effect of screw design on hopper drawdown of spherical particles in a horizontal screw feeder

Chemical Engineering Science 66 (2011) 5585–5601

Contents lists available at ScienceDirect

Chemical Engineering Science

0009-25

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/ces

Effect of screw design on hopper drawdown of spherical particles in ahorizontal screw feeder

Justin W. Fernandez a,b, Paul W. Cleary a,n, William McBride c

a CSIRO Mathematics, Informatics and Statistics, Private Bag 33, Clayton South, Victoria 3169, Australiab The University of Auckland, Auckland Bioengineering Institute, UniServices House, Auckland 1142, New Zealandc The University of Newcastle, Mechanical Engineering, Callaghan, NSW 2308, Australia

a r t i c l e i n f o

Article history:

Received 2 January 2011

Received in revised form

25 April 2011

Accepted 26 July 2011Available online 9 August 2011

Keywords:

Screw Feeder

Hopper drawdown

Screw design

DEM

Particle flow

Flow uniformity

09/$ - see front matter Crown Copyright & 2

016/j.ces.2011.07.043

esponding author.

ail address: [email protected] (P.W. Cleary

a b s t r a c t

Screw feeders are used to remove material from hoppers and bins at a controlled rate. The evenness of

the flow in the bin depends on the drawdown pattern, which in turn depends on the screw and hopper

design, shape of the particles and wall friction effects. A key design requirement is to ensure that a

progressive increase in the screws volumetric capacity is achieved along the entire length of the

hopper’s opening so as to produce even drawdown. If this is not achieved then compositional variations

in the outgoing stream and other operational problems (such as caking) can be created. Screw designs

to date have been generally based on analytical models and at times the predicted flow pattern is not

achieved. In this study, the Discrete Element Method (DEM) is used to predict particle transport in a

horizontal screw feeder system for a range of conventional screw designs including a variable screw

pitch, variable screw flight outside diameters and variable core diameters. The influence of screw choice

on the particle mass flow rate, the evenness of particle drawdown from the hopper, power

consumption, screw wear and wall friction variations are all investigated. Important features captured

by DEM that are not accounted for by the analytic model and which vary strongly between competing

screw designs, include the particle circulation in the hopper, shearing of the particle bed in the trough

just outside the screw and the spatially varying particle force along the hopper which leads to non-

uniform drawdown and to the existence of large stagnant or slow moving zones. The screw design and

consequent flow patterns also strongly affect the power draw with variations up to a factor of three and

screw wear with large changes in their distribution and magnitude. Finally, the surface frictional

properties of the screw are shown to strongly influence the rate of bed compaction within and along the

screw leading to strong variation in mass flow rate, uniformity of drawdown and power draw.

Crown Copyright & 2011 Published by Elsevier Ltd. All rights reserved.

1. Introduction

Screw feeders are used extensively in the food, plastics,household products, mineral processing and agricultural indus-tries to draw bulk materials from hoppers or bins and transferthem over short distances. They generally provide good through-put control and facilitate a level of environmental protection notpossible with belt conveyors. The typical configuration consists ofa bin and hopper coupled to a screw casing and a screw within. Asthe screw rotates material is drawn from the hopper andtransported along the casing. While mechanically simple inprinciple, the behaviour of material during the drawdown processand transport can be complex (Cleary, 2007; Owen and Cleary,2009).

011 Published by Elsevier Ltd. All

).

Screws have been extensively studied experimentally, such asby Bates (1969) who conducted experiments matching differentscrews and materials in a hopper to investigate flow patterns, andMarinelli (1996) who looked at matching hopper bin design withoptimum screw feeders. Theoretical models have also beenproposed by Yu and Arnold (1996) for a uniform flow patternbased on the pitch characteristic of screws, and Roberts and Willis(1962), Roberts et al. (1993), Roberts (2002) for uniform draw-down used to predict the flow patterns generated in hoppers for agiven screw. These methods have been used to analyse screwfeeder performance based on the bulk drawdown characteristicsin a hopper (Roberts and Manjunath, 1994). In that study, theirassumption was that the force exerted on the screw is uniformlydistributed along the screw length. Continuum models as used byRoberts et al. do not attempt to determine the depth of theintrinsic boundary layer surrounding the screw flight and as suchdo not consider this additional material in the discharge predic-tion. Furthermore, the forces acting on the screw vary along the

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J.W. Fernandez et al. / Chemical Engineering Science 66 (2011) 5585–56015586

screw length and can affect screw shear and power draw non-uniformly (Roberts and Manjunath, 1994; Roberts et al., 1993;Roberts, 2002).

Discrete Element Modelling (DEM) provides a way of looking atlocalised interactions within the hopper and screw and their influ-ence on bulk measurements. Previous DEM studies have focussed onhorizontal and vertical conveyers and comparisons between model-ling and empirical data (Shimzu and Cundall, 2001), long screwconveyers using a periodic slice model (Owen et al., 2003,Owen andCleary, 2009), hopper drawdown using an inclined screw conveyer(Cleary, 2004) and including the effect of particle shape (Cleary,2007). McBride and Cleary (2009) recently highlighted the use ofDEM to investigate a stationary screw flight in a rotating case (the‘OLDS elevator). In that study, DEM was shown to predict mass flowrates that were highly consistent with experiments, and also toinvestigate region specific transport velocities, particle recirculation,power draw and inter-particle frictional effects.

This study uses DEM to investigate the effect on total massflow rate, mass flow rate distribution along the screws, drawdownpattern, power consumption and abrasive screw wear for sixscrew designs. The screws used cover a wide range of commonlyfound designs including variations in outer blade diameter, innercore taper and screw pitch spacing. The study aims to evaluatethe relative performance of different screw options and to estab-lish the accuracy of the continuum based analytic models.

2. Screw variant designs

There are numerous screw designs used in industry, which arebased on the variation of blade diameter, screw core diameter andpitch angle. In this study, we investigate five typical designs and one‘‘optimal’’ screw based on screw design theory. Each of the screwsvaried one or more design variables while keeping the othersconstant. In this way, the influence of changing each variable couldbe observed. The ‘‘optimal’’ screw was designed so that the volumewithin the screw increased by equal amounts for each screw flightalong its length, theoretically giving uniform drawdown.

Consider Fig. 1, which shows a screw located in a hoppertrough of length, L. The screw section of interest is from the start,S, at the hopper rear to the point, F, at the hopper exit. All screwvariations occur in this initial length L of the screw. Once outsidethe hopper and in the screw casing there are no variations in thescrew design and the mass flow rates are constant. In this paper,we focus only on the behaviour in the screw directly under thehopper. The screw attributes that are normally varied are the

�

Figclea

resp

screw flight diameter D0 (the outer diameter of the helicalscrew thread),

. 1. Diagram of a variable pitch screw sitting in a hopper trough with length, L, var

rance, C, between the outer screw diameter and the trough casing is shown. The

ectively.

�

iabl

sta

screw core Di (the diameter of the central screw shaft) and
� pitch p (distance from one thread peak to the next).
Based on the choice of outer diameter, there will be a clearancedistance, C (see Table 1), between the outer diameter of the screwand the trough casing. This can potentially allow particle slippagearound the screw depending on the size of the particles. For thisstudy, linear variations along the screw for flight and core dia-meters and pitch were assumed since these are the most commonform of variations used in industry. The variable outer screw bladediameter, Do(x), at any point, x, along the screw length is therefore

D0ðxÞ ¼D0sþD0f�D0s

Lx, ð1Þ

where D0s and D0f are the outer screw diameters at the start andfinish, respectively. Similarly, the variable internal core screwdiameter is given by

DiðxÞ ¼DisþDif�Dis

Lx, ð2Þ

where Dis and Dif are the screw core diameters at the start andfinish, respectively. These are combined to give the screw cross-sectional area, A(x), per screw revolution along the screw,

AðxÞ ¼p4

D0ðxÞ2�DiðxÞ

2h i

: ð3Þ

The variable screw pitch, p(x), along the screw length, x, is alsolinearly varying using

pðxÞ ¼ psþpf�ps

Lx, ð4Þ

where ps and pf are the screw pitch at the start and finishpositions, respectively.

The screw conveyor configuration used here is a laboratoryscale one. This is suitable for investigation of the effects ofchanges in screw design. For industrial scale hoppers, the magni-tude and extent of variation in the solids stresses will be muchlarger with greater loads acting on the feeders leading also togreater torque and power requirements. It is assumed that thescrew design behaviours identified here do no scale muchdifferently from the laboratory to the industrial scale. The hopperbin, screw casing and six screw variants used for this study areshown in Figs. 2 and 3, respectively. Key dimensions are anno-tated on the figures. The key geometric dimensions of the screwvariations are given in Table 1. The screws investigated were:

(i)

e

r

constant flight diameter, constant core and a constant pitch(screw A);

(ii)
tapered flight diameter, constant core and a constant pitch(screw B);
outer screw blade diameter, D0, internal core diameter, Di, and pitch, p. The

t and finish locations of the screw within the hopper are marked S and F,

Table 1Geometric properties of the six screw designs.

Screw Outer blade

diameter

(D0) (mm)

Outer shaft

diameter

(Di) (mm)

Pitch (p)

(mm)

Maximum

screw

clearance

(C) (mm)

A 52.5 22.5 52.5 0.75

B 22.5–52.5 22.5 52.5 15.75

C 52.5 22.5 12.0–52.5 0.75

D 52.5 45.0–22.5 12.0–52.5 0.75

E 37.5–52.5 37.5–22.5 52.5 8.25

F 37.5–52.5 37.5–22.5 12.0–52.5 8.25

180 270

225

181

54

120

Screw casing

Hopper bin

Hopper trough

Fig. 2. Hopper bin, trough and screw casing geometry with dimensions shown

(mm).

Di

pD0

Fig. 3. Screw design variations. screw A: standard, with labelled outer screw flight di

flight; screw C: variable pitch; screw D: variable pitch and taper; screw E: tapered

variable pitch.

J.W. Fernandez et al. / Chemical Engineering Science 66 (2011) 5585–5601 5587

(iii)

amete

fligh

constant flight diameter, constant core and a variable pitch(screw C);

(iv)
constant flight diameter, variable pitch and a tapered core(screw D);
(v)
an expanding flight diameter, a tapered core and a constantpitch (screw E);
(vi)
an ‘‘optimised’’ expanding flight diameter with tapered coreand a variable pitch (screw F). Specifically, it has a quad-ratically expanding flight so as to give a theoretical constantdrawdown along the screw length.
3. Analytical model of flow in a horizontal screw

The traditional way of assessing and designing screws is viathe analytic approaches based on continuum methods. One highlyrecognised method is due to the work of Roberts and Willis(1962) Roberts et al. (1993); Roberts (2002). In this study, wepredict mass flow rates using DEM and then compare andcontrast the results of DEM with those due to Robert’s analyticmethod. From this theory, the total mass flow rate, Q(x), along thescrew length, x, is given by

Q ðxÞ ¼ ZvðxÞAðxÞpðxÞor, ð5Þ

where Zv(x) is the volumetric efficiency, A(x) is the cross-sectionalarea of the screw flight, p(x) is the pitch of the screw flight, o isthe angular screw velocity and r is the bulk density.

The volumetric efficiency, Zv(x), is defined as the ratio of theactual volumetric flow along the length of the screw, VL, to themaximum theoretical volumetric flow along the screw, VLt. Theactual flow will differ from the maximum theoretical flow(Robert’s et al., 1993, Roberts and Manjunath’s, 1994) because:

(i)
the axial velocity of the bulk solid along the screw will belower due to the shearing rotational motion generated bythe screw;
(ii)
slippage occurring in the clearance between the screw andhopper trough and
(iii)
once a critical speed is exceeded, the amount of particleswithin the screw flight will decrease with further increasesdue to the dominance of the centrifugal force so that particles
r (D0), inner core diameter (Di) and screw pitch spacing (p); screw B: taper

t and core with constant pitch; screw F: optimal flight, tapered core and


are not able to flow under gravity into the void spaces inthe screw.

The volumetric efficiency for a horizontal screw is defined,according to Roberts et al. (1993), Roberts and Manjunath (1994), as

ZV ðxÞ ¼VL

VLt¼

1

tanamðxÞtan½fsþamðxÞ�þ1, ð6Þ

where fs is the screw face wall friction angle and am(x) is the meanhelix angle of the screw flight along the screw length, x. The meanhelix angle is given by

amðxÞ ¼ tan�1 pðxÞ

pDm

� �, ð7Þ

where p(x) is the screw pitch along the screw length and Dm is theeffective mean screw diameter defined as the average of the outerscrew Do and inner core Di diameters.

4. Model description

4.1. Discrete element model

The Discrete Element Method (DEM) is a well-documentednumerical tool. The variant used here has been previously used tostudy the granular flow of material in many applications, seeCleary (1998, 2004, 2009) Cleary and Sawley (2002). Briefly, DEMsimulates granular flow by tracking individual particles andpredicting their interactions between each other and externalobjects such as the screw and hopper. The particles can bemodelled as a range of shapes including spheres, blocky shapedparticles using super-quadric descriptors, or as convex polyhedra.The particles are permitted to overlap each other and boundaryobjects and when coupled with a contact law, predict contactforce allowing the prediction of instantaneous positions, orienta-tions, velocities and particle spin. The present study uses a linear-spring dashpot model. The overlap scaled by a spring constant,provides a repulsive force coupled with a dashpot to dissipate aproportion of the normal energy in a collision. In a similar way,the tangential force has an incremental spring based on thetangential displacement and a dashpot to dissipate tangentialenergy. For more details of DEM and the implementation used inthis study see Cleary (1998, 2004) and Cleary and Sawley (2002).

4.2. Screw feeder configuration and particle properties

The six screw variants of the hopper with screw were createdusing CAD and then meshed using volume tetrahedral elements ata resolution of 2 mm to capture the screw curvature usingcommercial mesh generation software (Hypermesh, Altair Engi-neering, Inc.). All screws were rotated with a constant angularvelocity of 1 Hz (60 rpm).

The hopper bin was filled to approximately 80% full with 5 mmdiameter spherical grains resulting in �100 k particles and amass of 8.8 kg. A 1% variation was used for the diameter range toprevent unrealistic crystalisation from occurring. The solid den-sity of the particles was 1400 kg/m3. These are generic simpletype of material intended to be reasonably representative of bulkmaterials so that the analysis is not overly complex but themodelling conclusions are reasonably broadly applicable. Inpractice, bulk materials vary widely in size, shape and cohesiveproperties. The effect of each of these particle attributes will beconsidered in future work. The effect of particle shape on the flowin an inclined screw feeder has previously been studied in Cleary(2007).

The coefficient of restitution used was 0.5 for all materialcombinations. The coefficients of friction between particles,hopper wall and screw face were 0.6, 0.45 and 0.364, respectively.In particular, the screw face friction (0.364) is often lower thanthe hopper wall friction (0.45) as the screw is polished eitherpurposefully or by the flow of particles. The screw face friction of0.364 roughly corresponds to a wall friction angle of 201. Thesefrictional coefficients were chosen based on typical values foundin industry as measured using a Jenike shear tester. Such testshave been performed for many materials over many years but thevalues are rarely published (McBride, 2011). In cases, where thebulk material is corrosive the screw surface can become corrodedand have a friction coefficient that is comparable to or higher thanthe wall friction. The effect of such changes in the screw friction isconsidered in Section 10. The contact spring constant used was1000 N/m. This was chosen to produce an average contact overlapof �0.5% of the particle diameter, which suffices for givingaccurate predictions.

Particles in the hopper bin were then coloured into five evenlyspaced vertical bands to allow quantification of the drawdownfrom different regions of the hopper. For the analysis, particlesinitially inside the trough and surrounding the screw wereignored (and were coloured grey) so that the predicted flow rateswere based solely on drawdown from the hopper bin. Thesimulation mass flow rates were measured at six evenly spacedlocations along the screw length.

4.3. Measures used to assess relative screw performance

A number of measures were used to assess screw performancein this study. These included:

(i)
uniformity of the drawdown pattern within the hopper. Wedefine a hopper drawdown number (DN) by
DN¼1

DN1

XNc

i ¼ 1

pi�100

Nc

��, ð9Þ

where pi, is the percentage of the total mass flow rate thatcolour band, i, contributes and, Nc, is the total number ofbands. DN1 is the drawdown number for the worst casewhen only 1 band is drawn down. For the 5 coloured strataused in this study, drawdown of only 1 band would makeDN1¼160 and give DN¼1. DN then helps to quantify thedrawdown observed by measuring how much better thescrew is from the worst case. For example, for the five bandsused in this study, if each contributes 20% of the total massflow rate (a perfectly uniform drawdown) then DN would be0 indicating no deviation from the ideal drawdown or 100%better than the worst case;

(ii)
particle velocity field to show regions of preferential draw-down and stagnant zones;
(iii)
particle force distribution in the hopper to show how thebed weight is transmitted and regions of high force andpossible particle degradation;
(iv)
total mass flow rate which is used to assess the total flowcapacity of the screw;
(v)
mass flow rate for each coloured strata measured at thehopper exit to assess the evenness of the drawdown;
(vi)
power consumption to assess the cost of operating the screwfeeder;
(vii)
abrasive damage of the screw.
Whilst the DEM simulations are fully three dimensional, werestrict our analysis to the centre plane of the hopper, along theaxis of the screw. Due to the screw rotation, there will be stronger


feeding on the side of the screw which is moving downwards thanon the upward moving opposite side. Transverse flow is alsogenerated across the hopper leading to asymmetries in the flowand the drawdown. These transverse flows and front/back asym-metries have previously been identified and studied using DEM inCleary (2007). They are moderate in magnitude for sphericalparticles and are expected to be similar for all the different screwdesigns considered here and so are not included in theanalysis here.

5. Screw a: the reference case

Screw A is the simplest screw in this study and one of the mostcommon designs found in industry and so is used as the referencecase. The drawdown patterns for screw A at 0, 10, 30 and 80 s areshown in Fig. 4. The rear and front walls of the hopper are shownon the left and right, respectively. After 10 s, the majority of greyparticles initially filling the screw trough have been transportedout of the hopper. Material is only drawn down from the rearbands and dark blue material now dominates the content aroundthe screw. The base of the dark blue band has narrowed and redmaterial is starting to be drawn towards the first flight of thescrew creating a funnel shape. The yellow and green bands, whilerelatively unchanged in shape, have started to bend towards therear near the free surface, while the light blue band remains fairlyvertical and unchanged. The strong preferential rear draw hasgiven rise to a free surface that dips slightly at the hopper rear.

At 30 s, structural changes initiated in the bed at 10 s havebecome more distinct. The dark blue band has narrowed furtherand red particles are now funnelled into the first screw flight.These first two bands are the only material entering the screw.There are two pathways that particles follow to enter the screw

Fig. 4. Hopper drawdown pattern in the centre plane of the hopper for the

standard screw at (a) initial, (b) 10 s, (c) 30 s and (d) 80 s. The direction of material

migration is indicated by arrows in (c) and (d). The particles are coloured by

vertical strata from left to right as dark blue (black), red (dark grey), yellow (off

white), green (medium grey) and light blue (light grey). (For interpretation of the

reference to color in this figure legend the reader is referred to the web version of

this article.)

flight, which are shown by the arrows in Fig. 4c. Firstly, materialabove the first flight is drawn directly downwards into the screw.This flow is initially dominated by blue and red particles. Materialnear the top then flows down along the free surface towards therear of the hopper to replace the material being preferentiallydrawn down along the rear hopper wall by the first flight of thescrew. This is shown by the broadening of the tops of the yellow,green and light blue bands and by the increasing slope to the leftof the upper parts of the interfaces between these colours. Thesecond flow path involves a creeping flow throughout the hopperresulting in the slow migration of particles first to the left andthen diagonally down towards the first flight of the screw. This isdriven by the pressure differential across the bed which is createdby the inclination of the free surface (meaning more load on thebed on the right) and by the low pressure in the mobiliseddownward flowing material at the rear of the hopper (meaningless support on the left). This causes the bed to slowly deform,with the surface level subsiding and the colour bands wideningwith the interfaces between colours moving slowly towards therear of the hopper whilst remaining nearly vertical. The yellowcoloured particles are most affected by both modes.

There is also a thin layer of entrained material above the screwthat is sheared along its length from the rear (left) to the front(right) of the hopper. This layer is drawn from the first two bandsand located just above the top of the screw at the height wherethe screw trough meets the hopper walls. An important effect canbe seen near the screw exit from the hopper. The volume ofparticles entrained by the screw motion is larger than the exitfrom the hopper. The upper section of this entrained material(which is a mixture of red and dark blue) is pushed against thevertical end wall of the hopper and is forced slowly upwards. Thiscompletes a hopper wide recirculation pattern driven by theshear from the screw at its base.

At 80 s, the particle migration pattern more clearly shows therecirculation structure. The screw is now primarily filled with redparticles and then yellow. Very little of the dark blue material isleft in the hopper—just a narrow frictional boundary layertrapped against the left wall and some in the recirculatingmaterial forced upwards from the end of the screw trough. Theentire original vertical red band has also been drawn down.Yellow particles almost entirely surround the rear screw flightand is the only strata colour entering the screw. The top of therecirculating material that was entrained by the screw has nowmoved significantly above the top of the casing at the end of thehopper. It is slowly ’’extruded’’ or forced upwards by the highpressure at the screw exit. The rate of recirculation is controlledby the difference between the volume of material entrained bythe screw and the volume that can discharge through the casing.This has previously been observed (Cleary, 2007). Beyond the firsttwo flights, no additional material can enter the screw volume.The only path along which the yellow, green and light bluematerial can reach the screw is by flowing from the surfaceregions near the rear wall and towards the left end of the screw.The shape of the green band clearly shows the influence of thesurface deformation flow its material now reaching the rear walland just starting to be drawn down along the left wall. Thematerial recirculating from below has pushed up the bottom ofthe green band and caused it to tilt to the left. The light blue bandstill remains roughly vertical, with its base pushed upwards and asmall amount now flowing down the free surface. The free surfaceis flat and inclined at the angle of repose of the material, except atthe rear where a thin band of slow moving blue particles hascaused a small plateau.

Fig. 5a shows the instantaneous particle forces for the standardscrew (A). The highest force of 30 mN occurs at bottom of thefront wall where the screw exits the hopper. The particle force

10.0 -7.5 -5.0 -2.5 -0.0 -

Velocity (mm/s)30.0 -23.0 -15.0 -

7.5 -0.0 -

Force (mN)

Fig. 5. (a) Particle force profile and (b) particle velocity profile in the centre plane of the hopper for screw A at 30 s.

Screw D (30 s)

Screw E (30 s)Screw B (30 s)

Screw A (30 s)


above the first screw flight (on the left side) is close to zero,remains low over the first two flights when the particles arerelatively mobile and can flow into the screw and then increasessteadily to the maximum at the hopper exit. These peak forcesoccur because the particle mass entrained by the screw is largerthan the exit diameter and so particles are forced into the endwall. These particles have no choice but to move upwards. For thisto occur the entire weight of the particles above must be lifted,leading to the very high relative forces here. The screw volume isfilled completely in the first two flights and there is no spaceavailable further along the screw. This leads to the elevated forces(green and higher) along the last 70% of the hopper length. Theforces are low in the entire vertical draw down channel along theleft wall. This is the path of least resistance and therefore ofmaximal flow.

Fig. 5b shows the corresponding particle velocity field forscrew A. There is a triangular funnel shape region of mobilisedparticles above the drawdown location at the hopper rear. Itextends to the surface and acts to draw particles from the rearhalf of the free surface down towards the first screw flight.Particles accelerate as they are drawn down towards the screwreaching a maximum speed of 10 mm/s above the first screwflight. This closely corresponds to the region of low particle force(Fig. 5a). The front half of the hopper (right) has very lowvelocities in a triangular region stretching from the surface ofthe front of the hopper down towards the second screw flight andcorresponds with the regions of high force. At the very bottom onthe right there is a very small upward component to the velocitieswhich corresponds to the creeping flow that leads to the forma-tion of the extruded layer.

Screw F (30 s)Screw C (30 s)

Fig. 6. Hopper drawdown patterns at 30 s shown for a central slice along screw

length for screw A (standard), screw B (tapered flight), screw C (variable pitch),

screw D (variable pitch and tapered core), screw E (tapered flight and core with

constant pitch) and screw F (optimised flight, tapered core with variable pitch).

The initial free surface is indicated by the pink dashed line and the current free

surface shape is marked by the black solid curve. (For interpretation of the


this article.)

6. Comparison of hopper drawdown pattern for differentscrews

The hopper drawdown patterns (Figs. 6 and 7) and velocityand force distributions (Figs. 8 and 9) are shown in the centralplane of the hopper for all six screw designs.

6.1. Screw B: expanding flight

After 30 s of drawdown, screw B has delivered a more evenvertical settling of all bands compared to screw A. The mostnoticeable difference is that the high speed region on the left haschanged from a narrow funnel to a wide vertical down flow overthe first 2

3 of the length of the screw. The first four bands (darkblue to green) all flow into the screw. Screw B has twice as manycolour bands entering the screw volume as screw A. There is little

Screw D (80 s)

Screw E (80 s)

Screw F (80 s)

Screw A (80 s)

Screw B (80 s)

Screw C (80 s)

Fig. 7. Hopper drawdown patterns at 80 s shown for a central slice along screw

length for screw A (standard), screw B (tapered flight), screw C (variable pitch),

screw D (variable pitch and tapered core), screw E (tapered flight and core with

constant pitch) and screw F (optimised flight, tapered core with variable pitch).

The initial free surface is indicated by the pink dashed line and the current free

surface shape is marked by the black solid curve. (For interpretation of the


this article.)


evidence of flow along the free surface and much less slumping.This is consistent with the free surface which is much flattercompared to screw A, with no parts reaching the angle of repose.There are also only very weak signs of recirculation of entrainedmaterial being forced upwards by the end wall at the exit of thehopper. This implies that the forces in the right half of the bed aremuch reduced by use of this screw design. This is confirmed bythe force distribution in Fig. 9 which shows peak forces reducedby about a half. These lower forces are much less able to driverecirculation. The stagnant zone is also much narrower than forscrew A.

At 80 s, the bed structure is radically different to that of screwA. The original vertical bands are all still quite recognisable andnot far from vertical. The free surface is lowest over the red bandand is inclined upwards to both sides. The surface angle is muchless than that of case A. The inclined free surface still drives asurface slumping but this is much weaker than for screw A. The

broadening of the light blue band is less pronounced. The greenband is gently tilted to the left but the upper sections have notbeen bent sharply towards the left. The yellow band is similarlygently tilted and narrowed at the top. It occupies a completelydifferent part of the hopper than for screw A and has a completelydifferent shape, reflecting the strong differences in the underlyingflow for this screw. The dark blue band is still present and isvertical with some narrowing in its upper third. The red band isgently tilted and is narrower at the top. The amount of eachcolour removed by the screw is much more even than for screw A.There is still a small amount of recirculation of entrained materialfrom the screw back upwards on the right. So screw B leads tosignificantly more even drawdown and substantially reduces thestrength of the recirculatory flow.

Screw B has distributed the drawdown speed (Fig. 8) moreevenly along the screw length than did screw A. The uniformdrawdown region on the left has four times the length it had forscrew A. The first four flights have an average speed of 2.5 mm/swith a peak speed of 3 mm/s (which is less than a third of thatfound for screw A) occurring under the red band above the secondflight. This velocity peak under the second flight occurs becausethe blade height reaches one particle diameter at this point andmaterial can now be trapped by the screw and dragged along tothe right. Before this point material is less able to engage with theblade, which is much shorter and behaves more like a bumpysurface over which particles can slide. Once the blade height iscomparable to the particles it acts more as a physical obstaclepushing forwards the particles in front of it. There is a flow ratedifferential created with material leaving this part of the screwfaster than it arrives from the region of the screw to the left.Material is therefore drawn down from above to fill the additionalspace being made available at this point leading to the higherdrawdown velocity here. There remains a narrow stagnant regionabove the hopper exit but it is improved compared to screw A.

The change in the force distribution is also substantial withmuch more even and much lower magnitude. It is low above thefirst two-thirds of the screw, corresponding again to the regionwhere drawdown is occurring. Higher forces are present near andabove the hopper exit which still acts as a stagnation point. Animportant difference from screw A is that the high particle force isnow only located in a narrow region for screw B which willreduce particle damage.

6.2. Screw C: expanding pitch

Screw C has a reduced flight pitch at the rear of the screw. At30 s, the draw down pattern is part way between that of screws Aand B. The lowest point of the free surface is closer to the left wallthan was observed for screw B. The drawdown of the dark blueband is much stronger than for screw B but not as strong as forscrew A. The slumping deformation of the upper layers observedfor screw A is also observed here, but is considerably weaker. Thisbehaviour was largely suppressed by screw B. There is almost nosign of recirculation of entrained material with the light blueband extending all the way down to the stagnation point at thebottom of the right wall. At 80 s, parts of the free surface havereached the angle of repose with the lowest point around 25% ofthe way from the left wall. There has been a substantial removalof dark blue and red material, much more than for screw B butconsiderably less than produced by screw A. The lower sections ofthe other bands are tilted to the left as was found for screw B, butthere is much more twisting of their upper sections indicating areasonable amount of slumping is occurring along the steeper freesurface. This is the same type of behaviour as observed for screwA, but much less strong. There is now a weak accumulation of

Screw C Screw F

Screw A

10.0 -7.5 -5.0 -2.5 -0.0 -

Velocity (mm/s)

10.0 -7.5 -5.0 -2.5 -0.0 -

Velocity (mm/s)

10.0 -7.5 -5.0 -2.5 -0.0 -

Velocity (mm/s)

10.0 -7.5 -5.0 -2.5 -0.0 -

Velocity (mm/s)

10.0 -7.5 -5.0 -2.5 -0.0 -

Velocity (mm/s)

10.0 -7.5 -5.0 -2.5 -0.0 -

Velocity (mm/s)

Screw D

Screw B Screw E

Fig. 8. Distribution of particle velocity in the hopper for each screw design at 30 s. The arrows show the velocity direction and are scaled by magnitude. The colour also

shows the magnitude with dark blue zero and red the peak velocity. (For interpretation of the reference to color in this figure legend the reader is referred to the web

version of this article.)


entrained material (comparable to screw B) being slowly forcedupwards along the right wall by the weak recirculation.

The velocity distribution for screw C is also part way betweenthat of screws A and B. There is clearly a higher velocity over thefirst 20% of the screw as the rapidly widening pitch enablessignificant drawdown. The peak speed is around 8 mm/s which isaround three times that of screw B but is only 65% of that of screwA. The length of the drawdown region for screw C is three timesthat of screw A and 2

3 that of screw B. The force distribution forscrew C more resembles that of screw A, but with much lowerpeak forces. There is a clear peak at the bottom of the wall wherethe screw exits. The force decreases progressively to the left and islow in the vertical mobile drawdown region along the left wall.

6.3. Screw D: expanding pitch and tapered core

Screw D is the first of the screws to combine two designfeatures (an expanding pitch and a tapered core). At 30 s, theaddition of a tapered core has introduced a more even settling ofall the bands compared to screw C, which had a constant core. Thebehaviour is now very similar to screw B, except for slightly moredrawdown of the dark blue band. After 80 s, the drawdown

remains very similar to that of screw B but with a slightlyincreased removal of dark blue material leading to a flat freesurface for the first 25% of the bed. The red band is also a littlemore narrowed at the top. There is less material being recircu-lated from the trough than for any of the previous screws. Thevelocity distribution is also close to that of screw B with a verysimilar length of the drawdown region and a similarly smallstagnant zone on the right. The peak drawdown speeds near theleft wall are moderately higher than for screw B but much lessthan for screws A or C. This screw shows the most uniformdistribution of force. It is broadly similar to that of screw B butlacks the low force zone along the top of the screw and hasslightly lower peak forces around the stagnation point above theexit. The differentiating factor between these two otherwise verysimilarly performing screws, which would typically lead to screwD being better in service, is that screw B leaves significantstagnant material in the trough in the parts where the outerdiameter of the screw is smaller. This can be addressed bygeometry alterations to match the trough shape to the shape ofthe live regions of flow around the screw, but these are complexand can be expensive to implement. Screw D is an easier andslightly better performing option.

Screw C

30.0 -23.0 -15.0 -

7.5 -0.0 -

Force(mN)

Screw A

30.0 -23.0 -15.0 -

7.5 -0.0 -

Force(mN)

30.0 -23.0 -15.0 -

7.5 -0.0 -

Force(mN)

30.0 -23.0 -15.0 -

7.5 -0.0 -

Force (mN)

30.0 -23.0 -15.0 -

7.5 -0.0 -

Force (mN)

30.0 -23.0 -15.0 -

7.5 -0.0 -

Force (mN)

Screw F

Screw D

Screw B Screw E

Fig. 9. Distribution of particle contact forces in the hopper for each screw design at 30 s. The arrows show the force direction and their length is scaled by force magnitude.

The colour also shows the magnitude with dark blue zero and red the peak force. (For interpretation of the reference to color in this figure legend the reader is referred to

the web version of this article.)


6.4. Screw E: increasing tapered flight and decreasing tapered core

Throughout the discharge process, the drawdown pattern forscrew E is nearly indistinguishable from that of screw C. The freesurface deformation and the changes in the vertical bands areextremely similar. The velocity distribution is also very similar tothat of screw C with a similar drawdown length along the hopperand a similar size stagnant zone on the right. The vertical draw-down speed is more uniform along the drawdown region forscrew E compared to screw C with peak velocities at the start ofthe screw being reduced by around a half. The force distributionfor screw E is also nearly indistinguishable from that of screw C.

6.5. Screw F: expanding flight and pitch and tapered core

Screw F is the most complex design combining all threevarying features; a tapered core, expanding pitch and taperedflight. Unlike the previous screws, it was designed based on thecontinuum theory, to give an optimised drawdown along thelength of the screw. Compared to all the previous screws, screw Fshowed the most even drawdown with all bands remaining themost vertical, being just better than screws B and D. The freesurface is also closest to being flat with the smallest heightvariations. This screw also showed the lowest amount of recircu-lation of material from the trough back upwards along the right

wall. The velocity distribution for screw F is the most uniform ofall the screws. The length of the drawdown region is similar tothat of screw B, but the speed is more uniform and has a lowerpeak—almost constant at 3 mm/s over the first half of the screw.The last flight though still has a stagnant region above. This showsthat screw F achieves the intended flow behaviour for most of thescrew but still fails to maintain flow over the last flight. It has thelongest and most uniform downward flow region, which issignificantly better than screw A, is a considerable improvementover screws C, D and E, but only slightly better than screw B. Thisscrew also produces the most uniform and on average the lowestforce distribution in the hopper.

6.6. Quantitative variation of transport with screw design

DEM simulation enables the quantification of flow variablesthat are not possible to measure in experiments. Here, we considerthe variation along the length of the hopper trough of the:

�
mass flow rate from which the rate of drawdown can bededuced; � axial flow speed which is the rate at which particles are
transferred along the screw;
� Packing fraction—by dividing the mass flow rate by the axial
speed and normalising by the volume per unit length of free

Figpar


volume available to the particles outside the screw and withinthe trough, we can estimate the packing density of particlemicrostructure. This allows us to quantify any compaction ordensification of the particles in the trough.
�
0

5

10

15

20

25

30

35

Mas

s Fl

ow R

ate

(g/s

)

Screw

Dark blueRedYellowGreenLight Blue

B C D E FA

Fig. 11. Mass flow rates for the different strata colours, as measured in the DEM

simulation when discharging at the exit of the hopper trough after 30 s.

average particle force—which is a combination of pressureapplied by the bed above and force generated by the screw.This is a driver for compaction.

These quantities are shown for all the screws in Fig. 10. Thedischarge rates for the different colour bands (at 30 s) are shownin Fig. 11. The DN behaviour is given in Table 2.

The mass flow rate for screw A is nearly constant along thescrew length after the first two flights. Almost all the materialtransported by the screw has filled in the first 50 mm (first flight)and the last 10% has filled over the second flight. It has adrawdown pattern that is as far from uniform as is physicallypossible to obtain. The dark blue colour was the dominant onemeasured at the exit (see Fig. 11) followed by red with a flow rateof only 1

3 of the dark blue. Absolutely no drawdown was observedfrom any of these later colour bands. These discharge rates give aDrawdown Index DN of 0.75, which is only 25% better than theworst possible case when only one colour is drawn down. Theaxial flow speed is slightly lower over the first 100 mm anddeclines very slightly over the last 100 mm but is fairly close toconstant along the screw. The packing density is also fairly closeto constant along the length of the screw. There is a small increaseat 50 mm as the drawdown forces particles into the screw butthey have not yet accelerated to their maximum axial speed. Sothe particles pack at close to their maximum level during the

0

10

20

30

40

50

50

Mas

s Fl

ow R

ate

(g/s

)

Screw Length (mm)

0.4

0.5

0.6

50

Pac

king

Fra

ctio

n

Screw Length (mm)

screw A scrscrew D scr

100 150 200 250

100 150 200 250

. 10. Comparison for the different screws of the variation along the screw (at 30 s)

ticles in the trough around the screw and (d) particle force.

initial filling at the start of the screw and maintain this degree ofpacking throughout the transit of the screw. The force on theparticles in the screw increases almost linearly along the screwreflecting the high force in the particle bed above (as observablein the force distribution shown in Fig. 9).

The mass flow rate for screw B starts at a very low value. Itincreases along the screw, more quickly in the early stages andprogressively less quickly in its second half. The first flight fillsonly about 25% of the final screw transport volume. The secondflight captures �30% with the rate of drawdown declining after

0

50

100

150

Scr

ew P

artic

le F

orce

(mN

)A

xial

Par

ticle

Vel

ocity

(mm

/s)

Screw Length (mm)

ew B screw Cew E screw F

40

30

20

10

050 100 150 200 250

0 50Screw Length (mm)

100 150 200 250

of: (a) mass flow rate, (b) axial particle velocity in trough, (c) packing fraction of

Table 2Drawdown behaviour for the six screw designs.

Screw Drawdown Number (DN)

A 0.75

B 0.36

C 0.58

D 0.38

E 0.56

F 0.31


this. This is significantly more even than for the standard screw (A).It is consistent with the intention of the screw design, which is todrawdown less material at the rear of the screw (due to its smallblade diameter) and to increase the drawdown further along thescrew because of the gradual tapering of the screw flight. Thedischarge composition is a better mix of the first three colours witha small amount of green also being captured by the screw. Thisgives a Drawdown Index DN of 0.36, which is a 52% improvementover screw A, but is still not ideal. The axial speed starts at 10 mm/s and increases nearly linearly along the screw, but more slowlytowards the end. The resulting packing fraction starts at a muchlower level of around 0.42 at the end of the first flight. This meansthat the particles that have initially fallen into the screw are muchmore loosely packed than they are for screw A. This light packing isreflected in a relatively low particle force and means that the screwsurface is not well able to grip the particles and transport themleading also to the low initial axial speed. At the 100 mm point, thepacking density has risen sharply to 0.54, the axial speed hasincreased and the mass flow rate has increased more strongly. Bythe end of the screw, the packing fraction reaches the same level asfor screw A (at around 0.54). This is fairly close to the random closepacking limit for spherical near-mono-disperse particles of around0.6. At the exit, the mass transfer rate, the axial speed and thepacking density are all close to that of screw A, but the drawdownevenness is much improved and the particle forces along the screware consistently around half the level.

This behaviour reveals a new and important mechanism thatcontributes to the degree of uniformity of the drawdown. As theparticles are transported along the screw, they become morecompacted leading to a progressive increase in the packing density.This occurs as the initially loosely packed material is sheared bythe rotating screw leading to continual rearrangement of theparticle microstructure and increasing density. This shear inducedcompaction or densification reduces the amount of space that theparticles initially in the screw fill up and so makes space availablefor additional particles to enter the screw trough from above. Thiscompaction occurs over a distance of approximately 1–4 screwflights which is heavily dependent on the screw design. Controllingthe rate of the microstructure compaction is a potentially new wayof influencing the evenness of the drawdown. Previously, designershave expected that control needed to be exercised via the variationof the screw design along the screw length on the geometric basisof the progressive release of new volume. For screw B, thiscompaction mechanism is reasonably important.

The variation of the mass flow rate along the screw for case Cis similar in shape to that of screw B but has lesser magnitude.About 40% of the screw volume was filled in the first 50 mm. Thedischarge at the hopper exit contained more than 50% of darkblue followed by 30% red. Only small amounts of yellow andtraces of green were able to be drawdown. This is reflected in theDrawdown Index DN of 0.58, which is mid-way between screws Aand B. The axial speed variation is similar to that of screw B but isconsistently moderately higher. This leads to a packing fractionthat is again low (at around 0.44) for the initial packing of the firstflight due to the difficulty in gravity filling the compartments

between screw flights. This screw then compacts these particlesmore rapidly leading to a packing fraction of 0.57 by 100 mmwith an even higher value of 0.58 in the middle of the screw. Thedegree of packing then declines gradually over the later half of thescrew as the axial speed increases more rapidly than the massflow rate, giving a final packing density that is just slightly higherthan that of screws A and B. So for screw C, the compactionmechanism provides some modest enhancement to the evennessof the drawdown but it is much less important than for screw B.The force distribution is also very similar to that of screw B.

For screw D, the mass flow rate increases linearly over the first250 mm, with only 20% of the screw transport volume being filledin the first 50 mm. For the last 50 mm, the mass flow rate is onlymodestly increased indicating that little drawdown is occurring.They are almost the same as for screw B at the start and end of thescrew, but increase more uniformly in the middle sections indicat-ing more even drawdown. There are four colours being drawdownwith the dark blue being largest, red slightly behind and a lesseramount of yellow. There is also a modest amount of green but nolight blue reflecting the presence of the stagnant region at the endof the hopper. This distribution is very similar to that of screw B.The strong similarity of the quantitative measures for screws B andD is consistent with the strong similarities observed in the flowpatterns, velocities and forces (in Figs. 6–9). The discharge ratesgive a DN measure of 0.38, which is also comparable to that ofscrew B. The axial flow speed behaviour is similar to that of screwB, but is consistently higher. In magnitude, it is similar to that ofscrew C but the variation is more non-linear. The resultant packingbehaviour for the particles in screw D is quite different to that ofscrews B and C, with a much higher initial density and much lowerincrease along the screw. Peak compaction occurs at 150 mm andis followed by mild relaxation leading to a discharge packingdensity that is comparable to screws A, B and C. The densificationmechanism is weaker than for any other screw apart from screw A,due to the very low screw blade height above the tapered corewhich makes it difficult to loosely pack particles given the high bedpressure above. The stand out difference of screw D compared tothe earlier screws is the very high particle force (which can lead toparticle degradation and wear problems) over the first 50 mm. Theinitial forces are around seven times greater than for the otherscrews and three times that of the highest force found at anylocation for any of the other screws. The combination of large coreand negligible screw blade height means that the full weight of theparticles above is transmitted through the small number ofparticles above the screw. The transport performance is compar-able to screw B which does not have these issues.

The mass flow rate behaviour for screw E is almost the same asfor screw C, increasing quickly over the first half of the hopperand then progressively more slowly. Around 40% of the screwvolume filled in the first 50 mm. This drawdown is less uniformthan for both screws B and D. The discharge rates for the differentcolours also show very similar behaviour to that of screw C. It hasa DN of 0.56, which is again very similar to that of screw C andalso midway between screws A, B and D. The axial speed alongthe screw is, however, much higher than for screw C, being closerto that observed for screw A. This results from all the particle-blade contacts occurring at a large radius, because of the presenceof the large core, so the average screw peripheral speed is higherfor this design. The high axial speed also compensates for the lowvolume available outside the large core for transporting theparticles, leading to a mass flow rate that is very similar to screwC. Screw C has a large volume capacity and lower speed whilescrew E has a higher speed but a lower volume capacity. Thesetwo screws have a similar initial packing density and a similarpattern of variation along the screw. However, the packingdensity is consistently around 0.03 lower for this screw.


Over the second half the increase in the axial speed is strongerthan that of the mass flow, so the packing loosens leading to thelowest discharge packing density of all the screws at 0.53. Thisarises because the method of making volume available within thescrew is due to the shrinking core. This assumes that the particlesare sufficiently mobile within the screw to move inwards into thisextra space. The reduced packing fraction over the last 1

3 of thescrew indicates that this is not fully justified and that the particlesdo not have the opportunity to compact as much. This is likely tobe the result of bridging between the adjacent sections of theblade. This behaviour was not observed for screw D because thesimultaneously increasing pitch gradually increases the separa-tion of adjacent blade that turns leading to natural collapse of anyparticle arching structures. Volume release methods that makespace available at the outside of the screw appear preferable sincethe already stably packed particles closer to the screw do not haveto flow or alter their structure in order to facilitate new particlesentering the screw. So screw E is a design with some inherent riskof under-utilisation for regions near the core. This occurs despitethe generally higher particle forces that are transmitted to theparticles within the screw.

The mass flow rate for screw F increases linearly over the first200 mm of screw length and then more slowly over the next50 mm. About 20% of the screw transport volume filled in the first50 mm, which is equal lowest (and best) with screw D. This is themost uniform drawdown achieved, being slightly better than thatof screw D. The final mass flow rate is the lowest of all the screws,being around 10% lower than the other screws. The flow rates forthe first two colour bands (dark blue and red) are equal makingthis the only screw to achieve this goal. The discharge rate for theyellow is only modestly lower. The flow rate for the green is lessthan half of the earlier colours, but this is the best rate ofdrawdown of the green by any of the screws. Finally, screw F isthe only screw that was able to capture and transport materialfrom the light blue band near the exit, albeit at a very modestrate. These discharge rates give screw F a DN measure of 0.31,which is the best achieved, being modestly better than screws Band D and much better than the others. Although screw F wasintended to have uniform drawdown, according to the designrules of Roberts (2002) and gave the best performance, it is still a

0

10

20

30

40

50

50

Mas

s Fl

ow R

ate

(g/s

)

Screw Length (mm)

Screw A (DEM)Screw B (DEM)Screw C (DEM)Screw A (Roberts analytic)Screw B (Roberts analytic)Screw C (Roberts analytic)

100 150 200 250 300

Fig. 12. Comparison of total mass flow rate along the screw length from rear to fron

constant core diameter screw cases and (b) tapered core screw cases.

reasonable way from providing the desired performance. Thestagnant zone at the discharge end of the hopper is the problemwhich prevents fully uniform drawdown from occurring.

The axial speed distribution is very similar to that of screw Bbut drops off more quickly at the end of the screw. The resultingpacking fraction is moderate at 0.49 at the start of the screw andrises steadily and almost linearly along its length. This means thatthere is a steady rate of densification along the screw and thatadditional screw volume is being made progressively available asthe microstructure compacts. This is the only screw that shows anincrease in the packing fraction in the last 50 mm, which ispartially why this is the only screw to draw down particles fromthe last colour band. It has the second loosest final packing andthe lowest exit speed, which combine to give the lowest massflow rate. So there is a discharge rate penalty for obtaining theimprovement in uniformity of the drawdown. The particle forcedistribution is very similar to that of screw E. The elevated forcelevels over the first half of the screw arise from the large corediameter in this region.

7. Using DEM to inform screw design

The screw design theory makes a number of assumptions in itsformulation. To date it is not clear to what extent these assump-tions are valid or what the implications are of these not being metor only partially met. The most identifiable theoretical assump-tions include:

1)

1

2

3

4

5

Mas

s Fl

ow R

ate

(g/s

)

t fo

the motion in the hopper is vertical at all points along theentire length of the screw;

2)
the stress field in the hopper is uniform along the screw; 3) the packing density of material within the screw and trough is
constant along the screw and
4) the mass flow is controlled only by the design of the screw
geometry.

Fig. 12 shows the comparisons of the DEM mass flow rates tothe theoretical flow rates (Eq. (5)) for each of the screws. Theyare presented as two groups for clarity with Fig. 12a showing the

Screw D (DEM)

Screw E (DEM)Screw F (DEM)Screw D (Roberts analytic)Screw E (Roberts analytic)Screw F (Roberts analytic)

0

0

0

0

0

0

Screw Length (mm)50 100 150 200 250 300

r screws from the DEM simulations at 30 s and the analytic theory with; (a)


sub-group of constant core screws and Fig. 12b showing sub-group of tapered core screws. The additional information gainedusing DEM can provide insights used to inform improvement inthe theory.

�

Fig. 13. Variation of steady state power consumption and screw surface area with

screw design.

The assumption of a uniform vertical velocity leading to avertical drawdown is clearly not supported by the observeddrawdown velocities in Fig. 8. Within the hopper, there aretwo clear pathways for material to travel down and into thescrew. Firstly, there is a strong but slow circulation of particlesupwards from the front of the hopper, along the free surfaceand down along the rear wall of the hopper. Secondly, there isa preferential funnelling of particles into the screw at the baseof the hopper which involves horizontal motion of the parti-cles. These non-vertical motions are most obvious for screw A,but are also evident for all other screws including the opti-mised screw F, which still has surface flow at the hopper front.The vertical velocity also varies spatially in magnitude withstrong flow shown at the rear and stagnant zones towards thehopper front. Material is also sheared along the top of thescrew rather than being drawn down vertically from above.These non-uniform velocity distributions indicate that screwswill not be filled by vertical drawdown of material that isdirectly above. So the underpinning assumption of verticalflow is not well supported.
� The particle force was found to be spatially varying in both
magnitude and direction throughout the hopper (Fig. 9). Theseforces ranged from broad regions with larger forces for screw Ato very narrow regions of high force on the hopper wall abovethe exit for screw F. There were also high particle forces instagnant zones from which there was low or no drawdown.These are reflected in quite strong spatial variation of theparticle forces within the different screws. These ideas couldbe incorporated into the theory by having a non-uniform forcedistribution along the screw, which can weight the drawdownregions, where drawdown is inversely proportional tothe force.
� The screw packing density was shown to increase along the
screw length as the particles rearranged to produce betterpacking. This means that additional material can enter thescrew beyond that which is predicted on the basis of con-tinuum analysis of the different screw geometries. The theo-retical mass flow rates (Fig. 11) are generally lower than thosepredicted using DEM in the middle regions of the screw wherethis compaction mechanism is most important, which sup-ports the view that a non-uniform packing fraction would bebetter used in the theory.
� The theory assumes that the particle flow generated by the
screw is only within the diameter of the screw blade. However,transport of material outside the screw is also observed in thesimulations. This is most extreme for screw B where the rearblades had a clearance of 15.75 mm from the trough (slightlymore than 3 particle diameters) and where the entrainment ofparticles outside the screw was largest. In this case, there issignificant under-prediction of the mass flow rate in themiddle sections of the screw for design B. The theoreticalprediction can be improved by using the diameter of theentrained region instead of the outer diameter of the screw.

8. Power draw

The power draw of any process equipment is an importantdesign consideration. It is important from both the perspective ofgiving the best energy efficiency for the system and from theperspective of particle degradation and equipment wear with

more energy consumed by the system leading to worse wearoutcomes. Power consumption on the screw can be calculated inDEM simulations as the product of the screw rotation rate and thenet torque applied to the screw by all the particle contacts. This isdescribed in Cleary (2001). Fig. 13 shows the power consumptionfor each screw. Rating the screws by total power draw, screw Bhas the lowest power draw, with screw F only slightly higher.Screws E, C and D show progressively higher power draw. ScrewA, the standard screw, has by far the highest power draw. Thiscoupled with the worst drawdown behaviour makes the standardscrew a poor choice for most applications. The power draw isclearly highly influenced by the screw design. This is illustratedby screws B, D and F having similar drawdown patterns buthaving substantially different power draws.

Particle interaction with the screw surface is an importantcomponent of the energy dissipation and controls the energyinput into the particles and their mobilisation. The area of thescrew interacting with the particles could influence the degree ofenergy transfer to the particles. To assess whether the screwsurface area is a relevant consideration in screw design, correla-tions between the power draw and screw surface area wereinvestigated. Fig. 13 also shows the total surface area of thescrew for each design. It is clear that there is no correlationbetween surface area and power draw. There are in fact largedifferences. For example, while screw B has the lowest powerdraw and the lowest surface area, screw C has the highest surfacearea but draws only a mid-range amount of power. Screw A hasby far the highest power draw of all the screws, yet has only amid-range surface area.

9. Abrasive screw wear

In a shearing environment such as around the screw in a screwfeeder, the damage to the surface is predominantly from abrasion.Higher wear leads to higher maintenance costs and more frequentreplacement. It is therefore important to understand the distribu-tion and strength of the wear. The rate of abrasive wear isproportional to the rate of energy absorption by each part of asurface by particles sliding over it. The method for calculating thisis described in Cleary (2001). Fig. 14 shows the distribution ofabrasive damage along its length for each screw design. The backof the hopper is on the left and the particles exit into the screwcasing on the right. For all screws there was a consistent trend ofhigher abrasion on the outside of the screw blades at large radiidecreasing towards the core. This was due to the higher contactvelocities that increased radially away from the screw core. Allscrews also showed increasing abrasive damage where the

Screw A Screw D

Screw B Screw E

Screw C Screw F

500 -105 -

21 -4 -0 -

500 -105 -

21 -4 -0 -

500 -105 -

21 -4 -0 -

500 -105 -

21 -4 -0 -

500 -105 -

21 -4 -0 -

500 -105 -

21 -4 -0 -

FrontRear

Fig. 14. Shear power density (W/m2) as a measure of abrasion for each screw design. The rear and front of the screw are indicated for screw A. The wear increment is

measured over 30 s of operation.


particles exit from the hopper and enter the screw casing. This isconsistent with the hopper force distribution in Fig. 9, whichshows increasing particle force above the screw near the exit forall screws. There were also screw specific wear variations,specifically:

�
screw A has increasing abrasion along the screw from left toright. There is wear on both the blades and screw core alongthe entire length. This is consistent with the increasing particleforce in the hopper and the increasing particle force within thescrew; � screw B has low wear over the first three flights and then high
wear on the last two. This is consistent with the particle forceand packing density slowly increasing along the screw length.When the blade is short its edge radius and therefore edgespeed are lower so the slip velocity between particles and thescrew blade is smaller leading to lower wear. As the bladeincreases in height, the wear on its outer sections thereforeincreases;
� screw C shows a similar pattern of wear to screw A, but with a
lower rate of increase. This is consistent with the lowermonotonic rate of increase in the force applied to the screwby the particles.
� screw D has very high wear on the first screw flight and last
screw flight at the exit of the hopper and a low wear rateunder the middle of the hopper. The screw clearance betweenthe screw and trough at the extreme rear (left) just matchesthe particle size so particles are likely to be jamming in the gapleading to very high particle force at the extreme rear (morethan six times that of the other screws). This rear region is themain contributor to the high power draw for this screw;
� screw E has fairly uniform wear along both the screw blade
and the core with a slight reduction after the second flight near

150 mm of screw length, which corresponds to a weak mini-mum in the particle force on the screw and
� screw F shows higher wear on the flights whose height is
comparable to or higher than one particle diameter and thendecreases moderately with distance along the screw. Towardsthe exit there is a slight peak in wear. The low wear on theearly flights is due to the particles poorly engaging with andflowing over the blade rather than being pushed along by it.The high wear corresponds to the location of the highestdrawdown as the screw blade properly engages the particlesand accelerates them. The lower wear on the second half of thescrew arises from the lower particle pressure applied there.

10. Influence of screw surface friction for an optimal screw

The screw surface friction coefficient, fs has been reported asan influential parameter in the conveying efficiency. Due to itsaffect on the rotation of the bulk material in the conveying zone,it also influences the mass flow rate (Roberts, 2002). Screwsurface friction can be reduced by choosing the most appropriatewall material in the design phase based on laboratory data, andsubsequently by polishing the screw. Many screws ‘‘self-polish’’during use resulting in a reduction of power consumption,however, for some critical applications the flight may be polishedprior to use. In some applications, where the bulk material iscorrosive, the screw friction coefficient can also increase and behigher than the wall friction. Understanding the extent of influ-ence that screw surface friction has on mass flow rate anddrawdown can help to understand the effect of screw polishingand corrosion. Since screw F had the best performance, we usethis case in investigating the effect of screw surface friction.

Fig. 15. (a) DEM mass flow rates at different locations along the screw for screw F; (b) axial particle velocity and; (c) particle packing fraction for increasing screw face

friction, at 30 s.


Fig. 15a and b shows the mass flow rate and the axial velocityalong screw F for screw surface friction values of fs¼0.364 (thebase case—equal to a 201 wall friction angle (wfa)), fs¼0.164(lower friction—9.51 wfa) and fs¼0.564 (higher friction—

29.51 wfa). Increasing the friction coefficient marginally decreasesthe flow rate in the first half of the screw length by 4%. From themiddle of the screw the decrease is larger with a peak reduction of7%. The axial velocity is the same for the first 100 mm, but is veryslightly lower for the remainder of the screw. The decline in themass flow rate is higher than that of the axial velocity which meansthat the packing density of the particles (see Fig. 15c) within thetrough is moderately and fairly uniformly reduced by around 0.015.This arises because the increased surface friction restricts the degreeof rearrangement of the particles during the shearing that helpscompact the material in the screw as it is transported along. Thefriction increase also leads to a four times increase in power draw(from 2.2 to 8.8 W). So, whilst the flow changes are small there is asignificant increase in power draw for increasing surface friction.

Reducing friction however, leads to much stronger increases inthe mass flow rate along the entire length of the screw, up to 40%in the first flight and 25% at the exit. The axial velocity increasesalong the screw length, but less strongly particularly in the last100 mm. The initial packing fraction of 0.5 at 50 mm is the sameas for the intermediate friction value. However, the degree ofpacking increases more strongly over the next 50 mm andincreases further to a peak packing density of 0.565 after whichit remains constant. This means that there has been significantlymore compaction of the particles being transported along withinthe screw. This is due to the particle contacts on the screw beingable to slide more easily allowing more re-arrangement andtherefore more densification of the microstructure. The powerdraw also decreases sharply to a quarter of that of the base case(from 2.2 W down to 0.55 W). So reducing the screw face friction

strongly reduces the power draw and significantly increases thedegree of compaction leading to an increased mass flow. Thisexplains how reduced friction produced by regular screw polish-ing leads to the observed reduction in power consumption as wellas improvements in the rate of drawdown by the feeder.

Fig. 16 shows the influence of screw face friction on drawdownpattern and velocity in the hopper for friction values of 0.164 and0.364 (the base case). The high friction case showed only subtlechange to the base case and is therefore not shown. The mostnoticeable difference is that at low friction the high speed regionat the rear extends further towards the free surface and to theupper right. The vertical drawdown velocities are also higher overthe full length of the screw reflecting the increased mass transfercapacity of the low friction screw. This is also reflected in thedrawdown patterns for the vertical bands. For a friction of 0.364the vertical bands remain roughly vertical but for friction of 0.164there is a modestly faster drawdown of the first two colour bands,leading to a more inclined free surface, which leads to moreslumping of the green and light blue bands. At low friction thereis also increased shearing of the material along the top of thescrew. This is most noticeable for the red and yellow bands.

Fig. 17 shows the effect of the screw friction on the differentcolour band flow rates for screw F. Lower friction not only increasesthe total mass flow rate but increases the percentage of the first twobands measured at the discharge. This is consistent with the higheramount of dark blue and red particles being entrained along the topof the screw in Fig. 16. The Drawdown Measure (DN) is now 0.38(22% worse than for the base friction case), scoring worse than screwB and the same as screw D in terms of drawdown evenness. So whilea lower friction has increased the mass flow rate by allowing morematerial to enter the screw, it has reduced the uniformity of thedrawdown because the compaction mechanism operates much morequickly as so that all the additional volume arising from densification

Screw F (friction = 0.364)

5.0 -3.6 -2.5 -1.2 -0.0 -

Velocity (mm/s)

Screw F (friction = 0.164)

5.0 -3.6 -2.5 -1.2 -0.0 -

Velocity (mm/s)

Fig. 16. (a–b) Hopper particle velocity and (c–d) drawdown pattern for screw face friction coefficients of (left) 0.364 and (right) 0.164, all at 30 s.

0

4

8

12

16

20

Mas

s Fl

ow R

ate

(g/s

)

Screw F Friction

Dark blue Red Yellow Green Light Blue

0.167 0.367 0.567

Fig. 17. Screw F strata colour mass flow rates for varying screw face friction, as

measured in the DEM simulation when discharging at the exit of the hopper

trough after 30 s.


is made available in the first third of the hopper. Increasing frictionreduced the mass flow rate only slightly and led to only slightchanges in the proportions of the first three bands, giving anunchanged Drawdown Measure (DN) of 0.31.

11. Conclusions

Evaluating the six screws based on the uniformity of draw-down of each colour band and power usage placed screw F

marginally first. It showed the most even drawdown and powerdraw across all screws. Screw B was a close second in terms ofdrawdown, but was observed to take longer to transport particlesaway from the hopper rear due to a small blade diameter. Screw Bprovided the lowest power draw for a similar drawdown to theoptimised screw F. This would lead to lower wear and mayprovide operating cost savings. Screw D was third providing asimilar drawdown to screw F, but had nearly twice the energyconsumption. This screw could therefore have higher operatingcosts and shorter screw life. At fourth and fifth were screws E andC, respectively. They exhibited similar draw from the rear, but Eused 18% less power than C. Screw A performed the poorest withno drawdown from the front 60% of the hopper and had thesecond highest power draw.

This study demonstrates the use of DEM to inform screwdesign choice through analysis of particle movement, regionspecific mass flow rates, power draw, wear patterns and frictionalinfluence. DEM can assist with matching screw designs withspecific bulk materials to enhance control of the drawdown.Complex spatially varying particle flow and force patterns controlperformance and DEM shows how these contribute to the finaldischarge measured as well as to power draw and screw wear.

Within the hopper, two clear particle drawdown pathwayswork to make material available to the screw. The dominantparticle transport involves particles flowing along the free surfacestarting at the front of the hopper towards the rear hopper,downwards along the rear wall in a mobilised flowing zonewhose shape depends on the screw design and then into thescrew. For some screws there is a weaker slow slumping flow asthe particle bed deforms with material migrating slowly throughthe middle of the hopper back towards the down flow region.With screws that are designed with additional volume along the


screw length, the vertical drawdown region extends further alongthe screw. Vertical drawdown was strongest at the rear and thereare regions of stagnant flow near the hopper front above the exitto the screw casing. This was still observed with the optimisedscrew (screw F) even though this design should have theoreticallyproduced uniform draw down. The flow in the screw entrainsparticles in the trough and in the bottom of the hopper. Theseentrained particles that are above the exit are pushed into thefront wall of the hopper and forced upward to complete a hopperwide recirculation. The degree of recirculation is highest for screwA and is dependent on the screw design.

All screws showed some degree of stagnant flow and highparticle force at the front wall of the hopper above the exit. Itsextent depends on the screw design and how much additionalvolume for drawdown is made available along the screw. Forthose screws that have less available screw volume then the highforce stagnant region is broader. For those screws that havegreater screw volume available along the screw length the highforce stagnant regions are narrow. Blade heights less than aparticle diameter are inefficient at generating transport. So screwblades of varying height (whether because of variable bladediameter or variable core) are ineffective in their early stages.

A new mechanism based on the compaction of the particleswithin the screw was identified which contributes to progres-sively making screw volume available along the screw length.Compaction occurs as the rotating screw shears the particlesleading to steadily increasingly density of the packing. When theparticles were packed close to maximum early in the screw thiswas linked with higher particle force. In contrast, screw designsthat gradually increased the particle packing produced lowerparticle forces that gradually increased towards the end of thescrew. This mechanism provides an additional control that canpotentially be exploited to improve drawdown and reduce parti-cle forces. It also means that if compaction is not properlyconsidered in the design, then screws can function more sub-optimally. Analytic theory normally considers the density to beconstant in the trough and so ignores this mechanism.

Power draw was found to vary substantially for screws thatproduced similar drawdown patterns and the variation was foundto not correlate with the screw surface area.

Abrasive wear was found to be influenced by particle force(related to packing fraction), particle slip velocity along the screwand the screw blade height and clearance with respect to particlesize. All screws showed a gradual increase in wear consistent withthe increase in particle force along the screw from the rear to exit.Wear was highest at the exit consistent with particle build-up andhigh forces above the exit. Wear was also high on the outer bladeof the screws due to increased contact velocity at larger radiiaway from the core. Screws designed with blade height less thanone particle diameter gripped particles less effectively producingless slip velocity and hence less wear. One screw design showedincreased wear due to the particle size being larger than thescrew clearance and jamming.

Reducing screw friction for screw F increases the total massflow rate along the screw length and at the exit to the screwcasing. This is partially due to reduced friction allowing theparticles to slide and pack better within the screw. The uniformityof drawdown deteriorates moderately. There is increased material

entrained along the top of the screw and significantly reducedpower draw. Conversely, higher friction leads to slightly lowermass flow rates, does not affect the evenness of the draw down,but sharply increases the power draw.

The standard analytic method showed subtle variations fromthe DEM results based on the assumptions of vertical drawdown,constant packing fraction and flow only influenced by bladediameter. In general, flow along the screw middle was slightlyunder-predicted by the analytic model, which did not take intoaccount the increased potential screw volume created byimproved particle packing. For the simple screw, the analyticmodel over-estimated the flow at the rear by assuming that alldrawdown occurs at the rear, while simulation shows that thisoccurs over the first flight. The analytic method underestimatedthe flow for screws which had small blade diameter and largeclearance. DEM showed that shear flow around the screw adds tothe total flow rate and is not accounted for properly for thesedesigns. Overall, the analytic method provides a reasonably goodestimate of flow rate for most screws justifying its usage. How-ever, DEM predictions can be used to improve these flowestimates by incorporating into the theory the influence of non-uniform drawdown velocity and force, increased particle packingand the geometric influence of the entrained hopper diameter asopposed to just the screw diameter.

References

Bates, L., 1969. Entrainment patterns of screw hopper dischargers. ASME Journal ofEngineering for Industry, 295–302.

Cleary, P.W., 1998. Discrete element modelling of industrial granular flowapplications. TASK. Quarterly Scientific Bulletin 2, 385–416.

Cleary, P.W., 2001. Recent advances in DEM modelling of tumbling mills. MineralsEngineering 14, 1295–1319.

Cleary, P.W., 2004. Large scale industrial DEM modelling. Engineering Computa-tions 21, 169–204.

Cleary, P.W., 2007. DEM modelling of particulate flow in a screw feeder. Progressin Computational Fluid Dynamics 7 (2–4), 128–138.

Cleary, P.W., 2009. Industrial particle flow modelling using discrete elementmethod. Engineering Computations 26 (6), 698–743.

Cleary, P.W., Sawley, M., 2002. DEM modelling of industrial granular flows: 3Dcase studies and the effect of particle shape on hopper discharge. AppliedMathematical Modelling 26, 89–111.

Marinelli, J., 1996. Choosing a feeder that works in unison with your bin. Powderand Bulk Engineering 10 (12), 43–57.

McBride, W., Cleary, P.W., 2009. An investigation and optimization of the ‘OLDS’elevator using discrete element modeling. Powder Technology 193 (3),216–234.

McBride, W., 2011, Private Communication.Owen, P.J., Cleary, P.W., 2009. Prediction of screw conveyor performance using the

discrete element method (DEM). Powder Technology 193 (3), 274–288.Owen, P. J., Cleary, P.W., McBride, B., 2003. Simulated granular flow in screw

feeders using 3D Discrete Element Method (DEM). CHEMECA 2003, 31stAustralasian Chemical Engineering Conference. isbn:0-86396-829-5.

Roberts, A.W., 2002. Design and performance criteria for screw conveyors in bulksolids operation. Bulk Solids Handling 22 (6), 436–444.

Roberts, A.W., Manjunath, K. S., 1994. Volumetric and torque characteristics ofscrew feeders. In: Proceedings of the Powder and Bulk Solids Conference,Rosemont, USA, pp. 189–208.

Roberts, A.W., Manjunath, K.S., McBride, W., 1993. The Mechanics of Screw FeederPerformance for Bulk Solids Flow Control, Vol ME18 #1. Transactions ofMechanical Engineering, Institution of Engineers, Australia.

Roberts, A.W., Willis, A.H., 1962. Performance of Grain Augers. Proceedings of theInstitution of Mechanical Engineers, London 197 (8), 67–73.

Shimizu, Y., Cundall, P.A., 2001. Three-dimensional DEM simulation of bulkhandling screw conveyors. Journal of Engineering Mechanics 127, 864–872.

Yu, Y.,, Arnold, P.C., 1996. The influence of screw feeders on bin flow patterns.Powder Technology 88 (1), 81–87.

isbn:0-86396-829-5

effect of screw design on hopper drawdown of spherical particles in a horizontal screw feeder

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