- Email: [email protected]
Simulation of self-segregation of a low density spherical particle in a bubbling bed
Chemical Engineering Journal 181–182 (2012) 842–845
Contents lists available at SciVerse ScienceDirect
Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej
Short communication
Simulation of self-segregation of a low density spherical particle in a bubbling bed Piroz Zamankhan ∗ Faculty of Industrial, Mechanical Engineering and Computer Sciences, University of Iceland, Hjardarhagi 2-6, IS-107 Reykjavik, Iceland
a r t i c l e
i n f o
Article history: Received 11 June 2011 Received in revised form 20 November 2011 Accepted 22 November 2011 Keywords: Self-segregation Bubbling beds 3D and 2D simulations GPU computing Shaking
a b s t r a c t The segregation of fuel particles in a fluidized bed combustor or gasifier is of primary concern for efficient operation of reactors. In this study, the interaction between a single, low density, large sphere and a bubbling bed of glass beads has been investigated via 3D computer simulations. It is shown that the low density sphere which was put on the bed’s free surface was pushed into the bed by convective currents. The predicted self-segregation of the low density sphere in a bubbling bed by the model is validated with experiments. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Volatile matter release and conversion of solid fuels in fluidized bed reactors including combustors, pyrolysers and gasifiers has been extensively investigated [1]. Volatile matter release controls temperature profiles in the different sections of a reactor. Uneven volatile matter burning is undesirable due to the formation of hot spots at places where devolatization is enhanced [2]. In addition, the release of unconverted volatile matter from the dense bed and the splash zone of a fluidized bed combustor to the freeboard can possibly increase the formation of pollutants and cyclone overheating [1]. The role of hydrodynamic interaction between the fuel particles and the bed material including FCC particles has been characterized using the X-ray imaging techniques by Bruni et al. [3]. In their experiments which were carried out at incipient bubbling conditions a single particle was fed at a time by means of a singleparticle-injector. The aforementioned interaction can be further investigated using computer simulations on graphics processing units (GPU) [4]. Pak and Behringer [5] observed a transition to a bubbling state of solid particles in the form of glass beads inside a container which was exposed to vertical sinusoidal vibrations. In this case, a dimensionless parameter may be defined as = Aω2 /g, which measures the peak acceleration relative to gravity. Here, A is the physical amplitude of the vibrating container and ω is the angular frequency
∗ Tel.: +354 525 5310. E-mail address: [email protected] 1385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cej.2011.11.092
of the vibration. A transition was observed from a static state to a bubbling state when the frequency of vibration exceeded a certain threshold value ωb that corresponded to a critical value of b = 6.7 [5]. In this attempt, spherical particles are used as the bed material in a container which is exposed to vertical vibrations. The control parameter (by changing ω at fixed A) is varied in order to observe a transition from a static state to a bubbling state. Then, a single, low density, large spherical ball is put onto the bed’s free surface and its hydrodynamic interaction with the bed material is investigated using 3D computer simulations [6]. In brief, a combined Lagrangian (particle-based) and Eulerian (grid-based) methods (Eu/La) is used in which the gas dynamics is solved using large-eddy simulations (LES) while the dynamics of grains is described through molecular dynamics, where the interaction between the grain surfaces is modeled using the generalized form of contact theory developed by Hertz [6]. In addition, the coefficient of kinetic friction is assumed to depend on the relative velocity of slipping. The computational predictions are compared to the experimental observations. Finally, concluding remarks are presented. The present attempt may prove useful for further understanding of the hydrodynamic interaction between the fuel particles and the bed material which has been disregarded in previous studies addressing fluid bed conversion of solid fuels. 2. Simulation results and experimental observations The container used in the simulations has an irregular round cross section with a minimum and maximum inner diameter of db = 1.34 cm, Dc = 7 cm, respectively, and
P. Zamankhan / Chemical Engineering Journal 181–182 (2012) 842–845
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Fig. 1. (a) Sketch of the computational model for the container and some nomenclatures. Inset: the container side-wall profile. (b) The initial configuration of the mixture of the particles used in the simulations.
height Hc = 7.5 cm. The container side-wall profile, expressed as z(x) = 7.241 − 16.636x + 19.341x2 − 11.914x3 + 3.78x4 − 0.5x5 , as shown in Fig. 1(a) and its inset. Spherical particles with material density of s = 2500 kg/m3 , elastic modulus of E = 6.3 × 1010 Pa, and Poisson’s ratio of v = 0.244 were used as the bed material in the present simulation. A ternary mixture of the particles with diameters l = 600m, m = 500m, and = 350m was poured into the container to a height of H0 ≈ 7.1 cm, as shown in Fig. 1(b). The volume fraction of the smallest particle size in the mixture was ss = 0.1. The total solid volume fraction in the container was s = 0.64 and the solid volume fraction of the largest particles was sl = 0.33. The angular frequency of the vibration, ω, was gradually increased in order to observe a transition from a static state to a bubbling state. The aforementioned transition was observed when the frequency of vibration exceeded a certain threshold of ωb that corresponded to a critical value of b = 6.056. At b = 6.056, the bed tilted with the tilt angle of d , as shown in Fig. 2(a). A large spherical ball with diameter dp = 2.85 cm and the density p = 238 kg/m3 was put onto the bed’s free surface, as shown in Fig. 2(b). Fig. 3(a) shows that the fully submerged ball is in contact with the side wall. In this case, the bed exhibits behaviour strongly
Fig. 2. (a) The instantaneous configuration of the bed material at the incipient bubbling condition. The solid line represents the slope of free surface. (b) The configuration of the system after a low density, large ball was put on the bed’s free surface.
reminiscent of boiling, as when water vapor bubbles form at the bottom of a boiling pot of water, rise to the surface and escape. When a large object of low density is put on the free surface, the convective current pushes it into the bed which indicates that the bed resistive forces are highly reduced. The lateral position of the cutaway plan located at y = 1.1 cm. Fig. 3(a)–(d) illustrate the position of the ball, which is caught in the convective current of the bed, at times t, 0, 11.8, 23.8, and 24.6 s, respectively. These figures indicate that the ball whose flow dynamics is controlled by the convective current moved down towards the bottom of the container and curved back towards the free surface and becomes partially submerged as shown in Fig. 3(d). Note that some layers of the solid mixture in Fig. 3(a)–(d) have been cut away in order to show the ball in the bulk Fig. 3(e) represents the computed instantaneous air velocity field on a cutting xz-plane at t = 24.6 s. This figure and its inset indicate formation of large fluid vortices in the bed. The convective current in the bed results from the response of the bed to these complex fluid structures. In this case, the Reynolds number is approximately 3000, which indicates that the flow regime is transition (neither fully laminar nor fully turbulent). Fig. 3(f) shows the instantaneous configuration of bubbles around the ball at t = 24.6 s. The present model can be further generalized to investigate the leakage of volatile matter through the solid mixture as the volatile bubble is formed around the fuel particle. As stated earlier, fluid movements induce the convective current of the solid mixture in the bed [5]. Fig. 3(g) illustrates the computed instantaneous, volume averaged velocity field of the solid mixture on the same cutting xz-plane as in (f). As can be seen from Fig. 3(g), the solid particles move down at the side-wall towards the bottom of the container and then recirculated, curving back towards the free surface. More details of the complex solid recirculation in the bed is shown in the insets of (g). The solid mixture velocity is defined as Vmix = Vsl sl + Vsm sm + Vss ss , where Vsl , Vsm and Vss are velocity of the large, medium and small size particles, respectively. Fig. 3(h) shows the single-particle vertical velocity distribution function (VFD) in the bed. This VFD is highly non-Gaussian with close to t-distribution. A correlation between the deviations from Gaussian statistics and super-diffusion for the particles can be found which indicates a connection between granular superdiffusion and non-Gaussian statistics To validate the simulation results, the experiment is carried out in an apparatus, consisting of a mechanical shaker (PASCO SF-9324) with a straight and vertical driving shaft, a signal generator, a power
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P. Zamankhan / Chemical Engineering Journal 181–182 (2012) 842–845
Fig. 3. The process of submersion of the ball. Times t are (a) 0 s, (b) 11.8 s, (c) 23.8 s, and (d) 24.6 s. Here, some layers of the solid mixture have been cut away in order to show the ball in the bulk. (e) The computed instantaneous air velocity field on a cutting xz-plane whose lateral position is y0 = 0 cm at t = 24.6 s. Inset: Large vortices are magnified for better visualization. (f) The computed instantaneous configuration of bubbles around the large ball at t = 24.6 s. (g) The computed instantaneous solid mixture velocity field on the same cutting xz-plane as in (e) at t = 24.6 s. Inset: merging of two solid streams. (h) The probability distribution function of the vertical velocity component of the solid mixture at t = 24.6 s.
P. Zamankhan / Chemical Engineering Journal 181–182 (2012) 842–845
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detailed in Hoomans et al. [8]. Substantial CPU time can be saved by employing the aforementioned 2D model. However, some details including the fuel lateral movements and the leakage of volatile matter through the bed cannot be predicted by performing 2D simulations. Recently, Liu and Lu [9] performed 2D simulation to investigate cluster flow behaviour in the riser of circulating fluidized beds. Berrouk and Wu [10] suggested that there are severe shortcomings of the phase coupling scheme used in Ref. [9]. It is worth nothing that in a 2D system the particles are disks and therefore Eq. (6) in Ref. [10] should be corrected as follows: −
Ni ∂p Ni 2 Ni di + fd,i − g mi = 0 4 ∂y i=1 i=1 i=1
(1)
The addition of Eqs. (1)–(4) in Ref. [10] (i.e., −εg ∂p/∂y x y − Ni f i=1 d,i
Ni 4
i=1
− x yεg g g = 0) yields,
di2
Ni ∂p −g mi −εg x y(∂p/∂y)− x yεg g g = 0 ∂y i=1
(2)
Ni
It is worth nothing that /4 i=1 di2 euqals to (1 − εg ) x y. Thus, the pressure gradient in the vertical direction is given as: −
Fig. 4. Experimental results of self-segregation of a low density spherical particle in a bubbling bed at the incipient bubbling condition. Still images from videos which illustrate the process of pre-submersion and submersion of a low density spherical particle in a bubbling bed at ω/2 = 45 Hz that corresponds to a value of = 6.056. (a and b) The process of pre-submersion. (c–f) The process of submersion. The average time between submersion and surfacing was approximately 27 s.
amplifier, a connector box, and the container whose geometry is shown in Fig. 1. The amplifier receives sinusoidal voltage waves with a controllable amplitude and frequency produced by the signal generator. The amplified current is sent through the connector box to the mechanical shaker. The container is connected to the driving shaft using a splined joint. The acceleration of vibration in the vertical direction is precisely monitored using an accelerometer (AST). A ternary mixture of the glass beads with diameters l = 600 m, m = 500 m, and s = 350 m are used as the bed material. In the experiment the mixture was poured into the container to a height of Hp0 = 7 cm. The volume fractions of the smallest, medium and largest particle size in the mixture were ss = 0.1, sm = 0.21 and sl = 0.33, respectively. Fig. 4(a)–(f) are still images from videos [7] which illustrate the process of self-segregation of a low density spherical particle in a bubbling bed at ω/2 = 45 Hz that corresponds to a value of = 6.056. The solid line in Fig. 4(d) indicates the tilt angle of the bed which is nearly the same as that computed in the simulation as depicted in Fig. 2(a). Fig. 4(f) shows the ball surfaced at t = 27 s. Note that the computed time between submersion and surfacing is 24.6 s. The model is therefore deemed to be sufficiently flexible to capture a number of salient features of experiments of hydrodynamic interaction between a single, large spherical particle and the bed material at incipient bubbling conditions. In addition, the model can be generalized to study the leakage of volatile matter through the solid mixture as the volatile bubble is formed around a large fuel particle. The 3D simulation detailed in this section was performed using GPU computing [4]. Self-segregation of a large fuel particle at incipient bubbling condition can also be studied using a 2D model as
∂p = (1 − εg )p g + εg g g ∂y
(3)
Eq. (3) states that the pressure drop across a bed at the incipient fluidization state is equal to the weight of the bed. Here, p represents the pressure, p is the particle material density, g is the gas density, g is the acceleration due to gravity, and εg is the void fraction. 3. Concluding remarks 3D Simulations were performed to investigate the role of hydrodynamic interaction between the fuel particles and the bed material at incipient bubbling conditions. A number of salient features of experiments were captured by the model including the fuel selfsegregation and the leakage of volatile matter from the fuel to the bed material. The simulations were performed on a graphics processing unit (GPU). The promising effort in GPU computing detailed in this study may position the GPU as a compelling future alternative to traditional simulation techniques in Chemical Engineering. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cej.2011.11.092. References [1] E. Turnbull, J.F. Davidson, Fluidized combustion of char and volatiles from coal, AIChE Journal 30 (1984) 881. [2] B. Leckner, B.A. Andersson, J. Vijil, Combustion of Tomorrow’s Fuels-II, Engineering Foundation, New York, 1984. [3] G. Bruni, R. Solimene, A. Marzocchella, P. Salatino, J.G. Yates, P. Lettieri, M. Fiorentino, Self-segregation of high-volatile fuel particles during devolatilization in a fluidized bed reactor, Powder Technology 128 (2002) 11. [4] P. Zamankhan, Solid structures in a highly agitated bed of granular materials, Applied Mathematical Modelling 36 (2012) 414. [5] H.K. Pak, P.R. Behringer, Bubbling in vertically vibrated granular materials, Nature 371 (1994) 231. [6] P. Zamankhan, Bubbling in vibrated granular films, Physical Review E 83 (2011) 021306. [7] See supplemental videos for experimental details. [8] B.P.B. Hoomans, J.A.M. Kuipers, W.J. Bruels, W.P.M. van Swaaij, Chemical Engineering Science 51 (1996) 99–118. [9] H. Liu, H. Lu, Numerical study on the cluster flow behavior in the riser of circulating fluidized beds, Chemical Engineering Journal 150 (2009) 374–384. [10] A.S. Berrouk, C.L. Wu, Chemical Engineering Journal 160 (2010) 810–811.
Contents lists available at SciVerse ScienceDirect
Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej
Short communication
Simulation of self-segregation of a low density spherical particle in a bubbling bed Piroz Zamankhan ∗ Faculty of Industrial, Mechanical Engineering and Computer Sciences, University of Iceland, Hjardarhagi 2-6, IS-107 Reykjavik, Iceland
a r t i c l e
i n f o
Article history: Received 11 June 2011 Received in revised form 20 November 2011 Accepted 22 November 2011 Keywords: Self-segregation Bubbling beds 3D and 2D simulations GPU computing Shaking
a b s t r a c t The segregation of fuel particles in a fluidized bed combustor or gasifier is of primary concern for efficient operation of reactors. In this study, the interaction between a single, low density, large sphere and a bubbling bed of glass beads has been investigated via 3D computer simulations. It is shown that the low density sphere which was put on the bed’s free surface was pushed into the bed by convective currents. The predicted self-segregation of the low density sphere in a bubbling bed by the model is validated with experiments. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Volatile matter release and conversion of solid fuels in fluidized bed reactors including combustors, pyrolysers and gasifiers has been extensively investigated [1]. Volatile matter release controls temperature profiles in the different sections of a reactor. Uneven volatile matter burning is undesirable due to the formation of hot spots at places where devolatization is enhanced [2]. In addition, the release of unconverted volatile matter from the dense bed and the splash zone of a fluidized bed combustor to the freeboard can possibly increase the formation of pollutants and cyclone overheating [1]. The role of hydrodynamic interaction between the fuel particles and the bed material including FCC particles has been characterized using the X-ray imaging techniques by Bruni et al. [3]. In their experiments which were carried out at incipient bubbling conditions a single particle was fed at a time by means of a singleparticle-injector. The aforementioned interaction can be further investigated using computer simulations on graphics processing units (GPU) [4]. Pak and Behringer [5] observed a transition to a bubbling state of solid particles in the form of glass beads inside a container which was exposed to vertical sinusoidal vibrations. In this case, a dimensionless parameter may be defined as = Aω2 /g, which measures the peak acceleration relative to gravity. Here, A is the physical amplitude of the vibrating container and ω is the angular frequency
∗ Tel.: +354 525 5310. E-mail address: [email protected] 1385-8947/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cej.2011.11.092
of the vibration. A transition was observed from a static state to a bubbling state when the frequency of vibration exceeded a certain threshold value ωb that corresponded to a critical value of b = 6.7 [5]. In this attempt, spherical particles are used as the bed material in a container which is exposed to vertical vibrations. The control parameter (by changing ω at fixed A) is varied in order to observe a transition from a static state to a bubbling state. Then, a single, low density, large spherical ball is put onto the bed’s free surface and its hydrodynamic interaction with the bed material is investigated using 3D computer simulations [6]. In brief, a combined Lagrangian (particle-based) and Eulerian (grid-based) methods (Eu/La) is used in which the gas dynamics is solved using large-eddy simulations (LES) while the dynamics of grains is described through molecular dynamics, where the interaction between the grain surfaces is modeled using the generalized form of contact theory developed by Hertz [6]. In addition, the coefficient of kinetic friction is assumed to depend on the relative velocity of slipping. The computational predictions are compared to the experimental observations. Finally, concluding remarks are presented. The present attempt may prove useful for further understanding of the hydrodynamic interaction between the fuel particles and the bed material which has been disregarded in previous studies addressing fluid bed conversion of solid fuels. 2. Simulation results and experimental observations The container used in the simulations has an irregular round cross section with a minimum and maximum inner diameter of db = 1.34 cm, Dc = 7 cm, respectively, and
P. Zamankhan / Chemical Engineering Journal 181–182 (2012) 842–845
843
Fig. 1. (a) Sketch of the computational model for the container and some nomenclatures. Inset: the container side-wall profile. (b) The initial configuration of the mixture of the particles used in the simulations.
height Hc = 7.5 cm. The container side-wall profile, expressed as z(x) = 7.241 − 16.636x + 19.341x2 − 11.914x3 + 3.78x4 − 0.5x5 , as shown in Fig. 1(a) and its inset. Spherical particles with material density of s = 2500 kg/m3 , elastic modulus of E = 6.3 × 1010 Pa, and Poisson’s ratio of v = 0.244 were used as the bed material in the present simulation. A ternary mixture of the particles with diameters l = 600m, m = 500m, and = 350m was poured into the container to a height of H0 ≈ 7.1 cm, as shown in Fig. 1(b). The volume fraction of the smallest particle size in the mixture was ss = 0.1. The total solid volume fraction in the container was s = 0.64 and the solid volume fraction of the largest particles was sl = 0.33. The angular frequency of the vibration, ω, was gradually increased in order to observe a transition from a static state to a bubbling state. The aforementioned transition was observed when the frequency of vibration exceeded a certain threshold of ωb that corresponded to a critical value of b = 6.056. At b = 6.056, the bed tilted with the tilt angle of d , as shown in Fig. 2(a). A large spherical ball with diameter dp = 2.85 cm and the density p = 238 kg/m3 was put onto the bed’s free surface, as shown in Fig. 2(b). Fig. 3(a) shows that the fully submerged ball is in contact with the side wall. In this case, the bed exhibits behaviour strongly
Fig. 2. (a) The instantaneous configuration of the bed material at the incipient bubbling condition. The solid line represents the slope of free surface. (b) The configuration of the system after a low density, large ball was put on the bed’s free surface.
reminiscent of boiling, as when water vapor bubbles form at the bottom of a boiling pot of water, rise to the surface and escape. When a large object of low density is put on the free surface, the convective current pushes it into the bed which indicates that the bed resistive forces are highly reduced. The lateral position of the cutaway plan located at y = 1.1 cm. Fig. 3(a)–(d) illustrate the position of the ball, which is caught in the convective current of the bed, at times t, 0, 11.8, 23.8, and 24.6 s, respectively. These figures indicate that the ball whose flow dynamics is controlled by the convective current moved down towards the bottom of the container and curved back towards the free surface and becomes partially submerged as shown in Fig. 3(d). Note that some layers of the solid mixture in Fig. 3(a)–(d) have been cut away in order to show the ball in the bulk Fig. 3(e) represents the computed instantaneous air velocity field on a cutting xz-plane at t = 24.6 s. This figure and its inset indicate formation of large fluid vortices in the bed. The convective current in the bed results from the response of the bed to these complex fluid structures. In this case, the Reynolds number is approximately 3000, which indicates that the flow regime is transition (neither fully laminar nor fully turbulent). Fig. 3(f) shows the instantaneous configuration of bubbles around the ball at t = 24.6 s. The present model can be further generalized to investigate the leakage of volatile matter through the solid mixture as the volatile bubble is formed around the fuel particle. As stated earlier, fluid movements induce the convective current of the solid mixture in the bed [5]. Fig. 3(g) illustrates the computed instantaneous, volume averaged velocity field of the solid mixture on the same cutting xz-plane as in (f). As can be seen from Fig. 3(g), the solid particles move down at the side-wall towards the bottom of the container and then recirculated, curving back towards the free surface. More details of the complex solid recirculation in the bed is shown in the insets of (g). The solid mixture velocity is defined as Vmix = Vsl sl + Vsm sm + Vss ss , where Vsl , Vsm and Vss are velocity of the large, medium and small size particles, respectively. Fig. 3(h) shows the single-particle vertical velocity distribution function (VFD) in the bed. This VFD is highly non-Gaussian with close to t-distribution. A correlation between the deviations from Gaussian statistics and super-diffusion for the particles can be found which indicates a connection between granular superdiffusion and non-Gaussian statistics To validate the simulation results, the experiment is carried out in an apparatus, consisting of a mechanical shaker (PASCO SF-9324) with a straight and vertical driving shaft, a signal generator, a power
844
P. Zamankhan / Chemical Engineering Journal 181–182 (2012) 842–845
Fig. 3. The process of submersion of the ball. Times t are (a) 0 s, (b) 11.8 s, (c) 23.8 s, and (d) 24.6 s. Here, some layers of the solid mixture have been cut away in order to show the ball in the bulk. (e) The computed instantaneous air velocity field on a cutting xz-plane whose lateral position is y0 = 0 cm at t = 24.6 s. Inset: Large vortices are magnified for better visualization. (f) The computed instantaneous configuration of bubbles around the large ball at t = 24.6 s. (g) The computed instantaneous solid mixture velocity field on the same cutting xz-plane as in (e) at t = 24.6 s. Inset: merging of two solid streams. (h) The probability distribution function of the vertical velocity component of the solid mixture at t = 24.6 s.
P. Zamankhan / Chemical Engineering Journal 181–182 (2012) 842–845
845
detailed in Hoomans et al. [8]. Substantial CPU time can be saved by employing the aforementioned 2D model. However, some details including the fuel lateral movements and the leakage of volatile matter through the bed cannot be predicted by performing 2D simulations. Recently, Liu and Lu [9] performed 2D simulation to investigate cluster flow behaviour in the riser of circulating fluidized beds. Berrouk and Wu [10] suggested that there are severe shortcomings of the phase coupling scheme used in Ref. [9]. It is worth nothing that in a 2D system the particles are disks and therefore Eq. (6) in Ref. [10] should be corrected as follows: −
Ni ∂p Ni 2 Ni di + fd,i − g mi = 0 4 ∂y i=1 i=1 i=1
(1)
The addition of Eqs. (1)–(4) in Ref. [10] (i.e., −εg ∂p/∂y x y − Ni f i=1 d,i
Ni 4
i=1
− x yεg g g = 0) yields,
di2
Ni ∂p −g mi −εg x y(∂p/∂y)− x yεg g g = 0 ∂y i=1
(2)
Ni
It is worth nothing that /4 i=1 di2 euqals to (1 − εg ) x y. Thus, the pressure gradient in the vertical direction is given as: −
Fig. 4. Experimental results of self-segregation of a low density spherical particle in a bubbling bed at the incipient bubbling condition. Still images from videos which illustrate the process of pre-submersion and submersion of a low density spherical particle in a bubbling bed at ω/2 = 45 Hz that corresponds to a value of = 6.056. (a and b) The process of pre-submersion. (c–f) The process of submersion. The average time between submersion and surfacing was approximately 27 s.
amplifier, a connector box, and the container whose geometry is shown in Fig. 1. The amplifier receives sinusoidal voltage waves with a controllable amplitude and frequency produced by the signal generator. The amplified current is sent through the connector box to the mechanical shaker. The container is connected to the driving shaft using a splined joint. The acceleration of vibration in the vertical direction is precisely monitored using an accelerometer (AST). A ternary mixture of the glass beads with diameters l = 600 m, m = 500 m, and s = 350 m are used as the bed material. In the experiment the mixture was poured into the container to a height of Hp0 = 7 cm. The volume fractions of the smallest, medium and largest particle size in the mixture were ss = 0.1, sm = 0.21 and sl = 0.33, respectively. Fig. 4(a)–(f) are still images from videos [7] which illustrate the process of self-segregation of a low density spherical particle in a bubbling bed at ω/2 = 45 Hz that corresponds to a value of = 6.056. The solid line in Fig. 4(d) indicates the tilt angle of the bed which is nearly the same as that computed in the simulation as depicted in Fig. 2(a). Fig. 4(f) shows the ball surfaced at t = 27 s. Note that the computed time between submersion and surfacing is 24.6 s. The model is therefore deemed to be sufficiently flexible to capture a number of salient features of experiments of hydrodynamic interaction between a single, large spherical particle and the bed material at incipient bubbling conditions. In addition, the model can be generalized to study the leakage of volatile matter through the solid mixture as the volatile bubble is formed around a large fuel particle. The 3D simulation detailed in this section was performed using GPU computing [4]. Self-segregation of a large fuel particle at incipient bubbling condition can also be studied using a 2D model as
∂p = (1 − εg )p g + εg g g ∂y
(3)
Eq. (3) states that the pressure drop across a bed at the incipient fluidization state is equal to the weight of the bed. Here, p represents the pressure, p is the particle material density, g is the gas density, g is the acceleration due to gravity, and εg is the void fraction. 3. Concluding remarks 3D Simulations were performed to investigate the role of hydrodynamic interaction between the fuel particles and the bed material at incipient bubbling conditions. A number of salient features of experiments were captured by the model including the fuel selfsegregation and the leakage of volatile matter from the fuel to the bed material. The simulations were performed on a graphics processing unit (GPU). The promising effort in GPU computing detailed in this study may position the GPU as a compelling future alternative to traditional simulation techniques in Chemical Engineering. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cej.2011.11.092. References [1] E. Turnbull, J.F. Davidson, Fluidized combustion of char and volatiles from coal, AIChE Journal 30 (1984) 881. [2] B. Leckner, B.A. Andersson, J. Vijil, Combustion of Tomorrow’s Fuels-II, Engineering Foundation, New York, 1984. [3] G. Bruni, R. Solimene, A. Marzocchella, P. Salatino, J.G. Yates, P. Lettieri, M. Fiorentino, Self-segregation of high-volatile fuel particles during devolatilization in a fluidized bed reactor, Powder Technology 128 (2002) 11. [4] P. Zamankhan, Solid structures in a highly agitated bed of granular materials, Applied Mathematical Modelling 36 (2012) 414. [5] H.K. Pak, P.R. Behringer, Bubbling in vertically vibrated granular materials, Nature 371 (1994) 231. [6] P. Zamankhan, Bubbling in vibrated granular films, Physical Review E 83 (2011) 021306. [7] See supplemental videos for experimental details. [8] B.P.B. Hoomans, J.A.M. Kuipers, W.J. Bruels, W.P.M. van Swaaij, Chemical Engineering Science 51 (1996) 99–118. [9] H. Liu, H. Lu, Numerical study on the cluster flow behavior in the riser of circulating fluidized beds, Chemical Engineering Journal 150 (2009) 374–384. [10] A.S. Berrouk, C.L. Wu, Chemical Engineering Journal 160 (2010) 810–811.