A numerical study of fluidization behavior of Geldart A

A Numerical Study Of Fluidization Behavior Of Geldart A-Free PDF

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130 M Ye et al Powder Technology 139 2004 129 139, neous fluidization behavior of small particles rejecting where e is the porosity and qg u s and p are the density. Foscolo and Gibilaro s purely hydrodynamic analysis Rie velocity viscous stress tensor and pressure of the gas phase. tema et al 4 12 argued that the concept of effective elastic respectively The source term Sp is defined as. modulus could be related to some kind of mechanical Z X. structure induced by the interparticle van der Waals forces 1 bVa. Sp u va d r ra dV, Although the viewpoint of Rietema et al 4 12 has a clear V a 0. physical basis it proves difficult to find a quantitative relation. between the interparticle van der Waals forces and the Note that V is the volume of the fluid cell Va the volume of. macroscopic physical quantities of the bed The reasons are particle va the particle velocity and Npart the number of. twofold Firstly up to date there is no technique that can particles The d function ensures that the drag force acts as a. measure the detailed microscopic structure inside a gas point force in the central position of a particle To calculate. fluidized bed Secondly the interparticle van der Waals forces the interphase momentum exchange coefficient b we. are short range forces and strongly depend on the shape and employed the well known Ergun equation 19 for porosities. surface properties of particles lower than 0 8 and Wen and Yu correlation 20 for porosities. In this research a 2D soft sphere discrete particle model higher than 0 8. DPM has been used to simulate the fluidization behavior The gas phase equations are solved numerically with a. of Geldart A particles One of the features of such models finite differencing technique in which a staggered grid was. is that the realistic particle particle and particle wall employed to ensure numerical stability. interactions such as the interparticle van der Waals forces The porosity is calculated according to the method of. and particle particle collisions can be readily incorporat Hoomans et al 14. ed Since this kind of models have been proved very useful 2 3 2. to study the complicated gas solid flows in a gas fluidized e 1 p. bed 13 15 so far it allows for investigating the physical p 3. mechanism of the homogeneous fluidization The drawback where e2D is obtained from the positions of the particles. of such a detailed description however is the small size of The equations of motion of an arbitrary particle a follow. the beds employed in the simulations In this respect the from Newton s law. model should be regarded as a learning model, When this paper was being prepared we became aware of ma d2 ra F Va b. cont a Fvdw a u va Va jp, the work by Kobayashi et al 16 and Xu et al 17 dt 2 1 e. Kobayashi et al 16 studied the effect of both the lubrication. forces and the van der Waals forces on the homogeneous 4. fluidization by use of a discrete particle model They also. observed an expansion of the bed in the absence of both the. lubrication forces and the van der Waals forces which is in. agreement with the results reported in this paper However Ia X a Ia Ta 5. Kobayashi et al 16 did not give out a detailed analysis of. their results Xu et al 17 investigated the force structure in where ma is the mass of the particle Fcont a the contact force. the homogeneous fluidization regime with a discrete particle Fvdw a the van der Waals force Ta the torque Ia the moment. model in which they found that the van der Waals forces of inertia Xa the rotational acceleration and xa the rota. acting on the particles are balanced by the contact forces We tional velocity Eqs 4 and 5 are solved numerically using. also found the same phenomenon in our simulations and will a first order time integration scheme. address it in the future publication,2 Model description.
The gas flow is modeled by the volume averaged Navier. Stokes equations 18 xa x 0, B eqg The contact force between two particles or a particle and. j eqg u 0 1, Bt a sidewall is calculated by use of the soft sphere model. developed by Cundall and Strack 21 In that model a. B eqg u linear spring and a dashpot are used to formulate the normal. j eqg uu ejp Sp j es eqg g, Bt contact force while a linear spring a dashpot and a slider. are used to compute the tangential contact force where the. 2 tangential spring stiffness is two seventh of the normal. M Ye et al Powder Technology 139 2004 129 139 131, spring stiffness 22 Also we employed two different. restitution coefficients Thus a total of five parameters are. required in order to describe the contact force in our model. the normal and the tangential spring stiffness the normal. and the tangential restitution coefficient and the friction. coefficient, To calculate the interparticle van der Waals forces we.
adopt the Hamaker scheme 23 24,A 2r1 r2 S r1 r2,3 S S 2r1 2r2 2. S S 2r1 2r2,S r1 r2 2 r1 r2 2, Fig 1 The inlet conditions for the superficial gas velocity of the. where S is the intersurface distance between two spheres A simulations Three different Hamaker constants have been used. the Hamaker constant and r1 and r2 the radii of the two. spheres respectively However Eq 7 exhibits an apparent. numerical singularity that the van der Waals interaction Geldart s classification 1 The input parameters used in. diverges if the distance between two particles approaches the simulations are shown in Table 1 The cut off value of. zero In reality such a situation will never occur because of the intersurface distance between two spheres S0 should. the short range repulsion between particles In the present be less than the intermolecular center to center distance. model we have not included such a repulsion however we 24 Here a commonly used value S 0 0 4 nm is. can avoid the numerical singularity by defining a cut off employed 25 26 Air is taken as the continuous phase. maximal value of the van der Waals force between two. spheres In practice it is more convenient to use the 3 2 Procedure and initial condition. equivalent cut off value for the intersurface distance S0. instead of the interparticle force In principle the Hamaker constant A can be related to the. material properties such as the polarizability In this research. however the primary goal is to investigate the effect of the. 3 Numerical simulation interparticle van der Waals forces on the homogeneous. fluidization To this end three simulations have been con. 3 1 Input parameters ducted using three different levels of van der Waals forces. where the Hamaker constants A equals 10 20 10 21 and. We consider a system consisting of monodisperse 10 22 J respectively In each simulation we follow the. spheres with a diameter of 100 Am and a density of 900 approach adopted by Rhodes et al 27 in which the. kg m3 which are typically group A particles according to superficial gas velocity is increased from below the minimum. fluidization velocity Umf to above the minimum bubbling. velocity Umb step by step If the interparticle van der Waals. Parameters used in the simulations forces are relatively weak A 10 21 and 10 22 J the. Particle diameter dp 100 Am simulation typically runs for 1 s in real time for each velocity. Particle density q 900 kg m 3 In case of the strong van der Waals force A 10 20 J the. Normal restitution coefficient en 0 9 simulation time for each velocity will be adjusted to ensure. Tangential restitution coefficient et 0 9 that the particles and fluid have enough time to interact with. Friction coefficient lf 0 3, each other Fig 1 shows the superficial gas velocities and the. Normal spring stiffness kn 7 N m, Tangential spring stiffness kt 2 N m corresponding simulation time. CFD time step 4 2, 10 5 s The initial packed bed has been generated as follows.
Particle time step Dt 4 2, 10 6 s Firstly the particles were placed at the sites of a SC lattice. Hamaker constant A 10 22 10 21 10 20 J and the superficial gas velocity was set to a relatively large. Minimum interparticle distance S0 0 4 nm, value 0 04 m s When the bed bubbles the superficial gas. Channel height H 12 5 mm, Channel width L 5 5 mm velocity is switched to zero which causes the particles to. CFD grid height Dy 250 Am drop The initial state then has been defined as the state. CFD grid width Dx 250 Am where the pressure drop across the bed tends to zero and the. Shear viscosity of gas l 1 8, 10 5 Pa s bed height becomes stable The average porosity of this. Gas temperature T 293 K,initial state is 0 37,132 M Ye et al Powder Technology 139 2004 129 139.
4 Results and discussion It seems quite difficult to determine the minimum. bubbling points solely from the data plotted in Fig 2 It. 4 1 Macroscopic phenomena observed from the has been found by previous researchers that there could be. simulations a decrease of the bed height near the minimum bubbling. point 29 The mechanism underlying this collapse is not. 4 1 1 Bed height and pressure drop well known However no such collapse has been observed. The bed height and pressure drop are two important in our simulations This may be due to the relatively large. parameters in the investigation of the homogeneous fluid particle size dp 100 Am in our simulations In a recent. ization behavior In this research the bed height has been paper of Menon and Durian 30 a collapse for particles. defined in the following way First the fluidized bed is with a diameter of 49 Am was observed but not for. divided into a number of narrow subregions along the x i e particles with a diameter of 96 Am. width direction The width of each subregion is limited to The minimum bubbling points on the other hand can. two times the diameter of a single particle Then the y be determined from the observation of the macroscopic. coordinate i e height of the highest particle in each motion of particles Snapshots from the three simulations. subregion is identified which defines the height of this are shown in Figs 3 5 From Fig 3 it is obvious that the. subregion The average height of all subregions has been minimum bubbling velocity Umb is about 0 028 m s when. taken as the bed height the Hamaker constant A 10 22 J In the case of A 10 21. The relative bed height H and pressure drop p as a J the first obvious bubble see Fig 4 appears at. function of superficial gas velocity are shown in Fig 2 Umb 0 030 m s which is somewhat higher than that for. where H and p are defined as A 10 22 J If the Hamaker constant becomes larger i e. A 10 20 J however no obvious bubble appears even for. H H0 a superficial gas velocity U0 as high as 0 052 m s see Fig. H0 5 Instead a chainlike network can be found A close. check of the simulation results revealed that channels. Dp existed near the two sidewalls at U0 0 04 m s It seems. qp gH0 1 e0 that the gas flows try to escape from the bed by forming. channels which is similar to the behavior of Geldart C. where H0 and e0 are respectively the height and porosity of particles 1. the initial packed bed For the particles studied in this research the minimum. bubbling velocity estimated from the empirical correlations. 4 1 2 Minimum fluidization velocity and minimum bubbling 28 is around 0 01 m s which is lower than the simulation. velocity results However the experimental work by Donsi and. From Fig 2 it is clear that for all three levels of van der Massimilla 31 and simulation work by Xu et al 17 seem. Waals forces the minimum fluidization velocity is nearly to support our results for this particle system It is worthy. identical Umf 0 004 m s which indicates that the effect of mentioning that although Xu et al employed a larger A. the van der Waals forces on the minimum fluidization point is 2 1. 10 21 J for the homogeneous fluidization the gran, small This value however is over predicted compared to the ular Bond number Bo the ratio of the interparticle van der. value calculated from the approximate relation of Wen and Yu Waals force to the single particle weight is in the same. 0 003 m s 28 with a porosity emf 0 37 range of ours 32. 4 1 3 Homogeneous expansion, In the case of relatively weak interparticle van der Waals. forces A 10 22 and 10 21 J the homogeneous expan, sion of the bed can be observed as shown in Figs 6 and 7. It has been found by previous researchers that for Geldart. A particles the gross circulation of particles would prevail. in the absence of obvious bubbles 1 In Figs 8 a and. b we show the typical velocity fields of particles. corresponding to the central snapshots of Figs 6 and 7. respectively It can be seen from Fig 8 that the particles. near the bottom move upward from the middle zone while. particles near the top of the bed move downward along two. sidewalls Such a circulation of particles eventually causes. the system to become well mixed Obviously the gas flow. fed through the distributor and the friction between the. Fig 2 The dimensionless bed height and pressure drop of the fluidized bed particles and sidewalls are the main causes of such a. M Ye et al Powder Technology 139 2004 129 139 133, Fig 3 Snapshots of simulation results for Hamaker constant A 10 22 J. circulation Besides this gross circulation local small temperature which is defined as the mean squared velocity. circulations can also be observed fluctuation of particles Since the velocity fluctuation is not. always isotropic 33 it is essential to separately consider. 4 1 4 Fast bubbles the mean square fluctuation of the x defined . A numerical study of fluidization behavior of Geldart A particles using a discrete particle model M Ye M A van der Hoef J A M Kuipers Fundamentals of Chemical Reaction Engineering Faculty of Science and Technology University of Twente

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