Hypervelocity wind tunnel investigation of  turbulent boundary undergoing adverse pressure  gradient and cross flow along plane of symmetr

Calarese, Wladimiro

Wang, C. R.

Zakkay, Victor

English

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i\IEk? YORK UNIVERSITY 
New York, New York 
A,N EXPERIlvWNTA-L LNVESTIGATION OF T m  TURBIIUBT '30UNi)ld?Y 
LAYER UNDEXGOING BOTH ADVMSE PRESSURE C-RWIz 4'2 i"X3 CROSS 
FLOW ALOIJC A PLANE: OF SXSDETEY 
by 
Victor Zakkay 
Professor of Aeronautics and Astronautics 
Wladimiro Calarese 
Assistant iiesearch Scientist 
C. 13, Wang 
Research Assistant 
De~artment of Aeronautics and Astronautics 
Prepared for The Office of' University Affairs 
National Aeronautics and Space Administration 
under Research Grant ~~~-33-016-0@ 
February 1971 
AN TXPERIMENTAL INVESTIGATION OF THE TURBULENT BOUNDARY T,AYER IINE?T; SO - Z 
BOTU ADVERSE PRESSURP, GRADIENT & CROSS FLOW ALONG A PLANE OF S W E T L Y  
by 
Victor  zakkayS, Wladimiro CalareseSS , C. R .  Wang t FS 
Experimental da t a  have been obtained f o r  a compressible turbulecc  bi i : ~ d a r y  
l aye r  i n  adverse  pressure  g rad ien t  wi th  and without  favorable  c ros s  .l~.cri, a long 
a plane of symmetry of a f l a r e d  sur face .  The experiments were perforiiled a: 
7 
Dlach Number 6 and Reynolds Number up t o  4,4 x PO /ft. The compressi.c~i o- r r  
t he  f l a r e d  s u r f a c e  was of t h e  order  of 50. T rans i t i on  was achieved l i a t r r i - ~ ~ l y  
w e l l  ahead of t he  compression reg ion  and the  c ros s  flow was e s t a b l i s t ~ e d  i/ 
plac ing  on the  compression s u r f a c e  two l a t e r a l  p l a t e s .  Boundary layar- p r ~ f  i i e s  
of s t a t i c  p re s su re ,  p i t o t  tube pressure ,  s t agna t ion  temperature,  and h e a L  - c a ~ s f e ,  
r a t e s  were measured. Measurements were taken on t h e  windward s jde  OL rhe A ~ r h c e ,  
- - The presence of t he  c ross  flow a l t e r s  s i g n i f i c a n t l y  t h e  value of rhs ;i~; - - -  
Neat t r a n s f e r  r g t e s  a r e  i n  good agreement wi th  t h e x e t i c a l  values air,., A,~, ..y 
t he  f l a t - p l a t e  r e f e rence  erpthalpy methodd. A second p a r t  w i l l  foPZoti V,I~ICI , :ic 
$:This reporg was prepwed under t he  fol lowing Grants ,  NGL-33-016-06'7 
and NGR-33-016-161. 
SProfessor  of Aeronautics and As t ronau t i c s ,  New York Univers i ty  
?-/-Assistant Research S c i e n t i s t ,  New York Univers i ty  
f-??Research A s s i s t a n t ,  New York Un ive r s i t y  
present  da ta  w i l l  be rrsed t g  c a l c u l a t e  the Mach NumSer and v e l o c i t y  p ~ - o f ~ ~ L e s ,  
together  with the  boundary layer  parameters. 
NOMENCLATURE 
C 
f s k i n  f r i c t i o n  c o e f f i c i e n t  
P pr es  s u r e  
%7 
h e a t  t r a n s f e r  r a t e  
s streamwise d i s t a n c e  measured from beginning of f l a r e  
u v e l q a i t y  i n  t he  streamwise d i r e c t i o n  
w v e l o c i t y  i n  t h e  p e r i p h e r a l  d i r e c t i o n  
-1. 
w v e l o c i t y  r a t  j o  W- 
u 
e  
x a x i g l  d i r e c t i o n  
Y g iyec t lon  normal t o  t bp  body a x i s  
6 boundary l a y e r  th icgness  
q l o c a l  ang le  between che axis d i r e c t i o n  and t h e  body surface 
c? pe r iphe ra l  d i r e c t i o n  
Subsc r ip t s  
0 i n i t i a l  condi t ions  a t  t h e  beginning of t h e  compression f i a re  
1 s t a t i c  
2 behind normal shock 
e  edge of boundary layer  
t geagnat ipn condi t ions ,  
03 f r e e  s t ream condi t ions  
INTRODUCTION 
Present  i n t e r e s t  i n  three-dimensional hypersonic t u rbu len t  boundary Layers 
over i n l e t s  of a i r  b rea th ing  propulsion systems has  s t imula ted  t h e  present  i n -  
v e s t i g a t i o n .  The e f f q c t  of c ros s  flow on a boundary l aye r  s u b j e c t  t o  a large 
adverse  p re s su re  g rad ien t  is  of utmost importance i n  t h e  de te rmina t ion  of the 
o v e r a l l  performance of t h e  system and a l s o  i n  order  t o  e s t a b l i s h  the upTer 
l i m i t  on the  maximum pressure  r i s e  without  s e p a r a t i n g  t h e  flow wi th in  the i n -  
l e t .  Some i n v e s t i g a t o r s  (Refs. 1-4) have presented d e t a i l e d  pressure  rneasure- 
ments on three-dimensional  boundary l a y e r s  i n  absence of adverse  pressure  
g r a d i e n t s ,  and o t h e r s  (Refs . 2 -3-5) have confined themselves t o  measurements 
of boundary l aye r s  on axisymmetric bodies  a t  ze ro  angle  of a t t a c k ,  The present  
d a t a ,  i n s t eqd ,  have been obtained f o r  t h e  case  of both adverse  pressure  g rad ien t  
and favorable  c ross  flow. Measurements without  c ros s  flow have been teken for 
comparison. I n  s p i t e  of t he  f a c t  t h a t  a n  adverse  c ros s  flow, a s  the one that 
r e s u l t s  from t h e  w a l l s  of t h e  i n l e t ,  a c t u a l l y  determines the  upper criteria 
f o r  s e p a r a t i o n ,  t h e  measurements r e f e r  t o  t h e  favorable  c ros s  flow condi t ion  
a t  t h e  meridian plane of a n  axisymmetric body. 
The comparison of t he  p re s su re  p r o f i l e s  wi th  and without  c ros s  flow i n  
t he  long i tud ina l  d i r q c t i o n  s h ~ w s  t h a t  t h e  c ros s  flow r e l i e v e s  the pressure 
d i s t r i b u t i o n  a long  t h e  body s u r f a c e  and, t he re fo re ,  de lays  s e p a r a t i o n ,  The 
pressure  v a r i a t i o n  i n  t h e  p e r i p h e r a l  d i r e c t i o n  inc reases  cons iderably  along 
t h e  compression s u r f a c e  due t o  t he  adverse  pressure  g rad ien t .  
To ta l  temperature and h e a t  t r a n s f e r  p r o f i l e s  have been compared w i t h  
t h e o r i e s  and previous experimental  r e s u l t s  a t  zero  angle  of a t t a c k .  
EXPERIMENTAL ABP4RATUS 
A l l  t e s t s  were conducted i n  t h e  New York Univers i ty  b lowdown- t y p e  tunne L 
equipped wi th  a Mach 6 a x i a l l y  symmetric contoured nozzle .  The t e s t  s e c t i o n  i s  
1 f t .  i n  diameter and c o n s i s t s  of  a uniform flow 9 inches i n  diameter and 3 fe, 
o i n  length .  The tunnel  s t a g n a t i o n  temperature was approximately 800 R f o r  a l l  
t h e  t e s t s ,  and t h e  s t a g n a t i o n  pressure  v a r i e d  between 1800 ps i a  and 2800 p s i a ,  
The model cons i s t ed  of a s t reaml ined  c y l i n d r i c a l  forebody generated from one of  
t h e  nozzle  s t r eaml ines  s t a r t i n g  i n  t h e  s e t t l i n g  cha=mber of t he  nozz le .  A 
r i g h t  c i r c u l a r  cy l inde r  14.91 inches long and 4.62 inches i n  diameter was 
connected a t  t h e  te rmina l  p a r t  of t h e  forebody. To t h i s  cy l inde r  a compression 
f l a r e  6.3 inches i n  length ,  descr ibed  by a f o u r t b  order  polynomial, was connected. 
0 Its maximum tu rn ing  ang le  was 44 (Figs.  1 - 3 ) .  The o v e r a l l  a x i a l  length of the 
model, from t h e  nozz le  t h r o a t  t o  t h e  t e s t  s e c t i o n ,  was 77 inches long, The model 
was made of 304 s t a i n l e s s  s t e e l  and po l i sh  t o  h igh  f i n i s h .  It was placed a t  z e ro  
ang le  of a t t a c k  and p a r t  of t h e  tes ts  were performed i n  t h e  presence o f  an adverse 
pressure  g rad ien t  only. Sqbsequently,  two l a t e r a l  curved p l a t e s  were symme";cicaiEy 
placed on the  s i d e s  of t he  model s o  t o  c r e a t e  a n  expansion i n  t he  peripheral 
d i r e c t i o n  and e s t a b l i s h  a favorable  c ros s  flow on t h e  windward s i d e  o f  t h e  f l a r e ,  
i n  a d d i t i o n  t o  t he  adverse  p re s su re  g rad ien t .  The c ~ m p r e s s i o n  f l a r e  was equipped 
with  78 p re s su re  t a p s ,  0.02 inches i n  diameter d r i l l e d  normal t o  the su r f ace  and 
d i s t r i b u t e d  on t h e  upper su r f ace ,  i n  order  t o  ob ta in  t h e  long i tud ina l  as w e l l  as 
t he  p e r i p h e r a l  p re s su re  d i s t r i b u t i o n .  The f l a r e  was a l s o  equipped with chrornel- 
alumel thermocouples t o  measure w a l l  temperatures and t r a n s i e n t  heae transfer 
r a t e s .  In  order  t o  o 5 t a i n  measurements of s t a t i c  and p i t o t  tube pressures, 
s i n g l e  probes were used a t  d i f f e r e a t  s t a t i o n s  of the  compression f l a r e  a l o n g  
t h e  plane of symmetry. An unshielded,  open- t ip  c h r o m e l ~ a  lumel themocouple  
was used t o  measure t h e  s t a g n a t i o n  temperature throughout t he  boundary layer ,  
EXPERIMENTAL RESULTS 
The flow f i e l d  of t h e  upper f l a r e  compression reg ion ,  a s  seen i n  SchLieren 
photographs i s  shown i n  Fig.  4. Fig. 5 shows t h e  s u r f a c e  pressure  d i s t r i b u t i o n  
on t h e  f l a r e  w i th  and without  c ros s  flow and t h e  d i s t r i b u t i o n  obtained b y  
Hoydysh and Zakkay (Ref. 2 ) . 
The s t a t i c  p re s su re  p r o f i l e s ,  obtained a t  var ious  s t a t i o n s  of t h e  campression 
f l a r e  a r e  p l o t t e d  i n  F igs .  6 t o  13, and the  p i t o t  p re s su re  p r o f i l e s  i n  Figs, 14 
t o  21. These p r o f i l e s  r e f e r  t o  both cases  w i t h  and without  c ros s  f low.  I t  i s  
seen  t h a t  t h e  c ros s  flow r e l i e v e s  t he  pressure  d i s t r i b u t i o n  along the  canpression 
f l a r e ,  a c t i n g  as s u c t i o n  and t h e r e f o r e  reduces t h e  growth of t h e  boundary l aye r  
parameters,  de lay ing  s e p a r a t i o n  on t h e  windward s i d e  of t h e  f l a r e .  
The experimental  t o t a l  temperature p r o f i l e s  a r e  p l o t t e d  i n  F igs ,  22 t o  2 9  
and compared t o  t h e  p r o f i l e s  obtained by us ing  the  Crocco r e l a t i o n ,  Zt i s  seeE 
t h a t  t h e  Crocco r e l a t i o n  g ives  a  f a i r l y  good approximation of t he  total temperacure 
v a r i a t i o n  throughout t h e  boundary l s y e r .  
F igs .  30 and 3 1  show t h e  pressure  d i s t r i b u t i o n  a long  the  pe r iphe ra l  
L 
d i r e c t i o n ,  a t  d i f f e r e n t  s t a t i o n s ,  and the  v a r i a t i o n  of t he  parameter 1 .&-E 
pe 2:lp2 
a t  t he  meridian p lane ,  i n  t h e  long i tud ina l  d i r e c t i o n .  The s u b s t a n t i a l  variation 
of t h e  p e r i p h e r a l  p ressure  d i s t r i b u t i o n  along t h e  long i tud ina l  direct ion is  due 
t o  t h e  presence of a  l a r g e  adverse  p re s su re  g rad ien t  on the  compression flare, 
Since  t h e  magnitude of t h e  c ros s  flow i s  d i r e c t l y  p ropor t iona l  t o  t h e  parameter 
n L 1 3 pe 
, i t  inc reases  continuous l y  w i t h  t h e  cornpres s i o n  s u r f a c e  length,  
pe 3J2 
Fig.  32 cQmpares t h e  experimental  va lue  of t he  h e a t  t r a n s f e r  f o r  t he  case 
without  c ros s  flow t o  the  f l a t  p l a t e  r e f e rence  en tha lpy  method and t o  Zakkay 
and Calarese  theory  (Ref. 6 ) .  The agreement i s  considered good downstream of 
t h e  compression f l a r e .  
CONCLUSION 
lzxperimental measurements of p re s su re ,  temperature and h e a t  transfer have 
been taken over t h e  meridian plane of a f l a r e d  s u r f a c e  placed i n  a Mach 6 
hypersonic s t ream i n  presence of a n  adverse  pressure  g rad ien t  and favorable cross 
flow. I t  has been concluded t h a t  t h e  p r o f i l e s  a r e  reduced by the  cross f l o w  
e f f e c t  and t h a t  boundary l aye r  s e p a r a t i o n  over t h e  windward s i d e  of the com- 
pres s ion  s u r f a c e  is  t h e r e f o r e  delayed. The magnitude of t he  c ros s  flow increases 
with  inc reas ing  s u r f a c e  length ,  due t o  t h e  presence of the  adgerse pressure 
grad ien t .  
The c ross  flow e f f e c t  should,  t he re fo re ,  be  taken i n t o  cons ide ra t ion  when 
boundary l aye r  parameters,  a s  displacement and momentum th ickness ,  are t o  be  
p red ic t ed .  
The p re sen t  d a t a  w i l l  be  used i n  the  second p a r t  of t h i s  work t o  obtain 
a c c n r a t e  experimental  va lues  of a l l  t h e  boundary l a y e r  parameters a t  the meridian 
plane  of t h e  model. 
REFERENCES 
1 )  Braun, W.H., 1959, "Turbulent Boundary Layer on a Yawed Cone i n  a 
Supersonic Stream," NACA TN 4201'3. 
2 )  Hoydysh, W.G. and Zakkay, V. ,  "An Experimental I n v e s t i g a t i o n  o f  Hypersonic 
Turbulent Boundary Layers i n  Adverse Pressure  Gradient ,"  A W  J. 4 ,  Jan ,  1969, 
p. 105. 
3)  McLafferty,  G.H. and Barber, R , E , ,  1962 "The E f f e c t  of  Adverse Pressure 
Gradients  on t h e  C h a r a c t e r i s t i c s  of Turbulent Boundary Layers i n  Supersonic 
Streams," J .  Aerospace S c i . ,  2 ,  1-11. 
4 )  Rainbird,  W.J., 1968, "Turbulent Boundary Layer Growth and Separa t ion  on 
a Yawed Cone," AIAA J. ,  3 ,  2410. 
5 )  S t roud ,  J.F. and M i l l e r ,  L.D., 1967, "An Experimental and Ana ly t i ca l  
I n v e s t i g a t i o n  of Hypersonic I n l e t  Boundary Layers," Technical  Report, 
AFFDL TR-65-123. 
6 )  Zakkay, V. and Calarese ,  W . ,  "Cross Flow E f f e c t s  on Compressible Turbulent 
Boundary Layer Over Bodies of  Revolution," I s r a e l  Jou rna l  of TeeknnoLogy , 
Vol. 8,  No. 1-2, 1970, p. 127. 
LIST OF FIGURES 
7 
FIGURE 
View of F lared  Surface  wi th  L a t e r a l  F l a t e s  
S ide  View of Flared Surface without  L a t e r a l  P l@tes  
Kela t ion  Between Local Sur face  Angle and Surface  Length 
Flow F i e l d  Conpress ion  Region a s  Seen i n  Sch l i e r en  Photographs 
Wall Pressure  D i s t r i b u t i q n  on Flared  Surface  
S t a t i c  Pressure  P r o f i l e  a t  q = 0' 
S t a t i c  Pressure  P ~ o f i l e  a t  = 10' 
S t a t i c  Pressure  P r o f i l e  a t  q = 15' 
S t a t i c  Pressure  P r o f i l e  a t  q = 20' 
0 S t a t i c  Pressure  P r o f i l e  a t  q r 25 
S t a t i c  Pressure  P r o f i l e  a t  q = 30' 
S t a t i c  Prassure  P r o f i l e  a t  q = 35* 
0 S t a t i c  Pressure  P r o f i l e  a t  q = 40 
P i t o t  Pressure  P r o f i l e  a t  q = 
P i t o t  Pressure  P r o f i l e  a t  q = 10' 
P i t o t  Pressure  P r o f i l e  a t  q = 15' 
P i t o t  Pressure  P r o f i l e  a t  q = 20' 
0 P i t o t  Pressure  P r o f i l e  a t  q = 25 
P i t o t  Pressure  P r o f i l e  a t  q = 30' 
P i t o t  Presspre  P r o f i l e  a t  q = 35' 
P i t o t  Pressure  P r o f i l e  a t  q = 40' 
FIGURE 
Stagnation Temperature Prof i l e  a t  = 0' 
Stagnation Temperature Prof i l e  a t  q = 10' 
Stagnation Temperature Prof i l e  a t  q = 15 Q 
0 Stagnation Temperature Prof i l e  a t  = 20 
3 Stagnation Temperature Prof i l e  a t  q = 25 
Stagnation Temperature Prof i l e  a t  q = 30' 
Stagnation Temperature Prof i l e  a t  = 35' 
0 Stagnation Temperature Prof i l e  a t  q = 40 
Peripheral  S t a t i c  Pressure Distr ibution 
Cross Flow Parameter Evaluated a t  the Meridian Plane 
Heat Transfer Rates without Cross Flow on Flared Surface 





Fig. 6 S t a t i c  P r e s s u r e  P r o f i l e  a t  7 = 0' 
V 
(IN. 
F i g .  7 S t a t i c  Pressure P r o f i l e  a t  = 10' 
V 
(IN. 
F i g .  9 S t a t i c  P r e s s u r e  P r o f i l e  a t  q = 20' 
F i g .  10 Static P r e s s u r e  P r o f i l e  at q = 25' 

F i g .  12 S t a t i c  P r e s s u r e  P r o f i l e  at yl = 35' 
Fig.  13 S t a t i c  Pressure  P r o f i l e  a t  = 40' 
F i g .  14 Pitot Pressure P r o f i l e  at = 0' 
25* 
F i g .  15 P i t o t  P r e s s u r e  P r o f i l e  a t  7 = lo0  
Fig. 16 P i t o t  P r e s s u r e  P r o f i l e  a t  n = 15O 
F i g .  17 P i t o t  Pressure P r o f i l e  at q = 20' 
V 
(IN, 
0 
F i g .  18 P i t o t  P r e s s u r e  P r o f i l e  a t  q = 25 
F i g .  19  P i t o t  P ressure  P r o f i l e  a t  Q = 30' 
30,  
Fig. 20 P i t o t  Pressure P r o f i l e  a t  q = 35' 
F i g .  2 1  P i t o t  P r e s s u r e  P r o f i l e  a t  q = 40' 

Pig. 23 Stagna t i on  Temperature P r o f i l e  a t  q = 10' 







F i g .  31 Cross Flow Parameter Evaluated a t  the Meridian Plane 
IC2. 



An experimental investigation of the turbulent boundary layer undergoing both adverse pressure gradient and cross flow along a plane of symmetry

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