The asymmetric flow around an impeller in a volute exerts a force upon the impeller.  To study the rotordynamic force on an impeller which is vibrating around its machine axis of rotation, the impeller, mounted on a dynamometer, is made to whirl in a circular orbit within the volute.  The measured force is expressed as the sum of a steady radial force and an unsteady force due to the eccentric motion of the impeller.  These forces were measured in separate tests on a centrifugal pump with radically increased shroud clearance, a two-dimensional impeller, and an impeller with an inducer, the impeller of the HPOTP (High Pressure Oxygen Turbopump) of the SSME (Space Shuttle Main Enginer).  In each case, a destabilizing force was observed over a region of positive whirl

Acosta, A. J.

Arndt, N.

Brennen, C. E.

Caughey, T. K.

Franz, R.

English

Caltech Authors - Main

~ o t o r d y n u i o  Forces on Contr i fuaal  P l r p  Impr l le r s  
R. Pranz, N. Arndt, T.K. i h n g h q ,  C.E. Braanon, and A.J. h o s t .  
C.1 i f  o r n i a  I n r t i t n t a  of Teohnolow 
Pasadena, CA. 91121 USA 
The a r y m t r i o  f l w  aronmd a n  impel le r  i n  a  v o l u t e  e l o r t s  a  foroa 
upon the impeller.  To study t h e  r o t o r d y n u i c  fo roe  on an impel le r  which 
i s  v i b r a t i n a  around i t s  machine ax is -of  r o t a t i o n ,  t h e  l a p e l l e t ,  mounted on 
a  dynamometer, i s  made t o  whi r l  i n  a  o i r c u l a r  o r b i t  w i t h i n  t h e  volute .  
The aeasured f o r c e  i s  expressed 8s t h e  sum of a  s teady r a d i a l  foroo and a n  
unsteady force d w  t o  the  e c c e n t r i c  n o t i o n  of t h e  impeller.  Them f o r c r s  
were measued  i n  separate  t e s t s  6n a c e n t r i f u ~ a l  porp w i t h  r a d i o a l l y  
inoreased shroud olearanoe, a  two-dimensional k p e l l o r ,  amd a n  l a p o l l e t  
w i t h  an inducer, the impeller  of t h e  (High k e s s u r o  0 q g o n  Tor- 
bopumg) of the  SSME (Spear S h u t t l e  l h i n  Engine). I n  eaoh oaso, a  &st* 
b i l k i n g  foroe was observed over  a  region of p o s i t i v e  whir l .  
NommabTtlBB 2 2 
[A] hydrodynuio  foroe matr ix,  non-dimensional i red  by pnu r2b2 
'Lt impellor o a t l o t  a rea  (2nr2b2) 
impeller  discharge width 
, oompnents  of the  ins tan taneous  l a t e r a l  foroe r t h e  
impellor  i n  t h e  r o t a t i n g  d y n u a o e t e r  referenoe frame 
Fx,Fy oomponents of the  ins tan taneous  l a t e r a l  foroe on tho 
i m p s l l $ r 3  i n  tho  f  ixe,d l a b o r a t o r y  f  r m e ,  non-dimensional i r e d  
by pna, r b 
n l w s  o# 4 and P i f  t h e  i . p e l l o r  war a t  
P0x*F9 the o r i a i n  of the ~ a b r a t o ~  frame (volute  u n t o r ) ,  
3  nord imens iona l i red  bT pnu r,b, 
components of the  l a t e r a l  foso; on tho  h p o l l e r  noad 
t o  and t a n p n t i a l  t o  t h o  w i 1 o r b i t ,  a v e r a ~ e d  w o r  the  ozb i t ,  2 5 
nord imens iona l  izod bT pnu r bqe 
r a t i o  of whi r l /  k p o l l e r  &af% apoods 
flow r a t e  
impeller  disohar#e r a d i n s  
time 
instantaneous o o o r d i ~ ~ t e s  of t h e  l a p e l l o r  o r a t o r  la t h e  f i x e d  
labora tory  f  n r e ,  non-dimonsioaal izod by r 
rad ius  of the  c i r c u l a r  whi r l  o r b i t  (1.3 um? 
sngular  p o s i t i o n  of t h e  impel le r  on the  whi r l  o r b i t ,  measured 
f r a n  the  vo lu te  t o q u e  i n  t h e  d i r e c t i o n  of impeller  r o t a t i a n  
dens i ty  of water  
w o o f  f  i o i e n t  based on t h e  impoller  discharge a rea  and t i p  speed, 
Mr % r a i i a n  frequency of t h e  impel le r  ( s h a f t )  r o t a t i o n  
rad ian  f reqwncy of t h e  whi r l  motion = I ~ / J  
High Pressure Oxygen Turbopump 
Space S h u t t l e  b i n  Engine 
the l a t e r a l  force 
f n  the rotat fn  
(as P1,P2), ia the 
stationary volnta 
teat  sect ion,  with 
shortonad. 
CIRCULAR WHIRL 
ORBIT 
The f o r c e  expe r i enced  by a  r o t a t i n g  turbomachine h a s  a n  unsteady com- 
ponent r e l a t e d  t o  t h e  l a t e r a l  v i b r a t i o n  of t h e  r o t o r .  Knowledge of t h e  
uns t eady  fo rce  i s  c r u c i a l  t o  unde r s t and ing  t h e  ro tordynamics  of t h e  tu r -  
bomachine. T b i s  f o r c e  has  been  measured on pump i m p e l l e r s  by v a r i o u s  
a u t h o r s :  J e r y  [I-21, Ohashi [3-41 and B o l l e t e r  [ S l .  P resen ted  i n  t h i s  
pape r  a r e  r e s u l t s  f o r  a  c e n t r i f u g a l  pump w i t h  an  e n l a r g e d  a n n u l a r  r e g i o n  
surrounding t h e  shroud, a  two dimensional  i m p e l l e r  and a l s o  of one h a l f  of 
t h e  double-suct ion i m p e l l e r  of t h e  EPOTP (High P r e s s u r e  Oxygen Turbopump) 
of  t h e  SSME (Space S h u t t l e  Main Eng ine ) .  
EXPERIMENTAL FACILITY 
The r e f e r e n c e s  [I-21 p rov ide  a  d e s c r i p t i o n  of t h e  f a c i l i t y  p r i o r  t o  
t h e  c u r r e n t  m o d i f i c a t i o n s .  B r i e f l y ,  t h e  dynammeter ,  composed of two 
p a r a l l e l  p l a t e s  connected by fou r  s t r a i r g a g e d  p o s t s ,  i s  mounted between 
t h e  i m p e l l e r  and t h e  d r i v e  s h a f t .  The i m p e l l e r  i s  made t o  w h i r l  i n  a n  
o r b i t  about t h e  v o l u t e  c e n t e r ,  i n  a d d i t i o n  t o  t h e  normal s h a f t  r o t a t i o n .  
Refe r ing  t o  Pig.  1 t h e  l a t e r a l  f o r c e  on t h e  i m p e l l e r ,  i n  t h e  s t a t i o n -  
ary  v o l u t e  frame of r e f e r e n c e ,  c a n  be r e p r e s e n t e d  by 
T h i s  f o r c e  can be cons ide red  a s  t h e  sum of two f o r c o s :  a f i x e d  f o r c e ,  
r e p r e s e n t e d  by Fo and F , which the  i m p e l l e r  would expe r i ence  i f  l o c a t e d  
a t  t h e  v o l u t e  c e n t e r ,  anaYan unsteady f o r c e  due t o  t h e  e c c e n t r i c  mot ion of 
t h e  impe l l e r ,  r e p r e s e n t e d  by a  f o r c e  m a t r i x  [Al. The g r a v i t a t i o n a l  and 
bouyancy f o r c e s  on t h e  r o t o r  a r e  s u b t r a c t e d  ou t .  Dimensionless  q u a n t i t i e s  
a r e  u s e d  throughout  (see  N m e n c l a t u r e  f o r  d e f i n i t i o n s ) .  
EXPERIHJlNTS AND RESULTS 
The f o r c e s  on a  f i v e  b l aded  Byron-Jackson c e n t r i f u g a l  impe l l e r ,  
d e s i g n a t e d  impo l l e r  X, i n  v a r i o u s  v a n e l e s s  and vaned d i f f u s e r s ,  among them 
a  s p i r a l  v o l u t e  (vo lu te  A), were measured u s i n g  t h e  dynammeter  [I-2). 
Subsequent ly  wi th  t h e  i m p e l l e r  a t  f i x e d  p o s i t i o n s  on i t s  w h i r l  o r b i t ,  
p r e s s m a  measurements were  t a k e n  a t  t h o  v o l u t e  e n t r a n c e  and i n  t h e  a n n u l a r  
r e g i o n  around t h e  f r o n t  shroud. Based on t h e s e  measurements, t h e  computa- 
t i o n  of t h e  hydrodynamic f o r c e  m a t r i x  [A] co r re spond ing  t o  a  w h i r l  r a t i o  
of z e r o  had a  s i g n i f  l c a n t  c o n t r i b u t i o n  f r w  t h e  f r o n t  shroud. Adbins 16- 
71. During t h i s  program, t b e  i n l e t  f l a n g e  of t h e  t e s t  s e c t i o n  was shoe- 
tened,  exposing t h e  a n n u l a r  r e g i o n  t o  t h e  hous ing  r e s e r v o i r ,  a s  sho rn  i n  
Fin.  2. The f o r c e s  on i m p e l l e r  IL were measured and p a r t i a l l y  r e p o r t e d  
f6-71. k i n g  t h e s e  t e s t s ,  r i n g s  were  i n s t a l l e d  w i t h i n  t h e  v o l u t e  w i t h  an 
a x i a l  c l e a r a n c e  of .13 mm f r m  the  i m p e l l e r  t o  reduce leakage flow f r m  
t h e  v o l u t e  t o  t h e  i m p e l l e r  i n l e t .  
I m p e l l e r  2, a  two-dimensional model of i m p e l l e r  X w i t h  l o g a r i t h m i c  
b l a d e s  and a  b l ade  ang le  of 2S0,  was t e s t e d  i n  v o l u t e  A w i t h  the  t e s t  sec- 
t i o n  modif l e d  t o  e l i m i n a t e  t h e  a n n u l a r  r eg ion ,  Fig.  3 .  Throughont t h e s e  
t e s t s ,  t h e  f ace  s e a l  c l e a r a n c e s  a t  t h e  f r o n t  and back of t h e  i m ~ e l l e r  wore 
.13 mm. 
The s t eady  f o r c e  IFo) a s  a  f u n c t i o n  of f l w  c o e f f i c i e n t  i s  p l o t t e d  i n  
Fig.  4.  I n c l u d e d a r e  p r e v i o u s  r e s u l t s  of impe l l e r  X i n v o l u t e  A w i t h o u t  
F i g u r e  4 .  The mag- 
n i t u d e  and d i r e c -  
t i o n  of t h e  s t eady  
f o r c e  [Po) a s  a  
f u n c t i o n  of flow 
c o e f f i c i e n t  a t  1000 
RPM of impe l l e r  X 
i n  v o l u t e  A, wi th  
and wi thou t  t h e  
f r o n t  f l a n g e  shor- 
tened,  of impe l l e r  
Z in v o l u t e  A and 
of i m p e l l e r  R i n  
v o l u t e  E. 
F igure  5 .  Average 
normal f o r c e  a t  
1000 RPM w i t h  a  
f low c o e f f i c i e n t  of 
0.06 of impe l l e r  x 10 
i n  v o l u t e  A  w i t h  
and w i thoa t  t h e  
f  rou t  f l a n g e  shor- 
t ened  and of i 
i m p e l l e r  Z i n  
v o l u t e  A. 
B 
- 2 
- 1 . 8  - 8 . 5  0 0 .5  I .  0 
1, ' 
I I . . . ~ . ~  
F i g u r e  6 .  Average F t  -- - IYPELLER X FFOH' FL4NbE SHORT 
t a n g e n t i a l  fo rce  a t  o I f lPELLEF Z 
1000 BBM w i t h  a  PPl1=1080 
f low c o e f f i c i e n t  of 1 W l = . @ b  
0.06 of impe l l e r  X 0 
i n  v o l u t e  A  w i t h  J 
and wi thou t  t h e  
f r o n t  f l a n g e  shor- 
t ened  and of - 
impe l l e r  Z i n  - 
v o l u t e  A. g 
P I , . .  , , , , . I ,  
- 1 . 0  - 8 . 5  0 0.: I .  0 
I J 
I M P E L L E R  R VOLUTE E 
5 
0 
c i e n t s .  
the  f r o n t  f l ange  shortened. b a s o r e m e n t s  of impeller R i n  v o l u t e  B w i l l  
be discussed l a t e r .  The impeller  dimensions used t o  n o r d i m e n s i o n a l k e  
t h e  f o r c e s  a r e  l i s t e d  i n  t a b l e  1 .  For impeller  X t h e  fo rce  magnitude i s  
m a l l e r  when t h e  f r o n t  f l ange  i s  shortened. Impeller  Z has a  smaller  ma$- 
nitude. (F I h a s  a  r i n i r r n  f o r  bo th  impel le r s  i n  the  vane less  vo lu te  A. 
The d!agon81 elements of t h e  hydrody-io fo rce  mat r ix  [A(o/u)] a r e  
m a r l y  equsl m d  t h e  off-diagonal elements a r e  m a r l y  equal b u t  of oppo- 
s i t e  sign. The mat r ix  w i l l  be presented i n  terms of the  average normal 
and t a n l e n t i d  forces,  Fn and Ft, given by 
I - 
Fn and Pt f o r  the t r o  impel le r s  a r e  presented i n  Fig. 5-6 f o r  a  flow 
coef f  i o i e n t  of 0.06. Under reverse  whi r l  both F and Pt f o r  impeller  X 
a r e  o a l l e r  wi th  t h e  f r o n t  f l ange  ahortemd.  Under p o x a r d  whi r l  Ft i s  i n  
t h e  same d i r e c t i o n  a s  t h e  whi r l  motion, thus  des tab i l i z ing ,  w e r  a  nmaller 
range of whi r l  r a t i o .  Tha f o r o e s  on impeller  Z a r e  smaller.  Observe t h a t  
the  p ro jeo ted  a r e a  of impeller  Z i n  t h e  r a d i a l  d i r e c t i o n ,  upon which a  
p r e s s m e  unbalanoe l i v e s  a  l a t e r a l  fo rce ,  is  smaller.  
h e  h a l f  of t h e  dauble-suotion impel le r  of t h e  HPOTP of the  SSME, 
d e s i l n a t e d  a s  i m m l l e r  R, was i n s t a l l e d  i n  vo lu te  E. The impel le r  haa 
e i g h t  b l a b s  and a n  i n d w e r  w i t h  f o o r  blades.  It was modified p r i o r  t o  
i n s t a l l a t i o n ,  g r i n o i p a l l y  t h e  o u t l e t  diameter was reduced s l i g h t l y .  
Volute B has  seventeen, o i r o u l a r  a r c  vanes and a n  e l l i p t i c a l  c ross  rsc- 
t ion.  Fig. 7 s h w s  impel le r  R i n s t a l l e d  i n  v o l u t e  E. 
The s teady force  f a r  i m p l l e r  R was included i n  Fig. 4. There i s  a  
m a l l  v a r i a t i o n  r i t h  flow c o e f f i o i e n t .  F and F a r e  presented i n  Fig. 
8-9. For d 1 0 . 1 4  t h e  0-0 of Fn has  a  par.%olic &ape and F can be 
approximated by a s t r a i g h t  l i n e ,  with the region of d e s t a b i l f z i n g  whi r l  
O < O / P ~  < 0.2. For 4 - 0 . 0 9  Ft i s  approximately constant  w e r  a  w h i r l  r a t i o  
of -0tl<O/u < 0.4, while  f o r  da0 .07  Ft resembles a  cubic func t ion .  Since 
Ft o roasss  t h e  a x i s  t h r i e  times, t h e r e  e x i t  regions of * s t a b i l i z i n g  and 
d e s t a b i l i r i q  whir l  f o r  0.0 < O/u < 0.6.  At these l o r e r  flow coeff  i- 
o ien ts ,  F h a s  departed f r m  o a o o t h  parabola w e r  t h i s  whi r l  r a t i o  
ran le .  &ports C8-91 presen t  t h e  above d a t a  f o r  more f l m  c o s f f i o i e n t r .  
T u f t s  were plaoed upstream of t h e  induoer. i n  o rder  t o  make observa- 
t i o n s  on flow reversa l .  At a  p o s i t i o n  of S mm upr t rean  of t h e  inducer  
leading edge, f l o r  r w e r s a l  vas  observed f o r  d < 0.095. For d < 0.075 
f l o r  r w e r s a l  was observed i n  a  region extending t o  o m  inducer dicmeter 
upstream of t h e  iaduoer l ead ing  edge. 
Exgosins t h e  a m u l a r  r e l i o n  sorroanding t h e  shroud t o  t h e  housing 
r e s e r v o i r  reduoed tho  f o r c e s  upon l a p e l l e r  X and reduced t h e  d e s t a b i l i z i n g  
whir l  r a t i o  range of t h e  average t a n g e n t i a l  force.  These r e s u l t s  ind ioa ta  
the  importanoe of the  e x t e r n a l  shroud r e s i o n  upon the  impeller  fo rces .  
Impeller  Z. a two-dimensional model of impeller  X, had a  nmaller 
steady force and a  hydrodynamic f o r c e  mat r ix  wi th  mnaller elements. The 
average t a n g e n t i a l  force was d e s t a b i l i z i n g  w e r  a  whir l  r a t i o  range com- 
parable  t o  impeller  X i n  the  m o d i f i e d  t e s t  sect ion.  
Impeller  R. one ha l f  of t h e  double-suction impeller  of the HPOTP o f  
the SSME, had t h e  l a r g e s t  magnitude of t h e  average tangent ia l  force i n  t h e  
region of d e s t a b i l i z i n g  whi r l .  With decreasing f  lor coeff i c i e n t ,  t h e  
curve of Ft changed frcm an approximately s t r a i g h t  l i n e  t o  a  cubic, with a 
corresponding inc rease  i n  the  region of d e s t a b l  i z i n g  whi r l  from 6l/o < 0.2 
t o  Sk/o < 0.6. Th is  t r a n s i t i o n  i n  the curve of Ft appears  t o  coincide w i t h  
t h e  occurrence of flow reversa l  upstream of the inducer .  
ACKNOWLEDGEMENTS 
The au thors  a r e  indebted t o  t h e  NASA George k r s h a l l  Space F l i g h t  
Center  f o r  continued sponsorship of t h i s  research  under c o n t r a c t  NAS8- 
33108. 
REFERENCES 
J e r y ,  B., Prennen, C.E.. Caughey, T.K., and Acosta. A.J., "Forces on 
Cantr i f  ugal Pump Impel lers ,"  "Second I n t e r n a t i o n a l  Pump Symposim," 
Houston Texas, Apri l  29-Mag 2 ,  1985. 
Je ry .  B., "Experimental Study of Unsteady Eydrodynamic Force Matr ices  
o n  Whirling Cent r i fuga l  Pump Impel le r s , "  Fh.D. Thesis ,  Div i s ion  of 
Engineering and Appl ied Science,  C a l i f o r n i a  I n s t i t u t e  of Technology, 
1987. 
Ohashi, H.. and Shoj i, H., "La te ra l  F l u i d  Forces  Acting on a Whirling 
Cent r i fuga l  Impel ler  i n  Vaneless and Vaned Di f fuse r , "  Workshop on 
Rotordynamic I n s t a b i l i t y  Problems i n  High Performanco Tnrbomachinery, 
Texas AQM Univers i ty ,  May 1984, NASA CP2338, pp. 109-122. 
Ohashi, H., Batanaka, R . ,  and Sakurai .  A.. "Fluid Force Tes t ing  
Machine f o r  Whirling Cent r i fuga l  Impel ler ."  I n t e r n a t i o n a l  Conference 
on Rotordynamics, Tokyo, Japan, Sept.  14-17, 1986. 
B o l l e t e r ,  U . ,  Wyss, A., Welte, I., and S t i i r ch le r ,  R., "Measurement of 
Hydrodynamic I n t e r a c t i o n  Matr ices  of B o i l e r  Feed Pump Impel le r s , "  
ASME 85-DET-148, 1985. 
Adkins, D., "Analyses of Hydrodynamic Forces  on Cent r i fuga l  Pump 
Impel lers ."  W.D. Thesis .  Div i s ion  of Engineer ing and Applied Sci- 
ence, C a l i f o r n i a  I n s t i t u t e  of Technology, 1986. 
Adkins, D., Brennen. C.E. , "Analyses of Hydrodynamic Radial Forces  on 
Cent r i fuga l  Pump," Fourth Rotordynamic I n s t a b i l i t y  Problems i n  High 
Performance Turbomachinery Workshop. Roust on, Texas, June 2-4, 1986. 
Franz , R. and Arndt , N. , "Measurements of Rydr odynamic Force s on a 
TwwDimensional Impeller and a Modified Cent r i fuga l  Pump,'' Divis ion 
of Engineering and Applied Science,  C a l i f o r n i a  I n s t i t u t e  cf Technol- 
ogy, 1986, Report No. E249.4. 
Franz, R. and Arndt, N. ,  "Measurements of I~ydrodynamic Forces  on t h e  
Impel le r  of the HPOTP of the SShE," Divis ion  of En ineer ing  and 
Applied Science, C a l i f o r n i a  I n s t i t u t e  of Technology, 198%. Report No. 
249.2. 
LIST OF TABLES Impel le r  r2(mm) b 2 ( m )  


Rotordynamic Forces on Centrifugal Pump Impellers

~ o t o r d y n u i o  Forces on Contr i fuaal  P l r p  Impr l le r s  
R. Pranz, N. Arndt, T.K. i h n g h q ,  C.E. Braanon, and A.J. h o s t .  
C.1 i f  o r n i a  I n r t i t n t a  of Teohnolow 
Pasadena, CA. 91121 USA 
The a r y m t r i o  f l w  aronmd a n  impel le r  i n  a  v o l u t e  e l o r t s  a  foroa 
upon the impeller.  To study t h e  r o t o r d y n u i c  fo roe  on an impel le r  which 
i s  v i b r a t i n a  around i t s  machine ax is -of  r o t a t i o n ,  t h e  l a p e l l e t ,  mounted on 
a  dynamometer, i s  made t o  whi r l  i n  a  o i r c u l a r  o r b i t  w i t h i n  t h e  volute .  
The aeasured f o r c e  i s  expressed 8s t h e  sum of a  s teady r a d i a l  foroo and a n  
unsteady force d w  t o  the  e c c e n t r i c  n o t i o n  of t h e  impeller.  Them f o r c r s  
were measued  i n  separate  t e s t s  6n a c e n t r i f u ~ a l  porp w i t h  r a d i o a l l y  
inoreased shroud olearanoe, a  two-dimensional k p e l l o r ,  amd a n  l a p o l l e t  
w i t h  an inducer, the impeller  of t h e  (High k e s s u r o  0 q g o n  Tor- 
bopumg) of the  SSME (Spear S h u t t l e  l h i n  Engine). I n  eaoh oaso, a  &st* 
b i l k i n g  foroe was observed over  a  region of p o s i t i v e  whir l .  
NommabTtlBB 2 2 [A] hydrodynuio  foroe matr ix,  non-dimensional i red  by pnu r2b2 
'Lt impellor o a t l o t  a rea  (2nr2b2) impeller  discharge width 
, 
oompnents  of the  ins tan taneous  l a t e r a l  foroe r t h e  
impellor  i n  t h e  r o t a t i n g  d y n u a o e t e r  referenoe frame 
Fx,Fy oomponents of the  ins tan taneous  l a t e r a l  foroe on tho i m p s l l $ r 3  i n  tho  f  ixe,d l a b o r a t o r y  f  r m e ,  non-dimensional i r e d  
by pna, r b 
n l w s  o# 4 and P i f  t h e  i . p e l l o r  war a t  
P0x*F9 the o r i a i n  of the ~ a b r a t o ~  frame (volute  u n t o r ) ,  3  
nord imens iona l i red  bT pnu r,b, 
components of the  l a t e r a l  foso; on tho  h p o l l e r  noad 
t o  and t a n p n t i a l  t o  t h o  w i 1 o r b i t ,  a v e r a ~ e d  w o r  the  ozb i t ,  2 5 
nord imens iona l  izod bT pnu r bqe 
r a t i o  of whi r l /  k p o l l e r  &af% apoods 
flow r a t e  
impeller  disohar#e r a d i n s  
time 
instantaneous o o o r d i ~ ~ t e s  of t h e  l a p e l l o r  o r a t o r  la t h e  f i x e d  
labora tory  f  n r e ,  non-dimonsioaal izod by r 
rad ius  of the  c i r c u l a r  whi r l  o r b i t  (1.3 um? 
sngular  p o s i t i o n  of t h e  impel le r  on the  whi r l  o r b i t ,  measured 
f r a n  the  vo lu te  t o q u e  i n  t h e  d i r e c t i o n  of impeller  r o t a t i a n  
dens i ty  of water  
w o o f  f  i o i e n t  based on t h e  impoller  discharge a rea  and t i p  speed, 
Mr % 
r a i i a n  frequency of t h e  impel le r  ( s h a f t )  r o t a t i o n  
rad ian  f reqwncy of t h e  whi r l  motion = I ~ / J  
High Pressure Oxygen Turbopump 
Space S h u t t l e  b i n  Engine 
the l a t e r a l  force 
f n  the rotat fn  
(as P1,P2), ia the 
stationary volnta 
teat  sect ion,  with 
shortonad. 
CIRCULAR WHIRL 
ORBIT 
The f o r c e  expe r i enced  by a  r o t a t i n g  turbomachine h a s  a n  unsteady com- 
ponent r e l a t e d  t o  t h e  l a t e r a l  v i b r a t i o n  of t h e  r o t o r .  Knowledge of t h e  
uns t eady  fo rce  i s  c r u c i a l  t o  unde r s t and ing  t h e  ro tordynamics  of t h e  tu r -  
bomachine. T b i s  f o r c e  has  been  measured on pump i m p e l l e r s  by v a r i o u s  
a u t h o r s :  J e r y  [I-21, Ohashi [3-41 and B o l l e t e r  [ S l .  P resen ted  i n  t h i s  
pape r  a r e  r e s u l t s  f o r  a  c e n t r i f u g a l  pump w i t h  an  e n l a r g e d  a n n u l a r  r e g i o n  
surrounding t h e  shroud, a  two dimensional  i m p e l l e r  and a l s o  of one h a l f  of 
t h e  double-suct ion i m p e l l e r  of t h e  EPOTP (High P r e s s u r e  Oxygen Turbopump) 
of  t h e  SSME (Space S h u t t l e  Main Eng ine ) .  
EXPERIMENTAL FACILITY 
The r e f e r e n c e s  [I-21 p rov ide  a  d e s c r i p t i o n  of t h e  f a c i l i t y  p r i o r  t o  
t h e  c u r r e n t  m o d i f i c a t i o n s .  B r i e f l y ,  t h e  dynammeter ,  composed of two 
p a r a l l e l  p l a t e s  connected by fou r  s t r a i r g a g e d  p o s t s ,  i s  mounted between 
t h e  i m p e l l e r  and t h e  d r i v e  s h a f t .  The i m p e l l e r  i s  made t o  w h i r l  i n  a n  
o r b i t  about t h e  v o l u t e  c e n t e r ,  i n  a d d i t i o n  t o  t h e  normal s h a f t  r o t a t i o n .  
Refe r ing  t o  Pig.  1 t h e  l a t e r a l  f o r c e  on t h e  i m p e l l e r ,  i n  t h e  s t a t i o n -  
ary  v o l u t e  frame of r e f e r e n c e ,  c a n  be r e p r e s e n t e d  by 
T h i s  f o r c e  can be cons ide red  a s  t h e  sum of two f o r c o s :  a f i x e d  f o r c e ,  
r e p r e s e n t e d  by Fo and F , which the  i m p e l l e r  would expe r i ence  i f  l o c a t e d  
a t  t h e  v o l u t e  c e n t e r ,  anaYan unsteady f o r c e  due t o  t h e  e c c e n t r i c  mot ion of 
t h e  impe l l e r ,  r e p r e s e n t e d  by a  f o r c e  m a t r i x  [Al. The g r a v i t a t i o n a l  and 
bouyancy f o r c e s  on t h e  r o t o r  a r e  s u b t r a c t e d  ou t .  Dimensionless  q u a n t i t i e s  
a r e  u s e d  throughout  (see  N m e n c l a t u r e  f o r  d e f i n i t i o n s ) .  
EXPERIHJlNTS AND RESULTS 
The f o r c e s  on a  f i v e  b l aded  Byron-Jackson c e n t r i f u g a l  impe l l e r ,  
d e s i g n a t e d  impo l l e r  X, i n  v a r i o u s  v a n e l e s s  and vaned d i f f u s e r s ,  among them 
a  s p i r a l  v o l u t e  (vo lu te  A), were measured u s i n g  t h e  dynammeter  [I-2). 
Subsequent ly  wi th  t h e  i m p e l l e r  a t  f i x e d  p o s i t i o n s  on i t s  w h i r l  o r b i t ,  
p r e s s m a  measurements were  t a k e n  a t  t h o  v o l u t e  e n t r a n c e  and i n  t h e  a n n u l a r  
r e g i o n  around t h e  f r o n t  shroud. Based on t h e s e  measurements, t h e  computa- 
t i o n  of t h e  hydrodynamic f o r c e  m a t r i x  [A] co r re spond ing  t o  a  w h i r l  r a t i o  
of z e r o  had a  s i g n i f  l c a n t  c o n t r i b u t i o n  f r w  t h e  f r o n t  shroud. Adbins 16- 
71. During t h i s  program, t b e  i n l e t  f l a n g e  of t h e  t e s t  s e c t i o n  was shoe- 
tened,  exposing t h e  a n n u l a r  r e g i o n  t o  t h e  hous ing  r e s e r v o i r ,  a s  sho rn  i n  
Fin.  2. The f o r c e s  on i m p e l l e r  IL were measured and p a r t i a l l y  r e p o r t e d  
f6-71. k i n g  t h e s e  t e s t s ,  r i n g s  were  i n s t a l l e d  w i t h i n  t h e  v o l u t e  w i t h  an 
a x i a l  c l e a r a n c e  of .13 mm f r m  the  i m p e l l e r  t o  reduce leakage flow f r m  
t h e  v o l u t e  t o  t h e  i m p e l l e r  i n l e t .  
I m p e l l e r  2, a  two-dimensional model of i m p e l l e r  X w i t h  l o g a r i t h m i c  
b l a d e s  and a  b l ade  ang le  of 2S0,  was t e s t e d  i n  v o l u t e  A w i t h  the  t e s t  sec- 
t i o n  modif l e d  t o  e l i m i n a t e  t h e  a n n u l a r  r eg ion ,  Fig.  3 .  Throughont t h e s e  
t e s t s ,  t h e  f ace  s e a l  c l e a r a n c e s  a t  t h e  f r o n t  and back of t h e  i m ~ e l l e r  wore 
.13 mm. 
The s t eady  f o r c e  IFo) a s  a  f u n c t i o n  of f l w  c o e f f i c i e n t  i s  p l o t t e d  i n  
Fig.  4.  I n c l u d e d a r e  p r e v i o u s  r e s u l t s  of impe l l e r  X i n v o l u t e  A w i t h o u t  
F i g u r e  4 .  The mag- 
n i t u d e  and d i r e c -  
t i o n  of t h e  s t eady  
f o r c e  [Po) a s  a  
f u n c t i o n  of flow 
c o e f f i c i e n t  a t  1000 
RPM of impe l l e r  X 
i n  v o l u t e  A, wi th  
and wi thou t  t h e  
f r o n t  f l a n g e  shor- 
tened,  of impe l l e r  
Z in v o l u t e  A and 
of i m p e l l e r  R i n  
v o l u t e  E. 
F igure  5 .  Average 
normal f o r c e  a t  
1000 RPM w i t h  a  
f low c o e f f i c i e n t  of 
0.06 of impe l l e r  x 10 
i n  v o l u t e  A  w i t h  
and w i thoa t  t h e  
f  rou t  f l a n g e  shor- 
t ened  and of i 
i m p e l l e r  Z i n  
v o l u t e  A. 
B 
- 2 
- 1 . 8  - 8 . 5  0 0 .5  I .  0 
1, ' 
I I . . . ~ . ~  
F i g u r e  6 .  Average F t  -- - IYPELLER X FFOH' FL4NbE SHORT 
t a n g e n t i a l  fo rce  a t  o I f lPELLEF Z 
1000 BBM w i t h  a  PPl1=1080 
f low c o e f f i c i e n t  of 1 W l = . @ b  
0.06 of impe l l e r  X 0 
i n  v o l u t e  A  w i t h  J 
and wi thou t  t h e  
f r o n t  f l a n g e  shor- 
t ened  and of 
- 
impe l l e r  Z i n  - 
v o l u t e  A. g 
P I , . .  , , , , . I ,  
- 1 . 0  - 8 . 5  0 0.: I .  0 
I J 
I M P E L L E R  R VOLUTE E 
5 
0 
c i e n t s .  
the  f r o n t  f l ange  shortened. b a s o r e m e n t s  of impeller R i n  v o l u t e  B w i l l  
be discussed l a t e r .  The impeller  dimensions used t o  n o r d i m e n s i o n a l k e  
t h e  f o r c e s  a r e  l i s t e d  i n  t a b l e  1 .  For impeller  X t h e  fo rce  magnitude i s  
m a l l e r  when t h e  f r o n t  f l ange  i s  shortened. Impeller  Z has a  smaller  ma$- 
nitude. (F I h a s  a  r i n i r r n  f o r  bo th  impel le r s  i n  the  vane less  vo lu te  A. 
The d!agon81 elements of t h e  hydrody-io fo rce  mat r ix  [A(o/u)] a r e  
m a r l y  equsl m d  t h e  off-diagonal elements a r e  m a r l y  equal b u t  of oppo- 
s i t e  sign. The mat r ix  w i l l  be presented i n  terms of the  average normal 
and t a n l e n t i d  forces,  Fn and Ft, given by I - 
Fn and Pt f o r  the t r o  impel le r s  a r e  presented i n  Fig. 5-6 f o r  a  flow 
coef f  i o i e n t  of 0.06. Under reverse  whi r l  both F and Pt f o r  impeller  X 
a r e  o a l l e r  wi th  t h e  f r o n t  f l ange  ahortemd.  Under p o x a r d  whi r l  Ft i s  i n  
t h e  same d i r e c t i o n  a s  t h e  whi r l  motion, thus  des tab i l i z ing ,  w e r  a  nmaller 
range of whi r l  r a t i o .  Tha f o r o e s  on impeller  Z a r e  smaller.  Observe t h a t  
the  p ro jeo ted  a r e a  of impeller  Z i n  t h e  r a d i a l  d i r e c t i o n ,  upon which a  
p r e s s m e  unbalanoe l i v e s  a  l a t e r a l  fo rce ,  is  smaller.  
h e  h a l f  of t h e  dauble-suotion impel le r  of t h e  HPOTP of the  SSME, 
d e s i l n a t e d  a s  i m m l l e r  R, was i n s t a l l e d  i n  vo lu te  E. The impel le r  haa 
e i g h t  b l a b s  and a n  i n d w e r  w i t h  f o o r  blades.  It was modified p r i o r  t o  
i n s t a l l a t i o n ,  g r i n o i p a l l y  t h e  o u t l e t  diameter was reduced s l i g h t l y .  
Volute B has  seventeen, o i r o u l a r  a r c  vanes and a n  e l l i p t i c a l  c ross  rsc- 
t ion.  Fig. 7 s h w s  impel le r  R i n s t a l l e d  i n  v o l u t e  E. 
The s teady force  f a r  i m p l l e r  R was included i n  Fig. 4. There i s  a  
m a l l  v a r i a t i o n  r i t h  flow c o e f f i o i e n t .  F and F a r e  presented i n  Fig. 
8-9. For d 1 0 . 1 4  t h e  0-0 of Fn has  a  par.%olic &ape and F can be 
approximated by a s t r a i g h t  l i n e ,  with the region of d e s t a b i l f z i n g  whi r l  
O < O / P ~  < 0.2. For 4 - 0 . 0 9  Ft i s  approximately constant  w e r  a  w h i r l  r a t i o  
of -0tl<O/u < 0.4, while  f o r  da0 .07  Ft resembles a  cubic func t ion .  Since 
Ft o roasss  t h e  a x i s  t h r i e  times, t h e r e  e x i t  regions of * s t a b i l i z i n g  and 
d e s t a b i l i r i q  whir l  f o r  0.0 < O/u < 0.6.  At these l o r e r  flow coeff  i- 
o ien ts ,  F h a s  departed f r m  o a o o t h  parabola w e r  t h i s  whi r l  r a t i o  
ran le .  &ports C8-91 presen t  t h e  above d a t a  f o r  more f l m  c o s f f i o i e n t r .  
T u f t s  were plaoed upstream of t h e  induoer. i n  o rder  t o  make observa- 
t i o n s  on flow reversa l .  At a  p o s i t i o n  of S mm upr t rean  of t h e  inducer  
leading edge, f l o r  r w e r s a l  vas  observed f o r  d < 0.095. For d < 0.075 
f l o r  r w e r s a l  was observed i n  a  region extending t o  o m  inducer dicmeter 
upstream of t h e  iaduoer l ead ing  edge. 
Exgosins t h e  a m u l a r  r e l i o n  sorroanding t h e  shroud t o  t h e  housing 
r e s e r v o i r  reduoed tho  f o r c e s  upon l a p e l l e r  X and reduced t h e  d e s t a b i l i z i n g  
whir l  r a t i o  range of t h e  average t a n g e n t i a l  force.  These r e s u l t s  ind ioa ta  
the  importanoe of the  e x t e r n a l  shroud r e s i o n  upon the  impeller  fo rces .  
Impeller  Z. a two-dimensional model of impeller  X, had a  nmaller 
steady force and a  hydrodynamic f o r c e  mat r ix  wi th  mnaller elements. The 
average t a n g e n t i a l  force was d e s t a b i l i z i n g  w e r  a  whir l  r a t i o  range com- 
parable  t o  impeller  X i n  the  m o d i f i e d  t e s t  sect ion.  
Impeller  R. one ha l f  of t h e  double-suction impeller  of the HPOTP o f  
the SSME, had t h e  l a r g e s t  magnitude of t h e  average tangent ia l  force i n  t h e  
region of d e s t a b i l i z i n g  whi r l .  With decreasing f  lor coeff i c i e n t ,  t h e  
curve of Ft changed frcm an approximately s t r a i g h t  l i n e  t o  a  cubic, with a 
corresponding inc rease  i n  the  region of d e s t a b l  i z i n g  whi r l  from 6l/o < 0.2 
t o  Sk/o < 0.6. Th is  t r a n s i t i o n  i n  the curve of Ft appears  t o  coincide w i t h  
t h e  occurrence of flow reversa l  upstream of the inducer .  
ACKNOWLEDGEMENTS 
The au thors  a r e  indebted t o  t h e  NASA George k r s h a l l  Space F l i g h t  
Center  f o r  continued sponsorship of t h i s  research  under c o n t r a c t  NAS8- 
33108. 
REFERENCES 
J e r y ,  B., Prennen, C.E.. Caughey, T.K., and Acosta. A.J., "Forces on 
Cantr i f  ugal Pump Impel lers ,"  "Second I n t e r n a t i o n a l  Pump Symposim," 
Houston Texas, Apri l  29-Mag 2 ,  1985. 
Je ry .  B., "Experimental Study of Unsteady Eydrodynamic Force Matr ices  
o n  Whirling Cent r i fuga l  Pump Impel le r s , "  Fh.D. Thesis ,  Div i s ion  of 
Engineering and Appl ied Science,  C a l i f o r n i a  I n s t i t u t e  of Technology, 
1987. 
Ohashi, H.. and Shoj i, H., "La te ra l  F l u i d  Forces  Acting on a Whirling 
Cent r i fuga l  Impel ler  i n  Vaneless and Vaned Di f fuse r , "  Workshop on 
Rotordynamic I n s t a b i l i t y  Problems i n  High Performanco Tnrbomachinery, 
Texas AQM Univers i ty ,  May 1984, NASA CP2338, pp. 109-122. 
Ohashi, H., Batanaka, R . ,  and Sakurai .  A.. "Fluid Force Tes t ing  
Machine f o r  Whirling Cent r i fuga l  Impel ler ."  I n t e r n a t i o n a l  Conference 
on Rotordynamics, Tokyo, Japan, Sept.  14-17, 1986. 
B o l l e t e r ,  U . ,  Wyss, A., Welte, I., and S t i i r ch le r ,  R., "Measurement of 
Hydrodynamic I n t e r a c t i o n  Matr ices  of B o i l e r  Feed Pump Impel le r s , "  
ASME 85-DET-148, 1985. 
Adkins, D., "Analyses of Hydrodynamic Forces  on Cent r i fuga l  Pump 
Impel lers ."  W.D. Thesis .  Div i s ion  of Engineer ing and Applied Sci- 
ence, C a l i f o r n i a  I n s t i t u t e  of Technology, 1986. 
Adkins, D., Brennen. C.E. , "Analyses of Hydrodynamic Radial Forces  on 
Cent r i fuga l  Pump," Fourth Rotordynamic I n s t a b i l i t y  Problems i n  High 
Performance Turbomachinery Workshop. Roust on, Texas, June 2-4, 1986. 
Franz , R. and Arndt , N. , "Measurements of Rydr odynamic Force s on a 
TwwDimensional Impeller and a Modified Cent r i fuga l  Pump,'' Divis ion 
of Engineering and Applied Science,  C a l i f o r n i a  I n s t i t u t e  cf Technol- 
ogy, 1986, Report No. E249.4. 
Franz, R. and Arndt, N. ,  "Measurements of I~ydrodynamic Forces  on t h e  
Impel le r  of the HPOTP of the SShE," Divis ion  of En ineer ing  and 
Applied Science, C a l i f o r n i a  I n s t i t u t e  of Technology, 198%. Report No. 
249.2. 
LIST OF TABLES Impel le r  r2(mm) b 2 ( m )  


Adkins, D., &quot;Analyses of Hydrodynamic Forces on Cent r i fuga l Pump Impel lers .&quot; W.D. Thesis . Div i s ion of Engineer ing and Applied Science, C a l i f o r n i a I n s t i t u t e of Technology, 1986.

Adkins, D., Brennen. C.E. , &quot;Analyses of Hydrodynamic Radial Forces on Cent r i fuga l Pump,&quot; Fourth Rotordynamic I n s t a b i l i t y Problems i n High Performance Turbomachinery Workshop. Roust on, Texas, June 2-4, 1986.

Analyses of Hydrodynamic Forces on Cent r i fuga l Pump Impel lers .&quot; W.D. Thesis . Div i s ion of Engineer ing and Applied Science, C a l i f o r n i a I n s t i t u t e of Technology,

Analyses of Hydrodynamic Radial Forces on Cent r i fuga l Pump,&quot; Fourth Rotordynamic I n s t a b i l i t y Problems i n High Performance Turbomachinery Workshop. Roust on,

B o l l e t e r

B o l l e t e r , U . , Wyss, A., Welte, I., and S t i i r ch le r , R., &quot;Measurement of Hydrodynamic I n t e r a c t i o n Matr ices of B o i l e r Feed Pump Impel le r s , &quot; ASME 85-DET-148, 1985.

Experimental Study of Unsteady Eydrodynamic Force Matr ices o n Whirling Cent r i fuga l Pump Impel le r s , &quot; Fh.D. Thesis , Div i s ion of Engineering and Appl ied Science, C a l i f o r n i a I n s t i t u t e of Technology,

Fluid Force Tes t ing Machine f o r Whirling Cent r i fuga l Impel ler .&quot; I n t e r n a t i o n a l Conference on Rotordynamics,

Forces on Cantr i f ugal Pump Impel lers ,&quot; &quot;Second I n t e r n a t i o n a l Pump Symposim,&quot; Houston Texas, Apri l 29-Mag 2 ,

J e r y , B., Prennen, C.E.. Caughey, T.K., and Acosta. A.J., &quot;Forces on Cantr i f ugal Pump Impel lers ,&quot; &quot;Second I n t e r n a t i o n a l Pump Symposim,&quot; Houston Texas, Apri l 29-Mag 2 , 1985.

Je ry . B., &quot;Experimental Study of Unsteady Eydrodynamic Force Matr ices o n Whirling Cent r i fuga l Pump Impel le r s , &quot; Fh.D. Thesis , Div i s ion of Engineering and Appl ied Science, C a l i f o r n i a I n s t i t u t e of Technology, 1987.

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https://authors.library.caltech.edu/209/1/FRA081.pdf

Rotordynamic Forces on Centrifugal Pump Impellers

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