Conference on Modelling Fluid Flow (CMFF 3) The 12 th International Conference on Fluid Flow Technologies Budapest, Hungary, September 3 6,23 THE DIFFUSION AND SEGREGATION (TURBOPHORESIS) OF DUST-PHASE AT THE TURBULENT FLOW OF DUST/GAS MIXTURES. László BOROSS, associate professor Department of Energy Engineering Budapest University of Technology and Economics Tamás RÉGERT, PhD Student Department of Fluid Mechanics Budapest University of Technology and Economics *Corresponding author: Lágymányosi u.15. H-1111 Budapest, Hungary Tel/Fax: (36 1) 3869 358, Email: boross@energia.bme.hu ABSTRACT The formation of core/annulus zones - as macroscale flow-effect - begin above the airdistributor of a circulating-fluidized riser because of the acceleration of the dust in the core and sinking of it in the boundary-layer. The differences of dustweight in radial direction reacts to the increased gas-velocity in the core and decreasing it at the wall. The dust-collisions, chiefly the inelastic ones of the dust and wall flows up the dust-concentration in the boundary-layer too. The turbulence has mixing effects in the direction of homogenizing the dust, but also the fluctuations can direct the particles towards the wall. These two effects can be approximated by a simple model. On the basis of this model an Eulerian method for the dust segregating velocity offers a faster calculation, than the Lagrangeian method. Key words: circulating fluidized bed, dust cloud, solid/gas aerodynamics. NOMENCLATURE c x [m/s] dust-velocity. in vertical direction c y [m/s] dust-velocity in horizontal direction H [m] distance from the air-distributor elt angle of phase shift k [m 2 /s 2 ] kinetic energy of fluctuations u [m/s] gas velocity comp in x direction u [m/s] gas fluctuating velocity s y [m] amplitude of dust track v tm [m/s] maximal tangential velocity x [m] coordinate y [m] coordinate x v [m] distance of vortexes D [m] diameter of the riser G s [kg/m 2 /s] external dust recirculation H [m] height of the riser R a [m] radius of the vortex-core U o [m/s] average gas-velocity ε [m 2 /s 3 ] dissipation of k µ [kg/kg] local dust content µ o =G s /(ρu o ) external dust/gas flow-ratio - ρ [kg/m 3 ] gas density ν [ kg/m 3 ] kinematical viscosity ω [ 1/s] anguler velocity of fluctuation Subscripts p particle r radial x axial 1. INTRODUCTION It is known when the flow of dust/gas mixture with relatively high dust content and low (2-6 m/s) velocities are in a vertical tube: (i.e. circulating fluidized bed: CFB) that considerable radial inhomogenities of dust content occur: higher concentrations at the wall and low in the middle core region develop. The question is why the turbulent diffusion of dust in the gas do not homogenize the differences of dust concentrations. The reason for a dust transport towards the walls is not clear. Some studies suggest, that the reason is the (inelastic) collision between the particles, others the interchange of particle-
turbulence and collisions, or the effect of large-scale unsteady fluctuations as fundamental. The inelastic dust-collisions on the wall certainly cause dust transfer to the direction of the wall. The hypothetical turbophoresis refers to particle transfer from the region of high turbulent velocity fluctuation to the region of low velocity fluctuation There is a consensus on the basis of very many experimental publications, that a core/film structure develops in the riser of a CFB and the radial gasvelocity profile is more inhomogeneous, than in the dust-free tube: in the boundary layer the velocities are relatively lower and in the core higher. The gas pressure and velocities, dust concentrations have chaotic pulsations. Contrary of the dust-concentration measurements, there are few data for the radial dust-transport in the riser-flow. In the upper dilute region of CFB it was shown [1]:, that the magnitude of the radial dust transfer both inwards and outwards are similar and are in the range of the external circulations: 2 9kg/m 2 /s, growing in the direction to the wall and have maximal values near the boundary of the core and annulus region.. The net flux: the difference of the dust-streams outwards and inwards was low, but the fluctuation of the local dust-concentration was high. Its standard deviation was growing towards the wall having a similar character, than the dusttransports. The effect of the dust collisions at high concentrations is also significant. The inelastic character of the dust collision with the wall causes an apparent dust transfer towards the wall: the rebounding particles remain nearer to the wall, than its former path. Radial dust-velocities produced by the dust collisions bring momentum-exchange in the crosssection and also originate radial dust transfer towards the stagnating zone near the boundary layer. Bolton and Davidson (1988) [2] developed a core-annular model. They related the radial particle transfer from the core to the annular region with a deposition coefficient proportional to the turbulent velocity fluctuation. Dasgupta et al. (1997) [3] revealed that particle segregation in radial direction is driven by turbophorezis: a particle transfer from a region of high turbulent velocity fluctuation to a region of low velocity fluctuation. The phenomenon was studied by detailed simulation. The bases of there investigations are the transport-equations of the gas and dust momentums and material balances. In the solid momentumequations can be found a conduction part and the different models estimate the conduction-factor, namely the viscosity of the solid-phase. A given dust-weight distribution determines a shear-stress distribution and through an aerodynamic model can give a gas/dust velocity-function of the relative radius (with the particle concentrations as well). The main problem is the high and variable viscosity of dust phase in the bottom dense region of the riser. This can be estimated by complex transport-equations for example on the bases of the granular temperature theory. According the data of Miller and Gidaspow [4] the viscosity of the dust/gas mixture is a high value (somewhat decreasing near the wall).6 -.1 Pas. Dasgupta et al. [5] use higher viscosities with a magnitude. These studies also show a significant effect of the elasticity factor of the particles (which differs at the wall collisions and that of the particles). The concentration inhomogenities are growing with decreasing elasticity factor. 2. DISCUSSION OF THE KINETICS OF GAS- DUST FLOW Diameters of laboratory and pilot-scale equipments are in the range of 5 15mm (sometimes 4mm). The heights are 4 12m. That means: the geometry and the flow can have qualitative differences in the smaller scales from the industrial operations. 2.1. The development of the core/annulus structure In the bottom, dense region above the air distributor begin dust inhomogenities. In the boundary layer of a riser above the air-distributor at the wall is an upwards decreasing gas-velocity and the "falling" dust causes a dust-concentration and this turns the gas inwards. In the middle of the riser the forced gas has an increased velocity and the accelerated dust-flow gives decreased solid-concentration (from the balance of the accelerated solid-material). This effects towards the direction of the core/annulus segregation [6]. Thus radial concentration-differences take place. From the unstable dense-region dust-strands (jets) are blowing out and cause inhomogeneous velocity and concentration distributions.
2.2. The instabilities of the inhomogeneous dust dispersion If a dust-cloud already exists, beside which a lower concentration occurs (perpendicular to the gravity) the difference of the weight causes a turn up effect [7]. (See Figure 1.) Figure 1. Dust cloud in a gas stream The effect of the riser's roof: the centrifugal force and reflexions cause a dust-concentration in the annulus. To the essential influence of the exit geometry several authors refer, e.g. [8]. The entering of the dust-return at the bottom of the riser has a momentum downwards and inwards. This asymmetry causes a gas-drive towards the axis and a decreased gas-velocity at the wall [6]. 2.3. Numerical experiments The similarity criteria of the differentialequations are as follows: µ, UD Re =, U t /U, ν U Fr = (1) gd This calculation demonstrates that differences in the dust-concentration quickly develop at a low height from the constant initial concentration. In practice there is a difference in the dust-content in the dense-phase with higher values near the wall. From such an initial state higher and growing concentrations can be expected upwards. In the governing differential-equations of gas/dust-flows the reaction of the dust-phase to the gas is completed by a drag-low of individual particles and the local dust-content, originating from the mass balance of solids. Depending on the boundary conditions, considerable inhomogenities of the dust concentration is developed which, across the gas-velocity-gradients increases the turbulent gas fluctuations. While the calculation of the gas flow is by an Eulerian method, the modelling of the dust-moving in several codes applies a Lagrangeian method.. In the calculation of characteristic dusttracks the routines (e.g. FLUENT versions) have a special stochastic approximation for the effect of the unsteady turbulent gas-fluctuations to the dusttracks. (depending on the k.5 quantity and a characteristic eddy lifetime of the gas-flow). These dust tracks show sometimes the effects of dust- diffusion, occasionally the dust transfer to the direction of the wall. An example of flow fields made by FLUENT 4 [6]: 1. Calculation: The dust enters at the bottom of the riser Gas velocity U = 4m/s at the air-distributor, gas density:.316 kg/m 3, D =.158m. The exit-cross-section is in 3m height, with a roof and an opening having a diameter of.6m. Dust-size.9mm, solid density 16 kg/m 3 Factor of inelasticity:.8. The dust concentrated at the walls after.1m and higher levels. (See Figure 2)
U, k 6 5 4 3 2 1..1.2.3.4.5.6.7.8 Radius [m] U [m/s] ρrk[kg/m3] k Figure 2. Gas velocity and dust concentration in level.2 m At unsteady case and calculation time >.5s along the riser's wall and at higher levels in the core too are forming agglomerates and lack-zones of particles.. The dust-concentration is the highest at the roof and in the narrow end-section. The dustcollisions on the roof and the high (also radial) gasvelocities in the exit-tube concentrate the dust in the corner, roof, edge and core of the tube - in surprisingly high values. 2. calculation: In a CFB equipment a concentrated dust-stream enters to the riser as recirculation. The gas cannot carry the majority of this, the rest will sink to the air-distributor, dispersed on the cross-section of this and starts from a small velocity accelerating upwards. The dust enters only on the wall region ( in.2m height) in.44kg/s quantity. Solid/gas massflow-rate: 17.75kg/s/(kg/s). The agglomerations are not eliminated by any "dust-diffusion". Agglomerates and lack-zones of particles are forming along the riser's wall and at higher levels in the core too. The differences of concentrations are generating gas-turbulence. The results give an impression, that the gasturbulence is able to transfer dust to the direction of the wall according to the applied Lagrangeian solidvelocity calculations. The FLUENT code does not contains any dissipative effect of the dust-content to the gas-turbulence, therefore the "segregationvelocities" are perhaps higher, than in a practical regime. We mentioned in point 2.1. the "dust-strands" kind of the dust-clouds. These are often developing at 1 m/s gas-velocity as a result of the pressuregradient existing in the dense-zone and have lower dust-concentration in a small tube than its.2 m szint surroundings. The dust in it accelerates upwards, later blowing out to the lean-zone. These rising dust-strands have greater concentration and velocity, than in the lean-zone. Later they lose their excess velocity and can sink. Wirth [1] based a theory on these sinking strands and constructed numerical functions of the solid/gas mass-flow-rate and gas-velocities. A model of dust tubes, connecting the bubbles can also be found in van der Schaaf [11] and Yamazaki et al.[12]. These are turbulence generating factors too. What is important the details of the conductive dust-transport have less influence on the flow and concentration field in the bottom- (and "splash") zone, than the convection. 3.THE CHARACTERISTICS OF THE TURBULENT SEGREGATION MECHANISM 3.1. The FLUENT mechanism The calculations in turbulent flows contain stochastic gas cross-flows, influencing the dust tracks. This fluctuating gas-velocity is depending on the u'= k quantity and a characteristic time, that is proportional to k/ε. That means k 1.5 /ε is a definitive parameter. In developed state this parameter increases from the wall towards the core. At the bottom of the riser (in the calculated cases) this quantity has a maximum near the wall growing outside from the axis of the tube. 3.2.Single particle in sinusoid-fluctuating gas When applied a sinusoidal fluctuation velocity in a calculation of a single particle's movement, we receive a sinus-function to the dust-velocity and no segregation towards the wall. If there are in a given place depending on the time: the fluctuation of gas velocity u' = u' sin( ωt ) dc' dt for the particle (in Stokes region: Rep is low) ( u' c' )g = Ut u' sin( ϖt ) c' sin( ϖt elt ) = ϖu' cos( ϖt elt ) Ut (2) with elt phase shift. The solution give: the particle follows the gasfluctuation with less amplitude and some phase shift. If OM = ϖu t /g (the similarity criteria for phase shift)
c' u' = 1 1+ OM 2 < 1 If U t =.5 m/s, the range of the variables are, as follows: Table 1. Values of the variables Dust amplitude ϖu t /g elt c o /u o ϖ /s s y /u o.2 11.3.981 3.92.25.3 16.7.958 5.88.163.5 26.57.894 9.81.91 1. 45..77 19.61.36 There are stationary tracks and no segregation towards the wall. In an unsteady case, if the neighbouring flow field-regions have increasing frequencies of the gasfluctuation towards the wall, the dust will have a "segregating" velocity with a fluctuating character. 3.3. k.5 µ model It is supposed, that a dust domain transfer is proportional to the dust-concentration and gasfluctuation i.e. µ k.5 quantity The following considerations are based on the Prandtl conception, but are practically the same also in the k - ε model. The magnitude of the velocity fluctuations are κydu/dy, (according to the mixing length hypothesis ), of the turbulent diffusivity: du (κy) 2 dy of the turbulent frequency: du u * κ = dy y The particles fall with a relative velocity to the gas downwards and - if starts towards the wall because of the fluctuations - travels to a region characterised by decreasing diffusivity and increasing frequency. (The direction of its movement turns back later, but because of the inertia it can't return to the former y position by the higher frequency. It has a net segregating-velocity towards the wall proportional with the velocityfluctuation. Starting to the axis: in the core-region the fluctuations and the mixing length tends to be constant and the turbulent diffusions homogenize the dust-content.) The average segregation-transport of the particle is: the difference of segregation and diffusion, in a steady state: du dµ 2 du dµ C1κ yµ = Dt = ( y) (3) dy dy dy dy From this differential-equation we can receive a distribution of dust-concentration : dµ C1µ = ( κy) or C1 µ = l dy k dµ dy In the central space l k const. and C1y µ = µ exp lk near the wall: µ µ = ( C1/ κ ) ( y / y ) An example is in Figure 3. solid conc. 4.5 4 3.5 3 2.5 2 1.5 1.5.5 1 1.5 r/r Figure 3. Dust concentration according to the model 3.4. Single particle in moving vortex-series. A Large Eddy Simulation was performed by several authors for gas, or gas/solid flows, e.g. [9]. The superposition of transported vortexelements to a steady gas flow give local gasfluctuations in the flow. If we take a vortex with Ra core-radius and v tm maximal tangential velocity in this place, a linear variation of the tangential velocity v tm r/r a if r/r a < 1 And a potential-vortex in larger radius: v tm R a /r if r/r a > 1 The induced velocity-components of a single vortex are: v = v x tm R y a 2 2 ( x + y )
v y = v tm R x a 2 2 ( x + y ) with y and x coordinates relative to the axis of the vortex. It is clear, that a single moving vortex causes local fluctuations, but the induced velocity at a great distance from the axis will decreases. A vortex-row transported by a gas-flow in a range of.7 < r/r a < 1.4 induces approximately sinusoidal fluctuating velocities, similar manner as mentioned in capital.3.2. Two vortex rows (with same circulations) transported with the same (4 m/s) velocities and different subsequent distances, induce fluctuations with local different frequencies and magnitudes. A particle with U t terminal-velocity is sinking in this system and pathing different radial gas-fluctuations. They have a maximal tangential gas-velocity of.924m/s and parameters as follow: core radius.8 -.4m yv distance.2 -.1m in cross-direction to the gas transport velocity xv distance.44 -.22m parallel of the gas velocity, They cause an average gas-fluctuation in a cross-direction:.512 m 2 /s 2, and negligible in axial direction. Its effect to a particle (having.5 m/s terminal velocity) transfer it in y direction.12m. Reflecting with a wall, as symmetry axis the vortex-series with opposite rotations, in this integrated flow-field the wall will be a straight streamline. We apply four vortex rows with the former, different R a, xv parameters as Figure 4 shows. Characteristic streamlines and dust-tracks can be seen in Figure 5 and 6. Figure 5. Streamline dust-path 2+2 vortex row The transfer in y direction will be less near the wall (1 2mm) It is important, that the dust velocities will be less approaching the wall and distance among the particle trajectories will be less. These cause growing local dust concentration. Figure 6. Streamlines dust-path 2 vortex-row This estimation shows that a turbulent dusttransfer is possible from the region of less fluctuation to the region of higher one. Figure 4. Position of vortex series SUMMARY Dust-concentrates, inhomogenities occur in varied forms in CFB-flows. The formation of core/annulus zones - as macroscale flow effect - begins above the air-distributor of the riser because of the acceleration of the dust in the core and sinking of it in the boundary layer. The differences of dust-weight in radial direction reacts to the increased gas-velocity in the core and decreasing it at the wall. These effects arise also in laminar flows. The roof of the riser and the outlet geometry increases the dust-content in the annulus at the upper region that has an effect also on the bottom.
The dust-collisions, chiefly the inelastic ones of the dust and wall step up the dust-concentration in the boundary-layer too. The turbulence have mixing effects in the direction of homogenizing the dust, but also the fluctuations can direct the particles towards the wall. These two effects can be approximated by a simple model. ACKNOWLEDGEMENT The financial support by the OTKA T32951 project of the Hungarian Academy of Science is gratefully acknowledged. The authors wishes to thank the staff of TU Budapest Dep. Energetics (Dr J. Czinder) and Department of Fluid Mechanics for their cooperation in this work. REFERENCES [1] Jiang et al: On the Turbulent Radial Transfer of Particles in a CBF Riser, Proc. of the 6th Int. Conf of CFB (CFB-6). Würzburg, pp 83-88. [2] Bolton, Davidson, 1988, Int. Conf. on CFB II pp 139-146 [3] Dasgupta, et al., 1997 Developing flow of gas-particle mixtures in vertical ducts,, Ind. Eng. Chem. 36. 3375-339. [4] Miller, Gidaspow, 1992 Dense Vertcal Gas - Solis Flow in a Pipe,, AIChe J. (1992) V. 38, No.11 pp 181-1815. [5] Dasgupta, et al.,1993, Int. Conf. CFB-4 pp 367. [6] Boross, 22: The Development of Core/Annulus Structure and Dust Clouds in Circulating Fluidization, Manuscript (will be published in Powder Technology 23) [7] Boross, 1969, Energietechnik 19 Jg. 8. pp 344-247. [8] Brereton, Grace, 1993 End Effects in CFB Hidrodynamics, pp137-144. CFB -4 [9] Uchiyama, Naruse. A numerical method for gas-solid two-phase free-turbulent flow using a vortex method, Powder Technology, 119 (21) 26-214. [1] K.E. Wirth: Fluid Mechanics of CFBs, (1991) Chem. Eng. Technol. pp 29-38. [11] van der Schaaf et al., 1999 Proc of CFB-6 pp44- [12] Yamazaki, et al.,1993, Proc. of CFB-4 pp 69-614 [13] Documentation of FLUENT 5.