Conveyor Torque&Differential

8/13/2019 Conveyor Torque&Differential

1/6

In the second article in a series on Dry Solids decanters,N Corner- Walker, Alf L aval, USA, and F A Records,formerly of

Alfa Laval, UK , discuss the impact of conveyor torque anddgerential on cake dryness.

t has been shown [l] that the decanter centrifuge canachieve high dryness in its discharged cake, when operatingin DS (Dry Solids) mode. Scaling of a decanter in this statefrom one size to another is determined, at least in part, by a

jj cake compaction factor. The DS decanter differs from thestandard decanter in a number of ways, and the impact of the maindifferences on the achievable cake dryness is discussed in this article.

Cake Dryness Conweyor TorqueThe dryness of compres sible cakes produce d by decante r cen-trifuges can be significantly better than that achieved by a simplebottle spin centrifuge [ 21. Thi s 1s so even if the bottle spinner isoperated at the same g level and liquor level as the decanter, andfor an i&-rite time. It is apparent that the movement of the con-veyor in the decanter is, by some means, able to enhance the dewa-tering mechanism.

With this knowledge, some ten years ago, a range of decanters wasintroduc ed into the market to produce extra dry cakes, with drynessesin the order of twice that achieved by the bottle spinner. These DrySolids decanters generally for etlluents, are distinguished from star-dard e ffluent decanters by the way they are built, the way they are setup and the way they are controlled.

The scrolling torque required for the conveyor is proportionalto the cake dryness produced by efluent decanters [ 3 1. However,as far as we are aware, it has never been published as to how thistorque/dryness relationship is translated from one size ofdecanter to another. It is the object of this article to remedy thisomission.

The Dry So lids DecanterConsider the schematic diagram of the decanter shown in Figure 1.Feed enters the decanter at D and separates into a liquid whichdecants at C, and a cake which is scrolled under a restriction at Athen up the conical beach to be discharged at B. The conveyor withflight pitch P scrolls the cake against a torque T, while the liquidflows through a clarifying distance, often equal to the cylindricallength of the bowl, L.

The restriction is an important feature and may take one of anumber of forms. Some manufacturers utilise a variable cant to theflight to form the restriction and at the same time knead the cake.Others use a change of pitch to provide a back pressure on thecake. In its simplest form the restriction can be a disc or cone tocreate an annular restriction. In some designs the level of liquor inthe cylindrical part of the bowl is set above the level of the cake

discharge to afford assistance with the

18 OcWber2000

scrolling by virtue of the resultanthydraulic head.To compare the performance oftwo decanters, both centrifugesshould be operated at the limit of theirDry Solids performance, when thedecanters will be virtually full of cake.

The torque developed by a decantercentrifuge (T) has a number of com-ponents including:

the torque necessary to convey thecake and overcome the frictioninvolved (TC);


2/6

the torque necessary to lift the cake from the bowl wall to the dis-charge diameter (TL); and the torque needed to accelerate thefeed to the bowl speed (TA) .

These torque components can be, to a limited extent, offset by aseparate component (TP), which is created by the pressure differ-ential between the front an d back of the scrolling surfaces whenoperating with a pond level above the cake discharge. The compo-nents can be expressed by Equatio n 1:

T = Tc + TL + TA - T P (1)

In standard dewatering, 7c is usually ne gligible compared with TL,and TA is small compared with TL. In this mode pond levels are notset appreciably above the cakse discharge level, and therefore Tpmay be ignored. Thus:

T=T, (2)c

In the Dry Solids mode of operation, the conveying torque risesconsiderably, because of the increased frictional forces within thecake, as more massaging of the cake is applied by the conveyor. Inthis mode T, predominates, and:

T= Tc (3)

It is now necessary to relate this conveying torque to the forcesor stresses on the cake. The decanter centrifuge maximisesscrolling efficiency by minimisin g friction between conveyor flightand cake, and by having finite friction between the moving cakeand bowl, or more precisely between the moving cake and the stat-ic heel. A t best the cake will m ove almost axially, in fact perpendic-ularly to the flight face. At worst it will move almost circumferen-tially with low efficiency. In practice, the actual angle will besomewhere in between these two extremes, and will depend uponthe size of gap under the baffle, or its equivalent, as well as the fin-ish on the scrolling surfaces.

In the low scrolling efficiency case, where the conveyor is pad-dling the cake around circumferentially, with only a small axialmovement the torque of the conveyor is counterbalanced by thefrictional forces or shear between the cake and its heel. The result-ing force on the conveyor - being in a circumferential direction -can be determined from:

F = Tc/r2 (4)Now:

Tc/rz = ?rrz L (5)

where Zis the average shear stress betwe en cake and heel and isproportional if not equal to the yield shear stress of the cake forthe moisture content being produced.

Rearranging Equatio n 5 and expanding it produces:

andz = TJ2a rz2L

22 - i 2 Tc=p23F(r,Z2 - r,2)L.

(6)

(7)

Now the cylindrical cake volume is effectively the same as thepond volume(V), where:

v = K (rr2- $)L (8)

Substituting Equation 8 into Equatio n 7 results in :

z = l/ 2(1- :)(T)r; V (9)

odober2ooo 19


3/6

36.0 I I I I I I I I

In the hi@ scrolling efficiency case, where the conveyor flightsare pushing the cake almost axially the circumferential force isconverted because of the screw action of the conveyor to an axialforce. This force against the baffle an d beach section develops apressure with in the cake. As in a screw press or a filter press, thepressure or normal stress at equilibrium is proportional to theyield shear stress ( zJ, of the cake at that dryness. The highe r the

shear stress a pplied to the cake the higher the resulting cake dry-ness.

The relation between yield shear stress and cake drynessfor effluent sludges is normally found to be a power law relation141:

where n is a constant between 2 and 4, depend ing on the typeof sludge. Over sufficiently small ranges of 2, cake dryness can beconsidered proportional to Z. Dry Solids decanters do normallyproduce a small range of cake dryness, so that a linear relation canbe expected:

The conveyor torque may be considered as equivalent to a force(F,) acting at a mid-point on the conveyor flight say between thepond surface at radius (r,) and the bowl wall radius (rJ. The forceFA divided by the total area of the conveyor flights (A,) will be atequilibrium equal to the pressure applied to the cake. This pressureor normal stress uproportional to the cake yield sheer stress 2,acts over a distance - from the front hub of the bowl to a bafflerestriction which is generally placed at the foot of the beach asshown in Figure 1.

Thus:

F, = Mechanical Advantage xTorque/ Mean Radius (l-2)Shea r Stress cc Norm al Stress = Force/Area = F,/A, (13)

From equation 12:

FA = 27~ T-2L.cp mwhere r, = mean radius.

Considering the cylindrical part of the bowl only:

A, = Ic(r* L v-r,2)Xp=p

(14)

(15)where:

L = cylindrical bowl len gth;P = conveyor pitch.

Combining Equat ions 13, 14 & 15 :27~ T PZ=Q= rnXCX-P r, V

Simpl i fying Equat ion 16:(16)

(17)Now, in practice, the cake movement is neither circumferential

nor ax ial, but at an angle @, to the axis.Thus, Equation 4 should bewritten:

Tc = FrJ sinc ~ (18)

20 oc&Dber2ooo F-


4/6

Equatio n 9 then becomes:

r, TcT=1/2{(1-:)/sin@). -r2 i 1 (19)As r, approaches rz the effect of the baffle reduces and 4,

I 2decreas ing sin@. Thus, the factor (I- 1) / sin 42 in Equat ion 19,within the practical range of 5 for decanter designs, varies very

r2l ittle. In practice the real relationship will be something inbetween Equations 17 & 19. Wherever it is, the relationship canbe simplified to:

XsZ(Tc/V) (20)So far, only the cylindrical section of the decanter bowl has been

considered. In practice, there w ill be some torque on the beach inDry Solids work, although the scrolling efficiency markedly increas-es once the cake passes the baflle. This ad ditional load, as well as theother torque components given in Equation 1, is small in compari-son with the conveyor torque, so that, as in Equation 3, the mea-sured torque can be equated with the conveyor torque.

It is thus postulated that cake dryness is proportional to theratio between the measured conveyor torque, T, and the totalneutral volume of the centrifuge, 1:

xS=Z=(T/V) (21)The term neutral infers that the pond level is at the beach dis-

charge radius, even though the pond used is often dee per. Pleasenote also that in the theory the scrolling area of the conveyor isused, assuming it extends from the bowl wall to the surface of thepond; however, in practice the inner edge of the flight sometimesis below the pond surface. One has, therefore, to be careful withdata where the centrifuge is not operated to its full performancecapacity when the bowl is not full of compacting cake. Care alsohas to be taken with axial flow decanters where conveyor flightshave excessively large windows reducing the flight area in contactwith the cake. If there is not a clearly defined location for the cakerestriction, then the volume (v) chosen for the formula has to becarefully chosen.

C 425 86D 424 98E 450 233F 450 233G 57.5 355H 575 392

575 392737 633

A &B - laboratory decanters of l ight ly di&rent designsD- developme nt version of machine CF - similar to E, but with higher torque capabil i tyG - similar to H &I, but with ( I shallower beach angleI a di jkent bafle design to all the other decanters.

In order to test the theory using practical data, as a first approx-imation, the cake dryness (x,) has been plotted against (T/ v). If thisis done for various decanter sizes, then a useful correlation shouldresult, if inde ed dryness is a functio n of shear stress.

FltLratbwSeparatian octmber2ooo2l


5/6

Throughout the cake depth, the cake is continually shearing as itis turned over by the conveyor and as it is moved over the cakeheel. In the cylindrical section of the bowl, the cake movement ismuch more circumferential than axial because of the balIle restric-tion, creating a lot of shearing within the cake. It has yet to be seenhow closely the actual yield shear stress of the cake for a given dry-ness relates to the shear stress used in the foregoing equations.

DataAlfa Lava1 has accumulated a mass of relevant data over the yearsfrom various eflluent treatment works throughout the world thatuse a variety of decanter designs and sizes. The data are plotted ascake dryness (xs - % w/w total so lids) again st the ratio (T/VN/cm*), where T is the measured conveyor torque, and V is thetotal volumetric capacity of the rotating bowl. Sometimes a side-by-side test of two or more machine sizes has been possible, butmore often such tests were conducted consecutively, and in theodd extreme case some years apa rt. The range of sizes of decantersused in this study is shown inTable1.

The data in Figure 2 are from a UK Municip al digested sewage,using machines C, G, H & I in 1998. It can be seen that the datacorrelate reasonably well to a straight line for a wide range ofmachine sizes and configurations.

Figure 3 comprises data from a Scandinavian digested sewageplant using machine types C, E & F. Here the variation in T/V is

22Dcbber2DoD

much larger, and the power law relation between z and cakedryness is evident. The exponent (n), is found to be much largerthan on most of the other data presented here, which coincideswith sludges that are difficult to dewater. Naturally there will be alimit to which any sludge can be dewatered and that limit is moreeasily reached on difficult sludges, by definition. This work wasconducted in 1993.

A better correlation from centrifuges with an even greater dif-ference in size, machines A, B & D is seen in Figure 4. The varia-t ion in T/V is smaller, and therefore a more linear correlation isfound. The sludge was again a UK digested sewage from a differentsite and the work was executed in 1993 and 1996 .

Figure 5 includes data from another UK digested sewage p lant,but this time the machines were of type D & J. Again a good linearcorrelation is obtained. The smaller machine work was done in1992, while the production machine work was completed a fewyears later after installation.

A comparsion of two standard decanters (type C), with onehaving a conveyor with an extra 5 0% flight pitch is depicted inFigure 6. The sludge this time is a difficult Dutch carousel sludge.This work was completed in 1997.

Finally Figure 7 shows data from machine type D at a UK munic-ipal mixed raw sewage plan t in 1990. This time the centrifuge wasoperated at four different bowl speeds and the good linear fit con-firms the theory that the correlation is independ ent of g-level.

DiscussionThe graphs in Figures 2-7 cl early demonstrate that (T/V) is pro-portional to cake dryness, but independ ent of a number of pararneters such as g-level, beach a ngle, conveyor pitch or baffle design.Nevertheless, it is not possible to predict the maximum dryness ofcake which is achievable.

When treating the dryness data from two different decanters,for a good correlation or for scaling, it is essential that thedecanters be operated at the limits of their performance and withsimilar pond levels relative to the cake discharge diameter. Themaximum performance level is when polymer dosage is at theminimu m to obtain acceptable centrate quality and the conveyortorque is the maximum, although less than the gearbox limit, forthe feed rate set. Alternatively, the feed rate is at the maximum forthe level of gearbox torque set. The degree of correlation willoften de pend upon how close to the limit of centrifuge perfor-mance each data point is.

ConclusionsCake dryness from a decanter centrifuge, processing a compressiblesolid such as a municipal eflluent, can be correlated with the quo-tient: conveyor torque divide d by bowl volume.This correlation,with data obtained under controlled conditions, is independ ent ofcentrifuge g-level, conveyor pitch, baflle design and beach angle.

Cake Dryness ad Couveyor DmweltlalIn conventional decanters it is customary to operate with a fixeddifferential between bowl and conveyor. The centrifuge is started,brought up to speed, the feed is admitted and differential set togive acceptable dryness. In some applications there is no built inmeans to adjust differential while running.

As shown above, cake dryness in the DS decanter is related to theconveyor torque. For best DS performance it is normal to operate ata fixed torque by modula ting differential. By operating thus, a


6/6

consistent cake dryness is achieved and the differential modulatio ncan cater for wide fluctuations in feed rate and consistency.Nevertheless it is necessary to know the cake handling capacity for agiven differential because this will affect the choice of gearbox ratioand the required brake or back drive size.

In conventional decanter operation, the space between consec-utive flights is seldom full and the efficiency of scrolling is general-ly less than 100%. However in DS operation the situation is thereverse. All flights are generally full, up to the pond surface, andscrolling is very efficient. The scrolling efficiency is best whenusing the benefit of a hydraulic head in the cylindrical sectionabove the cake discharge, giving a pressure differential across a baf-fle or some back pressure device. This is sometimes known as neg-ative dam or negative pond operation. Nevertheless one mightexpect that the scrolling efficiency will be affected by feed rates, g-level and/or the conveyor pitch. Differential slip of the cake couldoccur as the pitch of the conveyor gets wider.

In practice this is not the case. In DS operation the volumetricscrolling capacity is directly proportional to the swept volumeunder the major restrictions, independ ent of beach angle and g-level, and directly proportional to pitch. With restrictions inseries, the proportionality constant is a weighted average of theserestriction areas. For any given sludge the dry solids cake dischargerate will, for a given differential, increase as the cake gets dryer.This is shown by the following data.

DataThe data are displayed as wet solids rate plotted against conveyor

differential. Each data set is for a fixed sludge type, irrespective ofcake dryness, centrifuge feed rate and polymer dosage. The testwork has been conducted at various municipa l sewage worksthroughout Europe. The sludges tested were mostly digested, but acarousel and a mixed raw sludge are also included. The decantersused in these studies are shown in Table 2.

Figure 8 shows a good linea r correlation of cake rate against dif-ferential, while Figure 9 shows the variation of capacity with sludgetype. The theory involves the correlation of volumetric capacity w ithdifferential, whereas the graphs use a gravimetric capacity. Cakeweight is much easier to calculate than a volume. This is acceptablewhen only one sludge type is involved. The change that occurs whendifferent sludges are involved is often q uite small and will be propor-tional to the change of density.

Figure 10 compares a standard pitch conveyor performancewith a wide pitch. The ration of pitches was 1: 1.5 while thescrolling rates measured were 1 : 1.7. This shows that efficiencyincreases with pitch rather than decreases as might have beenexpected. Earlier work on the same sized centrifuge with a nar-row pitch gave relative scrolling rates proportional to pitch.However the performance of the narrowest pitch conveyor wasmore erratic giving an inferior correlation, indicating perhaps

FPltration+SeparatCon

that some bridging was occurring Figure 11 demonstrates thatthe scrolling efficiency is unaffected by g-level in the range of1000 to 2500g.

The uniform scrolling capacity can be experienced with all sizes ofdecanter from the largest to the smallest, which is shown as Figure 12.

ConclusionsIn a properly designed and operated decanter the wet cake dis-charge rate is directly proportional to differential, the scrolling

efficiency is independ ent of g-level cake dryness and feed rate, andthe scrolling rate is proportional to pitch, which has only a smalleffect on scrolling efficiency.

AcknowledgementsThe expert work of the several test engineers in obtaining the datais gratefully acknowledged. They include J G Joyce, J Delin, K ASmith, B Pedersen, H Afman, and J Hester.

Nomenclature4 Scrolling area of flights in cylindrical section (L2)F Resu lting force on conveyor (ML-IT-)F* Axia l force on cake (ML-1T-2)L Cylindrical length of decanter (L)n ConstantP Conveyor pitch (L)rl Pond surface radius (L)I2 Inside radius of bowl (L)rfn Mean radius of conveyor flights (L)T Conveyor torque (ML2Te2)TA Compone nt of conveyor torque providing process

acceleration (ML2Tm2)Tc Compone nt of conveyor torque which conveys the cake

(ML2Tm2)TL Compone nt of conveyor torque lifting cake to discharge

level (ML2Tm2)TP Compone nt of conveyor torque provided by hydraulic

head (ML2Te2)v Cylindrical wetted volume of decanter (L3)x, Cake drynessa Universal constant0 Norm al stress on cake (ML-Te2)

;Cake yield shear stress (ML-IT-)Angle of cake pa th to axis ()

References1. N Corner-Walker. 2000. The Dry Solids Decanter Centrifuge:

Capacity Scaling. Filtrat ion+Separation, 37/4 (Mmay), p.28-32.2. R Denkert & E A Retter. 1992. Quickhme P&Con ditioning

of Sludge to be Dewatered in Centrifuges Lowers DisposalCosts. Rebild Ho tel and Conference Centre, June.

3. W-F Leung. 199 8. Torque Requirement for High-SolidsCentrifugal Sludge Dewatering. Filtrat ion-tSeparat ion, 35/9(November) p.883-887.

4. F Colin. 1970. Application of RheologicalTechniques to theStudy of Sewage Sludge. Trib Cebede au, 3 17, p. 178.

Forfurther information contact: N Corner- Walker, A@ Lava1 Separat ion Inc,955 Mearns Road, Warminster, PA 18974, USA. Tel: + 1 215 443 4000; Fox:+ I 2154434112.

october2ooo 23

Conveyor Torque&Differential

Documents

Transcript of Conveyor Torque&Differential