Nasa Balde Theory

8/8/2019 Nasa Balde Theory

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T E C H N I C A L N O T E

JJLOAN COPY: R E T U R h r r gKIRTLAND AFB, N M S

0- gFWkL (WLIL-2) w m-- 2 L

BLADE-ELEMENT PERFORMANCEOF 0.7 HUB-TIP RADIUS RATIOAXIAL-FLOW-PUMP ROTOR WITHTIP DIFFUSION FACTOR OF 0.43by James E. Crozcse a n d D o n ald M . SandercockLewis Research CenterCleueland, OhioN A T I O N A L A E R O N A U T I C S A N D SP AC E A D M I N I S T R A T I O N W A S H I N G T O N , D. C. 0 SEPT EMBER 1 9 6 4


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TECH LIBRARY KAFB, NMIlllllllllllllllllllllllllllllllllllllll Ill.0079b03

BLADE-ELEMENT PERFORMANCE OF 0.7 HUB-TIP RADIUS

RATIO AXIAL-FLOW-PUMP ROTOR WITH T I PDIFFUSION FACTOR OF 0.43

By James E. Crouse and Donald M. SandercockLewis Rese arch CenterCleveland, Ohio

NA TIO NA L AERONAUTICS AND SPACE ADMINISTRATION~~ ~

For sa le by the Off ice of Techn ical Services, Department of Commerce,Washington, D.C. 20230 -- Pr ice $1.00


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BLADE-ELEMENT PEEFORMANCE OF 0.7 WB-TIP RADIUSRATIO AXIAL-FLOW-PUMP ROTOR WITH TIP

DIFFUSION FACTOR OF 0.43by James E. Crouse and Donald M. Sandercock

Lewis Research Center

SUMMARYA 9-inch-diameter ax ia l- fl ow pump w a s t e s t e d i n water. T!ne double-c i r c u l a r- a r c - b l ad e d r o t o r ha d a h u b -t i p r a d i u s r a t i o of 0.7, t i p s o l i d i t y of

1 . 0 2 , and desig n D-fa ctors of 0.43 and 0.70 a t t h e t i p a nd hub, r e s p e c t i v e ly .The in ves t ig a t io n covered opera t ions under bo th n oncav i ta t ing and ca v i ta t in gcondi t ions . Rad ia l surveys of f low cond i t ion s a t t h e r o t o r i n l e t and o u t l e twere tak en, and performance acr os s a se le ct ed number of bla de elem ents w a s com-puted and presented.The lar g es t va r i a t io n of b lade-element performance parameters wi th i n l e tf lo w o cc ur re d i n t h e b l a de t i p re g i on , t h u s i n d i c a t i n g t h e c r i t i c a l i t y of d e -s ig n i n t h i s a re a. Over th e upper 30 perc ent of b la de hei gh t , lo ss -c oe ff i c i en td i s t r i b u t i o n s w i t h i n ci d en c e a n g l e s f o r t h i s r o t o r c o n f ig u r a ti o n i n d i c a t e d t h a t

p o s i t i v e b l a d e s t a l l ( s h a r p i n c r e a s e i n l o s s c o e f f i c i e n t ) o c c u r r e d v e r y c lo s et o th e minimum-loss incidence angle , but th e l o s s c o e f f i c i e n t i n c re a s ed v er yslowly moving from reference incidence angle toward a nega t ive s t a l l condi t ion.A t des ign flow t he de sig n and measured performance compared fav ora bly a t

a l l r a d i a l l o c a t i o n s e x c e p t a t th e t i p e lement . Because of a d e cr e as e i n t h ei n l e t - f l o w c o e f f i c i e n t a t t h i s element (probably due t o cas ing boundary la y er ) ,t h e t i p r o t o r e lem en t o pe r at e d a t an incidence angle above the design value andv e ry c l o s e t o a blade s t a l l condi t ion . Consequent ly , the t ip - re g io n per f o r -mance showed s i gn if ic an t de via t io ns from the pre dic ted design values . Fur-thermore , a l though a t de s ign f low most of th e blade e lements were op erat i ngnear t h e i r res pe ct i ve minimum-loss ope rat in g po in ts , th e f low margin betweendesign and blade s t a l l w a s s m a l l .

The measured pump ro t o r perfo rma nce i s compared w i t h p r e d i c t e d v a lu e sus ing th e des ign p rocedures o f re fe ren ce 1.cedure a t h ig h i n l e t - f l o w a n g l e s i s demonstrated, and t h e n eed f o r a d d i t i o n a ld a t a a n d/or m o d i f i c a t io n s t o t h e d e s ig n s yste m f o r u s e i n t h e high i n l e t - f l o wa n g le a r e a i s ind ica ted .

The s e n s i t i v i t y of t h e d e s ig n p r o -


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I111111111111111 I I

Tests u nd er c a v i t a t i n g c o n d l t i o n s showed th a t t h e e f f e c t s o f c a v i t a t i o n onrotor b lade performance were f i r s t noted a t a ca vi ta t i on number of approxi-mately 0.19.

INTRODUCTION%e succ ess of th e des ign of an axial-flow-pump rotor (or s t a t o r ) d ep en dsp r i m ar i ly on t h e a b i l i t y to p r e d i c t a c c u r a t e l y t h e f o ll o wi n g:(1)Devia t ion of the f lu id - f lo w ang les from th e b lade ang les( 2 ) Level of l o s s of th e f low process through the cascades o f b lades( 3 ) Inc idence ang le (or a n g l e of a t t a c k ) a t which the l o s s i s i n aminimum-loss range

Considerat ions of maximum b la d e lo a d ing , f lo w r an ge , and s t a b i l i t y g e n e r a l l yg u id e t h e s e l e c t i o n of t h e p re v io us b a s i c p a ra m e te r v a lu es . F in a l l y , t h e b l a d eelemen ts should be matched f o r o v er a ll optimum design.I n r e f e r e nc e 1 h e blade-elem ent performance from a l a r g e nuniber of c as -

cades and rotors u t i l i z i n g a i r a s t h e t e s t f l u i d a r e c o r r e l at e d , and e m pi r i ca lr u l e s for pr ed ic t i ng minimum-loss incidence angle , de vi a t io n angle , and l o s sar e formulated. The ov e ra l l and blade-element performance of an ax ia l - f l owrotor pumping water i s p r e s en t e d i n r e f e r e n c e s 2 and 3. I n a d d i ti o n to t h ed i f f e r e n c e s of f l u i d s and fl ow v e l o c i t i e s , t h e most s i g n i f i c a n t d i f f e r e n c e fromt h e d a t a of r e f e r e n c e 1 s t h e l a r g e b l ad e s t a g g e r a n g l e s (or i n l e t a n gl e s) a twhich th e wate r pump o pe ra te s as compared t o tho se used by a i r -compressor ro to rblades .wa te r wi th tho se p red ic t ed f rom the des ign r u l e s p r e s en t e d i n r e f e r e n c e 1 r emade.

Comparisons o f th e observed r e s u l t s of t h i s pump ro to r opera t ing i n

To e v a lu a t e f u r t h e r t h e u t i l i t y of a pp ly in g t h e d a t a of r e f er e n ce 1 oth e des ign of ax ial -fl ow pumps, th e performance of t h i s second pump ro to r w a si n v e s t i g a t e d .t i p r a d iu s r a t i o t h an t h a t r ep or te d i n r ef e re n ce 2. The design and o v er a l lp er fo rm an ce of t h i s r o to r a r e r e p o r t e d i n r e f e r e n c e 4. This r e p o r t p r e s e n t sth e performance of th e in di vi du al bla de elements and compares i t w i th t h e d e -s i gn c r i t e r i a of r e fe r e n ce l. Cavi ta t ion per fo rnance i s a l s o p r e s e n t e d .

This r o t o r h a d a higher l e ve l of b lade load ing and a higher hub-

APPARATUS AND PROCEDUREThe r o to r d e s ig n p ro c ed u re , t e s t f a c i l i t y , i n s tr u m e n ta t io n , and t e s t meth.

ods a r e p re s en t ed i n some d e t a i l i n r e f e r e n c e 2; consequent ly , only a b r i e fresume of sa l i en t po in ts w i l l be made herein.appendix A. ) ( A l l symbols a r e d e f in e d i n

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Rotor DesignThe pump r o t o r w a s 9 inches i n diameter w i t h a 0.7 h u b -t i p r a d i u s r a t i o .

TABLE I. - RADIAL DISTRIBUTIONS OF DESIGN PARAMETERS[Rotor t i p diameter , 9.00 inches; number of

b lades , 19 . ]Rot orr a d i u sr a t i o

hub- t ip

r/ rtTip L O C.9:

.9c.8.5

.8C.7.5Hub .7C

D i f f U-s i o nf a c t o r ,D

0.426.433.464.505.555.615.693

Cnci-h n c eIngle >1,de g

6.42. 0.9-5.61 .01 .2

Devia-t i o n% l e

6,deg4.65.46.97.88 .38.89.3

:ambertngle 7

CP Jdeg

0l l . 816.419.822.124.627.6

j o l i d i t y ,U

1.011 . 0 61.121.191.261.351.44

Zhord,i n .CY

~

a

j e t t i n g,r67.164.962.860.558.255.352.2

i a t i o ofmaximumihicknes:;o chord;t m d c0.0700.0725.0750.0775.0800.0825.OB50

The des ign u t i l i z ed a blade e lement concept wi th design calcula t ions madea c r o s s a se le ct ed number of blad e elements. These a re the n stack ed t o form ablade.The veloci ty diagrams were constructed ut i l iz ing the fol lowing assump-t i o n s and s e l e c t i o n s :

Zc-60783

(1)N o i n l e t w h i r l (Vo,l = 0 )( 2 ) I n l e t r e l a t i v e f lo w a ng le

of 73.6O a t t he t i p ( i d e a li n l e t -f l o w c o e f f i c i e n t of0.294 when combined with(1)

( 3 ) I n l e t - f l o w c o e f f i c i e n t 01cons tan t a t a l l r a d i i( 4 ) Rad ia l ly cons tan t energya d d i t i o n (q i = 0.294)( 5 ) Assumed r a d ia l d i s t r ib u t io nof l o s s c o e f f i c i e n t( 6 ) Radia l equ i l ib r ium

(ah/& =


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I I1 1111111111 II

s i re d f low con dl t io ns . Blade incidence and de vi a t io n angl e were computed fromthe equ a t ions of re f e ren ce 1w i t h s l i g h t m o d i fi c a ti o n s a s d e s cr i b ed i n r e f e r -ence 4.

R a d i al d i s t r i b u t i o n s of s i g n i f i c a n t d es i g n p ar am e te rs a r e g i ve n i n t a b l e Iand on th e performance f ig ur es .u re 1.

A photograph of t h e rotor i s shown i n f i g -

T e st F a c i l i t yThe pump performance w a s inve s t iga ted i n th e Lewis Research Cente r wa te r

During oper at i on th e ga s con tent remains below 3 p a r t s p e r m i l l i o n b yThe f i l t e r i n g s y st em i s capable of removing so l i d mat te r l a rg er than

tunne l . The major components of t h i s f a c i l i t y a r e shown schemat ica l ly i n f i g -ure 2.weight.5 microns.

T e s t Procedure and Ins t rumentat ionThe t e s t p rocedure con s i s te d o f s e t t i ng flow, speed , and i n l e t p res sure

and th e n o b t a in in g r a d i a l s u rv ey s of t o t a l and s t a t i c h ea ds p lu s f low ang le a tth e b lade i n l e t and ou t le t . The survey ins t rume nts shown i n f ig ur e 3 con-s i s t e d of a claw-type probe t h a t measured t o t a l press ure and angle and a wedge-type p robe t h a t measured s t a t i c p ressu re and ang le .loca ted approx imate ly 1 in ch upstream and downstream of t he blad e le ad ing andt r a i l i n g e dge, r e s p e c t i v e l y . A h ea d c a l i b r a t i o n f a c t o r f o r e a ch s t a t i c wedgeMeasur ing s ta t ions were

,-Circulating pump forHeat exchanqer ,/ degasification process

\-Test section

r ressureI control l ingI accumulator /1.,--- --,..... .(a) Total-pr essure claw. (b ) Static-pressure wedge.

Figure 3. - ProbesI/ D-6902Figure 2. - Lewis water tu nne l.

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w a s de te rmined i n an a i r t u n n e l and a p p l i e d t o t h e m easured s t a t i c p r e s s u r e s i nt h e w a t e r tun nel . Rotor speed w a s obtained f r o m an e lec t ron ic speed coun te rused i n con junc t ion with a magnetic pickup, and f l o w w a s measured by means of aventur i f lowmeter . Water temperature w a s mainta ined a t a constant value ofapproximately 80 F. The estimated accuracy of t h e fo llow ing measurements rep-r e s e n t s t h e i n h e r e n t a c c u r a c y of t h e measuring and recor din g dev ices employed:Flow ra te , Q, p e r c e n t . . . . . . . . . . . . . . . . . . . . . . . . < + L ORotat ive speed, N, p e r c e n t . . . . . . . . . . . . . . . . . . . . . . . f0.5Head rise, AH, p e rc e nt of f u l l s c a l e . . . . . . . . . . . . . . . . . < +0.5Flow angles , p , deg . . . . . . . . . . . . . . . . . . . . . . . . . . k1.0Discrepancies a r i s i n g from unsteady flow cond i t ion s , c i r c u m f e re n t i a l v a r i a t i o n sof f l o w , c a v i t a t i o n on th e probes , e t c . , could not be evaluated.

The equat ions necessary for ca lcula t ion.of the desi red performance param-e t e r s a r e p r e s en t e d i n a pp en dix B.Figure 4 provides some check on th e re l i a b i l i t y of th e d at a by comparing

9 c0

Net positivesuct ion head,fl ' Hs: Ifl14 133

. 3 3 .35 .3 7

Rotative1.39 .4 1Average flow coefficient, Q

(a ) In let measuring stat ion .

. 3 1 . 3 3

b

- c1

(b ) Out let m easuring stat ion .F i g u re 4. - Co mp ar i so n of integrated weight f lows a t blade in let an d outlet with those measu red by ven tur i m eter .

t h e in tegra ted weigh t f l ows a t t h e b l a d e i n l e t a nd o u t l e t w i th t h o s e measuredby th e ve nt ur i f lowmeter. The comparisons a t both th e i n l e t and ou t l e t mea-s u r in g s t a t i o n s a r e c o n s id e r e d good and presage conf idence i n the v a l id i t y ofthe observed flow measurements.

Se le ct io n of Blade-Element Parameters f o r Ana lysis

3.4 1The a n a l y s i s of r o t o r p erfo rm an ce p a r a l l e l s t h e d e s ig n p ro ce du re i n t h a tindividual element performance i s a na ly ze d a nd t h e n i n t e g r a t e d t o o b t a in t h eo ve ra ll blad e row performance. Through a given b lade passage th e f low pa t te rn sa r e p r i m a r i ly a f f e c t e d by

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s e p u a t e s ec ti on s.For t h i s p a r t i c u l a r r o t o r o p er at in g i n wa te r a t a b la d e t i p s pe ed of

141.5 f e e t p e r se co nd , as th e system head w a s reduced t h e i n i t i a l e f f e c t s ofcavi ta t ion on measured rotor performance occurred a t an i n l e t head o f approxi -mately 1 1 7 f e e t (cor responding t o a su ct i on spe ci f i c speed of approximately7600). A t t h e s e o p e r a t i n g c o n d i t i o n s c a v i t a t i o n on t h e b l a d e s u r f a c e and i nt h e t i p v o rt ex w a s v i s i b l e t h r o u g h a t r a n s p a r e n t a c r y l i c p l a s t i c c as in g.c r e a s in g t h e i n l e t p re ss ur e t o 160 f e e t e l i m i n at e d t h e b l a d e s u r f a c e c a v i t a t i o nb u t n o t a l l t h e t i p v o r t e x c a v i t a t i o n ; h en ce , p er fo rm an ce o b t a in ed a t an i n l e thead of 160 f e e t (or g r e a t e r ) i s p r e s e n t e d h e r e in as noncav i ta t ing .

In -

I n g e n e r a l, t h e c u r v es p r e s e n t e d a r e s e l f - e x p l a n a to r y a nd only p o in t s o fs p e c i a l s i g n i f i c a n c e w i l l be discussed.

Noncavitating PerformanceOverall performance. - The n o n c av i t at i n g o v e r a l l -erformance i s presen ted

i n f i g u re 5 with mass -averaged head- r i se coef f ic ien t JI a n d e f f i c i e n c y 7

.x)\x34

\

t ip suction head,Rotor Net positiveI I I I I I II1

00

.38 .42 .26 .?uAverage flow coefficient , (p

speed,ftlsec

113"tl

,+

.3 4 .38 .42Figure 5 - Overall performance of axial-flow-pump roto r for noncavita ting conditions.

shown a s func t ions o f f l o w c o e f f i c i e n tpar i son . S ince th e ov er a l l per fo rmance i s d i s c us s e d i n r e f e r e n c e 4, o n ly t h em ajor p o i n t s a r e r e p e at e d b r i e f l y h e r e i n.

v. Design valu es ar e included f o r com-A t d e sig n- f lo w c o e f f i c i e n t (assuming a 3-percent boundarv la ye r b lockage

f a c t o r ) t h e r o t o r p rodu ced a s l i g h t l y h ig h er -t h an - de s ig n h ead r i s e a t a higher -t h a n -d e s ig n e f f i c i e n c y . If th e whole range of op era tio ns i s cons idered , th rees ig n i f i c a n t pe rf orm an ce f e a tu r e s a r e n o te d f o r t h i s rotor, namely,(1)High l e v e l of e f f i c i e n c y

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( 2 ) Re la t ive ly wide range o f ope ra t io n over which a h i g h e f f i c i e n c y(>O. 90) w a s a t t a i n e d

( 3 ) Smal l flow marg in be tween th e des ign po in t and an opera t in g co nd i t ion(6 0.271) below which excess ive r i g v ib ra t i on s p reven ted p ro longedo p e r a t o n

Blade-element performance. - Figure 6 p r e s en t s t h e r a d i a l d i s t r i b u t i o n sof f low and se le ct ed blade-element performance param eters f o r a range of ope r-a t i n g c o n d i ti o n s . Th is type of p l o t d i s p l a y s t h e r a d i a l d i s t r i b u t i o n s of flo wand r a d i a l matching of blade-elem ent performance under va rio us modes of ope r-a t i o n . It a l s o i n d i c a t e s t h e r an ge of i n l e t - f l o w c o n d i t i o n s a succeeding s ta-tor row would be required to accept .

Over th e range of f low covered by fi g u re 6, th e i n l e t cond i t ions show nos i g n i f i c a n t change i n t h e r a d i a l d i s t r i b u t i o n s of f low parameters. Axial ve-l o c i t i e s are n e a r ly c o n s t a n t a c r o s s t h e p a ss a ge w ith t h e s m a l l dropoff i n t h et i p r e g i o n p r ob a bl y due to ef fe c t s of cas ing boundary lay er . Refe rence 4 a l s oshowed a decrease i n i n l e t t o t a l head a t t h i s s t a t i o n f o r a l l opera t ing cond i -t i o n s. F r e r o t a t i o n of t h e f l u i d i s s m a l l a t a l l o p e r a t i n g p o in t s a n d , i n gen-e r a l , i n c re a s e s s l i g h t l y as f low i s decreased.

The r a d i a l d i s t r i b u t i o n of o u t l e t - f l o w c o n d i t i o n s an d p er fo rm an ce r e l a t e st h e ind iv id ua l e lement per fo rmances th rough th e ra d i a l equ i l ib r ium requ i r e -ments.formance a t a g i v e n i n l e t flow, some knowledge of th e v a ri a ti o n of de vi at io nangle and loss with inc idence ang le f o r each element must be ava i lab le .type of inform at ion i s p r e s e n t e d l a t e r i n t h i s s ec ti on .)t i on s of ou t l e t - f low condi t io ns and e lement pe rformance f o r t h i s rotor i n d i c a t et h a t t h e bl ad e t i p r eg io n d is p l a ys t h e g r e a t e s t s e n s i t i v i t y to changes i nin le t - f lo w co ef f ic i en t . The fo l lowing observ a t ions a r e made:

To c o n s t r u c t t h e r a d i a l d i s t r i b u t i o n of o u t l e t - f l o w c o n d i t io n s and p e r -( T h i sThe r a d i a l d i s t r i b u -

(1) or any g iven va lue o f b lade load ing (a s ind i ca te d by D-fac to r va l -u e s ) , t h e l e v e l of l o s s m easured i n t h e t i p r e g i o n i s s e v e r a l t im e s t h a t ob-served a t any o t h e r r a d i a l l o c a t i on . This i n d i c a t e s t h e o cc u rr e nc e of t i pc l e a r a n c e and s ec on d ar y f lo w s and t h e i r e f f e c t s o n t h e l e v e l of l o s s i n t h i sregion.

( 2 ) The energy ad d i t ion var ia t io n w i t h i n l e t f l ow c o e f f i c i e n t i s cons ider -A s im p le v e lo c i t yb ly l a r g e r i n t h e t i p r e g i o n t h a n a t o t h e r r a d i a l s t a t i o n s .d iagram an a ly s i s , a ssuming th e dev ia t ion ang les or o u t l e t - r e l a t i v e - f l o w a n g l e sre ma in c o ns t a n t, i n d i c a t e s t h a t f o r a given change of ou t le t - f low co ef f i c i en tt h e e n er gy a d d i t i o n qiang le inc reas es . I n an ac tu a l app l ica t ion , however, th e changes ob ta ined f romt h e s e i d e a l i z e d c a l c u l a t io n s are t empered by ra d ia l equ i l ib r i um requ irementsand t h e e f f e c t s of t h e r a d i a l g r a d i e n t of l o s s on t h e r a d i a l v a r i a t i o n of a x i a lv e l o c i t y .

change w i l l b e g r e a t e r as t h e o u t l e t - r e l at i v e - f l o w

( 3 ) The e f f e c t s of t h e r a d i a l v a r i a t i o n s of l o s s c o e f f i c i e n t a r e o bs er ve don b o th t h e d i s t r i b u t i o n s of a c t u a l h e a d - r i s e c o e f f i c i e n t and o u t l e t - f l o wc o e f f i c i e n t CP I n b o th c a s e s t h e g r a d i e n t s i n t h e t i p r e gi on a r e l e s s t h an28


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.1

. 3 ,

. 2

.1

Design,1 ;

--.\-h

.7

nL- .50c

cVI.-2 . 3--n

.1.3 5

3cc.s .25y.-= Im0VI.-P .15i

.051. 7 . 8 .9 1.0

mmrom--m5cm>.--n

I

110

H) I 1 1

.451 !

.35I

.251

.7 .8 .9 1.0Rotor hub-tip radius ratio, r/ rt

ccV.-.-=, .18VIv)

0

.7 .8 .9 1.0

Figure 6. - Radial distributions of flow and blade-element performance parameters for noncavitating conditions. Rotor tangential velocityat tip, 141.5 feet per second; ne t posi tive suc ti on head, >160 feet.

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. . ... . .. .... . .-


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might be expected f rom th e observed sharp gra di en ts of energy addi t ion . Thisi s n oted p a r t i c u l a r l y when co mp arin g r a d i a l d i s t r i b u t i o n s a t i n l e t - f l o w c o e f -f i c i e n t s of 0.302 and 0.284.

For comparison with desig n, th e da ta obta in ed a t a flow c o e f f i c i e n t o f0 .284 (designa r y l a y e r on t h e v e l o c i t y i n t h e t i p re gi on s r e s u lt e d i n a lower- than-designa x i a l v e l o c i t y at t h e t i p and a s l i g h t l y h i gh e r- th a n- d es ig n a x i a l v e l o c i t y a ta l l o t h e r s t a t i o n s . T h is i s res po nsi ble f o r th e comparison of design and mea-sured incidence angle shown.a t a l l r a d i i i n c om pa ris on to th e d esig n assumption of no i n l e t w h i rl . A t t h edesign le v e l of performance a t th e hub measuring s t a t io n ( r / r t = 0.728) anin l e t - f l o w a n g l e o f 2.7' r e s u l t s i n a d i f f e r e n c e o f 0.5' i n i n c id e n c e a n g l e anda 3- to 4 - pe r ce n t d i f f e r e n c e i n e ne rg y a d d i t i o n .

@ = 0 . 2 8 2 ) are used . A t t h e i n l e t t h e e f f e c t s of c a s in g bound-

Smal l pos i t ive - f low ang les (


13/37

l o s s i n c id e n ce a n g l e s p lu s t h e l o s s l e v e l and d e v i a t i o n a n g le a t t h e r e f e r e n c einc idence ang le . A t r a d i a l p o s it i on s 1 and 2 ( r / r t = 0 . 9 7 1t i v e l y ) th e f low ranges covered def ined minimum-loss incidence angle s reason-abl y wel l . Both of th es e blad e e lements d i sp la y a very sharp inc rease i n l o s son th e po si t i ve (high incide nce) s id e of th e minimum-loss poin t and a gradua li n c r e a s e i n l o s s on th e n egat ive (low inc ide nce ) si de of t he minimum-losspo in t . A t the remaining r a d i a l measuring st a ti o n s minimum-loss in cide nce an-g l e s a r e n o t w e i l d e fi n ed , b u t a l l elements show a r e l a t i v e l y s m a l l inc rease i nl o s s on the negative side of minimum-loss incidence angle. A s a r e s u l t of t h i sp a r t i c u l a r v a r i a t i o n of loss f rom the minimum-loss p oi nt t o h igher incidenceangles , a t b o th r a d i a l p o s i t i o n s 1 and 2 t h e maximum e f f ic i e n c y and m i n i m u ml o s s o cc ur a t the same incidence angle.

and 0.906, respec-

. aYL1nE,= . 4c0m>mu

.-cc.-

Cer ta in bas ic per fo rmance t re nds on b l a de s t e s t e d i n a two-dimensionalcascade a re r e p o r t e d i n r e f e re n c e 6, I n l e t f lo w a n g l e s up t o 70 a re covered.From th es e cascade t e s t s the recommended des ign angle of a tt ac k i s s e l e c t e d b y

o - -

examining measured blade surface

13z- . 2alV

W0

.-.-c :Ii;

-3 1 5

pressure g rad ien ts and des igna t ing the ang le

d

il.70

60mW0&Iai 50-mc6

30

I20

sd Rotor tip 1 pa,..ivespeed, su ct ion head,Ut.ftlsecI

- 113.2I I141.5 I

-4 0 4Incidenc e angle, i , deg(a) Radial position 1; rotor hub-tip radius ratio, 0.972.

Figure 7. - Rotor-blade-element performance characteristi cs for no ncavitat ing conditions,

133I


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of a t tack a t which no veloci ty peaks appeared on e i t he r b lade sur face as o p t i -mum or design. The c a sc a de r e s u l t s showed th e f o l l o w in g r e l a t e d resu l t s :(1)For a given cambered blad e, th e ang le of a t t ac k op erat ing range de-c r e a s e s as i n l e t - f l o w a n g l e i s increased.( 2 ) For o p e r a t i o n a t a 70' i n l e t - f l o w angle, t h e a n g l e of a t t a c k o p e r a t i n grange decreases as camber i s inc reased . Also, t h e p o s i t i v e s t a l l angle of

a t t a c k a p pr oa ch es t h e d e s ig n a n g l e of a t t a c k more r a p id ly t h a n t h e n e g a ti v es t a l l ang le of a t t ack .

.1t

The pe rf or ma nc e c h a r a c t e r i s t i c s of t h e b l a d e e l em e n ts of t h i s r o to r a p p e art o comply wit h th e tr en ds noted previ ous ly. Assuming t h a t minimum loss and t h emost f a v o r ab l e b l a d e s u r f a c e v e l o c i t y d i s t r i b u t i o n s OCCUT a t th e same ope rat i ngp o i n t ( a n g l e of a t t a c k ) , t h e small difference between the minimum-loss and pos-i t i v e b la d e s t a l l o p e r a t i n g p o in t s would i n d i c a t e t h a t t h e t i p e le me nt s of t h i srotor a r e r e l a t i v e ly h ig h ly l o ad ed , e ve n p o s s ib ly a pp ro a ch in g a l i m i t l o a d in gcondi t io n f o r b lade e lements approx imat ing t h i s i n l e t ang le range. The t i pe le me nt ( r a d i a l p o s i t i o n 1 (RP 1)) n c u r r e d a D-factor of 0.44 a t t h e minimum-l o s s ope rat in g poin t . By th e

Rotor tip Net positivespeed, su ct io n head.-

WVW

.-.-cVILVm,.-

.1

-8 -4 0 4

mWroW

cmccm

-m.-.-tn

D

0Vc0VIcD

IcI.-.-

szz sg zz 0.5) a s compared t o t h e l e v e l o f l o s s c o e f f i c i e n t o b se rv ed i n t h e t i pr e g i on f o r lo we r l e v e l s of b l a d e l o a d in g le a d t o s p e c u la t i on t h a t r a d i a l t r a n s -po rt of th e low-energy blade boundary la ye r i s occurr ing even wi th the se sho r tchord blades.

Losses a s soc i a t ed w i t h ca s i ng bounda ry l aye r (R P 1 s

The very low l o s s l e v e l s (u,< 0.02) observed a t

A method f r eq uen t l y u sed t o e s t a b l i sh t he p os i t i v e and nega t i ve s t a l lpo i n t s o f a r o t o r ( an d t hus d e f i ne t he u sab l e fl ow ranges ) i s t o assume th a tt h e y occur when t h e l o s s i s some m u lt ip le of t h e minimum-loss v alu e. A t t h e

00

0

0 '

00

Incidence angle, i, deg

Rotdr ti p Ne; posit'iveI-- s ' suction head,Hsv,ftlsec

I4133 l l,160

50

-8 -4 0 4(c) Radial posit ion 3; rot or hub- tip ra diu s ratio, 0.850,

Figure 7 - Continued. Rotor-blade-element performance charac terist ics for noncavitating conditions.

13


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t

0O-e-

I l lRotor ii p Net positivespeed, suc ti on head,-Hsv*l.zF8

. 4

f t l s ec ft133

I

Y25cecc.-.-LV

cclU.-.-c$ 3lVILUm0)

.-

El 38 z-VI .Em u0

Y

Ln5ccc>0

.-.-

LSlU.-.-c$ 3lVILUma

.-

I.-=I 3g c-v) .Eu cm u

;I0C1 KxJ

IjI4

!A

-mlE!0

IrB

I

4Incidence angle, it deg(d) Radial position 4; rotor hub-tip radius ratio, 0.794.

Roto; tip ' Net bositivespeed, su ct io n head,Ut. Hsv,ftlsec ft: 113.2 13380 [0

I1

I148 -4 0Incidence angle, i, deg -8 -4 0(e ) Radial position 5; roto r hub-ti p ra diu s ratio, 0.728.

Figure 7 - Concluded. Rotor-blade-element performance characteristics for no ncavitati ng conditions.14


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des ign- flow opera t ing po in t , the t i p element l o s s c o e f f i c i e n t i s approximatelytwic e th e minimum-loss va lue . Together w i t h t h e s h ar p i n c r e a s e i n l o s s , t h i sind ica tes th a t sepa ra t ion of the b lade sur face boundary lay er has occur red ori s imminent. Apparently, a t a e s ig n c o n d i t i o ns , t h en , t h e t i p 1 0 percen t of t h eb l a d e h e ig h t w a s o p e r a t i n g i n a s t a l l e d c o nd i ti o n.oper at ing very c los e t o th e i r minimum-loss po in ts , however ; hence, th e o ve ra l le f f ic ie nc y remained h igh .

A l l other elements were

A t the lowes t f low (h ighes t inc idence ang le ) a t which survey da ta weretaken, lo ss es show a sharp inc rease (approx imate ly th r ee t imes) over theminimum-loss value a t r a d i a l p o s i t io n s 1 and 2 ( l o c a t e d a t 10 and 30 percent oft h e pa ss ag e h e ig h t , r e s p e c t i v e l y ) . Thus, i n the opera t ing range f rom des ignCp = 0.284 t o = 0 .271 , the ra d ia l ex t en t of b lade s t a l l condi t ions inc reasedfrom- t l e a s t 10 t o 30 percen t of the b lade he igh t .a t r i g v ib ra t io ns became excess ive and prolonged operat i on wasdeemed inadvisable. I t seems l ikely t h a t complete blade s t a l l occurred a tthese lower f low (q< 0 .271) condi t ions .

-It w a s n oted e a r l i e r t h a t

CP < 0.271

While b lade-e lement ch ar ac te r i s t i c curves such a s p resen ted i n f igu re 7have been used p r imar i ly fo r es tab l i sh ing des ign-po in t da t a , t h e y a l s o p ro v id eth e necessa ry va lues of dev i a t ion ang le and lo ss co ef f ic ie n t for p r e d i c t i n goff-design performance. A t p r es e nt t h e i r u t i l i t y l i e s i n d i r e c t a p p li c a ti o n oft h e t r e n d s t o s i m i l a r blade rows. With th e acq u is i t io n of add i t io na l da ta theymay a i d i n the fo rmula t ion o f d e t a i l e d o f f -des ign per fo rmance ca l cu l a t i on p ro-cedures.

Comparisons with co rr e l a t io ns of refe rence 1. - A spe c i f ic purpose of t h i si n v e s t i g a t i o n w a s t o c o n sid e r t h e a p p l i c a b i l i t y of t h e d e s ig n sy ste m f o r a x i a l -f low a i r -compressor ro to rs p resen ted i n re fe rence 1 o t h e d e s ig n of a x i a l - fl o wpmps . A n op era tin g cond itio n commonly se le ct ed a s t h e d e s ig n p o in t i s t h eminimum-loss op er at in g po in t. For each bl ad e element minimum-loss l e v e l s andth e dif fe re nc e between the observed pump r o to r minimum-loss in ci de ix e (and de-v i a t i o n ) a n g l e a n d a va lue c a lcu l a ted f rom co r r e l a t io n of cascade da ta ,ip - iZ-Dnd 6p - 6 2 - ~ r e compared w it h s i m i l a r values recommended froma ir - co m p re s so r r o to r t e s t s i - i2-D nd 6c - 62-D. The fol low ing procedurew a s fol lowed: C

(1)From figure 7 val ues of minimum-loss co ef fi ci en t and th e correspondingPncidence angle i d e v i a t i o n a n g l e 6p, and d i f f u s io n f a c to r s f o r e ac h e l e -ment were s el ec te d.

( 2 ) Fluid -flow an gl es were computed by using th e va lue s of (1) l u s b l a d ein l e t and o u t l e t a ng l es .( 3 ) From flow ang le s and blade-elem ent geometry {s o l i d i t y , maximum-th ickness -to -chord ra t i o , and camber ang les ) re f e renc e inc idence and dev ia t ionangle s based on two-dimensional cascade co rr e l a t io ns (i2-Dnd 62-D, r e -

sp ec ti ve ly ) were computed from methods of re fe re nc e 1.( 4 ) Comparisons of measured rotor performance parameters a t r e f e r e n c e con-ip - i2-D,

15

di t i on s with th e computed value s f rom ( 3 ) a r e p r e s e n t e d i n th e form


18/37

FjP - 62-D, andon tab le I1 t o g e th e r w i th c o r r e c t i o n f a c t o r s f o r i n c id en c e and d e v i a t i o nangles obtained from numerous a i r compressor tes ts .CO cos pz/2a. The observed val ue s f o r each element a r e shown

TAELE 11. - COMPAKISON OF MEASURED MINIMUM-LOSS PERFOFWINCE PAR/IMETERSWITH THOSE COMFDTED FROM DESIGN RuL;ES OF REFERENCE 1

Radi-a1 Approx- Minimuk-loss 1 Correction factorsimate performance

2 1 30

p90 0.011.11131o.015j0.00510.007) 7.115.71 2.33.53.4Lc - i 2 - D :

deg

-2.5-2.0-1.6-1.0-0.7

Loss co-effi-cient,20

; cos p;

0.01590.00600.00220.00120.0017

D i f f u .s i mfac-tor,D

3.4411.4401.479I. 5111.575

W hile t h e d a t a p r e s e n t e d i n t a b l e I1 r e f e r o n l y to a minimum-loss designp o in t , t h e y do prov ide s uf f i c i en t ev idence t h a t some ex tens ion and poss ib lymodi f ica t ion o f c e r ta in p a r t s o f the des ign system of re fe rence 1 a r e n e c e s -s a r y f o r a c c u r a te p r e d i c t i o n o f r e f e r e n ce inc idence and dev ia t ion ang le s fo ra x i a l flo w pumps. The performance r e s u l t s of a similar type rotor r e p o r t e d i nre fe rence 3 l e d to the same conclusion. A more d e t a i l e d d i sc uss io n app ly ingthe exper imenta l r e s u l t s f r o m t h i s r o t o r to an eva lua t io n of t he design systemfol lows i n th e se ct io n Evaluat ion of Blade Design System.I n f i g u r e 8 t h e l o s s - c o e f f i c i e n t p a r a m e te r s a t minimum-loss incidence

ang le fo r two ro to rs opera t ing i n water are compared with s i m i l a r r e s u l t s ob -ta in ed f rom s in gle -s t age axia l - f lo w air -compressor rotor s . The shaded are ar e p r e s en t s t h e r e g i o n i n which t i p l o s s p ar am et er s f e l l . The a d d i t i o n a l r o t o rd a t a p lo t t e d on f i g u r e 8 w a s t aken f rom re fe ren ce 3 where s i m i l a r comparisonswere made.

The l o s s p ar am e te r p l o t t e d i n f i g u r e 8 i s a si mp li fie d form of t he wakemomentum thickness developed iri reference 7. T h i s t h e o r e t i c a l l o s s a n a l y s i s( r ep o r te d i n r e f . 7 ) e s t a b li s h e s blade-wake momentum thi ck ne ss a s the p r imarywake c h a r a c t e r i s t i c d e s c r i p t i v e o f t h e t o t a l p r e s s u r e d e f e c t r e s u l t i n g fromboundary layer f low around a b la d e el em en t an d e s t a b l i s h e s r e l a t i o n s f o r e s -t i m at i ng t h i s b la d e p r o f i l e l o s s . Thus, wake momentum th ic k ne ss r e p r e s e n t s agenera l ized l o s s paramete r tha t i s a func t ion on ly of ind iv idua l b lade wakesand independent of th e blad e row geometry ( s o l i d i t y and a i r an gl es ). The es -tabl ishment of a genera l ized l o s s parameter i s f u r t h e r i n v e s ti g a te d i n r e f e r -ence 8 by an an al ys is of exper imental l o s s c h a r a c t e r i s t i c s of lo w-s pe ed a i rc as ca de s e c t i o n s i n t er m s of wake momentum th i c k n e s s and a b l a d e v e l o c i t y d i f -f u s i o n f a c t o r . I n r e f e r en c e 1 he si m pl if ie d wake momentum th ic kn es s e xp res -

16


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height f rom.10 outer wal l

0c!-2313z- .06-a?u.-.-a=8* .04BA

.02

0

--- 1030HI--A- 70

- 90

--m-.08--*--

--b-

Tailed symbolstaken f rom ref . 3

///I. I . 2

an gl es of t h e pump r o t o r as compared t o those encountered i n the co r r e la t io nof th e cascade and a i r compressor rotor data . A t p r e s e n t , no g e n e r a l i z a t i o nw i l l be attempted on the b a s i s of t h e performance of t h i s limited number ofr o to r s o th e r t h a n t o recommend c a u t i o n i n a pp ly in g t h i s l o s s p ar am eter t ob l a d e s w i th h ig h o u t l e t b l a d e a n g l e s.

Ca vi t a t i ng PerformanceThe ty pe of r o t o r whose performance i s p r e s e n t e d h e r e in i s o r d i n a r i l y n otexpec ted t o opera te i n an env ironment conducive t o cav i ta t ion . I t s high hub-t i p r a t i o and l e v e l of l o a di n g a r e t y p i c a l of t h e t y p e of r o t o r used i n t h eh igh-pressure po r t i on of a multistage axial-flow pump. I n orde r t o know th el e v e l of i n l e t head needed bef ore such a r o t o r c a n be used, however, a minimumamount of c a v i ta t i o n performance w a s obtained and i s presented. Although a l lth e da t a t aken a r e p resen ted , a d i scu ss ion of th e cav i ta t i ng performance i sl i m i t e d t o a f e w s i g n i f i c a n t f e a t u r e s .Overal l performance. - The o v er al l performance i s p r e s e n t e d i n f i g u r e 9

5, f f i c i e n c y T ,n t e r m s of mass-averaged valu es of head-r is e co ef f i c i en tand f low coef f ic ien t '5;.son. Non cavi tatin g performance i s also shown for compari.-me ov er a l l per fo rmance i s d i s cu s s ed i n r e f e r e n c e 4, and t h e r e s u l t s a resummarized by the following:

s i o n i s c o r r e l a t e d w i t h l o s s -es measured i n th e th r ee -dimensional environment ofs ingle-s tage compressorr o to r s .A s p e c i f i c e x p l a n a t i o nf o r t h e g e n e r a l l y lo we r l e v-e l s of th e wake momentumthi ckn ess expre ss ion fo r pumpr o t o r s a s compared t o a i r -compressor rotors i s notre ad i l y apparen t. B lade-geometry features (bladeshape, camber , sol id i ty , as -p e c t r a t i o , b l a d e t h i c k n e s st o chord r a t i o , e t c . ) a r es i m i l a r . Also, the l e ve l s

of l o s s c o e f f i c i e n t G f o ra g iv en l e v e l o f b l a d e l o a d-i n g ( D - f a c to r ) a t t h e v a r -i o u s b l a de elements a rec lose . ?"ne o n e s i g n i f i c a n td i f f e r e n c e i s t h e h ig h f l ow

(1) n i t i a l e f f e c t s of c a v i t a t i o n on perform ance of t h i s r o t o r a re f e l ta t an Hsv of approximately 116 f e e t . The dropoff i n performance is observed17


20/37

a,\

I l lNet positivesuct ion headftHS,

o >1600 1160 89A 72bl\40

Flow coefficient, qFigure 9. - O v era l l p er f orman ce f o r cav i ta t in g an d n o n -cavi tat ing condi t ions.

f o ll ow i ng g e n e r a l e f f e c t s and r a d i a l

on ly a t h ig h f l o w a t t h e s e i n l e t c on di-t i o n s .( 2 ) A t des ign- f low coef f ic ien t ,c a v i t a t i o n d i d n o t a f f e c t r o t o r h eadr i s e u n t i l a n

reached.H,, < 89 f e e t w a s

( 3 ) R o to r e f f i c i e n c y 5 w a s de-creased f rom the n o n c a v i t a t in g v a lu e sa t a l l i n l e t pressures below an Hsv ofLl.6 f e e t .

Blade-element performance. - Fig-u re 1 0 p r e se n t s t h e r a d i a l d i s t r i b u t i o n sof f low and blade-element performancef o r a n Hs v of 72.5 f e e t and th re ei n l et - fl o w c o e f f i c i e n t s c o v er in g t h erange of operat ion . These flow condi-t i o n s r e p r e s e n t s u c t i o n s p e c i f i c s pe ed sof 9009 (x= 0.148) t o 10,220(k= 0.100) f o r i n l e t -f l o w c o e f f i c i e n t sof 0.273 and 0.348, re sp ec tiv el y. Too bs er ve t h e e f f e c t s of c a v i t a t i o n onp er fo rm a nc e, t h e d i s t r i b u t i o n s of f i g -ure 10 should be compared with th ecurves of f ig ur e 6 ( n o n c a v i t a t i n g p e r -formance). With th e except ion of c avi-t a t io n number k the in le t - f low param-e t e r s a t t h e two modes of op er at io n a res im i la r , i n d i c a t i n g t h a t i n l e t - f l o w g e -ometry i s be in g maintain ed. Comparisonof t he ou t l e t - f lo w condi t ion s and e l e -ment performance parameters i nd ic at e th ev a r i a t i o n s :

(1)B oth t h e i d e a l and a c tu a l he ad c o e f f i c i e n t s a r e similar , but underc a v i t a t i n g c o n d it i on s (Hsv = 72.5 f t ) th e l e v e l of performance i s decreased.-( 2 ) L o s s - c o e f f i c i e n t p lo t s show th e s a m e high va lues o f u) i n th e t i pr e g io n compared t o o th e r r a d i a l l o c a t i o n s .

wi th occur rence of cav i ta t io n .Also, the l e v e l of loss i n c r e a s e s

( 3 ) The genera l t r en d o f d ev ia t ion ang le i s t o i nc r ea s e a s Hsv i s low-e r e d ( c a v i t a t i o n i n cr e a s i n g ) .

( 4 ) D i f fe r e nc e s i n r a d i a l e q u il i br i u m r e qu i re m en t s a r e r e f l e c t e d i n t h er a d i a l d i s t r i b u t i o n s of f lo w c o e f f i c i e n t . R a d i a l e q u i l i b ri u m r eq u ir e m en t sv a r y a s c a v i t a t i o n (or change i n mode o f op era t io n) a f fe c t the ra d ia l g rad ien tsof the element performance parameters.r a d i a l d i s t r ib u t i o n of a x i a l v e l o c i t y under c a v i t a t i n g (Hsv = 72.5 f t )

A t t h e h i g h f l ow s (v = 0.350) t h e18


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41IIO1

-2

-0 0.35- .32

15

10

5

0

mWdEW-mccm>

.-.-n

mW.-WmcW

VV

-E.-- z

cac--.-3cE-Vcu-W0WVILmmW

.-

.-

-mW-

13cE-V.-c8VI)3

. 2

- 4(u3ccV.P .?.-B

- 4 1

a 3 i

. I1480.7a .9Rotor hub-tip radius ratio, r /r t 1.0 . 8 . 9 1.0.8 . 9 1.0

Figure 10. - Radial distributio ns of flow and blade-element performance parameters under-c avitati ng conditions. Rotor tangential velocityat tip, 141.5 feet per second; ne t pos itiv e suct ion head, >160 feet.19


22/37

aln5c Y .4

G o

c0m>.-c.-3

.25

mL .05

13

malro

i

0mc .4n-

100

EULalL

Net p o h v i Isuction head,ff

>16007 M

t l20-7

Incidence angle, i, deg(a) Radial position 1; rotor hub-tip radius ratio, 0.972.

Figure 11. - Blade-element performance characteristics for cavitatingand noncavitating conditions. Rotor ti p speed, 141.5 feet persecond.

and noncavi ta t ing (Hsv > 160 f t )f low a re s u r p r i s i n g l y c l o se . A tl o w e r f l o w c o e f f i c i e n t s it ap-p e a r s th e c a v i t a t io n e f f e c t s a remore severe and comparisonswould not be a s f a v o r a b l e . I nsummary, ca v it a ti on would a f f e c tth e l e v e l of performance of t h ero to r and p resen t match ing p rob-l e m s i n a succeeding blade rowas w e l l .

F ig u r e 11 p r e s e n t s t h e p e r -formance of th e indi vid ua l b la deelements by showing the varia-t i o n s o f se l ec t ed per fo rmanceparamete rs wi th inc idence ang le .Both non cavi ta t in g and cavi-t a t i n g d a t a a re recorded.

The same g e n e ra l e f f e c t sof ca vi ta t i on on performancenoted previously (comparison off i g s . 6 and 1 0 ) a r e a g a in e v i -denced by th e p l o t s of f i g -ure 11. One a d di ti o n al r e s u l tof c a v i t a t i o n i n d i c a t e d b y t h e s ecurves i s t h a t it appeared t odecrease th e low-loss inc idencea n g l e range.

Radia l Equi l ib r iumThe des ign of t h i s ro t o r

assumed t h a t s imple ra d i a l equ i -l i b r i u m ( n e g l e c t i n g e f f e c t s ofr a d i a l a c c e l e r a t i o n s ) d e fi n ed b y

a d e q u at e ly e x p r e s s e s t h e r a d i a l g r a d i e n t o f o u t l e t - f l o w c o n d i t i on s .which i s reproduced from re fe re nc e 4, compares measured a x i a l ve l oc i ty d i s t r i -bu t i ons wi th tho se computed us ing the s imple r a d i a l equ i l ib r iu m express ion .The p lo t s b o th v a l i d a t e t h e d e s ig n a ss um pt io n and i n d i c a t e t h a t t h e s im ple r a -d i a l e q u i l i b r i u m e x p r e s s io n would b e a p p l i c a b l e u n de r a l l f low condi t ions , b o thc a v i t a t i n g a nd n o n c a v it a ti n g , e x pe r ie n ce d i n t h e s e r o t o r t e s t s .

F ig u r e 1 2 ,

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-3 5 1.E 1.- Ic

0 -2 5 IUmI m i 5 i.05

- suct ion head,HSVJft

>160-.":'11"1

Ii

Incidence angle, i, deg(b) Radial position 2; rotor hub- tip radiu s ratio, 0.906.

Figure 11. - Continued. Blade-element performance characteristic sfor cavitatin g and noncavitating conditions. Rotor tip speed, 141.5feet per second.

Eva luati on of BladeDesign System

The de sig n whose pe rf or -mance i s r e p o r t e d h e r e in i s char -a c t e r i z e d b y h i gh i n l e t - r e l a t i v e -f lo w a n g l e s , r a d i a l l y c o n s t a n tenergy addi t io n, and high hub-t i p r a di us r a t i o .ing d i scu ss io n the per fo rmancer e s u l t s from t h i s r o t o r and e x-per iences dur ing the fo rmal iz ingof th e d esig n ar e examined withr e f er e n c e t o g e n e r a l a p p l i c a t i o nof t he bla de des ign system.

I n t h e f o ll o w-

The u t i l i t y of a des ign sys -tem i s judged on i t s a b i l i t y t oproduce blad e rows th a t provide

(1)The des i r ed l ev e l o fh ea d r i s e and a n a c c e p t a b l e e f -f i c i e n c y a t the des ign f low( 2 ) Adequate s ta bl e oper-a t i n g f lo w m ar gin on e i t h e r s i d e

of th e d esi gn flow based on con-s i d e r a t i o n s of s t a r t u p , a c c e l -e r a t i o n , and en gi ne t h r o t t l ea b i l i t y r eq ui re m en tsThis pump blade design sys-tem f o r a x i a l - f lo w s t a g e s i s

c l o s e l y p a t t e r n e d a f t e r t h e b l a d e d e s i g n s ystem f o r a x i a l- f lo w a i r compressorsrepor ted i n r e f e r e n c e 1. The equations take the form

where i2-D nd 62-D a r e suggested desi gn valu es of incidence and de via t io nangles , res pe ct i ve ly , obta ined f rom co rr e l a t io ns of two-dimensional low-speeda i r -cascade per fo rmance da ta . Rules f o r p re d ic t in g thes e va lues a s a f u n c t i o nof i n l e t - f l o w a n g l e , b l a d e s o l i d i t y , and maximum blade th ic kn es s a r e pr ese nte di n r e f e r e nc e 1. The ip - i2-D nd 6p - 62-D repr esen t ad justments, o r cor -r e c t i o n f a c t o r s , f o r t h e e f f e c t s of o p e r at i n g i n a three-dimensional environ-ment.

P o t e n t i a l d i f f i c u l t i e s i n ap pl yi ng t h i s system co uld a r i s e i n s e ve r alareas :

21


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L

_ _ ~ .Net positivesuction head,ft

0 >1600 107

100

80

60

Incidence angle, i, deg(c) Radial position 3; rotor hub-ti p radius ratio, 0.850.

Figure 11. - Continued. Blade-element performance characteristic sfor cavitati ng and noncavitating conditions. Rotor tip speed, 141.5feet per second.

(1) n gener al , pumps ut i -l i z e h ig h er i n l e t - re l a t i v e -f l o wa n g l e s t h a n a i r compressors. I nmany pump de si gn s, in cl ud in g t h ed e s ig n r e p o r t e d h e r e in , a numberof e lements of th e PLXIQ n t h et i p r eg io n w i l l h a v e i n l e t an-g l e s above t h e maximum va lu escovered in-cascade in ve st ig a-t i o n s ( p 1 < 70).i n l e t a n g l e r an ge , t h e d e s i gnsystem curves have s te ep andchanging slopes; consequently,e x t r a p o l a t i o n i s uncer ta in andth e a c c u r a c y of t h e c a l c u l a t e di2-D a lu e s i s a l s o unknown.

I n t h i s h i gh

(2) I t i s not known whetherth e t h r e e - d im e n s ion a l c o r r e c t i o nf a c t o r s ic - i2-D nd6, - 6 2 - ~ m p i r i c a l l y d e t e r -mined fo r a i r compressors may bea p p l ie d d i r e c t l y .

O p t i m u m des ign-po in t pe r -formance would be obtained i fa l l th e ro to r e lements were op-e r a t i n g a t t h e i r minimum-lossinc idence ang les a t t h e d e s i g nflow. Blade-element performanceind ica ted t h a t t he measured ro to r minimum-loss incidence angl es were high erthan t he ca l cu la t ed two-dimensional v a luesThus, ip - i2-Dr e c t i o n f a c t o r scompressor ro to rs a re nega t ive ( s e e t a b l e 11).

i 2 - D by 2.3' ( t i p ) t o 3.4' (hub) .i n e q ua ti o n (2) shou ld be po s i t ive .i, - i2-D

By con t ra s t , thes e cor -recommended f o r low i n l e t Mach number a i r -

I f i t i s assumed th a t th e blade-element performance c urves obta ined f romt h i s r o to r a r e somewhat t y p i c a l of t h o s e f o r t h i s t y p e o f r o to r d es ig n , a s i g -n i f i c a n t f e a t u r e i s t h a t t he minimum-loss incid ence angle occurs very c lo se t othe e lement s t a l l opera t ing inc idence (cons idered he re i n a s e f f e c t i v e l y o cc ur -r i n g when cu = %,l). I f an inc r ease i n s t ab le ope ra t ing f low range be tweendesign and blade s t a l l i s de sir ed , th e de sig n inc iden ce would be moved towardth e high flow s id e of t he minimum-loss inci den ce by usin g lower va lue s ofip - iZ-Dhan thos e noted prev ious ly f o r minimum-loss poin t .e le me nt c h a r a c t e r i s t i c s i n d i c a t e t h a t o n ly a s m a l l p e n a l t y i n i n c r e a s e d l o s sc o e f f i c i e n t would r e s u l t fro m lo c a t i n g t h e d e s ig n p o in t a t an inc idence ang les l ig h t l y lower than t he minimum-loss incidence an gle .

-

The blade-

It i s t h u s i n d i c a te d t h a t a p r e f e r a b l e d e s ig n f l o w o p e r a t i n g p o in t for a22


25/37

ro to r row of t h i s type wouldu t i l i z e a n in c id e nc e a n gl e e qu a lt o o r s l i g h t l y l a rg e r t ha n th eca lc -d at ed two-dimensional value;t h a t i s , ip - iZeD0s l i g h t l y po s i t ve . Cons e quent y ,the calcula ted two-dimensionald e v i a t i o n a n g l e s 82-D a r e com-pared with measured ro to r devia-t i o n a n g l e s i n t h e ra ng e of i n c i -dence angles i 2 - D


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Net positivesuction head.

4

-8 -4 0 i 4

01W

roW--mccm5l.-.-nnL0cV

c5'cn

c

.-VI-w t i - h . . . I

-8 -4 0 4Incidence angle, i, deg(e) Radial position 5; rotor hub-tip radius ratio, 0.728.

Figure 11. - Concluded. Blade-element perform ance charact eristi csfor cavitating and noncav itatin g conditions. Rotor ti p speed, 141.5feet per second.s imple a na ly si s (n ot es f rom Penn. S ta te Univ.

(1) n t h e t i p r eg io n t h el o s s c o e f f i c i e n t w a s s i g n i f i -cant ly h i g h er t h a n t h e v a l u e i n -dicated f rom cascade resu l t s , b u tit d i d f a l l ins ide th e band ofdata obta ined f rom air -compressorrotor t e s t s .

( 2 ) A t th e mean rad iu s th el o s s c o e ff i c i e n t w a s s l i g h t l ylower than th e cascade va lue f o rt h e same D-factor and among thelower l e v e l of va lue s measured i na i r -compressor rotor t e s t s .

( 3 ) I n t h e hub r e g io n t h eloss c o e f f i c i e n t w a s s i g n i f i -ca n t ly lower than t he cascadevalue and among the lowest valuesmeasured i n air-compressor t e s t s .

The r a d i a l d i s t r i b u t i o n ofl o s s coef f ic ien t s and the compar -i s o n w i th c a s ca de v a lu e s f o r s i m -i l a r D - f a cto r l e v e l s of l o a d in gind ica te th e p resence and impor-ta nc e of secondary flows. Forth e p resen t , secondary f low e f -f e c t s w i l l be accommodated byc o n s id e r in g t h e l o s s parameter asa func t ion of b lade load ing( D - f ac t o r) a nd r a d i a l l o c a t i o n .Some ins ig h t i n to the sev er i ty ofsecondary f lows occu r r ing i n ade si gn may be ob tai ne d from aseminar, 1958) t h a t i n d i c a t e st h a t t he qu an t i ty of f low invo lved i n secondary motions i s

(1)D i r e c t l y p r o p o r t i o n a l to the square o f t h e c i r c u m f e r e n t i a l p r o j e c t i o nof a b la d e( 2 ) I n v e r s e l y p r o p o r t i o n a l to t h e a n gl e b etw een t h e i n l e t r e l a t i v e f lo w

(or b l a d e i n l e t camber l i n e ) and t h e c i r c w n f e r e n t i a l d i r e c t i o nThe use of t he se two parameters pro vide s some qu a l i ta t i v e di re ct io n to t h e s e -l e c t i o n of a r a d i a l g r a d i e n t of l o s s .

The r e s u l t s o b ta i n ed i n t h i s i n v e s t i g a t i o n p o i n t o u t t h e n e c e s s i t y of a c -c u r a t e l y d e f i n i n g t h e i n l e t v e l o c i t y dia gr am s f o r a d e si g n w i th t h i s l e v e l ofl o a d in g and i n l e t a n gl e . I n t h i s c a s e t h e o u t e r c a s in g b ou nd ar y l a y e r ca us edth'e t ip-e lem ent f low ve lo ci ty to f a l l below i t s a n t i c ip a t e d d e s ig n v a lu e a nd

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xa

45 0-

I .*a41

55

45

45

357ti8B

I .2841 1. 7 .8 .9 1.09 1.0

Average how A d a g e :otorcoeffi,cient,

35

_I_a .9 ;.0Rotor hub-tip radius ratio, rlrt(a) Noncavitating condition. (b) Cavitating condition; net p s i -Figure 12. - Comparison of measured axial velocity distribution behind rotortive su ction head, 72 feet.with axial velocity distributi on calculated by simple radial equilibri um.the b lade e lement t o ope ra tea t a h ig h e r t h a n d e s ig n i n c i -dence va lue. Th is re su l t edi n pre ma tu re s t a l l i n g f l owc o nd i ti o ns i n t h e t i p r e g io nand w a s p a r t l y r e s p o n s i b l ef o r t h e small flow margin be-tween design flow and thep o s i t i v e b l a d e s t a l l p o in t .

P r e d ic t in g t h e e f f e c t sof cas i ng boundary la ye r ont h e i n l e t flow d i s t r i b u t i o ni s v e ry d i f f i c u l t , and i f t h eboundary layer ve loc i ty g ra -d i e n t c o u ld b e a c c u r a t e lyp r e d i c t e d , it could not bein c or p o r at e d i n t o t h e b l a d edesi gn system because of th epr oh ib i t i ve amounts of b la det w i s t involved. Perhaps th eo n ly c o r r e c t i o n t h a t c an bea p pl ie d i n t h i s a r e a i s t oa n t i c ip a t e t h e b o u n d a r y l a y e re f f e c t s and a l lo w f o r them i nth e blad e design method, p r i -mar i ly i n th e use of lowervalues of ip - i2-D.m -proved methods of ca lc ul at in gr a d i a l g r a d ie n t s of i n l e tv e l o c i t y due t o s t re a m l in ecu rva tur e, however, should beappl ied. Reference 8 d i s -cusses t h i s p roblem i n mored e t a i l .

I n t h e de s ig n of t h i sr o t o r as d i sc u ss e d i n r e f e r -ence 4 it w a s noted t h a t mod-i f i c a t i o n s t o t h e c a lc u la te db lade paramete rs i n the t i p reg ion were made. The n e c e s s i t y f o r t h i s becomesc i e a r i n t h e f o l lo w in g d i s c u s s io n o f t h e s e n s i t i v i t y o f t h e b l a d e camber d e s ig nequa t ion a t h ig h i n l e t - f l o w a n g l es t o v a r i a t i o n s i n t h e c o r re c t io n f a c t o r sip - i2-Dnd ip - 62-D. These l a t t e r f a c t o r s a r e t h e t y p e of i n fo r m at io nt h a t must be ob ta ined f rom ro to r pe rformance re s u l t s o f i nv es t iga t io ns such asr e p o r t e d h e r e i n and i n r e f e r e n c e 3 or from low-speed air-compress or r o to rt e s t s . To d e m on s tr a te t h i s s e n s i t i v i t y , t h e d e s ig n v e lo c i t y d ia gr am s and s pe c-i f i e d b l a d e s ha pe , s o l i d i t y , and b l a d e t h i c k n e s s v a lu es f o r t h i s r o to r w ere ap -p l i e d t o t h e b la de camber des ign equa t ion f o r fou r d i f f e r en t s e t s of assump-t io ns . Calcula te d desi gn valu es of b lade carriber angle , incidence , and devia-t i o n a n g l es f o r t h e t i p , mean, and hub b l a d e e le m e nt s a r e l i s t e d i n t h e f o l -lowing t a b l e :

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Three-dimensionalcorrection factors,

01~

-1.75-.501.501.50-. 0-2.50

Zamb r%%le,

'Po ,deg-11.619.827.60.328.0

33.7-18.618.430. 76.2

25.226.6

Incidenceangle

i,deg

10.7.51 .2

3.0-5 .1-3.213.4

.9. 50 . 7

-3.7-.6

Ieviat orangle6,deg

-2.87.89.31 .410.410.9

-7.06.911.6

5 . 19.16.5

P a r t 1 i s t s t h ei n i t i a l va lues o f th r ee -dimens iona l cor rec t ionf a c t o r s used i n t h e d e-s i g n of t h i s r o t o r . A tth e t i p e lement, wheret h e t i p i n l e t - r e la t i v e -f l o w a n g l e n e c e s s i t a t e de x t r a p o la t i n g c e r t a i nc ur ve s t o c a l c u l a t e i2-13and 62-D, nega t ive val-ues of camber and de vi a-t i o n ang les and an unusu-a l l y h ig h v a lue o f d e s ig nincid ence a ng le were ob-t a i n e d as shown. Thet ip -e lement b lade sec t ionw a s a r b i t r a r i l y c h a n g e das n ot ed i n r e f e r e n c e 4.

P a r t 2 p r e s e n t s t h e b l a d e p ar am et er s c a l c u l a t e d f o r t h i s d e s ig n i f no cor-r e c t i o n s are made for p r e d i c t i o n o f t h r e e- d im e n s io n a l e f f e c t s .P a r t 3 shows th e blad e parameter val ues when the de via t io n angle c orr ec-

t i o n sp - 82-1) as deduced from air -compressor t e s t s i s used; that i s ,6p - 62-D = 6, - 8 2 - D

The 3O i n c id e n c e a n g l e c o r r e c t i o n f a c t o r w a s used i n o rder t h a t compar isonsw i t h t a b l e I ( se e p. 3 ) values could be made.

P a r t 4 l i s t s t h e v a lu e s of ip - i2-D nd 8p - 82-1) t h a t would probablybe recommended f o r app l ica t io n i n th e b lade des ign equa t io n fo r a redesign oft h i s r o t o r on t h e b a s i s of pre sen t informat ion. The ip - iZ-Da r i a t i o n w a sse lec ted t o p rov ide f low margin between t he des ign and po s i t iv e b lade s t a l l op-e r a t i n g p o i nt s . I n p a r t 4 th e blad e parameters a r e computed based on the ex-i s t i n g v e lo c i t y d ia gr am d e s ig n v a lu e s . A t r ue red es ign would suggest c e r ta inc ha ng es i n t h e v e lo c i t y d ia gr am d e s ig n t h a t i n t u r n would be r e f l e c t e d i n t h eb lade des ign va lues .

The fa c t th a t th e ca lcu la t ion s g ive nega t ive camber and dev i a t ion ang lesThe combination of h ig h i n l e t - f l o w a n g l e , s m a l l r e -i n d i c a t e s t h e n eed f o r a ca re fu l eva lua t i on of th e des ign sys tem fo r use a th ig h i n l e t - f l o w a n g l e s .quired f l u i d tur nin g ang les , and minimum al lowable blad e th ic kn ess es found fo rth e t y p i c a l t i p el em en t make t h i s re g io n of t h e b l a d e e s p e c i a l l y s e n s i t i v e .

Comparisons of t h e val ue s of p a r t s 1 o 4 i l l u s t r a t e t he s e n s i t i v i ty oft h e b la d e d es ig n e q u at i on s t o v a r i a t i o n s of t h e c o r r e c t i o n f a c t o r s f o r i n c i -dence and dev ia t ion angle . They a l s o in di ca te the need f o r pr ec is e measure-

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m en ts d u r in g t e s t i n g and c a r e f u l d e f in i t i o n s o f r e f e r e n c e a n g l e s fro m d a t ap l o t s .F in a l l y , t h e p erfo rm an ce c h a r a c t e r i s t i c s of t h i s rotor t o g e th e r w i th t h eda ta of re fe rence 6 i n d i c a t e t h a t a t high va lues o f bo th in le t - f low ang le andload ing small changes can resul t i n s i g n i f i c a n t v a r i a t i o n s i n b la d e d es i gn orblad e performance parameters . Consequently , i n b lad e rows of t h i s type, i f

a c ce p ta b le l e v e l s of d e s ig n p o i n t p e r f o r m c e a nd b l a d e s t a l l margin a r e to beobtained, ca re fu l a t t e n t io n shou ld be made to a l l d e t a i l s of t h e d es ig n.

SUMMARY OF RFSULTSAn axial-flow-pump rotor with a 0.7 hub- t ip r a t i o and des ign D-fac to rs o f

0.43 and 0.70 a t t h e t i p and h ub, r e s p e c t i v e ly , w a s t e s t e d i n w a te r. The f o l -lowing summarize the principal resul ts observed from the rotor blade e lementperformance:Under no ncav i ta t in g condi t i ons

1. A t design f low a comparison of the blade element performance with de-s ig n v a lu e s i n d i c a t e s t h e f o l lo w in g :( a ) I n l e t axia l v e l o c i t y w a s h i g he r t h a n d es i g n e xc ep t i n t h e t i p r e -gion, where it w a s lower than des ign (p robab ly because o f e f fe c t s o f ou te rc a s in g b ou nd ary l a y e r ) . T h i s f o r c e d t h e t i p e le me nt t o o p e r a te ve r y c lo s et o a b la d e s t a l l condi t ion .( b ) Measured lo ss es w e r e l ow er t h a n d e s ig n ex c ep t i n t h e t i p r e g io n ,where they were cons iderab ly h igher th an th e p r ed ic ted des ign va lues .( c ) E xc lu ding t h e t i p r e gio n , e ne rg y a d d i t i o n w a s lower than designbut combined with t he lower- than-design lo ss es to produce a c lo s e - to -d e s ig n h e a d - r i s e c o e f f i c i e n t . I n t h e t i p re g i on t h e e ne rg y a d d i t i o n w a shigh er than desi gn and produced a h ig h e r - t h a n - d e s ig n h e a d - r i s e c o e f f i c i e n t( i n s p i t e of h ig he r - th a n - de s ign l o s s e s ) b u t a t a lower - than-des ign e f f i -c iency.

2. For th i s s pec i f i c ro to r geometry and le v e l o f load ing , a t y p i c a l l o s s -coe f f ic ien t a ga in s t inc idence ang le ch ar ac te r i s t i c showed th e fo l lowing :( a ) Minimum l o s s , where defined, occurred over a very narrow flowrange.(b ) Flow (or inc idence angle) margin between minimum-loss operatingc o n d i t i o n and p o s i t i v e s t a l l p o in t ( d e f in e d as p o i n t a t which the loss

c o e f f i c i e n t w a s twic e t h e minimum value on th e hig h incid enc e (low-flow)si de of th e minimum-loss oper at in g po in t) w a s very small.( c ) G ra du al i n c r e a s e i n l o s s c o e f f i c i e n t a s t h e f lo w w a s var ied f romth e minimum-loss va lue to higher f lows ( lower incidence angle) .

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3. A comparison of the measured results with those predicted from the de-sign rules of reference l, and interpretation of these results indicate that

(a) Application of the design rules to designs with inlet-flow anglesoutside the range covered by the two-dimensional air-cascade data used toformulate the design procedure is dangerous.the higher inlet-flow angles would be desirable.

Additional cascade data at

(b)-The blade design equations are very sensitive to small anglevariations at high inlet-flow angles. This indicates the need for precisemeasurements and careful interpretation of the data from investigations ofthis ty-pe of pump rotor.

(c) With the type of loss coefficient - incidence angle characteris-tic measured for this ty-pe blade, considerations of flow margin betweendesign and positive blade stall points indicate that the minimum-loss op-erating condition may not be a desirable design point for many applica-tions.

(d) Significant differences between reference blade deviation anglesobtained from two-dimensional cascade results and three-dimensional rotortests occurred only in hub and tip regions where loss levels indicatedsecondary flow effects were significant.

Under cavitating conditions1. At a r o t o r tip speed of 141.5 feet per second the effects of cavitation

on rotor performance are first noted at a net positive suction head of 116 feet.This corresponds to an average cavitation nwiber of approximately 0.191.

2. Cavitation generally affects rotor performance in the following ways:(a) Increases losses(b) Decreases energy addition(c) Decreases low-loss operating range

Lewis Research CenterNational Aeronautics and Space Administration

Cleveland, Ohio, June 23, 1964

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APPENDIX A

SYMBOLSC

DgHHsvc\H

hh,ikNQrUvPY6rlK

blade chord , i n .d i f f u si o n f a c t o ra c c e l e r a t i o n d ue t o g r a v i t y, 32.17 f t / s e ct o t a l head, f tn e t p o s i t i v e s u c t i o n h ea d, f th e a d r i s e , f ts t a t i c head, f t

2

vapor head, f tincidence angl e , degca vi ta t i on numberrota t ive speed, rpmf l o w ra te , ga l /minr a d iu s , i n .

r o t o r t a n g e n t i a l v e l oc i ty , f t / s e cf l u i d v e l o c i ty , f t / s e cf low angle , angle between di re ct io n of f low and ax ia l d i r e c t i o n , d e gb lade se t t in g ang le , ang le between chord l i n e and ax i a l d i r e c t i o n , d e gdev ia t ion ang le , dege f f i c i e n c y , p e r c e n tblade angle , angl e between tangent t o b lad e mean camber l i n e a n d a x i a ld i r e c t i o n , d e gb l ad e s o l i d i t y , c / sf lo w c o e f f i c i e n tblade camber angle, K~ - K ~ , eg

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Jr head-rise coefficientcu rotor relative total head-loss coefficientSub scripts

-

ChimmaxPtze2-D12

parameter obtained from air-compressor stage investigationshubidealmeasuredmaximumparameter obtained from pump-stage investigations

tipaxial directiontangential directionparameter obtained from two-dimensional air-cascade investigationmeasuring station at rotor inletmeasuring station at rotor outlet

Super cripts- averaged valueI relative to rotor

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APPENDIX B

EQUATIONSBlade Element Equations

I d e a l h ead r i s e :

R oto r r e l a t i v e t o t a l h e ad - lo s s c o e f f i c i e n t :

B la de d i f f u s i o n f a c t o r :

o r , f o r rl = r2

E f f i c i e n c y :

Cavitation number:

H e a d - r i s e c o e f f i c i e n t :

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Ideal head-rise coefficient:

Flow coefficient:

Incidence angle:

Deviation angle:

Overall and Averaged Parameter EquationsMass-averaged total head:

Mass-averaged efficiency:

Mass-averaged head-rise coefficient:

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Average inlet axial velocity:- 144%

t,l h,l

Average inlet-flow coefficient: -...

Average blade cavitation number:

Net positive suction head:Hsv = H1 - hv

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REFERENCES1. Members of the Compressor and Turbine Research Division: Aerodynamic Design

of Axial-Flow Compressors, vol. 11. NACA RM E56B03a, 1956.2. Crouse, James E., Montgomery, John C., and Soltis, Richard F. Investiga-

tion of the Performance of an Axial-Flow-Pump Stage Designed by the Blade-Element-Theory - Design and Overall Performance. NASA TN D-591, 1961.

3. Crouse, James E., Soltis, Richard F., and Montgomery, John C.: Investiga-tion of the Performance of an Axial-Flow-Pump Stage Designed by theBlade-Element Theory - Blade-Element Data. NASA TN D-1109, 1961.

4. Crouse, James E., and Sandercock, Donald M.: Design and Overall Performanceof an Axial-Flow-Pump Rotor with a Blade Tip Diffusion Factor of 0.43.NASA TN D-2295, 1964.

5. Lieblein, Seymour, Schwenk, Francis C., and Broderick, Robert L.: DiffusionFactor for Estimating Losses and Limiting Blade Loadings in Axial-Flow-Compressor Blade Elements. NACA RM E53D01, 1953.

6. Herrig, L. Joseph, Emery, James C., and Erwin, John R.: Systematic Two-Dimensional Cascade Tests of NACA 65-Series Compressor Blades at LowSpeeds. NASA TN 3916, 1957.

7. Lieblein, Seymour, and Roudebush, William H. : Theoretical Loss Relationsfor Low Speed Two-Dimensional-Cascade Flow. NACA TN-3662, 1956.

8. Lieblein, Seymour: Analysis of Experimental Low-Speed Loss and Stall Char-acteristics of Two-Dimensional Compressor Blade Cascades. NACA RME57A28, 1957.

9. Lysen, J. C., and Serovy, G. K.: Estimation of the Velocity Distributionat the Inlet of an Axial-Flow Turbomachine. Paper 63-WA 162, ASME, 1963.

34 NASA-Langley, 1964 E-1968


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