b.s. hay 1973, - nasa...cv h ii adjusted section drag coefficient adjusted normal-force coefficient...
TRANSCRIPT
,
/
William Grier Sewall
B.S. Hay 1973, Rensselaer Polytechnic Institute
A Thesis
The
submitted to i
Faculty
of
3
I
The School of Engineering and Applied Science
of the Preorge Washington University in
partial satisfaction of the requirements
for the degree of Master of Science
August 1982
1
I
https://ntrs.nasa.gov/search.jsp?R=19820024508 2020-07-28T02:40:19+00:00Z
APPLICATION OF A TRhl6ONIC SMILARIIT RULE TO
CORRECT TEE EFFECTS OF SIDewAu BOUNDARY LAYEIS XI
' I W O - D ~ I O W TRA13So#IC WIND Tueams
by
W i l l i a m G . Sewall
ABmm
A t ransonic s i m i l a r i t y r u l e which accounts f o r t h e e f f e c t s of
attached s i d e s a l l boundary l a y e r s is presented and evaluated by COQ-
p r i s o n with t h e characteristics of a i r f o i l s t e s t e d i n a twodlmenslonal
t ransonic tunnel with d i f €erect s idewal l boundary-layer thlckaesses.
The r u l e appears v a l i d provided t h e s idewal l boundary layer both remains
attached i n the v i c i n i t y of the model and occupies a small enough
f r a c t i o n of t he tunnel width t o preserve s u f f i c i e n t two-dlmeosionality
i n t h e tunnel.
AummumGmEurs The author w b k s to recognlze aad thmL the follmdmg IadlvSduals
f o r their umttibut&ons to this research e f f o r t : Dr. Rlcbard W. BaruweU
for the or*- suggestitm of the project and for his helpful
emc-t; ~oai L. ~fperbart for asshtlmce vitb the -layer
dam &ti=, 8 a e 8 t f o n of the lAIlllff of mff$c$dly tbi- t k
s idewal l boundary l ayer , and &dance in the operation of the Langley
6- by 19-Incb Trarmon*c 'hamel; Boyce Lavender and his group of
technicians f o r conscious e f f o r t s fm c a r e f u l l y coaducthg the vrlmen;
Jean Foster of Laac and Sue Davp of SDC for software management e f f o r t s ;
Chr i s t ine Barnet t f o r her typing servkes; Dr. Douglas Dwoyer for
serv ing as t h e thesis advisor; Bla i r G l o s s f o r bis valuable guidance
in using t h e p l o t t i n g rout ines ; and Betty Mil lard f o r her he lp In
f i g u r e preparat ion.
,
I
TABTA OF C O m
pess AB!mAcT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
A - i m S . . . . . . . . . . . . . . . . . . . . . . . . . T W O F - . . ....................... I V
L I S T O F F I G U U E S . . . . . . . . . . . . . . . . . . . . . . . . . . Vi LIST OF smLs . ......................... x
CHAPTIW
1. IrnrnCTIoN ......................... 1
2. EXPQCMENTALAPPARATUSAAlDTESTPROCEDURES . . . . . . . . . . 3
Faci l i ty a d T e s t Conditions . . . . . . . . . . . . . . . . 4
M o d e l s . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Arti f ic ia l Thickening of the S idewal l Boundary Layer . . . . 6
3. ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Primary Concepts . . . . . . . . . . . . . . . . . . . . . . 10
Approximate Mach Number Increment . . . . . . . . . . . . . . 15
4. EXPERIMEN'fALRESULTS . . . . . . . . . . . . . . . . . . . . . 17
Equivalent Freestream Mach Number . . . . . . . . . . . . . . 17
MACA 0012 and SC-27 Airfoil Tests . . . . . . . . . . . . . . 17
NLR-1 Airfoi l T e s t . . . . . . . . . . . . . . . . . . . . . 21
Summary of Airfoi l Tests . . . . . . . . . . . . . . . . . . 25
5. CONCLUDINC REMARKS . . . . . . . . . . . . . . . . . . . . . . 27
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
. I 4
d
i
Temperature Distribution in the Boundary Layer . . . . . . . . . 30
Displacement Thickness and Momentum Thickness Calculations . . 31
A P P W I X B - TBB BBLATIONSBIP OF THE VEMCITlt GRADIENT THE S W E FACTOR GRADIENT . . . . . . . . . . . . . . . . . . . . 35
F I G U R E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
!
V i
LIST OF FIGURES
Figure P.P. 1. Photograph of the Larrgley 6- by l9-Inch ¶'ransonic Tumel
showing a top view of t h e test s e c t i o n . . . . . . . . . . . . 37
2. Photograph of t y p i c a l models instrumented f o r pressure tests. 19.24-ca d e l i n foreground and 10.1- d e l i n backround . . . . . . . . . . . . . . . . . . . . . . . . 33
3. Photograph of the t h r e e a r t i f i c i a l boundary-layer thickening conf igura t ions showlag t h e p l a t e s with pins that are 3.80 cm and 2.94 c m long. and a p l a t e without p i n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4. Experimental apparatus used i n the Langley 6- by 19-Inch Transonic Tunnel to investigate t h e e f f e c t s of t h e s idewal l boundary-layer displacement th ickness on two-dimensional t e s t i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5 . Sketch of t h e rake-tube probes used to survey t h e s idewal l boundary l a y e r s i n t h e Langley 6- by 19-Inch Transonic Tunnel. A l l dimensions are i n cm. . . . . . . . . . . . . . . 41
(a) Top and f r o n t view . . . . . . . . . . . . . . . . . . . . 41 (b) Side view . . . . . . . . . . . . . . . . . . . . . . . . 42
6. Nondimensional v e l o c i t y d i s t r i b u t i o n i n a r t i f i c i a l l y thickened s idewall boundary layers . . . . . . . . . . . . . . 43
7. %dimensional v e l o c i t y d i s t r i b u t i o n f o r law of t h e wake c o r r e l a t i o n of a r t i f i c i a l l y thickened s idewall boundary layers.. . . . . . . . . . . . . . . . . . . . . . . . . . . 44
8. The v a r i a t i o n of t h e measured boundary-layer displacement thickness near t h e model s t a t i o n . . . . . . . . . . . . . . . 45
9. Sketch of a i r f o i l model and tunnel s idewal l s with t h e coordinate systeza used . . . . . . . . . . . . . . . . . . . . 46
I
10. Var ia t ion of equivalent f reestream Mach number wi th measured freestream Mach number for t h e t h r e e oideatell boundary-lave: displacement thicknesses . . . . . . . . . . . 47
Figure
vi1
p.ga 11.
12.
13.
14.
15.
Var ia t ion of shock wave loca t ion wi th freestream Mach nwnbex f o r t he NACA 0012 a i r f o i l t e s t e d wi th three s idewal l boundary-layer displacement thicknesses . -le of a t t a c k is 0 degrees . . . . . . . . . . . . . . . . . (a) Shock wave loca t ion vs. m e a s u r e d f rees t ream Mach number . (b) Shuck wave loca t ion vs. equivalent f rees t ream
Mach m b e r . . . . . . . . . . . . . . . . . . . . . . . Var ia t ion of sec t ion d rag c o e f f i c i e n t with f rees t ream Hech number f o r t he NACA 0012 a i r f o i l t e s t e d wi th th ree s i d e u a l l boundary-layer displacement thicknesses. Angle af a t t a c k is 0 degrees . . . . . . . . . . . . . . . . . . . . . . . . . (a) Sect ion drag c o e f f i c i e n t vs. measured freestream
Mach number . . . . . . . . . . . . . . . . . . . . . . . (b) Adjusted sec t ion drag c o e f f i c i e n t vs . equiva len t
freestream Mach number . . . . . . . . . . . . . . . . . . Varia t ion of normal-force c o e f f i c i e n t with freestream Mach number f o r the NACA 0012 a i r f o i l t e s t ed with th ree s idewal l boundary-layer displacement thicknesses . Angle of a t t a c k is 1.0 degree . . . . . . . . . . . . . . . . . . . . . . . . (a) Normal-force c o e f f i c i e n t vs. measured freestream
(b) Adjusted normal-force c o e f f i c i e n t vs. equivalent Mach number . . . . . . . . . . . . . . . . . . . . . . . freestream Mach number . . . . . . . . . . . . . . . . . .
Varia t ion of s ec t ion drag c o e f f i c i e n t with freestream Mach number fo r the NACA 0012 a i r f o i l t e s t ed with th ree s idewall boundary-layer displacement thicknesses . Angle of a t t a c k is 1.0 degree . . . . . . . . . . . . . . . . . . . . . . . . (a) Sect ion drag c o e f f i c i e n t vs. measured freestream
(b) Adjusted sec t ion drag c o e f f i c i e n t vs. equivalent Mach number . . . . . . . . . . . . . . . . . . . . . . . f reestream Mach number . . . . . . . . . . . . . . . . . .
Varia t ion of normal-force c o e f f i c i e n t with freestream Mach number f o r t h e SC-27 a i r f o i l t e s t ed with thrc s idewall boundary-layer displacement thicknesses . Angle of a t t a c k is 0 degrees . . . . . . . . . . . . . . . . . . . . . . . . . (a) Normal-force c o e f f i c i e n t vs. measured freestream
Mach number . . . . . . . . . . . . . . . . . . . . . . . (b) Adjusted normal-force c o e f f i c i e n t vs. equivalent
f reestream Mach number . . . . . . . . . . . . . . . . . .
48
48
49
50
50
51
52
52
53
54
54
55
56
56
57
Figure
16. Variation of normal-force coefficient with freestream Hach number for the SC-27 airfoil tested with three sidewall boundary-layer displacement thicknesses. is 1.0 degree . . . . . . . . . . . . . . . . . . . . . . . . Angle of attack
v i i i
Page
,
1 ! !
(a) Normal-force coefficient vs. measured freestream
(b) Adjusted normal-force coefficient vs. equivalent Mach number . . . . . . . . . . . . . . . . . . . . . . . freestream Mach number . . . . . . . . . . . . . . . . . .
17. Variation of normal-force coefficient with freestream Mach number for the NLR-I airfoil tested with three sidewall boundary-layer displacement thicknesses. is 0 degrees . . . . . . . . . . . . . . . . . . . . . . . . . Angle of attack
(a) Normal-force coefficient vs. measured freestream
(b) Adjusted normal-force coefficient vs. equivalent Mach number . . . . . . . . . . . . . . . . . . . . . . . freestream Mach nmber . . . . . . . . . . . . . . . . . .
18. Chordwise local Mach number distribution on the NLR-1 airfoil. Angle of attack is 0 degrees . . . . . . . . . . . . . . . . .
x (3) M, = 0.85 . . . . . . . . . . . . . . . . . . . . . . . . (b) E, = 0.86 . . . . . . . . . . . . . . . . . . . . . . . . -
19. Variation of normal-force coefficient with freestream Mach number €or the NLR-1 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of attack I s -1.0 degree . . . . . . . . . . . . . . . . . . . . . . . . (a) Normal-force cooff icient vs. measured freestream
(b) Adjusted normal-force coefficient vs. equivalent Nach number . . . . . . . . . . . . . . . . . . . . . . . freestream Mach number . . . . . . . . . . . . . . . . . .
20. Chordwise local Mach number distribution on the NLR-1 airfoil. Angle of attack is -1.0 degree . . . . . . . . . . .
21. Variation of normal-force Coefficient with freestream Mach number for NLR-1 airfoil tested with three sidevall boundary-layer displacement thicknesses. Angle of attack is 1.0 degree . . . . . . . . . . . . . . . . . . . . . . . . (a) Normal-force coefficient vs. measured freestream
(b) Adjusted normal-Eorce coefficient vs. equivalent Mach number . . . . . . . . . . . . . . . . . . . . . . .
58
58
59
60
60
61
62
62 63
64
64
65
66
67
67
freestream Mach number . . . . . . . . . . . . . . . . . . 68
11,
..
Figure
lx
Paee
. l
22.
23.
2 4 .
2 5 .
26.
Variation of normal-force coefficient with freestream Mach number for the mR-1 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of attack is 2.0 degrees . . . . . . . . . . . . . . . . . . . . . . . . (a) Normal-force coefficient vs. measured freestream
(b) Adjusted normal-force coefficient vs. equivalent Mach number . . . . . . . . . . . . . . . . . . . . . . . freestream Mach number . . . . . . . . . . . . . . . . . .
Variation of section drag coefficient with freestream Nach number for the NLR-1 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of attack is 0 degrees . . . . . . . . . . . . . . . . . . . . . . . . . (a) Section drag coefficient vs. measured freestream
(b) Adjusted section drag coefficient vs. equivalent Mach number . . . . . . . . . . . . . . . . . . . . . . . freestream Mach number . . . . . . . . . . . . . . . . . .
Variation of section drag coefficient with freestream Mach number for the NLR-1 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of attack is -1.0 degree . . . . . . . . . . . . . . . . . . . . . . . . (a) Section drag coefficient vs. measured freestream
(b) Adjusted section drag coefficient vs. equivalent Mach number . . . . . . . . . . . . . . . . . . . . . . . frzestream Mach number . . . . . . . . . . . . . . . . . .
Variation of section drag coefficient with freestream Mach number for the NLR-1 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of at tack is 1.0 degree . . . . . . . . . . . . . . . . . . . . . . . . (a) Section drag coefficient vs. measured freestream
(b) Adjusted section drag coefficient vs. equivalent ? ? x h number . . . . . . . . . . . . . . . . . . . . . . . f reestream Mach number . . . . . . . . . . . . . . . . . .
Varitlticn of sect i on drag coefficient with freestream Mach number for the NLP-1 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of attack is 2.0 degrees . . . . . . . . . . . . . . . . . . . . . . . . (a) section drag Coefficient vs. measured freestream
(b) Adjusted section drag coefficient v s . equivalent Mach number . . . . . . . . . . . . . . . . . . . . . . . freestream Mach number . . . . . . . . . . . . . . . . .
69
69
70
71
71
72
73
73
7 4
75
75
76
77
77
78
c
X
LIST OF SYMBOLS
The u n i t s used f o r t h e physical q u a n t i t i e s i n t h i s paper are given
i n t he In t e rna t iona l System of Units. The measurements and c a l c u l a t i o n s
were made i n U.S. Customary Units .
b tunnel width, 15.72 c m
cP ?’local - P=
&. s ta t ic pressure c o e f f i c i e n t ,
C a i r f o i l chord, 15.72 CIC
sec t ion drag c o e f f i c i e n t , C Cd‘
poin t drag c o e f f i c i e n t ,
C Wake
‘d
‘d *
C n sec t ion normal-force c o e f f i c i e n t . c Lh upper ‘P c c Ax
lower ‘P c - surf ace sui f ac e
P
‘d
‘n P
P C
cV
H
ii
adjus ted sec t ion drag c o e f f i c i e n t
ad jus ted normal-force c o e f f i c i e n t
s p e c i f i c heat a t constant pressure
s p e c i f i c heat a t constant volume
boundary-layer shape f a c t o r ,
- (LJ’ - 1
(2) - 1
2/7
displacement thickness 3 momentum thickness
transformed shape fac:or, ;c - : ) d e
;‘I
c
.\
I
xi
L
M
M,
A 03
AM
N
P
p t , m
P"
r
T
e f f e c t i v e length of a f l a t p l a t e having the same b0unda.y layer as a wind-tunnel s idewall
l o c a l Mach number
measured freestream Mach number
equivalent freestream Mach number
d i f f e rence between the equivalent f reestream Mach wmber and =
the measured freestream Mach number, M, - M, exponent f o r power l a w used i n boundary-layer v e l o c i t y
d i s t r i b u t ion
f a c t o r used i n the series approximations for the boundary- layer displacem. \t thickness and momentum thickness ,
0.1793 M:
2 1 + 0.1793 Me
t o t a l pressure measured on t r ave r s ing survey probe and used i n the Cd ca l cu la t ion , kPa
freestream s tagnat ion pressure or t o t a l p re s su re , kPa
s t a t i c pressure measured on tunnel sideraall near t r ave r s ing ?
survey probe and used i n the C d ca l cu la t ion , kPa
freestream s t a t i c pressure, kPa
freestream dynamic pre3sure, Wa
universa l gas constant
recovery f a c t o r used i n t h e temperature d i s t r i b u t i o n equation
l o c a l s t a t i c temperature, OK
s tagnat ion temperature, OK
€or t he b a n d a r y layer, 0.8963
maximum thickness-to-chord r a t i o
longi tudina l component of ve loc i ty
f reestream ve loc i ty
xii
U longi tudina l component of pe r ,u rba t ion ve loc i ty ,
vertical component of per turba t ion v e l o c i t y
u - IJ - Uap
V
spanwise component of per tu rba t ion v e l o c i t y t r
l ong i tud ina l axis, p o s i t i v e i n t h e downstream d i r e c t i o n
ver t ical axis
X
Y
spanwise axis z
f a c t o r i n governing equat ions conta in ing s idewal l boundary- s
l aye r parameters, b
A i v a r i a b l e used i n t h e f i r s t -o rde r approximation of t h e s idewai l 26* 1
boundary-layer e f f e c t s , ~ ( 2 + - d) 6
6*
s idewal l boundary-layer thickness , c m
s idewall boundary-layer displacement thickness , c m l6 (1 - ") dz Peue
0 sidewall boundary-layer momentum thickness , c m
E(l - e-dz 'e",
P local s t a t i c dens i ty
w a l l shear stress TW
Suhscr i p t s:
e condi t ion a t the edge of the boundary lay t r
1 i d e n t i f i e s t h e f i r s t flow f i e l d used i n t h e s i m i l a r i t y r u l e
2 i d e n t i f i e s t he second flow f i e l d t h a t is similar t o the first flow f i e l d used i n the. s i m i l a r i t y r u l e
x i i i
Abbreviations :
A.O.A. angle of attack, degrees
RN Reynolds number based c;n the a i r f o i l chord, :-nless Gtherwise mentioned
TRANS. transition From laminar to turbulent boundary layers on a i r f o i l upper and lower surfaces
1
., L" .
1
CHAPTER 1
!
1
INTRODUCTION
Since t h e development of wind tunnels, extiasive a t t e t t i o n
has been devoted t o t h e i n t e r f e r e n c e on wind-tunnel models caused
by the tunnel w a l l boundaries. This i n t e r f e r e n c e is caused by
t h e a l t e r a t i o n of t h e s t reamlines near t h e w a l l from t h e i r free-
air posi t ions. Wind-tunnel i n t e r f e r e n c e i n both two- and three-
dimensional f a c i l i t i e s has been addressed with a n a l y s i s and
f a c i l i t y modifications to reduce or e l imina te it.
I n t h e past , t h e primary i n t e r e s t i n two-dimensional w a l l
in te r fe rence concerned t h e upper and lower w a l l e f f e c t s .
of t he l i n e a r a n a l y t i c a l methods t h a t have been developed to
account f o r these e f f e c t s a r e presented i n rcference 1. Some
nonlinear methods have a l s o been developed for t ransonic two-
dimensional tunnels and a r e described i n re ferences 2 and 3.
A t t e m p t s t o reduce these in te r fe rence e f f e c t s have r e s u l t e d i n
f a c i l i t y modifications by making t h e upper 3nd lower walls with
e i t h e r longi tudinal slots, porous surfaces , o r a d j u s t a b l e contours.
The in te r fe rence e f f e c t s caused by t h e s idewalls i n two-
dimcisional wind tunnels occur because of t h e presence of t h e
sidewall boundary l aye r s . The in te r fe rence of a t tached s idewal l
boundary layers i n two-dimensional tunnels r e s u l t s i n a modifica-
t i o n of t h e cont inui ty equation because che geometric tunnel width
Several
,
2
is e f f e c t i v e l y reduced by twice t h e s idewall boundary-layer dls-
placement thickness . The two s idewall i n t e r f e rence problems which
have received the most a t t e n t i o n o r e t h e growth of t h e s idewall
boundary layer due to t h e shear ing stress a t t h e s idewall and the
separa t ion of t h e s ldewal l boundary layer due to Interaction with
la rge model-induced pressure grad ien ts . The problem of boandaty-
layer growth due t o shear ing stress is accounted f o r i n some wind
tunnels by 3 s l i g h t outward inc l ina t ion of the walls, and t h e
problem of t he s idewall boundary-layer separa t ion can be con-
cont ro l led to some exten t with suc t ion or t angen t i a l blowing on
the s idewall .
This studv concerns the intermediate problem of the a t tached
s idewall boundary-layer i n t e r a c t i o n with the pressure f i e l d of
the model a t t ransonic speeds. Earlier methods of accounting f o r
t h i s e f f e c t havt. been proposed for incompressible flow, as
described i n re ferences 4 and 5 . These methods considered the
e f f e c t of the sidewi.11 boundary layer as a change i n t he c i r cu la -
tion about t he c i r fb i l .
For subsontc and t L ansonic compressible flow, t h i s effect
can be formulated i n t o s imi la r i ty r u l e s of t he s idewall boundary
layer t o the model-induced pressure f i e l d . The a n a l y s i s presented
i n t h i s study a p p l i e s elements of the de r iva t ion of t he s i s l l a r i t y
ru l e g i v e n i n re ference 6 t o the von Karman t ransonic similari ty
I 3
r i
. 1
!
rule. Expermental r e s u l t s from three a i r f o i l tests, each conducted
w i t h varying sidewall boundary-layer thicknesses, are also presented.
These r e s u l t s are used to evaluate the v a l i d i t y of the s lml lar l ty
rule a t transonic speeds.
i - i i
t
4
CHAPTER 2
I
,
ExPERImtrrAL APPARATUS
F a c i l i t y and Test Conditions
The e f f e c t s of t h z s idewall boundary l a y e r s i n subsonic and tran-
sonic two-dimensional tunnels were inves t iga ted i n t h e Langley 6- by
19-Inch Transonic Tunnel, presented i n f i g u r e 1. This f a c i l i t y .
described i n d e t a i l i n reference 7, is e s s e n t i a l l y a blowdown tunnel
that opera tes a t Mach numbers ranging from 0.3 to 1.0 with correspondip4
u n i t Reynolds numbers of 5.0 mil l ion to 7.5 mil l ion per foo t .
The tunnel a x i s is or ien ted v e r t i c a l l y with the flow d i r e c t i o n
upward, a s shown i n f i g u r e 1. The test s e c t i o n has s o l i d , parallel
s idewal l s and s l o t t e d w a l l s jo in ing t h e s idewal l s t h a t minlmiee t h e top
and bottom w a l l in te r fe rence mentioned i n reference 1.
This tunnel is configured for t e s t i n g a i r f o i l models, whicn span
t h e tunnel, as shown i n f i g u r e 1, and havc constant c r o s s s e c t i o n s con-
s f s t i n g of the a i r f o l l shapes. Each e d ol t h e model mounts i n t o a
t u rn t ab le t h a t f i t s f l u s h i n t o the sidewall of t h e test sec t ion . The
turn tab les r o t a t e together , allowing changes In t he model angle of
a t t a c k .
total-hmd tube probes and t r a v e r s e s t h e wake of t h e model t o o b t a i n
wake t o t a l pressure measurements used i n t h e drag c a l c u l a t i o n method
from reference 8 .
A movable rake mounted behind t h e model is equipped with four
S t a t i c pressure measurements both i n the test s e c t i o n and in t h e
cont rac t ion region 45.7 crn upstream of thc s t a r t of t h e test s e c t i o n
5 !
1
. .
- i !
I
r i ,
1
_ I
' ,
are provided by a centerline row of o r i f i c e s i n t h e s u r f a c e of one elde-
w a l l .
obtain t h e Hoch m b e r e t t h e model s t a t i o n when runniag tunnel empty
f o r tunnel c a l i b r a t i o n .
On t h e same sidewall , a t u r n t a b l e with 17 o r i f i c e s is used t o
Models
A photograph of two t y p i c a l m d e l s t e s t e d i n t h e f a c i l i t y is shown
i n f i g u r e 2.
of 15.72 cm, and are instrumented f o r pressure d i s t r i b u t i o n tests. The
15.72-cm chord model, which was t h e type used i n t h i s experiment, has
rectangular tangs machined on the ends of t he model to t r a n s f e r t he
model aerodynamic loads t o t h e model support s y s t e m . The tubes have
been placed in s ide t h e model and t h e coverp la te has been welded i n place
over t he tubes. The o r i f i c e s are located in chordwise rows near t h e
midspati of t he model and have A diameter of 0.35 nun.
accurac ies f o r these experiments were within 20.013 am.
Both models are constructed of s t a i n l e s s steel, have a span
The model contour
Three a i r f o i l shapes were used for t h e experiment. The f i r s t model
was a NACA 0012 a i r f o i l model, which Is a symmetrical a i r f o i l t h a t had
been t t -*-ed in many t ransonic f a c i l i t i e s . The second a i r f o i l t o be
t t ~ d w a s t he s u p e r c r i t i c a l SC-27 a i r f o i l t ha t represented t h e modern
c l a s s of t ransonic a i r f o i l s . This p a r t i c u l a r a i r f o i l has been exten-
s i v e l y t e s t e d i n two neighboring f a c i l i t i e s and Ravc t h e f irst indica-
t i o n of an in te r fe rence problem t h a t w a s thought t o be caused by the
s id -wa l l boundary layer . The l a s t model teslcd was t h a t of t h e NLR-1
a i r f o i l , another s u p e r c r i t i c a l a i r f o i l t h a t was designed for r o t o r c r a f t
appl ica t ions and was tt.s:c*d i n (1 neighboring f a c i l l t y .
I
?
E
1
6
I
I -i i
i
1 - 1 ?
. I
'I I
A l l of t h e airfoil models were tested with a spanwisa s t r i p of
c a r b r u n d m g r i t on both upper and lower s u r f a c e s to f o r c e the laminar-
to-turbulent boundary-layer t ransi t ion. For t h e NACA 0012 a i r f o i l , t h e
t r a n s i t i o n particles were located a t 0.075 x/c and were 0.089 mo i n
nominal height.
t ion p a r t i c l e s located a t 0.05 x/c with a nominal particle height o f
0.076 aim.
i n su re s u f f i c i e n t s i z e f o r complete t r a n s i t i o n without contributing
extra protuberance drag.
The SC-27 and NLR-1 a i r f o i l models both had t h e transi-
The particle sizes were der,ermined by re ference 9 so as to
A r t i f i c i a l Thickening of t he Sidewall Boundary Layer
The s idewall boundary e f f e c t s on tw-dimensional n i r f o i l t e s t i n g
were studied by examining r e s u l t s of s e v e r a l a i r f o i l tests conducted
with successively thickened s idewall boundary layers .
boundary layers were thickened with 3 device similar to t h a t invest i -
gated i n reference 10, which cons is ted of t h i n p l a t e s , each having
th ree rows of pins protruding from the surface, as shown In f i g u r e 3.
One p l a t e w 3 s mounted on each s idewall i n t h e tunnel c o n t r a c t i o n region
(f ig . 1). a t n s t a t i o n 114 cm upstream ol t h e m o d e l leading edge as
indicated i n f i g u r e 4. The thickness of t h e s idewall boundary l a y e r
was cont ro l led by the d is tance t h a t t he p ins protruded from t h e p l a t e
surface. Three p a i r s of p l a t e s were used:
t he second p a i r had p i n s extending out 2 .56 cm, and t h e t h i r d pair had
p ins extending out 3.80 cm.
was conveniently possible t o a l low t h e wakes from t h e Individual pino
The s idewal l
t he f i r s t pair had no pine,
The p l a t e s were mounted as f a r upstream as
i
to be s u f f i c i e n t l y mixed 80 that no pecu l i a r behavior would exist in the
s idewal l boundary l a y e r s c l o s e to t h e model s t a t i o n .
The s idewal l boundary l a y e r was surveyed a loag t h e test s e c t i o n
c e n t e r l i n e us ing total-head f ixed rake-tube probes.
sisted of two rows of 0.76 mm 0.d. tubes and are shown i n f i g u r e 5.
tubes were posit ioned t o survey out t o 5.10 e m from t h e s idewal l surface.
The tube closest to t h e s idewal l r e s t ed on t h e s idewal l and was used t o
determine t h e sk in - f r i c t ion c o e f f i c i e n t from t h e Pres ton tube ca l ib ra -
t i o n i n re ference 11.
t i o n on t h e s idewal l was determined from t h e s ta t ic pressure measured a t
the s idewal l l oca t ion nea res t t o t h e probe l o c a t i o n without t he probe
inserted. Th i s s t a t i c pressure was c a l i b r a t e d a g a i n s t t h e f rees t ream
Mach number sc t h a t with t h e probe mounted, t h e boundary-layer static
p res su re was determined from t he freestream Mach number.
These probes con-
The
The s ta t ic pressure a t t h e rake-tube probe p3i-
The ve loc i ty r a t i o , U/Ue, was ca lcu la t ed a t each tube p o s i t i o n on
the rake-tube probe €or t h e d i f f e r e n t s idewal l boundary-layer thick-
nesses. F i r s t , t he Cal ibra ted s t a t i c pressure was assumed cons tan t
through t h e boundary layer, and with t h e l o c a l t o t a l p ressure a t a
p a r t i c u l a r xube, t h e l o c a l Mach number was ca lcu la t ed . Next, a static
temperature d i s t r i b u t i o n through the boundary layer, given by t h e
equat ion
2
1 A
f
8 I
1
4
. I
; ! i
from references 1 2 and 13, was used t o c a l c u l a t e t h e l o c a l speed of
sound.
from both t h e local Mach number and speed of sound.
The local v e l o c i t y at each tube location was then determined
Af ter t h e local v e l o c i t i e s through t h e boundary l aye r were obtained,
the boundary-layer th ickness was determined from a least-squares regres-
s ion using t h e power l a w
- 5 " (f "e
With the values of 6 and N and the static tempera'ane given by
equation (1). i n t eg ra t ions were performed t o ge t t he displacement thick-
ness, 6* , and the momentum thickness , 8. Details of these procedures
are given i n Appendix A.
To examine the s i m i l a r i t y of the thickened s idewall boundary
layers, the ve loc i ty p r o f i l e s a t the model s t a t i o n were compared.
Figure 6 shows the resul ts of t h i s comparison where the v a r i a t i o n of t he
loca l ve loc i ty r a t i o , UIU,, with the nondimensional he ight , z/6*,
appear for a l l th ree boundary-layer thickening configurat ions. ThlJe
p r o f i l e s were considered t o match q u i t e w e l l .
Another c h a r a c t e r i s t i c inves t iga ted €or the thickened boundary
l aye r s concerned the r e l a t ionsh ips between the v e l o c i t i e s i n t h e
boundary layer and the wall shear stress.
l e n t boundary l a y e r s i n a zero pressure grad ien t has been e s t ab l i shed
with the law of the wake of re ference 14 . The c o r r e l a t i o n of t h e th ree
a r t i f i c i a l ly - th i ckened boundary l aye r s with the law of t he wake Is shown
One r e l a t i o n s h i p f o r turbu-
\
I
!
-. I , . ,,. . ....___ . ... .J
9
i n f i g u r e 7. The v r r e l a t i o n is reasonable except for t h e inner regions
of the boundary layers . This is as expected because t h e l a w of t h e wake
a p p l i e s t o the outer reg ions of t he boundary l aye r while t he more
commonly known l a w of t h e wall a p p l i e s t o t h e inner region.
tube boundary-layer probes used appear t o de f ine pr imar i ly t h e ou te r
region of t h e boundary layers .
The rake-
From t h e law of t h e wake c o r r e l a t i o n i n f i g u r e 7 and the s i m i l a r i t y
of t he v e l o c i t y d i s t r i b u t i o n s i n f i g u r e 6 , i t is concluded that t h e
th ree boundary-layer thickening conf igura t ions produced turbulen t
boundary layers similar t o those on a smooth f l a p l a t e .
The a r t i f i c i a l ly - th i ckened s idewall boundary layers were also sur-
veyed i n the v i c i n i t y of t h e model s t a t i o n , tunnel empty, t o f ind t h e
v a r i a t i o n of boundary-layer displacement thickness . Figure 8 shows t h i s
v a r i a t i o n t o be small f o r a l l t h ree boundary-layer thickening configura-
t ions .
to t h a t due t o the shear ing s t r e s s on a long, f l a t p l a t e .
T h i s slow growth rate of the s idewall boundary layer is similar
The v a l u e of the shape f a c t o r , H, ranged from 1.39 t o 1.59 f o r
the three boundary-layer thickening configurat ions. i
10
I
CHAPTER 3
ANALYSIS
Primary Concepts
Consider steady, i s en t rop ic , small-per turbat ion flow in a nominally
two-dimensional a i r f o i l wind tunnel. L e t t h e Cartesian coord ina tes In
the f reestream, normal, and spanwise d i r e c t i o n s be x, y , and z; and
the r e soec t ive v e l o c i t y components be U, v, and w, as shown i n fig-
u re 9 . The e f f e c t i v e tunnel width is b-26" where b and 6* can
vary s l i g h t l y with respec t t o x and y, and t h e bocndary condi t ions
for t he a i r f o i l model and t he upper and lower w a l l s are independent
of z. It is a l s o assumed that t h e tunnel is narrow enough f o r t h e flow
a t each s idewall t o be s t rongly influenced by t h e o the r s idewall bound-
a r y layer.
ve loc i ty v a r i e s l i n e a r l y with the spanwise coordinate z as
Reference 6 i nd ica t e s t h a t t o the lowest order , t h e spanwise
In wider tunnels the dis turbance caused by the s idewall boundary l aye r
decays nonl inear ly with d i s t ance from the s ldewall so that equat ion (3)
is not ba l id .
The flow i n the wind tunnel described above is governed by t h e
small per turhc t ion form of the con t inu i ty equation, which can be wr i t ten
as
I
i
!
t
i
11
where M, is t h e f reestream Mach number, u 0 U - U, is t h e v e l o c i t y
per turba t ion i n t h e x-direction, and y is t h e ratio of s p e c i f i c h e a t s
of t h e gas.
The dynamics of t h e s idewall boundary l a y e r are modeled wi th t h e
von Karman momentum integral, which is given i n reference 12 and can be
wr i t ten as
ad* 6" 2 au 6" aa T~ ax U ax H ax + 2 - - - -(2 + H - M )- + - -
L
where 3 is t h e dens i ty and 6". TW, and H a t% the sidewall dis-
placement thickness, m'li shear stress, and shape facto:, respect ively.
For t h e present problem, equation ( 5 ) can be s impl i f ied because t h e
s idewall boundary layers i n t h e tes t s e c t i o n s of most a i r f o i l wind
tunnels can be approximated as f l a t - p l a t e boundary layers with l a r g e
equivalent lengths , L, and hence, r e l a t i v e l y l a r g e Reynolds numbers.
The model pressure f i e l d is considered t o cause a r a t h e r l o c a l i z e d
v a r i a t i o n i n t h i s l a r g e length-scale s idewall boundary l aye r , and by
applying t h e following order of magnitude ana lys i s , t h e shear stress
term can be neglected from equation ( 5 ) .
F i r s t , t he shape f a c t o r g rad ien t , ax, '' can be r e l a t e d t o t h e
v e l o c i t y a rad ien t , - by t h e following expression derived I n
Appendix B; ax'
aH (H + 1 ) ( H - 1) - - ax U ax
. ' I
I L .- .
,' I
Therefore, for a flat plate boundary layer wlthout a pressure gradient,
both aulax and a t t / k vanish in equation U), lea- only the shear
stress term, T ~ / ~ U * , to affect the sidewall boundatplayer growth rate,
a6*/ax. 'ile order of magnitude of ax in the test section i8 P/L
which should be the same order as TJPU~.
For the sidewall boundary layer with a pressure gradient due to au the Podel, - is of t b order so that the first two terms ia
equation (5) are of the order 6*/c.
the sidewall boundary layer, L,
length, c, the hequality
ax C
Because the equivalent length of
is much larger than the model chord
t 2 appl ies , and the shear stress tern,
equation 0) as a first approximation.
form becomes
rw/pU , may be neglected from
With equation C6), the final
1 2 au - M ) ax - = - a6* -&* (2 + ax U
an au With equation C8), equation (3), and the observation that = ax the derivative
i
1 2 au w,26* ( 2 + - - M ) - ae o H ax
2 6*/c raagiog from 0.0lb
heasurementa of skin friction and 6" shoved values of r,/pU taagigg from 0.0010 to 0.0012 and valueo of to 0.052, which experhentally verified Inequality (7).
ORIGINAL PAGE IS *F Pr\lcIR QUALIW 13
I s obtained. tor small disturbance flow, M In equation (9) can be
replaced by the freestteam Mach number M,.
bined with equation (4) to give
Equation (9) can be com-
or
where
For this study, the values of 6* and H measured at the model
station, tunnel empty, are used as constant values in equation (10) so
that the von Karman transonic similarity rul:, discussed in reference 15,
car. be applied. This rule relates the pressure coefficients of two flow
fields, denoted by Cp,l and Cp,2, as i
where the flow fields satisfy the constraint
- 2 0,
.
F .r,
I
i
I
ORIGML PA= IS OF POOR QUAJJTy
14
For the same model and test gas (tl = t29 Y1 = Y2)& equation !14)
becomes
= An interference-free equivalent Mach number M, can be defined
with equation (15) and the condition 6" = 0 as
Mm u-
314 8 3 1 2 (1 - it)
This equivalent Mach number represents a flow in a:' ideal two-
dimensional tunnel without a sidewall boundary layer which is otherwise
the same as the actual two-dimensional tunnel with A sidewall boundary
layer. The pressure coefficient can be adjusted from the value in the
actual two-dimensional tunnel to the nlue in the ideal two-dimensional
tunnel having a similar flow without a sidewall boundary layer with
equation (13) with y1 - y2 (same test gas). The exptc.Jsion is
where E is the pressure coefficient in the ideal two-dimensional
tunnel.
coefficients formulated by integrating the surface pressures:
P Equation (17) results in the following adjusted airfoil force
F
adjusted sectiou normal-force coefficient,
= adjusted section drag coefficient, cd,
- Cd = J 1 - M, Cd
where cn and cd are the measured section normal-force and drag
coef f IC ient s.
Approximate Mach Number Increment
An approximate expression for the Increment M, - zm can be formulaced from a flrsL-order Taylor series expansion of both s i d e s of
equation (16). First, M, and 8 are rewritten as, - 31
0
M, 5 M, + AM
and
- $ = \I- (21)
where
A8 - = ~ ( 2 26* + 1 - t42)
and Is treated as a single variable. Equation (16) then appears as
I
16
I
uhare the only
about AN and
of both series
- variables are AM and h$. Both eidee are -8d.d
&E equal to rero. Retention of the firrt-order terms
results In
, + ... (1 - 1 -[(. - 314 + 3
3
The first-order approximation Is
- This equatlon can be solved for AM in terms of AB to give
G %xi m a - 2(2 + MZ)
or
For M- ranging between 0.7 end 0.9 and H ranging from 1.4 to 1.6,
this increment is approximately
28* A M : - - b
which represents the fraction of the tunnel width occupied by the two
sidewall boundary-layer displacement thicknessca.
.... _. ..
17
- I
: i
’!
EXPERIPIENTAL RESULTS
Equivalent Freestream Nach Nuar3er
The e f f e c t i v e n e s s of t h e s idewal l s i m i l a r i t y rule ha8 been evaluated
by cumparing measured a i r f o i l test dam obtained a t d i f f e r e n t sidewall
boundary-layer displacement thicknesses . F i r s t , t h e equivalent Mach
d e r , Sm, was determined for t h e t h r e e boundary-lzyer th icknesses
wlth equatioos (12) and (16). The value, of 6* and R used i n equa-
t i o n (12) were measured a t t n e model s t a t i o n , tunnel empty, as suggested
by t h e ana lys i s . Figure 10 shows t h e v a r i a t i o n of gm with M, f o r
t he t h r e e boundary-layer thicknesses and shows a n increment betveen t h e
equivalent Mach number and t h e measured freestream Mach number of
approximately 26*/b as indicated i n equat ion (28).
NASA 0012 and SC-27 A i r f o i l T e s t s
Next, t h e a i r f o i l tests were conducted beginning with the NACA 0012
a i r f o i l . This a i r f o i l has some i n t e r e s t i n g t ransonic behavior a t zero
angle of a t t a c k i n t h a t t h e chordwise shock wave l o c a t i o n v a r i e s almost
l inear ly with freestream Mach -imber up t o values of approximately 0.86.
The v a r i a t i o n s i n shock wave loca t ion wit.^ both and M, were com-
pared f o r t h e th ree sidewall boundary-layer thicknesses , as shown i n
f i g u r e 11. A s i g n i f i c a n t l y improved c o r r e l a t i o n was obtained when
r a t h e r than M, was used.
I
The d a t a fo r t h e f i r s t two s i d e w a l l boundary-layer th icknesses are
shown in f i g u r e 11 wlth centered symbols, while t h e da t a for t h e t h i r d ,
t 1
18
or th i ckes t , s idewal l boundary l a y e r are shown with open symbols.
observations that w i l l be mentioned later i n t h e paper indica ted that tk
t h i c k e s t s idewall boundary layer lsay have introduced excessive t h r e e
dimensional i ty that was not addressed by t h e present ana lys i s .
fo re , the centered symbols denote t h e d a t a f o r which t h e s i m i l a r i t y rule
can be appl ied with t h e moat confidence.
O thm
There-
The o the r two transonic characteristics investigated were t h e
v a r i a t i o n of normal-force and s e c t i o n drag c o e f f i c i e n t w i th f rees t ream
Mach number a t a f ixed angle of a t t ack .
r equ i r e s t he app l i ca t ion of equat ions (18) and (19) t o form the valuea
of t he ad jus ted normal-force and sec t ion drag c o e f f i c i e n t s , ca and Cd'
The v a r i a t i o n s of t he measured normal-force and s e c t i o n d rag c o e f f i -
c i e n t s , c and Cd, with the measured freestream Mach number, M,,
were compared to t h e v a r i a t i o n s of the ad jus ted normal-force and s e c t i o n
drag c o e f f i c i e n t s , cn and cd, with the equivalent freestream Mach
number,
Here, the s i m i l a r i t y tule
I - n
m I
I M,, f o r t he th ree s idewall boundary-1.-yer thicknesses .
Continuing with the NACA 0012 a i r f o i l a t zero angle of a t t a c k , t h i s
phase of the inves t iga t ion began with the comparison of t he v a r i a t i o n of
the measured drag c o e f f i c i e n t , Cd, with Mm t o t he v a r i a t i o n of t h e
adjusted drag c o e f f i c i e n t , cd, with M,. This adjustment actually
a p p l i e s only to the component of pressrire drag i n the drag c o e f f i c i e n t
and does not account f o r the s k i n - f r i c t i o n component. Figure 12 shows
the comparison between cd vs. M, and cd vs. M, f o r t he th ree side-
-11 boundary layers.
s u b s t a n t i a l l y improved drag c o r r e l a t i o n i n the drag- r i se region, but
I R
= - I n f i g u r e 12, the s i m i l a r i t y r u l e provides a
i i
. " \
I
19
loses q u a l i t y below t h e drag rise.
majori ty of t h e drag comes from the s k i n f r i c t i o n b e l o w drag rise
whereas t h e adjusted drag c o e f f i c i e n t addresses only the pressure drag.
The c o r r e l a t i o n improves as the pressure drag becomes a larger f r a c t + n
of t he t o t a l drag, as seen i n t h e drag rise region.
This is probably bemuse t h e
Figure 12 ind ica t e s more s c a t t e r i n t h e drag d a t a measured with the
th i ckes t s idewal l boundary layer . This boundary layer was approximately
5.2 an t h i c k a t t h e model s t a t i o n , tunnel empty, so that che two side-
w a l l boundary l a y e r s occupied approximately two-thirds of the tunnel
width.
three-dimensional secondary flows not addressed by t h e ana lys i s , and
could possibly have adverse e f f e c t s on both t h e drag measurerents with
the wake probe and t h e a i r f o i l suLface pressure measurements. There-
fore , t h e da t a f o r t he th i ckes t s idewall boundary l aye r are presented
with open symbols, while t h e da t a f o r t he two th inner s idewall boundary
layers, where the s i m i l a r i t y r u l e is more appl icable , are presented with
centered symbols. This depic t ion wa3 a l s o used i n f i g u r e 11 and w i l l
follow f o r a l l f i g u r e s present ing measured a i r f o i l d a t a with the th ree
s idewall boundary-layer thicknesses .
This l a r g e amount of s idewal l boundary layer is thought t o cause
The v a r i a t i o n of normal-force c o e f f i c i e n t with freestream Mach mrm-
ber was first s tudied using t h e NACA 0012 a i r f o i l a t one degree angle of
a t t ack . Again, t he s i m i l a r i t y r u l e w a s evaluated by comparing the
v a r i a t i o n of t he measured normal-force c o e f f i c i e n t , cn, with M, t o
the v a r i a t i o n of t he adjusted normal-force c o e f f i c i e n t ,
Figure 13 shows t h i s comparison. The s i m i l a r i t y r u l e provides a
= cn, with k.
20
s i g n i f i c a n t l y improved co r re l a t ion , p a r t i c u l a r l y f o r t h e two thinner
sidewall boundary layers.
t h i c k e s t s idewal l boundary layer , probably because of the previously
mentioned problems assoc ia ted with its l a r g e thickness . Some l o s s in
c o r r e l a t i o n a l s o Eppears f o r t h e two th inner s idewall boundary l a y e r s
near t h e maximum normal-force c o e f f i c i e n t . This is thought to be caused
by i n t e r a c t i o n s between t h e shock wave on t h e a i r f o i l upper su r face with
the s idewall boundary layer .
The c o r r e l a t i o n q u a l i t y diminishes for t h e
The v a r i a t f o n of sec t ron drag c o e f f i c i e n t with f rees t ream Mach num-
ber was a l s o s tudied f o r t he NACA 0012 a i r f o i l a t one degree angle of
attaclc. Figure 14 provides a comparison of cd vs. M, and cd vs . M,.
The r e s u l t s are genera l ly similar t o t h e zero angle-of-attack case f o r
t h i s Same a i r f o i l i n t h a t t h e c o r r e l a t i o n improves i n the drag rise
region.
3 =
The SC-27 s u p e r c r i t i c a l a i r f o i l was used t o examine the c o r r e l a t i o n
of t he ad jus ted normal-force c o e f f i c i e n t with the equivalent ?iach number.
This a i r foi l has a much weaker shock wave than that on the NACA 0012 air-
f o i l a t t h e same normal-force c o e f f i c i e n t .
v i a t e the poss ib le in t e rac t ion between the a i r f o i l shock wave and the
s idewall boundary layer t h a t was suspected f o r t he NACA a i r f o i l .
This would hopeful ly alle-
= = Figure 15 shows the comparison between cn vs . M, and cn vs . €4,
for the SC-27 a i r f o i l a t zero angle of a t t a c k . The c o r r e l a t i o n is very
good f o r the f i r s t two s idewall boundary layers, but degraded somewhat
f o r t he th i ckes t s idewall boundary layer. In comparison with the
NACA 0012 a i r f o i l shown i n f i g u r e 13, t h e c o r r e l a t i o n f o r the SC-27 air-
f o i l f o r t h e two t h innes t s idewall boundary l a y e r s is improved even wi th
the SC-27 a t higher va lues of ad jus ted normal-force c o e f f i c i e n t .
The c o r r e l a t i o n of Cf, with was examined f o r t h e SC-27 a i r f o i l
a t higher va lues of and, therefore , stronger a i r f o i l shock waves.
Figure 16 shows t h e comparison between cn vs. M, and cn VS. M, f o r
an angle of a t t a c k of one degree. While t h e cn vs . M, c o r r e l a t i o n is
still much b e t t e r than that for cn vs . MOD, t he c o r r e l a t i o n f o r the two
th innes t s idewall boundary layers w a s of lower q u a l i t y than that shown
i n the zero angle-of-at tack case i n f i g u r e 15. Therefore, t he shock
wave s t r eng th on the a i r f o i l appears t o l i m i t t he performance of t h e
s i m i l a r i t y r u l e s .
cn m m
= =
NLR-1 A i r f o i l T e s t R e s u l t s
The NLR-1 a i r f o i l test provided a study of t he c o r r e l a t i o n of the
adjusted normal-force and sec t ion drag c o e f f i c i e n t s with equivalent Mach
numbers f o r severa l angles of a t t a c k .
desc r ip t ion , the NLR-1 is a s u v e r c r i t i c a l a i r f o i l f o r r o t o r c r a f t
appl i ca t ions.
A s mentioned i n the models'
I = Figure 17 shows the comparison of c vs. M, and c, vs. M, for n
an angle of a t t a c k of zero.
boundary layers is iaprcved using c, vs . M, r a the r than cn vs. M,,
but with d i f f e r e n t r e s u l t s than those observed f o r the NACA 0012 and
SC-27 a i r f o i l data . The l a r g e s t values of c n f o r the second s idewal l
boundary layer exceed those of the f i r s t or t h innes t s idewall boundary
layer .
The c o r r e l a t i o n for t h e th ree s idewal l 5 =
R
i
22
The reason the second sidewall boundary layer produced a larger
maximum value of Gn mined from an examination of the local Mach number distributions.
Figure 18(a) shows the lacal Mach number distributions on the kzR-1
airfoil with the two thinnest sidewall boundary layers.
normal force coefficients are near their maximum respective values shown
in figure 17, and these values occur at essentially the same equivalent
freestream Mach number. Except for the lower-surface region near
30 percent chord, the local Mach numbers for the thinner sidewall
boundary layer are slightly less than those for the thicker sidewall
boundary layer at the same location. This condition is required for
matched values of the adjusted pressure coefficient which relate
directly to the value of c . The value of c for the thinner side- n n
wall boundary layer is slightly lower than that jf the thicker sidewall
boundary layer because the lower-surface local Mach numbers at 30-
percent chord for both sidewall boundary layers are practically the sane.
This causes the adjusted pressure coefficients for the thinner sidewall
boundary layer to have a larger negative magnitude than that of the
thicker sidewall boundary layer in this lower-surface region, and
results in a lower value of c . n
than the first sidewall boundary layer 9108 dater-
The adjcsted
m P
R
Figure 18(b) compares the local Mach number distributions for the
same two sidewall boundary layers with a small increase in equivalent
freestream Mach number. With the thinner sidewall boundary layer, the
local Mach numbers on the lover surface between 20- and SO-percent chord
have substantially increased from those seen in figure 18(a) with only a
k- -
P
23
very small change in the equivalent freestream Mach number (0.850 to
0.864).
layer are significantly higher than those for the thicker sidewall.
boundary layer.
adjusted pressure coefficlants in this lawersurface region produce a
much lower value of cn for the thinner sidewall boundary layer. The
local Mach numbers for the thicker sidewall boundary layer in this same
lower-surface region also have a noticeable increase in values compared
to those in figure 18(a).
the thicker sidewall boundary layer has only changed from 0.852
(figure 18(a)) to 0.858 (figure 18(b)). This sensitive development of
supersonic flow on the lower surface caused an abrupt loss in normal
force wixh increased equivalent freestream Mach number.
These local Mach numbers for the thinner sidewall boundary
The corresponding higher negative magnitude of the
I
The equivalent freestream Mach number for
This study included two positive angles of attack shown in figures
21 and 22. The correlations of the normal-force coefficient with
freestream Mach number for these angles of attack appear very similar
to the results for the NACA 0012 airfoil at one degree angle of attack,
f.s indicated by figure 13. First, the c vs M, provides an
unquestionable improvement in correlation over the c vs M,. Second,
the correlation of ‘c vs M, loses quality for the data with the
thickest sidewall boundary layer as compared t o the two thinner eide-
wall boundary layers. Third, these two thinner sidewall boundary layers
show a slight loss in correlation at the maximum values of
is probably duo to the presence 01 strong shock waves on the airfoil
interacting with the sidewall boundary layer.
E I
n
n =
n
I
cn, which
These shock waves
p"
e
. .- _" . . .. . . - . ,^. - . . ..
21
contributed largely to the rapid drop in tn that follows the
maximum value.
Drag measurements were also obtained for the NLB-1 airfoil. These
drag data, which are presented in figures 23 through 26, in m a y
cases indicate very similar correlation behavix to that ahown for
the NACA 0012 airfoil in figures 12 and 13.
c vs M, show no real improvement over cd vs M, until the drag
rise region.
boundary layer often seem to show more scatter than that from the
two thinner sidewall boundary layers, again, probably because of the
large fraction of the tunnel width occupied by the thickest sidewall
boundary layer.
The correlation of I I
d
Drag measurements involving the thickest sidewall
25
Surmnary of A i r f o i l Tests Resul t s
For t h e a i r f o i l d a t a measured with the t h r e e L d e w a l l boundary
layers, t h e similarity r u l e produced an improved c o r r e l a t i o n f o r the
v a r i a t i o n of t h e sd jus ted normal-force and s e c t i o n drag Coef f i c i en t s
with t h e equivalent f reestream Mach number as compared t o the variation
of t he measured c o e f f i c i e n t s with the measured freestream Mach number.
The normal-force c o e f f i c i e n t s appear t o form th ree d i s t i n c t zones
f o r each s idewal l boundary l aye r when p lo t t ed aga ins t t he measured free-
stream Mach number. The ad jus ted normal-force c o e f f i c i e n t s appear t o
have more converged zones f o r t h e th ree s idewall boundary l a y e r s when
p lo t t ed aga ins t the equivalent freestream Mach number, but the magni-
tudes of t h e ad jus ted wrmal-force c o e f f i c i e n t s do not e n t i r e l y
Converge.
The sec t ion drag c o e f f i c i e n t s appear to have two d i s t i n c t d rag rise
regions f o r t he two th innes t s idewall boundary layers when p lo t t ed
agai.nst the measured freestream Mach number. The ad jus ted s e c t i o n drag
c o e f f i c i e n t s show converged drag rise regions when p lo t t ed a g a i n s t t he
equivalent freestre- Mach number but show no improvement i n the magni-
tude of t he drag c o e f f i c i e n t when below drag rise.
An important effect of t he s i m i l a r i t y r u l e is that the maximum
adjusted normal-force c o e f f i c i e n t and t h e divergence t h a t fol lows occur
a t almost the anme equivalent freestream Mach numbers f o r a l l t h ree
s idewall boundary layers. Likewise, the drag r ise occurs a t almost t h e
same equivalent Mach number f o r the two th innes t s idewall boundary
' !
! ,
26
layers. The fact that the maximum normal force end drag rise occur
at different measured freestream Mach numbers fcr each of the three
s idewal l boundary layers but a t the same equivalent freestream Mach
number demonstrates the correction to the measured freestream Mach
number provided by the similarity rule.
\
!
!
. I I I
i
I
27
CHAPTER 5
CONCLUDING REMARKS
The e f f e c t s of a t tached s idewal l boundary l a y e r s i n two-dimensional
t ransonic tunnels have beer. c o r r e l a t e d with a t ransonic s i m i l a r i t y ru l e .
It ha been shown experimentally t h a t t h e a p p l i c a t i o n of t h i s s i m i l a r i t y
r u l e t o t h e a i r f o i l test d a t a obtained i n t h e Langlcy 6- by 19-Inch
Transonic Tunnel g ives an e f f e c t i v e f rees t ream Mach number c o r r e c t i o n .
The experimental d a t a a l s o i n d i c a t e t h a t t h e s i m i l a r i t y r u l e provides a
s u b s t a n t i a l co r rec t ion t o t h e nonnal-force c o e f f i c i e n t s and some correc-
t i o n f o r t h e s e c t i o n drag c o e f f i c i e n t s i n t h e drag rise region.
The s imi la r i ty r u l e c o r r e c t i o n a p p l i e s provided t h e s idewal l
boundary layer is small enough tu a;toid excess ive three-dimensional
i n t e r a c t i o n s with the model.
the s idewal l boundary layers have no apprec iab le separa t ion (due t o
shock wave/boundary layer i n t e r a c t i o n o r s i g n i f i c a n t t ra i l ing-edge
separa t ion) .
The s i m i l a r i t y r u l e can be used as long as
R
$
REFERENCES
23
1. Pindeola, M.; and Lo, C. F.: Roundary In t e r f e rences at Subsonic AEDC TR-69, May Speeds i n Wind Tunnels with Vent i la ted Walls.
1969.
2. Kemp, W i l l i a m B., Jr.: Transonic Assessment of Two-Dimensional Wind- Tunnel Wall In t e r f e rence Using Measured Wall Pressures. CP-2045, pp. 473-496, March 1978.
NASA
3. Murman, E. M.: A Correction Method f o r Transonic Wind-Tunnel Wall In te r fe rence . AIAA paper No. 79-1533, J u l y 1979.
4. Preston, J. H.: The In t e r f e rence on a Wing Spanning a Closed Tunnel, Aris ing from t h e Boundary Laye r s on t h e Sidewalls, with Spec ia l Reference t o t h e Design of Two-Dimensional Tunnels. Teddington, Middlesex, England, R & M 1924, March 1944.
N.P.L.,
5 . Winter, K. G . ; and Smith, J . H. B.: A Comment on t h r Origin of End- Wall In t e r f e rence i n Wind-Tusnel Tests of A i r f o i l s . RAE Tech Memo AERO 1816, August 1979.
6. Barnwell, R. W.: Simi la r i ty RGle f o r Sidewall Boundary-Layer Ef fec t i n Two-Dimensional Wlnd Tunnels. A I A A Journa l , Vol. 18, No. 9, pp. 1149-1151, Sept. 1980.
7. Ladson, C . t.: Descr ip t ion and Ca l ib ra t ion of t h t L?ngley 6- by 19-Inch Transonic Tunnel. NASA TN D-7182, 1973.
8. Baals, Donald D.: and Mourhess, Mary J.: Numericai Evaluation of the Wake-Survey Equations f o r Subsonic Flow Including the E f i e c t s of Energy Addition. NACA WR-L5, 1945. (Formerly NACA ARR L5H27.)
9. Braslow, Albert L.; and Knox, Eugene C.: Simplified Method f o r Determination of Crit ical Height of D i s t r ibu ted Roughness P a r t i c l e s f o r Boundary-Layer Trans i t i on a t Mach Numbers from 0 t o 5. NACA TN-4363, 1958.
10. Johnson. D . 2 . ; and Mi tche l l , G. A.: Experimental Inves t iga t ion of Two Methods f o r Generating an A r t i f i c i a l l y Thickened Boundary Layer. NASA TM X-2238, 1971.
11. Allen, J . M.: Evaluation of Compressible-Flow Preston TJbe Ca l ib ra t ions . NASA TN D-7190, 1973.
12. White, F. M.: Viscous F l u i d Flow. McGraw H i l l Book Co., New York, p. 607, 1974.
29
13. Schlichtiag, E.: Boundary-Layer Theory. HcGraw B i l l Book Co., New York, pp. 667-668, 1968.
14. Coles, D.: The Law of the Wake i n Turbuleot Boundary Layers. Journal of Fluid Mechanics, V o l . :, 1956, pp. 191-226.
15. Liepasam, 8. W.; and Rosko, A.: E l a e n t s of Gas Dynamics. John Wlley and Sons, Inc., New York, 1957, pp. 256258.
16. Green, J. E.: In te rac t ions Between Shock Waves and Turbulent Boundaiy Layers. Progress i n Aeronautical Sciences, Vol. XI, Pergaton Press, New York, 1970.
APPENDIX A
BOUNDARY-LAYER DATA RQ)UCTION
Temperature Distribution in the Boundary Layer
The velocities within the boundary layer were calculated from the
values of local Mach number and speed of sound. The local tamperature
within the boundary layer was given by equation (11, where the wall
temperature was assumed to be the adiabatic temperature Indicated in
reference 13 as
For the tunnel-empty sidewall boundary layer it was assumed that
Tm = Te,
0.8963, which was also obtained from reference 13. The temperature of
the chamber surrounding the test section usually remained within 5OK of
the value for Taw in equation (Al). Due to the rapid operatien in
blowdown testing, the wall temptrature was not expected to change
significantly.
M, = Me, and the recovery factor, r, was given a value of
The temperature distribution through the boundary layer was obtained
from reference 12 as
i k
1
31
or
where T t h e boundary l aye r . Since Taw is assumed to be t h e actual wall
temperature,
be combined t o provide equation (1) i n t h e text,
is t h e the-averaged local temperature a t some point with in
2 2 T,, and Ue = Mey(cp - cv)Te, equat ions (Al) and (A2) can
- 'e T 0 1 + 0 1793 Me *( 1 -5) where 7 is assumed to be t h e local s ta t ic temperature, T.
Displacement Thickness and Momentum Thickness Calcu la t ions
The s idewall boundary-layer thickness w a s determined from t h e
least-squares power-law regress ion given by equation (2) i n t h e tex t .
This procedure was used because the l a r g e s t s idewal l boundary-layer
thickness i n t h e experiment exceeded t h e h ighes t t o t a l head tube on t h e
boundary-layer rake-tube probe.
t he v e l o c i t , p r o f i l e i n t h e booiidary layer allowed a simple, closed-form
i n t e g r a t i o n f o r c a l c u l a t i n g t h e displacement thickness and t h e momentum
t h i c kness .
Using t h e power-law representa t ion of
The boundary-layer displacement th ickness 6* is defined as
n
.. I
32
From the i d e a l gas relation,
P Te pressure grad ien t i n the boundary l aye r , t h e expression - = - Pe T obtained so that equation (A41 becomes
p = PRT, and the assumption of zero normal
is
Using t h e power-law rep resen ta t ion of t h e v e l o c i t y p r o f i l e given i n
equation (2) and equation (A6), equat ion (AS) becomes
1 /N .=I[- (z/c 1
1 + 0.1793 M f G - !z/6)
Note t h a t t he second term of the integrand is of the form
(2/6)1/N 1 1 + 0.1793 Me 0.1793 M:
1 + 0.1793 Mf -
which can be r ewr i t t en as t h e geometrrc series
(A7 1
(A8 1
(z/s)l/N + P(z/s)2'N + P2(t/6)4/N + P3(z/s)"N . . j 1 + 0.1793 Mf
(A91 where
0.1793 M:
1 + 0.1793 Mf P = - (A101
I
ORIGINAL PAGE IS O f PooRQuAuTy
33
1 t
> -
Placement of t h e series i n expression (A91 i n t o equation (A7) allows a
term by term i n t e g r a t i o n which r e s u l t s in t h e series
1 + 0.1793 Me
o r
6
1 + 0.1793 Mf 6 * = 6 +
Q) Npk-l
(2k - 1) + N k-1 -
This series converges r a p i d l y and y i e l d s the necessary prec is ion when
k = 5 .
The momentum th ickness is defined as
and is ca lcu la ted i n a manner similar t o tha t used f o r t h e displacement
thickness. With the power-law representa t ion of t he v e l o c i t y p r o f i l e
and the d e f i n i t i o n of 6*, equat ion ( A 1 3 ) becomes
The l a s t term i n t h i s equation can a l s o be represented by t h e geometric
series
(* /a) 'IN 1 + 0.1793 Mf
: t
- t
. -. I
C
ORIGINAL PAGE IS OF POOR QUALW
0.1793 Uz
1 t. 0.1793 M: where P = as i n equation (A10). Term by term
integration yields
NP 1 + 0.1793 Me
34
which results i n the final equation
QD
6 0 = 6 - 6 " - 1 + 0.1793 Me kIl
This summation also required 5 terms for convergence t o the necessary
precis ion.
i
.
I 35
APPENDIX B
THE RELATIOKSHIP OF THE VELOCITY GRADIENT TO
THE SHAPE FACTOR GRADIENT
The conventional shape fac to r . H, has a s i g n i f i c a n t dependence on
f reestream Mach number and, therefore , is o f t e n replaced by the trans-
formed shape f a c t o r , H. Refererice 16 d e f i n e s t h e transformed shape
f a c t o r as
-
For compressible, tu rbulen t boundary l a y e r s with cons tan t to ta l tempera-
ture assumed through the boundary layer , re fe rence 16 ind ica t e s that H
is r e l a t e d t o fi by
h = (fi + 1)(1 + M') - 1
Reference 16 a l s o shows t h a t f o r large Reynolds numbers, such as those
appl icable to tunnel s ide t ia l l boundary layers , fi approaches one. t
This s i m p l i f i e s equat ion (B2) t o
H - 1 + (y - 1)M2
'The measured va lues of 'i ranged from 1.18 t o 1.26, but use of t hese va lues i n t he above a n a l y s i s d i d not provide any s i g n i f i c a n t d i f f e rence from using a = 1.
c
36
Use of t h e simple compressible f low r e l a t i o n s wi th cons tan t total
temperature r e s u l t s i n the expression,
i i
(B4! ,
1 + ( V ) M 2 D i f f e r e n t i a t i o n of both s i d e s wi th respec t t o x g ives
il -I/
of equat ion (B4) y i e l d s Divis ion of both s i d e s by 2U' and use
(B6)
which relates the v e l o c i t y grad ien t t o the Mach number grad ien t .
The shape f ac to r grad ien t can be r e l a t ed t o t h e Mach number
grad ien t by
with equation (B3), and the Mach number grad ien t can be r e l a t ed by the
ve loc i ty grad ien t with equat ion ( B 6 ) , so t h a t i
With equat ion ( B 3 ) . the expression (y - 1)M2 - H - 1
f i n a l form of equat ion (6) i n t he text is obtained as
resultcl , and the
I . .7 ._. -2, <
ORlGlNAL PA= 3F PO03 Q U A L m
TOP VIEW
4
Figure 4 . - Experimental apparatus used i n t h e Langley 6- by 19-Inch Transcnic Tuanel to i n v e s t i g h t e t h e e f f e c t s of t h e s i d e w a l l boundary-layer displacement t h i c k n e s s on two-dimensional t e s t i n g . A l l dimensions are i n cm.
40
of Pins With Lengths to
1
i
I
41;
I
Tube on wall surface , I i I I
. --I J 1 Top and front view.
Figure 5 . - Sketch of the rake-tube probes used to survey the s idewal l bounaary layers i n the Langley 6- by 19-Inch Transonic Tunnel A l l dimensions a r e i n c m .
c
ORIGINAL PAGE rs OF
E
42
,
brace for tubes .25 x .025
P1 ug
Tubes go t o transducers
Total-pressure tubes .051 i.d. x .076 0.d. [Not shown t o scale.:
3 ,
(b) Sidev iev i
Figure 5 . - Concluded.
Q
Q ".
8 s U
1" * cro 24s N
43
c
c
ORIGINAL P a Is OF POOR Q u m 44
.I
L’
1
E:
I
45
b 0 0
V \ X
0
a a C
i
I
0 (3 0
c3 0
0 II *
0 0 0 8 s
u --. x
d I
? \ s
3 U
46
I 1
ORIGINAL PAGE IS OF POOR QUALITY
I I ’ I I
47
ORIGINAL PA& Is OF POOR QUALITY
48
' I
A.O.A.= 0.0 deg.; FIXED TRANS. at 0.075 x/c; RN=3.4-3.8 X 10'
26.b 8 -028
7 o r a -070
0 . I O 0 1
t PERCENT CHORD
t I .s .6 .7 .8 -9 1 .o
%
10- I I I I I I 1
(a] Shock wave location vs. measured freestream Mach number.
Figure 11.- Variation of shock wave location with freestream Mach number for the NACA 0012 airfoil tested with three sidewall boundary-layer displacement thicknesses. 0 degrees.
Angle of attack is
I
i
I
.I
49
!
2ol
A.O.A.= 0.0 deg.; FIXED TRANS. at 0.075 x/c; RN=3.4-3.8 X 10'
267b 0 -028 ffl -070 0 .loo 88
m @ m
W
a
a30
mm
W - am
qeo
101 I I I I I I I I I I .5 .6 -7 - .8 .9 1 .o
%o
(b) Shock wave loca t ion vs. equivalent freestream Mach number.
Figure 11.- Concluded.
E
c
1 ' I 1 ; i
.06
.os
.04
C d
.03
.oz
-01
C
ORIGINAL PAGE IS OF POOR QUALm 50
A.O.A.= 0.0 deg.; FIXED TRANS. at 0.075 x/c; RN=3.4-3.8 X 10'
26*/b 8 .028 B .070
0 .loo
!
eP 0
ern O "0 0m 000
-L I I 1 I I I I I 1 ~~ ~
.5 .6 .7 .8 .9 1 .o
(a) Section drag coefficient vs. measured freestream Mach number.
Figure 12.- Variation of section drag coefficient with freestream Mach number for the NACA 0012 airfoil tested with three sidewall bomdary- layer displacement thicknesses. Angle of attack is t degrees.
i
-r( .
5 1
.06
.05
.04
c' d
.03
.02
.t: i
-
-
- -
-
-
-
-
-
-
A.O.A.= 0.0 deg.: FIXED TRANS. at 0.075 x/c; RNs3.4-3.8 X lo6
26'/b 0 .028 RI .070 Q .IO0
CB0 0
00 00
oQ 63 0
t O l 1 I 1 I I I I I d
.5 .6 .7 .0 .9 1 .o %a3
(b) Adjusted sec t ion drag coefficient vs. equivalent freestream Hach number.
A
Figure 1 2 . - Concluded.
I
.18
.16
.14
.12
c"
.lo
.08
.06
.04
,
-
-
-
-
-
-
-
-
ORIGINAL PAGE IS OF POOR QUALITY
A.O.A.= 1.0 deg.; FIXED TRANS. at 0.075 x/c; RNS.4-3.8 X 10'
267b 8 .028
19 .070 0 .loo
0
" 0 0 O 0
0
0 0
8
0 .5 .6 .7 .0 .9 1 .o
Ma
(a) Normal-force coefficient vs. measured freestream Mach number.
Figure 13.- Variation of normal-force coefficient with freestream Mach number for the NACA 0012 airfoil tested with three siiewall boundary-layer displaczment thicknesses. Angle of attack is 1.0 degree.
ORIGINAL PAW OF POOR QUUm
53
A.O.A.= 1.0 deg.; FIXED TRANS. at 0.075 x/c; RN=3.4-3.8 X ?Os
26*/b 0 .028
0 -100
* 1 8 t .16 1
0 0
.08 t
.06
.04
.02
0 0
0 0
01 I 1 I 1 1 1 1 I 'I .5 .6 .7 .8 .9 1 .o
k (b) Adjusted normal-force coefficient v8. equivalent freestream
Figure 13.- Concluded.
Mach number.
ORIGINAL PAM 1s OF POOR QUALm 54
A.O.A.= 1.0 d8g.; FIXED TRANS. at 0.075 X/C: RN=3.4-3.8 X lo6
.os **T ‘d -03 *I;_ r
.01 0°*
2 6 . b .028 .070
0 .loo
.* @ Q
I
01 I I 1 1 I -2 .5 .6 .7 .8 .9 1 .o
la) Section drag coefficient vs. measured freestream Mach number.
Figure 14 .- Variation of secti.on drag coefficient with f reestream Mach number for the NACA 0012 airfoil tested with three sidewall boundary-layer displacement thicknesses. 1.0 degree.
Angle of attack is
ORIGINAL PAGE IS OF POOR QUALITY 55
A.O.A.= 1.0 deg.; FIXED TRANS. at 0.075 x/c; RN=3.4-3.8 X 10'
.04 -
c' - d
.03 -
-
2 6 . h 0 .028 B .070 C .lo0
t 01 1 I I I I I I 1 I I .5 .6 *7 - .8 .9 1 .o
&I
(b ) Adjusted s e c t i o n drag c o e f f i c i e n t vs. e q u i v a l e n t freestream Mach number.
i
!
! .F
I -
1
I
I
Figure 1 4 . - Concluded.
1
f
ORIGINAL PAGE IS OF POOR QUALm 56
A.0.A.z b.0 deg.; FIXED TRANS. at 0.050 X/C; RN=3.4-3.8 X 10'
267b 0 .028
* 4 0 r .070
.22 c (a)
Figure 15.-
Normal-force coefficient vs. measured freestream Mach numher.
Variation of normal-force coefficient with freestream Mach number for the SC-27 airfoil tested with three sidewaLl boundary-layer displacement thicknesses. Angle of attack is 0 degrees.
a
-20
I
1 I I 1 1 I I I I I
I
I
-40
38
-36
3 4
.'
-32 z n
-30
-28
-26
-24
-22
ORIGINAL PAGE IS OF POOR QUALrrV
59
A.O.A.= 0.0 deg.; FIXt'D TRANS. at 0.050 x/c; RN=3.4-3.8 X 10'
2 6 3 ) - 0 .028
B .070
- 0 -100
8 - $
B B
m
(b ) Adjusted normal-force .eff ic ient with equivalent freestream b- number.
Figure 15 .- Concluded.
ORIGINAL PAGE IS OF POOR QUAwn 50
I
A.O.A.= 1.0 deg.: FIXED TRANS. at 0.050 x/c; RN=3.4-3.8 X IO' i 1
.42
.40 c"
I
' \
26 .b @ .c2a F .070 0 .loo
t %I
(38 B
m ,m
0
-30 LLL .5 .6 -7 .a .9 1 .o
MO,
(a) Normal-force coefficient vs. measured freestram Mach number.
Figure le.- Variation of normal-force coefficient with freestream Mach number for the SC-27 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of attack is 1.0 degree.
. I
i
1 1
A.O.A.= 1.0 deg.; FIXED TRANS. at 0.050 x/c; RNz3.4-3.8 X 10'
2633 e .om
.070
0 .loo
.48 t
.44 -T
.42 1 - Q
-30 1 I 1 1 I I I I I I .5 -6 .7 .a .9 1 .o
50
59
$ i i I
(l-' Adjusted ncm*al-fc\rce coeffici?nt vs. equivalent freestream Mach number.
Figure 16. - Conc: ucied.
ORlGlNAL PAGE IS OF POOR Quam
-20
. la
.16
-14
-12
c"
-10
.08
60
-
-
-
-
-
- -
.02
.A.= 0.0 deg.; FIXED TRANS. at 0.050 %/e; Rk3.4-3.8 X lo6
267b (9 .028 B] .070
0 .too
0@
I
O I L 1 I I I 1 I I I 1 .5 .6 .7 .8 .9 1 .o
Ma0
(a) Normal-force coefficient vs. measured freestream Mach number.
Figure 17.- Variation of nermal-force coefficient with freestream Mach number for the NLR-1 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of attack is 0 degrees.
P
I. P4
ortiGiNAL PAGE IS OF POOR QUALITY
61
A.O.A.= 0.0 deg.; FIXED TRANS. at 0.050 x/c; RN=3.4-3.8 X 10'
2 6 3
m ,070 @ -028
0 ,100
.14
E" -10 -I2[
.02 * O 4 I
eD 0
O I L - - - .5 .6 .7 .8 .9 1 .o -
Grn
(b) Adjusted normal-force coefficient vs. equivalent freestream Mach number.
Figure 17.- Concluded.
I I '
LOCAL MACH NUMBER DISTRIBUTIONS ON N U - 1 AIRFOIL A.O.As 0.0 DEG., FIXED TRANS. ATi0.05 X/C
1.4
13
19
1.1
18
9
Ml-1 -' -6
b
.4
3
9
.I
62
I
t .cI
!
!
I
Figure 18.- Chordwise local Mach number di6tr ibut ions 011 the NLR-1 a i r f o i l . Angle of attack fa 0.0 degrees. Open symbols indicate the a i r fo i l upper surface; centered symbols indicate the airfoi l laver surface.
ORlGiRlAL PAGE IS OF POOR Q U A L m
LOCAL MACH NUMBER DISTRIBUTIONS ON NLR-1 AIRFOIL A.O.A.=O.O DEG., FIXED TRANS. A T 0.05 X/C
1.4
13
1.2
1.1
1 .o
.9
.8
Mlocal .' .6
.5
.I
9
2
.1
( 1
.1 9 9 .4 b .6 .7 1 .9 1.0
63 1
1
(b) POD : 0.86
Figure 18.- Concluded.
A
t
.10
.08
.06
.04
-02
c"
0 -
-.02
-.04
-.06
-.08
i
-
-
-
-
-
-
-
-
-
64
-.lo I I 1 I I 1 I I 1
267b @ .028 B .070 0 .loo
0
0
Q 0
(a) Normal-force coefficient vs. measured freestream Mach number.
Figure 19.- Variation of normal-force coefficient with freestream Mach number for the NLR-1 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of attack is -1.0 degree.
t
- -
65
A.O.A.=-1.0 deg.; FIXED TRANS. at 0.350 x/c; Rk3.4-3.8 X lo8 263 )
@ ,028
ffl ,070 .08 0 .loo
O B 0 m Be
-.02
O I s o
--O4I+ -.06
-.08
6 1 I I I I I I @ I I
.6 -7 - .8 .9 1 .o -.to
-5 4 x 2
(b) Adjusted normal-force coefficient vs. equivalent freestream Mach number.
i
Figure 19.- Concluded.
66
.
LOCAL MACH NUMBER DISTRIBUTIONS ON NLR-1 AIRFOIL A.O.A.=-1.0 DEG., FIXED TRANS. AT 0.05 X/C
1.4
13
1.2
1.l
1.0
.Q
a
Mlocal -' .6
5
.I
3
9
J
(
Figure 20.- Chordwise local Mach number dlstrlbut1or.s on the NLR-1 a i r f o i l . Angle of attack is -1.0 degree. Open wabols indicate the a i r f o i l upper surface; centered symbols Fnaicate the a i r fo i l lower surface.
I
I
ORIGINAI- PAGE IS OF POOR QUALm 61
.30
.20
-26
-24
.22
c"
.20
.18
-16
.14
.12
.10
A.O.A.= 1.0 deg.; FIXED TRANS. at 0.050 x/c; RNz3.4-3.8 X lo6
2 6 . b Q .028 EI .070 0 .loo
0%
Q 0@0 8"
0
@ 1 I I 1 I I 1 U
.5 .6 .7 .8 .9 1.0 Ma0
(a) Normal-force coefficient vs. measured freestream Mach number.
Figure 21.- Variation of normal-force coefficient with freestream Mach number for the NLR-1 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of attack is 1.0 degree.
I
ORlGlNAt PAQE IS OF POOR QUALm 68
A.O.A.= 1.0 deg.; FIXED TRANS. at 0.050 x/c; RN=3.4-3.8 X 10'
267b 0 .028
e30r m .070
.2a 0 .loo
t .24
.22
?" .20
.18
.? 6
.14
.12
.10
0
&- I I I I I 1 I .5 .6 .7 .a .9 1 .o
Gri
(b) Adjusted normal-force coefficient vs. equivalent freestream Mach number.
Figure 21.- Concluded.
I
i
69
.40
* 38
.36
.34
.32
c" .30
.28
.26
.24
.22
.20
I
A.O.A.= 2.0 deg.; FIXED TRANS. at 0.050 X/C; RN=3.4-3.8 X 10'
267b 0 .028 EI .070 0 .loo
0 0
El 0 I
w
.5 .6 .7 .a .9 1 .o Ma3
(a) Normal-force coefficient vs. measured freestream Mach number.
Figure 22.- Variation of normal-force coefficient with freestream Mach number for the NLR-1 airfoil tested with three sidea. 11 boundary-layer displacement thicknesses. Angle of attack is 2.0 degrees.
" .
I
.40
.38
.36
.34
.32
=n
ORIGINAL PAGE IS 3F POOR QUALlW
-
-
-
-
-
7.1)
A.O.A.= 2.0 deg.; FIXCD TRANS. at 0.059 xic: RNz3.4-3.8 X lo6
.20 I 1 I I I I I I I I
26'/b 0 .028 EI .070 0 .loo
.22 I
0 b o 0
9 0
El 0 0
(b) Adjasted normal-force c o e f f i c i e n t vs. e q u i v a l e n t rzaestream Mach number.
Figure 22. - Concluded.
Y '
71
A.O.A.= 0.0 dec.; FIXED TRtXS. at 0.050 x/c; 9N=3.4-3.8 X 10'
2b*/b
c 'd
-03
-02 t t
t OL I 1 1 I I I I I-, I
.5 .6 .7 -8 .9 1 .o Ma? 1
(a! S e c t i o n drag c o e f f i c i e n t vs. measured freestream Mach nunber..
Figare 23.- v a r i a t i o n o f s e c t i o n drag c o e f f i c i e n t w i t h freestream Mach number ; :*- tne NLR-1 a i r f o i l t e s t e d w i t h t h r e e sifiitrall boundary-1ay.r displacement t h i c k n e s s e s . Angle of a t t a c x is 0 degrees .
!
4
72
A.O.A.= 0.0 dag.; FIXED TRANS. at 0.0W x/c; Rt9=3.4-3.8 X 10'
26'/b
m -070 @ ,028
0 .1oc
.os
t
.02 1 t
o l 1 I 1 I I I I I 1 I .5 .6 .7 .8 .9 1 .o
K (bj Adjusted section drag coefficient vs. equivalent freestream
Mach number.
Figure 23. - Cancluded.
c i
73
.OS
-04
'd
-03
-02
.01
A.O.A.=-'-0 deg.; FIXED TRANS. at 0.050 x/c; Rbb3.4-3.8 X 10'
- - -
-
-
-
-
-
-
'r
2a'/b 9 -028 3 .070
0 -100
9
e e
m
01 1 I I I 1 1 I 1 I I -5 -6 .7 -8 .9 1 .=,
%
(a) Sectian drag coefficient vs. measured freestream Mach number.
Fisure ,* l?arietiori of secticn drag coefficient with freestrew Mach number for the N L R - 1 airfoil Lested with three sidedall boundary-layer displacement thicknesses. -1.0 degree.
Angle of attack is .
74
A.O.A.=-1.C deg.; FIXED TRANS. at 0.050 x/c: RN=3.4-3.8 X lo6
2b.h 3 .028 y-
.070
-05 c -04 c
E d
e 6
8 I -03
-02
c
e
I
(b) A d j u s t e d section drag coefficient vs. equivalent freestream Mach number.
!
d' r
d
9
Figure 24. - Concluded.
i
f i ~!
t
-06
-05
.04
C d
-03
-02
.01
0
75
A.O.A.= 1.0 deg.; FIXED TRANS. at 0.050 x/c; RN=3.4-3.8 X 10'
267b - e -028
&I -070
0 .loo
0
f
I I I I 1 ---- J .6 .7 .a .9 1 .o .5
*a3
(a)
Figure 25.-
Section drag coefficient vs. measued freestream Mach number.
Variation of section drag coefficient with freestream Mach number for the NLR-1 airfoil tested with three sidewall boundary-layer displacement thicknesses. Angle of attack is 1.0 degree.
76
-06
.OS
-04
- C d
-03
A.0.A.z 1.0 deg.: FIXED TRANS. at 0.050 x/c; RNz3.4-3.8 X lo6
-
-
-
-
- - -
26'/b
Q .028 B .070
c -100
Oi 1 1 1 I I I I I 1 .5 -6 .7 - .a .9 1 .o -
(b) Adjusted s e c t i o n drag c o e f . ' i c i e c t vs. e q u i v a l e n t freestream Mach number.
Figure 25. - Corzluded.
ORIGINAL PAGE IS OF POOR QUALITY
77
A.O.A.= 2.0 deg.; FIXED TRANS. at 0.050 x/c; RNS.4-3.8 X 10'
267b 8 .028
a o 6 r .070 0 .loo t
r -04 r -03
.02 1 t I I
.01 t- I i
o i l - - - .5 .6 .7 .a -9 1 .o
Ma0
. (a) Sectibn drag coefficient vs. measured freestream Mach number.
Figure 26. - Variation of section drag coefficient with freestream Mach number for the NLR-1 airfoil tested with three sidewall hundary-layer displacement thicknesses. Angle of attazk is
. O degrees.
i
r
.06
-05
-04
* C d
ORIGINAL PAGE IS OF POOR QUALllY
- -
-
-
-
-
78
i
A.O.A.= 2.0 deg.; FIXED TRANS. at 0.050 x/c; RNz3.4-3.8 X 10'
2 6 3 @ .028
B .070 0 -100
(b) Adjusted section drag coefficient vs. equivalent frsestream Kach number.
Figure 2 6 . - Concluded.