Brown, W Byron

English

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NATIQNAL ADVISORY COMMITEE FOR AEWONAUWCS 
A u g u s t  1945 as 
R e s t r i c t e d  B u l l e t i n  ESG21 
COMPUTATION OF THE MEAN TANGENTIAL VELOCITY OF THE AIR LEAVING 
THE BLADE T I P S  OF A CENTRIFUGAL SUPF3CHARGER 
By W. B y r o n  Brown 
A i r c r a f t  E n g i n e  R e s e a r c h  L a b o r a t o r y  
C l e v e l a n d ,  Ohio 
NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of 
advance research results to an authorized group requiring them for the war effort,"" They were pre- 
viously held under a security status but are now unclassified. Some of & e ~ e  reports were not tech- 
nically edited. All have been reproduced without change in order to general distribution. 
e.. .. . .  
https://ntrs.nasa.gov/search.jsp?R=19930093574 2020-06-16T22:53:03+00:00Z
By 14. Byron Ecro~m 
SUTV~~K~Y 
The mean tangential velocit~7 of t2le a i r  leavilzg the b1ad.e t i p s  
of a ~ e n t ~ i f u g a l  sl.xpercherger was co~api~ted by the conventional tur- 
bine eq.uation, which cses ths ~ t c t i i a 1  incresse i n  t o t a l  ellthalpy, 
and by an equation -that uses tl:e ise;lt:r.opic il-icrease i n  t o t a l  
enthalpy. These computed -?eloci"Les are  compared with experimental 
valxes observed with three vaaeless d i f f i ~ s e r s  having d i a ~ e t e r s  of 
20, 24, an6 27 inches. Tip speeds; of 800, 1000, and 1200 f e e t  per 
second w e e  tested wi%h ee,ch diff;:ser, 
The mean tangential  veloci t ias  @en by the turbine equation 
averaged about 2 pel-cent kigher than tke observed valu-es, vhereas 
those couputed by the i s e n t r o p i ~  equat lm averaged about 15 percent 
lower than the o'rjserved values. %Then a correction derived from the  
aeasureinents of windage losses  was ayplzed t o  the turbine equa"uon 
t o  a1los.r f o r  the fric-lioilal torque of the f lxed shrowls, the corn- 
puted values agreed with the observed values wi+vhin 1 percent. 
In diffuser  destgn, es t iaa tes  of a i r  velocity at the impeller 
e x i t  have beer, made by u s i q  the turbine equation tha t  expresses the 
increase i n  t o t a l  enthalpy i n  t e m e  of the t i p  s ~ e e d  and tke Dean 
tangential a i r  velocit,v. The use of %he isentropic increase i n  
t o t a l  enthalpy instead of the actual  increase i n  t o t a l  enthalpy has 
been sv.ggssied 'by J, E. E l l o r  of the Bri t ish Air Comission, Packard 
Motor Car Company. Inasauci.1 as these tvc) increases often d i f f e r  3y 
as much a s  iO t o  20 percect, it i s  important, t o  determine which 
metliod i n  the more neayly correct value. 
A ser ies  of velocify measureme:lts was therefore made at the 
Clevelan6 laboratory of the TSCA with vaneless dtffusers  of three 
dif'ferext diaaeters ir, which each diffuser  was tested a t  three t i p  
speeds i n  order t o  deternine the tangen-bial velocitg of the air a t  
tne inpel ler  t-lp. T3ese measwed mean tangential  veloci t ies  were 
then compared with the val-nes camp~~ted by the coilventional twbine  
eqL1.ation and with those coillpckeed b r  an equation lxs in~  the  isentropic 
i ~ c ~ e a s e  i n  5otal  enikalpy . 
The following smbols a re  used i n  the cnalysls: 
breadth of vanelesa-dlffuser passage, f ee t  
specif ic  heat a t  constant pressure, foot-po~mdals per pound 
per OF 
liyrlraulic diameter cf f l o ~ r  passage, f e e t  
f r i c t i o n  coefficient 
acceleration due t o  g:c~Bv'ityk-, 32.1.: f e e t  per second per second 
a c t ~ ~ a l  increase i n  t o t a l  enthalpy yer wit mss, foot-poun%s 
per pound 
2 / ang21ar momen-Lu, fee t  /per  second 
rotat lorn1 speed, revol:~<fons per second 
t o t a l  pressure, inches of nercwy absolute 
t o t a l  presswe a t  impel-ler ex i t ,  inches of mercwy a b s o l ~ t e  
t o t a l  pressure a t  b p e l l e y  i n l e t ,  inches of mercu-cy a b s o l ~ ~ t e  
staCuic pressure, iilches of merc-my a b s c l ~ ~ t e  
vol~me flow of a i r  a t  impeller ex i t ,  cubic f ee t  per second 
Seynolds number 
radius, fee t  
NACA PJ3 No. E5G21 
TS s t a t i c  temperature, % 
Tts t o t a l  temperature, % 
I-l iti t o t a l  temperature a t  i i q d l e r  i n l e t ,  % 
U mean resu l tan t  a i r  ~ e l o c 2 ~ ~ y ,  f e e t  per  second 
m a n  r a d i a l  a i r  v e l o c i t ~ ~ ,  f e e t  per  second 
Ut mean tangent ia l  a ir  veloci ty ,  f e e t  per second 
AUt l o s s  i n  mean tangential  a i r  veloci ty  due t o  windage, f e e t  pe-r seeold 
V t i p  speed, f e e t  Ter seconrl 
W weight flow of a i ~ ~  pom.ds per  second 
CL angle between mean flow a36 zfrc:m?arrence, degrees 
P constant d e p e i l d e n h ~  n--m'5er acd d i-me-ker of blades and nature 
of impeller (open, half shrouled, o r  f dl. y s1:rouded) 
Y r a t i o  of spec l f i c  heats  
P viscos i ty ,  polmds per  foot-second 
P density,  poYmds per  cu55.c foo t  
Conventiorlal turbine  equation a d  correction f o r  f r i c t i o n a l  
torque. - The turbine equation is 
i f  the  air  has ~o a n g ~ ~ l a r  momentum a t  the  hpel ler  entrance. If 
the  windage correction Act i-s used, t5en 
The eqcation f o r  AU3 is aerlved as follows: 
4 NACA PU3 fJo, E5G21 
t~liere fkp i s  f r i c t i o n  horsepower and hp i s  horsepower input t o  
the  air. In  reference 1 the r e s u l t s  a r e  summzized i n  the  equation 
3y s: lbst i t~%i.on of eqm2;ion (4)  Ln equation (3 )  by use of t h e  
r e l a t i ons  
there  is  obtained 
From reference 1 
Because D is  1.02 f ee t ,  P is  1.40 and 
where O, nus t  be dctemined a't t h e  impeller e x i t .  
TW?I ine equation using j.ser;trcpic increase ir: t o t a l  en-Kaalpy. 
--- 
The equation proposed by J. E,  E l l o r  is  
fr:m which Ut i s  easFlp conpl~ted. 
NACA 33.3 No. E5G21 5 
Determination of 03se~ved resul tant  velocity.  - A t  each s t a t ion  
i n  the vaneless diffuser ,  the resul tant  air  velocity U was deter- 
mitried by means of the equatioil 
\- 
where I = /EL ! - 1 
\.%/ 
Becau-se of tha contin~t4-27 eqinatTon, the rad ia l  a i r  velocity Ur can 
be obtafned from $a1 
The s t a t i c  temperature Ts i s  fmljzd f r c a  %he t o t a l  temperatwe Tt 
by the re la t ion  .-, 
Then 
Thus Ut i a  known fo r  cer tain s ta t ions  several inches from the 
impeller t i p ,  
At the s ta t ion  nearest the impeller t i p  (5.5-in. radius),  values 
of s t a t i c  pressilxe ps and total. pressure P a re  unreliable because 
of the ~msteady flow near the diffuser  entrance. A t  the s ta t ions 
fa r ther  from the L q e l l e r  t i p  (0.0, 9.5, a ~ d  11.5-in. r a a i i ) ,  the 
observe6 valaes of P and ps a re  util>.all-y trnstworthy. Each of 
these 7iali:es i s  ac~ordlngly  redxced t o  the impeller-tip radius by 
adding t o  the meawred a rg i~ la r  noment~m the 1-oss between the inpel ler  
t i p  ~ n d  tile i3easuring s tat ion.  'Phis loss  i.s giren by t h n  f o L l o v i ~  
equation d e r i ~ e d  i n  ~e fe rcnce  2: 
&i,I -f d r  
- - 
14 - b s i n  CL 
Values of the f r i c t i o n  coefficient f are  found from the equation 
given by McP-dams (reference 3):  
NACA RB No, E5G21 
The Iie$molds number R is cmputed by 
where s i n  a = u,/u. 
APPARATUS A i i  TESTS 
The sqercharger  impeller used with the vaneless d i f f ~ m e r s  was 
a conventional design centTifugal, impeller of 12,23-inch d i a e t e r .  
Three vaneless diffusers  of the constant radial-area type were tested. 
The f i r s t  diffuser  hzd a diameter of 27 inches and was modified by 
cutting the d i a e t e r  down t o  24 inches and then t o  20 inches. The 
shaye of the a i r  passage is  shown i n  figure 1. 
The s t a t i c  pressure Tias measured 5y wall taps  a t  r a d i i  of 8.0, 
9.5, and 11.5 inches. Total pressures were measured by suriiey tu3es 
located a t  the sane r ad i i  b t ~ t  n.ot at the same azinuth a s  the w a l l  
tubes. (See f ig .  1 . )  A t  each survey s tat ion,  readings were taken 
a t  four  points across the channel width b: b/8, 3 b / ~ ,  55/8, aad 
7b/8 from the front  wall. The average of these readings w a s  taken 
a s  the average t o t a l  pressure for  the sect:on. 
The t o t a l  temperatures were measured only at the last s ta t ion  
i n  the out let  pipe as one of the standard over-all measurements. 
Unpublished t e s t s  by the NACA have shown tna t ,  i f  heat tyansfer is  
kept srnall by lagging the air ducts, the t o t a l  tenperatwe is 
unchanged frora the impellcr ex i t  t o  the o ~ ~ t l e t  pipe. The value 
measured a t  the out let  pipe was therefore used f o r  a l l  s ta t ions  
beyond the impeller exi t .  
The over-all measurements were made i n  accordance with the 
standard procedure of rat ing ax3 tes t ing  centrifugal superchargers 
given i n  reference 4. I)hotographs and a description of the t e s t  
r i g  a r e  presented i n  reference 5. 
RESULTS AND DISCUSSION 
The data obtained from the t e s t s  of the three diffusers  were 
inserted i n  the conventional turbine equation ( l ) ,  the corrected 
turbine equation (2), and tlie isentropic equation (6)  t o  obtain 
the tangential  a i r  velocity Ut. Because the absolute pressures 
were aeaswed within rfr0.c): i ~ c h  of mercw-y end because -the d i f fe r -  
ences on .r.&ick the veloci t ies  depend uere -12. (1 t o  5 in.  ), the 
experinenxal erTor of a single ob~erva t~ion  was large.  For t h i s  
i-eason, 63 t e s t  poi-n'cs were obser-~ed :%rid th,?s xethod of l e a s t  
squares was ~ s e d  t o  average the resul ts .  The ra.tios of the Cora- 
p1;tJed tartgential ve1oci. t~ 
Utconp 
t o  the observed velocity 
Utobs 
a r e  shown i n  tlie fol lo~riag table: 
Con~rent 3. om,l t.ur3ine (1 ) 1.017 f0.005 
Corrected con-vzntional t8urb2ne (2)  .993 Jc. 004 
Isentropic ( 6 )  ,853 f .005 
The error caused bx neglecting the windage i s  approximately 
2 percent. The isentroyic e q ~ a t i o n  gives values about 15  percent 
lower than the e x p e ~ h e n t a l  r e s d t s ,  id~ich  is  not s ~ ~ p r i s i n f :  i n  
view of the f ac t  that  it is baaad on the assm2tion of reversible 
compression i n  the -impeller. The consSdera3le l o s s  i n  s t a t i c  pyes- 
sure i n  the b p s l l e r  a f fec ts  equation (6)  but no-t the moment~rm 
equation on which equations (1)  a d  (2 )  a r e  based. 
Idhen the convent-ional ea,ua"ucn (1) w a s  used, it was found tha t  
the points coapu-Led fo r  l i g h t  loads near swge were noticeably 
higher than those near the losd cf peak sfficiency. This r e su l t  i s  
probably cacsed By  he large ~aov.nt of recirculated a i r  a t  t h i s  
coLdi_tion. The value of' actual  incrcaae i n  t o t a l  entl?al_py H un&er- 
goes a large incrcase i q i t h ~ ~ t  a ccrresponaing ef fec t  on ITt. A t  
f u l l  t h ro t t l e ,  the other extreme. the ~al1~1e of H %en6s t o  be lor?. 
Tke p i n t s  i n  figure 2 thas slzota'large departures frox the curve 
rcpresont these two extremz conditions. 
Because the points comp~zed by the isentropic equation (6)  a re  
based on total-pressma measureaer;ts near the i_mpeller t i p s ,  they 
a re  morz scattered thm those coaputed by the turbine equation (1). 
Chaotic flow conditions a t  tho impeller e x i t  give r i s e  t o  larger  
e r rors  i n  the measprements talcen there than i n  thoso taken far ther  
from the center. 
??either an increase i n  t i p  speed from 600 t o  1990 f e e t  per  
second and then t o  1203 f e e t  per secoxd nor successive ro&~ct ions  
8 TGCA RB No. E5G21 
i n  di-meter f r o a  27 t o  24 t o  20 inches affected the  r e su l t s .  Aside 
from extremely high an6 extremely low loads, t he  r e s u l t s  were con- 
cordant f o r  the  en t f r e  range of t i p  speeds and Oistmeters. 
Ai rc ra f t  Engine Research Laboratory, 
National Advisory Cami t t ee  f o r  Aeronautics, 
Cleveland, Ohio. 
1. Varley , V. E . : Fr i c t i on  rin A i r c r a f t  Supercharger Impell-ers . 
(From Tekchnika Vosdusb-na,vo Fl-ota ( ~ u s s i a n )  , No, 6, Ju3e 1937, 
p ~ .  61-'75), E r i t i s h  R.T.P. Trans. No. 663, Ministry of Ai rc ra f t  
Prod. 
2. Polikovsky, V.,  and Bevel-son, M. : The Performance of a '?anelese 
Diffuser Fan. S.4Cfr TM Do. 1030, 1942. 
3. McAdms, Willim H. : Eeat Tranmnission. McG-raw-Hill Book Co. , 
Inc;, 2d ed. ,  1942, p. 120. 
4. NACA S~~bcommlttee on Si~perchar'ger Com~ressors : S t ~ ~ n d z r d  Pro- 
cedwes f o r  Rating an& Test ine  Centyifugal Compressors. 
PJACA No. E 9 1 3 ,  1945. 
5. Ellerbrock, H e m n  H. ,  J r , ,  and Goldstein, Arthur 11.: Principles 
and Methoas of Rating and Testing Ceatrifxgrzl Superchargers. 
I'FACP. $32, Feb. 1942. 
N A C A  R B  NO. E5G21 F i g .  I 
F i g u r e  I .  - A i r - p a s s a g e  p r o f i l e  s h o w i n g  l o c a t  i o n  o f  s u r v e y .  
t u b e  i n  v a n e  l e s s  d i f f  u s e r s ,  
N A C A  R B  No.  E 5 G 2 1  F i g .  2 
500 
600 700 800 900 1000 1100 1200 
Observed  v e l o c i t y ,  f ps 
F i g u r e  2 .  - Mean t a n g e n t i a l  a i r  v e l o c i t y  v t  computed by t h e  u n c o r r e c t e d  t u r -  
b i n e  e q u a t i o n  and  b y  t h e  i s e n t r o p i c  e q u a t i o n .  


Computation of the mean tangential velocity of the air leaving the blade tips of a centrifugal supercharger

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