+ All Categories
Home > Documents > CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder...

CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder...

Date post: 22-Jan-2020
Category:
Upload: others
View: 0 times
Download: 0 times
Share this document with a friend
85
AD A131 8 HIGH REYNOLDS NUMBER CYLINDER FLOW S GOrES U) ALABAMA A / AND M UNIV NORMAL DE'PT OF PHYSICS AND MATHEMATICS M C GEORGE 10 JAN 83 ROSS 4-81-K 0479 UCASFIED F/G 20/ 4 L Emmmhhhhhmhlm
Transcript
Page 1: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

AD A131 8 HIGH REYNOLDS NUMBER CYLINDER FLOW S GOrES U) ALABAMA A /AND M UNIV NORMAL DE'PT OF PHYSICS AND MATHEMATICSM C GEORGE 10 JAN 83 ROSS 4-81-K 0479

UCASFIED F/G 20/ 4 L

Emmmhhhhhmhlm

Page 2: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

j 3.6 __

I - L 2.2

1.25 ~D~ I .

MICROCOPY RESOLU TION TEST CHARTNATIONAL 8BURE AU OF STANDARDS -'196 3

Page 3: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

II HIGH REYNOLDS NU[1ER CYLINDER FLOW STUDIES

II ' PREPARED FOR:

I, OFFICE OF NAVAL RESEARCHi UNDER CONTRACT

II SFRC NUTER N000I4-81-K-0479

I |

I

-DTICELECTEMMIAUG 8 98

I

Department Of Physics

Alabama Agricultural And Mechanical UniversityI OFFSICEO STATMENT A O Normal, AlabRm 3 H62

A ppioved, fo, public .. .es, (205) 859-730e8 83 08 05 0 46I UNt ibt- UCONmRtd

II_ __ _ _ ii __ _ __ _ __ _ __ _ _I _ _ __ _ _ ill _ _ __ _ __ __i _ _

1 +mllm -. _

... ... . . iii ii . . I Ii ii i i I ll~ .. . . .

Page 4: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

Accession Fir

NTIS GF10,flTIC T,"MUnmnnx ..

i J r i tut i-n/,-

Avni i,:",! lity cojesA v a i l w n u / o r ' .. . - +

Dist Special

HIGH REYNOLDS NLHfBER CYLINDER FLOW STUDIES

PREPARED FOR:OFFICE OF NAVAL RESEARCH

UNDER CONTRACTSFRC NUMBER N00@4-81-K-0479

DTICAtELEC;

DEPARTMENT OF PHYSICS Wr) 8 1983

ALABAMA A, & M. UNIVERSITY -NOP AL AL 35762 D

ISTATEMENT A

'I ,) public relea@OI I' ri:'~ ' n Unlimited

Page 5: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

%ECUP, ITY CLASSIFICATION OF THIS PAGE (When Date Entered)

READ INSTRUCTIONSREPORT DOCUMENTATION PAGE BEFORE COMPLETING FORMI. REPORT NUMBER 2. GOVT ACCESSIONO. 3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED

Final: 5/81 to 10/826. PERFORMING ORG. REPORT NUMBERHigh Reynolds Number Cylinder Flow Studies

7. AUTHOR(*) S. CONTRACT OR GRANT NUMBER(s)

M. C. George N00014-81-K-04799. PERFORMING ORGANIZATION NAME AND ADDRESS 10 PROGRAM ELEMENT. PROJECT. TASK

Department of Physics AREA a WORK UNIT NUMBERSAlabama A & M UniversityNormal, AL 35762

II. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATEOffice of Naval Research 10 January 1983Department of the Navy 13. NUMBER OF PAGESArlington, VA 22217 81

14. MONITORING tGENCY NAME & ADDRESS(II different from Controlling Office) 15. SECURITY CLASS, (of this report)

UnclassifiedISa. DECL ASSI FICATION/DOWNGRADING

SCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Approved for Public Release; Distribution Unlimited

17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20, If different from Report)

IS. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side if necessary mnd Identify by block nuimber)

Cylinder Flow Boundary Layer Flow TurbulenceWind Tunnel Data Roughness Effects Cylinder Drag

ABSTRACT (Continue on reverse ede If necessary aid identify by block nLmber)This document contains a description of a series of wind tunnel testsconducted in the NASA-Ames 12-foot pressurized wind tunnel. Experimentswere conducted on smooth aod rough cylinders at Reynolds numbers thatranged from(!05 to 7 x 1064 Roughnesses were obtained by using four sizesof wire mesh to cover the smooth cylinder. Sample results are included, butthe complete data set is the subject of a forthcoming report.

DD ,OAN73 1473 EDITION OF I NOV 65 IS OBSOLETE 1D/N 0102LF.014601 SECURITY CrA[l

'gol] l " 0

'bW -MJll'lrAE (Whiam Date Ent~ei)

Page 6: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

FINAL REPORT

HIGH REYNOLDS NUMER CYLINDER FLOW STUDIES

PREPARED FOR:

OFFICE OF NAVAL RESEARCHUNDER CONTRACT

SFRC NUMBER Ni 014-8j.-K-0479

-1

h.

Page 7: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CONTENTS

, TEST SETUP

' RUN MATRIX

. MEAN PRESSURE DATA

, INTEGRATED RESULTS

* BOUNDARY LAYER SURVEYS

, DYNAMIC DATA, TRANSITION EXPERIIENTS, CONCLUDING REMARKS

---2-

Page 8: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

ra 0 0 3

IC thS i

,a 0.0:I~~ica x

daE"C . . -(A. E"*,,

zd 0 1A .gui oow - a~ a. a. 0

0: be

Cduc

t a.-j & r4.

:1c & .9

0a a. Cd 9CL-

- C,

* . 0 04-11

Cdcc; nl~ i.

-. a.

.19L

0T, 4 1-

Jta

'a~ ..9 1 o ui

Page 9: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

w

0 'l

-jr ) w ~v--T I T F- -j

z0 -j1

0*-~u

'-t

PA0

W4

Page 10: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

w

i ix

wL)

w

H i I

__ fi E4_ _ C-)

0c

-5-

Page 11: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

~-4 -4 V. -4 -

- x

LU .A

0n cDc)

LU C:) C) kow l % FW0

;7 C ID -

WUw ;C;cXU

Page 12: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

'IIt

\ ,,--

\ - /

"-!/

7 /

-. ,Figure 3.6a Schematic of BoundaryLayer Probe in Cylinder

-7-7 /

Page 13: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

----------r---

gure 3.6 Boundary Layer Probe

.1 -8--P.

Page 14: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

AMES RESEARCH CENTER

Aeronautics Dlvis ionExperlmmntal Inveaigations Branch

Model: FAi P, Teat No. 224-/2

TABLE I - Key to Configurations

Cong COmounain Nocation

S SMOTH L2YLIUEP +- FRLE

4 Z- C~L I AJ 0L 1 NO. , 65MESt "- L I : "

3 C LlNK N0. 0 M E H C PI E

31 C 'YL.I/L*- N0 . (O MAESH S(L ± N+P,-

2 C V LIla7.k -- No, 2 0 M eSH 5SR REE N?/ CYLI--.P + No. 25'0 MESH . : eL,

-9-

Page 15: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

0 L

0 0

CA W t

T'--

Cl) '4- '4\ \

U0 NQ ~

T- C.. cot

7- 11 0' 0 - 1

.-4

-i C'JQ

-T- C\J CN.I~x. (I)0

0 Ha -

__ __ coC\J c4% Z)__T- 0

o C:)

___ ___ ~A.CO CD) o__ _ __ _

__ _C\J CO (D

Page 16: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

PW po ow 9- 4P P4 - 4 P4N N N P4 4 - -4 . s P -0 "

U.. W . o

.- -w o -a)w f.- U vNw v I.- ulw Q- J Nt'J NC.

P- 4 1-(' ~ - 1- c NA P1

* l )* % *L * *r W0 0 0l 0 0tr U 0 e Sn 0 0 * 4 l l n L W q i , W N W

U.~- f00nW4" % qa

)LJ 04 %." a- LA -- C- P_ -M 45 -- ."F --

vj I- M

:.at;e7v)a .- 4 M Go f4 a -a m o r- m ~ N enL - 0 w ' p.* w -U!- IJ C)0 0 1 9 0 4 0 0

'I 'I- ('" ;$ : a Qr V N DW f - 4(U W X , ,C c p 1 4 1P- 4 ao - )- l nLn"W C - Q-

-1 L C c t rj O " MU % P c c a %C Q4)P.r - W0 C rUCL tj a 'q c 7 4p o >->1>-

Page 17: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

K- 4.... W44 p-4 pPde4 9. V4 -44

0'- 44- ?.? C4-w4 o t C m m Cj m C r. f "

Ii W pu L ,% -U'&L' n i in.U t I k W% v U-&1 U i W% , L'.U u0 U ill W, .iLfL

I. 4 UII,% ,M -tC 0 1%r f neI NI % w" . 4P40a 009G ,0U. (' 0 - .0O r- r ~ a j P- p-( r-PUF f -I-Ff -. 1 0 1

Iuh in Nfl r S PO M r Co f.~-.- w t'C a"r 0a0N N

N 4 ~~~000 0 %04 0 0 0 ,09000 0 00 C 0 0%0 %0$c 0

00 1.4 11 q3-: 00 00000000 09 00C 00000 00N N 04"N fN NN4 NN IV'. "N1N N N N N

4.) so * 0 0s sAl C3 cfO "4 W ). A 4 e ' &w- MI, In% v. %04 w %t -we

i- r,' -C 't0 F*O' 0.G% a N % , 9 ,0CO 'Orf-- ma cW 00' 0 0 0e-s aN t0.

wq C3r wP4 00C 00Q0 QO' 0 C 00 a 4v-m-r ,U ~ ~ u Zr --4 4-~- -O F. o 0 C0 000 0 g oc a o

" F 0Irl m cc r 00 0 P. -4 p - -4 0

or oN 00 00 CC 0 P4 CC 0CCCD 0 00 Cr.0 040. -ly nr' '0.0 .0 . u'it k1 t V", Wor %(P.w )wI r

-ic.. 11 r 1 l r -4m In- f# 941 M-. CC~ Cnf.WCjM %Cr L~~- 4. -,4 . 0 00aC;8 0 , a 0 0 60 00 0 0 00 0

LL 00 00 0 # 0 a I0 0 0 0 0 a 0 0 0

4r! LL L 'c

LA -C - -a C. --414 -- -- .4 K- - K4 - a 4q 4C 42.

0. 7

0 C

Page 18: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

I I

NI-f N- r'"' CIN t u- C-4 C14 CV4 N4

uj' lo U- IW V0i ,f nI SY

Ii .dCC '00 .. 0d0CL cc. "d,'~N rJ'F~E I t %

z --N wU 0mz 4 0 0Q A%

LL U- N' Ui-iCN %'P-t G .t t J i O c naP- ".e00 0a .. 0 0 Q00

m P- r- 40 w 91 4; *; C4S ,' oUNc D tQ7c t

A ~ ~ ~ d N. :0 P 0 a :-?* um= 0 M ..40 .4o 49"4. a4 a 0 0 4r r o

KGn m -1 0.4 4'O'(7 a O O ~.4

-o 00 c'0 00 No- - -0u M 40 0'.4 UNtAc - cL.JL

- Nl U x- U 0 4.x > -d fn at4q N -co cq -M

>, (oN 4(r N

!U ur-~ceM MO U0 40'L'

Ca. a,'J%4e% eNO 23. ITT, -D "4.- 40c0 0x-T4!41%rV) Q 3:> >4 - "

V) p p-Z %C ]0 6 0 M.- Go *y OD a0 00 101 0 4 C 0a~". t~ oj O 00 o r- 00 004 0. Ma L V I - V r. C- .0 a W n r 1 CD r-p- F- O P0 MM- O %99> 1 'L

't U' 't % P.4 >~ ;) 44 04 44 *VI#) 7~- z 4r CY oo . 00 *0 r 0 p 0 0 ** 0 * .6 *

w4 U.. W% %TiI4..'V7 V) 00 -.4 > L o >o > M, In N l It 4 kNI oj I. P- . 0 9 -q 0 0 0 0 0 9L.;. 6z z x I t44Q 0 C0 c 44;4; 4; 44 4; *4; 44; 44 40 C

.4 L U

w' c l .7- 30 ) - , 0 0 - Q4" "40 4 )1. )N-4 )N-4 c" cc. "

z IL;4

I cm4rI 0 U W> w 0 w It U0 WU'l0 UIA l% N r -uw'w rN

Ir -- d -- pd W-r w w ' " rrr

IL

I - 4''" 4 c" 4 CJ (I" ~ "

CrJ fri,:rCM. - I-Tt or t 10 e e tr , 4 L0-. a:C '.o c cc g io g U-u r0 0 0 4 0

C"P4P - -

Page 19: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

q If I rU nW 9W % t N V

4 ac 4; * 0 0 0 0 0000*

t~00 00 00

a, *u'- .0coC

-j 1*--~ 00 %n Qk .O114 ~~~4 (n P- cc kn ca .4 t V

4001 tn r- N z -4InW& (j Nr-uI 0pJ U o

V"~ V 01 p-uie--c - - ff; IO(10 LIM J c ' -ool '

1>1tA 9- N C%~C~ g', 0@4aw cr-W

LL I 1 ^@ . . UQr UJ- m t4 Ie cI r

-9 U 4 - 0 0 0 40 0 a

T .xdO a .% oa U,0 oc q (r>-) t 4 %r' %t %t r 0#

10 rn p. CI4t C* 01'0I a x I C -6 C, -1 % 'C (-4p NC,4

i1 -I a. 7 .4 v -

2' p4

C

P-- -r - - rl cr C,

who.

Page 20: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

cc w 00I w 0ow.d1- P0.0m0

NC% rNNN CC CO cc.N~e4N06 0212 00 Sc o

I .UN -4 ' N0 NQ .9. -CV CQ

*1 A Al * O N, ~ ~ l . r

L6 ~ ~ ~ -00 O .r-F. 4Noa.4 '0 . Ia. '0% oll I -N

1 j m ir. Lm ON C9 0 yc0 W, LA *It0 C6' 1; Ao.011* . ;N e 4 4 .. m0 14 SO S

O'Q'~00 N I 00 0% 00CO ) 0- n o 0 4r CI0N -q LA m' In NNN

N. Cp 4 m4 . 4 , 4 40 440 l z. 11n 1-0 .04 4 41 1 N, 46 4 -

134 z U.04P- c

r"- a er% h 4r- u-t."1U. N'NM 4C~.. CWI m ,n 4 m Q0- " . q-.

%A "S do~m~ ( '4'I4~WI ~ ~ 4 '40

I~~ ~ 1-i fl

Page 21: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

c, m- .4N~-~4. 4 p.4 . 4 .4 -0 g4 P 4 - p4 P4 P14 40 4 0 (4 11 4

bw 000 00 00

LX e. a 0a 0 >*** * 0 00490a0044

criN Q C, V- p'N --t M 4 M d 41 440 N - N*10-4~

FL; - ao, I- -r- P.O ca Go0% g 00 %0 r- p f. P P - 0 i 0

In io M LJJ PJO in .4~ .. 4 0U1%L '0- d ' &A* P40'O "4 L I

IN zi 7) 4!d 0 .. * . aS 0 1 t0e , 9m

V P-' > 1 t *.-t n r- 00 nw eVC .i -o' ON W fl- -0 - N C A 004oo.4 004 -4o. .qWC . 4 .4(1 (n LA

i Z .4. 'no 0 0 0 0 a . 0N Zi <1 w~ CY %Q1 ZC W~ 0i' 0 LA' 0- -4 v-~ UN '0 A n (n (N .. i N Q0 r. " 04 P'- w '0 UIA

3r s4 .44 -d -*~ 'ON4 4 4r P

- CO 1Ci. MP I- -4 .00 4 c go 10 0'i 4i 1 N - r r rJ ?40M0 4G. C U. 'a. 6 * S S*0 0 00 &O 0L.L 0 cr cn D00- ( 9~o . -4 t; jOP! D C 4 U ' P!C CZIr W P "'D %Q N en 00 N

-e!,U-1 - I I U)I. 4 Si1 -C .4 N4 0M xCUNf t1 C 0-4jN .N .4%0 A C m

0 z!CC ) Vl i'. C T N GjV, CD m - '- P0.r 0 a-0 C 0N'rw-C f-U r W

O. uj I -- D . . 00 0-060 0 o 0 * 609 0 0 50

LM LI) X W1 1% a Nm N00 a C a. W44 zz 1. 040 cc c cc0 wP4 N NX (WZ 1 I D 0!400NIP- F4'P.LA '.0- %0'IQ Q'G0 f %D~' '040 P. %0 1-'0 W 0I:wj 01C'04 *" ,t t 4* 44 4 -r -r -t*4 4

4A .1y. C0tN N N I'N N r N N N N N N N N N Noz-a- z o"o0 1-o 00 o 00 0 0 0 0 00 00 0 0 0 0

C1' WCU LU LL, I4 7 -j ' 4 0001W1 22 0.. 0''~~a 0 )0-

u, - 0 wa N aza'44444 I 49.4 44 44. 9. M.99 w- c- 44 d 4 49 449 me

Lj L -4ftN NyN MN N N mN N NN f j"NN NNNNN Nm NN0--I

IU U

Z. fI - CLav- N1 f 4 ,0 p4 N Mt04 ' 040 Q 0 4p 04p N "040 f r 4 pQ mn. L)- 0F -r -P-r .- F -w = wc M D0 G .V gQ 40Crf P ""P 4 p or *04VV 4"0 S4N

Page 22: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

uj

c. I

0L a- Nl-0~Ou r NI.p-Ic .9 P go Q a ns 0 UUP. wo m owN9%

uj rq -4- U p - 6A0i'0 0j CL 01

N co 2. go N 30 C . 00 P") -ow ON w t 10 % )0 N C) P 0. Iw 4C M ~ 0- 0-

LAJ

'a' 3% 0,~~Q N4 90 Ntr~ 00 ( Vm 4cct 0A 6m

i-I 4N 4 0m0 NN r .N (I P co(n a,

f-,tN> .4 V.4 C' N e Zo v -4 -

ucx Z w U: 6- P- Q CD * v ca

U- aIU Z. s-N

*'1 I-- cc Nre , A z

W ?*- r'mq(' N- Ix l w O OwW b * 0 0 4 -w ,a m0

u m mj o. LA a l*o In

)X V)L. U4 10't U'U 1tIU inO NC P. 'C.l U(vC flU )I.u a)N VI,. s-q s-I

30 OO 0 .1 -I- 4 %-i It N Ivi > (\'C'E N400a NN N N N N N N N Na NN

x Ir

tI'0 c 0 o c44 L. u -17

Page 23: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-. P -W -. P4 9- -4 0.4 4 pwP4 F4-4w - 4 9 4 - 4 -- -4 NN N N

w i4.LL ,L"00 -0V " 10 . p0Cccoccocco

z **.* : 0 on

r- ' m ~ QDI 0 4 0 C, C0 cc iLA~ '0. fl-

4 4 r .- .-4 No ry()r : ,;,C% -W )UN wU4 O

as 0 4 .. ~~. 0O

N > wrW4 4 N .4 N' N0 -4 P-4 UN-4 00 LAS Q9 wCY CO 'td t04'.J U 0 N N "P U"~ 00 n '-4rU-% OD -Q0 0% 0 0 '0 0 '0 0' 0 0' Y C a rq P N N N N4C 4.4

44 N m-Nf~ C * * 0,0 V% o a -, ( N fr~ m c

N ~>>2-, %Cul~ rn ar- 0MW4 - 9 m- .40 a .N m N m N

@0 U00 00 00 a00 00 ) 0 0) .'

K L :, 'CI r- m -l CO'D '0 emr mnmN CM Q- N-C4N 0. q464 e-4-Os V .4 , v- eeIOw u > -a wrln1 0C % twC 0-O' 0%09 00 NNN N N N 4 449

km I. W, aDs N fnC NP

Ini4 V, CO- 4% u0 1- m WNr 0 w O w v4 alw fn ' C t- an P m mqz T. z ~ cc~'('u cc m!4 0f' f"Cn 4;4; 4 . 4; q ;

CIgf r.- p- r-~ C .4s mN f- In~ 'nr- O'w. OU4 *pw.. tv~ P.O W%~ P.O 0n W4 o&A Lm N (V NN cc. 00 00 04 P4 .4 00 "w4 N4:WL.Jb- w4 w4. .o 1o ac so s 0 * os *4W iL z 2: 00 00 00 at 00 0 0 0 0 a

'4 4U.W W u

46, V% In C" Cf" Im in~ 4 IngW In e m v .aLuj - )O 1. %0 'OO 0 %a UW I In~K 'W W% wWn WN Ul% W

CL m M ix cc a0 a 0 0 a00 00 0 0 0 0 * 1n0~ . ~Coo 0 ;0 ooCOCOO cc0 0 00> >. >

LLi

r..

V4 U-U l M 0fIf " - 0F - - 4r P 4v 4 v qVu C;J riC%( (-

LLu

s. C )v- - - - 4 dvWo6- . - 0 4v4wdP - P W r -18-I V .4 -A--~ ''~.~ ' -jw wA' WO .N .nlW 1

uj iv t&\

Lr

Page 24: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

0-. V4 V40 4o .I 4 O 4P P 4- P AV 4o 4

In 4%w n 0 y 0T - UM W% a- -- P-o 4-~d Il44-- -

so0 0. .0 '0.z0 '0 0 Q a:0 QI '0 0w Xix0 c

I4 dK -9 O'- 0c It' ' a'

Cato >C0 ZP 0 C0 a >0 0 a > aOC >4 *S 4

Nt t 0 - 00 O0 '00 * a o 0::0I0u.tJr9. II 4 .4 4

a co P%. Pft . 00 O cc(c i-.4 -4oA r4 0 a0 0 0 Q% 71 0 C

Nj to t- 0Y 00

j I.J 0. CO " -.47.I ICY )I)." W 10 Ni U . N -)1- Ift -4 crULO0%

VA *)-1 -9 130 0 *0 04. . .0 4 0 0 0

1 -c %gc tcc cP ?-I fI a, p-4 C, I--~ W a WN dU ?N-. - 14 4t41 -r' v%4 -ao ocoac ) m -r 4 omr

w.) W 4u 44 4 O '''UiN'! --- c m. wo lo m

00 >O-4 )w 0P owN u -Z ur)I r4 @ 0 IN'O u N

11 r f"N w4' -l f (Tcc-r I)P- 44W In4." ' WW 'OW f0 60accwU o w wt U w4 v7'0, 0

CX W Z 0 a *g 4 . 0 000 1 0 0 0

co 0 - Gow O w IM WO f*- P- P14D- W N W @m w o-#-4 - & 4. 't w. 44 *'t .. -t w -t -P -*4

V)a %4a E.#x C, c ,, N %jN NYMN NI. N r N NON N N (4 NN9- 0 0.4 -it 4 :: a * 't.*. aOo

x cc 0 > >0 :x- 00 00000c c-d 4U Ou4 0" Uu

co ** 0 00 '9 *. 1-d4 CL 0 u' ItU I1" noW OO tUO w'u'U, CU" U' n o ouW 01 !l

?- j C94 C -4 C - VN NI' 9'i-4 C e4 IrvE V-0 21C' e C N N INN N

cc U. f-I O .4 .- - u-g " -a. u. -.4

- -4 . -

Ni Z- f" mIei nf n(nt n tv( " e nc Nm m

0 QN u

1 U.

N p fn I -41y -'r - O I'Cr o 4 Id, r- 00~ n c r vi C-) '

C- m N N v I f I -rj1- j 4rC C1 '-

4

Page 25: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

A

*: : :*: I::, * *1 "'I.. ..... ..

o: : -: -. . .: -: -. a ... -....- ..

..... .. ...o3 .. . . . * . . . .

.. ... ..-. - - ....-.... . . . . . . . . . . . . .. . . . . .

........ .....

.. II I .. I....

.~~. .. .. .. . ... .. .... '......... ~~~~- .... :J ... . . .I. . . . . .

...... I. .. .. .. .. .. .... C.. .. . ... ... .......... ~~ ~ .. .. ..... ...

4. 43

Page 26: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-. 0

DI >r)

p 4 : ;. .:7 ,. ... .. . . . .. ..4

. . . .. I . .. 1 i t

* ~ ~ ~ ~ H .. I.I: 1ri ,"9W-

.. . .... .3 W

I+..~44 h.s. 4. tit4 q..&

g ~3. ~ II~ j~ 3

.. .. ..

.... .. .. .

.. .... ... ....:.. .......

.. . . . . . .

pg. .. ..... .. 4F ...... .. O

.. ........ ~PS ~ -.. . . .. . .

0. .. .. ...... ~U .. .....

.o. . . . . . . . .. . . . . . . .. . . .

iH 'iul'-2 . ..... ....

Page 27: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-2.00 -21 -200-31 4 0.0 0.1 1.0 Ls 2.0

...........8. . . . . .

. .. .. ..0 .....

.... ... ... .. ... ... .. .. ... ... ... .... . . . . .

.. . .. . . . . . . . . .. ........

.. . .. . .. .. .

T Z0..0 ....

.... .. .

........ . .. .

.. . . .......

. ........4. ... ... ..... . ::.... ... ... .. ... . .... . . . . .... .. ... ...

.... ...................... . ..................

Page 28: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CPIU

IS -.0 2.5 -2. -I. -10 -. S .0 Os 10 L 2.

. . . .... . .. .. ... ....

.. . . . . . . .

.. . .. . ... . . . . .

. .. .. . . ... .. .. . ... .. . . . ...

t t .2 .0. ~ ~ ~ : . .. .....

.. .4. .. . .. ... .. ... .. . .... . . . . . . . . .. .. . . . . ....... ...

.... . .. ... ... .... .. ... ...I0. . .. . . .

.... ... .. ....... ... ... ...

... . .. .... .. .. .. .. . . .. .. .. .. ...-.. ...-

Page 29: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

.*.. . .. .. .. . .. .. ..

-,*,:I -- -: ,e~ - -. :

- -. .... ... .... . . . . . . . . . . . . . .

0................ .... .

.t ... .f.. . .

.. . . . . . . . . - - - - - - - -. . . . . . .

.. . . . . . . . . . . . . . . . . . . . . .

......... ..

.... ~ ~ ~ G . ..... .

-.2.. 4-....

.4,. ... ..... ... . 1 .... ... .

Page 30: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

*I -2.0 -2. -2.0 -IIS c1. -a.$ 0.0 0.1 1.0 1.S 2.0.. . .. ... .. ..0. .. .

.. . . .

.. . .. . .

. -.: :-a:::::: *:::*:-.... ... .... .. ........ ...

HH ...6 .... ... .... * .. :i :: .. ......

........ 4

.....-tt . ....

... .. . ...

.... .... ... .... .. . . .. . ... ... ...

'H. H 'H0

i-H ! H ! : -!i! ... .. .. . .... . . . .. ... .. .. .0

.... ... ... .. .. . ... ... ... ......... .. ... ... ...

.. . . . . . . .. a.. .......4. . ... ....

.. . . .. . .

.. . . .. . .... .. . .

Page 31: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CPIU

-3. -1-.0 -I. -1. -4.1 0.0 0.1 1.0 IIS 3.0aN

... .. ... .. ......0.. . .

.... .... .... . . .... ... ....

*- * ! . l ii. .. ........ .... ...

. .. .. .. ... . . .. .. ... .. .. ... .. .

.. .. . . . ..

i ' ii. H .; . . . ;. .. . .. 4 .. i 0awi l;-- : .... :... . .

.. .. . . . . . . . . . . . . . . . . . .

.. . . . . . .. .. . . . .

.. .. .. .

Page 32: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

- 3 3l -3 0 -2 3 -3 .0 * I . 1 . . 9 0 .* 0 .6 1 .0 . 3 .0

. ... . ....

.. ..... ..

I.. ... ....

.. .. ....

...a. . . . . . . . . . . . . . . . . . . ... ....... . .. . . . .. . .. .. ...

.a. .... .... ....

r7 = 7.... .

.......

Page 33: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CPIU-23 -2.0 -l.S 1.0 -O.S 0.0 O.S 1.0 Ls 2.0

...... ....... ......... ....... ... ....

... .. .. ... ..... . .........

WH i ...... ....

.... ......... ... .. ... ......... ... .........a ........ ......... ......... ......... ......... ..... ....... ............ ......... ... I ..... .........i4 ....... :! ::::::: 1: !......... ..... ......... .................. ....... ......... ...... . :::: - ::::::::: :::- :::: ::::::::: 11:.......... .. .... .......... ...... :.: :,:: ::::: !'" ll" !o ... ........... ......... .........

......... .. ... ..... LA....... .......

... .. ......... ..

.. ............... ... . .... ......... . .. .... ......

. .............. .......... ......... ......... . ... .... ......... ......... ..... .......

. ........ .. . ... . ...... ......... . .

. ........ .. ...... -- ------ -......... ..... ..... ......... ......... ......... . .

......... ....... ...... ......... ......... ......... ....

. .......... ......... ......... ... ..... ......

...... ......... .........

. .......... ......... ........ .......

....... ... ..... ......... ... ...

... ......... .... .................. .......

......... ...... . . ....... ....... .... . ....... ...... .. ..... ........

A 6 -- - -------..... ... ........ ....

..... . ........ ........ ....

......... ....... . .... ......... ......... .........

......... ........

. ........

..... ............. .... ------ - ... .... ... ... ....... ......... ............ ... .........

-------- -- .... ........ ............... ............ ... .... .............. .. ........ ........... . ......... .

......... .......6 77;.. ......... ..... . .. .... ....... ::::: :::::::::

.... .. .. ... .... ... .... .. .. ... .

.. .......... ..... CY)

......... ....... ............... ... ..... 14

.... ....... .. ......... ....... ...... ........ ...... ....... LIA

.. ......... ..... .. . ... .... ..... ......... .. :::::::-O il ........... .... ..... -

....... - ------ 4.-....... ....... ......... .......

......... .... - --------- ---- :::::- -::, :: ..... ......... .... ... ... ...

........ ........ ......... .....

....... ......... ............. ........... ...... .... .. ... ......

7'0 : W.; 7:

. . .. .. .. .. .. . .. .. .. ......... . . ...... ...... ...

... .. .. ......

:qq

. ....... .. ..... ......... ....

Page 34: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CPtU*. -. 0 -2.S -2.0 -3.1 -1.0 -0.1 0.6 6.5 l.0 L., 2.0

.. . ..a. . . .. . . . . . . . .

. ... .... ...... .. ... .. ... .. .. .. ... . .... .. ... .. ..

.a. . . .. ...... .....

..8 . ........ .. .... ....

-- --4- .....

a . . . . . . . . .. . . . . . . . . . .

.. ... . . ..

. . . . . . . .

. ............ .. ... .. .... ....... ...... ... 0.

.. 4...- ...

. .. .. .. .. .

.a . . . . . . . . . . . . . . . . . . . . .

.- .. 4.. . . .. .. . ..

.. . . . .

......... .

Page 35: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CP:U-3.S -1.0 -L.1 -3.0 -9.1 -9.0 -0.1 0.0 0.1 1.0 L.1 Le

.0 . . . . . . . .

.. . . . . .

..a . .. .

.... ..... .......

. .. . ............ .... H HS.. . . . . . .

.. ... .... . .. . . .

a . . . . .. .. . . . . . ...0 . . . . . . . . . .

.. . . . . .. ...-...-.

06.. . .. . .

a ... . . ...

.. . . . . . .

.. . ..0 . . ... . . . . . .

-: :=

... ..a.. .. 41 ,:.. . ... ... ... ... ... ...

iaii ..... 4.--iH i .++. iii- i .... .... ....

.. .. .. .. ..

.. . . . ... . .

...... ...... -3.... -

Page 36: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

*l.S -3.0 -LS -2. 1 S -.0 -0.1 0.0 0.1 1.0 IIS 2.0

... ...... .... ....

.. .. .... ...

.. ...8. ... .... .. .

.... .... ... ... . . ... .... ... ...

. .. . .. .. . ... . .. .. ..

:.iH H ! i i .. .. . . .. ... ... ... ... . .v i H H

. . .. .. . .. .. .. .. .. ..

- . .. . . .

.... ... ...... ... ... ... ... ...... . ... .. .....

. . . . ...0 ........ . ......

------ -- .. .... ........ ...- . ..

.... .... ... :_: ... ... ...

=.-:* -_-::::*:*. ... 3..-

Page 37: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-3.S -1.0 -2.5 -2.0 *I.5 . -0.5 0.0 0.5 1.0 L.5 2.0

.. ... ...... .. .. .. ....... ..

.. . .. . ..

.... .. . .. . .... .... .... .. .....

.... ... ... . ... ........ ... .. ... .. .. .....:. ... ...... . ..... ...... . .... .. .... Hii;0

..... .... .. .. ... .. . .. .. .

.... .... .... .... .. . .. 0

:--*I-a . "-.... . ... .. . ::-:- : -:: : - -: . .. . ... .. 0

.. . . . . .. . . . . . . . .. . . . . . . ...: . . . .

.. . .. . ... .. ... ..Z ---- --- -- .. .. ..... . ... ..

.. . . . .. . . .. . . .

Page 38: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CaI

-03 00 O. 1.0 s 2.

i

.. ... ......

..... ...

Ao ZH.-. . ... ..4-. . . ... ...

.0 . . . . .

. .. ~ .. . . .. . ... ... ... . ..

:n .*;. * :: :;: ! .. ... .. ... .. .. ..

... .... ...

. .. .... ... .. .... . .

Page 39: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-3.S -1.0 -2.1 -2.0 -1.1 -1.0 O0.1 0.0 0.1 1.0 I.1 3.0

.. .. .... .. .....

. .. .... . .. ... 8.. .. .... ... .....

. .... ... .. ..

.... - . .. . .

. ........

.... .... ... .... . . ...

... . .... .. .. . 4 0

. ... .. ...

.. .... ... .... .. .. .. . ... . ....

. .. ... .. ... ....... ... ... ... ..

3 .... ...4..

Page 40: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CFJU-3S -3.O -2.S -2.0 -1.1 1.O -01S 0.0 0.1 1.0 1.1 2.0

.... .... .... ....... ... .... . . .... .. . ..... . . . . . . .

a" : : : ''l,. .. . ..

... .. ... .. ......a....

6 .. . .. ... .... .. . ....

... .... ..... . o

.... . ..... ....

. ... . ... . .. ........ .... . ........ ...

----- ------

..... ... ... ....

........ I.. . . . .

.... ... .... .. .. . ...

.. .. ... . .. ..64

Page 41: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-2.5 .3.0o -2.5 *.0.. -3.5 -I.0D -0.5 0.0o 0.5 2.0 L.5 20.

... ... . . .. ... ..... .. .. ... .. .. ... ....i H iH'H .... ... ... .... ... .... .8

.. . . . . . . . . . .

..0. ..

.. . . . . .. . . . .

8 s. ..A .... ...........0.........

.. .. .. .. . . . . .

- - -- ----

oa ......

Is M... . .

-- --o- - - -

..0. .. .

... ... ...

.. . .. . . . . . . . . . . ..4 .. . . . . .

Z= T'. .. ... .. .... .. 4.. .. . . .. . . . .. . . . .

.. ... ... ..

Page 42: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-1.S -3.0 -2.S -2.0 -5.5 -5.0 4O.5 0.0 0.5 5.0 I15 2.0............................................

.. ..... .... .. .... ...

. 8..0.:........ ....

.. . ..0

. . . . .. . .

............................................... ........0. . . . . .. . . .

..... ...-0f i H i i - - -- - . . . .. .. . . .

......... ... ~~~~.. .... - ----

.......... ....4 ---- ..IL. .- ii ,*...

.. .. . .. . .... .. .4 ..-- ------ ..-- - - --- - -~. .. . . . . . . . . . .

.. . . . . . ... .. .. . . . . . .. . . .. . .

. . . . .. .. .... . .

Page 43: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CPU'

. ... .. . . . ... .

.. .. .. -. ....,.... ... .... ... ....... ... .. .... . ... ... ... ....... .. ... .. . ... ... ...

... ......

0 . . . . . . . . .

.. . .. . .

.. . . . . . .. . . . . . . .

.. .. .. . . .. . . . . I. . . . . . . . .. ......

.. .. . .. . ... .. . .. . .. . . ... .. ..

.. . .. .... .... .. ..

.. .... .. . .. . .. .... . .... . ... ....ii....

Page 44: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CPIU

-2.0 -I.S -1.0 -G.s 0.0 G.S 1.0 Ls 2.0

. ......... H H !... .... .

::: ...... ......... .. ............ ......... .......... ......... ......... ..... .........

........ ......... .........'.*:* .... ......... ......... ......... ....... ......... .... ..... ................... ........ ................... .................. .................. ......... ....... .... .. . ... ...... .......................... ................. ......... ....... .. ... ......... ........ j :: ........ .. ............. ...... .... ........ .. ...., ... . ................. ......... ......... ..... ......... ... . . .....

......... .......... ...... . . ......... ................ ......... ......... ............... ..... .. ......... ....

.... ......... ......... ......... .....----- .....

........ ......... .. ... .. .. . .. . .... ... . .. . .

....... .. .......... ........ .........

.. ......... ...... .. .. ... .. .. . ... .. . . .... ... .. .. .. ... .. ... .. . ... ... .. .. .. . . .

....... ......... .

.... ......... ..

......... ......... ......... ......... ........ ... I ...... .. ......... .. ............. ....

.... ......... .......... .........

.......... ..... ....... ... ..... .. ......... ......... ....... ........... ......... ...... ....................... .........

....... ....... ....... . ...... ............ ... . ...... .. ......... ...... ....... 4+ ........

........ . .. ......... . ........ ......... . .............. . ... .........

.. ......... ...... ...... . .... ......

------ ---- ........ .... . .................. . ..... .................. .

.. ...... LA....... .....

.. ......... .......... ......... .......... .. -

. .. .. . ... .. . .. .. .... . . ......... ........ ......... ........ ..

......... .. . ......... .......... ......... ......... .. ..... ..... ... ..... ..

.. ... .. ... . ... .. .. .. .. ...... ......... ...... .........

LD

....... ......... .... ... . .. .. .. ....... ......... .. .. . .... ... ..... ....... ........

-39-

Page 45: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

.. .. .. .

0 .. .. .. ..

.. ~- .8.. . .. . . .

.. . . .. . . .. . .

.. . ....... L.

.. . ......

- - - - - - -- - - -- .. . . .. .

4 .. .. .. . ..0 .. .... ...

. .. . .....

. ... . .. . . . ..3. ... .... .

... . .. ..

. .. ... . ....0 . ... .. -.. .-. . .. . . .. . . . . . . . . . . . . . . . . . . . .

0. . . ... ...

C3 ~ ~~~~~ ~ ~ ~ ~ .o .- . . ............ ...

Page 46: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CPIU.1 -1.0 -2.s -2.0 -2.1 -1.0 -0.1 0.0 0.1 1.0 L.1 2.0

.. .. . ...

.. .. . ...-.. .. .... 4

.. ... ..... ... ... 8.. ..... .. ......S

... .. ... .... ... ...

a 4 . .... .... . ...

...4. . .

.. .. .. . . . 0.

-- -- - - -4. . ... . . . . . . .. ....

4. . . . . .. . . . . . . .. .. ........ . ... ..... .... ...

. . . : : : : . . .. :.. . .. . . ...4

d . .. . . .. . .. .... . . . . . . . .. ... . . .... . -.

C2 . ..... .... 1

Page 47: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-s -3, -2. -2.O-. .0 -a'sO.0 O 1.0 1. 2.0

.. ......... .....

.. . . . . . . . I. . ..'. . ..4. . . . . . . ... .. .. .. .

:::: :::: :. * :: l:,! t:I L. .. . . . . . .. . . ... .. .. ... . .. . ...

. . . .. ... .. C ,

64 -......... C.. . ..0.

B~. -.......-..

C3,.. .. -- D

0n

....... -w

....... . ....::: ::I.: : ::: :: :; :: I. . .. . . . . . . . . . .

- ... .. .. .. ...-. ..C3'

..... .... .... .... .... .....-. -....... .. .. ..

.. . . . . . . . ... . . . ..-......-.

.. ... .

..... .... . ....4..-

....... ....... ..

Page 48: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

ie.0-O -03S 0.0 0.1 . Ls 2.o

-.. -... ::::* ++r -0--:: - - -

0 . .. .. ..

0. .. . ... . . . .

.. .. .. . .

. .. . . ....... .......

................... . . .. . . .. . . .. . . . . . . . . .. .. .. ..

7-7

- ~ ~ . ..- ........-.-a ...........

U. . .. . . . . . . . . . . . . . .

.~~~ ..... ......

. .& ... . . .-C... ~ .J .... .......

.~~~~ ... .- .... . 00..

:x~~C ... . ...C 3 . ... .. . ... . .. . ..

-43-

Page 49: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

Ir - ...-...-.-.- .-

.. .. .. ..

. ..... ....

03 .... ... .. .. ............ .-

.... ------ - - --- --- . ... .... LA~C .........-. ... :-.........-..

-- ------ - -- - -- ::: :::: C:

a ::..~:u. - - - -. ......M

......... ...

.44. ----- ---- 4-- -

Page 50: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-. -. 0 -2.S -2.0 -13 - 0.0 0.0 0.1 3.0 L.1 2.0

.. . . . . .*~. .........

a :.2::::: ::s- -

.... ... .. . .

. ......

.... .. . ... ... .. ... . .... ... . .. ...

.... ... .... ... .... ... ....

.. .. .. .& ...... C~.~~~~. .. . . . C" ... ....... ......... ~ .. . . .........

........ ~ ~ ~ ~ ~ ~ ( ...... ...... ........ .

... .. .. .

Page 51: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

*a.S -2.0 -,.i *a.0 -oLS 0.0 a.i 1.0 si a.0

...... .. ...

... . .. .... . .... .... ...

....-.... . . . . . . .. . . . . . . . .

...... ....... .. ....... .... ..... .......

.. . . . .. ...... .. .. ....

.8 -. .. .... .: : : :

... . .. .. . .. .. ....... .... ... z

. . . . . . . . .4.... ... .... ... . .. ....

.... ... ... ... . .. ... .. . ... ... ...

-. . .. . .. . . . . . . .

.. . . . . ... .. . .. .. . . .. .. . .. .. .. .. .. . .. .. . .. . . .. .. . .. .0.

.. . .. . .

.. .. . . . . . . . . . . .. . . . .

.. . . . .. . .,.. .

z

.. . . .. . .

. .. .. .. .. .. .. . . . . .. ..%L.... ...

.. . . .. . .

.. ...7.. .

Page 52: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

I. .0 23 .2.0 1.1 -1.0 -O.1 0.0 0.1 1.0 .1 .0

. .. . ... .. . .. .. .

... .... ... .... .... ...

............... ........

..... .. ... ... . .. .. .. ...... 7...t.... .... ...t....... ... . . . . .. ... .I.. .. . ... .. .. .

a. .4.. . . .. . . .

. . ... . .

,----- . .. ...........

.. . .. .. .U'l

.. .. . . . .. . ..... . .. .... tm:

.. . .. ... .. ...L. .. . . . . .. .0.. .

. .... ..... ... .. .... . . . . . . .

... .. . . .- J. . . . . .

. .... .... 0. .. . . .. . .'

.... .. . . . . . .. . . . . .. . . . . .

iia ..... . . . . . .

.. . . . .. . ..-.. . . . . .

.....a

--------- 3

. ....... t

Page 53: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CPt.J

B IS -. 2S -. IS 10 -. . . . . .

0 .... ....

... .. .. . . . .. . ....... ... . .....

:: : : .. . .. .. .. ... .. .. ..

.... . . ... ... ... ... ... .. .. .... ... . . . .. ... .. .... ... ... ...

...... ....... . ..... . ...

. . . . . . .. .... ...

.... .... ... ....

.. . .. .. .. .. .. . .. .. .. .. . .. .. .. .. . .. .. . .. .. .

. . .. .. .. .. .. .. .. . ... . .. .. .. . . . .. ... . ... .. .0

.. ... . . .. ... . . ... ... .. ...... ... . ..... :'.

..... .....

-. -:. .* :: 1 ::.t,........ ......... .... ... .... ..

.. .. . .. . .. ... .. .. .. .. .. .. .. . .. . . .. .. .. . .. .. . .. .. . .0.

. . . . .....

..

............... ....

--- -- ---- ....

:: : .. . .. . .. .. .. . .... . .. .. .. . .. .

Page 54: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

- 30 -. 20 -. -1. - 00 Os 10 L 20

...... .. ..

... ..... .:.... .... ....

.... .. ..... I . .... ...

I. .: ...

.. .. .. .... . .......... ~~~~~~~~~~ ~ ..... . ......... .........

------------C... .. .. ..

Page 55: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

a l 3.0 -2.S -2.0 -l.5 1.0u -O. 0. OA 1.0 . 1.5 2.0. . .. . . ... . .. . ..

.... .... ... ........ ........

.. . . .

... .. .......... .... ... . ....................

..- .. .... .. . ..... . . .. . . . . . . .. . . . . . . . .

.a. .. . . . ... . . . . ....-. . . . ...-. . . .

.. . .... . .

.. . . . . . . . . . . .. . . . . .. . . .

.. . . . . . . .4 -. . . . . . .. . . . .

.. .. .. .... ..... ...... .. 0

..a . . . . . . . . .L

... . .. . . .. . .

.. .. .0. . .. . . . . .

I .. . .. . .-. . . .. . . .

o 0

... 4......

. . . . . . .

.. .. . . . . .. .

. .. . .. . . ...1

k..

Page 56: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

I.S -1.0 -2.S -2.0 -1.5 1. -O.S 0.0 6.1 1.0 3.1 2.0

.. . . .. ... ..

3 .... ...

. . . . .. ......

C, :: " " " ....- *... .. . . . . .

... .. .. .. . .. .. . .. .. .. .. .. .... . .... .. . .... ...

..... ... ... .. .. . ..... . . . .. . . . .. . .. . .. . . .

. .. .. . . .. ..: . .... .. .... ...

. . . . . . .. ... ......

.. . . . . . . ..... ... ... ... . .. ... .. ... ... .. ... ... .... .. ... .. .... . . ... . . .... .. ... ...

- --- - --- - -- -- -

........... .. . . . .. . . . . . . . . .

. .........

. . . .. .. I

Page 57: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

.. -. 0 -1 -2.0 -IIS -. -0.1 0.0 0.1 1.0 I.S 2.0

.....o.

...... ......a . . . . . . . . . . . .

...... ...: : : : ... ...... .... ..

.. . . . ... .4. . .: , * , : .*:* .

.. . .. . , "i - ,. . . .. ..a.. ...:L.

.. . . . . . . . .a . . . . .

.. . . . ... - o

.. .. . . .. . . .

. .. . . .

.. . . ..a. . .

.. . . . . .

.. . . . . . ... .. .. .

.. . . ..0. . . . . . . . . . . ... . . ...0.

.. ........ 53-

.. ... ..... ..... .... . ..... ... . ....... ..... ... .. : : : - :* : :: ... . . .. .. .

...4.. ...,. ..

Page 58: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

cptu

....... ....

- . .. - . . .. .. .. .. ..

.- - .... .. .

.. .. .. .... . . .

.. ... ... . .. . 4. ... .....a..

....

.. . . .- ...-

.. . . .. . . .. .. .... . . ... .... .. . ...

.... . . .. . . ... .. . .. ... .. . ......... .. ....... .... .. .. . .. .... ... ..... ....

.. . .. .

. .~ . . . ..-.. . . . . . . . . . . . . .. . . . .

. . . . . . .. . . .....

C0. . . . . .. . .

... . ... .. . ... . . I .. .. .. ... .. .

.......- .. . .w

. . . . . ... . . . . ... .. . .0 .. : : : : ".: ...a . . . . . . . . . . .

. . . .. .. ..

.. . . . . . . . . . . . . . . . .

.. . .......... .... ...- . .... ... -

.. . . . ..

.... .....-. 4 -

Page 59: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CP'U

--a-2.S -2.0- i .o -o.S 0.0 0.1 1.0 I.1 2.0 ~

. ... . .. .. . F

...... .. .. .. .. .. .

. . . . . . . . . .

7 -:0

.. .. . .. .a a

..... ....... .. .. .. ..

. . . . . . . . . .. ... .. ...

.. .. . . . . . . . . . ... . ... . . ... .. : .. . . ...

.. .. .. . .. ...... a -.. . . . .. .. . .. .. .. .. . ... . . .. ..

.. .. . . .z.. .. . .. : :: ::

a 43o -- - - - - -

.. . . .. . . .

-.55-........

Page 60: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

*,.i-~o *as -a~ -'.9 -1. O. .0OI1O 1. .

.-......

.4 4........ -.. .... ...

42 . . . . .. : .

.. .. .... ..

.. . . . . . .. .. . . . .... ..

.. .. . .. . . . ...-

.. ... .. ..

0. .. .. ..

.. .. . .. .. . .. . .

......... .. .. ..

. . .. . . ..-.

0w :. w

0l.. .. . .. . . . .. . .

.. . . . .-. .... ..o. . . 10

... ..~~- . . . . .. . . . . . . .. . . . . . . . . .. . . . . .

. . . . . . .... ...... .. . . . I . . ... . .. . .. .

.. . .. . . .. . .. . ..... . .. ... .. . .... ..

..... ... . ..... . . . . . . . . . . ....

.. . . . . . .. . . . . .. . . . . . . .4

1D- ... -... . -CA

o~

.. . . . . . . ... .. ... . .. .. . .. .-.. .

-. ....6-. .. .

Page 61: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-,, 10 2.S *3.0 -l.S .0 -05S 0.0 0.5 1.0 2.5 3.0... ......

..... . ... ..

.............. .....

.. ..... ....

. . . . . . . . L- - . : : : ... .... .... .. .. .. . . .. . .... ... .. .... .. .... . . ... ... .. ...

.... ........ .... .... ........ ... ..... . .... ....

::::: ::: : ... ... ....

..0 ..... .. ............... .... ............ ........... .... ..... ......... ... ....

.. . . . ...0. . .. . . .:a a . . . . . . . . . . . . . . . . . .

.. . .. . . .0I" . . " ' l . : * : : . . . . . . . . ..... ... .... .. .... . 0

.... .. ... L..... ......

.. .. . . . . . .. .. . .. .. ... .. . .0C

.... ...

.. ..0. . . .

.... ..... .. .. ..-.............

Page 62: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CP

-30 -3 - 0 5I. .0. 0..0 L. 1.0 LI 3

....... ............ ...

44 t.. ... ..... . : : : : -:

.... ... .. .. .. . .. .. .. . ..4. . ..8-.--.... ..-.... -

.a

.4 . ... ....... ...

........ .. . . . 4. . .. .. ...

.8 - ....

-.. .. ......-.

.. . . . . ..a. .

........a...................... ........ ......£. ...- 4 -: : . . . . . . . . . .

..... .... .. .. . . .. . .. . .. . . . .

.. . .. . .0 . . . . . . . . . . . . .. . ... .. .. ....

-.. . ... . .. . .. ., :a: : : : :* :: :,

.... .... .... . .. . . .0... .. .-. . . .. ...- .. . . ...a.

. . .. .. . . . .. 0

a qI

. .... ... .... .. ... .... .. .. .. -. . -. . .. .. -C D.. .. .. .. 0.. . . ... . . .. .

. . . . .. .. ... . . . . . . . .. . .. .

--------- -------- .- -o. .. . .. . . .......

3

Page 63: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-1 -. 0L2L0. 2 S .0 1.2.0

. . . . . . . . . . .

..... .. .. ....

.. . . .. .. . . . . . ... .. .. .. .. ..

.. .. .. ...

.... ... ... .

.. . ..a. . .. . . . . .. . .. ....

.. . . . .. ..

..-.. -. .. . . . ....- ..

.. . .. . .

.. .. . ..- . . . . . . . . . .. . ..

..... ... ..... . .. .. ).. ... .. .... .. . .. .. .....

-. .. . .. ..

Do F9

a. . . .. . .

CID

* 59

a - - -- - - - -- - -

Page 64: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

11 -1.0 -3.S -3. I0 -0.5 0.0 0.5 1.0 I.s 3.0

a., .. ..... ..... ..

.. .. ... .

.. . ... . ... .

.. ... .....

. . . . . . .. .. . .

..... 4.... .... . .. ..... .... .... .... ... ....

.:::: 4:.*:::.*.:: :::.. ....m' *, : :

.. , ;T ::a: . : : . . . . . . .

.. . . . .

.. ... . . . . . . . . . .

.. . . . . . .

. . ... . ..

... .. .. .. ..

.. .. . . .. . . . .. . . .. . . . .

.. . . . . . .. . .. . . . . . . . . .

.. . ..0. . ... . . . . . . .

60......

.. ..... ..L

Page 65: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-IS-10 -2 20 ~ 10 0.S 0.00O.11.0 . 2.0 J.. .... .

.. .. . .. .. f ... .. . . . - .: : : : -.

. ...... .3 - - ......-...4 -... ...

... .........-.. .. .... ... .... ... .... ... ..... .... ..-.. -.... ...4.

... .. . . ..... . .....

.. .. . . . ... ... ....a. . . . . . .

- .. . . . .. C... ., . . .

.... .... ... .... !l....... ... ..

.... .. . . .. . . . . . ... .. . . . . .. . . . . . . . . . . . . .

. . . ... . . . .. . .. .. . . . I a .. m; .. . .. .

. .. . . . .. . . ... ...o.

o..................... ....... ......... .......... ...... ................

.... ... ... . 0.. ... ... .... .....4

IAA

Page 66: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

1. 30 -3S -0-0.1 0.0 O.i 1.0 I.1 2.0 %

.. ..... ... ... .. .. ....

........ .

;i H !Hi. H * .. .. .... . .. .... . ..

8. ..... ....... . ......... ...

. .. .. .

t ....

.........~~~ .. . . ... . .. . .

.~~~ .. 0 . . .. .

.. .. ... ... . - ... .... ...

7: : . :.:a: . .. . . . . . . . . . .

.. . . ...0t 7:: ::

.... ... .... .. .. .. ... .... ...

Page 67: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

3I.S -3.0 -2.S -2.0 -1% 10 -0.1 0.0 0.5 1.0 I.1 2.0 N

0 . .. . . . .

.. . . . . . .

. 8.. .. .. . ...

.a. . . . .. . . . . . ... ... ....

.. . . . . . . . . . . . . . . . .

. .... .. .. .... . . .. . . .

.. . . . . . . .. . . . . . .

.. . . .. . . .

...r. . .. . . . . . . . . . .14-4-.....

.. . . . . . . . . . . . . . ... .. . . . .. .

.. . .. . .

.a. . . . .. . .. .. .. .. .

7: 7 ... ... .0

.~~~~ ~ ~ ~ . 4w w ... ..441

. . .. . . . .... ... .. .. ..... ..

.... . ... .. .. ... . ... . ...-6 3 - ..

Page 68: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

-3S -. 2S -20 -. t0 -o.s 0.0 0.I 1.0 I.S 3.0

....... 8. ... ..... ....... .. . .. . -. .... ..0. ...- .. .. ... ...

.. .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.- .. .. . ....- . . .... .. .-

.. . .. .

0L

.. .. .. .. . .. .. .. . . . .. . .

... . . .. . .. .. . . .. .. .. . .. . . ... .. ...... . . ....

.i . . . .. . ....-.. . .. .

. . . ... ... .. ...

.. .. .. . .0.. . .

.. .. ... ... .

0 . . . . . . . . .

.0. . . . .. .. . . .

. .. . .. ..

.. . . ..0. . . . . . . . . . . . . . . .

.- .....-. .....

0: : .-:: -.. -. . . . . . . . . . . . . . . . .

............. ...

rl ... . .. ..... 6 4... . ... . ....

Page 69: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

CPII-3. - 30 2. - 20 19 -1. -O. -. -. . .

.. .. .. .

. . . . . . . . . . . . .

- -~~~... -.........-- -- -- -

. . .. . ... ...

0 . . . .

.~ ......... ......I. . . . . . . . . .... .. ... .. ..

.. .. .. . .. .. . ... ..... ~ ~ ~~ ... .. .. . ... . .

.. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ... .. .. ... . .. . . . . . . . : : : :. . : : m : : : :

-.. . .. . ..6.5- . .1 . . . .

Page 70: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

10~

_1 --- _ - - . ro- --- - ____

7 .. . .. .. '-.-.. . J-- - .... . . .. . .. . . .. . . -...

.- - ---.- --- _.

.... - -- --- ----------------- -- -- -- -

. . . .. .. ..- -- . . . .. • . . . . . . .

~Ala.

- - 4 . .- ... . . ... .- ----- -- - - -

t .. . . ..' ... . . .

... - :: CZ-- ... ii.. -- ... .. . . . .-- ... ... .. . ..

. .. ... . . . . .-. . . . . . . . . . . . . . . . . . . ... ... . .... ... .. t. . ... . . . . . . . S

- - . . . . . .. . .. . . . . . . . . . . . . . . . . . . ....... .-.r..... . ....... . . .... . .

3" ', . . . . . .- .--. *- . - -_

k __ __ ..-.. _ .__. .

. • ir - ml i ,,i ,i. . . . . -1-111-*-*-i--...... - . . .

Page 71: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

Sal.

-1------ ~ L -a----

-~44

-T4V

C,-.77

00r --67-

Page 72: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

I II

LEJ

I -D

acI-j

I ne- I-

In 0

4d --" UA

CD b- 16

4. UJ LAJ -4

P.-4

O% IC-2

0

Page 73: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

C)

N

0 C=)LLJ Ul "z LU LU XLAJ 2t = - I LAJ= = A C) >

C71 toLU 2

C/3 LC%

Lz:ce. r-I (.0 lkC" L.Lo rl QQ cn ON t:UJ LAJ -4 a cm

I.- I.- - LU >. = 44c -j oc Ac 31-0

cc 0 cc 0: cc ui LUC)z A ui Lu LLS = Se 1= x 4c

UJ uj = -J -J uj (i= = CA -1 -1 > wU U 0 - - := r4

C/) 4c OC C= ZZ cm C/) LUCFo a 0 1> 4 0 0

M 00 Ln

C; C3

69 -

Page 74: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

--~ -- ---

6p =_____

4--N

-------- 41

3-70

Page 75: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

'41

0)

-44

0

-~ Lu

Page 76: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

~l.

-NV)'

ItIi

C- ) CL I'

~ I-

LLU

LL- L

Iz I-1 -

C-Q LUD

I L. -j< LUJ LUa

-72-

Page 77: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

_ _ _ _ -- - ----- -- -1 . .I

* I ........................................... ... ..... . ............

.. -.. =77

7-A

-77 --- ------- _ _ _ ----------- L: L

* ~ ~ ~ ~ ~ ~ .... ............. ~........ -

.~....~7 -~-777-

<_ _ __ _ I ..

... ~~~ ~ ~ .. .. .. ... -: ...2..

. .. .. ... .. .

7::T~ ~ ~ F' . .....Kl. .. ....

47 7 .......

226

a7

_ _. .... all_

-7--- -- -- - - - -

4 4A

tie_ _

Page 78: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

9

q~J 'I-. I

'4

*~ *** ~ - .... . .

>J ~

. I *-~~~~~1'1~ i.- II I

-. 0. *...~-. -

0~ * * -

_____ I 1 _____ ___ 8_______ _____ _____-- --------- e~-

0a.- 04 .

-r I

b ~- -

~ 04 S

'is * S

a

LU

4

I I

.KI.< I- ,s I

I . IPu a * t - ...- I______I ________ ___L --..------------..-- _____________ V

-J I.) . I * * .

.~ . -S.,..-

>*~- L'"~ . I 10.

I-. I* - ~.. K ~0

00-~~il ___

I _______

I I- . . . . . . I

i 20 ~. A

- 74-

Page 79: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

! I I" -

______ -c--- ~ !&U77 ...I-.. T---, i 4 6

- -. .. . . . . . . . . .

I I; I®... . .Q Q. .... . .* . O . . ..

" -Jn i r t . . .. .

Il. .... ,. ... ... . ...

J II

.............. .............

,t -------- .--.- - - 4

;.t .-- *.

t--- -..-,... - 4- - - - ----,.... .. .. .

00

4.

Page 80: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

f. - I

.1* I

* I I -~---

I I I ~ !- -

T_________ ..-- IG- I

- I . ,. ---. -

* ~. .1..- .

- .-- . . . I -

~.. .~~~x2L~-_- 7- --

N I 0K ~ _ ___ ________ _______ 9'

a

'UOx

l~ *4~ 1 A. 1J -

-~ - . . . I

a

I. a-- 1-~~-

I:'

2 ...........................................................................IAV.-

I - . . . .. K .

U

I. *~ .

I I

0 £ I i

a0 I . . . . . N

I----

1--

+ ' ~ -

77 ~ a ~ c~ 49 L4

Page 81: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

': T T ~ ,-~.-- J~*~-

4- - - - ----- -

4: 1

PHIS- /T.

i- fV

£ 3 .. ................ .-. ..

t 4-, .. _ _ _ _. ..

Page 82: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

. 3 .... ...

- --

r37

.. . . . . .

--- -------- ---- -------.77 7 --- - -- . . . .

.2 . ._ _ . .

:: -7 -.

........ .

7~ :7 7 -. -- ----

/ ...........

.................. . . .. . . .

---------

-1 -- -- -

.- .

. . . . . . . ._._.

. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ..4 . ...

-_ _ _ __ _ _ _ - -__-_-_-_-_ _-_-_-_-_-__-_-_-_-_-

-__-__- -_ _ _ -_ _ _ _ _ _ _ _ -_ _ __----_ _ __-- -- _ _ __----_ ---- ---- . ... ..-- -- .. ....

Page 83: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

.2

LID MN

>- af (Qm10_

of > -~- mn!D

0y -< -llrCG

(Ni LIZ0-,

0(I) M

CD I

= -Vc~ ~aN

-80-

Ic

Page 84: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

RECO9MENDATION

STEADY PRESSURE DATA NEEDS FURTHER SCRUTINY

, BAD POINTS SHOULD BE ELIMINATED FROM INTEGRATEDOR AVERAGED RESULTS

FINAL PLOTS WITHOUT BAD POINTS REQUIRED' PERFORM DATA ANALYSIS

NEED A CRITERION BASED ON VORTEX SHEDDING STRENGTHTO DEFINE PRESENCE OF PERIODIC SHEDDING

CHECK ACCURACY OF DYNAMIC DATA WITH CORRECTED TANDATA: COMPLETE DATA ANALYS IS

TURBULENT ROUG14 WAl BOUNDARY LAYER ANLYSIS WITHPRESSURE GRADIEiNT:

* P[OFILE CALCULATIONSBL ITEGRAL PROPERTIESSKIN FRICTION

, SIMILARITY IDEAS

-81-

-8I

Page 85: CYLINDER FLOW S GOrES U) ALABAMA A / M L Emmmhhhhhmhlm · ad a131 8 high reynolds number cylinder flow s gores u) alabama a / and m univ normal de'pt of physics and mathematics m

Recommended