computational fluid dynamics (cfd) modelling of transfer chutes: a study of the influence of model...

7232019 Computational Fluid Dynamics (CFD) modelling of transfer chutes A study of the influence of model parameters

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Computational Fluid Dynamics (CFD) modelling of transfer

chutes A study of the in1047298uence of model parameters

Xiaoling Chen n Craig Wheeler

Centre for Bulk Solids and Particulate Technologies The University of Newcastle NSW 2308 Australia

H I G H L I G H T S

The Two Fluid Model can be used to simulate the large particlendashgas 1047298ow in transfer chutes

Experiments were conducted to verify simulation results Air velocities are very sensitive to the specularity coef 1047297cient values less than 01 In the zone close to the base of the chute particle velocities cannot be predicted by any of the combinations of parameters investigated Best modelling parameters were determined to describe this particular application

a r t i c l e i n f o

Article history

Received 22 January 2013

Received in revised form

8 March 2013

Accepted 17 March 2013Available online 27 March 2013

Keywords

Transfer chutes

Computational Fluid Dynamics (CFD)

Dust emission

Particle Image Velocimetry (PIV)

a b s t r a c t

Transfer chutes are essential components in almost all bulk material handling plants Belt conveyors

utilize transfer chutes to load and redirect bulk materials from one conveyor to another with their

reliability and performance being critical to the overall operation of the plant While reliability and

operational performance is typically measured by availability and throughput transfer chutes must also

operate with minimal environmental impact Consequently the design of transfer chutes in relation to

entrained air 1047298ow with the aim of minimizing fugitive dust emissions is an area of ongoing research and

investigation requiring the analysis of complex multiphase systems Computational Fluid Dynamics (CFD)

has been successfully applied to evaluate potential dust emissions from transfer chutes with theimplementation of appropriate models and modelling parameters shown to be critical to the overall

accuracy of the simulation results A notable shortcoming in the current research is the lack of systematic

guidelines available to appropriately select model parameters The aim of this paper is to offer guidance

in this regard and provide a better understanding of the in1047298uence of the maximum fractional packing

limit and evaluate the most appropriate model parameters for simulations including particlendashparticle

restitution coef 1047297cient values and solid slip conditions For this purpose the two-phase three-dimensional

EulerndashEuler model of commercial CFD software Fluent has been selected to model the granular and air

1047298ow in the transfer chute Air velocities were measured experimentally by Particle Image Velocimetry

(PIV) with the simulated velocity pro1047297les being in good overall agreement with the experimental data

amp 2013 Elsevier Ltd All rights reserved

1 Introduction

Belt conveying systems rely extensively on transfer chutes toload and redirect bulk material The performance of a transfer

chute has a signi1047297cant impact not only on the ef 1047297ciency of the belt

conveyor system but also on the level of fugitive dust emission

across the bulk material handling plant This paper presents the

application of Computational Fluid Dynamics (CFD) to analyse and

evaluate potential dust emissions from transfer chutes and focuses

on the selection of appropriate modelling parameters within the CFD

software

There are two approaches commonly used to model bulkgranular 1047298ows namely the Discrete Element Method (DEM) and

the Continuum Method DEM follows the principle of simulating

real particle motion involving collisions with walls and other

particles and linear motion between these collisions In contrast

the continuum method models the granular 1047298ow as a continuous

1047298ow stream rather than a large number of individual particles in

space The continuum method has the advantage of utilising

experimentally determined bulk material properties measured

by well-established test methods and standards Both methods

facilitate the analysis of the forces and moments acting on

different elements of the transfer chute however DEM has the

advantage of being able to visualize the bulk material 1047298ow and the

Contents lists available at SciVerse ScienceDirect

journal homepage wwwelseviercomlocateces

Chemical Engineering Science

0009-2509$- see front matter amp 2013 Elsevier Ltd All rights reserved

httpdxdoiorg101016jces201303032

n Corresponding author Tel+61 040339129

E-mail addresses cxling612126com XiaolingChenuoneduau (X Chen)

CraigWheelernewcastleeduau (C Wheeler)

Chemical Engineering Science 95 (2013) 194ndash202



capability of analysing considerably more complex 1047298ow patterns

but does so at the expense of considerably longer analysis times

When considering fugitive dust emissions from transfer chutes

neither the continuum nor DEM can be used to predict the air

1047298ow For this application CFD shows good potential for simulating

the multiphase 1047298ow and has proven accurate in predicting the air

velocity and location of 1047298ow recirculation zones due to the effect

of the bulk material stream (McILVENNA and MOSSAD 2003

Witt et al 1999 Donohue et al 2009) Previous studies (Chenet al 2012 Goniva et al 2012) undertaken by the authors indi-

cate that two-phase CFD simulations correlate well with scale

model experimental tests indicating that this approach can be

used to effectively predict likely dust emissions from transfer

chutes

The selection of appropriate models and modelling parameters is

found to be critical for the successful simulation of multiphase 1047298ow

Considerable research has been published on this topic but most

articles are focused on circulating 1047298uidized beds and spouted beds

with only 1047297ne or small particles Du et al (2006) investigated the

in1047298uence of the frictional stress maximum packing and coef 1047297cient of

restitution of particles for CFD simulations of spouted beds

Almuttahar and Taghipour (2008) conducted a study to evaluate

the effect of modelling parameters including different drag models

wall restitution coef 1047297cient values and solid slip conditions To the

authorsrsquo knowledge there are no known guidelines available for

the selection of models and model parameters (such as values of the

restitution and specularity coef 1047297cients) to simulate coarse granular

1047298ow in transfer chutes The aim of this paper is to investigate

the in1047298uence of the maximum fractional packing limit and evaluate

the most appropriate model parameters for simulations including

particlendashparticle restitution coef 1047297cient values and solid slip

conditions

It is well know that experimental studies are required to

evaluate any multiphase CFD model Particle Image Velocimetry

(PIV) which is used to obtain instantaneous measurements and

related properties in 1047298uids was used to determine the air velocity

pro1047297le at the outlet of a number of scale model transfer chutes PIV

is widely used to measure 1047298uid 1047298ow in both wind and water

tunnel experiments Furthermore PIV has also been successfully

used to measure granular 1047298ow named ldquogranular PIV rdquo (Du et al

2006 Almuttahar and Taghipour 2008 Ansart et al 2009 Ansart

et al 2011) Recently Ansart et al (2009 2011) used PIV to

investigate both the free falling particle plume and the in1047298uence of

the hopper outlet on the dust plume generated during free falling

Like other laser based measurement methods such as Laser-Doppler

Anemometry (LDA) and Particle Tracker Velocimetry (PTV) PIV is

minimally invasive and fast enough to measure velocities in turbu-

lent 1047298ow Furthermore unlike point measurement techniques PIV

provides velocity measurements across a whole plane in the 1047298uid at

any instant

The main objective of the current work is to develop a two-

phase three-dimensional CFD model to simulate the granular andentrained air 1047298ow in a transfer chute using the commercial CFD

simulation software FLUENT The solid particle behaviour near the

wall was investigated using different slip conditions the in1047298uence

of the particlendashparticle restitution coef 1047297cient studied and the

effect of frictional viscosity investigated by altering the maximum

packing limit Since the air velocity is considered to be one of the

main factors in1047298uencing dust generation the air 1047298ow patterns and

magnitudes of the velocities around the outlet of transfer chute

are used as one of the main criterion to evaluate the performance

of different model parameters PIV experiments were conducted to

visualize and measure the air 1047298ow at the outlet of scale model

transfer chutes The validity and accuracy of the CFD simulations

for different models and parameters were evaluated by qualitative

and quantitative comparison with experimental results obtained

from PIV Predicted particle velocities were also compared with

theoretical results calculated using a continuum approach

2 Experimental work

21 Experimental setup and procedure

Scale model experiments were undertaken to compare the

performance of a number of different transfer chute designs The

experimental procedure involved scale model testing of a number

of different transfer chute designs in an enclosure Bulk material

was fed through each chute and the velocity of the dust exiting the

transfer chute measured using PIV

The experimental procedure involved containing the transfer

chutes in a large enclosure to capture the fugitive dust to ensure

the repeatability of each experiment and eliminate any danger

caused by exposure to the class 4 laser and at the same time

minimize interference of external light The enclosure measured

25 m wide 25 m long and 30 m high and is shown pictorially in

Fig 1 The laser head of the PIV system was mounted at the end of

the enclosure facing the chute outlet A high speed camera wasmounted to the side using a sliding panel to facilitate adjustment

while concealing the light

While a range of different transfer chute designs were tested

during the course of the experimental test program Fig 2 shows

two of the scale model chutes tested These chutes are labelled A

and B and include A ndash baseline case B ndash a chute with an inbuilt

restrictor plate in the vertical leg in addition to the lower removable

cover 1047297tted and lower openings closed

The test procedure involved the use of a forklift and hydraulic

kibble (not show in the 1047297gure) to load the bulk material into the

top of the vertical section that feeds the transfer chute The 1047298ow

rate of bulk material from the kibble was controlled by a slide gate

at the discharge point and remained in a 1047297xed position for all

tests with the average mass 1047298ow rate calculated from the total

time of discharge Once the material passes through the chute it is

directed onto a conveyor belt located along the length of the

enclosure that transports the bulk material into a storage drum in

preparation for the following test

The bulk material used in all tests was screened Iron Ore with a

particle size distribution of 59 in the range of 40ndash475 mm 28

in the range of 475ndash60 mm 11 in the range of 6ndash11 mm with

the remaining 2 sub 4 mm

Fig 1 PIV Experimental setup

X Chen C Wheeler Chemical Engineering Science 95 (2013) 194ndash 202 195



22 Data acquisition

Particle velocity measurements of the entrained dust particles

exiting the chute were measured using a two-dimensional digital

PIV system The PIV system illuminates a particle-seeded 1047298ow 1047297eld

with two laser sheet pulses separated by a time delay and captures the

images with a charge-coupled device (CCD) camera The PIV system

used in this study is an Oxford Fire1047298y diode laser and a high

performance digital 12bit CCD camera with a resolution of 13921040 pixels The PIV system synchronizes the camera and laser to

obtain a pair of images separated by a small time delay (400 μs) Pairs

of images were obtained at a frequency of 10 Hz The camerarsquos 1047297eld of

view is set to capture a region about 180 250 mm To minimize the

random error at least three tests were run for each chute

PIV is an indirect measurement technique where the particle

velocity is determined instead of the 1047298uid velocity The selection

and concentration of the seeding particles used in PIV work is

critical to the success and quality of the measurements In this case

the iron ore dust itself served as ideal seeding particles Further-

more very often the seeding particles must be injected into the

1047298ow shortly before the gaseous medium enters the test section Inthe present work it was possible to adequately mix the dust and

the bulk material so the seeding particles 1047298owed through the

transfer chute with the bulk material ensuring a more accurate

velocity measurement of the entrained dust particles

Seeding particle size and concentration are responsible for the

particlersquos 1047298ow tracing quali1047297cations and optical characteristics

(Schmitt et al 1995) There are some compromises that need to

be considered when choosing the seeding particles The 1047297rst one is

the size of the seeding particle A smaller particle will more

faithfully follow the 1047298uid 1047298ow increasing measurement accuracy

while a larger particle will scatter more light increasing signal

strength and result in greater measurement precision It

is a compromise between a quick response of the tracer particles

in the 1047298uid requiring small diameters and a high signal-to-noise

ratio (SNR) of the particle images necessitating large diameters

The second compromise is the concentration of the seeding

particles More particles will provide a good correlation

signal and increase measurement accuracy while too many

particles will increase the background noise and absorb the light

resulting in measurement failure (Melling 1997 Meinhart et al

2000)

3 CFD simulation

There are two commonly used approaches to model gasndashsolid

1047298ow namely the discrete phase model (DPM) and the two-1047298uid

model (TFM) These approaches are represented as the Eulerndash

Lagrangian model and EulerndashEuler model respectively in FLUENT

The former model is suitable for dilute gasndashsolid 1047298ow and the

later for dense phase simulations being much more applicable to

complex multiphase 1047298ows For the TFM approach the different

phases are mathematically treated as interpenetrating continua

and the conservation equations have similar structure for each

phase The air is assumed to be incompressible and at a constant

density while the particles are assumed to be spherical and have a

uniform density Due to the complexity of the particle volume

fraction in the transfer chute problem a TFM approach was

adopted

31 Model equation

We propose in the current work to solve the governing equa-

tions of mass and momentum by means of a multiphase Eulerian

model incorporating the Kinetic Theory of Granular Flow (KTGF)

available in the software Fluent The energy conservation equation

was ignored as the 1047298ow is isothermal A brief summary of the model

equations are list below

Fig 2 Scale Model Transfer Chutes (a) Chute A (b) Chute B

X Chen C Wheeler Chemical Engineering Science 95 (2013) 194ndash 202196



311 Mass conservation equations

The conservation of mass for the gas and solid phase can be

written as

part

partt ethε g ρ g THORN thornnablasdotethε g ρ g v

g THORN frac14 0 eth1THORN

part

partt ethεs ρsTHORN thornnablasdotethεs ρs v

sTHORN frac14 0 eth2THORN

where ε ρ and v are the volume fraction the density and theinstantaneous velocity respectively The volume fraction con-

straint requires ε g thorn εs frac14 1

312 Momentum conservation equations

Assuming no mass transfer between phases and no lift and

virtual mass forces due to the large difference in their densities

only the drag force and gravity are considered in this study thus

the conservation of momentum for each phase can be expressed

as

part

partt ε g ρ g v

g

thorn nablasdot ε g ρ g v

g v

g

frac14nablasdotτ g minusε g nablaP thorn ε g ρ g g thorn K sg v

sminus v

g

eth3THORN

part

partt εs ρs v

s

thorn nablasdot εs ρs v

s v

s

frac14nablasdotτ sminusnablaP sminus εsnablaP thorn εs ρs g thorn K sg v

sminus v

g

eth4THORN

where τ is the stress tensor P is the pressure g is gravity and K sg is

the momentum exchange coef 1047297cient that represents the drag force

between the gas and the solid phase Details of these parameters

are explained below

The stress tensor for each phase is given by

τ g frac14 ε g μ g nabla v

g thorn nabla v

g

T

thorn ε g λ g minus2

3 μ g

nablasdot v

g I eth5THORN

τ s frac14 εs μs nabla vs thorn nabla vs T thorn εs λsminus

2

3 μs

nablasdot vsI eth6THORN

where λs and λ g are solid and gas viscosity respectively The

granular bulk viscosity λs represents the resistance of granular

particles to compression or expansion and is modelled by Lun

et al 1984 as

λs frac14 4

5εs ρsdseth1 thorn eTHORN

ffiffiffiffiffiffiΘs

π

r eth7THORN

where ds is the particle diameter e is the particlendashparticle restitu-

tion coef 1047297cient and Θs is the granular temperature

The granular pressure P s is derived from the kinetic theory of

granular 1047298ow and is composed of a kinetic term and a term due to

particle collisions In the current work the model proposed by Lun

et al 1984 is used and is given byP s frac14 εs ρsΘs thorn 2 ρseth1 thorn eTHORNε2

s g0sΘs eth8THORNwhere g 0s is the radial distribution function that modi1047297es the

probability of collisions between particles and is given by Lun et al

(1984) and expressed as

g 0s frac14 1minusεs

εsmax

13

minus1

eth9THORN

The in1047298uence of the drag model is not covered in this study

with the Gidaspow et al (1992) model selected for all work The

Gidaspow et al (1992) model is given by

K sg frac14 150ε2

g μ g

ε g d

2

s

thorn 175ε g ρ g j v

sminus v

g jd

s

ε g o08 eth10THORN

K sg frac14 3

4C D

ε g εsjvsminusv g jds

εminus265 g ε g ge08 eth11THORN

where C D

C D frac14 24

Res1 thorn 015ethResTHORN0687h i

Reso1000 eth12THORN

C D frac14 044 Res41000 eth13THORN

The Reynolds number of the particles is given by

Res frac14 ρ g j v

g minus v

sjds

μ g

eth14THORN

313 Granular shear viscosity

The solids stress tensor contains shear and bulk viscosities

arising from particle momentum exchange due to translation and

collision In other words the solids shear viscosity consists of a

collision term a kinetic term and a friction term and is given by

μs frac14 μscol thorn μskin thorn μsfric eth15THORNThe collision viscosity is taken from the kinetic theory of

granular 1047298ow by Gidaspow et al (1992)

μscol frac14 45ε2

s ρsds g 0seth1 thorn esTHORN ffiffiffiffiffiffiΘs

π

r eth16THORN

The kinetic viscosity is expressed by Gidaspow et al (1992) as

μskin frac14 10 ρsds

ffiffiffiffiffiffiffiffiπ Θs

p

96eth1 thorn esTHORN g 0s

1 thorn 4

5εs g 0seth1 thorn esTHORN

2

eth17THORN

The friction viscosity is expressed by Schaeffer (1987) as

μsfric frac14 P s sin ϕ

2 ffiffiffiffiffiffiffi

I 2D

p eth18THORN

where the constant ϕfrac14 300007 is the default angle of internal

friction value and I 2D is the second invariant of the deviatoric

stress tensor which can be written as

I 2D frac14 16 ethDs11minusDs22THORN2 thorn ethDs22minusDs33THORN2 thorn ethDs33minusDs11THORN2h i

thornD2s12 thorn D2

s23 thorn D2s31 eth19THORN

Dsij frac14 1

2

partusi

part x j

thorn partus j

part xi

eth20THORN

32 Boundary conditions and numerical procedure

At the inlet all velocities and volume fractions of both phases

were speci1047297ed The inlet velocity pro1047297le is assumed to be uniform

and the volume fraction constant The average solids velocity at

the inlet is calculated from the shape of the kibble and it is

assumed that the inlet air has the same velocity as the solid phase

At the outlet the pressure is assumed to be atmospheric while theremaining opening areas are de1047297ned as pressure inlets The

specularity coef 1047297cient is speci1047297cally used in the multiphase

analysis with granular 1047298ow to express the slip coef 1047297cient At the

wall the gas phase was set to the no-slip condition meaning the

air velocity is zero at the surface of the wall while different slip

conditions between the solid and the wall were conducted to

assess the effect of slip at the wall

In the present investigation the interaction of gas and solid

phases was represented by the well-known Gidaspow drag model

The Gidaspow model has been successfully applied in similar

applications such as spouted bed simulations (Lan et al 2012)

While the turbulence model selected for this study was the

standard kminusε model Unsteady simulations were performed with

a small initial time step of 1 10minus4

s while 20 iterations per time




step were used to ensure numerical stability A convergence

criterion of 110minus3 was speci1047297ed for the relative error between

two successive iterations The typical computational time for each

simulation was 5ndash10 days on a 267 GHz workstation

33 Grid independency

To con1047297rm that the CFD results are independent of the mesh

size simulations of Chute A with four different meshes were

performed A coarse mesh was created using a maximum face

size of 15 mm an intermediate mesh using a maximum face size of

12 mm a 1047297ne mesh using a maximum face size of 10 mm and a

1047297ner mesh using a maximum face size of 8 mm The air velocity is

an important characteristic parameter that can be used to deter-

mine how well numerical models capture the behaviour of the

transfer chute As shown in Fig 3 the 1047297ne and 1047297ner mesh cases

predicted similar outlet air velocities however considering the

minor variation in results and computational time a 1047297ne mesh

with a maximum face size of 10 mm was used in subsequent

simulations

4 Results and discussion

To provide guidance on the selection of values for the particlendash

particle restitution coef 1047297cient and the specularity coef 1047297cient when

simulating granular 1047298ow in transfer chutes an investigation into

the most appropriate model parameters was performed Chute Awas used to perform the parametric studies while Chute B was

used to verify the applicability of the chosen model parameters

41 In 1047298uence of the particle-wall slip condition

The specularity coef 1047297cient is a measure of the fraction of

collisions which transfer momentum to the wall and varies from

zero (smooth walls) to one (rough walls) The effect of the slip

condition between the solid phase and wall was investigated by

altering the specularity coef 1047297cient for the solid phase The free-slip

condition for the solid phase at the wall is usually obtained by

setting the shear condition to zero In total eight different

specularity coef 1047297cients were analysed to study the effect of the

particlendash

wall slip condition using a default particlendash

particle

restitution coef 1047297cient value of 09 The air velocities along the

centreline of the chute outlet for both the simulation and experi-

mental results are shown in Fig 4 with the specularity coef 1047297cient

and particlendashparticle restitution coef 1047297cient referenced as R and S

respectively There are no PIV measurements for the lower section

of the chute since the chute is 1047297tted with metal gussets in the

corners

Comparison between simulation results and experimental data

at the outlet of the scale model transfer chute showed signi1047297cant

variance with different specularity coef 1047297cients Differences mainly

occurred for specularity coef 1047297cients less than 01 with values less

than 001showing signi1047297cant differences both in the magnitude

and distribution from that of the experimentally measured values

From further inspection of Fig 4 the specularity coef 1047297cient values

less than 01 show the maximum air velocity position occurring

further away from the wall and increasing with an increase in the

value of the specularity coef 1047297cient Qualitatively speaking the

overall trends of the predicted air velocity pro1047297les are quite similar

for the data obtained from the specularity coef 1047297cients larger than

005 in spite of some quantitative differences In reference to the

experimental data it is clear the simulation results are lower

overall potentially resulting from a different particle 1047298ow depth

between the simulations and experiment

The specularity coef 1047297cient indirectly affects the air velocity by

affecting the particle behaviour The simulated particle velocity

pro1047297les and particle volume fractions at the outlet for the range of

specularity coef 1047297cients are illustrated in Fig 5(a) and (b) respec-

tively Due to dif 1047297culties in measuring the outlet particle velocitythis velocity was calculated using the classic continuum method of

Roberts (2003) An equivalent friction coef 1047297cient of 08 was used

based on the average measured value of the particle wall friction for

iron ore on PVC and steel Based on the continuum method

calculation a schematic drawing of particle velocity distribution is

given in Fig 5(a) for comparison to the other simulation results It is

noted that the continuum method calculation gives a single velocity

for the entire bulk material stream rather than a pro1047297le throughout

the stream thickness

As shown in Fig 5(a) the simulated particle velocity pro1047297les

indicate the particle velocities are gradually decreasing with an

increase in the specularity coef 1047297cient For specularity coef 1047297cient

values of 02 and 03 the results show similar velocity pro1047297le

predictions The simulated particle velocities sharply decrease to

00 10 20 30 40 50 60

000

002

004

006

008

010

012

H e i g h t o f O u

t l e t ( m )

Air Velocity (ms)

Coase Intermediate Fine Finer

Fig 3 Outlet air velocity pro1047297le of different mesh for Chute A

00 10 20 30 40 50 60000

002

004

006

008

010

012

H e i g h t o f O u

t l e t ( m )

Air Velocity (ms)

R=09Free slip R=09S=0005 R=09S=001 R=09S=003 R=09S=005 R=09S=01 R=09S=02 R=09S=03

Experiments

Fig 4 Outlet air velocities for different specularity coef 1047297cient values




zero from a height of 8 mm from the wall indicating the particle

velocities near the wall cannot be predicted by the simulation The

distance of 8 mm is about twice the particle diameter used in this

simulation From further inspection of Fig 5(a) results illustrate

that when the specularity coef 1047297cient values are smaller than 01

the simulated particle velocities greater than 40 mm above the

bottom surface of the chute have the same distribution This can

be explained by the simulated particle volume fractions shown in

Fig 5(b) indicating the volume fraction of particles greater than

40 mm above the bottom surface of the chute approach 0

Quantitatively the simulated velocities obtained from the larger

specularity coef 1047297cient values of 02 and 03 show better agreement

with the theoretical result in terms of the maximum velocity

42 In 1047298uence of the particlendash particle restitution coef 1047297cient

The particlendashparticle restitution coef 1047297cient describes the

amount of the energy dissipation due to collisions between solid

particles It in1047298uences the momentum conservation and granular

temperature conservation of the particle phase In transfer chute

analysis the concentration of the particles can vary considerably

throughout the transfer chute with inter-particle collisions being

subject to signi1047297cantly different energy losses Coef 1047297cient values of

090 075 060 045 and 030 were chosen to examine the

in1047298uence of particlendashparticle restitution in the CFD simulations

Furthermore it is noted that the free slip condition cannot

describe the real situation from the particlendashwall slip condition

study thus the particlendashparticle restitution coef 1047297cient study was

carried out using a specularity coef 1047297cient equal to 01

The results shown in Fig 6(a) illustrate the air velocities are notvery sensitive to variation in the particlendashparticle restitution

coef 1047297cient Air velocities greater than 70 mm above the bottom

surface of the chute are found to be quite similar for different

particlendashparticle restitution coef 1047297cients For the same specularity

coef 1047297cient values the overall trends of the air velocities are almost

the same for different particlendashparticle restitution coef 1047297cient

values with the only difference being the magnitude This 1047297nding

indicates that the velocity pro1047297le trend is more dependent on the

specularity coef 1047297cient rather than the particlendashparticle restitution

coef 1047297cient The smaller the particlendashparticle restitution coef 1047297cient

the lower the air velocity and particle velocity The percentage

decrease in velocity was not found to be proportional to the

decrease of the particlendashparticle restitution coef 1047297cient value with

the effect of particlendash

particle restitution coef 1047297cient on the velocity

000

002

004

006

008

010

012

H e i g h t o f O u t l e t ( m )

Particle Velocity (ms)

00 10 20 30 40 50 00 01 02 03 04

000

002

004

006

008

010

012


Particle Volume fraction

Fig 5 Outlet particle velocity (a) and particle volume fraction (b) for different specularity coef 1047297cient value


Air Velocity (ms)

R=09S=01 R=075S=01 R=06S=01 R=045S=01 R=03S=01 Experiments

00 10 20 30 40

00 05 10 15 20 25

000

002

004

006

008

010

012

000

002

004

006

008

010

012



R=09S=01 R=075S=01 R=06S=01 R=045S=01 R=03S=01 Calculated

Fig 6 Outlet air velocities (a) and particle velocity (b) for different particlendash

particle restitution coef 1047297cient values




becoming weaker with decreasing values Quantitatively the

simulated velocities obtained from the particlendashparticle restitution

coef 1047297cient value of 03 show the best agreement with the experi-

mental result in terms of the predicted air velocity pro1047297le while

the results obtained from the particlendashparticle restitution coef 1047297-

cient value of 06 show the best agreement with the theoretical

result in terms of the maximum particle velocity

43 In 1047298uence of fractional packing limit

In view of the potential high volume fraction for the solid phase

around the hood section the Schaeffer model was selected to take

into account the friction between particles The frictional stress

will be added to the stress predicted by the kinetic theory when

the solids volume fraction exceeds a critical value known as the

Fractional Packing Limit (FPL) The FPL represents a threshold

volume fraction at which the frictional regime becomes dominantIn order to investigate the effect of the FPL three fractional packing

limit values were investigated in this study including 061(default

value in FLUENT) 050and 040The specularity coef 1047297cient and

particlendashparticle restitution coef 1047297cient were set to 01 and

09 respectively The outlet air and particle velocities obtained from

the three different FPLs are shown in Fig 7(a) and (b) respectively

Fig 7(a) illustrates that a smaller FPL value generally leads to

lower air velocities while Fig 7(b) generally follows the same

trend with some discrepancy at higher particle velocities In terms

of the air velocity pro1047297le the results obtained from the FPL value

of 061 show better agreement with the experimental data While

the particle velocities which are obtained from the FPL values

equal to 04 are closer to the theoretical results given the purpose

of this study the accuracy of air velocity prediction is moreimportant and thus an FPL equal 061 will be used in subsequent

simulations

44 Combination of parameters

In order to 1047297nd the appropriate modelling parameters to

successfully simulate the Iron Ore and induced air 1047298ow in the

scale model transfer chutes different combinations of particlendash

particle restitution coef 1047297cient and specularity coef 1047297cient were

analysed Four different specularity coef 1047297cient values and 1047297ve

different particlendashparticle restitution coef 1047297cient values were com-

pared In total seven different combinations of specularity coef 1047297-

cient and restitution coef 1047297cient were investigated with the

selected parameters listed in Table 1

The air and particle velocity pro1047297les for different combinations

as well as the experimental air velocity pro1047297le and theoretically

calculated particle velocity pro1047297le are shown in Fig 8(a) and (b)

respectively

Fig 8 shows that up to a height of 50 mm greater particle ndash

particle restitution coef 1047297cients result in higher air and particle

velocities while higher specularity coef 1047297cients result in lower air

and particle velocities As noted previously specularity coef 1047297cients

greater than 01 show better correlation with the predicted air

velocities regardless of the particlendashparticle restitution coef 1047297cient

values

From the point of view of air velocity best overall agreement

between the model predictions and experimental data is obtained

using 045 as a particlendashparticle restitution coef 1047297cient and 02 as a

specularity coef 1047297cient This combination results in a maximum

variance between the measured and simulation values of 19 with

an average variance of 11 Although this combination gives the

closest results to the experimental data it is obvious that the

difference between the predicted particle velocities and theore-

tical result is large This combination resulted in a variance of 25

in terms of the maximum predicted particle velocity

From the point of view of particle velocity best overall agree-

ment between the model predictions and theory was obtained

using 06 as a particlendashparticle restitution coef 1047297cient and 01 as aspecularity coef 1047297cient with a variance of 6 in terms of the

maximum predicted particle velocity This combination resulted

in an average variance of 21between the measured air velocities

and the simulation results with a maximum variance of 51 Good

agreement with the measured and theoretical particle velocity is

also observed from the results obtained from the specularity

coef 1047297cient value equal to 02 and the particlendashparticle restitution

coef 1047297cient value of 075This combination resulted in an average

variance of 19 between the measured air velocities and simula-

tion results with a maximum variance of 41

Considering air and particle velocity prediction the seventh

combination using 045 as a particlendashparticle restitution coef 1047297-

cient and 02 as a specularity coef 1047297cient is considered the best

overall compromise

000

002

004

006

008

010

012

H e i g h t

o f O u t l e t ( m )

Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25

000

002

004

006

008

010

012

H e i g h t



Fig 7 Outlet air velocities (a) and particle velocity (b) for different fractional packing limit values

Table 1

Different combinations of specularity coef 1047297cient and restitution coef 1047297cient

Combinations 1 2 3 4 5 6 7

Restitution coef 1047297cient 045 090 030 060 075 060 045Specularity coef 1047297cient 003 005 005 010 0 20 020 020




45 Application of selected model parameters

To further evaluate the chosen modelling parameters Chute B

was investigated Due to the introduction of the restrictor plate

Chute B involved more particlendashwall and particlendashparticle inter-

actions than Chute A Based on the previous discussion the

combinations of modelling parameters labelled as 5 and 7 in

Table 1 were investigated

Fig 9 shows the simulated air velocity and particle velocity

distributions at the outlet of transfer Chute B using different

combinations of modelling parameters As expected the para-

meters have a similar performance on Chute B as Chute A In both

000

002

004

006

008

010

012


Air Velocity (ms)

00 10 20 30 40 00 05 10 15 20 25 30000

002

004

006

008

010

012



Fig 8 Outlet air velocities (a) and particle velocities (b) for different modelling parameters

000

002

004

006

008

010

012

H e i g

h t o f O u t l e t ( m )

Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25 30000

002

004

006

008

010

012

H e i g



Fig 9 Outlet air velocities (a) and particle velocities (b) for different modelling parameters applied to Chute B

Fig 10 Air vectors for Chute B (a) from PIV experiments (b) from CFD analysis




cases the particle velocities are underestimated with the primary

difference being that the air velocities are slightly underestimated

in Chute A while for Chute B the air velocities are slightly over

estimated Overall the trends of the air velocities agree well with

the experimental results This is best illustrated in Fig 10 where

the measured air vectors from the PIV experiments and the air

vectors predicted from the CFD analysis for Chute B are compared

directly

Fig 10 illustrates that the predicted 1047298ow patterns agree wellwith the measured results Note there is no experimental data

available beneath the black line in Fig 10 (a) due to the steel

gussets in the corner of the chute The turbulence is captured quite

well in the PIV results and can be clearly seen in the CFD results

The experimental results are not as smooth as the simulation

results but this is most likely due to the uneven distribution of

seeding particles Quantitatively the CFD analysis generally over-

estimates the air velocities when compared to the velocities

measured by the PIV system but given the nature of the experi-

mental work satisfactory conclusions can still be drawn

5 Conclusion

A two-1047298uid model (TFM) approach using the commercial CFDsoftware FLUENT has been used to simulate the granular and

entrained air 1047298ow in a transfer chute The solid particle behaviour

near the wall was investigated using different slip conditions the

in1047298uence of the particlendashparticle restitution coef 1047297cient studied

and the effect of frictional viscosity investigated by altering the

maximum packing limit Several cases with different specularity

coef 1047297cients (S frac140 0005 003 005 01 and 02) particlendashparticle

restitution coef 1047297cients (Rfrac1409 075 06 045 and 03) and max-

imum fraction packing limit (FPL frac14061 05 04) were simulated to

evaluate their impact on the 1047298ow behaviour Corresponding

experimental studies were conducted to evaluate the multiphase

CFD model The air and particle velocities at the transfer chute

outlet were compared and discussed with the following conclu-

sions drawn from the study

(1) Generally smaller specularity coef 1047297cient values result in

larger velocities however the change of air and particle

velocities is not proportional to the value of the specularity

coef 1047297cient Air velocities are very sensitive to the specularity

coef 1047297cient values less than 01

(2) Varying the coef 1047297cient of particle restitution did not affect air

velocity predictions for the top section of outlet where the air

volume fraction is 1 In the bottom section of chute outlet

higher particlendashparticle restitution values result in higher air

and particle velocities

(3) Decreasing the maximum fraction packing limit decreases the

air and particle velocities

(4) In the zone close to the base of the chute particle velocities

cannot be predicted by any of the combinations of parameters

investigated

(5) For the range of parameters investigated the combination

labelled 7 (Rfrac14045 S frac1402) proved to be the best overall

combination of parameters for this particular application

with good overall agreement between the calculated and

measured air velocities

References

Almuttahar A Taghipour F 2008 Computational 1047298uid dynamics of high densitycirculating 1047298uidized bed riser study of modeling parameters Powder Technol185 (1) 11ndash23

Ansart R Ryck Ad Dodds JA 2009 Dust emission in powder handling freefalling particle plume characterisation Chem Eng J 152 (2ndash3) 415ndash420

Ansart R Letourneau J-J de Ryck A Dodds JA 2011 Dust emission by powderhandling in1047298uence of the hopper outlet on the dust plume Powder Technol212 (3) 418ndash424

Chen XL Wheeler CA Donohue TJ McLean R Roberts AW 2012 Evaluationof dust emissions from conveyor transfer chutes using experimental and CFDsimulation Int J Miner Process 110ndash111 (0) 101ndash108

Donohue TJ Roberts AW Wheeler CA McBride W 2009 Analysis of transfer

chute performance focusing on reduced dust emissions In Eighth WorldCongress of Chemical Engineering 2009 Montreal Quebec

Du W Bao X Xu J Wei W 2006 Computational 1047298uid dynamics (CFD) modelingof spouted bed in1047298uence of frictional stress maximum packing limit andcoef 1047297cient of restitution of particles Chem Eng Sci 61 (14) 4558 ndash4570

Gidaspow D Bezburuah RDing J 1992 Hydrodynamics of circulating 1047298uidizedbeds Kinetic theory approach In Conference Seventh International Confer-ence on Fluidization Gold Coast Australia 75ndash82

Goniva C Kloss C Chen X Donohue TJ Katterfeld A 2012 Prediction of DustEmissions in Transfer Chutes by Multiphase CFD and Coupled DEM-CFDSimulations In BulkSolids Europe 2012 Berlin Germany

Lan X Xu C Gao J Al-Dahhan M 2012 In1047298uence of solid-phase wall boundarycondition on CFD simulation of spouted beds Chem Eng Sc 69 (1) 419ndash430

Lun CKK Savage SB Jeffrey DJ Chepurniy N 1984 Kinetic theories forgranular 1047298ow inelastic particles in Couette 1047298ow and slightly inelastic particlesin a general 1047298ow1047297eld J Fluid Mech 140 223ndash256

McIlvenna P Mossad DR 2003 Two dimensional transfer chute analysis using acontinuum method In Third International Conference on Computational FluidDynamics in the Minerals and Process Industries (CFD2003) MelbourneAustralia 547ndash551

Meinhart CD T WS Gray MHB 2000 Volume illumination for two-dimensional particle image velocimetry Meas Sci Technol 11 809ndash814

Melling A 1997 Tracer particles and seeding for particle image velocimetry MeasSci Technol 8 (12) 1406

Roberts AW 2003 Transfer chute performance and design for rapid 1047298owcondition Chem Eng Technol 26 (2) 163ndash170

Schaeffer DG 1987 Instability in the evolution equations describing incompres-sible granular 1047298ow J Differential Equations 66 (1) 19ndash50

Schmitt T Koster JN Hamacher H 1995 Particle design for displacementtracking velocimetry Meas Sci Technol 6 (6) 682ndash689

Witt PJ Carey KGNguyen TV 1999 Prediction of dust loss from conveyor usingCFD modelling In Second International Conference on CFD in the Minerals andProcess Industries CSIRO Melbourne Australia 281ndash286




capability of analysing considerably more complex 1047298ow patterns

but does so at the expense of considerably longer analysis times

When considering fugitive dust emissions from transfer chutes

neither the continuum nor DEM can be used to predict the air

1047298ow For this application CFD shows good potential for simulating

the multiphase 1047298ow and has proven accurate in predicting the air

velocity and location of 1047298ow recirculation zones due to the effect

of the bulk material stream (McILVENNA and MOSSAD 2003

Witt et al 1999 Donohue et al 2009) Previous studies (Chenet al 2012 Goniva et al 2012) undertaken by the authors indi-

cate that two-phase CFD simulations correlate well with scale

model experimental tests indicating that this approach can be

used to effectively predict likely dust emissions from transfer

chutes

The selection of appropriate models and modelling parameters is

found to be critical for the successful simulation of multiphase 1047298ow

Considerable research has been published on this topic but most

articles are focused on circulating 1047298uidized beds and spouted beds

with only 1047297ne or small particles Du et al (2006) investigated the

in1047298uence of the frictional stress maximum packing and coef 1047297cient of

restitution of particles for CFD simulations of spouted beds

Almuttahar and Taghipour (2008) conducted a study to evaluate

the effect of modelling parameters including different drag models

wall restitution coef 1047297cient values and solid slip conditions To the

authorsrsquo knowledge there are no known guidelines available for

the selection of models and model parameters (such as values of the

restitution and specularity coef 1047297cients) to simulate coarse granular

1047298ow in transfer chutes The aim of this paper is to investigate

the in1047298uence of the maximum fractional packing limit and evaluate

the most appropriate model parameters for simulations including

particlendashparticle restitution coef 1047297cient values and solid slip

conditions

It is well know that experimental studies are required to

evaluate any multiphase CFD model Particle Image Velocimetry

(PIV) which is used to obtain instantaneous measurements and

related properties in 1047298uids was used to determine the air velocity

pro1047297le at the outlet of a number of scale model transfer chutes PIV

is widely used to measure 1047298uid 1047298ow in both wind and water

tunnel experiments Furthermore PIV has also been successfully

used to measure granular 1047298ow named ldquogranular PIV rdquo (Du et al

2006 Almuttahar and Taghipour 2008 Ansart et al 2009 Ansart

et al 2011) Recently Ansart et al (2009 2011) used PIV to

investigate both the free falling particle plume and the in1047298uence of

the hopper outlet on the dust plume generated during free falling

Like other laser based measurement methods such as Laser-Doppler

Anemometry (LDA) and Particle Tracker Velocimetry (PTV) PIV is

minimally invasive and fast enough to measure velocities in turbu-

lent 1047298ow Furthermore unlike point measurement techniques PIV

provides velocity measurements across a whole plane in the 1047298uid at

any instant

The main objective of the current work is to develop a two-

phase three-dimensional CFD model to simulate the granular andentrained air 1047298ow in a transfer chute using the commercial CFD

simulation software FLUENT The solid particle behaviour near the

wall was investigated using different slip conditions the in1047298uence

of the particlendashparticle restitution coef 1047297cient studied and the

effect of frictional viscosity investigated by altering the maximum

packing limit Since the air velocity is considered to be one of the

main factors in1047298uencing dust generation the air 1047298ow patterns and

magnitudes of the velocities around the outlet of transfer chute

are used as one of the main criterion to evaluate the performance

of different model parameters PIV experiments were conducted to

visualize and measure the air 1047298ow at the outlet of scale model

transfer chutes The validity and accuracy of the CFD simulations

for different models and parameters were evaluated by qualitative

and quantitative comparison with experimental results obtained

from PIV Predicted particle velocities were also compared with

theoretical results calculated using a continuum approach

2 Experimental work

21 Experimental setup and procedure

Scale model experiments were undertaken to compare the

performance of a number of different transfer chute designs The

experimental procedure involved scale model testing of a number

of different transfer chute designs in an enclosure Bulk material

was fed through each chute and the velocity of the dust exiting the

transfer chute measured using PIV

The experimental procedure involved containing the transfer

chutes in a large enclosure to capture the fugitive dust to ensure

the repeatability of each experiment and eliminate any danger

caused by exposure to the class 4 laser and at the same time

minimize interference of external light The enclosure measured

25 m wide 25 m long and 30 m high and is shown pictorially in

Fig 1 The laser head of the PIV system was mounted at the end of

the enclosure facing the chute outlet A high speed camera wasmounted to the side using a sliding panel to facilitate adjustment

while concealing the light

While a range of different transfer chute designs were tested

during the course of the experimental test program Fig 2 shows

two of the scale model chutes tested These chutes are labelled A

and B and include A ndash baseline case B ndash a chute with an inbuilt

restrictor plate in the vertical leg in addition to the lower removable

cover 1047297tted and lower openings closed

The test procedure involved the use of a forklift and hydraulic

kibble (not show in the 1047297gure) to load the bulk material into the

top of the vertical section that feeds the transfer chute The 1047298ow

rate of bulk material from the kibble was controlled by a slide gate

at the discharge point and remained in a 1047297xed position for all

tests with the average mass 1047298ow rate calculated from the total

time of discharge Once the material passes through the chute it is

directed onto a conveyor belt located along the length of the

enclosure that transports the bulk material into a storage drum in

preparation for the following test

The bulk material used in all tests was screened Iron Ore with a

particle size distribution of 59 in the range of 40ndash475 mm 28

in the range of 475ndash60 mm 11 in the range of 6ndash11 mm with

the remaining 2 sub 4 mm

Fig 1 PIV Experimental setup




22 Data acquisition






































2000)

3 CFD simulation














adopted

31 Model equation













written as

part



part










as

part

partt ε g ρ g v

g


g v

g


sminus v

g

eth3THORN

part

partt εs ρs v

s


s v

s


sminus v

g

eth4THORN




are explained below



g thorn nabla v

g

T


3 μ g

nablasdot v

g I eth5THORN


2

3 μs





et al 1984 as

λs frac14 4



π

r eth7THORN











εsmax

13

minus1

eth9THORN




K sg frac14 150ε2

g μ g

ε g d

2

s


sminus v

g jd

s

ε g o08 eth10THORN

K sg frac14 3

4C D



where C D

C D frac14 24


Reso1000 eth12THORN



Res frac14 ρ g j v

g minus v

sjds

μ g

eth14THORN








μscol frac14 45ε2


π

r eth16THORN




p


1 thorn 4


2

eth17THORN




I 2D

p eth18THORN





thornD2s12 thorn D2


Dsij frac14 1

2

partusi

part x j

thorn partus j

part xi

eth20THORN










































simulations
















particlendash


particle







corners



































00 10 20 30 40 50 60

000

002

004

006

008

010

012

H e i g h t o f O u

t l e t ( m )

Air Velocity (ms)



00 10 20 30 40 50 60000

002

004

006

008

010

012

H e i g h t o f O u

t l e t ( m )

Air Velocity (ms)


Experiments















































000

002

004

006

008

010

012



00 10 20 30 40 50 00 01 02 03 04

000

002

004

006

008

010

012





Air Velocity (ms)


00 10 20 30 40

00 05 10 15 20 25

000

002

004

006

008

010

012

000

002

004

006

008

010

012





































simulations














respectively







values


























overall compromise

000

002

004

006

008

010

012

H e i g h t


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25

000

002

004

006

008

010

012

H e i g h t




Table 1


















000

002

004

006

008

010

012


Air Velocity (ms)

00 10 20 30 40 00 05 10 15 20 25 30000

002

004

006

008

010

012




000

002

004

006

008

010

012

H e i g


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25 30000

002

004

006

008

010

012

H e i g















directly











5 Conclusion





























investigated






References






















22 Data acquisition






































2000)

3 CFD simulation














adopted

31 Model equation













written as

part



part










as

part

partt ε g ρ g v

g


g v

g


sminus v

g

eth3THORN

part

partt εs ρs v

s


s v

s


sminus v

g

eth4THORN




are explained below



g thorn nabla v

g

T


3 μ g

nablasdot v

g I eth5THORN


2

3 μs





et al 1984 as

λs frac14 4



π

r eth7THORN











εsmax

13

minus1

eth9THORN




K sg frac14 150ε2

g μ g

ε g d

2

s


sminus v

g jd

s

ε g o08 eth10THORN

K sg frac14 3

4C D



where C D

C D frac14 24


Reso1000 eth12THORN



Res frac14 ρ g j v

g minus v

sjds

μ g

eth14THORN








μscol frac14 45ε2


π

r eth16THORN




p


1 thorn 4


2

eth17THORN




I 2D

p eth18THORN





thornD2s12 thorn D2


Dsij frac14 1

2

partusi

part x j

thorn partus j

part xi

eth20THORN










































simulations
















particlendash


particle







corners



































00 10 20 30 40 50 60

000

002

004

006

008

010

012

H e i g h t o f O u

t l e t ( m )

Air Velocity (ms)



00 10 20 30 40 50 60000

002

004

006

008

010

012

H e i g h t o f O u

t l e t ( m )

Air Velocity (ms)


Experiments















































000

002

004

006

008

010

012



00 10 20 30 40 50 00 01 02 03 04

000

002

004

006

008

010

012





Air Velocity (ms)


00 10 20 30 40

00 05 10 15 20 25

000

002

004

006

008

010

012

000

002

004

006

008

010

012





































simulations














respectively







values


























overall compromise

000

002

004

006

008

010

012

H e i g h t


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25

000

002

004

006

008

010

012

H e i g h t




Table 1


















000

002

004

006

008

010

012


Air Velocity (ms)

00 10 20 30 40 00 05 10 15 20 25 30000

002

004

006

008

010

012




000

002

004

006

008

010

012

H e i g


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25 30000

002

004

006

008

010

012

H e i g















directly











5 Conclusion





























investigated






References
























written as

part



part










as

part

partt ε g ρ g v

g


g v

g


sminus v

g

eth3THORN

part

partt εs ρs v

s


s v

s


sminus v

g

eth4THORN




are explained below



g thorn nabla v

g

T


3 μ g

nablasdot v

g I eth5THORN


2

3 μs





et al 1984 as

λs frac14 4



π

r eth7THORN











εsmax

13

minus1

eth9THORN




K sg frac14 150ε2

g μ g

ε g d

2

s


sminus v

g jd

s

ε g o08 eth10THORN

K sg frac14 3

4C D



where C D

C D frac14 24


Reso1000 eth12THORN



Res frac14 ρ g j v

g minus v

sjds

μ g

eth14THORN








μscol frac14 45ε2


π

r eth16THORN




p


1 thorn 4


2

eth17THORN




I 2D

p eth18THORN





thornD2s12 thorn D2


Dsij frac14 1

2

partusi

part x j

thorn partus j

part xi

eth20THORN










































simulations
















particlendash


particle







corners



































00 10 20 30 40 50 60

000

002

004

006

008

010

012

H e i g h t o f O u

t l e t ( m )

Air Velocity (ms)



00 10 20 30 40 50 60000

002

004

006

008

010

012

H e i g h t o f O u

t l e t ( m )

Air Velocity (ms)


Experiments















































000

002

004

006

008

010

012



00 10 20 30 40 50 00 01 02 03 04

000

002

004

006

008

010

012





Air Velocity (ms)


00 10 20 30 40

00 05 10 15 20 25

000

002

004

006

008

010

012

000

002

004

006

008

010

012





































simulations














respectively







values


























overall compromise

000

002

004

006

008

010

012

H e i g h t


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25

000

002

004

006

008

010

012

H e i g h t




Table 1


















000

002

004

006

008

010

012


Air Velocity (ms)

00 10 20 30 40 00 05 10 15 20 25 30000

002

004

006

008

010

012




000

002

004

006

008

010

012

H e i g


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25 30000

002

004

006

008

010

012

H e i g















directly











5 Conclusion





























investigated






References







































simulations
















particlendash


particle







corners



































00 10 20 30 40 50 60

000

002

004

006

008

010

012

H e i g h t o f O u

t l e t ( m )

Air Velocity (ms)



00 10 20 30 40 50 60000

002

004

006

008

010

012

H e i g h t o f O u

t l e t ( m )

Air Velocity (ms)


Experiments















































000

002

004

006

008

010

012



00 10 20 30 40 50 00 01 02 03 04

000

002

004

006

008

010

012





Air Velocity (ms)


00 10 20 30 40

00 05 10 15 20 25

000

002

004

006

008

010

012

000

002

004

006

008

010

012





































simulations














respectively







values


























overall compromise

000

002

004

006

008

010

012

H e i g h t


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25

000

002

004

006

008

010

012

H e i g h t




Table 1


















000

002

004

006

008

010

012


Air Velocity (ms)

00 10 20 30 40 00 05 10 15 20 25 30000

002

004

006

008

010

012




000

002

004

006

008

010

012

H e i g


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25 30000

002

004

006

008

010

012

H e i g















directly











5 Conclusion





























investigated






References
































































000

002

004

006

008

010

012



00 10 20 30 40 50 00 01 02 03 04

000

002

004

006

008

010

012





Air Velocity (ms)


00 10 20 30 40

00 05 10 15 20 25

000

002

004

006

008

010

012

000

002

004

006

008

010

012





































simulations














respectively







values


























overall compromise

000

002

004

006

008

010

012

H e i g h t


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25

000

002

004

006

008

010

012

H e i g h t




Table 1


















000

002

004

006

008

010

012


Air Velocity (ms)

00 10 20 30 40 00 05 10 15 20 25 30000

002

004

006

008

010

012




000

002

004

006

008

010

012

H e i g


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25 30000

002

004

006

008

010

012

H e i g















directly











5 Conclusion





























investigated






References


















































simulations














respectively







values


























overall compromise

000

002

004

006

008

010

012

H e i g h t


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25

000

002

004

006

008

010

012

H e i g h t




Table 1


















000

002

004

006

008

010

012


Air Velocity (ms)

00 10 20 30 40 00 05 10 15 20 25 30000

002

004

006

008

010

012




000

002

004

006

008

010

012

H e i g


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25 30000

002

004

006

008

010

012

H e i g















directly











5 Conclusion





























investigated






References

































000

002

004

006

008

010

012


Air Velocity (ms)

00 10 20 30 40 00 05 10 15 20 25 30000

002

004

006

008

010

012




000

002

004

006

008

010

012

H e i g


Air Velocity (ms)

00 05 10 15 20 25 30 35 00 05 10 15 20 25 30000

002

004

006

008

010

012

H e i g















directly











5 Conclusion





























investigated






References





























directly











5 Conclusion





























investigated






References




















computational fluid dynamics (cfd) modelling of transfer chutes: a study of the influence of model...

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