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{ PAPERMAKING I

Impel ler design choice is key to stockAxial-flow impeller design is bothmechan ically sound and energy-effi-cient for all top- and side-enteringstock agitation app licationsBy TOM C. DEVRIESs Although each stock agitator supplier has a designwith its own unique featu res, they all have one thing incommona drive design and an impeller design. Thecombination of these designs resu lts in an agitator de-sign. To solve a particu lar stock agitation problem, thesu pplier selects an im peller d esign and coup les this im -p eller to a m otor throu gh a m ech anical d esign consisting)f a shaft, bearings, and a speed red uction d evice. Sincem ost stock agitators are of the sid e-entering typ e, the fol-lowing d iscussion w ill focus on the d ifferences in var-iou s sid e-entering stock agitator d esigns from a p rocessan d m ech an ica l stan dp oin t.

AXIAL VS RADIAL FLOW IMPELLERS. First, it is n ec-essary to und erstand that a process resu lt, such as stockblend ing or storage, is a function of the im peller d esignemployed and the horsepower delivered by that impel-ler. In, other words, the key to a successfu l agitator in-stallation is the p rop er com bination of the im pellers d e-sign, its d iameter, and its delivered horsepower. To

Mr. Devries is m arket sp ecialist, p uIp and p aper, MixingEquipment Co. Inc., Roches te r, N .Y.

F/GUR.E 7:Top-entry agitator configuration.

Radial flow impeller Axial flow impeller

illu strate this p oint, tw o extrem es of im peller d esignsthe rad ial-flow and the axial-flow im pellerw ill be re-viewed . Figures 1 and z illustrate these two designs interms of d ischarge flow pattern in the top- and side-en-t er ing modes.As can be seen from Figure 1, the rad ial-flow impel-

ler generates a butterfly flow pattern, w herein the im -peller d raws material from both the top and bottom anddischarges rad ially toward the sides of the chest, as op-posed to the axial flow, which draws from the top andd ischarges tow ard the bottom . In th e top -entering m od e,either design is acceptable, and in fact, the rad ial-flowim peller w as used exclu sively for years until the ad ventof th e m ore efficien t axial-flow im peller.Placing a rad ial-flow impeller in a side-entering

m od e p rod uces a th rottled , in efficien t, an d u naccep tableflow pattern as depicted by Figure 2, which is exactlywhy rad ial-flow impellers shou ld not be used on side-entering agitators. The axial flow, on the other hand ,discharges along the chest floor, u p the back w all for re-turn to the suction side of the imp eller. This d iscussionw ill show that rad ial flow is an und esirable com ponentin an im peller d esign becau se of its inherent inefficien-cies in the sid e-entry m od e.

QUASI-AXIAL FLOW IMPELLERS. The next step isto review the axial-flow concep t as it relates to im pellerd esign. Bu ild ing a tru ly rad ial-flow im peller is easy, an dm ost vend ors of agitation equ ipm ent m anu factu re an es-sentially id entical rad ial-flow im peller produ cing thesame rad ial-flow pattern. It is not as easy to manufac-tu re a truly axial-flow im peller. To d o so requires accu -racy that is only available from a device such as a laser

FIGURE 2: Side-entry agitator configuration.r

Radial flow impeller Axial flow impeller

Reprinted with permission from PULP & PAPER September 1985.., ----- . . . ---- ------ . . . . . . . .. -.-, ----

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gi tator ef f iciencyvelocim eter to accurately measure and record the mag-nitude and direction of flow leaving the impeller. Thelaser operates from ou tsid e the test tank, and thereforedoes not interfere with in-tank flow patterns. Withoutthis technology, a truly axial-flow im peller could not bedeveloped. What results, then, is a quasi-axial flowim peller consisting of both axial-flow and rad ial-flowcomponents, as shown in Figure 3.Becau se the rad ial com ponent d oes exist, a resu ltantflow is produced that does not parallel the axis of theimpeller, and as a result, flow efficiency, expressed asflow per horsepow er, is reduced. Not only does the rad i-al component inhibit the impellers flow efficiency, italso creates additional mechanical loads on the entireagit ator system .Through the u se of a laser velocim eter, Lightnin Mix-

ers has developed the truly axial-flow A310/ A312 im-p eller for u se w ith its m ixer line. The A312 (the sid e-en-try equ ivalent of the top -entry A31o) has been sp ecific-ally developed for use on Lightnins Model VS side-entry stock agitator to withstand the severe serviceencou ntered in the p ap er ind ustry.Many energy-efficient im pellers h ave been d evel-oped. When the term energy-efficient is used in con-junction w ith an agitator, it im plies that an im peller re-quires less horsepower to d o the processi.e., the flowper horsepower is higher. There are two ways to renderan im peller energy-efficient (lower the horsepow er re-quirement) (1) develop a truly efficient axial-flow de-sign that is d ifferent in d esign to other axial-flow im pel-lers and that indeed requires less horsepower at thesame diameter, or (z) increase the impeller d iameter tolower the horsepow er required to make the im peller en-

HGU/iE 3: Quaai-axial flow impallar.

Radialcomponent

E7tcomponent

I

ergy-efficient.Lightnin chose the first approach through the devel-

opment of the A312. This impeller design generates atleast 30% more flow per horsepower when comparedwith the next most efficient axial-flow impeller of thesame d iamet er .

APPROACHTO ENERGYEFFICIENCY.Beca use th e r ad i:~al-flow com ponent exists in qu asi-axial im pellers, its re-sultant flow is at an angle to the impeller axis and isherefore less flow -efficien t. Th e axial-flow com pon en tis the component that does the work. The rad ial compo-nen t w astes energy becau se th is com pon en t r ecircu latesback to the suction sid e of the impeller. To bring the effi-ciency of the alternate d esign (ap proach N o. Z) im pellerup to that of the A312 impeller, the d iameter of the al-ternate impeller is increased at the same horsepower sothat the axial-flow component has a magnitude of 1.0(Figu re 4). Then both agitators have theoretically equ alp rocess cap acity at th e sam e h orsep ow er.The tw o equal-horsepower agitators in Figure 4 w ill

have equal process capacity only if the impellers are lo-cated properly with respect to the chest wall. To drawthe proper horsepower and to pump the necessary flow,a side-entering impeller must be located no less thanone half of its d iameter from the wall on which the agi-tator is mounted. As an example, an impeller locatedone third of its d iameter from the wall will draw i 5o ofthe power and deliver 60~0 of the flow of the same im-peller located one half its d iameter from the wall. Thisis a significant reduction in performance and is analo-gous to throttling the flow from a pump by restrictingthe available volume on the suction side of the pump. Top rov id e for p rop er off-w all clea ran ce for lar ger -d iameteimpellers, a longer shaft is required . This longer shaficombined with a larger-d iameter impeller, results in a umore mechanically demanding system, as shown in thefollowing discussion.

MECHANICAL REVIEW.To illustrate the effect of in-creasing the diameter of a particu lar impeller design atthe same horsepower to create an energy-efficient de-sign, a review of the mechanical loads on the agitationsystem follow s. First, tw o basic p rocess relationship smust be d escr ibed :

Horsepower, Hp = N3 D5N, SpeedD, DiameterProcess capacity = Hp X D, orMomentum, M = N2 D4

FIGURE 4: Effact of incraaaing impallar diamatar.

Diameter = D + X Diameter = DAlternate impeller Lightnin A312 -

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ELATIVEVALUENTF

TABLE IV

LIGHTNIN VS. THE COMPETITIVEEQUAL PROCESS CAPACITY MACH INES

COFWETITIVELIGHTNIN VS STANDARO SELECTION

75 Hp/ 50 A312 100 Hp/ 50 Impeller

propaxcLshaftMBGM6TD (at stuffing hex)

1.63.82.86

1.01.01.01.01.01.0

1.791.01.01.01.01.01.01.01.0

.94 1.0

.94 1.0

.82 1.0

.94 1.0

COMPETITIVEENERGY-EFFICIENT SEL

75 Hp/67 Impeller1.01.341.161.701.01.01.01.241.241.731.731.341.71

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As an exam ple, assu me the p rocess cap acity requ iredof a side-entry agitator is 5,000. Either a 100-hp, so-in.im peller or a 7.5-hp, 67-in. im peller of the sam e designw ill satisfy a p rocess cap acity of 5,000. Table 1 show s therelative comparison of speed and momentum for theseWO selection s. Table 2 reflects th e m ech an ical r elation -nips of torque and flu id force based on the follow ing:Torque, T = Hp/N (in. / lb)Fluid force, F = Na Db (lb)N, Impeller speedD, Impeller diameter

Each different im peller d esign incorporates its ow n flu -id forcesi.e., those forces reacting on the im peller andshaft as a resu lt of d isp lacing stock. The greater the rad i-al com ponent a particu lar im peller design has, the high-er the fluid forces generated by the impeller and thegreater the m echanical load s on the agitator.To mechanically compare the two equal process ca-

pacity machines of Table 1 on a relative basis, the fol-lowing parameters w ill be used:. Ben ding m ovem en tq Bend ing st ress. Tor sion al str essq Deflection,

The definition of these term s is as follow s:( )shati ~Bending moment, MB = F + WP,OP+ 2F = Fluid force (lb)w PrOP = Weight of impeller ( lb)W,h,t = Weight of shaft from inboard bearing to impeller (lb)L = Distance from inboard bearing to centerline of impeller

Bending stress, u~ = ~C = Shaft radius (in. )I = Moment of inertia at shaft (in,)

Torsional stress, a~ = ~T = Torque = Hp X 63025/N (in. /lb)

Deflection, A = & (2La + 3Lx X2)P= FF+WP,OP+YX = Distance from inboard bearing to point in question (in. )a = Bearing spacing (in. )E = Modulus of elasticity (psi)

TABLE 7:Reletive comperieon of speed end momentum.

Table 3 reflects the comparison of the tw o agitator de-signs, assu ming both agitators incorp orate equ al d iam e-ter shafts of the same material and have equal bearingsp acin g. (Sh aft len gth reflects on e-h alf-d ia-off-w all p lu s12 in. for wall thickness so that the units remain equalon a p rocess basis. ) Table 3 d em onstrates th at in creasin gimpeller d iam eter to reduce horsepow er results in a sig-nificantly more demanding mechanical system. Thisanalysis highlights the fact that equ al process capacitymachines using the same impeller design are not a le-gitim ate ap proach u nless the m echan ical cap abilities ofthe machines are equal. To produce mechanically equalmachines, the following review will show the shaft d i-ameter required on the energy-efficient selection toyield the sam e shaft stress as the stand ard selection.First, the shaft d iameter required to provide equal

bend in g stress is as follow s:dy&6 = 1.0MSwhere subscript E means energy-efficient selectionS means standard selection

6 MB@~from above * = 6W 1~ = 1.0MB~csIs

7rc~4

the equation becomes 41,735 =%4$ = 1,0G 7TCE414()E 3then c~ = 1.73and C, = 1.20 C~ for equal bending stress

Similarly, the shaft d iam eter required to provid e equaltor sion al stress is as follow s:6JE6 = 1.0Tsfrom above 6~ =TECE

6 Ts IETs CSIs

because ~ = 1.34 andthe equation becomes

1,34 ~ 7rcs414G 7rcE4/4()E 3then Cs = 1,34and C~ = 1.10 Cs for equal

= 1,0

1~ 7rcs4/4L= 7rcE414

= 1.0

torsional stressTABLE 2: Mechanical relationships of torque and fluid force.

Process Dia Relativa N Relative T Ratative Fcapacity Hp (in.) (impeller speed) (torque) (fluid force)5,000 100 50 1.79 1.0 1.05,000 75 67 1.0 1.34 1.16Based onempirical exponential valuesof a = 1.5,b = 3.5 in the fluid fo rc e e qua tio n.

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7

Because the shaft d iameter required for equal bend-ing stress is greater than that required for equal tor-sional stress, the d iam eter for equal bending stress con-t ro ls t he select ion.Therefore, th e altern ative energy-efficient selec-

tion must have a shaft d iameter that is 20% larger thanthe shaft d iameter of the standard selection in order tomake the two selections equal for both the process andmechanical designs. Anything less w ill resu lt in a pre-mature shaft failure as compared with the standardselection.To summarize the essence of this analysis, two facts

a re ev id en t: (1) within the same impeller design (sameblade shape, angle, etc. ) the horsepower required top rop erly agitate a stock chest can be red uced by in creas-ing the d iameter of that impeller design, but (z) the me-chanical demands imposed by the larger-d iameter im-peller necessitate a larger shaft to maintain the samed egree of m ech an ical in tegrity as th at of a h igh er-h orse-p ower / sm aller -im p eller d esign .Rem em bering that the above analysis w as done sole-

ly to exp lain th e p rocess an d m ech an ical con sid eration sinvolved in the alternative approach of increasing im-p eller d iam eter to low er horsep ow er, it is now n ecessaryto und erstand the basis for the d esign of Lightnins A312im peller and th e VS agitator.

AXIAL-FLOW IMPELLER. Lar ge-d iam eter im p eller sare often used to decrease connected horsepower re-quirements. This approach is taken solely for the pur-p ose of increasing the axial-flow com ponent (the w ork-horse of a side-entry impeller). Lightnins laser-de-veloped A312 has the ad vantage of being a purely axial-flow impel le r.Figu re 5 shows a comp arison of alternate im pellers at

d iameter D and diameter D + X to an A312 of d iameterD to show the proportionality of the axial-flow compo-n en t (QA).Because the A312 generates pure axial flow, the im-

peller horsepower can be reduced as well as the impel-ler d iameter. In essence, the Lightnin VS agitator can,based on laboratory analyses and comp arisons, offer thep ow er savings equ al to or greater than other energy-ef-ficien t selection s, in ad dition to offerin g a less d em an d-in g m ech an ical system .For the alternate energy-efficient selection to be of

m echanical in tegrity equ al to the Lightnin VS m achin e,the alternate shaft must be 23~0 greater in d iameter perthe sam e analysis d one above. Anything less w ill resultin premature shaft failure due to excessive bendingstress.

AGITATOR PROCESSEVALUATION. When ev alu atin gstock agitator p roposals based on pu mping capacity (thevalue of Q in Figure 5), cau tion must be taken to be surethat the basis for the pump ing rate is und erstood .First, only the primary pumping capacity shou ld be

consid eredthat is, the flow that is actu ally leaving thrimpeller, not the total pumping capacity, which include. ,the estim ated and immeasu reable second ary or in du ced flow. The primary Q that is ord inarily reported is thatflow that is associated w ith the resultant vector Q in Fig-ure 5.However, because only the axial flow contributes to

stock motion, the proper value of Q to be reportedshould be the axial portion (QA) of Q. In the case of theA312, these are the same. How ever, for the alternate im-peller, QA is certainly less than Q because of the rad ialcomponent. The approximate ratio of QA/ Q for the al-ternative im peller is 0.9, w hich d ed uces the fact that theratio of the rad ial component, QR, to the primary flow,Q , is 0.44.This means that more than 40~0 of the total flow is in

the rad ial d irectionan undesirable cond ition from am echanical stand point, as p reviou ly noted . To p rop erlyev alu ate an y agitator s r ep orted p um pin g cap acity, d ocu -mentation should be presented that substantiates theaxial -flow componen t.The use of hp x D, or momentum, for evaluation is

only valid when evaluating impellers of the same de-sign. As stated ear lier , each im peller d esign in cor poratesits own characteristics in terms of flow efficiency.Therefore, to evaluate the process capacity of a stockagitator, d ocumentation m ust be p resented th at su bstan-tiates an y claim s of flow efficien cy. s

TABL E 3: Comparison of equal-proceaa-capacity agitatora -----having alternate impellers of the same design.Energy-efficientRelative Standard selection selectionvalues 100 Hp/50-in. impeller 75 Hp/67-in. impetier

N 1.79 1.0T 1.0 1.34F 1.0 1.16w prop 1.0 1,70a 1.0 1.0x 1.0 1.0c 1.0 1,0L 1.0 1,24w,~, 1.0 1,24MB 1.0 1.73CM 1,0 1.736~ 1,0 1.34A (at stuffing box) 1.0 1.71

F/GURE 5: Axial-flow components of various impeller designa.--$j=:A~~:. ++::,Dlam;~2= DAlternate impellers

.-..