1980 national waste processing conference 34

8/2/2019 1980 National Waste Processing Conference 34

1/11

DESIGN MODLS OF TROMMLS FOR RSOURC

RCOVRY PROSSING

HARVEY ALTERChambr of Commerce of the Unted States

Washngton, D.C

JEROME GAVSepartment of Geogaphy and Envronmental Engineeng

Baltmore Mayand

MARC L RENARDNatona Cente fo Resouce Recovey, Inc.

Washington, DC

ATRA terial riding on the barrelsurface

The design of a trommel requires knowedge ofthe number of impingements necessary to achieve adesired eciency of separation of undersized material from a feed stream and of the radius, length,inclination angle, and rotational speed necessary to

= size of a spherical particleE(xo,xm = efciency of separation of

particles in the size rangeXo x


2/11

P(X) =probabiity that a particleof sizex passes through ahole in impingements

P(xoxm) probabiity that particles inthe size rangeX


3/11

eter d minge n a quare le deaa > dte raliy tat t wl a trug te lei

p da

2

Q (1

an equain riginally gien y Gaudin [1] Tequatin al decrie te raility tat earticle will a trug a circular le diameteraTe acr Qi terati te le area t tettalcreen urace area A Gaudin inted ut,ti i a lwer limit n te raiity, ince relectin rm e edge te le iignred Equatin (1 i rictly crrect raricle imingingnrmalt te creen urace, altug tere i nlyamall cange r mall deatin rm nrmalmngement [1] Wen te le i rectangular,terail ty ecme [1]

p _da 1 QA (2)wereaand A are te rectangular dimenin e le

Te cumulatie raity tata article wilatrug a le ater imingement i

n i np p 1 p (1 p (3)

j

In te aence articletarticle interactini i al te cumulatie raility tat a largenumer unirmly ized article will athrug a large numer leaer imingement

I te article are nt unirminize, teraii ty tat artcle izex 1 wi a aterimingement i

n1(1p f(xd

were 1 i te numer ractin article izeXI ie , te izeditriutin unctin te

artcle ealuated atXI Te railty r alarticleequal tr greaer tan a minmum izeXand equal t r le anamaximum izexm ie ntegral

n(xxm J f(x 1(1p dx (5)Xo

an equatin irt gien y ucer [13] .Sucer a al gien alernatie rmr

(5) uggeting tat te raity articleaing atte t imingement iaunctinte

cmitinte material ater te t imingemen rater tan te material aracing tet mingement rm te ( It mingementTen

363

It nt eident,a poriw ee equatinetter decrie reaity

Real artcle cure, are nt erical One

mean radening te deriatin tinclude nnerical article t alter te ditriutin unctin,f(xt relect an equialent erical ize diruiny incluin uitale ae actr rartice in eac ize range aternatie i t tain an eral ae actremirically rgentye eed material y cmarin te equtin wit exerimentaly determined raltie

Teactin a trmmel i t caue te eedmaterial t iminge time n te creen uraceaitae trug Eq (6 exree te cumul

tie raility tat aricle ranging in ize eweenXandX wile creened ut during teirjurnin te trmmel Te ttal ractin article in ti ize range in te eed i

wic i te cumulatie ize ditriutin etweenXandX. Te eciency te trmmeli hen

E(xx = (x,x/F(x, x (8)

In wrd, he eciency i exreed ateratie numer ractin underized material remedt te numerractin underized material inteeed t i imrtant t nte that te eciencyiexreed in term numer ractin raterthan weigt ractin, wc areuualymeaured

caue q (58) allw te eciency t e caculatedaaunctin wen te ize ditriutin,!(x i knwn, the numer mingementneceary t aciee a deired ractinal earatin underized material rm te eed can e deter

mined Becaue te ncreae in raility reultingrm reectin article rm te edge telea een negleced, te numer imingement needd t attan a ecied eciency mayemewatlwer tan te calculated numer inractice Ti i et, weer, y e decreae inrailityreuting rm articetarticle interactin e g , adein r deectin y clliinrrm linding le Becaue uc interactinincreae a eedrate increae te numer imingement needed t aciee a ecied eciency

mut increae a eed rate increaee diculty, i nt imiii ty mdelinge eect reectin rm he le edge andarticle-t-article interactin r te cmlex


4/11

mxtureof szesandshapes of the materas thatare processed n resource recovery facltes prevents pomodcaton of the equatons toaccount forthem Thecaculaton of the necessarynumber of mpngements by means of Eq (58should therefore be vewed as astartng pont towhch correcton factors obtaned emprcally for

dferent types of feed streams may be appled norder to obtan more accurate estmates

At ths pont the equatons descrbe any screenng acton whether natrommel or other knd ofreen

HE YNAM OF ROMMEL AON

erotatonal moton of the barrel and ts nclnatonrelatve to the horzontal provdethemeansby whch materal fedtothetrommel s

made to mpnge on the screen surface Thenumber of mpngements a mass ofpartclesexperencesdurng ts resdence n the trommel s afuncton ofthe trommel dmensons ts rotatonal speed andangle of nclnaton

n classcal appcatons n mnerals processngtrommels are rotated at angular veloctes at whchthe materal wthn them rdes less than 9(20 deg) above the horzontal dameter before falngback and mpnng on themateral rdng below Observaton of trommels used n resoure

recovery processng however ndcateshat theyare rotaed at hgher angUlar veloctes so that matera rdes hgher above the horzonta dameterenwhen the component of the gravtatonalforce norma to he surface becomes equal to thecentrfuga force the parcle leaves the surfacesng at rst because tstllhas vertcalmomentumbutthen arcng and droppngtothebottom ofthebarrel* Whe there does not appear tobeanydocumentatonof the reasons for suchamode ofoperatont s evdent that ths causes breakup of

aggregated masses of partcles ncreasesmxngand helps prevent blndg of screen holes n factltersrencorporated n many resource recoveryprocessng trommels norder to enhance ghtofpartces from the surface The quanttatve derpton of the mechansm of trommelacton leadng to desgn and scae-up crtera descrbedbelows based on ths mode of operaton fters however are not consdered_

*The operation in mnerals processng may be descrbed asa "supg mode" d n rsource recovery as a "cascad-

ing mode."

THE DNG ANGLE

Theangle above the horzonta dameter atwhchapartce of masm wl yfromthe surfaces a func ton of the angUlar velocty w andthe radus of the tromme R. Fgure a shows that long asthepartcle remansonthe surface the

centrfuga force w2Rm

,s equal to the sum of thenormal force exerted by the surface and henormal component of the gravtatonal forcemgsn When 0 the partcle wl leave the surface The condton for ths s

w2R s (9)g

e angular veloctyneededto reach the vertcal /2 (90 de g) s the crtca angular veloctyabove whch the partcle wll rde onthesurfacewthout fang Thus sn s the square of tefractonof the crtcal angular veloctyfor whchthepartcle wll rde to angle before leavg thesurface

Actualy because the barre s nclned wthrespect to he horzontal t s necessary to multpythe denomnator of he le sde of Eq (9by thecosne of the nclnaton angle Because s seldomldommore than /36 (5 deg) however cosandmay be neglected

THE LIGHT TAJECTOY

The pont-by-pont descrpton of the actualrajectory s of ltt e nterest What are neededarethe relatonshp between the pont of landng at thebottomof the barre and the ange and the tmenterva t durng whch the partces n ght

For the case where the partcle lands at the lowest pont of the barrel at the vertcal dameter thevertcadstancefrom where the partce eaves thesurfaceto where t strkes the bottom of the barrel ustrated n Fg b s gven by

(R + h = R +sn) =igt2 - wRtcos (0 as before he small nclnaton of the barrel fromthe horzontal s neglected Fromths

wt sncos sncos+ 2sn ( +sn)(

The rst term on the rght s he tme to reachtheapogeeof the trajecoryandthe second s the tmetofall from the apogee to the bottom of the barrelHvng a horzontal velocty wR sn the partcletravels the horzontal dstanceR cos durng thstme When R cos s set equal to wRt sn , theresult after smplcaton s

364


5/11

o

Rml

c

rcr " II 8

I

b.

;-

EGEND R GURE

G PARTCL E LGHT TRAECTRE N A

TRMMEa orces Acig o a Paicle Causig I o Ride o he

Barrel o AgeCb The Traeco o migeme a he Verical iam

eer =0c The Traeco or migeme a Agle rom he

Vercal

h'

IR

'"rajectry

co = [n' co' + 2 n { + n) n =nco+ [n'co' +2nco +n)f2)

Becue of 9) nd the fct tht n'+ co = 2) y be olved fo n to yeldn = 05 or = /6 30 deg)

ee no p

oeon tht theptcle utlnd t the vetcl dete t ple to how

tht f he ptcle to lnd t nge fo thevetc lutted n g c ) becoe

365

3)uton 2) tnfoed to

co e + n = [n' co '+ 2 n co + n )] n 4)

h the oluton

n = co 3 co = n 3 = 3 /2 5)


6/11

AB ROMM DSGN ARAM RS

sin a a- n f I.6 6T

56) 5

5

56 6

55 6

55 66

o .5 65)

66 6

6 55 55

6

hefrst three columns of able 1 lst valuesof 0an sn 0for sveral values of {

cause the partcle (n the even t oes nopass through a hole) hasa horzonal veloctysn 0, as wel as a vertcal velocty, ven bytheprouct of gan the racal erm on he rghts oJ q (1,t pnges on the surface at anangle whose cotangent s the ratoof the vercaltohorzontal veloctes hus, ater smplcaton

cot = 1 ( sn 0 + 2os { (6)s0 s0

e angles areven n column 4 of able 1 forthe lste valuesof 0 an { he angles an { areequal at 0071 (2 8 eg) when 0 = 0.190(4 eg ) hat s the partcle mpnges normaltothe surface an

06 (7g nTE NUMBE O MPNGEMENTS EAZED

Because the vertcal velocty of a partcle as t

leaves the barel surface s actualy a veocty perpencula to the barel axs whch s ncneat

66

6

anangle , as shown n g 2the partcle has ahorzontal component of velocty cos0sn Durngthe tme the partcle s n ght tmoves ahorzontalstance cos 0sn anastancepaallel tothe nclne axs cos 0tan where s gven by q (14an tan an sn havebeenapproxmate by , snce s a small angle n prac

tce n aton, thepartcleavances alongthebarel a stance eqUvalent to the pouct of totastance the patcle fals vetcally an sn Neglectng cos , as before the partcle avancesa stance (cos 0 + cos {)

hetota horzontal splacement per mpngement s then

Q ( cos 0 + cos 0 + cos {) (18whchmay be wrtten

Q

< ( cos 0 + cos0 + cos {) (19

Values of


7/11

wRt cos sinWCSIl

G 2 PL VN LNG NNBL WNG V N N

nQ nR (20)

Durig each revolutio of the barel, the paticlerests agast the suface durig the agula displacemet (8 /2 ). Duig the time the paticle isi ight, he agula diplacemet of the bael isw Thus, the barel makes the factio of a evoutio

(21)

hee is give by Eq (3), per impigeet ofthe particle o its suface The recipocal of [ is theumbe of impigemets per evolutio Values of[, correspodig to the values of 8 ad give icolums 1 ad 3, are listed i colum 6 of Table 1

The residece time, T, of a paticle i the tom

mel is the atio of the mber of revolutios, n,to the otatioal frequecy w/2 n

n[ [ R JT = (w/2r) = 2rn[ gsia (22)It has bee assumed i the deivatio of these

equatios that the ceter of mass of a particlerides o the suface of the bael at the adia distace, R, fom the axis The ceter of mass of a ealpaticle of ite size must actualy ide at a dista'cesmale tha R fom the axis Moeover, if mateial

des seveal paticles thick o h suface, the distaces ll be differet fo differet particles Thee, of couse, o ay to accout fo the dyamicsof each paticle a approximatio R, i theequatios, may be take to be the tommel radiusess oe-half he aveage thickess of the mateialdig o the bael surface The quatities calculated fom the equatios, l, the, be appoximately aveages about hich the real vaues maybe expected to scatter

A special ase s f = O. Horzontal trommes are used btwth lftes or tera solls formg a Arhmedes

srew to "pmp the matera rogh Obvosly, Eq

(18) does ot hold n sh ases. Presumably other ea-tons an be deveoped to desbe the movement

THE FEEDRATE

Equatios (9) ad (20) do ot completely deteme the desig of a trommel They provide olyto elatioships, give the hole size, amog thefour desig paameters w, R, ad (. I paticula,

they cotai o depedece o feedateAt a cosssectio of the bael ea its etace,

mateial idig o the barel i a layer of thickess alog the agular sectio (8 /2 ) occupies acrosssectioal are R (8 /2 ) Mateial iight occupies a cosssectioal area equivalet tothe mateia that ode o the barel duig the timeofght, , o Rw The mateial is ovig logtudiay alog the barel at a velocity (w/2)Q/e poduct of the crosssectioal aea occupied byhe material ad its velocity alog the barel ea theetace is the volumetic feedrate Whe multipliedby the desity of the material i the layer, P* thisves the mass feedrate, Ater substitutio fomEqs (9) ad (20) ad Simplicatio, M is expressedby

(23)hee

' = (si) ( cos si + cos8) (24)

th give by Eq (3), ad ih si repaced by because is small Values of' are listed colum

7 of Table 1 fo correspodig values of 8 ad aEquatio (23) provides aother relatioship

amog the variables if is ko ad is specied Although alloig to icease pemts largerfeedates at a xed R, doig so may decrease efciecy by aloig icreased particletopaticle iteactio, hole blidig, etc

It is ecessary to resot to expeimetal obsevatio o differet types of feed materias to deteme the depth of mateial, , that produces thegeatest observed efciecy at the smallest R t is

ot evidet, a pror that magitudes of greatetha the average dimesio of the feed materialead to moe optimal desigs

Because ' deeases as 8 decreases, M decreases 8 deceases for a give R ad Alteatively,large radius is eeded at Xed at a give feedrateas 8 decreases The gai from large 8, hoeve,may be offset by the loe eciecy caused by theresultig depature from ormal impigemet he0> 00711 (12 deg) Experimetal ivestiga

* Possbly b als the buk densty o the eed measurd

n the sal wy Howvr, ths s no t ertan ad b wll

have to b masred expermentaly by obervaton o

the fed en o te rotatng tommel

367


8/11

tion is needed to ascertain the best values of{ to beused wth different types of feed materials. It isreasonable, in the meantime, to specify normal impingement, wth { = 0.07 (2.8 deg.)and = 0.90 (34.3 deg).

O E A ROEL

e purpose of a trommel is to separate underzed material in the size range X ; x ; x with eciency x) from material fed to thetrommel at a mass rate,M In order to design a trommel to do so, it is necessary to specify the holeape and size, the fractional area of holes, therotational speed, radius,length, and angle of inclination.

Common practice in resource recovery processingspecifes circular holes (in order to minimize retetion of tetile and plastic material)and an angle ofnclination of /36 (5 deg) The hole size is determined by the dimension x. The fractional area ofholes should be as close to unity as possible consistent with the structural strength of the barrel Itsspeication is a function of structural desi andis not considered further here. Otherwise, te desgn is detemined by Eq (8) with Eqs. (7) and (5)or (6) Eqs. (9) (20) and (23).

Equation (8) with Eqs (7) and (5)or (6) allowscalculation of the number of mpingements neces

say to attain the required eciency Equations(9) (20) and (23) with sin = 0.5630 < = 3.34d 1= 23 then determine w R and L for thedesign feedrate and necessary number of impingements. Ths requires knowledge of te density and specication of te dept ofmaterial,,ridingte trommel barrel surface Until the results of eperiment and practice indicate otherwise, may betaken equivalent to the mean size of the feed materal.

APPLAO

eamples of how the ideas developed may beapplied in resource recovey processing, Eqs (58)w be used to ascertain the number of impingements needed to separate undersized material fromraw MSW through 4.75 in (20 mm) round holes,and the number of ipingements needed to separatemetal cans from a solid waste stream through holesof the same size Then Eqs (9) (20) and (23) willbe used to ilustrate the caculation ofrotationalspeed, radius, and length, for a typical feedrate.

NUMB O IMPINGMNTS QUID-

AWMSW

aw MSW is most oten characterized accordingto mass of material in different size ranges. Wnklerand Wilson 5 , however, have given number histograms for raw MSW from Cambridge, Massachusetts,

and Middlebury, Vermont, in different maimumparticle dimension ranges While distribution according to maimum dension does not account forparticle shape, the distribution functions derivedfrom the histograms can be used at least for ilustrative purposes

e histograms for MSW from both cities may t by the lognormal distribution

(x) ep X

ln

XQX

.oln (25)e geometric mean size X 6.0 in (52 mm) andthe standard devition ln 056 for Cambridge,Massachusetts, MSW The number fraction of minus475 in (20 mm) material in MSW from that city given when Eq (25) is inserted into Eq. (7).

7 F(O4.75) 0.73

ep - .26 Qn 6.0 x

(26)

e probabities, given by either Eq (5) or (6)ad Eq ( with the insertion of Eq. (25) are

P(O 475) 0.737

ep x

x26 Qn

6.00

nx

1- Q I +4.75

d

(0 475 = 0.73

7S

ep x

x

26 Qn 6.00

(27)

2

x - n (28)

Q + 4.75 x

Integration of Eqs (27) or (28) with differentvalues of gives P(O 4.75) as a function ofDvision by F(O 4.75) gves the efciency ofparation,(0 475) as a function of .

e integrals have een solved numericaly bymeans of Simpsons appromation method. ig

ure 3 where has been plotted as a function ofon a lognormal grid,ilustrates the results. urves

368


9/11

A B and C show as a function of(0, 475,determined for the probability calculated fromEq (27 with Q 1,05,and 03 respectively.Curve Dshows as a function of(, 475 forthe probability calculated from Eq. (28 with

Q 0.5The most strkng feature ofthe curves is thatthey each consist of two straight lines of differentope that are connected by a transition curve Inthis regard they are simlar to experimentaly determined curves of efficiency as a function ofsieving time on at screens described by Whitby 16] .e number of impingements necessary to achevea given efciency is approximately inversely proportional to Q as a comparison of curves A B andC show The number of impingements at a given

efciency for probablities calculated from Eq. (28are slightly lower than those for probabities calculated from Eq (27 along the lower parts of thecurves but differ negigibly aong the upper partsofthe curves, as curves B and Dillustrate

If the upper integration limits of Eqs (26 and(27 or (28 are decreased the integrations give theprobablities ofseparating < 475 in. (120 mm)material in a trommel with 475 in (120 mm)holesCurve E of Fig (3 is a plot of against (0 45wth Q 0.75,whe Curve F is a plot of against(0 4.25 with Q 1Remarkably the efciencyis log-normally distributed with respect to numberofimpingements up to very hgh separation efciencies Moreover the number of mpingementsneeded to achieve a gven efciency is very muchsmale especiay at hgh efciencies than whenundersized material up to the hole size is to be'parated

NUMBE OF IMPNGEMENTS EQUIED

CANS

If recovery of food and beverage cans is an objective a trommel may be an effective means ofparating them from raw MSW. f interfeence byother materials is ignored emphasis may be placedon eciency of separation of cans if the equationsare wrtten for distributions relative to cs aoneFor smplicity only unamaged cans of one sizewbe cnsidered 2.5 x 4 in (64 x 1 02 r).

The probability of passage ofa can through ahole is dependent upon the orientation at which itmpinges lorientations occur wth equal probablty however. Therefore the cans present themlves as particles uniformly distributed with respect to a longest dimension that ranges betweenthat of its diameter and that of its diagona 4.75

U.z:'tZC:

EFFICNCY

FG. 3 NUMBR OF MNGMNS NCSSARY O

ACHV SCFD FFCNCS OR RMOVAL

OF UNDRSZ MARAL RAW MSW N A ROM

ML W H 7 N 20 MM) HOLSA, B C. Removal o Mius 7 i Mius 20 mm)Materia with robabiites Calculated Accordig to q

27) or Q = 0 ad 03 RespectivelyD Removal o Mus 7 i Mius 20 mm) Mateial

with robabiltes Calculated Accodig to q. 28) orQ 0 Removal o Mius i Mius mm) Materia

wth robabilities Calcuated Accordig to q 27) or

Q = 07F Remova o Mius 2 i Mius mm) Material

with robabilties Calculated Accodig to q. 27) orQ = 1

in (120 mm). The distribution has the form

[(x) = -xm- x= 4.75

1

_2.5

= 0.444 (29)

e number fraction F(25,475 is easily shownto be unity The probablities are either

4.75

( 4.75 0444 1 1Q

or4.75

(25,4.75 0444 1 1

n1

4.75

n1+45

(31

Here the efciencies (2.5, 475 are equal numerically to the probabilitiesFigure 4 ilustrates the results of numerical in

tegration of Eqs (30 and (31 The curves are

369


10/11

mlar to thoe of Fg (3) Curve A B C are forproalte calculated accordng to Eq (30 forQ = ,05,0.3 repectvely. The curve for proa-lty calculated accordng to Eq (3) for Q = 05 undtnguhale from curve B

100(fZ'(z-

10

0.1 10 10 20 40 60 80 9095 99% FFICIEC

FIG. 4 NUMBER OF MPINEMENTS NECESSARY TO

ACHIEVE SPECFED EFFICIENCES FOR REMOVAL

OF 25 X 4 IN. ( X 1 00MM) CANS FROM RAW MSWN A ROMMELA, B C Removal with Probabiities Calculated Accordng

to Eq (30) Through 475 in ( 1 0 mm) oes for Q = 1 05 and03 Respectively

D Removal with Probabilities lcuated According toEq (30)through5 n (1 27 mm) Holes or Q = 1

Curve 0 llutrate how the numer ofmpnge-ment needed for a precred effcency marked-ly decreaed when hole larger than the can dagonalare ued. It wa calculated for 5 n. (27 mm) hole

from the proalte of Eq. (30) for Q = wththe term ( /4.75) replaced y ( /500) nthe ntegral. Thu, a mal ncreae n hole e re-duce the numer of mpngement neceary toattan y effcency, epecaly at hgh efcencee efcency lognormally dtruted wth re-pect to numer of mpngement up to 09

TROMMEl DESIGN

f, for eample, the trommel to proce 60ton/hr (55 t/h) of raw MSW and f an average den-ty for materal rdng the arrel urface at a depthequal to the gemetrc mean e, 6 n. (52 mm),

taken to e 5 /ft (80 kg/m), Eq (23) wth = 23 and { = /36 (5 de g), gve R = 5 (.5 m) The rered rotaton peed 8 rev/mn,accordng to Eq. (9) wth n 0563

If 70 percent effcency of removal ofmnu475 n. (mnu 20 mm) materal y a trommelwth

Q =05 peced curve B of Fg (3)how

that = 63 Then, Eq (20)wth < = 334 gveL = 94 (285 m). IfQ were 075, nterpolatonetween curve A and B of Fg 3 would gve = 45 for whch the length would e 67 ft (20.4m).Even maller length would e peced f removalof mnu 4.5 n. (mnu 4 mm) materal through4.75 n (20 mm) hole were requred. Thu, for70 percent of efcency of removal of uch materaly a trommel wth Q 075 curve E of Fg 3 howhat = 30, for whch L 45 (3.7 m)

Curve A of Fg 4 how that forQ =

05 and

= 63 the efcency of removal of can 67 pe-cent, whle nterpolaton etween curve A and Bof that gure how that for Q = 0.75 and = 30the ecency of removal of can aout 60 percent.

WHA HA EE AOPLHE-

WHA EE O E OE

The development preented provde mean forcalculatng:

a. The numer of mpngement neceary toparate undered matera from the feed to thetrommel,n any e range up to the hole dameter,a a functon of eparaton effcency The latter dened a the rato of the fracton of underedpartcle eparated to that n the feed. In order tocalculate the fracton t neceary to know thedtruton of partcle e accordng to numer nthe feed There lttle to dtnguh etween thetwo method ofcalculatng proalte of paagethrough the hole.

. The radu of the trommel neceary to pro-ce materal at a peced feedrate, f the thckneand denty ofthe materal rdng the arrel ufaceare known and the angle ofnclnaton peced.

c The length of the trommel needed to achevethe numer of mpngement calculated

provde the complete degn for pecfcapplcaton ecept for tructural factor Thereare, however, lack n nformaton aout materal

A hs val of a, = o h pacs mpg omalo h c sfac whch s h m axmum sz h ,

hc mos pobabl ad avag valu fo d

370


11/11

in rsourc rcovry procssing that introduc uncrtaty

a Siz distributions of raw MSW and of othrprocss strams ha usuay bn rportd accord-ing to wight fraction but not according to num-

br fractionb Shap factors for th irrgularly shapd ma-trials fd to trommls in rsourc rcovry pro-cssing ar not known

c. Dnsitis of h matrials that rid on thbarrl surfac hav not bn rpord.

In addition svral important paramtrs in drivd sign uations ar imprfctly spcid

a Bcaus particl shap factors ar unknownrction from th hol dgs has bn omittdfrom th drivation of fcincis.

b Whil normal impingmnt has bn suggstdfor us in dsign optimal cincy may occur atothr impingmnt angls

c thicknss of th matrial layr riding thbarrl surfac that lads to th optimal dsign for avn fcincy of sparation and fdrat may notb uivalnt to a man dimnsion of th fd ma-trial.

hr is nd for bttr charactrization offdmatrials with rspct to siz distribution accordingto numbr and to shap factor and for primn

tal programs in which optimal impingmnt angsand hicknsss ofmatrials riding th surfac arinvstigatd for diffrnt fd matrials It is hopdthat th rsults prsntd hr ar sufintly pro-vocativ to inspir ndd invstigation. hy arbut a rst stp toward a rational mhod for thdsign of trommls for siz sparation in rsourc

rcovry procssg

AKOEE

bginnings of this work wr ncouragd bysupport from Contract 68032632 from th U.S.Envionmnta Protction Agncy Ofc of R-arch and Dvlopmnt Mr Carlton Wils ProjctOfcr.

work was supportd in part through Indus

tia Rsarch Participation Grant SPI7907391from th National Scinc oundation.

REFEREE

[] Ao, "A Wesmiser W oder,"My Magazine

Ju 1 924 rered, Solid Wass o. 66 976 536539

[2 Ao, "The Gova Reuse Pla," Engineering

ol 26 98 . 577 64 70

[3 Carlso , Secer, , ad Csese, H,"MooeCou Resource Recover Projec," Proc Fifth

Mineral Waste Utiliation Symp. 976 96203

4] uk, H ad Russe, S. H, "eg ad Ma

ras Recover Ssem," Proc Fifth Mineral Was

Utilization Symp 1 976 3340

[5] Berheise, J , Bagalma, P M., ad Parke,

W S, "Trommel Pocessig o Muical od W asePrio o Sheddg,"Proc. Sixth Mineral Was Utilization

mp 978 254260.6] Wille, C R, "Te Marad viromeal

vce/Balimore Cou Resouce Recover aci, Texas,

Maad," Proc. Sixth Mineral Waste Utiation Symp

978 280285[7] aserbrook, G. , "The Acid Tes orBridge

or," Waste A, ol 9 No 5, 1 978 4652[8 Ale, H ad u, J J Energy from Waste -

merican and European Experiences Marcel ekker NY ,

iress ( 0)9] Woodru, K L , "Prerocessig o Mucal

lid W ase or Resou ce Recove wa Tromme,"

Trans. IME ol 260 976 60604

1 0 Wo odru, KL ad Bales, E P, PreressigoMuicia Solid W ase or Resouce Recover wih a

Tromme - Udae 977," Proc 978 National WasteProcessing Conf ASM, New Y ok, 249257

[1 1 ] Ware, J L, "The U o a Roag ree as

aMeas o Gadig Crude Reuse or Pulverizao ad

Comressio," Resource Recovery and Conseation

o 3 978 972

[2] Gaudi, A M, Prnciples of Mineral Dressing,

Graw Hil, New Y ork, 939 Chae

3 Sucher, R W , Sieving Theoretical and Ex

rimental lnvestigations Ph. sseaio, Kasas

Sae Uiv, 1 969

4 Taggar, A , Handbook of Mineral ssing

J Wie & Sos, New Y ork, 954 Secio 7 5 Wker, , ad Wso, G, "Sie Charac

erscs o Muicial Solid W ase," Compost ience

ol 4 No 5 1 973 6

[6 Whb, K T, "Te Mecaics o e Sievig"mer Soc. for Testing and Materials STP 234, 958 325

K s

Cassificaton

Concentraion

DesignEngineering

Mathematica Mode

parator

371

1980 national waste processing conference 34

Documents