aerodynamic coefficients and pressure distribution of solid flat and ringslot models in...
TRANSCRIPT
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AFFDL- TR- 72- 113
A E R O D Y N A M I C C OE F F IC IE N T S A N D P R E S SU R E
D I S T R I B U T I O N O F S O L I D FL AT A N D R I N G S L O T
M O D E L S I N O N E D I M E N S I O N A L
V E L O C I T Y G R A D I E N T S
H. G. HEINRICH
R. A. NOREE N
J. N. DALE
UNIVERSITY OF MINNESO TA
T E CH N IC A L R E P OR T A F F D L - T R - 7 2 - 1 1 3
D E C E M B E R 1 9 7 3
A ppro ved fo r pub l i c r e l eas e ; d i s t r ibu t ion un l imi ted .
A I R F O R C E F L I G H T D Y N A M I C S L A B O R A T O R Y
A I R F O R C E S Y S T E M S C O M M A N D
W R I G H T - P A T T E R S O N A IR F O R C E B A S E O H I O 4 5 4 3 3
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A E R O D Y N A M I C C OE F F IC IE N T S A N D P R E SS U R E
D I S T R I B U T I O N O F S O L I D FL A T A N D R I N G S L O T
M O D E L S IN O N E D I M E N S I O N A L
V E L O C I T Y G R A D I E N T S
H. G. HEINRICH
R. A. NOREEN
J. N. DALE
UNIVERSITY OF MINNESOTA
A pproved fo r pub l i c r e l eas e ; d i s t r ibu t ion un l imi ted .
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1973
FOREWORD
Thi s r epor t was pr epar ed i n t he Depar t ment of
Aer ospace Engi neer i ng and Mechani cs of t he Uni ver s i t y of
Mi nnesot a i n compl i ance wi t h U. S. A i r For ce Cont r ac t No .
F33615- 68- C- 1227, " Theor et i cal Depl oyabl e Aer odynam c
Decel er at or I nvest i gat i ons , " Task 606503, " Par achut e Aer o-
dynam cs and St r uct ur es, " Pro j ect 6065, " Per f or mance and
Des i gn of Depl oyabl e Aer odynam c Dece l e rat or s . " The ana l ys i s
pr esent ed i n t hi s r epor t was per f or med bet ween 2 Febr uar y
1970 and 31 J ul y 1972.
The st udy was s ponsor ed j oi nt l y by U. S. Ar my Nat i ck
Labor at or i es , Depar t ment of t he Ar my, and Ai r For ce Syst ems
Command, Depar t ment of t he Ai r For ce, and adm ni st er ed under
t he di r ec t i on of t he Recover y and Cr ew St at i on Br anch, Ai r
F or c e F l i ght Dynam c s Labora t o ry , Wr i ght - Pa t t er son Ai r F or c e
Base, Ohi o, wi t h Mr . J ames H. DeWeese, AFFDL/ FER, as Pr o j ect
Engi neer .
The st udy was accompl i shed i n cooper at i on wi t h
Mr . Thomas R. Hekt ner and sever al st udent s of Aer ospace
Engi neer i ng at t he Uni ver s i t y of Mi nneso t a . Mr . Edwar d J .
Gi ebut owsk i , U. S. Ar my Nat i c k Labora t o r i es , par t i c i pat ed
i n t hi s s t udy by pr ov i di ng val uabl e gui danc e and i dent i f i -
c at i on o f t he pr i nc i pal r equi r ement s .
Thi s r epor t was subm t t ed by t he aut hors i n
August 1972.
Thi s t echni cal r epor t has been r ev i ewed and i s
appr oved.
RUDI J . BERNDT
Act ' g Chi e f , Recover y & Cr ew St at i on Br anch
Ai r F or c e F l i ght Dynam c s L abor at or y
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ABSTRACT
_ The r esu l t s of wi nd t unnel s t udi es of t he aer o-
dynam c_c har ac t e r i s t i c s o f s ol i d f l at and r i ngs l ot par ac hut e
model s i n f l ow wi t h s ever al l i near o ne- di mens i onal d y 2 c
S e S r s
8
^ ? ^ ar e pr es ent ed. The model h S d n S i S S
di amet ers of about 16 i n. Gr adi ent s of 0% 107, 207 and
40% of c ent er l i ne dynam c p r es s ur e per f oot wi t h c e n t e Si n e
t h e t e s t s
S
1 u S J l '
8 8 6 M d 9
f t /
"
c We r e
e a t S l l S d f S "
t est s Sur f ace pr ess ur e measur ement s wer e made on r i ei d
porous mode l s , and dr ag coe f f i c i ent s obt ai ned by i nt egr at i on
of t he pr essur e di s t r i but i on. Aer odynam c f or ce aSd momen?
S S S b S - S j e S "
d e t 6 r mi n e d
* > . meas ur ement s c T '
iii
LINDA HALL LIBRARY
K i r m i
G ,
M.
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TABLE OF CONTENTS
Sec t i on
p a g e
I . I nt r o duct i on
I I . Dynam c Pr essur e Gr adi ent s . 2
I I I . Pr essur e Di s t r i but i on Measur ement s 12
A. Pr essur e Di s t r i but i on Model s 12
B. W nd Tunnel Test s 12
C. Resu l t s 16
I V. For ce Measur ement s 29
A. Par achut es Model s 29
B. W nd Tunnel Test Appar at us 29
C. Coef f i c i ent s 3 3
D. Resul t s 36
V. F r ee Suspensi on Test s
5 7
Appendi x I - Met hod of Pr essure I nt egr at i on 58
Appendi x I I - Tabul at ed Pr essur e Coef f i c i ent s 61
Ref er ences . . . . . 71
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I LL USTRATI ONS
FI GURE
PAGE
Rod Assembl y f or P roduc t i on of Ve l oci t y
Gr adi ent i n a 54 x 38 I nch W nd Tunnel
Test Sect i on 3
2
- Dynam c Pr essure vs Di s t ance at Var i ous
Gr adi ent s , Cent er l i ne P r essur e of
4. 0 and 9. 0 psf 4
3. Si de Vi ew of W nd Tunnel Test Sec t i on
Showi ng Rake and Par achut e Model Locat i ons
used i n Pr essure Gr adi ent Measur ement s . . . 5
Measur ed and Desi r ed Pr essur e Gr adi ent f or
G = 0. 1, q = 4. 0 psf
6
Measur ed and Desi r ed Pr essur e Gr adi ent f or
- U. l , q = 9. 0 psf . . . ,
7
Measur ed and Desi r ed Pr essur e Gr adi ent f or
o - 0. 2, q = 4. 0 ps f
g
Measur ed and Desi r ed Pr essur e Gr adi ent f or
0 - U. 2, q = 9. 0 psf
9
4.
5.
6
Measur ed and Desi r ed Pr essur e Gr adi ent f or
h
~ q = 4. 0 psf
1 0
Measur ed and Desi r ed Pr essur e Gr adi ent f or
G - 0. 4, q - 9. 0 ps f
n
8.
9.
10. Pr essur e Model s
,
0
13
Geomet r y of Pr essur e Measur ement Model s . . 14
S n S f
1
?
1 1
f P r e s s u r e
Tap Locat i ons and
Mode of Pr esent at i on .
15
13. Pr es s ur e Di s t r i but i on on a Sol i d Fl atPar ac hut e Model i n Uni f or m F l ow
1 7
JL /
14. Pr es s ur e Di s t r i but i on on a Sol i d F l at
Par achut e Model f or G = 0. 1, q f 4. O ps f . .
1 8
15. Pr es s ur e Di s t r i but i on on a Sol i d Fl at
Par achut e Model f or G = 0. 1, q = psf . .
1 9
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I LLUSTRATI ONS ( CONTD. )
FI GURE PAGE
16. Pr essur e Di s t r i but i on on a Sol i d F l at
Par achut e Model f or G = 0. 4, q = 4. 0 psf . . 20
17. Pr essur e Di s t r i but i on on a Sol i d Fl at
Par achut e Model f or G = 0. 4, q = 9. 0 psf . . 21
18. Pr essur e Di s t r i but i on on a Ri ngs l ot
Par achut e Model i n Uni f orm Fl ow 22
19. Pr essur e Di s t r i but i on on a Ri ngs l ot
Par achut e Model f or G = 0. 1, q = 4. 0 psf . . 23
20. Pr essur e Di s t r i but i on on a Ri ngs l ot
Par achut e Model f or G = 0. 1, q = 9. 0 psf . . 24
21. Pr essur e Di s t r i but i on on a Ri ngs l ot
Par achut e Model f or G = 0. 4, q = 4. 0 psf . . 25
22. Pr essur e Di s t r i but i on on a Ri ngs l ot
Par achut e Model f or G = 0. 4, q = 9. 0 psf . . 26
23. Ri ngs l ot Model I ns t al l ed i n t he W nd Tunnel . 31
24. W nd Tunnel Appar at us f or Par achut e
For ce Measur ement s 32
25. Vent Nor mal For ce Sensor 34
26. Coor di nat e Syst em of t he Aer odynam c
Coef f i c i ent s
3 5
27. Tangent For ce Coef f i c i ent s f or t he Sol i d
Fl at Par achut e Model f or Uni f or m F l ow
and G = 0. 1 3 7
28. Tangent For ce Coef f i c i ent s f or t he Sol i d
Fl at Par achut e Model f or G = 0. 2
and G = 0. 4 38
29. Nor mal For ce Coef f i c i ent s f or t he Sol i d
F l at Par achut e Model f or Uni f or m F l ow
and G = 0. 1 39
30. Nor mal For ce Coef f i c i ent s f or t he Sol i d
Fl at Par achut e Model f or G = 0. 2
and G = 0. 4 40
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I LLUSTRATI ONS ( CONTD. )
FI GURE
PAGE
31. Moment Coef f i c i ent s f or t he Sol i d F l at
Par achut e Model f or Uni f or m Fl ow
and G = 0. 1 ^
32. Moment Coef f i c i ent s f or t he Sol i d F l at
Par achut e Model f or G = 0. 2 and G = 0. 4 . 4 3
33. Tangent For ce Coef f i c i ent s f or t he
Ri ngs l ot Par achut e Model f or Uni f or m Fl ow
and G = 0. 1 ^
34. Tangent For ce Coef f i c i ent s f or t he
Ri ngsl ot Par achut e Model f or G = 0 2
and G = 0. 4 \
4 5
35. Nor mal For ce Coef f i c i ent s f or t he
Ri ngs l ot Par achut e Model f or Uni f or m Fl ow
and G = 0. 1
36. Nor mal For ce Coef f i c i ent s f or t he
Ri ngsl ot Par achut e Model f or G = 0
and G = 0. 4 . .
47
37. Moment Coef f i c i ent s f or t he Ri ngs l ot
Par achut e Model f or Uni f orm Fl ow
a n d G
- 0 -
1
38. Moment Coef f i c i ent s f or t he Ri ngsl ot
Par achut e Model f or G = 0. 2 and G =0 . 4 . .
49
Rat i o of C
T
at oC = 0 i n Gr adi ent F l ow
t o C
T
at 0L= 0 i n Uni f or m Fl ow vs Gr adi ent .
St abl e Angl es of At t ack f or t he Sol i d
Fl at Par achut e Model ^
St abl e Angl es of At t ack f or t he Ri ngs l ot
Par achut e Model
s i O C
53
40.
41.
51
42. Rat i o of dC / d * at ^ i n Gr adi ent Fl ow
t o dC / d c
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q
V
q + 0.2q x
4.0 psf
6 0 f ps
0.2 0.4
x
/w
Fig 6 Measured and Desired Pressure
Gradient for G =
0.2,
q =4.0 psf
RAKE POSIT IONS
o 1
2
1.4 a 3
4
o 5
v 6
8
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1.6
RAKE POSIT IONS
Fig 5 Measured and Desired P ressure
Gradient for 0= 0.1,q=9.0psf
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F ig 4 Measured and Des ired P ressure
G radient for G = 0.1,q = 4.0psf
6
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00
z
O
LUt
^00
< o
q:cl
vt- C\J OJ
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-2.0 -1.0 0 1 .0
x ( f t )
2.0
Fig 2 Dynamic Pressure vs Distance
at Various Gradients, C enterline
Pressures of 4.0 and 9.0psf
4
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3
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I I . DYNAMI C PRESSURE GRADI ENTS
A r ev i ew of t he avai l abl e l i t er at ur e showed t hat
t he met hod f or pr oduc i ng a vel oc i t y gr adi ent pr esent ed i n
Rexs 5 and 6 was best s ui t ed f or t hi s st udy. The r ef er enced
met hod was t o pl ace cy l i nd i ca l r ods spanni ng t he f l ow upst r eam
of t he t est ar ea and t o var y t he spaci ng bet ween t he r ods
I n order t o devel op a vel oci t y gr adi ent acr oss t he wi nd t unnel
t es t sec t i on, t he spac i ng woul d be wi de on t he hi gh vel oci t y
s i de and nar r ow on t he l ow vel oc i t y s i de. Ref er ences 5 and 6
gave met hods t o cal cul a t e an i ni t i al r od spac i ng t hen by
means of exper i ment s, t he r od spac i ng coul d be modi f i ed unt i l
t he des i r ed gr adi ent was es t abl i shed wi t h sat i s f ac t or y ac c ur ac y.
The det ai l s of t hi s pr oc ess ar e as f ol l ows . A r ow
of ver t i c al s t eel r ods f as t e ned t o al um num r ai l s was i ns t al l ed
at t he ups t r eam edge of t he t es t sec t i on ( Fi g 1) Sl ot t ed
s l eeves at each end of t he r od f i t over t he r ai l s and al l owed
var y i ng t he r od spac i ng ac r oss t he wi nd t unnel . A l i near
vel oc i t y gr adi ent c l osel y appr ox i mat i ng t he des i r ed l i near
dynam c pr essur e gr adi ent was s e l ect ed, and t he met hods of
Ref s 5 and 6 wer e used t o c al c ul at e t he i ni t i al spac i ngs f or
t hi s l i near v el oc i t y gr adi ent . The r ods wer e s et at t hi s
i ni t i a l spac i ng and t he r esu l t ant pr essur e gr adi ent measur ed
The pr essur e di st r i but i on was measur ed wi t h a r ake whi ch
spanned t he t est sect i on. The r ake had 48 t ot a l pr essur e pr obes
and f our s t at i c pr essur e pr obes at i nt er val s of one i nc h.
Af t er t hi s f i r st measur ement , t he number and spac i ng of t he
r ods wer e changed and t he pr essur e di st r i but i on checked. Thi s
pr ocess was r epeat ed unt i l t he des i r ed dynam c pr essure
gr adi ent was es t abl i shed.
r - n n i
I l l
n
t
o
i S
" T n
6
^
t h e f o l l o w
i
n
g gr adi ent s wer e es t abl i shed
/ n ' J * L
a
" '
4 Wl t h
c ent er l i ne dynam c pr essur es of
4. 0 ps f and 9. 0 ps f , r es pec t i vel y. Fi gur e 2 i l l us t r at es t he
numer i c al f or m of t hes e gr adi ent s .
The ar r angement of t he r ods, t he r ake, and t he pos i -
t i on of t he par ac hut e, used i n t he l at er t es t s , i s shown i n
F i g 3. The dat a po i nt s , showi ng t he ac t ual l y es t abl i shed
gr adi ent s , ar e shown i n F i gs 4 t hr ough 9. The l i nes t hr ough
t he dat a po i nt s r epr esent t he des i r ed gr adi ent s . The dat a
poi nt s shown are onl y f or ever y t hi r d pr essur e pr obe on t he
r ake i n t he c ent r a l por t i on of t he t es t s ec t i on. Si mpl e ob-
se rvat i on of t he f l ui d hei ght s i n t he mul t i t ube manomet er
showed t hat t he pr essur es at t he ot her cent r a l pr obe l ocat i ons
f i t t he l i near pr essur e gr adi ent r equi r ement . Out s i de of t he
c ent r al ar ea the vel oc i t i es dec r eased bec ause of wa l l ef f ec t s
and boundar y l ayer s. The f i gur es show t hat t he agr eement
bet ween t he des i r ed and the es t abl i shed gr adi ent s i s sat i s -
f ac t or y i n t he ar ea i n wh i ch t he par achut e mode l wi l l be
l oc at ed.
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I NTRODUCTI ON
. , . ,
Th
? ;
s r e
P
r
t pr esent s t he r esul t s of wi nd t unnel
s t udi es of t he aer odynam c c har ac t er i s t i c s of s ol i d f l at and
r i ngs l ot par ac hut e model s i n f l ow wi t h var i ous l i near one-
di mens i ona l dynam c pr essur e pr of i l es c al l ed gr adi ent s . The
si ze o t he model par achut e and t he sl ope of t he gr adi ent s
wer e set so t hey wer e compar abl e t o a par achut e oper at i ng
i n t he wake o f a l ar ge a i r c r a f t ( Ref s 1, 2) . Based on par a-
chut e s i ze , t he gr adi ent s st udi ed wer e much st eeper t han a
t ypi cal a t mospher i c wi nd gr adi ent ( Ref 3) , and not near l y
? r J ^
t h e
5
a d i e n t i n
t he wake of a f or ebody or payl oad
(,Ker The gr adi ent s wer e est abl i shed by var yi ng t he
spaci ng bet ween many t hi n r ods pl aced i n a subsoni c wi nd
t unnel j us t ups t r eam of t he t es t s ec t i on. Cal c ul at i ons gave
an appr oxi mat e i ni t i a l r od spac i ng, and t hen t he gr ad enf s
wer e measur ed and t he spaci ng adj ust ed unt i l t he desi r ed
gr adi ent was obt a i ned. W nd t unnel t est s wer e conduct ed at
p r e s s u r e ^a t h e cent f -
6
f t
J ?
e C
?
n d 9 0
" / s ec ^ S i ' d ^ l c
pr essur es at t he c ent er l i ne of 4 ps f and 9 ps f , r espec t i vel y
p re ssu re
1
per
S
f oot ?
X
'
1 0 %
'
2
% M d 4
%
f
- nt er l f Se dynl m c
per f or manc e c har ac t er i s t i c s
r
i n t hi s gr a di ent f l o w- pr es s u r e
di st r i but i on measur ement s wer e made on
rigid
c l ot h
covered
T h
n
S
?
t 8 S t S W6 r e ma d e i n u n
i f o r m f l ow, and at t he
s mal l es t and l ar ges t gr adi ent f or eac h c ent er l i ne v el oc i t v
f or c e oef f i c i ent s f nr
nS We r e i n t e
^a t e d and e d u c e d " ? '
meas ur ement s ?
f
r c o m
P
a r i s
" wi t h t he r es ul t s of f or c e
Aer odynam c f or c e c oef f i c i ent s , r r and C
wer e measured as f unc t i ons o f angl e o f at t ack f or n m,
f l exi bl e J S i d l S J ' ,
T
^
f
- c e L a s u r e ^ f we ^ ^a d V wi t ^
Fi nal l y?
lor
a ^ i t a ^ ^ i ^ ^ f ^ J S S f c S J
0
?
1
? "
gr adi ent f l ow, t he model ? wer e f r l e ^ ^ e f a n f o ^ r v e d
1
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di s t ance f r om ax i s of symmet r y t o canopy ski r t
measur ed al ong canopy pr of i l e
nom na l ar ea
s/ s
max
t angent f or ce
c ent er l i ne vel oc i t y
t es t s ec t i on wi dt h, 54 i n
t es t sec t i on wi dt h c oor di nat e
t es t sec t i on hei ght c oor di nat e
par achut e angl e of at t ack
t r i m angl e, s t a bl e angl e of at t ac k, Q, = 0,
dC / dw < 0 T*
s t i f f nes s i ndex ( Ref 9 )
Ot her symbol s, when used, are def i ned i n t he
t ext .
Unl ess spec i f i c al l y expr essed ot her wi se t he
c oef f i c i ent s i ndi c at ed ar e based on nom na l ar ea
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SYMBOLS
dr ag c oef f i c i ent *
moment coef f i c i ent *
t ot al nor mal f or c e c oef f i c i ent *
pr es s ur e c oef f i c i ent
di f f er ent i al pr es sur e c oef f i c i ent
ext er nal pr es s ur e coef f i c i ent
i nt er nal pr es s ur e c oef f i c i ent
t angent f or c e coef f i c i ent *
nom nal di amet er
gr adi ent par amet er ,
hei ght of t es t s ec t i on,
3
f i
n
aer odynam c moment
t ot al no rmal f or c e
f r ont nor mal f or c e
vent nor mal f orce
f r ees t r eam s t at i c pr e ss ur e
l oc al ext er nal s t at i c pr es s ur e
l ocal i nt er nal s t at i c pr e ss ur e
l oc al dynam c pr essur e
c ent er l i ne dynam c p re ssur e
4. 0 ps f
9. 0 ps f
gr adi ent
l engt h measur ed al ong canopy
p r o f i l e
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TABLES
TABLE
PAGE
I .
Dr a g Coef f i c i ent s f r o m I nt egr at ed
Pr e ss ur e Di s t r i but i ons . .
. 27
I I .
Sol i d Fl at and Ri ngs l o t Par achut e Model s
. 30
I I I .
Pr es s ur e Coef f i c i ent s f or t he Sol i d Fl at
and Ri ngs l ot Model s , Uni f or m F l ow
. 60
I V.
Pr es s ur e Coef f i c i ent s f or t he Sol i d Fl at
Model , G = 0. 1, q = 4. 0 psf
. 61
V. Pr es s ur e Coef f i c i ent s f or t he Sol i d
F l at Model , G = 0. 1, q = 9. 0 psf
. 62
VI .
Pr es s ur e Coef f i c i ent s f or t he Sol i d Fl at
Model , G = 0. 4, q = 4. 0 psf .
VI I .
Pr es s ur e Coef f i c i ent s f or t he Sol i d Fl at
Model , G = 0. 4, q = 9. 0 psf
. 64
VI I I .
Pr es s ur e Coef f i c i ent s f or t he Ri ngs l ot
Model , G = 0. 1, q = 4. 0 ps f . . . . . . .
. 65
I X.
Pr es s ur e Coef f i c i ent s f or t he Ri ngs l ot
Mode l , G = 0. 1, q = 9. 0 ps f . .
. 66
X.
Pr es s ur e Coef f i c i ent s f or t he Ri ngs l ot
Model , G = 0. 4, q = 4. 0 ps f . . ? . . . .
. 67
XI .
Pr es s ur e Coef f i c i ent s f or t he Ri ngs l ot
Model , G = 0. 1, q = 9. 0 ps f . . ?
68
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I LLUSTRATI ONS ( CONTD. )
FI GURE PAGE
43. Rat i o of dCj ^ dc*. at
cX
T
i n Gr adi ent F l ow
to dC
M
/ dj X at
DC
_ i n Uni f or m Fl ow f or t he
i x
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-0.2 0 0.2 0.4
x
/
/ W
F ig 7 M eas ured and Desired P ressure
Gradient for G =0.2 , q= 9.0 psf
RAKE POSIT IONS
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RAKE POSIT IONS
o 1
2
A 3
* 4
o 5
v 6
O l
- 0 . 4 - 0 . 2 0
2
0 4 ~ ~
x
/wF ig 9 Measured and Desired P ressure
G radient for G=0.4 ,q
=
9.0 psf
i i
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1.6
1.4
1 2
1.0
0 8
0 6
0.4
0
I
R AK E P OSITIONS i
i
/
/
2
A 3
0- 4
O 5
v 6
I
I
I
/
2
A 3
0- 4
O 5
v 6
I
I
I
t
r
9
2
A 3
0- 4
O 5
v 6
I
1
/
s
/
/
3
r i
I
/
1
1
*
i
1
l
1
q = q + 0.4 qx
q = 9.0 psf
v = 9 0 fp s
/ s
/
11
i
q = q + 0.4 qx
q = 9.0 psf
v = 9 0 fp s
/
/
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I I I . PRESSURE DI STRI BUTI ON MEASUREMENTS
The mai n obj ec t i ve of t hi s s t udy i s , of c our se t he
es t abl i shment of par ac hut e aer odynam c c oef f i c i ent s i n gr adi ent
f l ow. Si nce no publ i cat i on on t hi s subj ec t coul d be f ound
i n t he l i t er at ur e, pr essur e di s t r i but i on measur ement s wer e
made t o pr ovi de a basi s f or checki ng t he measur ed f or ce
c oef f i c i ent s agai ns t t he f undament al pr es s ur e di s t r i but i ons
f r om whi c h t hey der i ve.
A
- Pr es s ur e Di s t r i but i on Model s
The pr ess ur e di st r i but i ons wer e made on r i gi d con-
cave bodi es const r uc t ed of heavy wi r e f r ames wi t h r adi a l
member s f o rm ng c i r cul ar a rcs . The wi r e f r ame
was
cover ed wi t h
h
/ y
- I L - C- 7020 c l ot h ( Ref 7) , and t he model s l ooked
l i ke hem spher es. F i gur e 10 shows t hese model s and F i e 11
shows t hat t he model s had a di amet er of 10 i n and a r oi
of
14 pr essur e t aps al ong a gr eat c i r c l e . One mode l had i nt e rnal
pr essur e taps and t he ot her had ex t er na l pr essur e taps J i t h
i dent i c al t ap l oc at i ons on each model . e ^ur e
c a p s Wl f c h
. . 1 s i mul at e a s ol i d f l at c i r c ul ar par ac hut e model
t he hem spher es wer e c ompl et el y c over ed wi t h t i ght l y f i t t l d
nyl on c l ot h. For s i mul at i on of a r i ngs l ot par af hut e m del
s l ot s were, c ut i nt o t he c l o t h at l oc at i ons shown inF i g11
The cons t ant s l ot wi dt h of 0. 04 i n was set f n
a
I
g
I .
poros i t y o f 4 6% based on t he sur f ace ar a of f he hemf s ph e ' "
Thi s por os i t y f i gur e was sel ec t ed t o mat c h the ge omJ S i c
por os i t y of t he f l exi bl e r i ngs l ot par ac hut e modf l
B* W nd Tunnel Test s
axi al s t i
n
r a n r i
r
h f l T %
d i S t r i b U
^
0 n m
d e l s w e r e
r un t e d on an
axi al s t i ng and hel d at z er o angl e of a t t ac k. The s t i n?
and suppor t syst em wer e t he same as descr i bed
l a K r
f ^t h e
f a r c
?
measur ement s. The model pr essur e t aps we?e i ni ? i a l l v
t hr ee t i mes W t h ^ * *
8 t l n
^ J n S me n L
cnr ee c i mes W t h a r ow of pr essur e t aps, bot h above anH
d l l T i n
c e n t e r
pl ane, t hi s
P
? J c e 3 S e gf ves pr es s ur e
dat a i n 45 i nc r ement s over t he who l e sur f ace nf t h f v , u
For uni f or m f l ow, one may assume that the p r e s s u r e d i s S bS t f '
i s ax i symmet r i c , and the r esu l t s nf
a
i i i di s t r i but i on
' T ^ r F I " t he gr adi ent f l ow i L ^ e S e ^ i K r ^ S o n " "
6
'
s houl d be s ymmet r i c about t he hor i z ont al p l a n e t e S L
gsrgs i s ^^u
^ w V ? ^
1
were tested? S f S ^ S ^ ^ t J ' V ? - ^ ^
12
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8/10/2019 Aerodynamic Coefficients and Pressure Distribution of Solid Flat and Ringslot Models in Onedimensional Velocity Gr
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;
r /
TTrXL
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CD
Z
C
CH
O
Ll
00
Z
o
*
V
O
O
oo
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G - 0. 4 f or bot h c ent er l i ne dynam c pr es s ur es . I nt er nal and
ext er nal pr essur es wer e measur ed usi ng a mul t i t ube manomet er .
C. Res ul t s
Al l of t he i ndi vi dual pr es s ur e c oef f i c i ent s ar e
shown i n F i gs 13 t hr ough 22 and ar e t abul at ed i n t he Appendi x.
The pr essur e coef f i c i ent s shown ar e based on cent er -
l i ne dynam c pr essu re ,
C
n
= C - C
P
d Pi P
On t he f i gur es t he +s * di r ec t i on i s i nt o t he hi gher vel oc i t y
f ol l ow ^ " " V
a n d
t he r ot at i on angl es i ndi c at ed
Y
f o l l ow F i g 12. These f i gur es show t hat t he pr i mar y ef f ec t
of t he gr adi ent i s t o r educe t he magni t udes of t he pressur es
Thi s i s par t i cul ar l y not i c eabl e i n
the
di f f er ent i al
P
pr l s s ur e
C
p
d
'
e 1 S mo r e r e d
u c t i o n wi t h s t eeper gr a di ent s ^
m "r ange
i n
Pr es sur e di s t r i but i on f r om t he l ef t
t o t he r i ght s i de i s qui t e s mal l . On t he s ol i d f l at par ac hut e
t her e appear s t o be a r eoccur r i ng unsymmet r y of C measur ed
at t ap l ocat i ons of 0 and 180 . Ot her unsymmet r i es ar e so
smal l t hat t hey ar e not t r aceabl e wi t h any degr ee of cer t a i nt y
On t he r i ngsl ot par achut e no unsymmet r i es can be det ect ed
One may assume t hat t he canopy s l ot s equal i ze t he S e s s S e s
t o t he ex t ent t hat no unsymmet r i es ex i s t or ar e L S smal l t o
be r ecor ded by t he exper i ment al met hod us ed.
The dr ag c oef f i c i ent s obt ai ned by i nt egr at i ng t he
pr es sur es ar e s hown i n Tabl e I . For t he u n i f o mf l o w E d i t i o n s
t he aver aged pr essur e di s t r i but i on was i nt egr at ed f or "
d l t l o n s
gr adi ent f l ow t he i ndi v i dual pr essur es obt ai ned at t he angul ar
of
S
t he c i r c ul ar
U
f l at
8 h
T
t h a t t h e
^a g' c o e f f S f e n? s
and t he r i ngs l ot par ac hut e ar e s i gni f i -
c ant l y smal l er i n gr adi ent f l ow and dec r ease as t he s t f eni t h
of t he gr adi ent i nc r e as es . s t r engt n
16
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1.6
A
A
A
1
A
A A
A
C p
A
A
\ A
A
L
c
P d
O
D O
o c
o
0.8
o
O
O 1
D O
O c
c
P i
q =4, 9p s f AVER AGE D
r\ / i
0
-0.
8
-0.4
0
0.4
.0.8
s
0.4
a
n -
3
D
c
0.4
a
-J U
u
t
P e
J -0 .8
Fig 13 Pressure Distribution on a
Solid R at Parachute Model
in Uniform Flow
17
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32/90
R g 1 4
^
r
f f
u r e
D is tribution on a
f o T
G
F
% / p ^ %
f
M o d e l
8
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o
I.D
2
\
0
r 2
C p
a S
a a
2
H
c
P d
0
r 2
C p
o
0
1
n r
O
S 6
0
6
a a
1
C
P ;
O
- 180
0.4
A - 135 ,2 25
9 0 \ 2 7 0
0
O - 0
a - 45 ,315
a - 9 0 , 27 0
-0.8
- 0 4
0
0.4
0.8
-HA
8
J a
A a
e
*
6
a 6
a 4
a
-0.8
C
P e
F ig 15 P res sure Distribution on a
Solid F lat P arachu te Model
for G = 0.1
j
q = 9psf
19
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Fig 16 Pressure Distribution on a
Solid F lat P arachute M odel
for G = 0 .4 , q =
4
psf
20
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1
.6
o
1.2
ft
C
P
0.8
0
8
8
6
1.2
ft
C
P
0.8
1
a
a
e>
a 2
c
1.2
ft
C
P
0.8
O
0
XT
R S
a 8 a
6
1.2
ft
C
P
0.8
a
i
^ 8
o o
A
A
s
o - 180
0.4
A 135
J
2 2 ^
- 9 0 ,270
o - 0
a 45 ,315
D
- 9Cf ,270
-0.8
OA
0
0.4 0.8
o
A
o
Q
2 9
4 O
fi
1
H
8
s
n
ci
A *
-0.8
C
P e
F ig 17 P ressure D is tribution on a
Solid F lat P arac hute Model
fo r 6=0 .4
j
q = 9psf
21
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36/90
F ig 18 P ressure D is tribu tion on a
R ingslot P a ra c hu te M o d e l
in U niform F low
22
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Fig 19 Pressure Distribution on a
Ringslot Parachute Model
for G = 0.1, q" = 4 psf
23
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F ig 2 0 P ress ure D is tribution on a
f
R
7
s , o t
Q i
P a r
f
hute
p
M o
d e
,
24
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39/90
&
o c
o
A
D
E
0
a 1 2
C
P
^0.8
ft '
* ft
0
a 1 2
C
P
^0.8
C
P d
a
0
a 1 2
C
P
^0.8
-
O
b o
O c
A
O
A
D
t f t
8 a
a
0
a 1 2
C
P
^0.8
A
b a
3 c
CP,
o - 180
0.4
A - 135 ,225
- 90 ,270
0
o - Cf
a - 45 ,315
- 9 tf , Z 7 0
-0.8
-0.4
0
0.4
S* 0.8
&
0.4
6 d
&
0.4
8
i
1 &
ft t
ft
-0.8
C P E
F ig 21 P res sure Distribution on a
R ingslot P arachute Mode
for G = 0.4 , q = 4 psf
25
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F ig 22 P ress ure D istribution on a
R ingslot P arachute Mode
for G =0.4 , q = 9 ps f
26
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o
Id
cr
O
u
f -
z
2
O i n
Ld
^ O
a f e
n
icr
i
no
O
O
a>
n
icr
i n
m
LO