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CFD–DEM simulation of the gas–solid flow in a cyclone separator(不同喂入量耦合仿真重点参考)

CFD–DEM simulation of the gas–solid flow in a cyclone separator(不同喂入量耦合仿真重点参考)
CFD–DEM simulation of the gas–solid flow in a cyclone separator(不同喂入量耦合仿真重点参考)

CFD–DEM simulation of the gas–solid?ow in a cyclone separator

K.W.Chu a,B.Wang a,c,D.L.Xu b,Y.X.Chen b,A.B.Yu a,n

a Laboratory for Simulation and Modelling of Particulate Systems,School of Materials Science and Engineering,University of New South Wales,Sydney,NSW2052,Australia

b Institute of Powder Engineering,School of Materials Science and Engineering,Xi’an University of Architecture and Technology,Xi’an710055,PR China

c Key Laboratory of Western China’s Environmental Systems,College of Earth an

d Environmental Sciences,Lanzhou University,Lanzhou730000,PR China

a r t i c l e i n f o

Article history:

Received25August2010

Received in revised form

1November2010

Accepted11November2010

Available online26November2010

Keywords:

Cyclone

Gas–solid?ow

Computational?uid dynamics

Discrete element method

Separation

Granular dynamics

a b s t r a c t

In this work,a numerical study of the gas–solid?ow in a gas cyclone is carried out by use of the combined

discrete element method(DEM)and computational?uid dynamics(CFD)model where the motion of

discrete particles phase is obtained by DEM which applies Newton’s equations of motion to every

individual particle and the?ow of continuum?uid by the traditional CFD which solves the Navier–Stokes

equations at a computational cell scale.The model successfully captures the key?ow features in a gas

cyclone,such as the strands?ow pattern of particles,and the decrease of pressure drop and tangential

velocity after loading solids.The effect of solid loading ratio is studied and analysed in terms of gas and

solid?ow structures,and the particle–gas,particle–particle and particle–wall interaction forces.It is

found that the gas pressure drop increases?rst and then decreases when solids are loaded.The reaction

force of particles on gas?ow is mainly in the tangential direction and directs mainly upward in the axial

direction.The reaction force in the tangential direction will decelerate gas phase and the upward axial

force will prevent gas phase from?owing downward in the near wall region.The intensive particle–wall

collision regions mainly locate in the wall opposite to the cyclone inlet and the cone wall.Moreover,as the

solid loading ratio increases,number of turns travelled by solids in a cyclone decreases especially in the

apex region of the cyclone while the width of solid strands increases,the pressure drop and tangential

velocity decrease,the high axial velocity region moves upwards,and the radial?ow of gas phase is

signi?cantly dampened.

&2010Elsevier Ltd.All rights reserved.

1.Introduction

Gas cyclones are widely used in industries to separate dust from

gas or for product recovery because of its geometrical simplicity,

relative economy in power usage and?exibility.The most impor-

tant performance variables of a gas cyclone are usually gas pressure

drop and solid separation ef?ciency,both of which are known to be

signi?cantly affected by solid loading ratio or concentration(Yuu

et al.,1978;Hoffmann et al.,1992;Fassani and Goldstein,2000).

Yuu et al.(1978)reported that the presence of dust reduced the

pressure drop by as much as30%even at extremely low concen-

trations such as0.2g/m3,and in one case the tangential velocity

reduced as much as40%.Understanding and modelling the physics

underlying this phenomenon is however very challenging.

In the previous numerical models of gas cyclones for the

simulation of gas?ow,conventional computational?uid dynamics

(CFD)method was mainly used.Boysan et al.(1982)developed one

of the?rst CFD models for gas cyclones and showed that the

standard kàe turbulence model was inadequate for simulating

?ows with swirl since it led to excessive turbulence viscosities and

unrealistic tangential velocities.Recent studies suggested that

turbulence models like Reynolds Stress Model(RSM)and Large

Eddy Simulation(LES)that can address anisotropic turbulence

problems should be used for gas cyclones and the corresponding

numerical results obtained are comparable with experimental

measurements(Hoekstra et al.,1999;Slack et al.,2000;Hu

et al.,2005).For the simulation of solid?ow,except for a few

continuum models(Meier and Mori,1998;Qian et al.,2007),the so-

called Lagrangian particle tracking(LPT)method is mainly used,

where the effect of solids on gas?ow and particle–particle

interaction force are usually ignored(Yoshida,1996;Pant et al.,

2002;Derksen et al.,2006;Wang et al.,2006).The LPT approach is

able to qualitatively study the effect of parameters such as

geometry,gas?ow velocity and particle size.However,it cannot

satisfactorily describe the effect of solids on gas?ow and conse-

quently parameters such as solid concentration or loading ratio.

Efforts have been made to overcome this de?ciency by various

investigators.For example,Crowe and Pratt(1974)developed a

two-dimensional(2D)model to predict the increase of the overall

collection ef?ciency with solid loading ratio.Recently,Derksen

et al.(2008)developed a modi?ed LPT model and showed that the

presence of solid particles causes the cyclone to lose some swirl

intensity and the turbulence of the gas?ow is strongly damped.

They also pointed out that the modelling of particle–particle

Contents lists available at ScienceDirect

journal homepage:https://www.wendangku.net/doc/b212635693.html,/locate/ces

Chemical Engineering Science

0009-2509/$-see front matter&2010Elsevier Ltd.All rights reserved.

doi:10.1016/j.ces.2010.11.026

n Corresponding author.Tel.:+61293854429;fax:+61293855956.

E-mail address:a.yu@https://www.wendangku.net/doc/b212635693.html,.au(A.B.Yu).

Chemical Engineering Science66(2011)834–847

interaction in a gas cyclone is important.By means of a similar approach,Wan et al.(2008)successfully predicted the signi?cant change of gas?ow?eld as a result of the presence of solid particles and spiral dust strand.Nonetheless,in theory the calculation of the reaction force on gas phase acted by solid phase is mainly based on solid concentration and the relative velocity between solids and gas;the accurate prediction of solid concentration depends on the modelling of particle–particle interactions that is not shown in the LPT models.

On the other hand,in recent years,the so-called combined approach of discrete element method(DEM)and CFD(CFD–DEM) has been developed(Tsuji et al.,1992;Xu and Yu,1997;Zhou et al., 2010)and accounts for both particle–particle and particle–?uid interactions.The CFD–DEM approach has proven to be effective in modelling various particle–?uid?ow systems(Tsuji et al.,1992;Xu and Yu,1997;Li et al.,1999;Xu et al.,2000;Rhodes et al.,2001; Kafui et al.,2002;Yu and Xu,2003;Limtrakul et al.,2004;Di Renzo and Di Maio,2007;Tsuji,2007;Kuang et al.,2008;Malone and Xu, 2008).In particular,efforts have been made to extend the CFD–DEM approach to study complex particle–?uid?ow systems (Kawaguchi et al.,1998;Rong and Horio,2001;Ibsen et al., 2004;Chu and Yu,2008a;Chu et al.,2009a;Chu et al.,2009b; Gui et al.,2009;Zhao et al.,2009).To date,to the authors’knowledge,few studies have been made on the gas–solid?ow in a gas cyclone by means of CFD–DEM approach.

In this work,a CFD–DEM model is developed to describe the gas–solid?ow in a gas cyclone.The effect of solid loading ratio is then investigated,aiming to generate a comprehensive under-standing of this complicated gas–solid?ow system.

2.Mathematical model

The CFD–DEM model used for the present work has been well documented in the literature(Xu and Yu,1997;Zhou et al.,2010). For brevity,therefore we only give a brief description of the method here.

The solid phase is treated as a discrete phase and described by the so-called discrete element method(Cundall and Strack,1979). According to the model,the translational and rotational motions of a particle at any time,t,can be described by Newton’s law of motion:

m i d v i

dt

?f pàf,it

X k i

j?1

ef c,ijtf d,ijTtm i ge1Tand

I i d x i

d t

?

X k i

j?1

eT ijtM ijTe2T

where m i,I i,v i and x i are,respectively,the mass,moment of inertia, translational and rotational velocities of particle i.The forces acting on solids are the gas–solids interaction force,f pàf,i,inter-particle forces between particles i and j,which include the contact forces, f c,ij,and viscous damping forces,f d,ij,and the gravitational force, m i g.In this model,the gas–solid interaction force includes the viscous drag force(f D,i)and pressure gradient force(f pg,i).The inter-particle forces are summed over the k i particles in contact with particle i.Torques,T ij,are generated by the tangential forces and cause particle i to rotate because the inter-particle forces act at the contact point between particles i and j and not at the particle centre. M ij is the rolling friction torque that is in opposition to the rotation of the i th particle.

The governing equations of gas phase are the same as those used in the two-?uid models(TFM)(Anderson and Jackson,1967; Gidaspow,1994;Enwald et al.,1996).There are three sets of governing equations in TFM,developed by Anderson and Jackson (1967).According to Zhou et al.(2010),Set II and in particular Set I can be used generally,and Set III can only be used conditionally.In this work,Set I is used.Thus,the conservations of mass and momentum in terms of the local mean variables over a computa-tional cell are given by

@er f eT

@t

tr Uer f e uT?0e3Tand

@er f e uT

tr Uer f e uuT?àr PàF pàftr Uee sTtr f e gtr Ueàr f u u u uT

e4Twhere e,u,u0,t,r f,P,F pàf,s and g are,respectively,porosity,mean and?uctuating?uid velocity,time,?uid density,pressure,volu-metric?uid–particle interaction force,?uid viscous stress tensor, and acceleration due to gravity.F pàf?e1=V cellT

P k c

i?1

f pàf,i,where f pàf,i is the total?uid force on particle i and k c is the number of particles in a CFD cell.àr f u u u u is the Reynolds stress term due to turbulence and solved by the Reynolds Stress Model(RSM) provided in commercial CFD software Fluent.The equations used to calculate the forces in Eqs.(1)–(4)are listed in Table1.They are very much standardised now(Zhu et al.,2007).

The?uid?ow?eld can be obtained by solving Eqs.(3)and(4)by use of a standard CFD method,and the solid?ow can be produced by solving Eqs.(1)and(2)by an explicit time integration method, facilitated by initial and boundary conditions for a given?ow.The modelling of the solids?ow by DEM is at the individual particle level,whilst the?uid?ow by CFD is at the computational cell level. Their two-way coupling(?uid forces act on particles and particles react on?uid)is numerically achieved as follows.At each time step, DEM will give information such as the positions and velocities of individual particles,for the evaluation of porosity and volumetric ?uid–particles interaction force in a computational cell.CFD will then use these data to determine the gas?ow?eld which then yields the?uid forces acting on individual particles.Incorporation of the resulting forces into DEM will produce information about the motion of individual particles for the next time step.The?uid force acting on individual particles will react on the?uid phase from the

Table1

Components of forces and torques acting on particle i.

Forces and torques Symbols Equations

Normal forces

Contact f cn,ijàE

3e1àvT

???????

2R i

p

d3=2

n

n

Damping f dn,ij

àc n

3m i E

??????????????????

2e1àv2T

p????????

R d n

p

!1=2

v n,ij

Tangential forces

Contact f ct,ij

à

m

s

f cn,ij

9d t9

1à1à

min9d t9,d t,max

èé

d t,max

3=2

"#

d t

Damping f dt,ij

àc t6m i m s f cn,ij

?????????????????????????

1àd t=d t,max

p

d t,max

!1=2

v t,ij Torque

Rolling T ij R i?(f ct,ij+f dt,ij)

Friction M ijàm r f cn,ij^x ij

Body force

Gravity G i m i g

Particle–?uid interaction force

Viscous drag force f D,i

0:63t

4:8

Re p,i

!2

r

f

9u

i

àv i9eu iàv iTp d2

i eàb

i Pressure gradient force f pg,i V p,i r P

where:n?R i=R i,v ij?v jàv i+o j?R jào i?R i,v n,ij?(v iján)án,v t,ij?(v ij?n)?n,

^o ij?x ij=o ij,Re p,i?ed i r

f

e i9u iàv i9T=em

f

T,

b?3:7à0:65exp?àe1:5àlogRe p,iT2=2 ,e?1àe

P k c

i?1

V iT=eD V cT

K.W.Chu et al./Chemical Engineering Science66(2011)834–847835

particles,so that Newton’s third law of motion is satis?ed(Xu and Yu,1997).

The above CFD–DEM principles have been well established.Our previous CFD–DEM programs are all in-house codes.For compli-cated?ow systems,the code development for the solution of?uid phase could be very time-consuming.On the other hand,com-mercial CFD software packages such as Fluent,CFX and Star-CD are readily available for this purpose.In order to take advantage of this CFD development,we have extended our CFD–DEM code with Fluent as a platform,achieved by incorporating a DEM code into Fluent through its User De?ned Functions(UDF).This approach has been successfully used in our recent study of various complicated ?uid–solid?ow systems(Chu and Yu,2008a,b;Chu et al.,2009a, 2009b),and is used in this work.

3.Simulation conditions

The cyclone considered is a typical Lapple cyclone.Fig.1(a) shows the geometry and notations of the cyclone dimensions and Table2gives their values.Fig.1(b)shows the computational domain,containing47,750CFD cells.The whole computational domain is divided by unstructured hexahedron grids.At the zone near wall and vortex?nder the grids are dense,while at the zone away from walls the grids are re?ned.Three grid domains were tested in our preliminary computation,containing25,900,47,750, 95,350cells,respectively(Wang et al.,2006).The difference is less than5%for all variables examined,suggesting that computed results are independent of the characteristics of the mesh size.

Totally6runs of simulation is carried out.The only parameter changed in each run is the ratio of solids to gas by mass at the cyclone inlet,which is0,0.5,1, 1.5,2and 2.5,respectively (correspondingly volumetric ratios at the inlet are0,0.002, 0.004,0.006,0.008and0.01,respectively).The other simulation conditions are summarized in Table3.Note that in the DEM simulation,the computational effort increases with the decrease of particle size exponentially.Therefore,in order to reduce computa-tional effort and to develop a mechanistic understanding,coarse particles are used in this work although?ne particles are normally encountered in gas cyclones.Moreover,the particles are assumed to be spherical.In principle,CFD–DEM simulations can be per-formed for non-spherical particles as,for example,recently done for ellipsoidal particles(Zhou et al.,2009;Hilton et al.,2010). However,such simulations are computationally very demanding, particularly for complex?ow systems like cyclones.On the other hand,it is noticed that for particles which are not so non-spherical, their?ow behavior can be simulated by adjusting the sliding and rolling friction coef?cients(e.g.see,Zhou et al.,1999;Yu and Xu, 2003;Zhou et al.,2004).The effectiveness of this approximation will be examined in details,in connection with our on-going work on hydro or dense medium cyclones(Wang et al.,2007;Chu et al., 2009b).In the simulation,the gas?ow is?rst solved by use of Fluent to reach its macroscopic steady?ow state(de?ned as the state when the macroscopic pattern and parameters of the?ow do not change much by time).Then particles are introduced at the inlet of the cyclone,with the number of particles added per second calculated according to the pre-set solid mass?owrate.After the ?ow reaches its steady?ow state,the pressure drop is calculated by the average static pressure at the cyclone inlet minus that at the outlet of the cyclone vortex?nder.

Physical experiments have also been conducted to validate the numerical model.The experimental method is the same as that in our previous work(Wang et al.,2006).In such an experiment,air was blown into the inlet of the cyclone,with its?owrate measured by a?owmeter.The inlet gas velocity was set to20m/s.The exit tube was open to the air and the gas pressure at the top of the vortex ?nder was around1atm.A?ve-hole probe consisting of

an

Fig.1.Schematic and grid representation of the cyclone considered,together with the de?nitions of the sections for discussion:(a)3D view of geometry;and(b)3D view of CFD grids;(c)top view of the sections;and(d)front view of the sections.

Table3

Parameters used in the work.

Solid phase a Gas phase

Particle diameter(mm)2Type of gas Air

Particle density(kg/m3)2500Density(kg/m3) 1.225

Particle inlet velocity(m/s)3Gas inlet velocity(m/s)20

Sliding friction coef?cient0.3Viscosity(kg/m/s) 1.8?10à5

Young’s modulus(N/m2)1?107Time step(s)1?10à4

Poisson’s ratio0.3Grid number62,105

Damping coef?cient0.3Grid type Hexahedron

Rolling friction coef?cient6?10à5

a For convenience,the wall is assumed to have the same properties as particles

but in?nitely diameter.

Table2

Geometry of the cyclone considered(D?0.2m).

a/D b/D De/D S/D h/D H/D B/D

0.250.50.50.625 2.0 4.00.25

K.W.Chu et al./Chemical Engineering Science66(2011)834–847

836

adjustable frame and ?ve pressure transducers was used to measure the pressure of the gas ?eld at the cyclone inlet.When the ?ve-hole probe was placed in a ?ow ?eld,voltage signals obtained through the ?ve pressure transducers were transferred to an ampli?er.The magni?ed voltage signals were acquired through a data acquisition system containing a microprocessor and a personal computer.The material used both in simulation and experiment is mono-sized glass beads with diameter of 2mm.

4.Results and discussion 4.1.Model validation

Pressure drop is one of the most important operational para-meters for gas cyclones and is used as the major parameter for the purpose of validation in this work.For pure gas ?ow,Fig.2shows that the simulated pressure drops under different inlet gas velocities agree with the experimental results.For gas–solid ?ow,Fig.3shows that the predicted pressure drop decreases with the increase of solid loading steadily,which is in good agreement with the experimental measurement.It also qualitatively agrees with the trends reported in the literature (Yuu et al.,1978;Hoffmann et al.,1992;Fassani and Goldstein,2000;Bricout and Louge,2004;Cortes and Gil,2007).

The phenomenon that the tangential velocity decreases with the increase of solid loading was found in experiments (Yuu et al.,1978)and can be captured by the current numerical model.From Fig.4it can be seen that the tangential velocity apparently decreases with the increase of solid loading and the trend agrees with the experimental measurements.Note that the comparison is only qualitative since the present simulations were not carried out under the same conditions as the experiment.

The information shown in Figs.2–4suggests that the developed CFD–DEM model can capture the major ?ow characteristics in a gas cyclone.One of the advantages of CFD–DEM model is that it is a ?rst-principle approach and at a particle scale,and can thus provide rich microdynamic information about the gas–solid ?ow.The analysis of this information can lead to better understanding of the ?ow structure and mechanics in a gas cyclone as discussed in the following sections.4.2.Gas–solid ?ow pattern

4.2.1.Particle ?ow

It is known that the macroscopic ?ow pattern of solids in gas cyclone is that most particles congregate at the wall immediately after entering the inlet and then descend in strands or bands (Muschelknautz and Greif,1997;Wang et al.,2006;Li et al.,2009).

This ?ow pattern in strands has not been well predicted in some of the previous LPT models (Wang et al.,2006;Derksen et al.,2008).However,as shown in Fig.5,it can be satisfactorily captured by

the

https://www.wendangku.net/doc/b212635693.html,parison of the simulated and measured pressure drops at different inlet gas

velocities.

https://www.wendangku.net/doc/b212635693.html,parison of simulated and measured pressure drops at different solid loading ratios.

Outer cylinder wall

Inner cylinder wall

Outer cylinder wall Inner cylinder wall

Solid loading ratio (kg solid per kg air)

Fig.4.Distributions of the tangential velocity of gas phase at the cylinder section of the cyclone under different solid loading ratios:(a)simulation results and (b)experimental measurement (Yuu et al.,1978).

K.W.Chu et al./Chemical Engineering Science 66(2011)834–847837

current CFD–DEM model.It can be seen that the ?ow reaches its macroscopically steady state ?ow after 2s.Particles have a higher descending angle and velocity in the cylindrical part than in the conical part,because of the supporting forces acting on particles by the cyclone conic wall (Wang et al.,2006).

It would be interesting to know the differences in the solid ?ow patterns when the reaction forces of solids on gas ?ow are ignored (one-way coupling)and considered (two-way coupling).Fig.6compares the ?ow patterns when solid load ratio is 2.5.It can be seen that the ?ow patterns are similar in the cylinder section of the cyclone except that the descending angle of solids under the one-way coupling is smaller than that under the two-way coupling condition.For the ?ow in the conic section,the ?ow patterns are however quite different.Under the one-way coupling condition,strands ?ow pattern is not clearly observed in the conic section.There are much more particles residing in the conic section than that under the two-way coupling condition.Furthermore,the axial velocities of particles under the one-way coupling condition are generally higher than those under the two-way coupling condition.The differences originate from the fact that solids affect the ?ow of gas signi?cantly,especially in the conic section as discussed in Section 4.2.They also highlight the need for two-way coupling for cyclones.In the following,unless otherwise speci?ed,all the results are based on the two-way coupling approach.

Fig.7shows the comparison of the solid ?ow patterns under different solid loading ratios.Clearly,strands ?ow patterns are observed,irrespective of solid loading ratios.However,the details

are different.It can be seen that the number of turns travelled by solids in the cyclone decrease with the increase of solid loading ratio.The ‘‘strands’’are wider when solid loading ratio is high,which qualitatively agrees with the ?nding by Trefz and Muschelknautz (1993).The overall axial velocity of particles decreases with the increase of solid loading ratio.

Fig.8shows that the mass of solids residing in the cyclone increases more than linearly with the increase of solid loading ratio.When solid loading ratio is 0.5,the mass of solids residing in the cyclone is 0.11kg (Point A).However,if the mass residing in the cyclone is assumed to increase linearly with solid loading ratio,then the mass of solids in the cyclone should be about 0.067kg (Point B),64%less than that in the real case.The reason why solids accumulate in the cyclone easier at lower solid loading ratios is that particles tend to keep rotating in the conic section when the ?ow is dilute and particle–particle interaction force is not big enough to make particles move downward.

4.2.2.Fluid ?ow

Pressure drop is one of the most important parameters in the operation of gas cyclone since it represents the energy consump-tion.It varies with solid loading ratio,as shown in Fig.3.Increasing solid loads decreases the pressure drop,which is consistent with the literature (Yuu et al.,1978;Hoffmann et al.,1992;Fassani and Goldstein,2000).This phenomenon was thought to be contrary to the rationale.For example,in ?uidization or pneumatic conveying,pressure drop usually increases with solid loading ratio.A notice-able ?nding from the present CFD–DEM simulations is that the pressure drop increases slightly at the beginning (t o 0.1s)and then decreases sharply,as shown in Fig.9.Actually,from Fig.5it can be seen that the ?ow at the inlet of the cyclone is similar to the one in pneumatic conveying,which results in the increase of pressure drop when solids are loaded at the beginning (t o 0.1s in the current case).The sharp decrease of pressure drop after t ?0.1s is caused by the gas–solid interaction which will be discussed in Section 4.3.

The inner ?ow structures of gas phase under different solid loading ratios at a vertical central plane of the cyclone are shown in Figs.10–13.Fig.10shows the pressure distributions with

different

Fig.5.Snapshots showing the dynamic ?ow of particles in the cyclone when solid loading ratio is 2.5(particles are coloured by particle velocity in Z

-direction).

https://www.wendangku.net/doc/b212635693.html,parison of solid ?ow patterns when the reaction of solids on gas ?ow is:(a)not considered (one-way coupling)and (b)considered (two-way coupling).Solid loading ratio was 2.5kg solid per kg air for both cases and snapshots were taken at t ?2s.Particles are coloured by the axial velocity of particles.

K.W.Chu et al./Chemical Engineering Science 66(2011)834–847

838

solid loading ratios.It can be seen that the pressure is high on the cyclone wall and can be negative in the centre of the cyclone.The magnitude of pressure near the cyclone wall decreases steadily with the increase of solid loading ratio.When comparing Fig.10(a)with Fig.10(b)–(d),it can be seen that the negative pressure zone in the apex of the cyclone disappears after loading solids.This suggests that the solids have a higher impact on the gas ?ow in the apex than in the other regions.Another obvious trend shown in Fig.10is that the length of the negative pressure zone decreases as the solid loading ratio increases.

Fig.11shows the tangential velocity distributions with different solid loading ratios.An obvious trend is that the tangential velocity decreases with the increase of solid loading ratio,especially in the apex of the cyclone.It also suggests that the solids have a higher impact on the gas ?ow in the apex than the other regions.Another trend shown in Fig.11is that the distribution of the tangential velocity is not symmetric.This is caused by the fact that there is only one inlet which is not symmetric in geometry.

There are limited experimental and numerical data about the axial and radial velocities in gas cyclones when solids are loaded.However,those velocities can be readily produced by the current

model.From Fig.12(a)and (b)it can be seen that when the solid loading ratio is 0.5,the high axial velocity region moves toward to the centre of the cyclone.This is particularly so in the lower region of the conic part.From Fig.12(b)–(d)it can be seen that the highest axial velocity region moves upward as solid loading ratio increases further.This trend is believed to be caused by the accumulation of particles in the cyclone which prevents gas from ?owing down-ward since the reaction force acting on gas phase by particles generally points upward in the axial direction (see Fig.19).

Fig.13shows the different radial velocity distributions with different solid loading ratios.Fig.13(a)demonstrates that the forced vortex in the centre of the cyclone for pure gas ?ow looks like a helical twisted cylinder.The axis of the forced vortex is not straight but curved.After a small amount of solids are loaded,as shown in Fig.13(b),the axis of the forced vortex at the cylinder part of the cyclone becomes almost straight while the twisted

forced

https://www.wendangku.net/doc/b212635693.html,parison of solid ?ow patterns (at t ?2s)under different solid loading ratios:(a)0.5;(b)1.0;(c)1.5;(d)2.0;and (e)2.5.

A B

Fig.8.The mass of solids residing in the cyclone under different

solid loading ratios.

Fig.9.Pressure drop vs.time under different solid loading ratios.

K.W.Chu et al./Chemical Engineering Science 66(2011)834–847839

vortex becomes more intensive in the conic area of the cyclone.As solid loading ratio increases further,the forced vortex in the conic part is dampened greatly (Fig.13(c)and (d)).

Fig.14shows the spatial distributions of pressure and tangential velocity of the gas phase in more details.It con?rms the signi?cant change of the ?ow after loading solids.It also shows that ?ow is largely symmetric even though the cyclone geometry is not symmetric,i.e.,there is only one inlet in the cyclone.

The change of gas velocities after loading solids can be further illustrated by considering the total kinetic energy of the motion of gas phase,as shown in Fig.15.Here,the kinetic energy is the sum of

the kinetic energy (P cell number cell ?1

e1=2Tm cell 9v cell 92

)in each computa-tional cell.m cell and v cell are the mass and velocity of gas phase in a CFD cell,respectively.The kinetic energy is also shown in different directions,calculated using the tangential,axial or radial compo-nents of v cell .According to this de?nition,the total kinetic energy is the sum of the kinetic energy in the tangential,axial and radial directions.It can be seen that the tangential kinetic energy decreases signi?cantly with the increase of solid loading ratio while the radial and axial kinetic energy are almost constant.As the kinetic energy is directly related to velocity,these ?ndings

con?rm

Fig.10.Pressure (Pa)distributions at the central section vertical to the cyclone inlet under different solid loading ratios:(a)0.0;(b)0.5;(c)1.5;and (d)

2.5.

Fig.11.Tangential velocity (m/s)distributions at the central section vertical to the cyclone inlet under different solid loading ratios:(a)0.0;(b)0.5;(c)1.5;and (d)

2.5.

Fig.12.Axial velocity (m/s)distributions at the central section vertical to the cyclone inlet under different solid loading ratios:(a)0.0;(b)0.5;(c)1.5;and (d)

2.5.

Fig.13.Radial velocity distributions at the central section vertical to the cyclone inlet under different solid loading ratios:(a)0.0;(b)0.5;(c)1.5;and (d)2.5.

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840

the signi?cant decrease in the tangential velocity.Moreover,Fig.15shows that the total tangential kinetic energy is much larger than the axial and radial kinetic energies and thus https://www.wendangku.net/doc/b212635693.html,paring Figs.3and 15suggests that the relationship between the pressure drop and solid loading ratio is very similar to that between the tangential velocity of the gas phase and solid loading ratio.Thus,the decrease of the pressure drop is strongly related to the decrease of the tangential velocity.

It should be noted that the pressure drop and tangential velocity may not always decrease with the increase of solid loading ratio in certain extreme cases,especially when particles are extremely ?ne (Bricout and Louge,2004).When a large portion of particles fed at the inlet are too ?ne to be collected in the spigot of the cyclone,the

majority of particles would not ?ow as strands in the region close to the outer wall of the cyclone.Instead,they would ?ow in the inner region of the cyclone and ?nally escape through the vortex ?nder.In this situation,the impact of particles in the inner region on gas ?ow may be different from that in the region close to the outer wall.Therefore,the effect of solids on gas ?ow obtained in this work is only applicable to the situation where particles are large enough to be collected at the spigot through the cyclone outer wall,which is important since about 95%of particles can be collected at under-?ow in most of the operations of gas cyclones.4.3.Forces governing the motion of particles

According to the model framework of the current work,the motion of particles in a cyclone is governed by the particle–?uid,particle–particle and particle–wall interaction forces.In this sec-tion,the three forces are examined to better understand the nature of the ?ow in a cyclone.

4.3.1.Particle–?uid interaction force

Two particle–?uid forces,i.e.,the gas drag force and pressure gradient force (PGF)are considered in this work.Fig.16shows the

total (P N p i ?19f i 9)and averaged (e1=N p TP N p

i ?19f i 9)forces acting by gas phase on particles for different solid loading ratios,where N p is the total number of particles residing in the cyclone.For conve-nience,the particle–particle and particle–wall interaction forces are also shown in this ?gure.The forces on a particle are all normalized by dividing the gravity force of the particle.Fig.16

(a)

Fig.14.Pressure (I)and tangential velocity (II)distributions at different sections (de?ned in Fig.1):(a)pure gas ?ow and (b)gas–solids ?ow when solid loading ratio is 2.5.

Fig.15.Kinetic energy of gas phase at a macroscopically steady state as a function of solid loading ratio.

K.W.Chu et al./Chemical Engineering Science 66(2011)834–847841

shows that both the total drag force and PGF increase with solid loading ratio but Fig.16(b)shows that the average values decrease slightly with the increase of solid loading ratio.The increase of the total forces should be due to the increased mass of solids residing in the cyclone (see Fig.8).The decrease of the average drag force and PGF should correspond to the decrease of the tangential velocity (see Figs.4and 11)and the pressure drop (see Figs.3and 10),respectively.Fig.16also shows the magnitude of the drag force is much larger than that of the PGF,suggesting the drag force is more dominant for this ?ow system.

The spatial distributions of the drag force and PGF acting on individual particles,when the solid loading ratio is 2.5,are shown in Figs.17and 18,respectively.Both ?gures show that the spatial distributions of the two forces are not uniform.They are higher in the inlet region of the cyclone and there are two separating regions in the strands:the regions close to the cyclone wall have lower drag forces and PGFs while the regions away from the wall have higher drag forces and PGFs.The drag force on particles is low because of the no-slip condition between the cyclone wall and gas phase,which may lead to low gas velocity and hence low drag force.The PGF is relatively low close to the cyclone wall because the pressure does not decrease signi?cantly near the wall regions but decreases signi?cantly in the centre regions (from positive to negative),as shown in Fig.10.PGF is proportional to the pressure gradient,as shown in Table 1.

In this work,the ?uid drag force is the only force considered that is related to the gas velocity.Therefore,it is expected that the distribution of the ?uid drag force will follow the trend of the velocity of the gas ?ow.This is indeed con?rmed by Fig.17,which shows that the ?uid drag force directs dominantly in the tangential direction.As shown in Figs.12–15,gas ?ows mainly tangentially since its tangential velocity is much larger than the axial and radial

velocities.On the other hand,Fig.18shows that the direction of the PGF is almost vertical to that of the drag force,pointing from the wall to the centre of the cyclone.This agrees with the radial

pressure

Fig.16.Normalized total (a)and averaged (b)forces in the cyclone under different solid loading ratios:line I,particle–particle interaction force;line II,particle–wall interaction force;line III,drag force;and line IV,pressure gradient

force.

Fig.17.Spatial distribution of the gas drag forces acting on particles in the cyclone when solid loading ratio is

2.5.

Fig.18.Spatial distribution of the pressure gradient forces acting on particles in the cyclone when solid loading ratio is 2.5.

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distribution where the pressure decreases gradually from the wall to the centre of the cyclone (see Fig.10).

According to the current model framework,the forces acting on particles (f p àf ,i )by gas phase are at a particle scale and the reaction forces acting on gas phase (V cell F f àp )by particles are at a CFD cell scale,while they obey Newton’s third law of motion,i.e.

F p àf ?e1=V cell TP k c

i ?1f p àf ,i .This force is shown in Fig.19.Two phenomena can be observed from the ?gure:The ?rst one is that the reaction force of particles on gas phase increases with solid loading ratio in the upper part but decreases generally in the lower part of the cyclone.This is because the magnitude of the reaction force depends on two factors:one is the magnitude of ?uid force on particles and the other one is the number of particles in a CFD cell or solid concentration.When solid loading ratio is low,the reaction force is small in the upper part of the cyclone since the solid concentration is low.When solid loading ratio is high,the reaction force is small in the lower part of the cyclone since the gas velocity and pressure gradient are relatively low in that part (see Figs.10–13).The other phenomenon is that most of the vectors are shown in red,which means that the reaction force acted by particles on gas phase is generally upward.The presence of solids in the cyclone will produce a resistant force to the downward ?ow of gas.

Fig.20shows the vectors of the reaction forces of particles on gas phase in a horizontal plane when solid loading ratio is 2.5.From Fig.20(a)it can be seen that the reaction force points upward,which means particles will prevent gas from ?owing downward.From Fig.20(b)it can be seen that the reaction force mainly points tangentially,because the ?uid drag force is mainly in the tangential direction and the PGF is much smaller than the drag force even though PGF mainly points radially.According to Newton’s third law of motion,this tangential force is in the reverse direction of the tangential velocity of gas phase.Thus,according to Newton’s second low,this force will decelerate the tangential ?ow of gas phase,which may explain why the tangential velocity of gas phase decreases signi?cantly after loading solids (see Figs.3and 10).When the tangential velocity of the gas phase decreases,the pressure drop will decrease correspondingly.

Yuu et al.(1978)suggested that the decrease of the tangential velocity is caused by the increase of friction due to the movement of particles attaching to the outer cylinder wall.They coated a layer of particles on the cylinder wall,making it rough and again measured the tangential velocity,and found that the decrease of the tangential velocity under rough outer cylinder wall condition was not as great as that under gas–solid ?ow condition.In our work,the decrease of the tangential velocity of gas phase after loading solids is captured,even though the effect of the presence of solids on the friction between gas and the wall is not considered.Thus,it is thought that the decrease of the tangential velocity of gas phase after loading solids is mainly due to the reaction force of particles on gas phase in the current conditions.Trefz and Muschelknautz (1993)has described this phenomenon as that ‘‘the exchange of tangential momentum between the slowly slipping wall layer of solids and the gas decelerates the vortex ?ow’’while they did not provide any

evidence.

Fig.19.Spatial distributions of the reaction force of particles on gas phase under different solid loading ratios:(a)0.5;(b)1.5;and (c)2.5.The vectors are coloured by the axial particle–?uid volumetric

force.

Fig.20.Vectors of the reaction force of particles on gas phase on a horizontal plane when solid loading ratio is 2.5:(a)front view and (b)top view.The force is àF fp term in Eq.(4).

K.W.Chu et al./Chemical Engineering Science 66(2011)834–847843

4.3.2.Particle–particle interaction force

Particle–particle interaction relates to particle breakage or attrition,which may be important when separating solid products from gas.The information regarding the particle–particle interac-tion at different solid loading ratios is shown in Figs.16and 21.Fig.16clearly shows that both the total and averaged particle–particle interaction forces are much larger than the other three forces,suggesting that the inclusion of particle–particle interaction is important in the modelling of gas–solid ?ow in gas cyclones.Moreover,this ?gure shows that the magnitudes of both the total and averaged particle–particle interaction forces increase with solid loading ratio.This is because the solid concentration in the cyclone increases with solid loading ratio.When solid concentra-tion is high,the chance for particle–particle interaction is high.

Fig.21shows the spatial distribution of particle–particle inter-actions.It can be seen that there are strong particle–particle interactions inside the strands of the solids.Outside the strands,there are very few particles in red,which means the particle–particle interaction force is quite small there.Fig.21(a)also demonstrates that the particle–particle interaction in the upper part of the cyclone is not strong when solid loading ratio is low,because a strand is not clearly formed there.Fig.21(d)shows the transient variation of the total particle–particle interaction force with time.It can be seen that the total particle–particle interaction forces increase from zero to a maximum value and then ?uctuates around a constant.The trends are different when the solid loading ratio is different.As solid loading ratio increases,the total particle–particle interaction force reaches its stable state quicker and the magnitude of both the ?uctuation and the absolute value become larger.Those trends look similar to that of the pressure drop as shown in Fig.8.

4.3.3.Particle–wall interaction force

Particle–wall interaction force in cyclones relates to the wearing of cyclone wall which could be a serious problem for cyclones operating at high solid loading ratios.For example,it is observed in practice that the apex of a cyclone in the preheating system in cement industry can be seriously worn out.The information of

particle–wall interaction is shown in Figs.16and 22.Fig.16shows that the magnitude of the particle–wall interaction is slightly lower than the particle–particle interaction,but higher than the particle–?uid forces.This suggests that particle–wall interaction is an important factor in the modelling of gas cyclones.Moreover,Fig.16(a)shows the total particle–wall interaction force increases with solid loading ratio but Fig.16(b)shows that the averaged particle–wall interaction force decreases with the increase of solid loading ratio.The increase of the total particle–wall interaction should be due to the increase of the solids residing in the cyclone,as shown in Fig.8.The decrease of the averaged particle–wall interaction force may be caused by the ‘‘shielding’’effect of particles.Not all particles can collide with the wall since some particles only collide with the particles bouncing back after colliding with the wall.

In this work,the spatial distribution of the particle–wall interaction is quanti?ed by use of the so-called Time Averaged Collision Intensity (TACI)which is related to wear (Finnie,1972),de?ned by TACI ?

P t ?T t ?0

P k m

i ?1

9f cn ,i tf dn ,i tf ct ,i tf dt ,i 9e5T

where A is the surface area of a sample wall,T is the simulation time or sampling time,k m is the number of particles making contact with the sample wall at a given time.Physically,it can be understood as the particle–wall interaction forces per unit (wall surface)area per unit time.

Fig.22shows the spatial distribution of TACI between particles and wall for different solid loading ratios.Generally speaking,the high TACI regions mainly establish on the wall opposite to the inlet of the cyclone and the conic and apex wall.The TACI on the wall opposite to the inlet is high because particles enter the cyclone from the inlet and then heavily collide with the cyclone wall where they change their ?ow directions signi?cantly.The conic wall gets high TACI because it constricts the diameter of particle orbits by particle–wall contacts.Fig.22also shows that the distribution of TACI varies with solid loading ratio,especially on the conic part

of

Fig.21.Spatial distributions of particle–particle interaction force (normalized by dividing particle weight)under different solid loading ratios:(a)0.5;(b)1.5;and (c)2.5,and (d)transient variation of the total particle–particle interaction forces with time.

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844

the cyclone.As solid loading ratio increases,the area of the cyclone wall experiencing particle–wall interaction decreases while the intensity of the particle–wall interaction increases.

Fig.22(d)shows the transient variation of the total particle–wall interaction force with time.It can be seen that the total particle–wall interaction forces increase from zero to a maximum value and then ?uctuates around a constant.The trends are different for different solid loading ratios.As solid loading ratio increases,the total particle–wall interaction force reaches its stable state quicker and the magnitude of both the ?uctuation and the absolute value become larger.Those trends are similar to that of the pressure drop (Fig.8)and the total particle interaction force (Fig.21(d)).None-theless,an obvious difference is that the magnitude of the total particle–wall interaction force is not so sensitive to solid loading ratio.It suggests that the wear may be improved under high solid loading conditions for a given amount of solid to handle.

5.Conclusions

A CFD–DEM model has been developed to describe the gas–solid ?ow in a gas cyclone.Its validity is demonstrated by its successful capturing the key ?ow features in a cyclone separator such as the ?ow pattern of particles along the cylinder wall in strands,and the decrease of pressure drop and tangential velocity after loading solids.The effect of solid loading ratio has been analysed on this basis,leading to the following conclusions:

As the solid loading ratio increases,there are less turns travelled

by solids,especially in the apex region of a cyclone,and the width of the strands increases.The total mass of solids residing in the cyclone does not linearly increase with solid loading ratio.More solids tend to accumulate in the cyclone when the solid loading ratio is low.

The gas pressure drop ?rstly increases and then decreases to reach a stable value when solids are loaded.When the ?ow reaches a macroscopically steady ?ow state,the pressure

drop and the tangential velocity of gas phase decrease steadily with the increase of solid loading ratio.At the same time,the high axial velocity region moves upwards and the radial ?ow of gas phase is signi?cantly dampened,especially in the apex region.

In general,the magnitudes of the particle–particle and particle–wall interaction forces are much larger than that of the particle–?uid force.On the other hand,the magnitude of the drag force is larger than the PGF.The drag force is mainly in the tangential direction but the PGF is mainly in the radial direction.The reaction force of particles on gas ?ow is mainly in the tangential direction and directs mainly upward in the axial direction.The reaction force in the tangential direction will decelerate gas phase and the upward axial force will prevent gas phase from ?owing downward in the near wall region.Both the total and averaged particle–particle interaction forces increase with the increase of solid loading ratio.The most intensive particle–particle interaction regions locate within the particle strands.The total particle–wall interaction increases but the averaged particle–wall interaction decreases with solid loading ratio.The intensive particle–wall collision regions mainly locate in the wall opposite to the cyclone inlet and the cone wall.When solid loading ratio increases,the area of the cyclone wall experiencing particle–wall interaction decreases but the intensity of the particle–wall interaction increases.

The ?ndings should be useful to the development of a compre-hensive understanding of the gas–solid ?ow in cyclones.However,it should be pointed out that the present study is carried out for large,cohesionless and spherical particles because of the current computer capability.Thus,the present study is largely qualitative and for fundamental understanding,while showing the capability of the CFD–DEM approach applied to gas cyclone.Therefore,more detailed,systematic studies are necessary in order to understand the effects of variables related to operational conditions,particle and material properties,and cyclone geometry,and hence generate results useful to engineering

application.

Fig.22.Spatial distributions of particle–wall Time Averaged Collision Intensity under different solid loading ratios:(a)0.5;(b)1.5;and (c)2.5,and (d)transient variation of the total particle–wall interaction forces with time.

K.W.Chu et al./Chemical Engineering Science 66(2011)834–847845

Nomenclature

A area,m2

c damping coef?cient,dimensionless

d particl

e diameter,m

E Young’s modulus,Pa

f c contact force,N

f d dampin

g force,N

f pàf particle–?uid interaction force,N

F volumetric force,N/m3

g gravity acceleration vector,9.81m/s2

G gravity vector,N

I moment of inertia of a particle,kg m

k cell number of particles in a computational cell, dimensionless

k i number of particles in contact with particle i, dimensionless

k m number of contacts in a sample,dimensionless

m mass of a particle,kg

M rolling friction torque,N m

n unit vector in the normal direction of two contact spheres, dimensionless

N p particle number,dimensionless

P pressure,Pa

D P pressure drop,Pa

R radius vector(from particle centre to a contact point),m R magnitude of R,m

Re Reynolds number,dimensionless

t time,s

T total simulation time,s

T driving friction torque,N m

u mean?uid velocity vector,m/s

u0?uctuating?uid velocity vector,m/s

v particle velocity,m/s

V volume,m3

V velocity vector,m/s

Greek letters

b empirical coef?cient de?ned in Table2,dimensionless d vector of the particle–particle or particle–wall overlap,m

d magnitud

e o

f d,m

e porosity,dimensionless

m f?uid viscosity,kg/m/s

m r coef?cient of rolling friction,m

m s coef?cient of sliding friction,dimensionless

n Poisson’s ratio,dimensionless

r density,kg/m3

s viscous stress tensor,N/m3

x angular velocity,rad/s

o magnitude of angular velocity,rad/s

^x unit angular velocity

Subscripts

c contact

cell computational cell

d damping

D drag

f?uid phase

ij between particle i and j

i(j)corresponding to i(j)th particle

max maximum

n in normal direction p particle phase

pg pressure gradient

pàf between particle and?uid phases

t in tangential direction

Acknowledgement

The authors are grateful to the Australia Research Council(ARC) for the?nancial support of this work.

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K.W.Chu et al./Chemical Engineering Science66(2011)834–847847

第七 章 CFD仿真模拟

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洁净厂房洁净区设计规 范 Document serial number【KKGB-LBS98YT-BS8CB-BSUT-BST108】

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CFD仿真技术在航空发动机中的应用

CFD仿真技术在航空发动机中的应用 摘要:随着科学技术的发展,航空航天和空间技术有了飞跃的发展,在这些飞 跃的发展技术中主要的技术就是CAE技术。航空工业可以说是CAE技术发展的摇篮,各种CAE技术正是在以航空工业为主的实际工业应用的推动下在不到半个世 纪时间里迅猛发展起来的。以ANSYS、LS-DYNA、Nastran、CFX、Fluent等为代表 的高端CAE软件早已活跃在全球航空工业中。 关键词:CFD仿真技术;航空发动机;应用 1 引言 目前国际知名企业的航空发动机研制周期从过去的10~15年缩短到6~8年 甚至4~5年,试验机也从过去的40~50台减少到10台左右。在发达国家的航 空企业里CAE已经作为产品研发设计与制造流程中不可逾越的一种强制性的工艺 规范加以实施,在生产实践作为必备工具普遍应用。 2、CFD技术国内外使用状况简介 CFD作为CAE技术的一种,已经越来越多的被国内外航空企业广泛的得以应用。第一个商用CFD软件包FLUENT,由与美国空军合作的流体技术服务公司Creare公司于1983年推出的。商业CFD软件的开发及应用,加速了航空工业的 发展,使得基于虚拟样机仿真的现代设计方法成为了可能。以波音公司航空研发 发展历史为例,不难发现,波音公司先后采用了经典的实验测试方法、半经验的 方法、空气动力学的计算、政府内部及企业的CFD代码及广泛的采用CFD商业代码。在波音公司2005年的软件应用报告中明确指明,在1998至2005年内,其 公司每年数值仿真成果的增加量都接近84%左右,采用CAE/CFD的速度超过了工 业的成长速度,CFD技术已经成为其设计的主要手段之一。另外从美国软件公司ANSYS公司的销售业绩报告上显示,航空工业上的应用产值是其公司的主要收益 来源之一。 CFD软件正以其强大的优势在研发中发挥的巨大的作用,例如在NISA的报告 中提到,原本需要7年完成的维吉尼亚级潜水艇的设计,通过CFD技术的应用, 5年就顺利完成;而预计需要11年完成的B-2轰炸机的飞行测试,则在短短的4 年内就通过了测试。 国内在CFD技术上的应用一般,特别是在航空发动方面的使用上,起步与国 外相比较晚,力度上也相差较多。 3、CFD技术的应用 目前在航空发动机的实际应用中是最广泛的一款CFD商业软件是ANSYS旗下 的商业软件FLUENT,其不仅容易使用,而且其准确性及行业的广泛性都是其它商业软件所不能比拟的。CFD软件的使用已经遍及了航空发动机的各个部分的研究,接下来本文通过对其它文献的分析逐一介绍CFD在航空发动机中的使用。 3.1 CFD技术在压缩机、涡轮方面的应用 气动稳定性的设计是当代航空发动机发展研制过程中的重要技术问题之一。 在航空发动机中,对气流最敏感的部件是风扇、压气机和涡轮。在以上3个部件中,CFD的主要应用集中在对压气机和涡轮效率分析上,多级压气机/涡轮最主要 的气动问题就是各级流动是否匹配,总的效率是否达到设计要求。在涡轮方面,CFD不仅可以计算涡轮效率,而且对涡轮叶片的冷却效果分析有着重要的应用。

医药工业洁净厂房的消防设计

仅供参考[整理] 安全管理文书 医药工业洁净厂房的消防设计 日期:__________________ 单位:__________________ 第1 页共6 页

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传热模拟CFD 总结

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