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Effect of local disturbance on the particle–tube collision in bubbling fluidized bed
Chemical Engineering Science 64 (2009) 3486 -- 3497
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Effect of local disturbance on the particle–tube collision in bubbling fluidized bed Nan Gui, JianRen Fan ∗ , Kefa Cen State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, PR China
A R T I C L E
I N F O
Article history: Received 30 July 2008 Received in revised form 30 March 2009 Accepted 23 April 2009 Available online 3 May 2009 Keywords: Fluidization Particle Multiphase flow Discrete element method Local disturbance Immersed tube
A B S T R A C T
A numerical investigation on the effect of local disturbance of gas turbulence on the probability distribution function (PDF, for shot) and the rate of particle–tube collision in bubbling fluidized bed is carried out. A two-dimensional (2D) fluidized bed with 6 and 18 immersed tubes (a tube bank) and a threedimensional (3D) bed with two immersed tubes are simulated, respectively. The local disturbance of gas turbulence is introduced by a blowing gas flow injected from the underneath of the immersed tubes (2D) and from the walls of the bed (3D), respectively. In two-dimensional, the blowing gas flow is injected upstream, downstream or not injected; whereas in the three-dimensional case the gas flow is injected from the side walls of the bed. A DEM-LES coupling simulation method is applied. The results indicate a great increase in particle–tube collision rates and a change in the PDF profiles when the local disturbance is introduced, especially for the case of upstream disturbance. Two main mechanisms are interpreted, i.e. the turbulence augmentation and the formation of weaker velocity regions which both contribute to the changes in characteristics of particle–tube collision but act in independent ways. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Fluidized beds are widely used in combustion and chemical industries. The immersed tubes are usually used for enhancement of heat transfer and control of temperature in fluidized beds. Many investigations have been devoted to fluidized beds with immersed tubes on various important aspects, such as bubble and particle behaviors (Kobayashi et al., 2000; Ozawa et al., 2002; Peeler and Whitehead, 1982; Rong et al., 1999), tube attrition, erosion or wastage (Bouillard and Lyczkowski, 1991; Macadam and Stringger, 1991; Lee and Wang, 1995; Fan et al., 1998; Johansson et al., 2004; Cammarota et al., 2005), heat transfer (Ar and Uysal, 1999; Kim et al., 2003; Stefanova et al., 2008; Wong and Seville, 2006), gas flow regimes (Wang et al., 2002) and ash particles (Tomeczek and Mocek, 2007), etc. The modes of heat transfer by immersed surfaces are mainly categorized into three types (Botterill, 1975): convection by gas, convection by particles at contact, and radiation. In fact, since the temperature in fluidized bed is relatively lower than the pulverized coal fired boiler (usually < 500 ◦ C for many processes utilizing the fluidized beds) and the radiation is of practical importance only at high temperatures ( > 800 K, Wong and Seville, 2006), the mode of radiation is of relatively secondary significance. Moreover, as the
∗ Corresponding author. Fax: +86 0571 87991863. E-mail address: [email protected] (J. Fan). 0009-2509/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2009.04.032
particle–tube collisions are intensive in fluidized bed and the dense particulate flows are chaotic, and the moving particles surrounding the immersed tubes are of large heat capacities, the second modes relevant to particle–tube collision would play a predominant role in heat transfer by the immersed tubes. Otherwise, erosion or anti-erosion of immersed tubes and particle–tube collision characteristics in fluidized bed are also important aspects to which lots of investigations have been devoted. For example, Bouillard and Lyczkowski (1991) presented a simplified version of the comprehensive monolayer energy dissipation erosion model, which predicts the trends of erosion rate dependency upon the particle diameter, fluidizing velocity and bed porosity. Lee and Wang (1995) discussed the metal wastage mechanisms and rates for in in-bed tubes and the particle–surface collision frequency in bubbling fluidized bed. They found that the distribution of collision frequency around the tube was affected by the locations of the tube and bed heights. Johansson et al. (2004) made a measurement of steel tube wastage in a fluidized bed with an immersed tube bank, which is composed of 59 horizontal stainless steel tubes. For numerical investigation, Fan et al. (1998) indicated a simple and efficient erosion-protection method in most industrial systems using fins fixed on tubes. Achim et al. (2002) presented a computational model of erosion in fluidized bed, etc. Moreover, the blowing phenomenon and dynamics are extensively studied by researchers and widely used in industrial applications (Pearlman and Sohrab, 1997; Hwang et al., 1999; Mathelin et al., 2002; Niazmand and Renksizbulut, 2003). For example, in
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Fig. 1. Sketches of configurations in the present simulation. (a) Case 1: 2D simulation with 6 in-line arranged immersed tubes; (b) Case 2: 2D simulation of a tube bank with 18 immersed tubes; (c) Case 3: 3D simulation of 2 immersed tubes.
combustion or heat transfer system, with regard to surface blowing, Pearlman and Sohrab (1997) carried out experimentally and theoretically investigations on the hydrodynamics around rotating porous spheres with surface blowing. They developed theoretical boundary layer analysis on porous spheres with surface blowing, and provided a closer model of evaporating or burning fuel droplets in spay combustion environments. Niazmand and Renksizbulut (2003) did a numerical study on heat transfer and thermal pattern around a rotating spherical particle with surface blowing. They explored the transient aspects of thermal wakes associated with the wake regimes. Additionally, Hwang et al. (1999) performed a numerical study of the effect of wall-blowing on the convective phenomenon, and Mathelin et al. (2002) did an experimental investigation on the dynamical and thermal behavior of the flow around a circular cylinder subjected to a non-isothermal (cold) blowing. Mathelin showed a dramatic effect of the blowing on the temperature field around the cylinder. In conclusion, the particle–tube collision characteristics are of great significance on various aspects of fluidized bed. To enhance the particle–tube collision is especially important to particle–tube heat transfer. As aforementioned, the blowing hydrodynamics is extensively explored and studied, and it is a common beneficial approach to affect the local gas turbulence. Thus, the present study aims to do an investigation of the effect of local disturbance of gas turbulence on the characteristics of particle–tube collision by
introducing an extra gas blowing flow, which may be positive to the second mode of particle–tube heat transfer, i.e. convection by particles, and negative to the tube erosion. The extra blowing gas flow is strong enough to change the local flow field and weak enough to not influence the state of fluidization. Thus, the extra gas flow is introduced into the fluidized bed only to disturb the local gas turbulence around the immersed tubes. Several different approaches of introducing the extra blowing gas flows are studied, respectively. For example, to inject a reverse flow upstream (`rev-', for short), a concurrent flow injected downstream (`con-', for short) both from the underneath of the immersed tubes (for 2D simulation) and to inject a horizontal flow near the bottom surface of the tube (for 3D simulation). The reverse direction is opposite to the mainstream direction of the bed (Fig. 1), whereas the concurrent direction is just the same as the mainstream. Moreover, the corresponding cases without any extra blowing gas flow (`non-', for shot) are also needed to simulate for comparison. The discrete element methods (DEM) are advantageous in tracing particles individually by solving Newton's equations of motion and in collection of detailed information of particle motion. It has been widely applied in numerical simulation of fluidized bed with the help of the great improvements of computer capacity and performance. The present study used the soft sphere model (Tsuji et al., 1993) which is one of the two main types of the DEM simulations (the other one is the hard sphere model (Hoomans et al., 1996)). The
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motion of gas phase in the present study is simulated by the large eddy simulation, in which the Smagorinsky sub-grid stress model is utilized. The verification of the numerical method has been carried out in our previous work (Gui et al., 2008). In the present study, the particle–tube collision number and rate for each tube are counted and accumulated numerically. The distributions of particle–tube collision on tube surfaces in the circumferential direction are also computed. Two main mechanisms, i.e. the effect of local augmentation of the turbulence and the formation of local weak velocity regions, are explored to interpret the changes in characteristics of particle–tube collision when the reverse blowing gas flows are introduced. Moreover, corresponding to each case of arrangement of immersed tubes, a regular fluidized bed without introducing any extra gas flows is also simulated for comparison. 2. Numerical description 2.1. Gas phase motion In the Eulerian–Lagrangian framework of numerical simulation, the governing equations of the gas phase and the discrete particles are the Navier–Stokes equations and the Newtonian equations, respectively. For the continuous phase, based on the conservation of mass and momentum, the two-dimensional (2D) and the threedimensional (3D) viscous incompressible Navier–Stokes equations, taking into account the gas voidages, are solved respectively. Moreover, the large eddy simulation has great potential advantages for numerical simulation of even industrial scale gas–solid flows, since it filters small scale turbulence and replaces it by some type of subgrid stress model. The Smagorinsky SGS tensor is one of the most widely used models for simulation of the sub-grid turbulence. Thus, let g be the voidage for gas phase, the equation of motions are:
*(g g ) *(g g u˜ i ) + =0 *t *xi *(g g u˜ i ) *(g g u˜ i u˜ j ) + *t *xj *p˜ * ˜ = g g g − g + g g g + (g (˜ij + SGS ij )) − fd *xi *xj
(1)
(2)
˜ g, ˜ ij , SGS where g , u˜ i , p, , f˜d are the fluid density, the velocity comij ponent, the pressure, the gravity acceleration, the filtered stress tensor, the sub-grid stress tensor and the drag force, respectively. The filtered stress tensor is: *u˜ i *u˜ j 2 *u˜ ˜ ij = g + (3) − g k ij 3 *xk *xj *xi where g is the fluid viscosity coefficient and ij is the Kronecker delta function. The above variables are all filtered by a characteristic length scale equivalent to the mesh spacing = (xyz)1/3 except . The SGS stress SGS is defined as SGS = the sub-grid scale stress SGS ij ij ij ˜ ˜ g (ui uj − ui uj ). In the Smagorinsky SGS model (Smagorinsky, 1963), based on the eddy viscosity concept, the sub-grid stress tensor is ˜ |S| ˜ = = 2t S˜ ij + (1/3)kk ij , where t = (Cs )2 |S|, expressed as SGS ij 1/2 and S˜ ij = 1/2(*u˜ i / *xj + *u˜ j / *xi ). Here, the eddy viscosity (2S˜ ij S˜ ij )
t ∝ lq, where l and q are the length scale and the velocity of the
unresolved fluid motion, respectively. Naturally, the length scale l is proportional to the filtering mesh size , which gives l = Cs (Cs is a constant and equals to 0.1 in this simulation). Moreover, similar to Prandtl's mixing length model, the velocity scale is related to the ˜ Hence the expression gradient of large scales flow, namely q = l|S|. 2 ˜ t = (Cs ) |S| is obtained.
The drag force fd in dense gas–solid flows depends on the gas voidage g , i.e. (Ding and Gidaspow, 1990): fd = (ug − up ) ⎧ 150(1 − g )2 g 1.75(1 − g )g |ug − up | ⎪ ⎪ ⎪ + ⎪ ⎨ dp g d2p = ⎪ −2.65 ⎪ 0.75Cd g (1 − g )g |ug − up |g ⎪ ⎪ ⎩ dp ⎧ 0.687 ) ⎪ ⎨ 24(1 + 0.15Rep Rep < 1000 Rep Cd = ⎪ ⎩ 0.43 Rep ⱖ 1000
(4)
g < 0.8 (5)
g ⱖ 0.8
(6)
where g , ug , up , dp , Cd , Rep =(g g |ug −up |dp )/ g are the gas viscosity and velocity, the particle velocity and diameter, the drag coefficients and particle Reynolds number respectively. To solve Eqs. (1) and (2), the staggered grids are used to discretize the flow domain based on the finite volume method and the Crank–Nicolson scheme is used for time advancement. As the time step in simulation is sufficient fine to meet the stable requirement of DEM simulation (Tsuji et al., 1993), the second order accuracy is able to obtain reliable results. The inlet at the bottom is a uniform velocity inflow boundary. The outlet boundary condition is the Neumann condition with *ui / *z = 0, where z is the direction of gas outflow. The immersed tube surfaces and the walls of the bed are all set as the non-slip boundaries. 2.2. Particle phase 2.2.1. Equation of motion The discrete element method is a powerful numerical method for tracing individually the motion of all discrete particles by integrating the Newton's equation of motion. Hence, the instantaneous forces and torques experienced by each particle are required to be directly computed or modeled. Suppose the forces and the torques are known, translational and rotational velocities are then obtained through solving the governing equations of motion for any particle: u˙ p =
(fC + fd + fpre ) +g mp
˙ p = Tp /Ip x
(7) (8)
˙ p , fC , fd , fpre , Tp , mp , Ip , g are the particle translational and where u˙ p , x rotational velocity, the inter-particle contact force, the drag force, the pressure gradient force, the torque, the mass and moment of inertia and the gravity acceleration respectively. The `•' denotes the time derivative. 2.2.2. Collision dynamics In a deterministic way, the particle–particle collisions are simulated by using the discrete element method (Cundall and Strack, 1979; Tsuji et al., 1993). In this kind of treatment for inter-particle collision, several basic ideas are viewed as key issues for this simulation: (1) the particle–particle collision procedure is usually coupled with the free motion procedure though they are treated, respectively, by solving two sets of the governing equations in turn. The collision procedure and motion procedure are both time dependent and always have mutual influences. (2) At any time in the collision procedure, the particles are assumed to be deformable but with a prescribed uniform stiffness. Thus, the duration of any particle–particle collision procedure would include several time steps, during which minor geometrical overlaps of particles always occur. (3) The collision forces in both the normal and the tangential directions are
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threefold, namely the elastic force (−kx), the damping force (− x˙ ), and the friction force. For example, the former two are expressed as: fCn = −kdn − vn ,
fCt = −kdt − vt ,
(9)
where k, x, are the stiffness factor, the displacements relative to the contact position before deformation, the coefficient of damping, respectively. The n and t denote the normal and tangential directions between the pair of collision particles. This kind of treatment of inter-particle collision has great potential advantages in numerical simulation of dense gas–solid flows and has been utilized by lots of researchers in various applications (Rhodes et al., 2001; Lu and Hsiau, 2008; Tsuji et al., 2008 etc.). However, there is still a main drawback in this approach. Since the intrinsic need for this method is a huge amount of computation, which is a severe challenge to the computer performance and capacity. Thus, a 3D simulation of the bubbling fluidized bed is still greatly restricted though some parallel computing techniques (Tsuji et al., 2008, etc.) were utilized.
3. Numerical setup 3.1. Some considerations The present work aims to investigate the effect of local disturbance of gas turbulence on the particle–tube collision by introducing extra gas flows. Intuitively, it is easy to introduce the extra gas flows into the bed through nozzles which are equipped at positions near the tubes. For example, the nozzles are equipped underneath the immersed tubes and the gas flows are injected upstream or downstream through the nozzles into the beds. However, for industrial consideration, this kind of approach is not promising since the nozzles are hard to equip and they are prone to be worn and destroyed by the heavy particle impacts. Alternatively, it is more convenient to introduce the second gas flows from the side walls. Thus, with extra entries open on the side wall, a three-dimensional simulation is necessary. The first approach, in which the extra gas flows are introduced from the nozzles underneath the tubes (2D), is especially suitable for numerical simulation since it is advantageous for yielding insight into the changes of characteristics of particle–tube collision. Thus, it is necessary to be investigated for laboratorial consideration or scientific interest. Moreover, another important issue arisen from introducing the extra gas flows might be the influences on the regime of fluidization. In the present study the value of velocity of the extra blowing gas flow is just the same as the fluidization velocity, but with its direction changed toward upstream or downstream. To use this value of velocity is just for simplicity, and there are some considerations related to it: (1) in the reverse blowing case, a reverse flow is possible to counteract with the main stream of the rising gas–solid flow and weaken the momentum of it. To consider in an extreme way, the fluidization state is possible to transit from the bubbling to the slugging state. The small particles will be elutriated and the large ones will be defluidized. Thus, to verify the extensive application of the extra blowing gas flows, simulation of a tube bank (2D) is needed. (2) with a small blowing velocity, the intensity of disturbance on local gas field may be not so large to affect the characteristics of particle–tube collision. All these above-mentioned issues are more or less needed to be taken into account. The key issue is the common effects of the different approaches on improving the characteristics of particle–tube collisions. The present study is devoted to the above issues and the results are suggestive on these issues.
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Table 1 Parameters used in the numerical simulation. Dimension of the fluidized beds Arrangements of tubes
Particle numbers Particle diameter and density Restitution coefficient Friction coefficient Collision stiffness Gas density and viscosity Superficial gas velocity Inflow velocity of the blowing gas flow (rev-, non-, con-) Simulation time (s) Time step (s) Grid numbers and size
300×800 mm (2D); 20×80×500 mm (3D) Case 1: 6 in-line arranged immersed tubes (2D); Case 2: 18 staggered arranged tubes (2D); Case 3: 2 in-line arranged tubes (3D). Np = 80 343 (2D); Np = 178 200 (3D) dp = 883 × 10−6 (m); p = 2650 (kg/m3 ) e = 0.9
= 0.3 Kn = 1000 g = 1.29 (kg/m3 ); g = 1.85e − 5 (Pa · s) Vg0 = 1.8 (m/s) (2D) Vinf = (−Vg0 , 0, Vg0 ) (2D); Vinf = Vg0 (3D) T = 5.0 (2D); T = 0.6 (3D)
t = 1.0−5 (2D); t = 2×10−6 (3D) 150×400 (2D); x = y = 2 (mm) 10×40×250 (3D); x = y = z = 2 (mm)
3.2. Simulation conditions In the two-dimensional simulations, a fluidized bed with dimensions of 300(width)×800(height) mm2 is used for the present study. Six immersed tubes arranged in-line as a representative case (Fig. 1a) for basic investigation is used and a tube bank with 18 immersed tubes located in a staggered arrangement (Fig. 1b) is used for complementary investigation. Underneath each immersed tube there is respectively an array of nozzles which are used to inject extra blowing gas flows into the fluidized bed. The blowing gas flows are injected upstream (rev-) or downstream (con-) depending on the operation conditions. The rest parameters used in the present study are all listed in Table 1. In the threedimensional simulation, a small fluidized bed with dimensions of 20(depth)×80(width)×500(height) mm3 is used (Fig. 1c). Two immersed cylindrical tubes arranged in-line with the diameters DT = 20 mm and the lengths LT = 20 mm are equipped horizontally in the depth direction. The extra blowing gas flow is discharged near the bottom of the tubes from the two side walls of the fluidized bed. For numerical simplicity, the effects of the nozzle volumes are neglected since in the 2D simulation it is only as scientific considerations to show the pure effects of local gas disturbance. The numerical implementation of the blowing gas flows is simply a source term added on the governing equations in the grids where the nozzles occupy. The rate of the mass and momentum generation is determined by the flow flux of the secondary blowing gas flows. In this way, the location of the nozzle is right below the immersed tubes and the width of it is only 8 mm. In the 3D simulation, the extra gas flows are injected from the side walls of the bed. Thus it is simply an inflow boundary condition with uniform velocities. 4. Numerical results 4.1. Flow visualization 4.1.1. Case 1: six immersed tubes (2D) For visualization, Fig. 2a shows the two-dimensional snapshots of the local fluid fields around the tube 2 and 5 among the 6 inlinely arranged immersed tubes at t = 5 s. It is a comparison of the instantaneous fluid fields among the cases with the con-, non- and rev-blowing gas flows respectively. For the case with the upstream reverse blowing gas flow (rev-), it is observed from Fig. 2a that the streamwise velocities in the regions underneath the immersed tubes are of low values, even with minus streamwise velocities. This is an important change in the characteristics of fluid field, and it would be explored further in the following analyses. By contrast, this
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Fig. 2. Snapshots of the simulated results and a comparison between them: (a) the flow fields for Case 1 at t = 5 s; (b) the particle motion for Case 2 at t = 5 s; (c) the gas voidages for Case 3 at t = 0.2 s.
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phenomenon does not occur in the other two subfigures (con- and non-) since in this way the flow field is not disturbed as largely as the former. 4.1.2. Case 2: a tube bank (2D) Since it is necessary to know if it is viable to carry out extensive applications of the extra blowing gas flows, a tube bank is need to be investigated. Thus, for verifying the effects of the reverse blowing gas flows on the characteristics of particle–tube collision in the tube-bank, Fig. 2b illustrates the snapshots of instantaneous particle motions with and without the reverse blowing gas flows (rev- and non- respectively) when t = 5 s. After only several seconds, it is observed that great discrepancies between the motions and distributions of particles with and without introducing the extra gas flows occur. This is a necessary condition for the change of particle–tube collision characteristic and is a basic precondition for the following findings. 4.1.3. Case 3: two cylindrical tubes (3D) As mentioned above, there are several main drawbacks which are unable to overcome within the framework of two-dimensional simulations. For example, the two-dimensional large-eddy simulation is in fact not appropriate since the vortex has spatio-temporal characteristics and it needs actually three-dimensional spaces to evolve. Moreover, the reverse gas flows underneath the immersed tubes in 2D case are not viable for industrial applications, since the utilization of nozzles in the fluidized bed is not acceptable, etc. A more feasible approach for implementation of introducing extra blowing gas flows is from the walls of the bed, but it needs a 3D simulation. For this reason, Fig. 2c is snapshots of the iso-surfaces of gas voidages at t = 0.2 s with and without introducing the extra gas flows from the two side walls of the fluidized bed. Compared to the bubble without the extra gas flow, it is observed that the bubble blow the lower tube seems to be enlarged and flattened by the influences of the extra gas flows. It is interesting and the present study will focus on the effect of the local turbulent gas disturbance on the particle–tube collision characteristics. 4.2. Particle–tube collision numbers and rates As above-mentioned, the particle–tube collision would be the most important event in considering the heat transfer and the tube erosion characteristics. The present study simulated the spatial motion of all particles individually and recorded every particle–tube collision, including when and where the collision occurred, which particle and which tube it collided, how long the collision lasted, etc. It is easily for the DEM simulation to count the total collision numbers on the immersed tubes. The collision rate Rc is then defined as the total number of particle–tube collisions on the tube surfaces per unit time. As shown on Fig. 3a, the temporal accumulation of particle–tube collisions on the tube 2 and 5 (Fig. 1) are almost linearly proportional to time, whereas the rates of slope are different. It is found that for both the tube 2 and tube 5 which are representatives of others, the particle–tube collision times with the reverse blowing gas flows are the largest, with the concurrent blowing gas flows the moderate, and the non-blowing the least. Moreover, the mean collision rates from t = 2 to 5 s for all immersed tubes are all listed on Table 2, including the cases with the con-, non- and rev-blowing gas flows. We found that the rates of increment of the collision rate Rc for the rev-blowing case compared to the non-blowing case are almost greater than 50%. It is evident that the rev-blowing gas flow will considerably increase the particle–tube collision frequency, whereas between the con-blowing case and the non-blowing case it is not evident to say which is better.
Fig. 3. Comparisons of collision numbers between different approaches of introducing extra blowing gas flows: (a) Case 1: collision numbers on tube 2 and 5 between the cases with a non-, con- and rev-blowing gas flow; (b) Case 2: collision numbers on all immersed tubes between the cases with and without a reverse flow.
Thus, it is interesting to study more about the comparison between the cases with and without the reverse blowing gas flows. Fig. 3b is an illustration of the collision rates for all the 18 staggered arranged tubes. It is found from Fig. 3b that the collision rates with the reverse blowing gas flow are greater than that without the extra blowing gas flow, despite which the tube is and where the tube occupies. Based on the above findings, and from the point of view of scientific research, it seems to conclude that the local disturbance of gas flows, by means of introducing extra upstream blowing gas flows, will cause great increase in the particle–tube collision frequencies. This is important for improving the particle–tube interaction characteristics, such as heat transfer, etc.
4.3. Probability distribution function The probability distribution function (PDF) is the distribution function of particle–tube collision in the circumferential direction
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Table 2 Mean collision rates Rc for particle–tube collisions (Case 1). Tube index
Con-blowing Rc,c (s−1 )
Non-blowing Rc,n (s−1 )
Rev-blowing Rc,r (s−1 )
Increment rates (Rc,r − Rc,n )/Rc,n (%)
1 2 3 4 5 6
19 950.9 14 642.0 14 367.1 14 287.9 14 304.2 14 777.4
16 793.2 11 889.7 17 270.3 12 626.9 9044.4 11 306.8
24 663.3 26 325.9 27 922.4 27 553.1 22 587.5 22 532.6
46.9 121.4 61.7 118.2 149.7 99.3
on the exterior surface of a tube. At any prescribed angular degree on the circumferential surface, it is a probability of the occurrence of particle–tube collision. Statistically, the PDF is appropriate to be defined as a ratio of the number of particle–tube collisions occurred in a prescribed region on the tube surface to the total number of particle–tube collisions on the whole circumferential surface: dN fˆ ( ) = N d
(10)
where N is the total number of particle–tube collision. is the angular coordinate in the circumferential counterclockwise direction as illustrated in Fig. 1. dN is the number of particle–tube collision in the d region. The PDF is important for investigating the particle–tube interactions. In the present study, to compare the absolute magnitudes of the particle–tube collision rates, Eq. (10) is modified as f ( )=dN/d . It is the number of particle–tube collisions occurred per unit circumferential and per unit time, and the unit of it is (◦ s−1 ). 4.3.1. Case 1: PDFs of the six immersed tubes Again, we take tube 2 and 5 as representatives for case study. The PDFs of tube 2 and 5 under the influences of the con-, non- and revblowing gas flows are all illustrated on Fig. 4a and b, respectively. From Fig. 4, several points are observed: (1) for local disturbances caused by the con- and non-blowing gas flows, the PDFs are almost similar, which means that the concurrent blowing gas flow has very little effects on changing the particle–tube collision. (2) By contrast, the PDFs under the effect of the reverse blowing gas flow are far different from the PDFs without the local disturbance of the extra gas flow. (3) Moreover, only in the local region disturbed by the extra reverse gas flow, does the particle–tube collision numbers and rates increase greatly; in other regions the changes in the particle–tube collision characteristics are not clearly distinguishable. This is an interesting phenomenon and has potential advantages for modification of the characteristics of particle–tube interaction. Moreover, the enhancement of particle–tube collision is not an isolated conclusion only for tube 2 and 5. In fact, for all the other immersed tubes, the results are still true. Thus, the increase of particle–tube collision is an intrinsic characteristic lying in the effect of the local disturbance caused by the reverse gas flow. This conclusion will be evidenced by the following complementary simulations. 4.3.2. Cases 2, 3: PDFs of the tube bank and the 3D simulation In this section, to verify the changes in the characteristics of particle–tube collision, it is necessary to know if it is true for tubes within the tube bank and for the three-dimensional application. In other words, it is needed to know if the results obtained above are universal for any other application. Figs. 5 and 6 are the results of PDFs of the particle–tube collision corresponding to the tube bank and the three-dimensional case, respectively. It is appropriate to take tube 7, 12 and 9, 14 among the tube bank for case study, since their locations are representative ones within the tube bank. From Fig. 5a it is observed that: (1) For both tube 7 and tube 12, the particle–tube collision rates in the local region (around 270◦ ) with the reverse blowing gas flow are not
Fig. 4. PDFs of particle–tube collision on the circumferential exterior surfaces of tube 2 (4a) and 5 (4b) of Case 1.
apparently different from that without the local disturbance. However, the collision rates in the former case are still more or less larger than the latter. (2) Moreover, within the region around 90◦ , namely the leeward side of the immersed tube, the particle–tube collision rates in the rev-blowing cases are greater than that in the
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Fig. 6. PDFs of the particle–tube collision for the 3-D simulation.
Fig. 5. PDFs of particle–tube collision on representative immersed tubes of Case 2: (a) for tube 7 and 12; (b) for tube 9 and 14.
non-blowing case. It seems that the tube bank owns an intrinsic characteristic on forming locally disturbed chaotic gas flow fields. It is due to the vortex shedding effect after the immersed tubes as well as the interactions between them. Thus it is not as apparent as before for the reverse blowing gas flows to influence the gas turbulence and the particle–tube collision. However, the positive effect of local disturbance of gas motion on the particle–tube collision enhancement still remains true, which is beneficial for industrial application of particle–tube heat transfer enhancement. Moreover, from Fig. 5b, it is observed that, the discrepancies between the cases with and without the reverse flowing gas flow are similar to that of Fig. 5a. But the enhancement of particle–tube collision rates with the effect of the reverse blowing gas flow compared to that without the local disturbance are more apparent than Fig. 5a. Additionally, to study the effect of local disturbance in the 3D application by means of introducing the secondary gas flows from the
two side-walls, Fig. 6 illustrates the results of particle–tube collision with and without the secondary gas flows in the three-dimensional bed. It is also observed that the particle–tube collision rates with the secondary blowing gas flows are greater than that without them. The increments are not as large as that of Case 1 since these are not upstream but cross-streamwise gas flows. The increases are almost uniform on the whole exterior surfaces of the tubes. It is absolute that the secondary blowing gas flows would cause a large amount of particle–tube collisions providing they go on for a long time. These results indicate that the introduction of the extra blowing gas flows will change the particle–tube collision characteristics and increase the particle–tube collision frequencies as they cause local disturbances on gas turbulence in the main stream. Compared to the tube bank, it is especially meaningful when the secondary gas flows are applied to a few immersed tubes. In this way the effect of local disturbance on the gas turbulence by the extra blowing gas flows is more apparent. Furthermore, the application of introducing a great many of gas flows will of course influence the fluidization state, even cause deterioration of fluidization. Thus it needs further verifications through experimental investigations and industrial applications that if or not a large amount of extra blowing gas flows are appropriate to be applied to a very large tube bank. This objective goes beyond the present study. However, it seems to be unnecessary, since for a very large tube bank, with intrinsic characteristics of vortex shedding after the tubes and the interactions between them, the effect of introducing extra blowing gas flows to disturb the local gas turbulence is not as effective as that for a few immersed tubes. 5. Discussions 5.1. The effect of turbulence augmentation The mechanistic interpretations of the enhancement of particle–tube collision by the reverse blowing gas flows are interesting. Firstly and intuitively, we assumed that the reverse blowing gas flows will enhance the gas turbulence and hence the particle motion will be influenced by the gas turbulence, resulting in the enhancement of particle–tube collision rates. For validation, Fig. 7a and b illustrate the gas turbulent intensities for Case 1 at the heights of H = 250 and 260 mm, respectively, i.e. below the upper row of the immersed tubes (H = 270 mm) with two
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Fig. 7. Turbulence intensities for Case 1 (7a and 7b) and Case 2 (7c) at different heights.
distances of d = 20 and 10 mm, respectively. From Fig. 7a and b, it is evident that for the extra blowing gas flows especially the reverse flows, there are three maximum values of gas turbulent intensities right below the immersed tubes (with width = 0.075, 0.15, 0.225 m on Fig. 7a and b, respectively). This validates our assumption on the augmentation of the gas phase turbulence. Moreover, the concurrent blowing gas flows are downstream disturbances, and there are no obvious effects on the upstream gas turbulence. Thus, it has only augmentation effects on the turbulence near the locations where the extra flows are injected (H = 0.26), whereas it has no evident effects on the upstream turbulence (H = 0.25). However, the above results are not exactly true for the tube bank, since the fluid field within the tube bank has strong interactions between the wakes of the immersed tubes. The tube bank acts also as disturbances on the flow field, which will mask or attenuate the influences of local disturbances by an extra blowing
gas flows. Thus the turbulence augmentation is not as apparent as that for a few tubes. For validation, Fig. 7c shows the turbulence intensities at heights H = 0.30 and 0.34 (the heights right below the tube 7 and tube 9) for Case 2 with the non- and the rev-blowing gas flows, respectively. It is observed from Fig. 7c that the turbulence intensities with and without local disturbances are equivalent with each other. The effects by introducing the reverse flows are not distinguishable. Conclusively, compared to the non-blowing case, it is evident that the turbulence intensity has important effects on the particle–tube collision characteristics especially for only a few tubes. Moreover, the discrepancies between the results with the reverse flow and the concurrent flow indicate the effects of approaches by which the local disturbance is introduced. In other words, the approach of enhancing the turbulent intensity will have different effects on the enhancement of particle–tube collision.
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Fig. 8. Mean rising velocities for Case 1 (8a and 8b) and Case 2 (8c) at different heights.
5.2. The effect of formation of weak velocity regions As mentioned above, the enhancement of particle–tube collision is approach dependent. Thus, turbulence augmentation is not the sole contribution to the changes in particle–tube collision. Interestingly, it is found that another important effect, namely the formation of locally weak velocity regions underneath each immersed tubes, will also cause positive effects on the particle–tube collision enhancement. Fig. 8a–c are representative evidences for the above interpretations. Fig. 8a and b show the mean rising velocities for Case 1 at heights H = 0.22 and 0.26 m (right below the two rows of tubes) respectively and Fig. 8c shows the mean rising velocities at H = 0.34
and 0.38 m for Case 2. It is observed from Fig. 8 that: (1) the mean velocities at locations where the immersed tubes occupy are relatively smaller than other locations; (2) the regions right below the immersed tubes are weak velocity regions with relatively lower rising velocities than other regions, even with minus mean flow velocities; (3) the effect of the reverse flow causes the mean rising velocity to reach even lower values than before; (4) within the tube bank, though the trends are alike, the effects of the reverse flows on the mean rising velocities are attenuated since only relatively minor discrepancies between the cases with and without reverse flows are observed. Referring to Fig. 7c, when the turbulence enhancement effects by the reverse flows are masked, the mechanism of formation of a weaker velocity region is still playing an important role.
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Fig. 9. Gas voidages for Case 1 at different heights.
Why the formation of a weak velocity region would result in the enhancement of particle–tube collision? Regarding the natural phenomenon of a river meeting the sea, there always exist an island at the meeting-point of the river and the sea. The formation of the island is due to the reverse tide from the sea delaying the movement of sand carried by the river. Thus, the sand deposits at the meeting-point. The formation mechanism of the interesting natural phenomenon might be analogous to the mechanism of enhancement of the particle–tube collision. The reverse blowing gas flow acts as the reverse upstream tide, delaying the movement of particles brought by the rising main stream. Then, in a statistical way, the particles will accumulate in the weaker velocity region, resulting in the enhancement of particle–tube collision. Moreover, it is illustrated from previous figures that for the case with extra blowing gas flows, the maximum values of the particle–tube collision rates around the circumferential regions occur about 270◦ , i.e. the region near the bottom of the tube. Since the reverse gas flow makes the region even weaker, the enhancement of particle–tube collision is hence reasonable. For validation, Fig. 9 is the representative time averaged gas voidages at the bottom of the immersed tubes (at height H = 0.25 m). It is observed from Fig. 9 that with the reverse blowing gas flows, a great reduction in gas voidages right below the immersed tubes exists, i.e. an increase in particle number density exists due to the deceleration, deposition and conglomeration of particles.
collision, in spite of locations and numbers of the immersed tubes. Two mechanisms contributing to enhancement of particle–tube collision were explored, e.g. the effect of turbulence augmentation and the effect of formation of a weak velocity region. As the degree of turbulence enhancement depends on the approach of introducing extra blowing gas flows, the enhancement of particle–tube collision is still approach dependent. Moreover, as the reverse extra blowing gas flow delays the downstream movement of particles brought by the rising main stream, the particles will accumulate in the weaker velocity region, which can also lead to enhancement of particle–tube collision. Thus, the reverse blowing flow has the strongest effect on enhancement of particle–tube collision. On the other hand, using a great amount of extra blowing gas would possibly cause deterioration of fluidization, though in the present study, the fluidization state with a tube bank is not changed. Thus, it is suggested that experimental validation is necessary for large scale industrial application. Acknowledgment The authors are grateful for the support of this research by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Z107332). References
6. Conclusion The present study studied an approach of introducing reverse blowing gas flows around immersed tubes in bubbling fluidized bed to enhance the particle–tube collision. Two cases of 2D simulations with a few immersed tubes and a tube bank respectively and a 3D simulation with two immersed tubes were carried out. The objectives are to study the effect of turbulence disturbance on the enhancement of particle–tube collision, which is related to the fundamental aspects for particle–tube heat transfer enhancement. In general, the simulation results show that the local disturbance of gas motion induced by introducing an extra reverse blowing gas flow can cause great enhancement of particle–tube
Achim, D., Easton, A.K., Schwarz, M.P., Witt, P.J., Zakhari, A., 2002. Tube erosion modelling in a fluidised bed. Appl. Math. Modelling 26, 191–201. Ar, F.F., Uysal, B.Z., 1999. Fluidized tube heat exchanger. J. Chem. Tech. Bio. 74, 169–175. Botterill, J.S.M., 1975. Heat transfer to immersed surfaces in fluidised and packed fluidised beds. In: Fluid Bed Heat Transfer.Academic Press, London, pp. 229–277 (Chapter 5). Bouillard, J.X., Lyczkowski, R.W., 1991. On the erosion of heat exchanger tube banks in fluidized-bed combustors. Powder Technol. 68, 37–51. Cammarota, A., Chirone, R., Salatino, P., Scala, F., Urciuolo, M., 2005. Attrition phenomena during fluidized bed combustion of granulated and mechanically dewatered sewage sludges. Proc. Comb. Inst. 30, 3017–3024. Cundall, P.A., Strack, O.D.L., 1979. A discrete numerical model for granual assemblies. Geotechnique 29, 47–65. Ding, J., Gidaspow, D., 1990. A bubbling fluidization model using kinetic theory of granular flow. A.I.Ch.E. J. 36, 523–538.
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Fan, J.R., Sun, P., Chen, L.h., Cen, K.F., 1998. Numerical investigation of a new protection method of the tube erosion by particles impingement. Wear 223, 50–57. Gui, N., Fan, J.R., Luo, K., 2008. DEM-LES study of 3-D bubbling fluidized bed with immersed tubes. Chem. Eng. Sci. 63, 3654–3663. Hoomans, B.P.B., Kuipers, J.A.M., Briels, W.J., van Swaajj, W.P.M., 1996. Discrete particle simulation of bubble and slug formation in a two dimensional gasfluidised bed: a hard-sphere approach. Chem. Eng. Sci. 51, 99–118. Hwang, J.J., Tsai, Y.P., Wang, W.J., Lai, D.Y., 1999. Effects of leading-wall blowing/suction on mixed convective phenomena in a radially rotating multiplepass duct. Int. J. Heat Mass Transfer 42, 4461–4474. Johansson, K., Norling, R., Hjornhede, A., Almstedt, A.-E., Johnsson, F., Nylund, A., 2004. Hydrodynamics and steel tube wastage in a fluidized bed at elevated temperature. Chem. Eng. Sci. 59, 31–40. Kim, S.W., Ahn, J.Y., Kim, S.D., Lee, D.H., 2003. Heat transfer and bubble characteristics in a fluidized bed with immersed horizontal tube bundle. Int. J. Heat Mass Transfer 46, 399–409. Kobayashi, N., Yamazaki, R., Mori, S., 2000. A study on the behavior of bubbles and solids in bubbling fluidized beds. Powder Technol. 113, 327–344. Lee, S.W., Wang, B.Q., 1995. Effect of particle–tube collision frequency on material wastage of in-bed tubes in the bubbling fluidized bed combustor. Wear 184, 223–229. Lu, L.S., Hsiau, S.S., 2008. Mixing in a vibrated granular bed: diffusive and convective effects. Powder Technol. 184, 31–43. Macadam, S.S., Stringger, J., 1991. Particle impact and impact distribution within a fluidized bed combustor environment. Wear 141, 373–394. Mathelin, L., Bataille, F., Lallemand, A., 2002. Flow around a circular cylinder with non-isothermal blowing. Exp. Therm. Fluid Sci. 26, 173–179. Niazmand, H., Renksizbulut, M., 2003. Transient three-dimensional heat transfer from rotating spheres with surface blowing. Chem. Eng. Sci. 58, 3535–3554.
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Effect of local disturbance on the particle–tube collision in bubbling fluidized bed Nan Gui, JianRen Fan ∗ , Kefa Cen State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, PR China
A R T I C L E
I N F O
Article history: Received 30 July 2008 Received in revised form 30 March 2009 Accepted 23 April 2009 Available online 3 May 2009 Keywords: Fluidization Particle Multiphase flow Discrete element method Local disturbance Immersed tube
A B S T R A C T
A numerical investigation on the effect of local disturbance of gas turbulence on the probability distribution function (PDF, for shot) and the rate of particle–tube collision in bubbling fluidized bed is carried out. A two-dimensional (2D) fluidized bed with 6 and 18 immersed tubes (a tube bank) and a threedimensional (3D) bed with two immersed tubes are simulated, respectively. The local disturbance of gas turbulence is introduced by a blowing gas flow injected from the underneath of the immersed tubes (2D) and from the walls of the bed (3D), respectively. In two-dimensional, the blowing gas flow is injected upstream, downstream or not injected; whereas in the three-dimensional case the gas flow is injected from the side walls of the bed. A DEM-LES coupling simulation method is applied. The results indicate a great increase in particle–tube collision rates and a change in the PDF profiles when the local disturbance is introduced, especially for the case of upstream disturbance. Two main mechanisms are interpreted, i.e. the turbulence augmentation and the formation of weaker velocity regions which both contribute to the changes in characteristics of particle–tube collision but act in independent ways. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Fluidized beds are widely used in combustion and chemical industries. The immersed tubes are usually used for enhancement of heat transfer and control of temperature in fluidized beds. Many investigations have been devoted to fluidized beds with immersed tubes on various important aspects, such as bubble and particle behaviors (Kobayashi et al., 2000; Ozawa et al., 2002; Peeler and Whitehead, 1982; Rong et al., 1999), tube attrition, erosion or wastage (Bouillard and Lyczkowski, 1991; Macadam and Stringger, 1991; Lee and Wang, 1995; Fan et al., 1998; Johansson et al., 2004; Cammarota et al., 2005), heat transfer (Ar and Uysal, 1999; Kim et al., 2003; Stefanova et al., 2008; Wong and Seville, 2006), gas flow regimes (Wang et al., 2002) and ash particles (Tomeczek and Mocek, 2007), etc. The modes of heat transfer by immersed surfaces are mainly categorized into three types (Botterill, 1975): convection by gas, convection by particles at contact, and radiation. In fact, since the temperature in fluidized bed is relatively lower than the pulverized coal fired boiler (usually < 500 ◦ C for many processes utilizing the fluidized beds) and the radiation is of practical importance only at high temperatures ( > 800 K, Wong and Seville, 2006), the mode of radiation is of relatively secondary significance. Moreover, as the
∗ Corresponding author. Fax: +86 0571 87991863. E-mail address: [email protected] (J. Fan). 0009-2509/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2009.04.032
particle–tube collisions are intensive in fluidized bed and the dense particulate flows are chaotic, and the moving particles surrounding the immersed tubes are of large heat capacities, the second modes relevant to particle–tube collision would play a predominant role in heat transfer by the immersed tubes. Otherwise, erosion or anti-erosion of immersed tubes and particle–tube collision characteristics in fluidized bed are also important aspects to which lots of investigations have been devoted. For example, Bouillard and Lyczkowski (1991) presented a simplified version of the comprehensive monolayer energy dissipation erosion model, which predicts the trends of erosion rate dependency upon the particle diameter, fluidizing velocity and bed porosity. Lee and Wang (1995) discussed the metal wastage mechanisms and rates for in in-bed tubes and the particle–surface collision frequency in bubbling fluidized bed. They found that the distribution of collision frequency around the tube was affected by the locations of the tube and bed heights. Johansson et al. (2004) made a measurement of steel tube wastage in a fluidized bed with an immersed tube bank, which is composed of 59 horizontal stainless steel tubes. For numerical investigation, Fan et al. (1998) indicated a simple and efficient erosion-protection method in most industrial systems using fins fixed on tubes. Achim et al. (2002) presented a computational model of erosion in fluidized bed, etc. Moreover, the blowing phenomenon and dynamics are extensively studied by researchers and widely used in industrial applications (Pearlman and Sohrab, 1997; Hwang et al., 1999; Mathelin et al., 2002; Niazmand and Renksizbulut, 2003). For example, in
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Fig. 1. Sketches of configurations in the present simulation. (a) Case 1: 2D simulation with 6 in-line arranged immersed tubes; (b) Case 2: 2D simulation of a tube bank with 18 immersed tubes; (c) Case 3: 3D simulation of 2 immersed tubes.
combustion or heat transfer system, with regard to surface blowing, Pearlman and Sohrab (1997) carried out experimentally and theoretically investigations on the hydrodynamics around rotating porous spheres with surface blowing. They developed theoretical boundary layer analysis on porous spheres with surface blowing, and provided a closer model of evaporating or burning fuel droplets in spay combustion environments. Niazmand and Renksizbulut (2003) did a numerical study on heat transfer and thermal pattern around a rotating spherical particle with surface blowing. They explored the transient aspects of thermal wakes associated with the wake regimes. Additionally, Hwang et al. (1999) performed a numerical study of the effect of wall-blowing on the convective phenomenon, and Mathelin et al. (2002) did an experimental investigation on the dynamical and thermal behavior of the flow around a circular cylinder subjected to a non-isothermal (cold) blowing. Mathelin showed a dramatic effect of the blowing on the temperature field around the cylinder. In conclusion, the particle–tube collision characteristics are of great significance on various aspects of fluidized bed. To enhance the particle–tube collision is especially important to particle–tube heat transfer. As aforementioned, the blowing hydrodynamics is extensively explored and studied, and it is a common beneficial approach to affect the local gas turbulence. Thus, the present study aims to do an investigation of the effect of local disturbance of gas turbulence on the characteristics of particle–tube collision by
introducing an extra gas blowing flow, which may be positive to the second mode of particle–tube heat transfer, i.e. convection by particles, and negative to the tube erosion. The extra blowing gas flow is strong enough to change the local flow field and weak enough to not influence the state of fluidization. Thus, the extra gas flow is introduced into the fluidized bed only to disturb the local gas turbulence around the immersed tubes. Several different approaches of introducing the extra blowing gas flows are studied, respectively. For example, to inject a reverse flow upstream (`rev-', for short), a concurrent flow injected downstream (`con-', for short) both from the underneath of the immersed tubes (for 2D simulation) and to inject a horizontal flow near the bottom surface of the tube (for 3D simulation). The reverse direction is opposite to the mainstream direction of the bed (Fig. 1), whereas the concurrent direction is just the same as the mainstream. Moreover, the corresponding cases without any extra blowing gas flow (`non-', for shot) are also needed to simulate for comparison. The discrete element methods (DEM) are advantageous in tracing particles individually by solving Newton's equations of motion and in collection of detailed information of particle motion. It has been widely applied in numerical simulation of fluidized bed with the help of the great improvements of computer capacity and performance. The present study used the soft sphere model (Tsuji et al., 1993) which is one of the two main types of the DEM simulations (the other one is the hard sphere model (Hoomans et al., 1996)). The
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motion of gas phase in the present study is simulated by the large eddy simulation, in which the Smagorinsky sub-grid stress model is utilized. The verification of the numerical method has been carried out in our previous work (Gui et al., 2008). In the present study, the particle–tube collision number and rate for each tube are counted and accumulated numerically. The distributions of particle–tube collision on tube surfaces in the circumferential direction are also computed. Two main mechanisms, i.e. the effect of local augmentation of the turbulence and the formation of local weak velocity regions, are explored to interpret the changes in characteristics of particle–tube collision when the reverse blowing gas flows are introduced. Moreover, corresponding to each case of arrangement of immersed tubes, a regular fluidized bed without introducing any extra gas flows is also simulated for comparison. 2. Numerical description 2.1. Gas phase motion In the Eulerian–Lagrangian framework of numerical simulation, the governing equations of the gas phase and the discrete particles are the Navier–Stokes equations and the Newtonian equations, respectively. For the continuous phase, based on the conservation of mass and momentum, the two-dimensional (2D) and the threedimensional (3D) viscous incompressible Navier–Stokes equations, taking into account the gas voidages, are solved respectively. Moreover, the large eddy simulation has great potential advantages for numerical simulation of even industrial scale gas–solid flows, since it filters small scale turbulence and replaces it by some type of subgrid stress model. The Smagorinsky SGS tensor is one of the most widely used models for simulation of the sub-grid turbulence. Thus, let g be the voidage for gas phase, the equation of motions are:
*(g g ) *(g g u˜ i ) + =0 *t *xi *(g g u˜ i ) *(g g u˜ i u˜ j ) + *t *xj *p˜ * ˜ = g g g − g + g g g + (g (˜ij + SGS ij )) − fd *xi *xj
(1)
(2)
˜ g, ˜ ij , SGS where g , u˜ i , p, , f˜d are the fluid density, the velocity comij ponent, the pressure, the gravity acceleration, the filtered stress tensor, the sub-grid stress tensor and the drag force, respectively. The filtered stress tensor is: *u˜ i *u˜ j 2 *u˜ ˜ ij = g + (3) − g k ij 3 *xk *xj *xi where g is the fluid viscosity coefficient and ij is the Kronecker delta function. The above variables are all filtered by a characteristic length scale equivalent to the mesh spacing = (xyz)1/3 except . The SGS stress SGS is defined as SGS = the sub-grid scale stress SGS ij ij ij ˜ ˜ g (ui uj − ui uj ). In the Smagorinsky SGS model (Smagorinsky, 1963), based on the eddy viscosity concept, the sub-grid stress tensor is ˜ |S| ˜ = = 2t S˜ ij + (1/3)kk ij , where t = (Cs )2 |S|, expressed as SGS ij 1/2 and S˜ ij = 1/2(*u˜ i / *xj + *u˜ j / *xi ). Here, the eddy viscosity (2S˜ ij S˜ ij )
t ∝ lq, where l and q are the length scale and the velocity of the
unresolved fluid motion, respectively. Naturally, the length scale l is proportional to the filtering mesh size , which gives l = Cs (Cs is a constant and equals to 0.1 in this simulation). Moreover, similar to Prandtl's mixing length model, the velocity scale is related to the ˜ Hence the expression gradient of large scales flow, namely q = l|S|. 2 ˜ t = (Cs ) |S| is obtained.
The drag force fd in dense gas–solid flows depends on the gas voidage g , i.e. (Ding and Gidaspow, 1990): fd = (ug − up ) ⎧ 150(1 − g )2 g 1.75(1 − g )g |ug − up | ⎪ ⎪ ⎪ + ⎪ ⎨ dp g d2p = ⎪ −2.65 ⎪ 0.75Cd g (1 − g )g |ug − up |g ⎪ ⎪ ⎩ dp ⎧ 0.687 ) ⎪ ⎨ 24(1 + 0.15Rep Rep < 1000 Rep Cd = ⎪ ⎩ 0.43 Rep ⱖ 1000
(4)
g < 0.8 (5)
g ⱖ 0.8
(6)
where g , ug , up , dp , Cd , Rep =(g g |ug −up |dp )/ g are the gas viscosity and velocity, the particle velocity and diameter, the drag coefficients and particle Reynolds number respectively. To solve Eqs. (1) and (2), the staggered grids are used to discretize the flow domain based on the finite volume method and the Crank–Nicolson scheme is used for time advancement. As the time step in simulation is sufficient fine to meet the stable requirement of DEM simulation (Tsuji et al., 1993), the second order accuracy is able to obtain reliable results. The inlet at the bottom is a uniform velocity inflow boundary. The outlet boundary condition is the Neumann condition with *ui / *z = 0, where z is the direction of gas outflow. The immersed tube surfaces and the walls of the bed are all set as the non-slip boundaries. 2.2. Particle phase 2.2.1. Equation of motion The discrete element method is a powerful numerical method for tracing individually the motion of all discrete particles by integrating the Newton's equation of motion. Hence, the instantaneous forces and torques experienced by each particle are required to be directly computed or modeled. Suppose the forces and the torques are known, translational and rotational velocities are then obtained through solving the governing equations of motion for any particle: u˙ p =
(fC + fd + fpre ) +g mp
˙ p = Tp /Ip x
(7) (8)
˙ p , fC , fd , fpre , Tp , mp , Ip , g are the particle translational and where u˙ p , x rotational velocity, the inter-particle contact force, the drag force, the pressure gradient force, the torque, the mass and moment of inertia and the gravity acceleration respectively. The `•' denotes the time derivative. 2.2.2. Collision dynamics In a deterministic way, the particle–particle collisions are simulated by using the discrete element method (Cundall and Strack, 1979; Tsuji et al., 1993). In this kind of treatment for inter-particle collision, several basic ideas are viewed as key issues for this simulation: (1) the particle–particle collision procedure is usually coupled with the free motion procedure though they are treated, respectively, by solving two sets of the governing equations in turn. The collision procedure and motion procedure are both time dependent and always have mutual influences. (2) At any time in the collision procedure, the particles are assumed to be deformable but with a prescribed uniform stiffness. Thus, the duration of any particle–particle collision procedure would include several time steps, during which minor geometrical overlaps of particles always occur. (3) The collision forces in both the normal and the tangential directions are
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threefold, namely the elastic force (−kx), the damping force (− x˙ ), and the friction force. For example, the former two are expressed as: fCn = −kdn − vn ,
fCt = −kdt − vt ,
(9)
where k, x, are the stiffness factor, the displacements relative to the contact position before deformation, the coefficient of damping, respectively. The n and t denote the normal and tangential directions between the pair of collision particles. This kind of treatment of inter-particle collision has great potential advantages in numerical simulation of dense gas–solid flows and has been utilized by lots of researchers in various applications (Rhodes et al., 2001; Lu and Hsiau, 2008; Tsuji et al., 2008 etc.). However, there is still a main drawback in this approach. Since the intrinsic need for this method is a huge amount of computation, which is a severe challenge to the computer performance and capacity. Thus, a 3D simulation of the bubbling fluidized bed is still greatly restricted though some parallel computing techniques (Tsuji et al., 2008, etc.) were utilized.
3. Numerical setup 3.1. Some considerations The present work aims to investigate the effect of local disturbance of gas turbulence on the particle–tube collision by introducing extra gas flows. Intuitively, it is easy to introduce the extra gas flows into the bed through nozzles which are equipped at positions near the tubes. For example, the nozzles are equipped underneath the immersed tubes and the gas flows are injected upstream or downstream through the nozzles into the beds. However, for industrial consideration, this kind of approach is not promising since the nozzles are hard to equip and they are prone to be worn and destroyed by the heavy particle impacts. Alternatively, it is more convenient to introduce the second gas flows from the side walls. Thus, with extra entries open on the side wall, a three-dimensional simulation is necessary. The first approach, in which the extra gas flows are introduced from the nozzles underneath the tubes (2D), is especially suitable for numerical simulation since it is advantageous for yielding insight into the changes of characteristics of particle–tube collision. Thus, it is necessary to be investigated for laboratorial consideration or scientific interest. Moreover, another important issue arisen from introducing the extra gas flows might be the influences on the regime of fluidization. In the present study the value of velocity of the extra blowing gas flow is just the same as the fluidization velocity, but with its direction changed toward upstream or downstream. To use this value of velocity is just for simplicity, and there are some considerations related to it: (1) in the reverse blowing case, a reverse flow is possible to counteract with the main stream of the rising gas–solid flow and weaken the momentum of it. To consider in an extreme way, the fluidization state is possible to transit from the bubbling to the slugging state. The small particles will be elutriated and the large ones will be defluidized. Thus, to verify the extensive application of the extra blowing gas flows, simulation of a tube bank (2D) is needed. (2) with a small blowing velocity, the intensity of disturbance on local gas field may be not so large to affect the characteristics of particle–tube collision. All these above-mentioned issues are more or less needed to be taken into account. The key issue is the common effects of the different approaches on improving the characteristics of particle–tube collisions. The present study is devoted to the above issues and the results are suggestive on these issues.
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Table 1 Parameters used in the numerical simulation. Dimension of the fluidized beds Arrangements of tubes
Particle numbers Particle diameter and density Restitution coefficient Friction coefficient Collision stiffness Gas density and viscosity Superficial gas velocity Inflow velocity of the blowing gas flow (rev-, non-, con-) Simulation time (s) Time step (s) Grid numbers and size
300×800 mm (2D); 20×80×500 mm (3D) Case 1: 6 in-line arranged immersed tubes (2D); Case 2: 18 staggered arranged tubes (2D); Case 3: 2 in-line arranged tubes (3D). Np = 80 343 (2D); Np = 178 200 (3D) dp = 883 × 10−6 (m); p = 2650 (kg/m3 ) e = 0.9
= 0.3 Kn = 1000 g = 1.29 (kg/m3 ); g = 1.85e − 5 (Pa · s) Vg0 = 1.8 (m/s) (2D) Vinf = (−Vg0 , 0, Vg0 ) (2D); Vinf = Vg0 (3D) T = 5.0 (2D); T = 0.6 (3D)
t = 1.0−5 (2D); t = 2×10−6 (3D) 150×400 (2D); x = y = 2 (mm) 10×40×250 (3D); x = y = z = 2 (mm)
3.2. Simulation conditions In the two-dimensional simulations, a fluidized bed with dimensions of 300(width)×800(height) mm2 is used for the present study. Six immersed tubes arranged in-line as a representative case (Fig. 1a) for basic investigation is used and a tube bank with 18 immersed tubes located in a staggered arrangement (Fig. 1b) is used for complementary investigation. Underneath each immersed tube there is respectively an array of nozzles which are used to inject extra blowing gas flows into the fluidized bed. The blowing gas flows are injected upstream (rev-) or downstream (con-) depending on the operation conditions. The rest parameters used in the present study are all listed in Table 1. In the threedimensional simulation, a small fluidized bed with dimensions of 20(depth)×80(width)×500(height) mm3 is used (Fig. 1c). Two immersed cylindrical tubes arranged in-line with the diameters DT = 20 mm and the lengths LT = 20 mm are equipped horizontally in the depth direction. The extra blowing gas flow is discharged near the bottom of the tubes from the two side walls of the fluidized bed. For numerical simplicity, the effects of the nozzle volumes are neglected since in the 2D simulation it is only as scientific considerations to show the pure effects of local gas disturbance. The numerical implementation of the blowing gas flows is simply a source term added on the governing equations in the grids where the nozzles occupy. The rate of the mass and momentum generation is determined by the flow flux of the secondary blowing gas flows. In this way, the location of the nozzle is right below the immersed tubes and the width of it is only 8 mm. In the 3D simulation, the extra gas flows are injected from the side walls of the bed. Thus it is simply an inflow boundary condition with uniform velocities. 4. Numerical results 4.1. Flow visualization 4.1.1. Case 1: six immersed tubes (2D) For visualization, Fig. 2a shows the two-dimensional snapshots of the local fluid fields around the tube 2 and 5 among the 6 inlinely arranged immersed tubes at t = 5 s. It is a comparison of the instantaneous fluid fields among the cases with the con-, non- and rev-blowing gas flows respectively. For the case with the upstream reverse blowing gas flow (rev-), it is observed from Fig. 2a that the streamwise velocities in the regions underneath the immersed tubes are of low values, even with minus streamwise velocities. This is an important change in the characteristics of fluid field, and it would be explored further in the following analyses. By contrast, this
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Fig. 2. Snapshots of the simulated results and a comparison between them: (a) the flow fields for Case 1 at t = 5 s; (b) the particle motion for Case 2 at t = 5 s; (c) the gas voidages for Case 3 at t = 0.2 s.
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phenomenon does not occur in the other two subfigures (con- and non-) since in this way the flow field is not disturbed as largely as the former. 4.1.2. Case 2: a tube bank (2D) Since it is necessary to know if it is viable to carry out extensive applications of the extra blowing gas flows, a tube bank is need to be investigated. Thus, for verifying the effects of the reverse blowing gas flows on the characteristics of particle–tube collision in the tube-bank, Fig. 2b illustrates the snapshots of instantaneous particle motions with and without the reverse blowing gas flows (rev- and non- respectively) when t = 5 s. After only several seconds, it is observed that great discrepancies between the motions and distributions of particles with and without introducing the extra gas flows occur. This is a necessary condition for the change of particle–tube collision characteristic and is a basic precondition for the following findings. 4.1.3. Case 3: two cylindrical tubes (3D) As mentioned above, there are several main drawbacks which are unable to overcome within the framework of two-dimensional simulations. For example, the two-dimensional large-eddy simulation is in fact not appropriate since the vortex has spatio-temporal characteristics and it needs actually three-dimensional spaces to evolve. Moreover, the reverse gas flows underneath the immersed tubes in 2D case are not viable for industrial applications, since the utilization of nozzles in the fluidized bed is not acceptable, etc. A more feasible approach for implementation of introducing extra blowing gas flows is from the walls of the bed, but it needs a 3D simulation. For this reason, Fig. 2c is snapshots of the iso-surfaces of gas voidages at t = 0.2 s with and without introducing the extra gas flows from the two side walls of the fluidized bed. Compared to the bubble without the extra gas flow, it is observed that the bubble blow the lower tube seems to be enlarged and flattened by the influences of the extra gas flows. It is interesting and the present study will focus on the effect of the local turbulent gas disturbance on the particle–tube collision characteristics. 4.2. Particle–tube collision numbers and rates As above-mentioned, the particle–tube collision would be the most important event in considering the heat transfer and the tube erosion characteristics. The present study simulated the spatial motion of all particles individually and recorded every particle–tube collision, including when and where the collision occurred, which particle and which tube it collided, how long the collision lasted, etc. It is easily for the DEM simulation to count the total collision numbers on the immersed tubes. The collision rate Rc is then defined as the total number of particle–tube collisions on the tube surfaces per unit time. As shown on Fig. 3a, the temporal accumulation of particle–tube collisions on the tube 2 and 5 (Fig. 1) are almost linearly proportional to time, whereas the rates of slope are different. It is found that for both the tube 2 and tube 5 which are representatives of others, the particle–tube collision times with the reverse blowing gas flows are the largest, with the concurrent blowing gas flows the moderate, and the non-blowing the least. Moreover, the mean collision rates from t = 2 to 5 s for all immersed tubes are all listed on Table 2, including the cases with the con-, non- and rev-blowing gas flows. We found that the rates of increment of the collision rate Rc for the rev-blowing case compared to the non-blowing case are almost greater than 50%. It is evident that the rev-blowing gas flow will considerably increase the particle–tube collision frequency, whereas between the con-blowing case and the non-blowing case it is not evident to say which is better.
Fig. 3. Comparisons of collision numbers between different approaches of introducing extra blowing gas flows: (a) Case 1: collision numbers on tube 2 and 5 between the cases with a non-, con- and rev-blowing gas flow; (b) Case 2: collision numbers on all immersed tubes between the cases with and without a reverse flow.
Thus, it is interesting to study more about the comparison between the cases with and without the reverse blowing gas flows. Fig. 3b is an illustration of the collision rates for all the 18 staggered arranged tubes. It is found from Fig. 3b that the collision rates with the reverse blowing gas flow are greater than that without the extra blowing gas flow, despite which the tube is and where the tube occupies. Based on the above findings, and from the point of view of scientific research, it seems to conclude that the local disturbance of gas flows, by means of introducing extra upstream blowing gas flows, will cause great increase in the particle–tube collision frequencies. This is important for improving the particle–tube interaction characteristics, such as heat transfer, etc.
4.3. Probability distribution function The probability distribution function (PDF) is the distribution function of particle–tube collision in the circumferential direction
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Table 2 Mean collision rates Rc for particle–tube collisions (Case 1). Tube index
Con-blowing Rc,c (s−1 )
Non-blowing Rc,n (s−1 )
Rev-blowing Rc,r (s−1 )
Increment rates (Rc,r − Rc,n )/Rc,n (%)
1 2 3 4 5 6
19 950.9 14 642.0 14 367.1 14 287.9 14 304.2 14 777.4
16 793.2 11 889.7 17 270.3 12 626.9 9044.4 11 306.8
24 663.3 26 325.9 27 922.4 27 553.1 22 587.5 22 532.6
46.9 121.4 61.7 118.2 149.7 99.3
on the exterior surface of a tube. At any prescribed angular degree on the circumferential surface, it is a probability of the occurrence of particle–tube collision. Statistically, the PDF is appropriate to be defined as a ratio of the number of particle–tube collisions occurred in a prescribed region on the tube surface to the total number of particle–tube collisions on the whole circumferential surface: dN fˆ ( ) = N d
(10)
where N is the total number of particle–tube collision. is the angular coordinate in the circumferential counterclockwise direction as illustrated in Fig. 1. dN is the number of particle–tube collision in the d region. The PDF is important for investigating the particle–tube interactions. In the present study, to compare the absolute magnitudes of the particle–tube collision rates, Eq. (10) is modified as f ( )=dN/d . It is the number of particle–tube collisions occurred per unit circumferential and per unit time, and the unit of it is (◦ s−1 ). 4.3.1. Case 1: PDFs of the six immersed tubes Again, we take tube 2 and 5 as representatives for case study. The PDFs of tube 2 and 5 under the influences of the con-, non- and revblowing gas flows are all illustrated on Fig. 4a and b, respectively. From Fig. 4, several points are observed: (1) for local disturbances caused by the con- and non-blowing gas flows, the PDFs are almost similar, which means that the concurrent blowing gas flow has very little effects on changing the particle–tube collision. (2) By contrast, the PDFs under the effect of the reverse blowing gas flow are far different from the PDFs without the local disturbance of the extra gas flow. (3) Moreover, only in the local region disturbed by the extra reverse gas flow, does the particle–tube collision numbers and rates increase greatly; in other regions the changes in the particle–tube collision characteristics are not clearly distinguishable. This is an interesting phenomenon and has potential advantages for modification of the characteristics of particle–tube interaction. Moreover, the enhancement of particle–tube collision is not an isolated conclusion only for tube 2 and 5. In fact, for all the other immersed tubes, the results are still true. Thus, the increase of particle–tube collision is an intrinsic characteristic lying in the effect of the local disturbance caused by the reverse gas flow. This conclusion will be evidenced by the following complementary simulations. 4.3.2. Cases 2, 3: PDFs of the tube bank and the 3D simulation In this section, to verify the changes in the characteristics of particle–tube collision, it is necessary to know if it is true for tubes within the tube bank and for the three-dimensional application. In other words, it is needed to know if the results obtained above are universal for any other application. Figs. 5 and 6 are the results of PDFs of the particle–tube collision corresponding to the tube bank and the three-dimensional case, respectively. It is appropriate to take tube 7, 12 and 9, 14 among the tube bank for case study, since their locations are representative ones within the tube bank. From Fig. 5a it is observed that: (1) For both tube 7 and tube 12, the particle–tube collision rates in the local region (around 270◦ ) with the reverse blowing gas flow are not
Fig. 4. PDFs of particle–tube collision on the circumferential exterior surfaces of tube 2 (4a) and 5 (4b) of Case 1.
apparently different from that without the local disturbance. However, the collision rates in the former case are still more or less larger than the latter. (2) Moreover, within the region around 90◦ , namely the leeward side of the immersed tube, the particle–tube collision rates in the rev-blowing cases are greater than that in the
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Fig. 6. PDFs of the particle–tube collision for the 3-D simulation.
Fig. 5. PDFs of particle–tube collision on representative immersed tubes of Case 2: (a) for tube 7 and 12; (b) for tube 9 and 14.
non-blowing case. It seems that the tube bank owns an intrinsic characteristic on forming locally disturbed chaotic gas flow fields. It is due to the vortex shedding effect after the immersed tubes as well as the interactions between them. Thus it is not as apparent as before for the reverse blowing gas flows to influence the gas turbulence and the particle–tube collision. However, the positive effect of local disturbance of gas motion on the particle–tube collision enhancement still remains true, which is beneficial for industrial application of particle–tube heat transfer enhancement. Moreover, from Fig. 5b, it is observed that, the discrepancies between the cases with and without the reverse flowing gas flow are similar to that of Fig. 5a. But the enhancement of particle–tube collision rates with the effect of the reverse blowing gas flow compared to that without the local disturbance are more apparent than Fig. 5a. Additionally, to study the effect of local disturbance in the 3D application by means of introducing the secondary gas flows from the
two side-walls, Fig. 6 illustrates the results of particle–tube collision with and without the secondary gas flows in the three-dimensional bed. It is also observed that the particle–tube collision rates with the secondary blowing gas flows are greater than that without them. The increments are not as large as that of Case 1 since these are not upstream but cross-streamwise gas flows. The increases are almost uniform on the whole exterior surfaces of the tubes. It is absolute that the secondary blowing gas flows would cause a large amount of particle–tube collisions providing they go on for a long time. These results indicate that the introduction of the extra blowing gas flows will change the particle–tube collision characteristics and increase the particle–tube collision frequencies as they cause local disturbances on gas turbulence in the main stream. Compared to the tube bank, it is especially meaningful when the secondary gas flows are applied to a few immersed tubes. In this way the effect of local disturbance on the gas turbulence by the extra blowing gas flows is more apparent. Furthermore, the application of introducing a great many of gas flows will of course influence the fluidization state, even cause deterioration of fluidization. Thus it needs further verifications through experimental investigations and industrial applications that if or not a large amount of extra blowing gas flows are appropriate to be applied to a very large tube bank. This objective goes beyond the present study. However, it seems to be unnecessary, since for a very large tube bank, with intrinsic characteristics of vortex shedding after the tubes and the interactions between them, the effect of introducing extra blowing gas flows to disturb the local gas turbulence is not as effective as that for a few immersed tubes. 5. Discussions 5.1. The effect of turbulence augmentation The mechanistic interpretations of the enhancement of particle–tube collision by the reverse blowing gas flows are interesting. Firstly and intuitively, we assumed that the reverse blowing gas flows will enhance the gas turbulence and hence the particle motion will be influenced by the gas turbulence, resulting in the enhancement of particle–tube collision rates. For validation, Fig. 7a and b illustrate the gas turbulent intensities for Case 1 at the heights of H = 250 and 260 mm, respectively, i.e. below the upper row of the immersed tubes (H = 270 mm) with two
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Fig. 7. Turbulence intensities for Case 1 (7a and 7b) and Case 2 (7c) at different heights.
distances of d = 20 and 10 mm, respectively. From Fig. 7a and b, it is evident that for the extra blowing gas flows especially the reverse flows, there are three maximum values of gas turbulent intensities right below the immersed tubes (with width = 0.075, 0.15, 0.225 m on Fig. 7a and b, respectively). This validates our assumption on the augmentation of the gas phase turbulence. Moreover, the concurrent blowing gas flows are downstream disturbances, and there are no obvious effects on the upstream gas turbulence. Thus, it has only augmentation effects on the turbulence near the locations where the extra flows are injected (H = 0.26), whereas it has no evident effects on the upstream turbulence (H = 0.25). However, the above results are not exactly true for the tube bank, since the fluid field within the tube bank has strong interactions between the wakes of the immersed tubes. The tube bank acts also as disturbances on the flow field, which will mask or attenuate the influences of local disturbances by an extra blowing
gas flows. Thus the turbulence augmentation is not as apparent as that for a few tubes. For validation, Fig. 7c shows the turbulence intensities at heights H = 0.30 and 0.34 (the heights right below the tube 7 and tube 9) for Case 2 with the non- and the rev-blowing gas flows, respectively. It is observed from Fig. 7c that the turbulence intensities with and without local disturbances are equivalent with each other. The effects by introducing the reverse flows are not distinguishable. Conclusively, compared to the non-blowing case, it is evident that the turbulence intensity has important effects on the particle–tube collision characteristics especially for only a few tubes. Moreover, the discrepancies between the results with the reverse flow and the concurrent flow indicate the effects of approaches by which the local disturbance is introduced. In other words, the approach of enhancing the turbulent intensity will have different effects on the enhancement of particle–tube collision.
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Fig. 8. Mean rising velocities for Case 1 (8a and 8b) and Case 2 (8c) at different heights.
5.2. The effect of formation of weak velocity regions As mentioned above, the enhancement of particle–tube collision is approach dependent. Thus, turbulence augmentation is not the sole contribution to the changes in particle–tube collision. Interestingly, it is found that another important effect, namely the formation of locally weak velocity regions underneath each immersed tubes, will also cause positive effects on the particle–tube collision enhancement. Fig. 8a–c are representative evidences for the above interpretations. Fig. 8a and b show the mean rising velocities for Case 1 at heights H = 0.22 and 0.26 m (right below the two rows of tubes) respectively and Fig. 8c shows the mean rising velocities at H = 0.34
and 0.38 m for Case 2. It is observed from Fig. 8 that: (1) the mean velocities at locations where the immersed tubes occupy are relatively smaller than other locations; (2) the regions right below the immersed tubes are weak velocity regions with relatively lower rising velocities than other regions, even with minus mean flow velocities; (3) the effect of the reverse flow causes the mean rising velocity to reach even lower values than before; (4) within the tube bank, though the trends are alike, the effects of the reverse flows on the mean rising velocities are attenuated since only relatively minor discrepancies between the cases with and without reverse flows are observed. Referring to Fig. 7c, when the turbulence enhancement effects by the reverse flows are masked, the mechanism of formation of a weaker velocity region is still playing an important role.
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Fig. 9. Gas voidages for Case 1 at different heights.
Why the formation of a weak velocity region would result in the enhancement of particle–tube collision? Regarding the natural phenomenon of a river meeting the sea, there always exist an island at the meeting-point of the river and the sea. The formation of the island is due to the reverse tide from the sea delaying the movement of sand carried by the river. Thus, the sand deposits at the meeting-point. The formation mechanism of the interesting natural phenomenon might be analogous to the mechanism of enhancement of the particle–tube collision. The reverse blowing gas flow acts as the reverse upstream tide, delaying the movement of particles brought by the rising main stream. Then, in a statistical way, the particles will accumulate in the weaker velocity region, resulting in the enhancement of particle–tube collision. Moreover, it is illustrated from previous figures that for the case with extra blowing gas flows, the maximum values of the particle–tube collision rates around the circumferential regions occur about 270◦ , i.e. the region near the bottom of the tube. Since the reverse gas flow makes the region even weaker, the enhancement of particle–tube collision is hence reasonable. For validation, Fig. 9 is the representative time averaged gas voidages at the bottom of the immersed tubes (at height H = 0.25 m). It is observed from Fig. 9 that with the reverse blowing gas flows, a great reduction in gas voidages right below the immersed tubes exists, i.e. an increase in particle number density exists due to the deceleration, deposition and conglomeration of particles.
collision, in spite of locations and numbers of the immersed tubes. Two mechanisms contributing to enhancement of particle–tube collision were explored, e.g. the effect of turbulence augmentation and the effect of formation of a weak velocity region. As the degree of turbulence enhancement depends on the approach of introducing extra blowing gas flows, the enhancement of particle–tube collision is still approach dependent. Moreover, as the reverse extra blowing gas flow delays the downstream movement of particles brought by the rising main stream, the particles will accumulate in the weaker velocity region, which can also lead to enhancement of particle–tube collision. Thus, the reverse blowing flow has the strongest effect on enhancement of particle–tube collision. On the other hand, using a great amount of extra blowing gas would possibly cause deterioration of fluidization, though in the present study, the fluidization state with a tube bank is not changed. Thus, it is suggested that experimental validation is necessary for large scale industrial application. Acknowledgment The authors are grateful for the support of this research by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Z107332). References
6. Conclusion The present study studied an approach of introducing reverse blowing gas flows around immersed tubes in bubbling fluidized bed to enhance the particle–tube collision. Two cases of 2D simulations with a few immersed tubes and a tube bank respectively and a 3D simulation with two immersed tubes were carried out. The objectives are to study the effect of turbulence disturbance on the enhancement of particle–tube collision, which is related to the fundamental aspects for particle–tube heat transfer enhancement. In general, the simulation results show that the local disturbance of gas motion induced by introducing an extra reverse blowing gas flow can cause great enhancement of particle–tube
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