades at the rotational speed of 1300 rpm. These draft fan-induced gas circulations could contribute to the entrainment of particles from the bed. The distributions of particle velocity vectors and solids volume fractions contour are shown in Fig. 17 at two rotational speeds at the hovering height of 1.0 m. Both cases show that particles located at the surface of the bed move horizontally toward the cylindrical domain, and then pass through the blade plane of the draft fan. With the increase of rotational speed, more particles are entrained because of more energy transfer from the blades to particles. The simulated results indicate that the rotational speed of the rotor effects on the entrainment of particles from the bed. The distributions of axial and lateral velocities of gas and particles are shown in Fig. 18 at three rotational speeds along lateral direction x/R. The lateral velocities of gas and particles are large at the x/R = 1.0 and small at the x/R = 0 along lateral direction, indicating gas and particles move horizontally toward the cylindrical domain along the surafce of the bed. The axial velocities of gas and particles increase from x/R = 0, reach maximum and then decrease at x/R = 1.0. Simulated results show that the axial and lateral gas velocities are larger than those of particles, indicating particles located at the surface of the bed are carried by gas flow induced by the rotation of the draft fan. Both velocities of gas and particles are increased with the increase of rotational speeds, indicating more particles are entrained from the bed. The distributions of averaged cross-sectional area volume fraction of particles are shown in Fig. 19 at three rotational speeds of the draft fan. The solids volume fraction increases with the increase of rotational speeds. Numerical simulations further illustrate that the vertical profile of solids volume fraction decay along the height from the surface of the particles bed in the cylindrical domain. The inflection of solids volume fraction profile stands for an interface between the dense and dilute regions, and the solids volume fraction drops rapidly. The variations of solids volume fraction are similar at three rotational speeds, indicating that the rotation speed of the draft fan does not affect the trends of overall
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Fig. 14. Profile of axial and lateral velocities of gas and particles at four hovering heights.
Fig. 15. Distribution of mass flux rate of entrained particles.
distribution of solids volume fraction, but their local solids volume fractions along dimensionless height and mean solids volume fractions in the cylindrical domain. The distributions of averaged cross-sectional area axial and lateral velocities of gas and particles are shown in Fig. 20 at three rotational speeds. Both velocities of gas and particles increase with the increase of rotational speed of the draft fan because more energy from the draft fan is transferred to gas and particles. Both
lateral velocities of gas and particles are reduced at the dimensionless height larger than 0.9 because of the effect of the hub of the draft fan. The distribution of instantaneous mass flux rate Gs of particles is shown in Fig. 21 at two different rotational speeds of the draft fan. The mass flux rates are larger at the rotational speed of 1300 rpm than that at the rotational speed of 700 rpm because the high rotational speed of the draft fan produces a large gas velocity at the surface of the bed. The pickup velocity is defined as the gas velocity necessary to suspend the particles initially at rest at the bottom of the pipeline or it may be defined as the gas velocity required to initiate sliding motion, rolling and suspension of particles. To determine the pickup velocity of particles, the empirical correlations are proposed in the axial flow field [31,32]. The diameter and density of particles and particle shape are the crucial factors in the determination of pickup velocity of particles [33]. Fig. 22 shows the calculated pickup velocities using Cabrejos and Klinzing [31] and Kalman et al. [32]. From numerical simulations, the radial and tangential velocities of gas at the surface of the bed is obtained, and the gas velocities ug,cd entering the cylindrical domain is determined at the cylindrical domain x/R = 1.0. The simulated radial and tangential velocities are shown in Fig. 22 as a function of rotational speeds and hovering heights. The gas radial and tangential velocities increase with the increase of rotational speed and the decrease of hovering height. We see that the simulated radial velocities entering the cylindrical domain are smaller than the calculated pickup velocities. From the momentum balance in the shear flow under the axial flow [34], the mechanism of the initial movement
Fig. 16. Gas velocity streamlines and contours at different rotational speeds of the draft fan.
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Fig. 17. Velocity vector and volume fraction contour of particles at two rotational speeds.
Fig. 18. Profile of axial and laterial velocities of gas and particles at three rotational speeds.
Fig. 19. Profile of solid volume fraction at three rotational speeds.
of dry particles occurs when the moment caused by the lift and drag forces is superior to those from the gravitational and adhesion forces. The draft fan-generated flow can be characterized as a swirling flow. The pickup velocity is different in the axial swirling flow fields. The swirl component gives rise to a significant enhancement of lift force acting on particles. The pickup velocity of coal particles was measured in the swirling flow field [35]. The pickup velocity of
particles was decreased when the tangential flow rate was sufficient to disturb particles. The measured pickup velocity demonstrated that the swirling flow with appropriate swirling intensity is beneficial to particle pickup. It anticipates that the entrainment of particles by the draft fan over the bed contributes to the additional disturbance induced by swirling flow. Fig. 23 shows the distribution of solid mass flux rate as a function of rotational speed and hovering height of the draft fan. The solid mass flux rates increase with the increase of rotational speeds and decrease of hovering height. This indicates that particles at the surface of the bed are entrained by gas induced by the draft fan, indicating that the transportation of particles from the bed is controlled by the rotation speed and hovering height of the draft fan. The sediment pickup rates were measured at the unobstructed and obstructed open channel flow [36]. The measured results showed that the pickup rate increased exponentially in the presence of vortices generated by a cross-flow cylinder. The pickup rate with the obstructed flow was larger than that at the unobstructed channel flow. This indicates the swirling flow generated by the draft fan is beneficial to particle pickup from the particle bed.
4. Conclusions In this study, the Euler-Euler TFM is applied to assess entrainment of gas and particles induced by an axial 4-blade draft fan hovering over the particles bed. The interactions of collisions between particles and blade wall-particles are modeled using
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Fig. 20. Profile of axial and lateral velocities of gas and particles at three rotational speeds.
Fig. 21. Profile of mass flux rate of entrained particles at two rotational speeds. Fig. 23. Distribution of solid mass flux rate as a function of rotational speeds and hovering heights.
Fig. 22. Profile of calculated pickup velocity and simulated gas radial and tangential velocities.
KTGF. The multiple reference frame model is used to simulate the rotating reference frame of the blades of the draft fan. With this method, the entrainment of particles is simulated to reproduce flow behavior of gas and particles induced by the draft fan.
Simulated velocity and volume fraction of particles show that the dense region with high solids volume fraction and low particles velocity near the surface of the bed and the dilute region with low solids volume fraction and large particles velocity exist along dimensionless height. The bulk density of particles falls off exponentially from the transition to the dilute region in the cylindrical domain. The gas radial and tangential velocities entering the cylindrical domain increase with the increase of rotational speed and decrease of hovering height. Simulated results indicate that the swirling flow induced by the draft fan generates an additional disturbance and is beneficial to particle entrainment from the bed. Present simulations show that this model is able to predict flow behavior of gas and particles using axial draft fan to control entrainment of particles. In the future, this modeling method will be applied to conduct parametric investigation of entrainment of particles induced by draft fan and to improve transport performance of particles from the bed. The numerical simulations and experimental measurements are needed to investigate the effect of rotational speeds and blade geometrical arrangements on entrainment of particles and particle pickup velocity by the draft fan for further study.
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Please cite this article as: X. Jiang, Y. Xu, Y. Geng et al., Entrainment of particles and gas induced by draft fan over the particles bed, Advanced Powder Technology, https://doi.org/10.1016/j.apt.2019.10.011