The Euler code is used extensively for computation of transonic unsteady aerodynamics. The boundary layer code solves the 3-D, compressible, unsteady, mean flow kinetic energy integral boundary layer equations in the direct mode. Inviscid-viscous coupling is handled using porosity boundary conditions. Some of the advantages and disadvantages of using the Euler and boundary layer equations for investigating unsteady viscous-inviscid interaction is examined

Pirzadeh, Shahyar

Whitfield, Dave

English

NASA Technical Reports Server

N89 = I925 0 
IJNS'L'EADY 'I'KANSONIC V I S C O U S - I N V I S C I D  IN'PISKACTION ' 
U S I N G  EULER ANI) BOUNDARY-LAYER EQUATIONS * 
SHAHYAR PIRZADEH 
AND 
DAVE WHITFIELD 
M I S S I S S I P P I  STATE U N I V E R S I T Y  
*This research was sponsored  by NASA Langley Research Cen te r .  It is 
a report  on work i n  progress. 
33 1 
https://ntrs.nasa.gov/search.jsp?R=19890009879 2020-03-20T04:14:46+00:00Z
OBJECTIVES 
T h i s  l ist is obv ious  for  a symposium on t r a n s o n i c  unsteady aerody- 
namics. The las t  three are the  most d i f f i c u l t  t o  ach ieve .  Turbu lence  
is i n  i t s  usual state of affairs. 
. VISCOUS-INVISCID INTERACTION 
. TRANSONIC 
. UNSTEADY 
. TURBULENT 
. THREE-DIMENSIONAL 
. EFFICIENT 
. ROBUST 
332 
APPROACH 
QRlGlNAL PAGE IS 
OF POOR QUALITY 
The E u l e r  code is one we've used e x t e n s i v e l y  f o r  some time now. 
The boundary-layer code s o l v e s  t h e  three-d imens iona l ,  compressible, un- 
s t eady ,  mean flow k i n e t i c  energy  i n t e g r a l  boundary-layer e q u a t i o n s  i n  
t h e  direct  mode. I n v i s c i d - v i s c o u s  coupl ing  is handled u s i n g  p o r o s i t y  
boundary c o n d i t i o n s .  
. EULER EQUATIONS 
. IMPLICIT 
. FINITE VOLUME 
. UNSTEADY 
. FLUX-VECTOR SPLIT 
. THREE-DIMENSIONAL 
. BOUNDARY-LAYER EQUATIONS 
. COMPRESSIBLE 
. THREE-DIMENSIONAL 
. UNSTEADY 
. MEAN FLOW KINETIC ENERGY 
. INTEGRAL 
. DIRECT 
333 
OUTLINE OF RESULTS 
T h i s  s l i d e  o u t l i n e s  t h e  order of t h e  r e s u l t s  t o  follow. S t e a d y - s t a t e  
r e s u l t s  are c o n s i d e r e d  first t o  v a l i d a t e  t h e  basic i n v i s c i d  and v i s c o u s  
codes, followed by t h e  u n s t e a d y  r e s u l t s  t h a t  have  been  o b t a i n e d  t o  date. 
. S T E A D Y - S T A T E  
3-D E U L E R ,  2-D BOUNDARY-LAYER ( W I N G - F U S E L A G E )  
3 -D E U L E R ,  3-D BOUNDARY-LAYER ( W I N G )  
UNSTEADY 
3-D E U L E R ,  3 -D BOUNDARY-LAYER ( W I N G )  
3-D E U L E R ,  3-D BOUNDARY-LAYER ( Q U A S I - S T E A D Y  A I R F O I L )  
3 -D  N A V I E R - S T O K E S  ( A I R F O I L )  
ORIGINAL PAGE IS 
OF POOR QUALITY 
I *..- .-. m d - e  iTens i onal  
code was used w i t h  the 
s t e a d y  vers ion  of  t h e  t u r b u l e n t  boundary-layer 
three-dimensional Euler  code i n  a s t r i p - t h e o r y  
f a s h i o n  t o  compute the  flow about t h e  s u p e r c r i t i c a l  Pa th f inde r  wing wi th  
fuse l age .  The r e s u l t s  are shown i n  Figure 1 .  These results are in-  
c luded  simply t o  i l l u s t r a t e  the  type  of r e s u l t s  t h a t  might be obtained 
us ing  t h e  boundary-layer i n  a s t r ip - theo ry  f a sh ion .  The results were 
obta ined  by D r .  Kei th  Koenig, Miss i ss ippi  State,  under a NASA Langley 
g ran t .  
8.88 
-8 
8.W 
.ma 
-8.48 
0 0  
0 
0 0 
I I 
0 I /  a 
8.28 0.*8 
x/c 
Figure la.  Sect ion pressure d i s t r i b u t i o n ,  %=0.7, a=2', Re=5.3*106; 
E = experiment, 13.1% span; , viscous ,  152 span. 
335 
0.88 
SP 
0.40 
.w 
4 . 4 e  
0 
0 
I I 
e a  
I \  I . 
88 0.40 0.69 0.m 
XX 
I 
0 
Figure l b .  E ,  29 .2%; calcul .at ion,  25;:. 
ORIGINAL PAGE IS 
OF POOR QUALITY 
336 
ORIGINAL PAGE IS 
OF POOR QUALITY 
.w I 
Figure IC. E ,  43.2%; calculation, 45%.  
337 
e.m 
-cP 
e. i e  
.m 
-8.18 
D 
I I. I 
0 
0 
0 
I \ 
Figure Id. E, 64X,  calculation, 65X. 
ORIGINAL PAGE IS 
OF POOR QUALITY 
338 
e.= 
-CP 
e. ie  
.BB 
-8.40 
0 
0 
0 0 - 0  
0 " 
I 
0.m 
X n :  
Figure le. E, 84I; calculation, 84%.  
339 
0 0  O 0 0 
X/C 
F i g u r e  I f .  E, 9 6 . 1 % ;  c a l c u l a t i o n ,  95Z. 
340 
A steady-state i n t e r a c t i v e  s o l u t i o n  us ing  the  three-dimensional 
unsteady Euler  and boundary-layer codes was obta ined  f o r  the ONERA M6 
wing. The streamwise momentum th i ckness  and shape f a c t o r  d i s t r i b u t i o n s  
a t  about f i f t y  percent  semi-span l o c a t i o n  are compared i n  Figure 2 w i t h  
t he  c a l c u l a t i o n s  of Schmit t ,  Destarac, and Chavmet. An i s o l a t e d  experi-  
mental  data p o i n t  a t  s i x t y  percent  chord l o c a t i o n  is a l s o  shown. 
0 ll< 
5.0 
2.5 
Y 103 
Ylb 
---- Calc. Ref. [31 0.525 
xx Calc. Present 0.500 
8 Exp. 0 .503 
I 
I 
I 
f 
ir 
/ 
0 0.5 1.0 
Fig. 2a. Boundary layer c h a r a c t e r i s t i c s  
on the upper surface of  the 
ONERA M 6  wing. M~0.84, 
Rec-11.7x1O6, ,a=3'. 
34 1 
- 
H L  
2.0 - 
1.0 - 
1.0 
x/c 0 0.5 
Fig. 2b. Boundary layer c h a r a c t e r i s t i c s  
on the lower surface of the ONERA 
M6 wing. M=0.84, Re C =11.7x10 , 
a=3O. 
6 
342 
Sur face  p r e s s u r e  d i s t r i b u t i o n s  f o r  t h e  same s o l u t i o n  as shown i n  
F igure  2 are compared i n  F igure  3 with  the  computations of Schmit t ,  et  
a l . ,  and experimental  data a t  about f o r t y - f i v e  percent  semi-span loca-  
t i o n .  The computations of Schmitt e t  a l .  used p o t e n t i a l  f low and a 
s t e a d y  s ta te  three-dimensional i n t e g r a l  boundary-layer code. 
v i s c o u s  0.45 
i n v i s c i d  0.45 
0 experiment  0.44 
------- 
-viscous Calc. 0.415 Y/b  
-----Inviscid Calc. 0 .  425 
0 0 Experiment 0.440 
1. 0 
(b )  Ref.  [ 3 ]  ( a )  P r e s e n t  c a l c u l a t i o n  
Fig.  3. Steady p r e s s u r e  d i s t r i b u t i o n  on t h e  ONERA M6 Wing. M=0.84, 0'3'
343 
A complete three-dimensional unsteady v iscous- invisc id  I n t e r a c t i o n  
s o l u t i o n  was obtained on a r e l a t i v e l y  coa r se  g r i d  f o r  t he  ONERA M6 wing 
as shown In  Figures 4 through 6. The wing was o s c i l l a t e d  i n  p i t c h  f 2 
degrees (mean ang le  of attack was O o )  about the  mid-chord a t  a reduced 
frequency of 0.3. For t h i s  case there was l i t t l e  v iscous  effect .  Flg- 
u re  4 shows unsteady v iscous  and i n v i s c i d  s u r f a c e  p re s su re  d i s t r i b u t i o n s  
a t  f o r t y - f i v e  percent  semi-span loca t ion .  It is a snapshot  a t  u = 
1 . 9 4 O .  
viscous 
----- inviscid 
Fig. 4. Unsteady pressure distributions on the ONERA 
M6 wing at M~0.84, k=0.3, a=1.94", and ylb10.45. 
Pitch oscillation about mid-chord -2" < a < 2". 
ORIGINAL PAGE IS 
OF POOR QUALITY 
344 
ORIGINAL PAGE IS 
OF POOR QUALITY 
F i g u r e  5 shows t h e  phase s h i f t  of t h e  viscous so lu t ion  d e s c r i b e d  on 
F i g u r e  4. 
1-88 
8.75 
e. 59 
e.2t 
.ee 
-e.zt 
-e. SB 
-e.= 
-1.88 
Fig. 5. Phase shift of the ONERA M6 wing lift coefficient 
(viscous solution). Pitch oscillation. 
M3Q.84, h 4 . 3 ,  -2" 5 a 5 2". 
345 
Figure 6 shows the viscous and inviscid resu l t s  of drag coefficient 
and number of supersonic ce l l s  for the Computation described on Figure 
4 .  
Period Period 
F i g .  6. Drag coefficient and number of supersonic cells. ONERA M6 w i n g  pitch oscillation. 
M=o.a4, h 4 . 3 ,  - 2 "  < a < 2 " .  
346 
F i g u r e  7 is a p l o t  of no rma l i zed  l i f t  and drag v e r s e s  p r iod for  a n  
NACA 0012 a i r f o i l  a t  M, = 0.776, Reynolds number o f  23.7 x 10 , o s c i l l a t -  
i n g  f 1 degree in p i t c h  abou t  t h e  qua r t e r - chord  p o i n t  a t  a reduced fre- 
quency of  0.3 u s i n g  quas i - s t eady  i n t e r a c t i o n  ( t h a t  is, uns teady  E u l e r  
c a l c u l a t i o n  w i t h  steady-state boundary-layer c a l c u l a t i o n ) .  
% 
1.59 
1.08 
0.m 
.a 
-e.= 
-1.08 
-1.58 
Fig. 7 Quasi-steady interaction for an NACA 0012 airfoil oscillating 
in pitch 2 1 degreg about the quarter-chord point for M = 0.776 
and Re = 23.7 x 10 at a reduced frequency of 0.3. 
347 
Figure 8 is a comparison of absolute values of lift verses period 
resulting from the quasi-steady interaction solution described in Figure 
7 and an unsteady Navier-Stokes solution for the same conditions. The 
Navier-Stokes solution is courtesy of Bruce Simpson, Eglin Air Force 
Base, FL. 
-1 -0 
-1.58 
#AcI 
Fig. 8 Lift coefficients for quasi-steady interaction and unsteady Navier- 
Stokes for an NACA 0012 airfoil oscillating in pitch f 1 degreg 
about the quarter-chord point for M = 0.776 and Re = 23.7 x 10 
at a reduced frequency at 0.3. 
348 
CONCLUSIONS 
This slide compares some of the advantages and disadvantages of 
using the Euler and boundary-layer equations for investigating unsteady 
viscous-inviscid interaction. 
ADVANTAGES 
. ENGINEERING ANSWERS 
. FASTER 
. LESS STORAGE 
. GRIDDING 
DISADVANTAGES 
. MUCH MORE DIFFICULT 
. SEPARATION (UNSTEADY) 
. DEVOTED LABOR (PARTICU- 
LAR EXPERTISE) 
. COUPLING 
. ROBUST 
. FEWER PEOPLE WORKING THE 
PROBLEM 
349 


Unsteady transonic viscous-inviscid interaction using Euler and boundary-layer equations

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