technical memorandum i - nasa · nasa technical memorandum i 01 493 rarefied flow past a flat plate...
TRANSCRIPT
NASA Technical Memorandum I 01 493
RAREFIED FLOW PAST A FLAT PLATE AT INCIDENCE
(bASA-TH-IOl493) B l A R E E l E D €LCY P A S P A P L A T B09- 13759 E L A T E AI X N C I C B l C k ( b A S A ) 3 1 CSCL 20D
Uaclas 63/34 o 1a3275
Virendra K. Dogra
James N. Moss
Joseph M. Price
September 1988
National Aeronautics and Space Administration
Langley Research Center Hampton, Virginia 23665-5225
https://ntrs.nasa.gov/search.jsp?R=19890004388 2019-12-31T12:22:44+00:00Z
RAREFIED FLOW PAST A FLAT PLATE AT INCI1)KNCIS
V. K. Dogra
Vigyan Research Associates, I n c . Hampton, V i r g i n i a 23666
James N. Moss and Joseph M. P r i c e
NASA Langley Research Center Hampton, V i r g i n i a 23665
Abstract
R e s u l t s of a numerical s t u d y u s i n g t h e d i r e c t s i m u l a t i o n Monte Carlo
(USMC) method are p r e s e n t e d f o r t h e t r a n s i t i o n a l f low about a Elat p l a t e a t
40 d e g r e e inc idence . The p l a t e h a s z e r o t h i c k n e s s and a l e n g t h of 1.0 m,
The €low c o n d i t i o n s s t m u l a t e d are t h o s e exper ienced by t h e S h u t t l e Orbiter
d u r i n g r e e n t r y a t 7.5 km/s. The range of f r e e s t r e a m c o n d i t i o n s are such t h a t
t h e freestream Kuudsen number va lues are between 0.02 and 8.4, t h a t i s ,
c o n d i t i o n s t h a t encompass most of t h e t r a n s i t i o n a l f low regime. The DSMC
s i m u l a t i o n s show t h a t t r a n s i t i o n a l e f f e c t s are e v i d e n t when compared w i t h
f ree molecule r e s u l t s f o r a l l c a s e s cons idered . The c a l c u l a t e d r e s u l t s
demonst ra te c l e a r l y t h e n e c e s s i t y of having a means o f i d e n t i f y i n g t h e
e f f e c t s O E t r a n s i t C o n a 1 f low when making aerodynamic f l i g h t measarements as
are c u r r e n t l y being made wi th t h e Space S h u t t l e Orbiter v e h i c l e s . P r e v i o u s
f l t g h t d a t a a n a l y s e s have r e l i e d e x c l u s i v e l y on a d j u s t m e n t s €11 t h e pas-
s u r f a c e L n t e r a c t t o n models without a c c o u n t i n g €or t h e t r a n r i t i o n a l e f f e c t
which can be comparable i n magnitude. The p r e s e n t calciilat i o n s show t h a t t h e
t r a n s € t i o n a l e f f e c t a t 175 kru would i n c r e a s e t h e Space S h u r t l e Orbi te r
l i f t - d r a g r a t i o by 90 p e r c e n t over t h e f r e e molecular va lue .
F
2
M -
u
V
X
Y
a
t‘
Yomenclature
d r a g c o e f f i c i e n t , 2D/ptoU&i
s k i n - f r i c t i o n c o e f f i c i e n t , ~F/,I,,,LJ?,X
t w , i t - t r.inst-(ar c .orff ic ic l i l1 , ‘!(I/, J IL l i f t c o e f f i c i e n t , x , / ~ J J ~ p r e s s u r e c o e f f i c i e n t , 2p/p,u2,
d r a g force
s k i n f r i c t i o n
f r e e s t r e a m Knudserl number, X.,/!?
l i f t f o r c e
l e n g t h of t h e Flat p l a t e
molecu la r weight of a i r
p r e s s u r e
h e a t f l u x
u n i v e r s a l gas c o n s t a n t , R = 8.3143 J/mol.K
f r e e s t ream speed r a t i o , U,fi/2RT,
thermodynamic t empera tu re
f r e e s t ream t empera tu re
s u r f a c e temper Ittire
f fees t ream v e l o)c i t y
v e l o c i t y component t angen t t o t h e p l a t e s u r € a c e
v e l o c i t v component normal t n the p la te s u r f a c e
coordi n , i t e measured along t h e plate s u r f a c e
c o o r d i n a t e meas:ired normal t o t h e p l a t e surf ace
a n g l e of i nc idence
f r a c t i o n of s p e c u l a r r e f l e c t i o n
freestream free pa th
2 ORIGINAL PAGE IS 08 POOR QUALITY
P m f r e e s t r e a m d e n s i t y
P d e n s i t y
ORIGINAL PAGE IS OF POOR QUALITY
1 n t rodu c t i on 4 --
The dt>veLopmc'nt ,ind app l i cat ion of Euture hyperson i ,- s p a ~ ~ v e h i c l e s
r e q u i r e a c c u r a t e p r e d i c t i o n s of aerotherm?L Loads d-lrir lg rr?enI.ry. A p o r t i o n
of the reentry f o r t h e s e v e h i c l e s w i l l t ake p l ace i? t h e t r a r i s i ' i o n a l f low
regime where nonequi l ibr ium 2 f f e c t s become impor tan t i n e s t a b l i s h i n g t h e
thermal and aerodynamic response of t h e s e v e h i c l e s . In order t o s i m p l i f y
the compiit a t i o n a l reqii i reme n t s , t h e 1-1 Et -drag c h a r a c t e r i s t i c s F 3r vehi c 1 es
such as the Space S h u t t l e O r b i t e r a r e o € t e n approximated1-- ' wi th a f l a t
p l a t e a t i n c i d e n c e f o r t h e f r e e molecular regime. For t h r t r a n s i t i o n a l f low
regime, e m p i r i c a l approximat ions a r e norinally used t o p r e d i c t the aerody-
namic f o r c e s f o r snch v e h i c l e s . Examples of such a p p l i c a t i o n s arc? g iven i n
iiefs. 1 , 2 , and 3 f o r the Space S h u t t l e O r b i t e r . T h e r e f o r e , nuinoi-ical
s t u d i e s on b a s i c c o n f i g u r a t i o n s such as a p l a t e a t i n c i d e n c e can provtde
u s e f u l in format ion and p h y s i c a l i n s i g h t concern ing the nat:ire of t r a n s i -
t i o n a l flows.
A f l a t p l a t e as a b a s i c a e r o d y n m i c s u r f a c e has rernaiwd the focus of
the transitional f l o w r e sea rch by seve ra l a u t h o r s [Ref s . 4-81. But most o €
t h e s e i n v e s t i g a t i o n s ,?re For zero inc idence *ind do not cover the range of
f l o w parameters of i n t e r e s t . There a r e ve ry few exper imenta l and t h e o r e t i -
c a l i n v e s t i g a t i o n s of the f l a t p l a t e a t i n c i d e n c e [Refs . 9 and 101. Sven
these do not cover thr. ldrp? inc idence and h igh speed r a t i o c h a r a c t e r i s t i c s
of hype r son ic f l l g h t . Furthermore, they are l i m t t e d t o t h e continuum flow
regime.
I n t h e p re sen t paper t h e d i r e c t s i m u l a t i o n Monte Car lo (DSMC) method of
B i r d , ''-I1 wi th t h e var iab le . hard sphe re (VHS) molecular model , i s used t o
s i m u l a t e t h e t r a n s i t i o n a l f low p a s t a f l a t p l a t e a t 53 degree i w l d e n c e .
The Flow c o n d i t i o n s anti i n c i d e n c e <ingle s imula t ed are thos:. Urhich t h e Space
S h u t t l e O r b i t e r e x p e r i e n c e s du r ing r e e n t r y . The DSMr, is t h e on ly s u i t a b l e
numprical t echn ique t o s i m u l a t e the t r a n s i t i o n a l f low regi:nr: a c n i r a t e l y
brcnuse i t a l l o w s t h e d i r e c t implementation of noneq:ii Librium flow models.
The v a r i o u s nonequ i l ih r ium phenomena are t h e main c h a r a c t ? r i s t i c s of t h e
t r a n s i t i o n a l f low regime, and t h e DBlC method sirni?latc?s t h e flow phys ic s
adequa te ly . The p r e s e n t c a l c u l a t i o n s show t h a t t h e i r a n s i t i o n a l e f f e c t f o r
a d i f f u s e s u r f a c e would i n c r e a s e t h e Space S h u t t l e l i f t - d r a g r a t l o by 90
pe rcen t over t h e free molecular value a t approx ima te ly 175 km a l t i t u d e .
Computational Approach
The DSMC method' ' - '* models the real gas by soInca thousands of s i m u l a t e d
molecules i n a computer. The p o s i t i o n c o o r d i n a t e s , v e l o c i r y wmponents , and
i n t e r n a l s t a t e of each molecrile are s t o r e d i n t he computer ,ind .are modif ied
wi th time as t h e moleciiles are c o n c u r r e n t l y fol lowed t'rirocigh r e p r e s e n t a t i v e
c o l l i s i o n s and boundary L n t e r a c t i o n s i n s imu la t ed p h y s i c a l space. The t i m e
pa rame te r i n t h e s i m u l a t i o n may be i d e n t € f i e d wi th physic;zl time i n t h e real
f low, and a l l ca l cu1a t io : i s are unsteady. When t h e boundary c o n d i t i o n s are I
such t h a t t h e flow is s t e a d y , then t h e s o l u t i o n is tile a sympto t i c l i m i t of
unsteady €low. The computation is always s t a r t e d from an i n t t i n l s ta te t h a t
permits an e x a c t s p e c i f i c a t i o n siich as a vacuum o r iini form e q u i l i h r ium
Elow. Conseqiirri t ly, the method does riot r e q u i r e an i n i t i , i l approximation t o
t h e f1owfiel.d and does riot i nvo lve any t t e r a t l v e procedures . A computa-
t i o n a l c e l l n e t m r k i s r equ i r ed i n p h y s i c a l space o n l y , and then on ly t o
f a c i l i t a t e t h e cho ice of p o t e n t i a l c o l l i s i o n p a i r s and t h e sampling of the
macroscopic flow p r o p e r t i e s . Furthermore, advantage may be taken of f low
ORIGINAL; PAGE Is OF POOR QlT41,?TY
symmetries t o reduce t h e dimensions of t h e c e l l network and t h e number of
p o s i t i o n c o o r d l n a t e s that need t o he s t o r e d f o r each molecul.e, brit t h e
c o n d i t i o n s a re s p e c i f i e d i n terms o f t he hehav lo r O F t h o i w i i v i d ~ i a l
molecules r a t h e r than t h e d i s t r i b u t i o n f u n c t i o n s . A L L pr, ,cedures may he
s p e c i f i e d i n such a manner t h a t t h e computa t iona l time is d i r e c t l y
p r o p o r t i o n a l t o the number of s imula t ed molecules .
Cond i t ions f o r C a l c u l a t i o n s
The f r e e s t r e a m c o n d i t i o n s cons ide red i n the p r e s e n t s tudy are f o r a n
a l t i t u d e range of 90 t o 130 km. For t h e 1.0- f l a t p l a t e v i t h z e r o t h i c k -
n e s s , t h e co r re spond ing f r e e s t r e a m Knudsen numbers are 0.023 t o 8 . 4 3 9 .
During the S h u t t l e ' s r e e n t r y t r a j e c t o r y , t h e same f r e e s t r e a m Knudsen numbers
based on t h e mean aerodynamic chord of 12 m correspnnd approx ima te ly t o a n
a l t i t u d e range of 100 t o 175 krn. The freestream velocity, i nc idence a n g l e ,
and wal l t empera tu re a r e assumed c o n s t a n t a t 7.5 krn/s, 40 deg, and 1000 K,
r e s p e c t i v e l y , t h a t i s , c o n d i t i o n s experienced by t h e Space S h u t t l e O r b i t e r
d u r i n g r e e n t r y . These c o n d i t i o n s are summarized Cn Table 1, where t h e
f rees t ream values are those given by .Jacchia f o r an exospher Lc temperature
oE 1200 K.
The s u r f a c e of t h e p l a t e is assumed t o be d i f f u s e d wi th f u l l t he rma l
accommodation and t o promote recombinati.on of t h e oxygen and n i t r o g e n
atoms. Recornhination prohahiLCties a p p r o p r i a t e €or t h e S h u t t l e t he rma l
p r o t e c t i o n t i l e s a r e imposed. The oxygen and n i t r o g e n recombinat ion
p r o b a b € L i t t e s are 9.0049 and 0.0077, r e s p e c t i v e l y .
S i n c e t h e computa t iona l r equ i r emen t s i n c r e a s e s i g n i F i c a n t l y with
i n c r e a s i n g f r e e s t r e a m d e n s i t y , computat ions are performed on ly i n t h e
t r a n s i t i o n a l f low regime.
5
R e s u l t s and D i s c u s s i o n
S t n c e t h e f l , i t p l a t e a t i n c i d e n w I:; a b a s i c element ,)F L i f t i n g
sur faces , i t i s o f t e n used f o r numertcal and e x p e r i m n t a l s t t i d i e s i n
hype r son ic f low r e s e a r c h . Furthermore, t h e c o n f i g u r a t i o n i s a l s o h e l p f u l i n
u n d e r s t a n d i n g t h e r e e n t r y oE space v e h i c l e s such as t h e Space S h u t t l e
O r b t t e r . T h e r e f o r e , a t t e n t t o n i s focused on t h e f low s t r i i c t u r e , s u r f a c e
q u a n t i t i e s , and aerodynamic c h a r a c t e r i s t i c s r e s u l t i n g from low-density flow
about a f l a t p l a t e a t 40 degree ang le of a t t a c k (Fig. 1).
F l o w f i e l d S t r u c t u r e
F i g u r e s 2 t o 7 p r e s e n t c a l c u l a t e d f l o w f i e l d q u a n t i t i e s on t h e
compression s i d e ( lower s u r f a c e ) of a f l a t p l a t e at two freestream Knudsen
numbers (0.023 and 8 . 4 3 9 ) . R e s u l t s a t t h r e e d i f f e r e n t l o c a t t o n s along the
sur face are p resen ted . Two r e g i o n s of i n t e r e s t are those near t h e plate
s u r f a c e and t h e shock wave. Near t h e s u r f a c e , a l a r g e incrrast. t n d e n s i t y
o c c u r s which is c h a r a c t e r i s t i c of a h i g h - v e l o c i t y flow about a 1-0113 w a l l .
These r e s u l t s a l s o c l e a r l y demons t r a t e t h a t t h e shock w a v e is f u l l y merged
with t h e vtscoiis l a y e r f o r Knudsen number va lues o€ 0.023 and 8.439. The
d e n s i t y and v e l o c i t y p r o f i l e s f o r a Knurlsen number va lue of 0.023 (Figs . 2
and 3) show t h a t t h e shock wave t h i c k n e s s increases g r a d u a l l y along t h e
surface of t h e plate. However, f o r a f r e e s t r e a m Knudsen number of 8.439
( F i g s . 5 and h), t h e e x t e n t of t h e f l o w f i e l d d i s t u r b a n c e s remains almost
c o n s t a n t a long t h e sur face b e c a m e of t h e l a r g e deg ree O F r a r e F a c t i o n a t
t h i s Knudsen number.
The o v e r a l l nondimensional. k i n e t t c t empera tu re , T/T,, shown i n
F igs . 4 and 7 f o r t h e freestream Knridsen number va lues of 0.023 and 8.439,
r e s p e c t i v e l y , i s d e f i n e d f o r a nonequ i l ib r ium gas as the weighted mean of
6
t h e t rans la t t ona l and i n t e r n a l t empera tu res . These Figurzs show t h a t t h e
o v e r a l l k i n e t i c t empera tu re r ise i n t h e shock wave precedes t h e d e n s i t y
r ise . The i n i t i a l r ise i n t empera tu re is due to t h e bimodal v e l o c i t y
d i s t r i b u t i o n : t h e molecular sample c o n s i s t s of most ly undist-rirhed
f r e e s t r e a m molecules w i t h j u s t a f e w molecules t h a t have been a f f e c t e d by
t h e shock. The l a r g e v e l o c i t y s e p a r a t i o n between t h e s e two classes of
molecu le s r e s u l t s i n t h e e a r l y t empera tu re i n c r e a s e .
The t empera tu re rise i n t h e shock wave is compara t ive ly l a r g e nea r t h e
l e a d i n g edge and then g r a d u a l l y d e c r e a s e s toward the t r a i l i n g edge (F igs . 4
and 7 ) . This obv ious ly shows t h a t t h e s t r e n g t h of t h e shock wave d e c r e a s e s
a l o n g t h e s u r f a c e of t h e f l a t p l a t e . The d i f f e r e n c e I n peak shock-wave
t empera tu res a t d i f f e r e n t l o c a t i o n s is less f o r t h e h i g h e r Knudsen number
c o n d i t i o n . The shock wave is v e r y d i f f u s e f o r t h e h i g h e r Knudsen number
c o n d i t i o n because oE t he l a r g e f r e e s t r e a m mean free p a t h . The t e m p e r a t u r e
and v e l o c i t y prof i l e s a l s o show a s i g n i f i c a n t t empera tu re jump and v e l o c i t y
s l i p a t t h e s u r f a c e f o r both v a l u e s of Knudsen number. Consequent ly , t h e
f l o w f i e l d e x h i b i t s t h e e f f e c t s of r a r e f a c t i o n f o r a l l t h e c a s e s cons ide red .
Su r f ace Quan t i t i e s
The s u r f a c e p r e s s u r e , s k i n f r i c t i o n , and h e a t t r a n s i e r c o e f f i c i e n t s art:
p r e s e n t e d i n F i g s . 8, 9, and 10, r e s p e c t i v e l y , f o r t h e 1 c ~ e r s u r f a c e of t h e
f l a t p l a t e a t rtO-detr, i nc idence . The e f f e c t s of r a r r E a c t i o n are shown by
comparing t h e r e s u l t s €o r d i f f e r e n t freestream Knudsen numbers. The v a r i a -
t i o n of t h e pressure c o e f f i c i e n t with r a r e f a c t i o n i s moderate provided t h e
gas-surface i n t e r a c t i o n is d i f f u s e , as assumed i n t h e p r e s e n t c a l c u l a t i o n s .
The c a l c u l a t e d p r e s s u r e c o e f f i c i e n t is g r e a t e r t han t h e f r e e molecular va lue
f o r large f r e e s t r e a m Knudsen numbers. In c o n t r a s t , t h e s k i n f r i c t i o n and
7
hea t t r a n s f e r c o e f f i c i e n t s (F igs . 9 and 1 0 ) a r e ve ry s e n s i t i v e t o
r a r + f a c t i o n e f f e c t s and approach the f r e e molecule v x l u e with i n c r e a s i n g
r a r e f a c t i o n .
Aerodynamic C h a r a c t e r i s t i c s
F i g u r e s 11 and 12 p re sen t the drag arid l i f t c o e f f i c i e n t s as a f u n c t i o n
of freestream Kniidsen number f o r the F la t p l a t e a t 40-deg i nc idence . These
r e s u l t s show the expected v a r i a t i o n i n t h e t r a n s i t i o n a l flow regime. The
drat: C o e f f i c i e n t irict-e.ases and the l i f t c o e f f i c i e n t d e c r e a s e s s u b s t a n t i a l l y
w i t h i n c r e a s i n g r a r e f a c t i o n , and both approach the €ree molecule l i m i t . The
change in t h e d rag and l i f t c o e i F i z i r n t s is due p r i m a r i l y t o a n i n c r e a s e i n
u the s k i n friction r a t h e r than t o a change in t h e p r e s s u r e c o e f f i c i e n t .
F igu re 13 p r e s e n t s the the l i f t - d r a g r a t i o as a f u n c t i o n of f r e e s t r e a m
Knudsen number dhere the t r e n d i s the same as t h e l i f t c o e f f i c i e n t d a t a ,
which e x p e r i e n c e a s i g n i f i c a n t d e c r e a s e wi th i n c r e a s i n g r a r e f a c t i o n .
The e f f e c t of a n g l e of i nc idence variation on t h e aerodynamic
c o e f f i c i e n t s i s demonstrated i n Figs . 14 t o 16 f o r t h e 8 . i Kmidsen vlulnber
case. The DSMC r e s u l t s are compared w i t h t hose ob ta ined i ising free molecule
e x p r e s s i o n s f o r l i f t atid drag c o e € f € c i e n t s and l i f t - d r a g r a t i o . F igu re 1 4
shows t h a t t h e l i f t c o e f € i c i e n t i n c r e a s e s wi th angLc of a t t a c k , reaches a
maximum v a l u e a t 4 5 deg, then d e c r e a s e s with f u r t h e r i l l c rease i n a n g l e of
a t t a c k . The DSZIC v a l u ~ s a r e c o n s i d e r a b l y h i g h e r t han the fret? molecule
vaLues, i n d i c a t i n g t h a t t r a n s i t i o n a l e f F e c t s are e v i d e n t e v e n a t t h i s hlghly
rart=fi .ed c o n d i t i o n . p igu re 15 shows t h a t the d rag c o e f f i c i e n t a g r e e s well
w i t h the free moleciilf> c a l c u l a t i o r l a f o r small inc idence . Uowever, a t h i g h e r
iric ldence the DSMC va lues are s l i g h t l y lower than f r e e molecrile va lues
because of the over p r e d i c t i o n of s k i n f r i c t i o n by the f r e e molecule
8
method. F i g u r e 16 p r e s e n t s the co r re spond ing l i f t - d r a g r a t i o comparison and
shows t h e same t r e n d of the t r a n s i t i o n a l e f f e c t s as in t h e L i f t c o e f f i c i e n t
d a t a . \
These r e s u l t s have impor t an t i m p l i c a t i o n s fo r t h e i n t e r p r e t a t i o n of
E l i gh t measurements used t o deduce aerodynamic c o e f f i c i e n t s under r a r e f i e d
c o n d i t i o n s . As e a r l y as 1985, i t w a s recognized (Ref. 1 4 ) t h a t t r a n s € t C o n a l
e f f e c t s r a t h e r t h a n s p e c u l a r r e f l e c t i o n might be i n f l u e n c i n g t h e i n t e r p r e -
t a t i o n of t h e f l i g h t measurements; however, no c a l c u l a t i o n s were a v a i l a b l e
t o e s t a b l i s h t h e fact . A t a l t i t u d e s of 160 km and above, t h e c o n v e n t i o n a l
p r o c e d ~ i r e l - ~ has been t o i n t e r p r e t t he f l i g h t measurements u s i n g the f r e e
mo'lecule flow c a l c u l a t i o n s . Such procedures are used t o e s t a h l € s h what
f r a c t i o n of t h e gas - su r face i n t e r a c t i o n is s p e c u l a r . Bu t C t can be s e e n
from t h e present c a l c u l a t i o n s t h a t t h e t r a n s i t i o n a l e f f e c t s persist even a t
very h igh a l t i t u d e s (160 km and above). This is c l e a r l y demonstrated i n
F i g . 16 where t h e t r a n s i t i o n a l e f f e c t i n c r e a s e s t h e l i E t - d r a g r a t i o by 90
p e r c e n t f o r a f l a t p l a t e a t 40-deg inc idence . The Freestream Knudsen number
f o r t h i s c o n d i t i o n i s 8.4 which corresponds t o S h u t t l e c o n d i t i o n s a t
approx ima te ly 175 km. T h f s t r a n s i t i o n a l e f f e c t is q u i t e l a r g e , and i f not
p r o p e r l y i n t e r p r e t e d could be m i s t a k e n for a c o n t r i b u t i o n due t o the
s p e c u l a r r e f l e c t i o n . For example, t h e free molecule r e suLt s f o r l i f t - d r a g
r a t i o as a f u n c t i o n of ang le of i n c i d e n c e f o r d i f f e r e n t fractions of
specular r e f l e c t i o n are shown i n Fig. 17. As t h e f r a c t i n r i O E s p e c u l a r
r e f l e c t i o n i n c r e a s e s , the l i f t - d r a g r a t i o a l s o i n c r e a s e s f o r a g iven
i n c i d e n c e angle . Sirice t h e s e two separate e f fec ts bo th produce i n c r e a s e d
L i f t -d rag r a t i o , t n t e r p r e t a t i o n of fLi.ght lneostirernents must account f o r t h e
t r a n s i t i o n a l e f f e c t s .
9
Conclusions
Results obtained with the direct simulation Monte Carlo (DSMC) method
for hypersonic flow past a flat plate at incidence show the effects of the
transitional flow regime on the aerodynamic characteristics. These effects
are significant even for large freestream Knudsen numbers. Thus, the
interpretation of aerodynamic flight data for space vehicles such as the
Space Shuttle Orbiter must be done in concert with calculations that
describe the transitional effects. Failure to account for this effect could
significantly distort the interpretation of the gas-surface interactions
under highly rarefied conditions.
References
'Blanchard, R. C., "Rarefied Flow Lift-to-Drag Measurements of the Shuttle
Orbiter," 15th Congress of International Council of Aeronautical Sciences,
Paper ICAS-86-2.10.2, London, England, Sept. 7-12, 1986.
2Blanchard, R. C., Hendrix, M. K., Fox, J. C., Thomas, D. J., and Nicholson,
J. Y., "Orbital Acceleration Research Experiment," Journal of Spacecraft and
Rockets, Vol. 24, No. 6, November-December, 1987.
3Aerodynamic Design Data Book, Volume 1, Orbiter Vehicle 102,
SD72-SH-0060, Volume lM, November 1980, Space Division, Rockwell Interna-
tional.
hogenitz, F. V., Broadwell, J. E., and Bird, G. A . , "Leading Edge Flow by
Monte Carlo Direct Simulation Technique," AIAA Journal, Vol. 8, No, 3, 1971,
pp. 304-310.
%ogenitz, F. V. and Takata, G. Y., "Rarefied Gas Flow about Cones and Flat
Plates by Monte Carlo Simulation," AIAA Journal, Vol. 9, No. 1, 1971,
pp. 91-100.
10
anakhore, E. M., "Raref ied G a s Flow Over a P l a t e P a r a l l e l t o t he Stream,"
USSR F l u i d Dynamics, 1973, pp. 119-126.
7 B e o t t c h e r , R. D., Yoppehwnllner, G . , and Legge, H . , " F l a t P l a t e Sk in
F r i c t i o n in t h e Range hetween Hypersonic Conti.nuiim anti Free "lolecular F low,"
I'roc. 10th I n t e r n a t i o n a l Symposiurn on RareEied G a s Dynamics, Aspen, CO,
Vol. 1, 1976, pp. 348-359.
8Hermina, W. L., 'Monte C a r l o S imula t ion of R a r e f i e d Flow Along a F l a t
P l a t e " , AIM Paper 87-1547, J u n e , 1987.
'Allegre, -3. and B i s c h , C . , "Angle of At tack and Leading F :d ,~e EEfects on t h e
Flow about a Flat P l a t e a t Mach Number 18," AIM J o u r n a l , Vol. 6 , No. 5 ,
1968, pp. 848-852.
'%ai, S . L . , "An ExperimentaL Study O F t h e Flow P a s t 3 F l a t P l a t e a t
I n c i d e n c e i n Supe r son ic Low Densit.y Stream,'' R a r e f i e d Gas Dynamics, Univ.
Tokyo P r e s s , e d i t e d by Oguchi H. , Vol. I , 1984, pp. 257-264 .
"Bird, G. A . , "Monte Car lo Siri iulation i n an Engineer ing Context ," AIM I_
P r o g r e s s i n A s t r o n a u t i c s and Aeronau t i c s : RareEied Gas Dynamics, Vol. 7 4 ,
Part 1, e d i t e d by Sam S. F i s h e r , 1981, pp. 235-239.
'2Ri rd , G. A . , Molecular Gas Dynamics, Clarendon P r e s s , Oxford, 1976.
13.Jacchia, 1,. C . , "Thermosphe.ric Temperature Dens l ty , and Composition: New . .
Models," Research in Space S c i e n c e , SA0 S p e c i a l Report No. 375, '-larch 1977.
Elanchard , R. C. and RutherEocd, J. P., " S h u t t l e a r b i t e r High Resolution I i t
Accelerometer Package Experiment: P r e l i m i w r y F l i g h t R e s u l t s ," J o u r n a l of
S p a c e c r a f t and Rockets , Vol.. 2 2 , Wo. 4, July-August, 1985, pp. 474-489.
ORIGINAL PAGE IS OF POOR QUALITY
11
T a b l e 1. Freest teain Conditions
[Length of the Elat plate , L, = 1 in, aiid angle of i n c i d e n c e , a , = 40 deg.
- IJ,, Om 3 ir w, S,
-D Itn/sec kg/m K Altitude, K, KN km g/mol
90 28.810 0.02'3 7 .5 3.418 x 10-' 158 23.1
100 28.257 0.137 7.5 5.640 x lo- ' 194.3 21.6
120 26.159 3.146 7.5 2.269 x lo-' 367.8 15.7 ~~~ ~~ ~
130 25.441 8.439 7.5 8.220 x lo-' 499.7 13.3
.OLRIGINAL PAGE Ts KB H X I R QUALITY
12
Y I L--P Irn '-m -
X
plate
Figure 1. Flat plate configuration at incidence.
13
-0.4
-0.3
-0.2
-0.1
0 4 a 12 16 20 24 P/Pm
Figure 2. Density profiles normal to the plate surface. (KN, = 0.023, and a = 40 deg.)
14
-0.5
-0.4
-0.3 Y 1 -
-0.2
x/1 .I .5 .9
i i i i /
0 Om2 Om4 0.6 0.8 1 m0 u/u*
Figure 3. Tangential velocity profiles normal to the plate surface. (KN, = 0.023, and a = 40 deg.)
15
-0.5
-0.4
-0.3 Y 1 -
-0.2
-0.1
0 I
14 28 42 56 70
Figure 4. Temperature profiles normal to the plate surface. (K = 0.023, and a = 40deg.)
N,
16
=I 6 r
=I 2
-4
0 2 4 6 PIP00
8 10
Figure 5. Density profiles normal to the plate surface.
(KN = 8.439, and a = 40 deg.) 00
17
-I 6
-1 2
Y - -8 .Q
-4
Figure 6.
WL? - .05 .45 .95
..--- ----- I
UlU,
Tangential velocity profiles normal to the plate (K = 8.439, and a = 40deg.)
No0
surface.
18
I .
-I 6
-I 2
-8
-4
1 0 5 10 15 20 25
TKm
Figure 7. Temperature profiles normal to the plate surface.
(KN = 8.439, and a = 40 deg.) 00
19
1.2
cP .8 \Free -------- molecule
I I I I I 0 0.2 0.4 Om6 Om8 1.0
0 8.439 0 3.144 0 Om137 A Om023
Figure 8. Effect of rarefaction on the compression side surface pressure coefficient. ( a = 40deg.)
1 .o
.8 '
s.6
CF .4
.2
0
h
0 8.439 0 3.144 0 0.137 A 0.023 %* -
XlR 0.2 0.4 0.6 0.8 1.0
Figure 9. Effect of rarefaction on the compression side surface skin-friction coefficient. ( a = 40 deg.)
21
.8
.6
.2
r Free molecule7
0 0
A 0
8.439 3.1 44 0.1 37 0.023
0 0.2 0.4 0.6 0.8 1.0
XI..
Figure 10. Effect of rarefaction on the compression side surface heat transfer coefficient. ( a = 40 deg.)
22
1.4
1.2
c
w60 w8Lu-dl 2 4 6 - 8 10
Figure 11. Drag coefficient ( a = 40 deg.)
versus Knudsen number.
CI 1
.6
.4
.2
0 2 4 6 8 1 0
Figure 12. Lift coefficient versus Knudsen number. ( a = 40 deg.)
L/D
0 2 4 6 8 1 0
Figure 13. Lift-drag ratio versus Knudsen number. ( a = 40 deg.)
25
.20
.I 5
CL . I O
.05
0
0 DSMC - Free molecular flow 0
0
0
I I I I I 20 40 60 80 100
Figure 14. Lift coefficient versus incidence angle for K N = 8.439. 00
26
2.5
2.0
1.5
cD
1.0
.5
(
0
flow
20 40 60 80 100
a, deg
Figure 15. Drag coefficient versus incidence angle for K N = 8.439. 00
2 7
0 DSMC - Free molecular flow
0
UD
J 0 9 20 60 80 100
a, deg
Figure 16. Lift-drag ratio versus incidence angle for K N = 8.439. 00
28
1.5
1
LID
0.5
0
- €=0.8 \
90
Figure 17. Flat plate free molecule lift-drag ratio versus incidence angle.
(So0 = 13.1 and Tw/Too = 2.0)
29
Report Documentation Page 1. Report No. 2. Government Accession NO.
NASA TM-101493 I
19. Security Classif. (of this report)
Unclassified
____-- 4. Title and Subtitle
20. Security Clauif. (of this page)
Unclassified
Rarefied Flow Past a Flat Plate at Incidence
7. Author(s1
Virendra K. Dogra James N. Moss Joseph M. Price
9 Performing Organization Name and Address
NASA Langley Research Center Ilampton, VA 23665-5225
12. Sponsoring Agency Name and Address
National Aeronautics and Space Administration Washington, DC 20546-0001
3. Recipient's Catalog No.
5. Report Date
October 1988 6. Performing Organization Code
8. Performing Organization Report No.
10. Work Unit No.
506-40-9 1-03 11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Memorandum 14. Sponsoring Agency Code
15. Supplementary Notes
Presented at the Sixteenth International Symposium on Rarefied Cas Dynamics, Pasadena, California, July 10-16, 1988. Submitted for publication in the proceedings of 16th RGD meeting. Virendra K . Dogra: Vigyan Research Associates, Inc., Hampton, Virginia. James N. Moss and Joseph M. Price: Langley Research Center, Hampton, Virginia.
Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for the transitional flow about a flat plate at 40 degree incidence. The plate has zero thickness and a length of 1.0 m. The flow condi- tions simulated are those experienced by the Shuttle Orbiter during reentry at 7.5 km/s. The range of freestream conditions are such that the freestream Knudsen number values are between 0.02 and 8 . 4 , that is, conditions that encompass most of the transitional flow regime. transitional effects are evident when compared with free molecule results for all cases considered. The calculated results demonstrate clearly the necessity of having a means of identifying the effects of transitional flow when making aerodynamic flight measurements as are currently being made with the Space Shuttle Orbiter vehicles. Previous flight data analyses have relied exclusively on adjustments in the gas-surface interaction models without accounting for the transitional effect which can be comparable in magnitude. The present calcula- tions show that the transitional effect at 175 km would increase the Space Shuttle Orbiter lift-drag r a t i o by 90 percent over the free molecular value.
16. Abstract
The DSMC simulations show that
17. Key Words ( S u w d by Author(s1) I 18. Distribution Statement
Transitional flow effects Aerodynamic characteristics Direct simulation Monte Carlo
Unclassified - Unlimited
Subject Category 34
21. No. of pages 22. Price --T-lY- I
IASA FORM 1628 OCT 86