THE DETERMINATION OF THE ANGLE OF FLOW OF SMELTER GRADE ALUMNA

T.K. SmithPrincipal Scient ist - Bauxite and Alumina

COMALCO ALUMINIUM LIMITED12 Creek Street,

Brisbane, QLD.4000AUSTRALIA

ABSTRACT

The unsatisfactory nature of the traditional "angle of repose" test in predicting the flow propertiesof smelter grade aluminas has been recognised. A simple method has been developed to measure

the angle described by residual material in a container from which alumina has flowed. The"oangle of flow" of an alumina may be regarded as complementary information to the time of

flow from a standard flow cone. The "angle of flow" is useful in understanding the behaviourof alumina in materials handling systems. An additional benefit of the procedure is that the bulk

density of the alumina is determined at the same time. The method is under consideration for

issue as an Australian standard.

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THE DETERMINATION OF THE ANGLE OF FLOW OF SMELTER GRADE ALUMINAI

T.K. SmithI

1.0 INTRODUhCTION

The flow properties of alumina are important, in predicting its behaviour in materialsI

handling and transfer systems. The traditional test in the alumina industry over many

years has been the familiar "angle of repose" determina tion, where the slIope angle of aIheap of alumina of a fixed height is measured (Tergaghi in Carr, 1965). This method hasbeen criticised by many workers, for example, Hsieh (1987) who considered that the"tangle of repose" represents the state of the bulk powder under static equilibrium whileflowability is related to the dynamic condition. However, from the point of view of theanalyst obliged to use the procedure, the most serious objection to the angle of reposetest is its lack of sensitivity, particularly when applied to the modem, sandy type ofsmelter grade aluminas. Aluminas of demonstrably different flow properties may exhibitangles of repose which differ by only a few degrees. Angles of repose are normally inthe range 30 - 33 degrees. When the precision of measurement is taken into account, theIdifferences may be scarcely significant.

Other procedures have been developed to give broader expressio n to the flow propertiesof a powder than the angle of repose. Carr (1965) mentions an ill-defined "angle of

spatula" test. Hsieh (1987) reported on the development of a test which relates flowabilityto the time taken for alumina to flow from a precision-made, calibrated "flow cone".

Roach and Reid (1988) have performed a comprehensive evaluation of this latterprocedure.

The method presented here has been designed to consider a powder under conditions of

free flow; and where particle to particle interactions are maximised.

The particular property measured is the angle of the funnel--shaped depression, after the

alumina has stopped flowing.

The procedure may be seen as providing complementary information to other testsdesigned to measure flowability. The method is under consideration for publication asIan Australian standard (DR 892 16:R, 1989). Since the method specifies an apparatus ofdimensions somewhat arbitrarily decided by this writer some time ago, it was decidedIto investigate the effect of vessel ("flow cup") dimensions on the "angle of flow"

determined on a range of commercial smelter grade aluminas.

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2.0 DEEINrIIN

The angle of flow of a powder such as smelter grade alumina is defined as the angle

described by the base of a flat-bottomed funnel (a "flow cup") and the slope of the residualmaterial in the funnel after flow of the powder has ceased.

3.0 PRINCIPLE

Alumina is poured into the flow cup under conditions of substantially constant flow and

from a fixed height. After levelling the alumina to the top of the cup, it is allowed to flowthrough a circular hole in the bottom. After the flow has ceased, the angle of flow maybe calculated fr-om the mass of material remaining in the cup; and the dimensions of thevessel. An estimate of the bulk density of the powder may also be made without additionalmeasurement.

4.0 APP~ARATUS~

4.1 Flwcu~

Eight flow cups were fabricated from aluminium. Dimensions of the cups arelisted in Table 1. Each cup was provided with a 4 mm diameter hole in the base.

Table 1Dimensions of flow cups

IInternal Diameter Internal Height Nominal VolumeMM MM Volume din3

72.56 72.55 0.300

72.56 145.10 0.600

91.46 91.41 0.600

72.46 217.65 0.900

104.64 104.65 0.900

108.40 108.36 1.000

72.56 290.02 1.200

115.18 1 115.17 11.200

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4.2 Assembled Apparatus

A schematic of the assembled apparatus is illu0stiated in Figure 1.

H

Figure 1: Schematic of AngleOf Flow Apparatus

5.0 UTfI~Q1LINE

Figure 2: Relevant Parameters

in calculation of

"'Cup Costnt

The top of the flow cup is adjusted to the horizontal with a spirit level.

With a finger or small stopper Obstructing the hole of the tup, a sample of the alumina

under test is poured into the cup Via a filling funnel and flow control funnel located under

Sufficient alumina should be taken to just overflow the cup. A sttaight edge is used tolevel the alumina with the top of the cup, taking card not to compact the alumina.

The edges and surrounds Of the cup are carefully brushed free of alumina, and a taredbeaker is placed under it,

The hole of the cup is uncovered, And the alumina allowed to flow into the beaker.

When the flow has ceased, the sides of the test cup are very lightly tapped with the

rubber-damped stick until no more material flows.

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IIIIIIIIIIIII1UIIUII

The mass of alumina collected in the beaker is determined as "rn" grams.

The residual amount of alumina is then poured into the same beaker, and the total amountweighed as "M" grams. This mass is of course, the total amount of alumina present in

the test cup at the beginning of the experiment.

The angle of flow, ot degrees, is calculated from the formula:

M -M.tanax=

MC3R 2H

2R3-R 2r +r 3 (1)

Where: R =internal radius of flow cup, mmnr = radius of hole at bottom, mmnH =height of cup, mm. (Figure 2)

It is clear that for any given cup, R, r and H are constants, and thus the expression

~3R 2 H is also a constant; a so-called "cup constant":

Thus only two determinations of mass are needed to find the flow angle of the sample.

A derivation of the formula required to calculate the flow angle is given in Draft Australian

Standard DR89216:R (1989). The bulk density D of the sample may also be calculated

fromM

6.0 ALUMINAS UNDER TEST

(2)

Samples of alumina were kindly supplied by one European and two Australianmanufacturers of smelter grade alumina. In total, seven different samples were tested.Two manufacturers supplied samples of alumina from the same works calcined in rotarykilns and stationary calciners.

Particle size distribution and specific surface area analyses were carried out at the

University of New South Wales, Australia.

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Table 2

Sample Origin and Specific Surface Areas

SAMPLE SPECIFIC SURFACE* CALCINER TYPE

IDESIGNATION AREA M2G

1 51.4 +1.4 ROTARY KILN

2 57.4 +0.5 STATIONARYCALCINER

3 67.2 (average of two ROTARY KILNdeterminations)

4 74.3 (average of two STATIONARY

determinations) CALCINER

05 45.2±+1.2 STATIONARYCALCINER

6 58.0 ± 0.3 STATIONARYCALCINER

7 51.4±+0.7 STATIONARYCALCINER

*BET Single-point measurement

7.0 EXPERIMENTAL

7.1 Sample preparation

All samples were passed through a 300 urn mesh sieve to remove sintered

aggregates and spalled refractory. Small representative samples were taken forparticle size and specific surface area analyses.

7.2 Angle of flow determinations

The determination was performed generally at least five times on each of the

seven samples in each of the eight cups. The time taken for the flow to cease

was recorded. The angle of flow was also calculated at this juncture. However,

it was frequently noticed that the surface of the funnel shaped residue was uneven

and unstable. A very light tapping with a rubber-damped rod would release alittle more material, and a relatively stable residue resulted. Angles of flow before

and after tapping were calculated. However only angles of flow obtained aftertapping are reported and discussed here. Untapped bulk densities were also

calculated in each instance.

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II1IIIIIIIIIIUUIIIII

8.0 R.ESULTS

Flow angles measured in cups with constant height to diameter ratios (H/D =1) were

shown to be substantially constant (Figure 3) with only slight increasing trends evidentin some cases.

45

40

ANGLE OF FLOW AS A FUNCTION OF FLOWOUP VOLUME(HEIGHT/DIAMETER - 1)

ANGLE OF FLOW. DE-GREES

0.3VOLUME OF FLOWCUP. D

r3

1.2

Figure 3

Figure 4 shows the effect on the flow angle on increased vessel height (at constant vessel

diameter).

45

40

FLOW ANGLE: EFFECT OF VESSEL HEIGHTAT CONSTANT DIAMETER

ANGLE OF FLOW, DEGREES

so 100 ISO no0

VESSEL HEIGHT, MMFigure 4

4

2IS

2-10 "D0

The general increasing trend observed in the angle of flow is probably due to a

corresponding increase in the untapped bulk density of the alumina, (Figure 5), caused

in turn by a denser packing of the powders in the taller cups.

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.4-.. . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . .

. ........ .........-4 4 ........

EFFETd br INTERNAL VESSEL HEIGHTON UNTAPPED RULk DENS§ITY

UNTAPPEDj bULK DENSITY kG M- -- # 7

........... ......... ... .. ... .. ...

...0.... .......................

.... .. .. .. ..... .. ................. ... .

073

040 . .. .. .. .. .

60

FigureS

16 '6 6

INTERNAL VESSEL EIGHT, MM260 300

As shown in Figure 4j differences in flow angles were mnost tlearly expresse6d When

detrmined in the tallest cups. Results from these vessel have been chosen for illustration.

The anigle of flow of the sandy alumina tested here appears to be sttongly related to the

fines contents of the poWders.

Figures 6A and 6b illustrate the strong linear relationships existing between flow angles

and the <45.8 urn fraction of the aluminas.

FLOW ANGLES (TAPPED) VS VOLUME % <45.8umFlo Ct* fuhme 0.00di

46.Sum DX -72.8*;17.7mrm Flo vohn*;i - .200 dii?% .40.um 0 X' H72.0m20.0nim

r 0.07

......................4.. .. 4......................... ... . ..... .. ........... ..............

FLOW.. .. ... .ANGL .......E... E. RE....OW.ANGLE.............E.~1 0 . . .. . . .. . . .. . . .. . . . .. . . .. . . .. . . .. . . .

Table 3 demfonistrates that strong linear relationships Actifflly exist for particle size

fractions in the range 39.5 to 71.4 urn.

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Fl~m @(a)

IIIIIUUIIIUIIIa1IIII

Table 3

Correlation between angle of flow and cumulative volume percent in particle size

fractions

FRACTION, urn CORRELATION COEFFICIENT, r

CUP SIZE, din3

0.900 1.200

39.5 0.980 0.958

45.8 0.97 1 0.930

53.0 0.977 0.928

61.6 0.975 0.940

71.4 0.907 0.899

The tenth percentile of the particle size distribution may also be used to evaluate the

effect of fines in the alumina on the angle of flow. This is the particle size under which

ten volume percent of the particles may be expected to lie. Figures 7a and 7b show the

linear relationship existing between angles of flow and the tenth percentile. It may be

noted that stronger correlations may be determined if exponential relationships are

assumed to exist.

FLOW ANGLES (TAPPED) VS TENTH PERCENTILE

OF PARTICLE SIZE DISTRIBUTION

40 4S As 435 d d l d 44 484 6d 4? 494 0 Be

FLOW ANGLE (TAPIPED) DEGMlEFloure 7(m)

so

70

so

so

40

Flow cup volume - 1.200 drd0 X H .?2. Sx 2900 0,,,,O(VO. I

38 30 Si SI 39 40 41 42 43 44 40 44 4? 49 49 80

FLOW ANGLE (TAPPED) DEGREESFlgNO 7(b)

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0-.92

.. ... . .P.. . . .. . . . .. . . ..I.. . .. . . .. . I. .. . .

0

The rate of flow of alumina from the test cups may also be correlated with the fines

content of the alumina, as illustrated in Figures 8a and 8b. In the taller cups, the residue

after the flow has stopped comprises relatively small proportion of the total volume.Differences in the flow angle will only have a minor effect on this volume; and so for

practical purposes, the volume of material flowing during the test is more or less constantfor sandy alumina types.

FLOW RATE VS TENTH PERCENTILEOF PARTICLE SIZE 0STIU AEVSVLM %cdu

0(V) 0.1 Flwcpvoue.0.06f

<20 .u 0 07.83 x1.7m

40 .. . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . .

1,0 OS 16 .8 le IA 170 01 - 1.4 LW. AE0J 1.0 1.

9.0 121SCUJSSION3

9.1 Flow cup dimnis

The method as originally conceived used a flow cup of volume 0.300 din3 withIdimensions diameter = height = 72.6 mm. The draft method under evaluation by

Standards Australia specifies a vessel of these dimensions. However, for today'sI

high quality aluminas, flow angles determined using'a vessel of this size are

probably insufficiently different to express real differences in the flow properties.I

It has been observed that vessels with a greater height/diameter ratio not only

give slightly higher angles of flow, but also a greater spread of results. The higherI

angles of flow are probably influenced by the increased packing, as witnessed

by the increases in the bulk densities of the aluminas tested. The 0.900 and 1.2001

din3 Vessels both showed a good spread of results.

9.2 Relationship between flow angle and particle size distribution

The demonstrated strong relationship between angle of flow and the quantity of

fines in the alumina under test suggests that this procedure is less sensitive to

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other parameters, such as particle morphology, which may be expected toinfluence flowability. The aluminas under test were either of different

manufacture, or calcined in different types of kilns.

If factors such as particle shape or surface roughness were to play a significantrole in determining the angle of flow, then the use of aluminas of different originmay have been anticipated to have accentuated the importance of these factors.

The strong reliance of the angle of flow on the fines content of the aluminasuggests that this determination may be used as a simple field test to checkalumina quality. The ability to determine the untapped bulk density on the same

sample adds to the usefulness of the test.

It is possible that a closer correlation between fines content and angle of flowmay be obtained with aluminas from a single source.

9.3 Observation of flow Patterns

After uncovering the aperture, and the alumina begins to flow, the smooth,levelled surface remains undisturbed for a few seconds. A small, flat, circular

depression then appears, which gradually broadens and deepens to form a funnel.

During formation of the funnel, complex patterns in the flowing sides are often

observed. It is considered that the flow from the vessel does not initially involvethe bulk of the particles. A small cavity above the aperture forms, which thenrises as a bubble-shaped cavity. The movement of the cavity through the massof the powder is marked by the continual collapse of powder into it from above.This phenomenon is illustrated in the photographs taken of alumina flowing forma perspex "sandwich" model (Figures 9a and 9b).

Brown and Richards (1960) have studied the flow of particles through apertures.They observed that the main movement of particles takes place in

a trumpet- shaped" region above the aperture (a "vena contracta"). The venacontracta. is readily observed in Figure 10.

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Figure 9(a)

Flow of alumina commencing from

perspex "sandwich' model. Note

upward movement of cavity.

Figure 9(b)

Alumina flow fully established. Note"tvena contracta" and angle of flow at

top.

Other phenomena described by Brown and Richards (1960) have been observed

in experiments with the flow cups. For apertures above certain critical diameters

(dependent on the particle size distribution of the particles) the particles will fall

from the cup through a region of smaller diameter than the aperture itself. There

is an annular "dead space" through which relatively few particles flow. This is

revealed in the tendency of the stream of falling powder to narrow or "focus"

some distance below the cup.

The presence of dilatant waves observed by Brown and Richards (1960) in the

moving mass of particles has also been inferred by a ripple effect observed on

the surface of the flowing alumina in some instances.

As well as quantitative results, careful observation of alumina flowing in the cup

can provide valuable qualitative information.

10.0 CONCLUSIONS

The angle of flow determination provides information about the flowability of alumina

which is complementary to that obtained from other procedures.

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.~ . ... ....

IIUIIIIIIIUIU'IIIIIII

The angle of flow is strongly related to the fines content of the alumina. The sub - 45

micrometre content, and the tenth percentile of the particle size distribution are convenientindicators of the fines content. The method may be used to determine particle size

distribution over a limited range.

The dimensions of the angle of flow vessel in the method under consideration by

Standards Australia are probably not ideal. A tall vessel, between 0.900 and 1.200 din3

capacity would permit a greater expression of differences in flowability, as determinedby the angle of flow. A vessel of 1.000 din3 would allow coincident determination ofuntapped bulk density under close to standard conditions.

11.0 AC~KNOQWLEDGiMENTS

The permission of Comalco Aluminium Limited to publish this work is gratefully

acknowledged.

Queensland Alumina Limited, Eurallumina S.p.A., and Alcoa of Australia Limited, forkindly supplying the samples. Mr Michael Scott, University of Queensland performed

much of the arduous experimental work, and made valuable comments.

Mrs Jan Noakes, Ms Caroline Levinson and Mr Simon Barker for their assistance in theproduction of this paper.

12.0 REFERJENCES

Brown, R.C., Richards, J.C., Profile of flow of granules through apertures. Trans. Instu.

Chem. Engrs. 38 (1960) pp 243-256

Carr, R.L., Evaluating flow properties of solids Chemical Eng2ineering - January 18, 1965pp 163-168

Draft Australian Standard DR 8921 6:R, (1989)

Hsieh, H.P. Measurement of Flowability and Dustiness of Alumina, Light Metals 1987,pp 139-149

Roach, G.l.D.,.Reid, G., Flowability of Smelting Grade Alumina, Proceedings. Alumina

Quality Workshop. Gladstone (1988) pp 186-196

Tergaghi and Peck, "Theoretical Soil Mechanics in Engineering Practice" Wiley. NewYork. 1948

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