An Experimental Investigation Of The Effect Of Mass Transfer On A Wedge Induced Laminar Separated Boundary Layer At Mach 12

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Content This dissertation has been microfilmed exactly as received 6 8-5856 BALL, Karlheinz Otto W illi, 1936- AN EXPERIMENTAL INVESTIGATION OF THE EFFECT OF MASS TRANSFER ON A WEDGE INDUCED LAMINAR SEPARATED BOUNDARY LAYER AT MACH 12. University of Southern California, Ph.D., 1968 Engineering, aeronautical University Microfilms, Inc., Ann Arbor, Michigan AN EXPERIM ENTAL INVESTIGATION OF THE E F F E C T OF MASS TRANSFER ON A WEDGE INDUCED LAMINAR SEPARATED BOUNDARY LAYER AT MACH 12 by K arlheinz Otto W illi Ball A D isse r ta tio n P r e se n ted to the FA C U LTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In P artia l F u lfillm en t of the R eq u irem en ts for the D egree DOCTOR OF PHILOSOPHY (Engineering) January 1968 UNIVERSITY O F S O U T H E R N CALIFORNIA T H E G RADUATE SC H O O L U N IV ER SITY PA RK L O S A N G E L E S, C A L IF O R N IA 9 0 0 0 7 This dissertation, written by ............................... under the direction of hls....Dissertation Com mittee, and approved by all its members, has been presented to and accepted by the Graduate School, in partial fulfillment of requirements for the degree of D O C T O R OF P H IL O S O P H Y e - .............. Dean Date February! ..1968 T A B L E OF CONTENTS P a g e A BSTR AC T ................................................................................. iv ACKNOW LEDGM ENTS ............................................................................ vi LIST OF FIGURES .................................................................................. vii LIST OF TABLES .............................................................................................. x LIST OF S Y M B O L S .............................................................................................. xi CHAPTER I. IN T R O D U C T IO N .............................................................................. 1 II. EXISTING THEORETICAL INVESTIGATIONS . . . . 3 G ENERAL .................................................................................. 3 INTEGRAL M E T H O D S ........................................................ 6 III. PREVIOUS EX PE R IM E N T A L WORK ............................... 8 IV. EX PE R IM E N T A L EQUIPM ENT AND PROCEDURES 10 TEST F A C I L I T I E S ................................................................. 10 PRESSURE M E A S U R E M E N T S ....................................... 11 G e n e r a l .................................................................................. 11 Spanw ise P r e s s u r e D i s t r i b u t i o n s ....................... 14 S tr e a m w ise P r e s s u r e D is t r ib u t io n s ................. 17 HEAT TRANSFER M E A S U R E M E N T S ...................... 18 MASS TRANSFER M E A S U R E M E N T S ...................... 19 OIL FLOW V IS U A L IZ A T IO N ........................................... 20 ii P a g e V. RESULTS AND DISCUSSION............................................. 21 PRESSURE D IST R IB U TIO N ................................... 21 HEAT TRANSFER D IST R IB U T IO N .................. 28 MASS T R A N S F E R ........................................................ 31 VI. CONCLUSIONS..................................................................... .... . . . 38 F I G U R E S ...................................................................................................................... 42 T A B L E S ............................................................................................................................... 7 8 A P P E N D IC E S ............................................................................................................. 95 A. MEASUREMENT U N C E R T A IN T IE S ............................ 96 B. MODEL CONSTRUCTION AND CALIBRATION . . . . 98 C. MASS FLO W C A L C U L A T I O N S .................................... 105 DETERM INATION OF rfi BY SONIC THROAT C O N SID E R A T IO N S............................... 105 DETERM INATION OF rfi BY SLOT BACK P R E S S U R E ..................................................................... 106 EX PER IM ENTA L DETERMINATION OF rfi . . . 107 D. SEPARATION PRESSURE RISE CORRELATION . . . 109 R E F E R E N C E S ............................................................................................................. 115 iii A B ST R A C T An e x p e rim en ta l in v e stig a tio n w as m a d e to d e te r m in e the quantitative e ffe ct of su c tio n on a h y p e r so n ic , sep a ra ted la m in a r boundary la y e r . The t e s t m o d el w a s a s y m m e tr ic a l fron t w ed g e of 12° half an gle fo llo w e d b y an a ft-w ed g e or fla p w h o se an gle could be v a r ie d fr o m 0 ° to 20 0 w ith r e s p e c t to the upper su r fa c e of the fron t w ed g e in o rd er to fo r m a c o m p r e s s io n c o rn er . The in stru m en ted s u r fa c e s of the m o d el w e r e of th in -s k in h o n ey co m b co n stru ctio n . S u ction w a s obtained by m e a n s of a sp a n w ise slo t of v a r ia b le w idth b e tw een th e fron t and aft w ed g e, allow in g c o n tr o lle d n atu ral flow fr o m the upper high p r e s s u r e r eg io n of the c o r n e r to the r e la tiv e ly low p r e s s u r e r e g io n at the b a se of th e fron t w ed g e. T he t e s t s w e r e m a d e in th e A e r o s p a c e R e s e a r c h L a b o r a to r ie s , W r ig h t-P a tte r so n A ir F o r c e B a s e , Ohio, u sin g a 20 - inch H y p e r so n ic Wind T unnel at a n om in al M ach num ber of 12. The lo c a l M ach num ber on the fron t w e d g e su r fa c e w a s a p p ro x im a tely 6. 7. The f r e e - s t r e a m R eyn old s n u m b er, b a se d on the le n g th of the 5 fro n t w ed g e, w a s 2. 83 x 10 . T he boundary la y e r w as la m in a r through r e a tta c h m e n t. The e s s e n tia l tw o -d im e n s io n a lity of the flow w a s v e r if ie d by co m p a rin g su r fa c e p r e s s u r e and h ea t tr a n sfe r r e s u lts w ith sm a ll iv fe n c e s ju st co v er in g the reg io n of sep a ra tio n to r e su lts obtained w ithout fe n c e s . The sy m m e tr y of the co n figu ration a lso h elp ed to m in im iz e end e ffe c ts. S u rfa ce p r e s s u r e m e a s u r e m e n ts at a w a ll to stagn ation te m p er a tu r e ratio of 0. 56 and h ea t tr a n sfe r m e a s u r e m e n ts at a w all to stagn ation te m p e r a tu r e ra tio of 0. 28 w ere m a d e for a ft-w ed g e d e fle c tio n a n g les of 0 , 5 , 10, 15 and 20° with v a r ia b le su ctio n obtained fo r each a n gle by v a r y in g the c o r n e r slo t width. The extent of sep a ra tio n is show n to b e e x tr e m e ly s e n s itiv e to su ction . R e m o v a l of a s m a ll p e r ce n ta g e of the boundary la y e r m a ss flow is su fficie n t to c o lla p s e the sep a ra ted flow r eg io n for the p r e se n t con figu ration . The e ffe c t of the su c tio n is to r e m o v e the low m o m en tu m flow n ear the w a ll, thus enabling th e rem a in in g shear la y e r to n eg o tia te a h ig h er c o m p r e s s io n at reattach m en t. T he m a s s tr a n s fe r req u ired for incip ien t sep a ra tio n w as d eriv ed fr o m in teg r a tio n of the f i r s t m o m en tu m in tegral equation w hich y ie ld e d good a g r e e m e n t w ith the e x p e rim en ta l data. The data p r e se n te d a re c o r r e la te d in th e p ertin en t p a r a m e te r s of the sep a ra tio n p h en om en a and p ro v id e gu id an ce for e x te n sio n of the p r e se n t r e s u lt s to other la m in a r flow con d ition s. v ACKNOWLEDGMENTS The author e x p r e s s e s h is gratitude to the m e m b er s of the d isse r ta tio n co m m ittee and e sp e c ia lly to Dr. R. S. H ickm an for advice, en couragem en t and c r itic a l reading of the m an u scrip t. Gratitude is due a lso to Dr. R. H. K orkegi and m e m b e r s of the staff of the A ero sp a ce R e se a r c h L a b o ra to ries, W righ t-P atter son Air F o r c e B a se , Ohio, w h ose a s sis ta n c e and coop eration m ade com pletion of this w ork p o ssib le . A lso the author w ish es to thank the United States Air F o r c e for the opportunity to participate in the acad em ic program at the U n iv ersity of Southern C alifornia under the Air F o r c e Institute of T echnology C ivilian Institute P ro g ra m and in the r e s e a r c h p rogram at the A ero sp a ce R e se a r c h L a b o ra to ries. Special app reciation and thanks are due to Mr. J. R. G reenup, S y stem s R e se a rc h L a b o ra to ries for h is invaluable a s sis ta n c e in the exp erim en tal program . v i LIST OF FIG U R E S F ig u r e P a g e 1. C o m p r e ss io n C orn er F l o w ..................................................................... 43 2. S c h e m a tic D ia g r a m of H y p e r so n ic Wind T u n n e l .................... 44 3. C en terlin e L on gitu d in al M ach N um b er D istr ib u tio n of the W ind T u n n e l .................................................................................... 45 4. S c h e m a tic of Wind T unnel M o d e l ....................................................... 46 5. D eta il of S lo t C on figu ration Show ing L o c a tio n of P r e s s u r e O r ific e B elo w T h r o a t.......................................................... 47 6. P r e s s u r e M odel I n s t r u m e n t a t io n ....................................................... 48 7. S ch e m a tic of P r e s s u r e M ea su rin g S y s t e m ................................. 49 8. F e n c e C o n f i g u r a t io n s ................................................................................. 50 9. H eat T r a n sfe r M o d el I n s t r u m e n t a t i o n .......................................... 51 10. S c h e m a tic of H eat T r a n sfe r M ea su rin g S y s t e m .................... 52 11. S ch e m a tic of M a ss F lo w M ea su rin g S y s t e m ............................ 5 3 12. S p a n w ise P r e s s u r e D istr ib u tio n at x = 3. 4 in ch es Showing C onstant P r e s s u r e O v er _+ 1 Inch fr o m C e n t e r l i n e .......................................................................................................... 54 13. C h o rd w ise P r e s s u r e D istr ib u tio n , 9 = 0 ° and 3. 75 ° . . 55 14. C h o rd w ise P r e s s u r e D istr ib u tio n , 0 = 5 ° ................................. 56 15. C h o rd w ise P r e s s u r e D istr ib u tio n , 9 ~ 1 0 ° ............................. 57 16. C h o rd w ise P r e s s u r e D istr ib u tio n , 9 = 1 5 ° ............................. 58 17. C h o rd w ise P r e s s u r e D istr ib u tio n , 9 = 20 ° ............................. 59 18. V a ria tio n of the P la te a u P r e s s u r e w ith S lo t Width . . . . 60 v ii F ig u r e P a g e 19. Incipient Slot Width V ariation w ith the Aft Wedge A ngle for Tw / T 0 = 0. 56 and 0. 2 8 ........................................... 6 l 20. C hordw ise P r e s s u r e D istrib u tion s for V arious Aft W edge D eflectio n s and No Slot Opening ................. 62 21. C hordw ise P r e s s u r e D istrib u tion with Aft Wedge E xtension, 0 = 1 0 ° ........................................... ....... ......................... 63 22. C hordw ise P r e s s u r e D istrib u tion with Aft Wedge E xtension, 0 = 2 0 0 ............................................................................. 64 23. T yp ical S ch lieren Photographs for 0 = 20 0 and d* = 0 and 0. 0 89 i n c h ........................................................................ 65 24. H eat T ran sfer D istribution, 0 = 0 ° ........................................ 66 25. H eat T ra n sfer D istribution, 0 = 5 ° ........................................ 67 26. H eat T ran sfer D istribution, 0 = 1 0 ° ........................................ 68 27. H eat T ran sfer D istribution, 0 = 1 5 ° ........................................ 69 28. H eat T ran sfer D istribution, 0 = 20 0 ........................................ 70 29. P lateau v e r s u s Slot P r e s s u r e Showing that Sonic F low was Obtained for A ll T e s t s ............................................... 71 30. Slot M ass F lo w per Unit Span for 0 = 5° and 10° . . . 72 31. Slot M ass F lo w per Unit Span for 0 = 1 5 ° ........................... 73 32. Slot M ass F lo w per Unit Span for 0 = 2 0 0 ......................... 74 33. V ariation of X with Tw / T Q in M ]^ 0^ = X ^ ................ 75 34. M a ss Suction R equired for Incipient Separation . . . . 76 35. V ariation of |3 with d* for 0 = 5, 10, 15, and 2 0 ° . . . 77 B1 C orrelation of H oneycom b P an el H eat T ran sfer Data. . 104 v iii F ig u r e P a g e D1 T e s t of the S e m i-E m p ir ic a l P la tea u P r e s s u r e E q u a t io n .................................................................................................... D2 T e s t of th e S e m i-E m p ir ic a l E quation for th e P la tea u P r e s s u r e w ith d* = 0 for V a rio u s M ach and R eyn old s N u m b e r s ....................................... .... ........................... 113 114 ix LIST OF T A BLES T a b le P a g e 1. S u m m ary of C o n figu ration s I n v e s tig a te d .................................... 79 2. P r e s s u r e M od el I n s t r u m e n t a t i o n ........................... 80 3. H eat T ra n sfer M odel I n s t r u m e n t a t io n ......................................... 81 4. O il M ix t u r e ...................................................................................................... 82 5. S p anw ise P r e s s u r e D istr ib u tio n s. . . . . . . . . . . . . 83 6. C h ord w ise P r e s s u r e D istr ib u tio n s, 0 = 0,3. 75, and 5°. ..................... 84 7. C h ordw ise P r e s s u r e D istr ib u tio n s, 0 = 10°............................ 85 8. C h ord w ise P r e s s u r e D istr ib u tio n s, 9 = 15°............................ 86 9. C h ord w ise P r e s s u r e D istr ib u tio n s, 0 = 2 0 ° . ........................ 87 10. C alcu lation of S ep a ra tio n L ength and R ea tta ch m en t P o i n t .................................................................................................................. 88 11. H eat T ra n sfer D istr ib u tio n s, 0 = 0, 3 .7 5 , 5 and 1 0 ° 89 12. H eat T ra n sfer D istr ib u tio n s, 0 = 15 ° .................................... 90 13. H eat T ra n sfer D istr ib u tio n s, 0 = 2 0 ° .................................... 91 14. D eterm in a tio n of rfi fr o m M ea su red S lot P r e s s u r e s . . . 92 15. D eter m in a tio n of rfi B a se d on Sonic S l o t .................................... 93 16. M ea su red M a ss F low C a lc u la tio n s .................................................. 94 x LIST OF SYMBOLS a speed of sound, ft / s e c b th ick n ess of heat tra n sfer su r fa c e, inches c sp ecific heat, B T U / °F -lb C co efficien t in lin ear form u la for v is c o s ity , C = T Q /j,/ T Ch Stanton num ber CL p r e ss u r e co efficien t ir d* slot w idth, inches h heat tr a n sfe r coefficien t, B T U /f t 2 - s e c - ° F k _ co efficien t of th erm al conductivity, ft2 - l b / s l u g °R K a constant L s length of slo t, in ch es L s e p length of sep aration region, in ch es M Mach num ber A m a ss flow rate, slu g s / ft2 - s e c Nu N u sselt num ber p p r e ss u r e , p sia or m m Hg P r Pr andtl numb e r q dynam ic p r e ss u r e , p sia 4 heat tra n sfer rate, B T U /f t 2 - s e c R gas constant, ft2 / s e c 2 -°R xi Re R eynolds num ber t tim e, secon d s T tem p era tu re, °R U, u v e lo c ity p a ra llel to su rfa ce, ft / sec V, v v e lo city norm al to su rfa ce, f t / s e c a lso v o lu m e, ft3 X ch ord w ise su rfa ce d istan ce fr o m m odel leading edge, inches y spanw ise d ista n ce fro m m o d el c en te rlin e, inches z front w edge b a se coordinate, inches a angle of strea m lin e d eflection at sep aration , d eg rees P m a s s tra n sfer ratio b ased on m a s s d efect, Eq. (6) y ratio of sp ecific heats 6 boundary la y er th ick n ess, inches 6p p r e ss u r e r is e in tank in m a s s flow m e a su rem en t, m m H g / sec 5 * boundary la y er d isp la cem en t th ick n ess, in ch es ® boundary la y er m om en tum th ick n ess, in ch es 0 aft w edge d eflection angle, d e g rees X - i / constant of proportionality, X = 9 x P v is c o s ity , s l u g s / f t - s e c £ constant in honeycom b calib ration p density, s l u g s / f t 3 X h y p erso n ic in teraction p aram eter \ = M 3 Re ^ Tw w all sh ear s t r e s s , l b / f t 2 x ii S u b scr ip ts aw adiabatic w a ll e lo c a l con d ition at edge of boundary la y e r HL hin ge lin e 1 in cip ien t con d ition L to ta l length of m od el m m o d el o f r e e s tr e a m stagn ation condition p plateau p. s. plum bing s y s t e m r r e attach m en t R r e s e r v o ir s sep a ra tio n , a lso su ctio n tr tr a n s fo r m e d w w a ll, a ls o w ed ge ! beginning of in ter a c tio n 2 conditions behind n o r m a l shock 3 conditions behind re attach m en t sh o ck °° f r e e s tr e a m condition x i i i CHAPTER I INTRODUCTION Of ex trem e im portance in the d esig n of a v e h ic le capable of flying at h y p erso n ic sp eed s is an understanding of the prob lem of h yp erson ic boundary layer sep aration and the a sso c ia te d p r e ssu r e and heat tra n sfer c h a r a c te r is tic s. Separation m ay affect the p e r fo r m an ce lim its and allow able d esig n configurations by creatin g u n desirable shifts in loads as w e ll as producing in c r e a s e s in lo c a l heat tra n sfer r a te s. The origin of the fo r c e giving r ise to boundary la y er sep aration is an a d v erse p r e ss u r e gradient. This a d v e r se p r e ssu r e gradient is n orm ally induced by the g eo m etry of a configuration or by extern al m ean s such as shock w ave im p ingem ent on the configuration. F o r a x isy m m e tr ic bodies at angle of attack the reduction or com plete elim in ation of the sep aration by the th re e -d im en sio n a l phenom ena of c ro ssflo w has b een noted by Libby, et al. (1) and Zakkay, et al. (2). In th is report is p resen ted an exp erim en tal in v estigation of the lam inar boundary layer behavior on a w ed g e-w ed g e m od el, i. e. , a c o m p r e ssio n co rn er, sim ulating a lift su rfa ce follow ed by a control su r fa c e . In p r a c tic e the ju n ctio n b e tw e e n the lif t and c o n tr o l s u r fa c e m a y n ot b e s e a le d , th er e b y c a u sin g m a s s tr a n s fe r to or fr o m the se p a r a te d reg io n . T h e m a in p a r a m e te r s v a r ie d in th is in v e s tig a tio n a re th e a ft-w e d g e a n g le and the flo w r a te fr o m th e se p a r a te d r e g io n th rou gh a sp a n w ise , con tou red s lo t at the ju n ctio n of the fron t and aft w ed g e. M e a s u r e m e n ts w e r e m a d e of th e h ea t tr a n s fe r ra te and both sp an - and c h o r d -w is e p r e s s u r e d istr ib u tio n s on the tw o w e d g e s and the flo w ra te th rou gh the s lo t. CHAPTER II EXISTING THEORETICAL INVESTIGATIONS GENERAL Separation of a tw o -d im en sio n a l lam in ar boundary la y er has been stud ied for a num ber of y e a r s . The underlying p rin cip les of the phenom enon m ay be supposed known and are d e scr ib e d in d etail in W uerer and Clayton (3). C onsidering the tw o -d im en sio n a l flow of a v isco u s flu id over a body, the fluid near the su rfa ce, i. e. , the boundary la y e r, is retard ed due to the effects of skin frictio n . The fluid v e lo c ity in the boundary la y e r v a r ie s fro m z e r o at the w all to ap p roxim ately the in v isc id v alu e at the outer edge of the boundary layer. With no other fo r c es acting to retard the flow , the v e lo city profile h as a p o sitiv e gradient at the w a ll and the gradient approaches zero at the outer edge of the boundary la y e r. If, in addition to the w all sh e a r, the flow encounters an u p strea m d irected fo r c e it is further retard ed . The kinetic en ergy of the fluid is then continuously d im in ish ed by doing w ork again st this fo r c e . The m om en tum of the fluid w ill even tually be balan ced by the fo rce and the flow w ill be brought to rest. The low m om en tum flow adjacent to the w a ll is the m o st e a s ily retard ed , so that a lin e of z e r o str e a m w ise v e lo c ity sep a ra tin g fo rw a rd and b a ck w a rd m ovin g flo w s w ill b e fo r m e d . T he n o r m a l v e lo c ity g r a d ie n t at the w a ll m u st b e p o s itiv e w h e n the flu id n ext to th e w a ll m o v e s w ith the s tr e a m , i. e. , atta ch ed flo w , and n e g a tiv e w h en the flu id in th is r e g io n flo w s a g a in st th e s tr e a m , i. e. , se p a r a te d flow . B e tw e e n th e s e co n d itio n s th e n o rm a l v e lo c ity g ra d ien t at the w a ll i s z e r o d efin in g the se p a r a tio n poin t of the flo w . In m o s t flu id d y n a m ic s itu a tio n s, th e fo r c e g iv in g r is e to se p a r a tio n is an a d v e r s e p r e s s u r e g ra d ien t, i. e. , th e p r e s s u r e is in c r e a s in g in th e s tr e a m w is e d ir e c tio n . T he a d v e r se p r e s s u r e g ra d ien t m a y b e g e n e r a te d by th e shape of the body or b y an e x te r n a l so u r c e . In th is in v e s tig a tio n th e fo r m e r i s stud ied ; th e a d v e r se p r e s s u r e g rad ien t is c a u se d by a c o m p r e s s io n c o r n e r . If se p a ra tio n o c c u r s fo r th is c o n fig u ra tio n th e s t r e a m lin e s of th e e x te r n a l flo w w ill be d e fle c te d . T h e e ffe ct of the se p a r a tio n i s to a lte r the flo w g e o m e tr y such that th e flow w ill b e c o m p r e s s e d in tw o s ta g e s th rou gh tw o sh o ck s in s te a d of th e one sh o ck fo r the in v is c id c a s e a s show n in F ig . 1. S ep a ra tio n r e d u c e s th e in itia l p r e s s u r e r is e b e c a u s e th e in itia l d e fle c tio n of th e in v is c id s tr e a m i s s m a lle r th an th at c a u s e d by the c o r n e r s . S in ce the m e c h a n is m of se p a r a tio n is dep en d en t upon the m agn itu d e of th is p r e s s u r e r is e , th e e x te r n a l flow and the se p a r a te d flo w a r e in terd ep en d en t th rou gh a p r e s s u r e i n t e r action . A t r ea tta ch m e n t the flo w is c o m p r e s s e d to th e fin a l v a lu e corresp on d in g to the lo c a l slope of the body at that point. The fluid w ith su fficien t m om en tum to o v erco m e the reattach m ent p r e ssu r e r i s e continues d ow n stream ; w h erea s that having in su fficien t m om entum is r e v e r se d b a ck into the sep arated region. For a steady flow , the dividing str ea m lin e at sep aration m u st a ls o be the dividing str ea m lin e at reattach m en t in order to sa tisfy continuity. T h erefo re, id ea lly the flu id in the sep arated region b e h a v es as a con stan t m a s s continually being circu la ted . Above the dividing str ea m lin e the v isc o u s la y e r behaves lik e a continuance of th e original boundary la y e r . H ow ever, on the dividing strea m lin e the v e lo c ity is not zero, sin c e m om en tum is continually tr a n sferred by v is c o u s shear fro m the extern al s tr e a m through the outer v isco u s la y e r into the separated region. T h is tra n sfer of m om en tum su sta in s the m otion of th e fluid in th e sep a ra ted region. A n alytical approaches encounter d ifficu lties in treating the p rob lem of sep arated boundary la y e r s . N ear the point of sep aration tw o of the assu m p tion s in the d erivation of th e boundary la y er equations are invalid, i. e. , near sep aration sign ifican t p r e ssu r e gradients m a y ex ist n o rm a l to the su rface, and d ow n stream of sep aration the th ick n ess of the v is c o u s layer in c r e a s e s m ark ed ly so that the boundary layer th ick n ess m a y no lon ger be n egligib le com pared to a rep resen ta tiv e body dim en sion . T h erefore, in p rin cip le, analytic approaches req u ire re-ex a m in a tio n of the com plete equations of v isco u s flu id m otion to determ ine if any sim plifying assu m p tion s m ay be m ad e. H ow ever, due to the com p licated flow g e o m e tr ie s and boundary conditions of sep arated and reattaching flo w s, no g en era lized sim p lification s have b een found so that at p resen t no exact solution of the p ro b lem se e m s fe a sib le . INTEGRAL METHODS S ev era l approxim ate solu tion s have b een developed for the p rob lem of sep arated flow (4-8). The m o st g en era l and p rom isin g of th e s e m ethods appears to be that of L ees and R e ev e s, w hich u tiliz es an integral technique w ith no introduction of s e m i-e m p ir ic a l fa cto rs. Integral techniques g en era lly m ak e use of polynom ial e x p r e ssio n s to denote the v elo city and enthalpy p ro files in the various te r m s of the in tegral equations of the boundary la y er. In the P ohlhausen m ethod the co efficien ts of the polynom ial are all e x p r e sse d in te r m s of one param eter that r e la te s the shape of the v e lo c ity p rofile in the boundary la y er to the lo c a l p r e ssu r e gradient. F ollow ing Tani (9), L e e s and R e e v e s u sed a different param eter w hich is e s s e n tia lly the non dim ension al slope of the v e lo c ity profile at the w all. H ow ever, rather than u se a quartic polynom ial expansion as in Tani, they u sed sim p le algeb raic functions of this p aram eter to r ep resen t flow te r m s of th e in teg r a l eq u ation s. U sing th e s e fu n c tio n s, found by cu rv e fittin g the s im ila r so lu tio n s of Cohen and R esh o tk o (10), the in teg r a l eq u ation s w e r e so lv ed s im u lta n e o u s ly w ith a P r a n d tl-M e y e r e x p r e s s io n r e la tin g the in c lin a tio n of th e lo c a l e x te r n a l s tr e a m lin e w ith th e lo c a l e x te r n a l M a ch nu m ber. The r e s u lt s a g r e e rath er w e ll w ith e x p e r im e n ta l p r e s s u r e d istr ib u tio n s. T he m eth o d of L e e s and R e e v e s a lso le n d s its e lf to stu d ies of s e p a r a te d flow w ith heat tr a n s fe r as w e ll as s im ila r it y m a s s tr a n s fe r . With th e ad d ition al p a r a m e te r of m a s s tr a n s fe r at the b od y su r fa c e , the so lu tio n s of C ohen and R e sh o tk o have to be r e c a lc u la te d to in clu d e th is new bou ndary con d ition . R e c e n tly , H ankey and C r o ss (11) obtained an a p p ro x im a te c lo s e d fo r m so lu tio n to th e sa m e g o v ern in g eq u ation s c o n s id e r e d by L e e s and R e e v e s . This s o lu tio n w a s found by noting that the r a tio of the boundary la y e r m o m en tu m th ic k n e ss to th e m e c h a n ic a l e n e rg y th ic k n e ss is a p p r o x im a te ly constant over a w id e ran ge of the L e e s and R e e v e s p a r a m e te r . S olu tion s to th e p r o b le m of sh o c k -b o u n d a ry la y e r in te r a c tio n and that of flow s e p a r a tio n ov er a r e a r w a r d fa cin g ste p w e r e in d ica ted . C H A PTER IH PREVIO US E X P E R IM E N T A L WORK M any p a r a m e te r s have b e e n noted in p r e v io u s e x p e rim en ta l w o rk s as p o s s ib ly havin g im p o rta n ce in the d e term in a tio n of the ch a r a cter of sep a ra ted flow . E x c e lle n t s u m m a r ie s a re g iv en in W u erer, et al. (3) and K aufm an (12). S te r r e tt and E m e r y (13) ex a m in ed the la m in a r boundary la y e r p r e s s u r e d istrib u tio n over a tw o -d im e n s io n a l, fla t-p la te w ed ge m o d el at a M ach num ber of 6 and con clu d ed that the equations fo r the plateau p r e s s u r e in a se p a r a te d r eg io n fo rm u la ted by Chapm an, et al. (5) at s u p e r so n ic sp e ed s cou ld be exten d ed to h y p er so n ic sp e e d s. M e a su r e s of p r e s s u r e and h e a t tr a n s fe r w e r e m ad e by B ogdonoff and V as (14) at M ach 10 in the r e g io n of sep a ra ted flow over a fla t p late w ith a 10° w ed g e. T h ey found that th e h ea t tr a n sfe r d e c r e a s e d b elow the fla t plate v alu e in the sep a ra tio n region , r o s e above the fla t plate v a lu e ahead of th e w e d g e , and r ea c h e d a m a x im u m in the rea tta ch m en t r e g io n on th e w ed g e. M ille r , H ijm an and C hilds (15) in v e stig a te d the h eat tr a n s fe r and p r e s s u r e d is t r i bution over fla t-p la te w ed ge m o d e ls at M ach 16. A lo c a l in c r e a s e in h eat tr a n s fe r ahead of the sep a ra tio n point w a s found, fo llo w ed by a 8 d e c r e a s e in the s e p a r a te d reg io n . It w a s su g g e ste d th at the point of m in im u m h eat tr a n s fe r c o in c id e s w ith the se p a ra tio n point. R e su lts of h ea t tr a n s fe r in la m in a r , tr a n s itio n a l, and tu rb u len t se p a r a tio n r e g io n s on fla t -p la t e w ed g e m o d e ls fo r a M ach n u m ber of 6 w e r e p r e s e n te d b y S te r r e tt and H o llo w a y (16). T h ey found that the m a x im u m h ea t tr a n s fe r r a te s on the w ed g e can v a r y c o n s id e r a b ly , depending upon the p o sitio n of tr a n sitio n ; and that the lea d in g ed ge th ic k n e s s a ls o a ffe c te d the m a x im u m h ea t tr a n s fe r . H old en (17) p e r fo r m e d an e x p e r im e n ta l study s im ila r to M ille r , e t al. at a M ach n u m b er of 1 0 and p r e se n te d h ea t tr a n s fe r r e s u lt s . He p r e se n te d a se p a r a tio n c r it e r io n b a se d on a d is tin c tiv e change in th e lo c a l h ea t tr a n s fe r p r o file at the b egin n in g of sep a ra tio n . It w a s a ls o found th at the r e a tta c h m e n t heat tr a n s fe r r a te s a r e str o n g ly depend en t on r e a tta c h m e n t a n g le, w h e r e a s little in flu en ce of the boundary la y e r th ic k n e s s at s e p a r a tio n or d o w n str e a m w a s found. H eat tr a n s fe r m e a s u r e m e n t s in the rea tta ch m e n t r e g io n w e r e c o r r e la te d in t e r m s of the h y p e r so n ic in te r a c tio n p a r a m e te r , X- K aufm an, et al. (12) p r e se n te d e x p e r im e n ta l h ea t tr a n s fe r and p r e s s u r e d istr ib u tio n data fo r flo w s at M ach 5, 8, 13, and 19 ov er a fla t-p la te w e d g e , in d icatin g that th e p r e s s u r e and h eat tr a n s fe r d istr ib u tio n and e x te n t of the s e p a r a te d flo w r e g io n s a re a ffec te d m a r k e d ly by c h a n g e s in the f r e e - s t r e a m unit R ey n o ld s n u m b e r s. CH APTER IV EX PER IM ENTA L EQUIPMENT AND PROCEDURES TEST FACILITIES The exp erim en tal w ork w as p erfo rm ed in the A ero sp a ce R e se a rc h L ab oratories' 2 0 -in ch h yp erson ic wind tunnel. The tunnel is an a x isy m m e tr ic fr e e jet fa cility d esign ed to operate at Mach num bers fro m 8 to 14. It is a blow -dow n type fa cility em ploying a se t of vacuum pumps and a vacuum sphere on the low p r e ssu r e side and c o m p r e sse d bottled air on the high p r e ssu r e side. A sch em a tic diagram of the wind tunnel is illu stra ted in F ig. 2. The fa c ility is d esign ed to operate at a m axim u m stagnation p r e ssu r e of 2500 p si and a m in im u m of 400 p si. An e le c tr ic r e s is ta n c e heater p rovides a m axim u m stagnation tem p eratu re of 2800 °R, w hich m ay occur at m a x im u m air flow of 2. 6 pounds per second and at a m axim u m e le c tr ic a l input to the heater of 1800 KW. A com p lete d escrip tio n of the fa c ility w ith its a sso c ia te d equipm ent m ay be found in r e fe r e n c e s (18-21). C alibration of the n o zzle, using stagnation p r e ssu r e probes, during the te s t p ro g ra m indicated le s s than one per cent per inch variation in the f r e e - s t r e a m M ach num ber in the longitudinal, tr a n s v e r s e and v e r tic a l d irection s w ith a u sea b le c o r e 10 in ch es in 10 11 d ia m eter. The variation of the calibration due to nozzle g eo m etry ch an ges, apparently due to throat erosion , a lso w as found to be le s s than one per cent over the th ree m onths te st period. F or exam ple, F ig . 3 shows the longitudinal cen terlin e Mach number distribution. PRESSURE M EASUREM ENTS G en eral The b a sic m odel is shown sch em a tica lly in Fig. 4. The m o d el had a 12 d egree h a lf-a n g le front w edge, 3. 5-in ch chord, with a 1. 5-in ch chord v ariab le aft w edge at the front wedge tra ilin g edge, thus form ing what is com m on ly r efe r r e d to as a c o m p r e ssio n co rn er m odel. The aft w edge is a lso called a ram p, flap or control su rfa ce as appropriate in the follow ing d isc u ssio n s. The span of both w edges w as 7. 5 in ch es. The leading edge of the m od el had a nom inal th ick n ess of 0. 003 inch. Due to the high density of su rface p r e ss u r e o r ific e s and th erm ocou p les on the fron t and aft w ed ge, it w as n e c e s s a r y to con stru ct sep arate p r e ssu r e and heat tra n sfer m o d e ls . This w as accom p lish ed by having rem ovab le pan els with the appropriate in stru m en tation , i. e. , either predom inantly p r e ssu r e o r ific e s or th erm o co u p les, as the top su rface of the front and aft w edge. Both typ es of panels w e re of a honeycom b sandwich con stru ction u tilizin g 321 sta in le s s ste el. M ethods of fab rication and calib ration of the honeycom b panels are given in the Appendix. 12 The aft-w ed ge angj.e could be v a ried by rotation of tw o slotted se c to r s about the screw s fixed in the m od el sid e support p la tes. The width of the slo t at the junction of the front and aft wedge could be v a ried by m ea n s of a s c r e w / s l o t arran gem en t fix e d to each of the p rev io u sly m entioned slo tte d s e c to r s. D etails of the contoured slo t a re shown in F ig . 5. The b a se plate of the fron t w edge, the only in strum en ted sectio n com m on to both the p r e ss u r e and the h eat tr a n sfe r m o d el, had six p r e ssu r e o r ific e s lo c a te d 0 .0 2 7 in ch below the m in im u m c r o s s - s e c t io n a l area of the slot a s w ell as tw o th er m o cou p les and an additional p r e ssu r e o r ific e for th e d eterm in ation of the b a se p r e ss u r e . The m a s s tra n sfer was obtained at the junction of the front and aft wedge by flow fro m the upper high p r e ssu r e region of the corn er to the r e la tiv e ly low p r e ss u r e reg io n at the b a se of the front w edge. The low p r e ss u r e at th e b ase w as obtained through the natural exp an sion of the flow around the base at the low er su rfa ce of the front w edge. The p r e ss u r e m o d el had 45 su rfa ce o r ific e s d istrib u ted as shown in F ig . 6. The p r e ss u r e lin es w ere type 304 s ta in le s s ste e l having a 0. 0 6 7 -in ch O. D. and a 0. 0 4 7 -in ch I. D. The tim e constant of each lin e w a s about 10 second s fo r the lo w e st p r e ss u r e s encountered in this in vestigation . T ab le 2 g iv e s the sp e cific coord in ates for the p r e s s u r e m odel instrum en tation . The sp an w ise o r ific e s w e re u sed to ch eck the tw o -d im en sio n a lity of the flow over the m o d el. The te m p e r a tu r e of the m o d el s u r fa c e s and of the m o d el stru ctu re w a s m o n ito red and r e c o r d e d during the p r e s s u r e d is t r i bution t e s t s by fiv e th e r m o c o u p le s. Tw o other th e r m o c o u p le s w e r e u se d to obtain h eat tr a n sfe r data. D e ta ils of the te m p er a tu r e m e a su r in g s y s t e m a r e g iv en in the se c tio n on heat tr a n sfe r m e a s u r e m e n ts. The p r e s s u r e m e a su r in g s y s t e m as w e ll as the c a lib ra tio n equipm ent is show n s c h e m a tic a lly in F ig . 7. The su r fa c e p r e s s u r e s on the fro n t and aft w edge w e r e obtained through u se of a m u ltip o rt v a lv e , e n c lo se d in a w a te r -c o o le d cy lin d er and lo c a te d in the tunnel t e s t cabin. The v a lv e con tain ed a 1 p sid tr a n sd u ce r r e fe r e n c e d to v a cu u m (15 m ic r o n s or l e s s ) . The lo w e st p r e s s u r e m e a su r e d in the b a s e r eg io n w as about 0. 8 m m Hg w h ile the lo w e s t su r fa c e p r e s s u r e m e a s u r e d about 5 m m Hg. C alib ration of th is tr a n sd u ce r w a s m a d e daily, p rio r to te stin g , u sin g an in clin ed s ilic o n e - o il m a n o m e ter and a 0 -5 0 m m of Hg gauge a s stan d ard s. The m o n o m e ter w a s u se d to c o v er the ca lib r a tio n of th e tr a n sd u ce r fr o m 0. to 25 m m of Hg; w h e r e a s the gauge, w h ich had p r e v io u sly b een c a lib ra ted a g a in st a m e r c u r y m ic r o -m a n o m e t e r , w a s u se d fr o m 0 to 50 m m of Hg. The tr a n sd u ce r c a lib r a tio n con stan t thus obtained v a r ied no m o r e than + 1% over the e n tir e t e s t p ro g ra m . The output of the tr a n sd u ce r w a s obtained for p erm a n en t u se on X -Y p lo tte rs and on tap e a s w e ll as hand r ec o r d e d fr o m a d igital v o ltm e te r output. 14 A ll t e s t s w e r e p e r fo r m e d at the fo llow in g n om in al con d ition s : M = 12, P Q = 1200 p sig , T 0 = 1900 °R, Tw = 1 060 °R fo r the p r e s su r e d istrib u tio n and m a s s tr a n sfe r t e s t s and Tw = 530 °R for the h ea t tr a n sfe r t e s t s . At th e s e con d ition s the u s e a b le c o r e of the fr e e jet w as 10 in c h e s in d ia m eter . The tunnel stagn ation te m p er a tu r e and p r e s s u r e as w e ll as the t e s t cab in p r e s s u r e w e r e r e c o r d e d on the m a g n etic tape s y s te m for each te st. S p anw ise P r e s s u r e D istrib u tio n s The t e s t p r o g r a m w a s in itia ted by a study of th e tw o- d im en sio n a lity of the flow over the m o d el. H o w ev er, it w a s e x p ected th at, due to the s y m m e tr ic a l con figu ration of the m o d el, the tip e ffe c ts w ould be m in im a l. Of p a rticu la r in t e r e s t w a s th e sp a n w ise p r e s s u r e d istrib u tio n in the v ic in ity of the gap, sin c e th is w ould d ictate the u n ifo rm ity of the slo t m a s s tr a n sfe r in su b seq u en t t e s t s . With the aft w ed ge se t at 0 = 0 °, a 12° h a lf-a n g le w ed ge w a s fo r m e d w h o se top su r fa c e w as about 5 in c h e s long w ith no slo t at the w e d g e / w ed ge junction; te s t s w e r e p e r fo r m ed w ith and w ithout s tr e a m w is e fe n c e s of Type II, F ig . 8. The fe n c e s w e re lo c a te d at + 3. 5 in c h e s fr o m the m o d el c e n te r lin e and w e re h eld in p la c e by an u n cu red rubber com pound. T h is com pound p rovid ed a r e lia b le bond and s e a l. 15 The seco n d configuration in v estig a ted in this s e r ie s of te s ts w as with 9 = 2 0 ° , again with and without str e a m w ise fe n c e s of Type I and III, F ig. 8. A typ ical p r e ss u r e distribu tion te s t w ill be b r ie fly d escrib ed . A fter ca lib ra tio n of the tran sd u cer in the m ultiport valve and setting of the proper s c a le fa cto rs for the sev e n th erm ocou p le outputs on the X -Y p lotters and a strip chart r ec o r d e r, the te s t cabin w as c lo sed and evacuated. With the tunnel in the b y -p a ss m ode, i. e. , the flow was ven ted to th e a tm osp h ere, the power settin gs w e re esta b lish ed to the h eater to obtain a nom inal stagnation tem p era tu re of 1900 °R as w ell as to allow stab ilization of the stagnation p r e ss u r e to a nom inal value of 1200 p sig. The tunnel w as then placed in the norm al m ode, i. e. , the in -flow m ode, by opening valve 2 and clo sin g valve 3 (F ig. 2) and injecting the m od el into the fr e e jet after all r ec o r d e rs w e re started . The tim e of injection for the p r e ssu r e m od el w as 0 .5 secon d s. The f ir s t te st of each day w as n orm a lly u sed to h eat the m od el to 150-200 °F and p r e ssu r e data w e re taken on subsequent te s ts. The su rface p r e ss u r e s w ere then obtained fro m the tran sd u cer output, beginning with the p r e ssu r e o rifice n e a r est to the m od el leading edge. T hose o r ific es not u sed during th is in vestigation w e re capped. The output of the tran sd u cer w as displayed on an X -Y plotter in the fo r m of p r e ssu r e v e r s u s tim e in order to d eterm in e the approach to the steady p r e ssu r e reading. The final stead y p r e ssu r e 16 for each orifice w as then record ed in te r m s of the tran sd u cer output d isplayed on a digital v o ltm eter. T his proced ure w as repeated for each surface p r e ss u r e o r ific e. Due to the num ber of o r ific e s that req u ired m onitoring for a determ in ation of the sp an w ise d is tr i bu tions, two runs w ere norm ally req u ired for each configuration, i. e. , a new 9 , fence type or location. The m o d el was alw ays co o led b etw een te sts to within the range stated above. The configurations in vestigated in this s e r ie s of te s ts are shown in Table 1. S ch lieren photographs w ere obtained for all te s ts in this se r ie s a s w ell as subsequent p r e ssu r e and heat tran sfer distribution t e s t s . The sch lieren s y s te m , a double p a ss type u tilizin g a continuous so u r ce , is d e scr ib e d in d etail in G oll and L apenas (22). The in itia l program included total p r e ss u r e b ou n d ary-layer su rv ey s at s e v e r a l str ea m w ise sta tio n s. H ow ever, the objective had to be elim in ated early in the spanw ise p r e ssu r e distribution te sts due to e x c e s s iv e ly large tim e lag in the m easu rin g sy ste m . During a norm al 2 0 0 -se co n d test, even the R ayleigh p r e ss u r e of the free str e a m was ju st approached with the probe u sed . The tip of the probe w as c ir c u la r and had a 0. 0 2 0 -in ch O. D. and a 0. 01 0 -in ch I. D. L arger I. D. probes w ere available but it was fe lt that th ese would crea te m ore than just lo c a l distu rb an ces in the flow , even if flattened. 17 F o r the 9 = 2 0 ° configuration, s e v e r a l te s ts w e re p erform ed with a sharp slot at the w e d g e /w e d g e junction. The sharp slot w as obtained by fasten in g 0. 0 0 1 5 -in ch thick strip s of sta in le s s ste e l gauge sto ck a c r o s s the ex istin g contoured slot, leavin g a p red eterm in ed gap width b etw een the two str ip s. The th in n ess of the strip s w a s dictated by the co n sid era tio n of m in im a l in terferen ce to the flow fie ld , sin c e the strip s w e r e m ounted on the top su rface by the uncured rubber com pound m entioned above. S trea m w ise P r e s s u r e D istributions Upon com p letion of the sp an w ise p r e ss u r e distribu tion t e s ts , the m o d el w as changed to the str e a m w ise p r e ssu r e distribution configuration by connecting appropriate s tr e a m w is e p r e ss u r e o r ific es to the m u ltiport v a lv e. Som e spanw ise p r e ss u r e orifice data w a s a lso obtained as a ch eck again st the p reviou s in vestigation . No ch anges w ere m ad e in the stru ctu ral tem p era tu re and the heat tra n sfer m on itoring s y ste m d e scrib ed in the p revious section . A ll of the p r e ssu r e data w e re obtained fr o m the m u ltiport valve tra n sd u cer w hose output w as m on itored on an X -Y plotter v e r s u s tim e fo r each o r ific e with the steady p r e ssu r e being h a n d -record ed from a digital v o ltm eter output. In addition, the tem p era tu re data as w ell a s the p r e ss u r e data w e re p laced on a m a g n etic tape through u se of a m agn etic tape data r e tr ie v a l sy ste m . Data w e re reco rd ed 18 for each te s t at 0. 1-se c o n d in terv a ls for the fir s t 8 seco n d s of te s t tim e for pu rp oses of heat tr a n sfe r evaluation, then changed to 1-seco n d in terv a ls for the rem aining running tim e. A typ ical te s t p ro g ra m p roceed ed as d escrib ed above but, due to the num ber of o r ific e s , it w as g en era lly n e c e s s a r y to p erform two or th ree 2 0 0 - second te s ts b efore the com p lete d istribu tion and b a se p r e ss u r e s w e re obtained. The o r ific e at w hich the te s t was term in ated w as rep eated as the start of the next te s t in order to in su re continuity. The m e a su r em e n ts w e re rep eatab le to w ithin 1%. The configurations in v estig a ted in this s e r ie s of te s ts are given in Table 1. HEAT TRANSFER MEASUREMENTS Heat tra n sfer rates to the c o m p r e ssio n corn er m od el w e re obtained by the " th in -sk in ” technique u tilizin g honeycom b sandw ich pan els. The distribution of th erm ocou p les is p resen ted in F ig. 9 w h ile T able 3 p resen ts the coord in ates for the instrum en tation of the heat tra n sfer m od el. The p r e ssu r e o r ific es shown w ere u sed to p erm it co rrela tio n with the p r e ssu r e distribution data. D etails of the m od el con struction and calib ration are given in the Appendix. The com p lete tem p era tu re record in g s y ste m is shown sch em a tic a lly in F ig. 10. T his s y ste m w as u sed for the m od el tem p eratu re m onitoring in the p r e ssu r e d istribu tion te s t s e r ie s as 19 w e ll as the h eat tr a n sfe r d istrib u tio n te s t s e r i e s . A ll th e r m o c o u p le s w e r e r e f e r r e d to a ju n ction of known te m p e r a tu r e . R eadout of the th erm o co u p le output w a s obtained on an 8 -ch a n n el str ip ch art r e c o r d e r , X -Y p lo tte rs and a m a g n etic tap e. The r e c o r d e r and p lotter w e r e u se d only to obtain quick r e s u lt s as to the v a lid ity of the data b ein g p la c e d on tap e. The data r e t r ie v a l s y s te m sa m p led ea ch th erm o co u p le at 0. 1 -s e c o n d in te r v a ls for the duration of a te st. T he m o d el w as in jected into the tunnel in about 0. 2 secon d , after the flow had b e e n e sta b lis h e d in the t e s t sec tio n . D ata w e re tak en fo r the in itia l 6 sec o n d s after w hich the m o d e l w a s e je cte d and co o led to ro o m te m p e r a tu r e , about 70 °F. J u d iciou s u s e of a g a se o u s n itro g en sp ray p e r m itte d th e co o lin g of the e n tir e m o d el to be p e r fo r m ed rapidly. The co n fig u ra tio n s in v e stig a te d are show n in T ab le 1. MASS TR AN SFER M EA SUR EM EN TS The m a s s r em o v ed fr o m the top s u r fa c e at the ju nction of the fron t and aft w ed ge w a s c o n tr o lle d by the s lo t w idth during the p r e s su r e and heat tr a n s fe r d istrib u tio n t e s t s . T o obtain a d ir e c t m e a s u r e of the m a s s flow through the slo t, the b a s e of the m o d el w as e n c lo se d and the flow ducted through a 1 -in c h tube to a 1 0 -cu b ic foot vacu u m 20 tank. The tank con tain ed a 0. 1 p sid p r e s s u r e tr a n sd u c e r , fr o m w h o se p r e s s u r e r i s e w ith tim e the m a s s flow w a s ca lcu la te d . F ig . 11 p r e se n ts a d ia g r a m of th e m e te rin g s y ste m . A ty p ica l te s t p r o g r e s s e d as fo llo w s : 1) the m o d el, w ith a sp e c ific slo t gap and a ft-w ed g e a n g le, w as in jected into the e sta b lis h e d t e s t s e c tio n flow ; 2) the p r e s s u r e o r if ic e s , F ig . 6, on the top s u r fa c e s w e r e m o n ito r ed un til the flow w as w e ll e sta b lish e d ; 3) the v a lv e w a s opened and the tank p r e s s u r e and te m p er a tu r e w e re r e c o r d e d v e r s u s tim e on a strip ch art r e c o r d e r ; 4) An X -Y plotter a ls o m o n ito red the m o d e l b a se p r e s s u r e s as w e ll as th e m o d el s u r fa c e p r e s s u r e s during the tim e , about 10 se c o n d s, of m a s s r em o v a l. The co n fig u ra tio n s in v e stig a te d in th is s e r ie s of t e s t s are g iv e n in T ab le 1. OIL FLOW VISUALIZATION In o rd er to obtain the s u r fa c e flow c h a r a c t e r is tic s on the w e d g e /w e d g e m o d el, a s ilic o n e o il-tita n iu m oxide pow der m ix tu re w a s applied to v a r io u s lo c a tio n s on the m o d el. The m o d e l u se d in th is in v e stig a tio n w as so lid b r a s s , to ta lly u n in stru m en ted , w ith r e p la c e a b le a ft-w ed g e b lo c k s. The con figu ration s stu d ied a re g iv en in T ab le 1 w h ile the co n stitu en ts of the oil m ix tu re are g iv e n in T ab le 4. CHAPTER V RESULTS AND DISCUSSION PRESSURE DISTRIBUTION T he r esu lts of the sp a n w ise d istrib u tion te s ts a r e g iven in Table 5. Of p articu lar in te r e st are the d istrib u tion s for 6 = 20° and d* = 0, w h ere d* is the slo t opening, im m e d ia te ly in fron t of the w e d g e /w e d g e junction; sin c e for th is con figu ration the s e v e r e s t th r e e -d im e n sio n a l effects are to be expected . The r e s u lts for th is configu ration, shown in F ig . 12, indicate p r a c tic a lly no v a ria tio n fr o m the cen terlin e p r e ss u r e over the cen tr a l 2 in ch es of the span of the m o d el. It is a lso notew orthy that the fe n c e s w hich e n c lo se d ju st the sep a ra ted flow region proved to be m o r e effectiv e in m aintaining a constant p r e s s u r e over the span than the la r g e r fe n c e s w hich e n c lo se the flow fr o m the m od el leadin g edge to the aft w ed ge trailin g edge. T h is is apparently due to the in tera ctio n of the boundary layer on the la r g e r fe n c e s with that of the m o d e l su rfa ce. The m a x im u m v a ria tio n in the cen terlin e p r e s s u r e for th e te s ts w ith the v a rio u s fen ce con figu rations shown in F ig . 12 w as 0. 2 m m Hg. F or r e fe r e n c e p u rp o ses the v a ria tio n of the sp an w ise p r e s s u r e for 21 22 6 = 0°, i. e. , no aft w edge d eflection, is a lso shown. The oil flow v isu a liza tio n technique a lso v e rified the flow to be tw o -d im en sio n a l + 1 inch fr o m the m od el cen terlin e. B a sed on the r e su lts of the sp an w ise p r e ssu r e distribution te s ts and oil flow v isu a liza tio n , the flow w as tw o -d im en sio n a l. T h erefo re, the str ea m w ise p r e ss u r e d istribu tion te s ts w ere perform ed without fe n c e s. T ables 6-9 p resen t the com p lete str e a m - w ise p r e s s u r e distribution data for the configurations in vestigated . The m e a su r ed su rfa ce p r e s s u r e s have b een non d im en sion alized through u se of the tunnel static p r e ss u r e , P = 0. 367 m m Hg. R ep resen tative str e a m w ise p r e ssu r e distribu tion s are given in F ig. 1 3-17, the a ft-w ed ge angle being constant in each figu re. A ll p r e ss u r e s at x = 0. 7 5 -in ch , o rifice 1, have b een d eleted fr o m th ese figu res sin c e they are c o n sisten tly lo w er than the p r e ss u r e s m ea su red at x = 1. 4-in ch , o rifice 2. T here is evid en ce fr o m the sch lie re n photographs that the flow is undergoing a sligh t c o m p r e ssio n ca u sed by the front of the honeycom b panel in se r t at x = 1. 0 inch. The height of th is discontinuity w hich rem ain ed constant during the p r e ss u r e distribu tion p rogram , betw een 1. C l inch fro m the cen terlin e,w a s at m o st 0. 00 2 -in ch b a sed on co m p a riso n with p r e c isio n gauge stock. With r efer en ce to F ig. 1 3-17, tfee sep a ra ted flow region is see n to c o lla p se sm ooth ly with in crea sin g slo t width until a certain width is attained at w hich no p r e ss u r e r is e is exhibited im m ed ia tely in front of the slo t. This particular width is defined as the incipient slo t width, d£\ Upon further in c r e a se of the slot, the lo c a l p r e s su r e s are reduced to a point w h ere the slot th roat is no lon ger sonic a n d /o r the upper su rfa ce flow is ra d ica lly affected by rem o v a l of m om entum . T h ese fea tu res are found in the plateau p r e ss u r e and are shown in F ig. 18, w h ere sonic conditions ex isted in the slo t for all c a s e s . A lso of in te r e st in this fig u re is the rapid d e c r e a se of the plateau p r e ssu r e as d* approaches d* and the m ark ed change in slop e for d* la r g er than df. Since the m a s s flow through the slo t is d ir e ctly related to the plateau p r e ssu r e for each configuration, v alu es of d* im ply a sp e cific m a s s flow . T h ese a sp ects w ill be d is c u s se d in the sectio n on m a s s tra n sfer r e su lts. The incipient slot w idth is p resen ted v e r su s the aft-w ed ge angle in Fig. 19. The lin ea r variation of d^ for aft-w ed ge an gles la r g e r than 10° should be noted. E xtrapolation of th is data to d^ = 0 in d icates that for d* = 0, 6i = 3. 75°. This angle w as a lso v e r ifie d e x p erim en ta lly by obtaining str e a m w ise p r e ssu r e distribu tion s for this c a s e . F ig . 20 p resen ts the str e a m w ise p r e ss u r e distribu tion s for 9 =0 ,5, 10, 15, and 20 d e g r e e s , r e sp e c tiv e ly , with the slot c lo se d . The distribu tion for 9 = 0 0 is in good ag reem en t w ith th ose p red icted by the tan gen t-w ed ge m ethod c o r r e c te d through the assu m p tion of lo c a l s im ila r ity (10) for the tem p era tu re ratio of 24 T w / T 0 = 0. 56. F o r the a ft-w e d g e a n g le s la r g e r than 3. 75° the bou n d ary la y e r is sep a r a te d . T he tan gen t w e d g e / l o c a l s im ila r ity p r e s s u r e c a lc u la tio n s a r e , of c o u r s e , s t ill v a lid up to the in itia l p r e s s u r e r is e . H o w e v e r , o n e -s h o c k in v is c id c a lc u la tio n s o v e r e s t im a te the a ft-w e d g e p r e s s u r e s c o n s id e r a b ly a s in d ica ted in the f ig u r e s . C a lcu la tio n s b a s e d on a tw o -s h o c k s y s t e m , i. e. , se p a r a tio n and r ea tta ch m e n t, r e s u lte d in m u ch b e tter a g r e e m e n t for the fin a l a ft-w e d g e p r e s s u r e s . T h e se c a lc u la tio n s a r e b a s e d on one e x p e r i m e n ta lly d e r iv e d v a lu e , n a m ely , e ith e r th e p r e s s u r e r i s e a c r o s s the s e p a r a tio n sh o ck w h ich th en d icta ted a flow tu rn at se p a r a tio n ; or the tu rn an gle, a , cou ld be m e a s u r e d fr o m s c h lie r e n p h otograp h s. T he la tt e r is in h e r e n tly m o r e in a c c u r a te s in c e it d ep en d s str o n g ly on the q u ality of th e s c h lie r e n p h otograp h s and is th e r e fo r e c o n s id e r e d only a ch eck of the c a lc u la tio n s b a s e d on th e se p a r a tio n p r e s s u r e r is e r a tio . O nce the flo w -tu r n a n gle is know n at sep a tio n , the fin a l w ed g e p r e s s u r e is th en d e te r m in e d by the fin a l flow tu rn at r ea tta ch m e n t, 6 - a . T he r e s u lt s of t h e s e c a lc u la tio n s are a ls o show n in F ig . 20. T h e m o d e l d im e n sio n s w e r e b a s ic a lly d icta ted by b lo ck a g e c o n s id e r a tio n s of the w ind tu nnel and th e n eed fo r tw o -d im e n s io n a l flo w o v e r a r e a s o n a b le p o rtio n of the sp a n u n a ffected b y s id e p la te s or f e n c e s . A la r g e s p a n - to -c h o r d le n g th r a tio fo r the aft w ed g e s a t is f ie s both r e q u ir e m e n ts , but it in tr o d u c e s th e q u e stio n of the effect of the chord length of the aft wedge upon the sep aration phenom ena to be studied. F o r th is reason tw o te s ts w e r e perform ed w ith a 1-in ch exten sion to the b a sic 1. 5 -in ch chord of the aft-w ed ge, thus yielding a span length to chord length ratio of 3 in stea d of the n orm al 5. S trea m w ise p r e s s u r e s w ere m e a su r ed for 9 = 20°; d* = 0 and 9 = 1 0 ° ; d* = 0. 038-in ch . The r esu lts of th e se te sts are shown in F ig . 21 and 22. F or neither configuration is the total p r e ssu r e r is e subsequent to reattachm ent fu lly ach ieved without the aft-w ed ge extension. The 9 =10° distributions agree v e r y w ell in total ch a ra cter, the d ifferen ce being attributed to the sm a ll sep a ration cau sed by the sligh t d ifferen ce in d* near d&. The con clu sion drawn fro m this c a se is that no significant u p stre a m effe cts are r e a liz e d by p rem atu rely expanding the flow p rior to com p lete p r e ssu r e rec o v e ry . The sa m e con clu sion m a y be drawn fro m the 9 =20° data; h ow ever, this data is m ask ed by the in teraction of the bow shock and the reattach m ent shock c lo se to the su rfa ce of the aft w edge at the beginning of the extension. The ex ten sio n w as not in stru m en ted for tem p eratu re but exp erien ced la r g e heating, as evid en ced by the d isco lo ra tio n of the sta in le ss ste e l su rfa ce. The p r e ss u r e s on the aft w edge and the exten sion req uired m uch longer tim e for stab ilization , so m e n ever really sta b ilized but would fluctuate around so m e m ean , as com pared to the te s ts with no extension. In fact, the data without the ex ten sio n w as obtained with 26 th ree 2 0 0 -se c o n d tunnel ru n s, w h erea s w ith the ex ten sio n 10 runs of the sa m e duration w e re req u ired . The d ifferen ce in the lo ca tio n of the sep a ra tio n p r e ss u r e r is e and the slig h tly higher plateau p r e s s u r e for the configu ration with the ex ten sio n is attributed to the high er su rfa ce te m p er a tu r e s due to the bow shock in tera ctio n on the aft- w edge su rface. The sep a ra tio n point as u sed in th is in v estig a tio n is tak en as the str e a m w ise coord inate at w hich the sep aration c o m p r e ss io n has reach ed half its fin al valu e, i. e. , the plateau p r e ss u r e . This v alu e has b een u se d by p reviou s in v e stig a to r s of lam inar sep aration and is substantiated by the s c h lie r e n photographs, w here the point is identified as an abrupt change in the boundary layer ed g e, and b y the oil flow v isu a liz a tio n , w h ere the point is taken as an average of the oil accu m u lation lin e over the cen tra l two in ch es of span. T y p ica l sc h lie r e n photographs are p r e se n ted in F ig . 23. T he boundary la y er is lam in ar through reattach m en t, b a sed on the s c h lie r e n photographs w hich show no change or d isto r tio n in the v isc o u s la y e r prior to reattach m en t. The d ifferen ce b etw een the hinge lin e or slot c en te r lin e and the sep a ra tio n point w as ch osen as a c h a r a c te r istic len gth sin c e it is difficult to define the lo cation of the reattach m ent fr o m the p r e ss u r e data. T he reattach m en t point m a y , of c o u r se , be calcu lated fr o m a know ledge of the sep a ra tio n point and the flow turn angle at sep a ra tio n for each g e o m etry , a ssu m in g that the sh ear la y er 27 p r o c e e d s lin e a r ly to w a rd s rea tta ch m e n t. H o w ev er, and in d ep en d en t ch eck i s not a v a ila b le fr o m the data of th is in v e stig a tio n . C a lcu la ted v a lu e s of the len gth fr o m s e p a r a tio n to r ea tta ch m e n t, L s e p, a re g iv e n in T a b le 10. B ound ary la y e r se p a r a tio n s that a re f r e e fr o m d ir e c t in flu e n c e s of d o w n str e a m g e o m e tr y h a v e b e e n a r b itr a r ily te r m e d " f r e e in t e r a c tio n s ." B a se d on ord er of m agn itu d e c o n s id e r a tio n s , the fo llo w in g r e la tio n has b e e n d e r iv e d fo r th e p r e s s u r e r i s e a c r o s s the se p a r a tio n (5), V a rio u s v a lu e s of K have b e e n rep o rted by d ifferen t au th ors ; the v a lu e s ranging fr o m 1. 1 2 to 1. 33. A ls o p la tea u p r e s s u r e e x p e r i m en ts h a v e b e e n r ep o rted w h e r e Eq. (1) w a s not c h e ck ed , or if c h eck ed , w a s found to y ie ld p r e s s u r e r i s e r a tio s in e x c e s s of th o se found e x p e r im e n ta lly (13). The r e s u lt s of th is in v e s tig a tio n (F ig . 20) show th at the s e p a r a tio n s a r e not of the " fr e e -in te r a c tio n " typ e, sin c e stro n g d ep en d en ce is found for th e se p a r a tio n p r e s s u r e r i s e on the fla p -d e fle c tio n an gle. A c o r r e la tio n a n a ly s is w a s p e r fo r m e d , A ppendix D, w h ich r e s u lt e d in id entifyin g the co n sta n t K as being p ro p o rtio n a l to a fu n ction of the c h a r a c t e r is t ic len gth , x^j^ “ x s - 28 The c o rrela tio n of [ L s „„Mf / x L (p3 / Pi )2] v s. R e , ® Xj proposed by N eedham and S tollery (23) w as not found to hold for the data of th is in vestigation , nor for th ose of Chapman, et al. ; M iller, et al. , and Ginoux [ G ray (24)] . S trea m w ise v o r tic e s as rep orted by Ginoux (25) w e re not ob served by the oil flow v isu a liz a tio n technique. HEAT TRANSFER DISTRIBUTION The resu lts of the heat tra n sfer distribution te s ts are given in T ables 11-13 and F ig . 2 4 -2 8 in te r m s of the Stanton number v e r s u s the str e a m w ise coord inate, x for d* = 0. The Stanton num ber is d erived through u s e of the ex p erim en ta lly d eterm in ed heat tra n sfer rate, an£i the follow ing rela tio n s : 4 = M T aw - T w)= ( 4 p m cm b) d T /d t Ch ~ k /P e u e c p ' The f ir s t equation d efin es the heat tra n sfer co efficien t, h, w h ile the second defin es the Stanton num ber. The adiabatic w a ll tem p eratu re w as calcu lated fro m Taw= Te <1 + M |) 1/ w here r = (Pr*) . P r * w as evaluated at T* [ E ck ert (26)] fr o m T* = T e + 0 .5 8 (Tw - T e ) + 0. 19 (Taw - T e ). 29 The w a ll te m p e r a tu r e , T w , w as tak en as the m o d e l te m p e r a tu r e p rio r to in jec tio n into th e tunnel, i. e. , Tw / T Q = 0. 28. F r o m the defining equations of h and C^, c h = (£ Pm cm b) (dT / dt) / p e ue ° p <Taw " Tw>- The d e n sity of 321 s ta in le s s s t e e l is 49 8 l b s / f t 3 and the s p e c ific h ea t, cm , is 0. 12 B T U / l b - ° F [M ille r , et al. , (15)] . V a lu es of d T / dt ran ged fr o m 2 to 20 °F per seco n d , evalu ated 1. 5 seco n d s fr o m the tim e of m o d el in jec tio n into th e tunnel. The te m p er a tu r e v e r s u s tim e tr a c e s w e r e lin e a r after the in jec tio n tr a n sie n t, thus elim in a tin g th e need for the u su a l cu rv e fittin g of the e x p e rim en ta l data to a r r iv e at a rate of te m p er a tu r e r is e . T he lin e a r ity of the te m p er a tu r e r i s e a ls o a s s u r e s that d T / dx in the th in -s k in s u r fa c e is n e g lig ib le. The v a lu e of £ , in the defin ing equation of the h ea t tr a n sfe r co e ffic ie n t, is an e x p e r im e n ta lly d ete r m in e d co n stan t that accou n ts for the d ev ia tio n of the m e a s u r e d h eat tr a n s fe r to the h on eycom b panel fr o m that w hich w ould be ex p ected , b a se d on o n e -d im e n sio n a l h eat tr a n sfe r a n a ly s is . A ca lib r a tio n p r o g r a m w a s p e r fo r m ed on a ty p ica l h on eycom b p an el r esu ltin g in a valu e fo r £ of 1. 07 for h eat tr a n sfe r r a te s evalu ated 1, 5 to 2. 5 sec o n d s after e x p o su r e of the panel to a high te m p er a tu r e en viron m en t. D e ta ils of th is c a lib r a tio n p r o g r a m are g iv en in the A ppendix. 30 A s s e e n in F ig . 2 4 -2 8 , th e th er m o c o u p le d istr ib u tio n on th e h ea t tr a n s fe r m o d e l d oes not a d eq u a tely d e fin e the se p a r a tio n p h en om en on . S p e c ific a lly , th e sh arp m in im u m in h e a t tr a n sfe r in the se p a r a te d r e g io n found by H o ld en (17) c o u ld not be v e r if ie d . O n ly the g e n e r a l c h a r a c te r of the heat tr a n s fe r d istr ib u tio n m a y be ob tain ed fr o m t h e s e f ig u r e s , i. e. , the m a r k e d d e c r e a s e in h e a t tr a n sfe r in the se p a r a te d r e g io n . Of sp e c ia l in t e r e s t i s th e low h e a t tr a n sfe r p a s t th e hin ge lin e fo r th e sep a ra ted flow c a s e s . Holden' s data sh o w an im m e d ia te r i s e a fter the hin ge lin e , w h e r e a s the p r e s e n t data a g r e e m o r e w ith th o s e of K aufm an (1 2 ). D elay i n the h eat tr a n sfe r r i s e p a st the h in g e is p la u sib le on p u r e ly p h y s ic a l grounds sin ce in a w e ll- se p a r a te d r e g io n th e flow con d itio n s on th e aft w ed g e a r e not e x p e cted to b e to o d ifferen t th a n in the r e g io n of se p a r a tio n on th e fro n t s u r fa c e . H igh h eat co n d u ctio n into th e s e p a r a te d reg io n fr o m the h ig h er r e a tta c h m e n t heat tr a n s fe r m a y account fo r rapid r i s e in Holden' s data as w e ll as that o f M iller, e t al. (15). In o rd er to defin e the c h a r a c t e r is t ic length of sep a ra tio n , XHL ~ x s' s c h lie r e n p h otograp h s w ere u s e d . F r o m a c r o s s p lo t of the in c ip ien t slo t w id th , d * , v e r s u s 9, th e in cip ien t w ed g e a n g le is found to b e about 5°, as s e e n in F ig . 19. MASS TRANSFER T he e ffe ct of m a s s tr a n s fe r from th e sep a ra ted r eg io n has a lr e a d y b e e n show n, if in d ir e c tly , in the d is c u s s io n of the p r e s s u r e and h ea t tr a n sfe r d istrib u tio n m e a s u r e m e n t s , i. e. , a s the slo t w idth is in c r e a s e d the m a s s tr a n sfe r i s a ls o in c r e a s e d and th e sep a ra tio n len gth as w e ll as the plateau p r e s s u r e is d e c r e a s e d . T h ree m eth od s w e r e u se d to d e te r m in e the m a s s flo w th rou gh a g iv en slo t opening. The f ir s t m eth od w a s b a se d upon p r e s s u r e m e a s u r e m e n ts slig h tly b elow the s lo t m in im u m c r o s s - s e c t io n a l a r e a . The r e s u lts of th e s e m e a s u r e m e n ts are g iv e n in F ig. 29. It is s e e n that th e p r e s s u r e r a tio a c r o s s the slo t is su ffic ie n tly la r g e to in su re so n ic con d ition s. The lo c i of attach ed flo w s are in d ica ted by the broken lin e. The sec o n d m eth od of d eterm in in g th e m a s s flo w w as b a s e d only on the p la tea u p r e s s u r e and son ic con d ition s at th e slot. T he w a ll te m p e r a tu r e rath er than the tu n n el stagn ation te m p er a tu r e w a s u sed in both of the above ca lcu la tio n m eth o d s s in c e it is b e lie v e d that th is is a m o r e r e p r e s e n ta tiv e value du e to an ticip ated s m a ll v e lo c itie s in the r e g io n of th e co n to u red slot. A ctual m e a s u r e m e n t s of the m a s s flow , through u se of the p r e s s u r e in c r e a s e w ith tim e in a la r g e tank, y ie ld e d the th ird m eth od . C a lcu la tio n s fo r the m a s s flow per unit span fr o m the th r e e m eth o d s a re g iv en in the A ppendix, w hile th e r e su lts a r e given in T a b le s 1 4 -1 6 and r e p r e s e n te d g r a p h ic a lly in F ig . 3 0 -3 2 . The f ir s t 32 m ethod, i. e. , m e a su r ed slot p r e ss u r e , c o n sisten tly yield ed a m a s s flow per unit span som ew h at la r g e r than eith er the secon d or the third m ethod; the la s t two being in ex cellen t agreem en t. The flow expansion below the slo t into the m od el b ase region is highly com p lex and attem pts to u tilize the m e a su r ed w all tem p era tu res in the b a se or to c o r r e c t the p h ysical g eo m etry of the slo t by a boundary la y er d isp la cem en t th ick n ess proved to be in co n clu siv e. A calib ration p rogram of the exp erim en tal m a s s flow m ea su rin g sy ste m had b een p erform ed prior to actual testing in the wind tunnel. This p rogram show ed that the m axim u m slo t width for the 7. 5 -in ch m od el span with so n ic conditions would be about 0. 015 inch for r e se r v o ir p r e s s u r e s above the slot, rep resen ta tiv e of the plateau p r e ss u r e s exp ected for 9 =20°. Widths la r g e r than this resu lt in choking of the flow in the plumbing of the m ea su rin g s y s te m betw een the slot and the large r e c e iv e r tank. A ttem pts w ere, th erefo re, m ade in the actual wind tunnel p rogram to reduce the span of the slo t in order to in su re son ic conditions at the slo t throat for th e la rg er v alu es of d*. H ow ever, th is proved to be u n sa tisfa cto ry sin c e th ree-d im en sio n a l effects becam e im portant. The p a rtia l-sp a n slo t was unable to low er the plateau p r e ss u r e su fficien tly due to a constant entrainm ent of c ro ssflo w fro m the adjacent higher p r e ssu r e area ex istin g w h ere no m a s s w as being rem oved . H igher m a ss 33 flow s w e r e thus en cou n tered , but w ith c o n sid e r a b ly l e s s e ffe ct on the r ed u ctio n of the sep a ra tio n reg io n . The p a r tia l-sp a n slo t y ie ld s in th is s e n s e an o p p o site flow str u ctu re to that of a p a r tia l-sp a n aft w edge or flap. E x te n sio n to la r g e r s lo t w id th s, w h e r e no e x p e rim en ta l data could b e obtained, w as m a d e sin c e e x c e lle n t a g r e e m e n t r e s u lte d b e tw e en the m a s s flow s c a lcu la te d by c o n sid e r in g so n ic co n d itio n s at the s lo t and th o se d e te r m in e d e x p e r im e n ta lly . The c o lla p s e of the sep a ra ted r e g io n to the in cip ien t c a s e m ay be obtained in d ep en dently through tw o g e o m e tr ic ch a n g es of the m o d e l; a .) R ed u cin g the a ft-w ed g e a n g le, 9 , until an angle is r e a c h e d , th rou gh w hich th e boundary la y e r can tu rn w ithout sep a ra tin g . H old en (28) has p ro p o sed , b a se d on e x p e rim en ta l in v e stig a tio n s, that - V z Mq o ^i ~ Xj/ (flat p late - ram p) w h ere the p ro p o rtio n a lity fa c to r a p p ea rs to be a function of the w a ll to stagn ation te m p e r a tu r e ra tio . B a se d upon a v a ilab le e x p e rim en ta l data, F ig . 33 in d ic a te s the v a r ia tio n of the fa c to r w ith te m p e r a tu r e , b. ) A pplying in c r e a s in g s u r fa c e su ctio n , in th is c a s e slo t su c tio n at the in te r fa c e of th e tw o s u r fa c e s , until again su fficie n t low e n e r g y has b e e n r em o v ed fr o m the boundary la y e r s o that it is able to n eg o tia te the tu rn angle 9 w ithout sep a ra tin g . T o obtain an e s t im a te of the slo t su ctio n r eq u ired to p rev en t sep a ra tio n , the f ir s t m o m en tu m in teg r a l is c o n sid e r e d . A s a f ir s t a p p ro x im a tio n © , the m o m en tu m th ic k n e ss , and the tr a n sfo r m e d fo r m fa c to r , Hj-r , a r e c o n s id e r e d co n sta n t over the sh o ck -b o u n d a ry la y e r in te r a c tio n at the ju n ction of the fron t and aft w ed g e (27). F u r th e r m o r e , at in cip ien t sep a ra tio n the w a ll sh ear s t r e s s , Tw , is z e r o so that Eq. (2) b e c o m e s but p e M | due = - u e d p e and w ith d (pe u e ) = p e dug + u e d p e Eq. (3) The in te g r a l of the le ft sid e of Eq. (4) is the d e s ir e d m a s s r em o v ed , (2) b e c o m e s (4) + 35 In ord er to in teg ra te th e seco n d te r m of E q. (4), th e follow in g ch an ge of v a r ia b le is m a d e : u e — = M * ~ lvle % % w h ere a* = (y R T 0) so that a* d M * = due [ y - 1 ❖ 2 1 x /z M e Su bstitution of th e se r e la tio n s into Eq. (4) and in teg ra tin g y ie ld s th e follow in g r e la tio n for th e m a s s suction r e q u ir e d to m a in ta in in c ip ien t sep a ra tio n , P e ^ e , Z z J , H. + y ± tr Po, P e 3ue 3 P e 1u e1 -1 Htr + 1 + 1 .2 5 1- M | 2 M* P e i + 1. 875 1- 1- M, o. 2 M * z ‘ ^ M* (5) * + 0 .7 6 5 s in -1 I 6 # M f (M*) w hich, for th e con d ition s of th is in v e stig a tio n , y ie ld s 0. 212 and 4 . 728 for the co n sta n ts of th e f ir s t and second t e r m s , r e s p e c tiv e ly , s in c e for T w = 0, Tw / T Q = 0. 56 and y - 1 .4 , H^r = 2. 9 4 [ Cohen and R esh otk o (10)] . 36 T h e r e fo r e , for know n flow con d itio n s u p str e a m of th e aft w e d g e , c a lc u la tio n s of the m a s s r e m o v e d m a y b e m a d e as a function of th e a ft-w ed g e a n g le. T he r e s u lt s a re g iv e n in F ig . 34 fo r the m a s s r e m o v e d in te r m s of the in v is c id sta tic p r e s s u r e r a tio a c r o s s the in ter a c tio n . T he a g r e e m e n t of th is s im p lifie d a n a ly s is w ith the r a tio n is s e e n to b e s u r p r is in g ly good. T h e above a n a ly s is d o es not, of c o u r se , p r e d ic t an in cip ien t a ft-w e d g e a n g le fo r w h ich no m a s s tr a n sfe r w ou ld be r eq u ired . C a lc u la tio n s of th e m a s s r e m o v e d , b a se d on th e boundary la y e r m a s s d e fe c t at x = xpjj^ w ith out se p a r a tio n , m a y be a ls o m ade th rou gh u se of (A ppendix C), w h e r e H is e v a lu a ted fo r the con d itio n s of th is in v e s ti gation fr o m s im ila r it y so lu tio n s at Tw / T 0 = 0. 56 and no s tr e a m w is e p r e s s u r e g rad ien t, i. e. , s in c e Htr = 1. 4 4 [C o h en and R esh o tk o (10)] and M e = 6. 66. The r e s u lt s of the c a lc u la tio n of th e in c ip ien t m a s s tr a n s fe r r a tio , (3 ^ , as w e ll a s the r a tio , |3, w ith se p a r a tio n , a r e show n in F ig . 35. e x p e r im e n ta lly d e te r m in e d m a s s flo w s r eq u ir ed for in c ip ie n t sep a - < *> ) M j = 2 3 .1 , 37 R em oval of about 12. 5 per cent of the boundary layer m a s s defect r e su lts in incip ien t sep aration for Q = 20° for the conditions of th is test. B ased on the above d isc u ssio n , the follow ing calcu lation p roced ure is p roposed for a given , RG o and 6 to obtain the pertinent p a ra m eters of the incip ien t phenom enon due to a d eflected control su r fa c e: 1. C alculate , R e^ and by standard m eth od s depending on the g eo m etry of the lifting surface. 2. F r o m Fig. 33 obtain X for the particular Tw / T0 and calcu late 0 i fr o m 6 j = ( X / (6 ^ in radians). 3. C alculate the incipient m a s s flow ratio fr o m Eq. (5) rh ------------------- = f (M *) P e 1u e 1 4. Since f (M g) = Kpx d f / p ^ u e^ (g > , d* is found aftei calcu lation of the boundary layer m om en tu m defect w ithout separation, at the junction of the two su r fa c es. C H A PTER VI CONCLUSIONS An in v e stig a tio n w a s condu cted in the A R L 2 0 - in ch h y p e r so n ic w ind tunnel to d e te r m in e the e ffe c t s of m a s s rem o v a l on the la m in a r boundary la y e r sep a ra tio n c h a r a c t e r is t ic s induced on a w ed g e by a tra ilin g edge flap . The t e s t s w e r e conducted at a M ach 5 num ber of 12. 3 and a n om in al R ey n o ld s nu m ber of 0. 79 x 10 per inch. T w o -d im e n sio n a l flo w w as obtained over th e c en tra l 2 in ch es of the m o d el w ithout u se of sid e p la te s or fe n c e s . P r e s s u r e d istrib u tio n and m a s s tr a n s fe r t e s t s w e r e p e r fo r m ed at Tw / T 0 = 0. 56 and h ea t tr a n sfe r d istrib u tio n t e s t s at Tw / T 0 = 0. 28. B a se d on the r e s u lt s of th is in v e s tig a tio n , the follow in g c o n c lu sio n s are in d ica ted : 1. Side p la tes or fe n c e s ju st co v er in g th e sep a ra ted reg io n a r e m o r e e ffe c tiv e than p la tes exten d in g fr o m th e m o d el lea d in g edge in red u cin g v a r ia tio n of th e s p a n -w is e p r e s s u r e d istrib u tio n , sin c e the boundary la y e r on the la r g e r fe n c e s a p p aren tly in te r a c ts w ith that on the m o d e l su r fa c e . D e p a r tu r es fr o m tw o -d im e n s io n a l flow a r e found to be n e g lig ib le. S e le c tio n of a s y m m e tr ic a l m o d e l co n fig u ra tio n w ith a la r g e span c o m p a r e d w ith th e c h a r a c te r is tic d im en sio n s of the sh e a r flow in the c r o s s plane con trib u ted la r g e ly to w a rd m in im iz in g edge e ffe c ts. 2. T h e u s e of th e fr o n t-w e d g e b a se p r e s s u r e is an e x c e lle n t m e a n s of obtaining n atu ral su ction fr o m the su r fa c e of th e m o d el. F u r th e r m o r e , w ith p r e s s u r e r a tio s g r e a te r than tw o a c r o s s the slo t, a so n ic th ro a t is obtained; w h ereb y the m a s s flow r e m o v e d by su c tio n can b e d e te r m in e d e a sily by u sin g e ffe c tiv e stagn ation co n d itio n s, w h ich in th e p r e se n t in v e stig a tio n w e r e tak en as the p lateau p r e s s u r e in th e sep a ra ted flo w r eg io n and the w ed ge w a ll te m p e r a tu r e . The m a s s flow s thus c a lcu la ted w e r e in e x c e lle n t a g r e e m e n t w ith m e a s u r e d v a lu e s. 3. R e su lts of a s e m i- e m p ir ic a l a n a ly sis y ie ld e d the v a r ia tio n of the p r e s s u r e r is e th rou gh the sep a ra tio n sh ock and th e c h a r a c t e r is tic length r a tio of sep a ra tio n a s, w h ere the fu n ction of X g/xjjj^ w h ich b e s t c o r r e la te d th e data w a s found to be (1 - x s / x ^ ^ ) ^ . It w a s a ls o noted that the c h a r a c t e r is tic len gth ratio could be c o r r e la te d to th e slo t w idth ra tio for sm a ll in cip ien t sep a ra tio n a n g le s by 40 Although no a n a ly tic a l d e v elo p m en t w a s achieved , n or was c o m p a riso n w ith other data p o s s ib le , th e constant of p roportion ality, b a se d on the d ata of this in v e stig a tio n , w as found t o be depend en t on the in cip ien t sep a ra tio n a n g le ratio, Q 6 , and p rob ab ly, although not v e r ifia b le fr o m this in v e s tig a tio n , on x . 4. T h e r e su lts sh ow , as e x p e cted , that f o r constant f r e e s tr e a m con d ition s and for a g iv en a ft-w ed g e a n gle th e sep a ra tio n r e g io n d e c r e a s e s w ith d e c r e a s in g w a ll te m p e r a tu r e . For th e w a r m e r w all th e boundary la y e r d e n s ity is le s s th a n that fo r th e c o o le r w all, ren d erin g the fo r m e r m o r e s u s c e p tib le to a c c e le r a tio n f o r c e s . 5. B y in teg ra tio n of the f ir s t m om entum in te g r a l eq u ation for a c o m p r e s s ib le boundary la y e r w ith th e a ssu m p tio n of co n sta n t m o m en tu m th ic k n e s s , an e x p r e s s io n i s obtained f o r the m a s s suction req u ired to m a in ta in in cip ien t se p a r a tio n , i. e. , T w = 0, at th e junction of the two s u r fa c e s . The r e s u lt s f r o m this a n a ly s is are in g o o d a g r ee m e n t w ith th ose ob tained ex p erim en ta lly . It i s found th a t the exten t of se p a r a tio n is e x tr e m e ly s e n s it iv e to s u c tio n . F o r th e condi tio n s in v e stig a te d , r e m o v a l of a s m a ll p ercen ta g e of the b ou n d ary la y e r m a s s flo w is su ffic ie n t to c o lla p s e the s e p a r a te d flow reg io n . In te r m s of th e boundary la y e r m a s s d efect, the s u c tio n r e q u ir e d for in cip ien t se p a r a tio n is a p p r o x im a te ly 1% for 5°, 4% for 10°, 8% for 15°, and 12. 5% for 20°. In g e n e r a l, th e effect of su ction i s to 41 r e m o v e the low m o m en tu m flow n ear the w a ll, thus enabling the rem a in in g sh e a r la y e r to n egotiate a h igh er c o m p r e s s io n at rea tta ch m en t. 6. R e co m m en d e d e x te n sio n s of the p r e se n t w ork in clu d e ex p e rim en ta l stu d ies to d eterm in e the e ffe c ts of M ach and R ey n o ld s nu m ber as w e ll as the in flu en ce of flap len gth on th e sep a ra tio n . A n a ly tica lly , the in te g r a l m eth o d s of L e e s and R e e v e s (8) m a y be a p p licab le fo r the a n a ly sis of the sep a ra tio n with m a s s tr a n sfe r , providing a prop er c h o ic e of w eigh in g fu n ction s is found fr o m s im ila r boundary la y e r so lu tio n s. FIGURES Shock Wave a) INVISCID, NO SEPARATION R eattachm ent Shock Separation Shock Dividing Streamline r~ u = 0 Line HL b) V IS C O U S , WITH SEPARATION FIGURE I. COMPRESSION CORNER FLOW a * . U > I.Rj control valve ZHot by-pass valve 3 B y -p ass to atmos. 4. Tunnel vacuum valve 5iPump house vacuum valve GMain air supply valve 7 Sphere vacuum valve Compressor o High Pressure Station Dryer I Storage Bottles x Test Section Cooling J Nozzle Water Diffuser Heat Exchanger Stagnation Chamber rw\ f W \ Vacuum Station Vacuum Sphere 9 m Vacuum Pumps By-Pass Nozzle [ Water Spray /Ov ^ u ii J l J i ii fW V 1500 KW Power D f Atmosphere FIGURE 2. SCHEMATIC DIAGRAM OF HYPERSONIC WIND TUNNEL iK F J j * 1200 psig 2.4 Model Leading Edge Model Trailing Edge 12.2 00 12.0 0 2 4 6 8 12 10 x, Distance from Nozzle Exit P lane, inches FIGURE 3. CENTERLINE LONGITUDINAL MACH NUMBER DISTRIBUTION OF THE WIND TUNNEL L n z — S o p> Slot Cover for d* = 0 Tests 0.141 0.120" \ - Throat d* Flap (£ _ of orifice Wedge d9 s .0 5 4 sin ( 12 + 0 ) M FIGURE 5. DETAIL OF SLOT CONFIGURATION SHOWING LOCATION OF PRESSURE ORIFICE BELOW THROAT -J r— Honeycomb Panel-i 53 48 49 S O REAR FRONT 46 O ze o 30 O 43 40 37 34 o o o o 4 I 8 35 V 47 O 3 < i 27 O WEDGE AFT WEDGE 25 O 23 O 18 O g & o O 1 4 Oil 8 5 2 O — o— 0— 0 o O O o o 1 3 10 7 4 i. 17 o 24 O 26 O FRONT WEDGE o Pressure Orifice + Thermocouple FIGURE 6. PRESSURE MODEL INSTRUMENTATION Model ^-T ypical of 5 3 Pressure Lines * 0 .0 6 2 5 “- O.D. Digital \ ^ o l t M eter '-^Amplifier [itO jQ O Q ol-------------------- • ! ------- Tape « --------> X-Y Plotter Scanivalve 8 ^ T ra n s d u c e r Cylinder t L Cooling P Water Li Lines VTunnel Wall Transducer — ^ o - A Tunnel Wall ^ X -Y Plotter — - \ b Inclined Silicone Oil Manometer (5 2 -M o d e l Surface 8 Slot Pressures) (C alibration) Amplifier (I-B a s e P ressu re) Atmosphere Vacuum Pump FIGURE 7. SCHEMATIC OF PRESSURE MEASURING SYSTEM Sharp Edge 20 \ 0 .256 2.000 .38 TYPE I 3.500 38 T 0.010 TYPE n 20 0.513 3.578 TYPE SI All dimensions in inches FIGURE 8. FENCE CONFIGURATIONS _ 5 i z - 27 X * IS o °1S REAR FRONT WEDGE r-Honeycomb Panel -i 21 17 X x 22 It X X 2 5 3B X o 39 23 l» X X 2 4 X AFT WEDGE 1 3 6 X x 7 X JL 2 x x W 14 Jk 4 I < X X x -x- X * S i * 1 6 JO X x FRONT WEDGE o - Pressure Orifice x - Thermocouple i C O FIGURE 9. HEAT TRANSFER MODEL INSTRUMENTATION M odel7 A ^-Typical of 3 7 Thermocouple Wires tit* Oscillograp h ^ Amp|ifie_ f — 4 o 7 - o ^ - - (Surface 8 Base Tem perature) Potentiom eter O Tunnel Wall DVM ft Tape Amplifier-, 4------ i°° -? J —■ _ _£ - A A A r * To IBM 7 0 9 4 merer-?- ■ A m plifier^ ■ ° y i _ --------------- ! ------------ |o o of - . (Surface Tem perature) rX-Y Plotter (Calibration) ( Internal S tructure T em perature) FIGURE 10. SCHEMATIC OF HEAT TRANSFER MEASURING SYSTEM 1.00" I.D.x7‘ Line Model Tunnel Wall Inclined Oil M anom eter' ******** ********* Tem perature [xh"-Q uick-O pening Valve Tank *IOcu. feet Amplifier Atmosphere — f a B - Oscillograph Vacuum Pump P ressure T ransducer > ■ j FIGURE II. SCHEMATIC OF MASS FLOW MEASURING SYSTEM 54 M © - 12.3 R eo j/in =7.9 X I04 d * =0 X = 3 .4 0 inches O - no fences O -s m a ll fences ± 3 .5 in-Type I □ — large fences ± 3.5 in - Type J L and H I 4 0 3 0 20 — 0 — — 0 — Q - 10 - 2 0 2 3 y, Spanwise Distance from Centerline, inches FIGURE 12. SPANWISE PRESSURE DISTRIBUTION AT X=3.4 INCHES SHOWING CONSTANT PRESSURE OVER ± 1 INCH FROM CENTERLINE 1 0 0 6 , deg. 0-0 0 - 3 . 7 5 d* = 0 Mqq = 12.3 R em /in.= 7.9 X 10 8 0 6 0 4 0 HL Tangent Wedge Inviscid 20 0 5 2 4 0 I 3 x, Distance from Leading Edge, inches FIGURE 13. CHORDWISE PRESSURE DISTRIBUTION: 8 = 0 ° AND 3 .7 5 ° 100 80 R e ^ /in .= 7.9X 10 4 60 HI- 40 i— 20 Inviscid ______ L l I I 1 2 3 4 5 x,Distance from Leading Edge,inches FIGURE 14. CHORDWISE PRESSURE DISTRIBUTION: 8=5° 0=K>° d * f in. 0-0 A - 0 .0 1 9 0 - 0 . 0 3 9 100 8 0 HL 6 0 £L P © 4 0 20 Inviscid 2 3 4 5 x, Distance from Leading Edge, inches FIGURE 15. CHORDWISE PRESSURE DISTRIBUTION: 10° tfl Moo* 12.3 R e ^ /in *7.9 X 10 HL 100 8 0 6 0 4 0 20 Inviscid 0 x, Distance from Leading Edge, inches FIGURE 16. CHORDWISE PRESSURE DISTRIBUTION . * 8=15° 120 Re— Vin.=7.9x10 1 0 0 0 = 20° d*,in. 0 - 0 A - 0 .0 3 9 O - 0 .0 6 9 < 3 > - 0 .089 8 0 P P 00 4 0 Inviscid 20 x,D istance from Leading E dge,inches FIGURE 1 7 . CHORDWISE PRESSURE DISTRIBUTION!0=20° Slot Width, inches X 10 100 8 ,deg. 0-20 O ' 1 5 □ - 1 0 A - 5 O - 3.75 0-0 R e ^ / i n - 7.9x10 W T 0 = 0 .5 6 8 0 IO 6 0 4 0 * - 20 7 6 10 0 4 5 8 9 II P p , Plateau Pressure, mm Hg FIGURE 1 8 . VARIATION OF THE PLATEAU PRESSURE WITH SLOT WIDTH 61 Mco =12.3 Reco / in.= 7 9 X 10 T o - 1 9 0 0 ° R 1 0 0 - ro O X < /> < u J Z o c « • J Z 6 0 ■o ? =0.56 ” 40 C V Q . < 3 _c * . l 2 0 T3 = Q28 20 8 , Aft Wedge Angle t degrees FIGURE 19. INCIPIENT SLOT WIDTH VARIATION WITH THE AFT WEDGE ANGLE FOR Tw / T 0 =0.56 AND 0.28 120 M q q = 12.3 Rem /in.= 7.9 X I04 Two-Shock Inviscid 100 6 , deg. 0-20 0-15 □ -10 A - 5 0-0 80 -— 15 6 0 - — 10 I -------- 4 0 Tangent Wedge 20 Inviscid o A r - 1 0 I 2 3 4 5 x , Distance from Leading Edge, inches FIGURE 20. CHORDWISE PRESSURE DISTRIBUTIONS FOR VARIOUS AFT-WEDGE DEFLECTIONS AND NO SLOT OPENING 100 R e _ /in .* 7.9X 10 8 0 O -d * = 0 .0 3 9 in., 1.5 in. chord aft. wedge A -d * = 0 .0 3 8 in., 2 .5 in. chord aft. wedge HL P P, G O 4 0 20 Inviscid 0 2 3 4 5 6 x , Distance from Leading E dge,inches FIGURE 2 1 . CHORDW ISE PRESSURE DISTRIBUTION WITH AFT WEDGE EXTENSIONQ = 10° C T - 120 Re,r)/in = 79 X I04 d * = 0 O -1.5" chord aft wedge A -2 .5 " c h o rd aft wedge 100 80 Bow Shock Interaction 60 40 HL 20 3 2 4 5 6 x, Distance from Leading Edge .inches FIGURE 22. CHORDWISE PRESSURE DISTRIBUTION WITH AFT WEDGE EXTENSION:6 =20° 0s * Mjq - 12.3 ReC Q/in. = 7 9 x I04 9 = 2 0 °, d*=0 0 = 20® d*= d*= 0 .0 8 9 " FIGURE 23. TYPICAL SCHLIEREN PHOTOGRAPHS FOR 0 = 2 0 °, d*=0 AND 0 . 0 8 9 -IN C H .Stanton Number x 10 5 0 • V 12-3 Re —/in. = 7.9 x 10 4 G O 0 =0° 0 - d * = 0 Theory (E ckert) 4 0 3 0 20 Uncertainty .c O HL x,D istance from Leading E dge,inches FIGURE 24. HEAT TRANSFER DISTRIBUTION! 0 = 0° a - ~ O' Stanton Number x 10 11^*12.3 R e ^ /in .5 7.9x10* 0 = 5° □ - d*=0 — Theory (Eckert) 5 0 4 0 30 HL Data Fairing i i x,Distance from Leading Edge finches FIGURE 25. HEAT TRANSFER DISTRIBUTION: 0=5° i ,Stanton Number x 10 5 0 R e^/in. = 7 9 x 10 0 = 10 ° O - d * = 0 Theory (Eckert) ^ 4 0 30 20 (Schtieren) o HL Data Fairing x,Distance from Leading Edge,inches FIGURE 26. HEAT TRANSFER DISTRIBUTION: 0 = 10° C T ^ CO A - d * = 0 Theory (Eckert) A i « / t / i (Schlieren) HL Data Fairing 5 4 3 2 I xfDistance from Leadrng Edge,inches FIGURE 27. HEAT TRANSFER DISTRIBUTION . * 0=15° Stanton Number x 10 < 3 > 66.8 Mc0 = l2.3 R e^/in . = 7.9x1 O' 0 = 20 ° O - d*=0 Theory (Eckert) 50 40 3 0 - (Schlieren) o HL ^ ^ - D a t a Fairing — | — .<$> x,Distance from Leading Edge,inches FIGURE 28. HEAT TRANSFER DISTRIBUTION! 8=20° .Plateau Pressure, m m Hg 71 12.3 R e ^ /in =7.9 x 10 Separated Flow Attached Flow d.deg. 0-20 <G>"I5 0-10 A - 5 0 - 3 . 7 5 0-0 d*lncreasing 10 8 6 4 2 Required for Sonic Flow at Slot 2.0 0 1 .0 P 9 , Slot P ressure,m m Hg FIGURE 29. PLATEAU VERSUS SLOT PRESSURE SHOWING THAT SONIC FLOW WAS OBTAINED FOR ALL TESTS d * t Slot Width, inches xIO3 72 Mco = '2.3 R e ^ /in . * 7 9 x 1 0 4 0 6-5° — Calculated ! Slot Pressure Calculated ! Plateau Pressure 20 0 6 0 O ^A ctual Measurement 4 0 20 0 0 5 0 10 20 3 0 4 0 m /L g , Slot Mass Flow per Unit S p a n ,slu g s/sec -ft.x IO 6 FIGURE 3 0 . SL O T M A S S FL O W P E R UNIT S P A N FOR 0 = 5 ° AND 10° d * , Slot Width, inches x 10 6 - 15° O - Actual Measurement — Calculated!Slot Pressure — Calculated!Plateau Pressure R e^/in. =7.9x10 1 0 6 0 4 0 20 - 10 20 30 4 0 50 6 0 © 6 m /Ls .Slot Mass Flow per Unit Span,slugs/sec-ft.xlO FIGURE 31. SLOT MASS FLOW PER UNIT SPAN FOR 0 = 15° , Slot Width .inches xIO ( MQQSI2.3 Rem /in.s 7 .9 x l0 8 0 O Actual M easurem ent — Calculated: Slot Pressure Calculated: plateau Pressure 6 0 4 0 20 0 10 20 4 0 7 0 3 0 5 0 6 0 m /L s , Slot Mass Flow per Unit Span t slu g s/sec -ft. xIO6 FIGURE 32. SLOT MASS FLOW PER UNIT SPAN FOR 5=20° -o tfc . 1.5 1 .0 0.5 O-Holden (28) □ -Townsend (29) Q-Needham (25) A-Ginoux (23) O " Present Investigation □ Data Fairing A D 0.2 0.4 0.6 0.8 1.0 V T o , _ 2 FIGURE 33. VARIATION OF X IN = XX, WITH T w/T 0 76 V / / s s M B = 6 .6 6 4 — Theory A - Experiment 3 2 0 10 8 6 0 2 4 FIGURE 3 4 . MASS SUCTION REQUIRED FOR INCIPIENT SEPARATION , Slot Width, inches xIO 1 0 0 10 8 0 20' Incipient Separation 6 0 4 0 T > 20 Percent of Boundary Layer Mass Defect at x s 3 .5 8 " Removed by Slot Suctiont% FIGURE 35. VARIATION OF p WITH d* FOR 8*5,10,15, S 20* „ TABLES TABLE 1 SUMMARY OF CONFIGURATIONS INVESTIGATED Spanwise Pressure Chordwise Pressure . Heat Transfer Mass Transfer Aft. Wedge Extension Sharp Slot Surface Oil Flow 6 , Fence, d*, deg. in. in. 0,deg. d*, in. 0,deg. d*, in. 6 , deg. d*. in. 9, deg. d*, in. 0,deg. d*, in. 0,deg. d*, in. ,0 - 0. + 3. 511 0. 20 - 0. + 3.51 0. + 3. 5III 0. ~ - .003 .009 . 030 .057 . 100 0 0. 3.75 0. 5 0. .005 .008 .014 10 0. .008 •012 .029 .033 .039 .043 15 0. .010 .020 .0 30 . 040 .050 .059 .064 .070 20 0. .010 .020 ■ M ■ M .069 . 078 .082 .089 .098 0 0. 3.75 0. 5 0. . 005 . 007 .009 .015 10 0. m .029 .035 .040 . 050 15 0. .012 :851 .040 .049 .058 ■ M .070 20 0. :81f . 033 .040 .053 .057 .078 .089 . 096 10 0.008 .010 . 014 15 0.005 .006 .014 .021 .043 20 0.005 .010 .015 .018 .040 .060 10 0.038 20 0. . 010 . 020 . 030 . 045 0 0.004 . 007 . 020 20 0.006 . 032 0 0. 5 0. . 009 10 0. . 039 . 064 20 0. 0.089 -vi vO TABLE 2 PRESSURE MODEL INSTRUMENTATION Orifice No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 17 18 19 20 21 22 23 Surface 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 15 48 49 50 Base 51 52 53 54 55 Extension 56 57 x, inches y, inches 0.75 0. 1.40 0. 1.60 . 25 1. 80 - .25 1.90 0. 2. 00 . 25 2. 20 - . 25 2. 30 0. 2.40 . 25 2. 60 - .25 2. 70 0. 2. 80 . 25 3.00 - .25 3. 10 0. 3. 40 0. 3.40 -1.00 3.40 1.00 3. 40 - . 50 3.40 . 50 3. 40 1.00 3. 40 -1.00 3. 40 1. 75 3. 40 -1.75 3. 40 2. 50 3. 40 -2. 50 3.78 -2. 50 3.78 2. 50 3.78 -1.75 3.78 1. 75 3.78 -1.00 3.78 1.00 3. 78 0. 3. 88 . 25 3.98 - .25 4.08 0. 4. 18 . 25 4. 28 - . 25 4. 38 0. 4.48 . 25 4. 58 - . 25 4. 68 0. 4. 78 . 25 4. 88 - . 25 4.98 0. 4. 78 1. 75 4.78 -1. 75 0. . 25 - .75 -2. 50 - . 25 2. 50 . 75 0. . 25 - .25 0. 80 , inches 0. 7 TABLE 3 81 HEAT TRANSFER MODEL INSTRUMENTATION Thermocouple No. x, inches y, inche 1 1.43 0. 2 1. 72 . 5 3 1. 78 - . 5 4 2. 05 0. 5 2.02 -1. 0 6 2. 63 2. 0 7 2. 63 1.0 8 2. 66 0. 9 2. 68 -1. 0 10 2. 69 -2. 0 11 2. 92 . 5 12 2. 99 - . 5 13 3. 26 2. 0 14 3. 26 0. 15 3. 23 -1. 0 16 3. 87 -2. 0 17 3. 84 2. 0 18 3. 87 . 5 19 3.91 - . 5 20 3. 87 -2. 0 21 4. 49 2. 0 22 4. 44 . 5 23 4. 51 - . 5 24 4. 48 -2. 0 25 4. 78 0. Orifice No. 1 0. 75 0. 16 3. 40 0. 39 4. 38 0. Note: Instrumentation on base of front wedge is identical to that of the pressure model {TABLE 2) 82 ! TABLE 4 OIL MIXTURE Ingredient Quantity 10 centi-stoke Silicone Oil 100 centi-stoke Silicone Oil Titanium Oxide Oleic Acid 7 cubic cm. 3 cubic cm. 3 m illi-liters 2 drops TABLE 5 SPANWISE PRESSURE DISTRIBUTIONS P/Pco e, degrees 0 20 d*. inches 0. 0. 0. 0. 0. . 003 . 009 . 030 .057 . 100 Fence Type none II none I i n none none none none none Orifice No. 10 12. 71 25. 71 26. 42 26.12 _ _ - - 11 12. 57 12. 82 25. 81 26. 57 26. 17 26. 55 26. 55 23. 49 13. 86 13. 79 12 12. 40 - 25. 86 26. 65 26. 24 - - - - - 16 12. 26 11. 96 25. 86 26. 78 26.40 26. 57 26. 48 24. 34 22. 86 11. 82 17 12. 82 12. 77 25. 86 26. 60 26. 42 - - - - - 18 12. 80 12. 92 25. 66 26. 60 26. 04 - - - - - 19 12.44 • 26. 01 26. 88 26. 65 27. 27 26. 83 24. 44 22.91 11. 70 20 12. 31 • 25. 84 26. 88 26. 27 26. 86 26. 60 24. 44 22. 88 11. 87 21 12.48 12. 26 25. 89 26.96 26. 32 27. 44 27. 04 24. 67 23.04 12.05 22 12. 35 12. 36 25. 94 26.93 26. 68 27. 37 27. 04 24. 59 22. 83 11. 77 23 12. 33 25. 27 26. 63 25. 73 - - - - - 24 12. 38 - 25. 48 26.70 26. 52 - - - - - 25 12. 03 12. 44 24. 59 26. 80 25. 12 26. 45 25. 86 23. 65 21. 69 11. 95 26 12.47 13. 18 24. 89 26. 63 25.94 26. 45 26. 14 24. 06 22. 02 12. 49 28 12. 63 24. 15 26. 78 24. 89 - - - - - 29 13. 11 25. 43 26. 70 26. 65 27. 21 26. 86 26. 27 27.78 41.92 30 12.91 ■ * 25. 15 26. 75 25. 85 27. 21 26. 68 26.09 28. 39 40. 82 31 13. 25 — 25. 61 26. 75 26.68 - - - - - 32 13.02 25. 45 26. 80 26. 32 - - - - - 33 13. 64 13. 15 25. 73 26. 75 26. 52 28. 28 27. 65 27. 16 28.05 40. 11 45 13. 37 13. 31 98. 86 94. 17 96.95 103.94 103.91 107. 94 - 117.27 106. 77 46 13. 39 13. 49 90. 20 81. 12 89. 79 96. 52 95. 20 103. 07 120.99 109. 06 47 13.91 13.97 88. 29 70.93 75. 77 91. 58 91. 55 100.45 121.19 112. 22 0 O TABLE 6 CHORDWISE PRESSURE DISTRIBUTIONS P/Poo 6 , degrees d#, inches 0 0. 3. 75 0. 0. .005 5 .008 . 014 Orifice No. 2 15. 86 15. 51 15. 65 15. 70 15. 88 15. 73 3 15.91 15. 62 15. 83 15.91 16. 04 15. 91 4 15. 70 15. 26 15. 65 15. 73 15. 88 15. 73 5 15. 62 15. 10 15.65 15. 73 15. 83 15. 73 6 15. 44 15.00 15. 54 15. 59 15. 70 15. 59 7 15. 18 14.79 15. 30 15. 30 15. 46 15. 36 8 15. 05 14. 81 15. 20 15. 17 15. 30 15. 20 9 14. 81 14. 53 14.99 14. 93 15. 12 14.99 10 14. 50 14. 14 14. 56 14. 48 14. 64 14. 59 11 14. 32 13.99 14. 40 14. 32 14. 64 14. 38 12 14. 17 13. 80 14. 24 14. 19 14. 35 14. 24 13 13. 83 13. 42 13. 82 13. 77 13. 93 13. 85 14 13. 60 13. 26 13. 77 13. 79 13. 71 13. 61 16 13. 39 12.92 14, 14 14. 14 13. 71 12. 87 33 13. 39 15. 85 - 19. 41 18. 72 17. 87 34 13. 68 - 19. 30 20. 52 19.94 19. 19 35 13. 80 - 20.60 21. 50 21. 36 20. 94 36 13. 80 18. 42 21. 80 22. 40 22. 19 21. 79 37 13.93 18.91 22. 69 23. 19 23. 06 22. 77 38 14.09 19. 55 23. 83 23. 99 24. 07 23. 83 39 14. 17 19.97 24.62 24. 68 24. 78 24. 65 40 14. 22 20. 33 25. 26 25. 23 25. 31 25. 20 41 14. 35 20. 87 26. 10 25. 79 26. 10 25. 97 42 14. 35 21. 01 26. 24 26. 18 26. 41 26. 41 43 14. 22 21. 01 26. 37 26. 24 26. 47 26. 45 44 14. 11 20.98 26. 47 26. 10 26. 55 26. 55 ■ 45 13. 31 19. 89 25. 49 25. 12 25. 42 25. 44 £ ............................ ....... ---------- - ........... --- ------------ --- ................ — - . . ... TABLE 7 CHORD WISE PRESSURE DISTRIBUTION P/P® 9 = 10° d*, inches 0. . 008 .019 . 029 .033 . 039 .043 Orifice No, 2 15. 54 15. 51 15. 33 15. 26 15. 20 15. 25 15. 64 3 15. 23 15.23 15.02 15. 00 14.92 15.46 15. 51 4 14.94 15. 00 14.79 14. 76 14.71 15. 33 15. 23 5 14. 87 14.92 14.71 14. 69 14. 61 15. 30 15. 17 6 14. 69 14.74 14. 56 14. 53 14. 51 15. 20 15.02 7 14. 38 14. 38 14. 32 14. 32 14. 27 14.99 14.76 8 14. 22 14. 40 14. 22 14. 20 14. 17 - 14.65 9 14. 04 14. 20 14. 04 14.01 13.99 14.97 14. 45 10 13.78 13.91 13. 83 13.75 13. 73 14. 42 14.06 11 13.68 13.78 13.63 13. 58 13. 58 14. 32 13.90 12 14. 14 13. 73 13. 44 13. 37 13. 34 14. 14 13. 70 13 17. 58 15. 54 13. 55 13.01 13.03 13.75 13. 31 14 18. 77 17.09 14. 56 12. 88 12.90 13.56 13. 12 16 21. 00 20. 25 18. 33 15. 49 15. 20 12. 81 12.45 33 22. 88 22. 26 21. 67 20. 66 20. 69 25. 34 25.05 34 23.92 23.74 23. 17 22. 75 22.78 28. 09 27. 80 35 25. 68 25.96 25.73 26. 01 26. 17 31. 56 31. 56 36 26. 89 27. 28 27. 28 27. 82 28.05 34. 16 34. 16 37 28. 18 28.68 28. 88 29. 24 30. 20 36.62 36. 62 38 30.15 31, 16 31.75 32. 45 33.07 39. 32 38. 88 39 31. 62 32. 86 33. 54 34. 26 34. 88 41. 86 41.08 40 32.92 34.08 34.93 35. 53 36. 43 43. 47 42.69 41 34.98 36. 64 37.75 38. 27 39. 38 45. 23 44. 53 42 36. 38 38. 11 39. 30 39. 35 40.90 47.59 45.98 43 37.00 38. 60 39.77 39. 84 41. 42 47. 72 46. 61 44 38. 11 40. 21 41. 47 41. 58 43. 23 47.93 46. 89 45 37. 65 39. 51 40. 85 40. 83 42. 40 47. 15 46.17 o d m . TABLE 8 CHORDWISE PRESSURE DISTRIBUTIONS P/Pco e = i s 0 d*, inches 0. . 010 .020 . 030 . 040 . 050 .059 . 064 . 070 Orifice No. 2 15.70 15. 55 15. 44 16. 02 15. 57 16. 03 15. 82 15.98 16. 00 3 15. 49 15. 21 15. 42 15. 65 15. 52 15. 66 15. 45 15.67 15. 64 4 15. 20 14. 93 15. 13 15. 36 15. 23 15. 40 15. 16 15. 41 15. 35 5 15.08 14. 88 15. 03 15. 28 15. 18 15. 32 15. 11 15. 36 15. 32 6 15. 03 14. 75 14. 87 15. 12 15. 02 15. 16 14.95 15. 17 15. 17 7 18. 88 16. 57 15. 21 14. 78 14. 71 14. 87 14. 66 14.91 14. 91 8 20. 73 18. 32 16. 24 14. 68 14. 60 14. 74 14. 59 14. 81 14. 78 9 22. 14 20. 47 18. 11 14. 76 14. 52 14. 53 14. 42 14.63 14. 58 10 24. 19 22. 91 21. 50 18. 46 14. 57 14. 35 14. 14 14. 34 14. 34 11 24.63 23. 42 22. 11 19. 88 16.96 14. 14 13. 95 14. 16 14. 11 12 24.99 23. 96 22. 83 21. 27 18. 88 14. 01 13. 74 13.93 13. 9 3 13 25. 70 24. 68 23. 80 22.77 21. 45 16.77 13. 35 13. 81 13. 51 14 25.74 24. 75 23. 83 22.95 21. 51 18. 38 13. 17 13. 26 13. 25 16 25. 81 24. 91 23.98 23. 19 22. 16 20. 37 16. 45 12.53 12. 24 33 26. 27 25. 55 25. 45 27. 14 26.62 26. 44 26. 01 29.44 29. 39 34 26.99 26. 78 27. 11 29. 51 29. 67 28.91 29. 85 34.91 34.78 35 28.47 28. 35 29. 04 31. 85 32. 35 32. 51 35. 13 41. 11 42. 25 36 21. 12 31. 22 32. 53 35. 69 35. 84 37.13 40. 18 47. 13 48. 06 37 34. 35 34. 55 35. 66 40. 12 40. 70 42. 20 46. 38 53. 43 54. 21 38 37. 45 37. 79 38.78 43. 80 44. 40 47.77 52. 55 59. 55 60. 85 39 43. 35 43. 35 44. 92 50. 81 51. 47 60. 36 66. 45 67. 38 40 48. 23 48. 23 51. 32 56.90 58. 08 62. 28 67. 66 70. 88 71. 53 41 51. 30 53. 53 56. 18 61. 94 62. 55 67.93 73. 79 74. 80 75. 32 42 57. 46 60. 26 62. 44 71. 39 69. 40 75. 26 78. 66 79. 21 78. 85 43 60. 64 63. 74 66. 31 74. 10 72. 79 78.99 81. 00 79.65 79. 55 44 62. 66 64. 13 67. 46 74. 57 76. 23 82.06 83. 05 80. 35 80. 35 45 65. 00 67. 08 69. 59 76. 51 76.99 83.59 83. 25 78.90 79- 65 oo o inc c e 2 3 4 5 6 7 8 9 10 11 12 13 14 16 33 34 35 36 37 38 39 40 41 42 43 44 45 TABLE 9 CHORD WISE PRESSURE DISTRIBUTION P/Poo 9 = 20° 0. .0 1 0 .0 2 0 .0 3 0 .0 3 9 .0 4 9 .0 5 9 .0 6 9 . 0 7 8 . 0 8 2 .0 8 9 .0 9 8 15. 76 15. 94 15. 81 15. 60 15. 60 15. 66 20. 75 17. 25 15. 47 23. 16 20. 15 15. 94 24. 86 23. 68 19. 73 26. 66 26. 03 24. 07 27. 02 26. 56 24. 88 27. 37 27. 08 25. 77 27. 92 27. 63 26. 76 27. 99 27. 81 26. 95 28. 07 27. 94 27. 13 28. 23 27. 99 27. 29 28. 23 27. 97 27. 26 28. 18 27. 84 26. 82 29. 01 28. 62 28. 83 30. 66 30. 01 31. 00 33. 35 32. 82 34. 45 38. 00 36. 48 39. 78 42. 29 45. 95 47. 47 50. 84 51. 41 57. 50 61. 66 68. 01 64. 95 70. 65 75. 82 71. 85 76. 50 82. 54 90. 28 96. 42 99. 45 96. 50 100. 10 103. 32 100. 51 104. 50 105. 91 16. 11 16. 25 15. 18 15. 75 15. 88 14. 84 15. 54 15. 62 14. 61 15. 47 15. 54 14. 53 16. 25 15. 42 14. 35 22. 17 18. 20 14. 17 23. 42 20. 82 17. 96 24. 59 22. 41 20. 12 26. 07 24. 72 22. 25 26. 23 25. 03 22. 82 26. 43 25. 40 23. 32 26. 72 25. 89 23. 92 26. 64 25. 87 23. 94 26. 23 25. 48 23. 73 30. 36 30. 10 34. 08 33. 71 33. 71 38. 47 38. 60 37. 43 45. 36 45. 88 43. 62 52. 87 52. 27 50. 74 59. 99 60. 93 59. 55 72. 60 71. 43 71. 53 80. 37 79. b s 79. 77 87. 31 87. ,'03 87. 60 97. 89 95. 66 96. 88 102. 13 99. 19 98. 88 104. 99 102. 94 101. 10 107. 17 103. 77 101. 40 15. 41 15. 07 14. 94 15. 02 14. 68 14. 63 14. 84 14. 43 14. 47 14. 76 14. 40 14. 39 14. 61 14. 22 14. 24 14. 37 13. 91 14. 06 14. 27 13. 86 13. 88 16. 11 13. 65 13. 72 20. 58 13. 39 13. 56 21. 38 13. 29 13. 38 22. 26 18. 22 13. 28 23. 45 20. 73 16. 81 23. 55 21. 04 18. 15 23. 47 21. 92 20. 34 29. 21 30. 38 25. 21 33. 25 25. 08 28. 84 38. 86 42. 84 34. 03 46. 64 51. 50 40. 85 56. 54 62. 25 49. 72 66. 85 74. 43 58. 75 81. 93 89. 99 72. 83 93. 09 100. 75 87. 17 102. 14 110. 44 98. 57 112. 82 119. 46 113. 29 114. 82 123. 11 119. 11 116. 59 122. 49 123. 22 118. 12 119. 90 124. 42 15. 12 15. 23 15. 74 14. 84 14. 84 15. 25 14. 58 14. 61 14. 81 14. 53 14. 56 14. 68 14. 39 14. 42 14. 45 14. 11 14. 19 14. 22 14. 03 14. 09 14. 01 13. 85 13. 91 13. 83 13. 59 13. 65 13. 67 13. 44 13. 50 13. 52 13. 28 13. 31 13. 29 15. 82 12. 12. 90 17. 33 12. 69 12. 67 19. 43 11. 74 11. 58 22. 32 44. 65 46. 43 28. 04 55. 56 56. 87 38. 57 70. 29 70. 34 47. 20 83. 24 84. 15 62. 09 93. 71 95. 60 101. 57 104. 31 109. 15 111. 66 110. 34 114. 19 112. 04 113. 96 112. 79 115. 15 112. 35 115. 09 112. 71 115. 33 112. 56 122. 49 oo TABLE 10 CALCULATION OF SEPARATION LENGTH AND REATTACHMENT POINT d* = 0 9 , L s e p = X j jl - X g / c o s a - (sina / tanf? ), degrees inches 5 10 15 20 0. 38 . 81 1. 79 2. 31 9, X r = XHL + L aep (sin a /sin 0 ), degrees inches 5 3. 65 10 3. 79 15 4. 08 20 4. 17 de; in me N 1 2 4 7 8 9 10 11 12 13 14 15 16 17 18 19 21 22 23 24 25 TABLE 11 HEAT TRANSFER DISTRIBUTIONS Ch x 104 0 0. 3. 75 0. 0. 5 . 009 10 0. . 040 12.53 12.68 9.95 10. 89 11. 04 10. 74 11. 34 11.94 8. 65 11. 34 11.94 11. 19 11. 39 11. 56 8.65 10.74 11. 04 10. 89 10.44 10.44 7. 76 10.44 10. 15 10. 29 11. 34 11. 64 8. 21 10.74 i 10. 74 10. 74 9. 25 9. 70 7. 16 8. 65 9. 25 8. 65 9. 25 9. 85 7.16 9. 25 9. 25 9. 10 9. 85 10. 15 7. 31 9.55 9. 85 9. 55 9. 10 9. 85 6. 86 8. 73 8. 80 8. 65 9. 10 9.40 6. 71 8. 88 8. 95 8. 95 8.95 8.95 6. 56 8. 88 8. 65 8. 50 8. 50 8.95 5. 67 8. 06 8. 21 8. 07 5. 37 6. 56 4. 33 5. 07 2. 83 5. 67 5.97 6. 86 4 .48 5.97 4. 77 6. 57 6. 86 7.46 5. 52 6. 86 5. 52 5. 52 5. 37 6. 56 4. 63 5. 52 4. 63 5. 52 5.97 7.16 5. 22 11. 34 6. 56 10. 59 6. 56 7. 16 5. 52 10. 59 6. 56 10. 00 7. 16 7. 76 6. 56 11. 64 7.91 11. 34 6. 56 6. 56 5.07 10.44 5.97 9. 25 6.71 9. 85 9. 55 11. 34 17.90 16. 71 TABLE 12 HEAT TRANSFER DISTRIBUTIONS Ch x 104 Q - 15° d#, inches 0. . 012 .021 . 032 . 040 . 061 The rmoc ouple No. 1 10.44 10.44 10.44 11. 04 10. 89 10.44 2 11. 34 10. 74 10. 59 11. 49 11. 34 10. 89 4 10. 44 10.44 10. 59 11. 04 11. 04 10. 00 7 9. 55 8. 95 10. 00 10. 00 10. 15 9. 25 8 9. 85 9. 10 9. 55 10.44 10. 74 9. 85 9 3. 28 4. 63 8. 21 8. 80 8. 80 7. 91 10 3. 28 4 .4 8 8. 50 9. 25 9. 10 7. 91 11 3. 43 5. 07 8. 95 9. 55 9. 55 8. 80 12 3. 73 5. 67 8.06 8. 80 8. 95 8. 07 13 3. 13 3. 88 9. 55 9. 25 9. 40 8. 21 14 2. 83 2. 98 8. 06 8. 65 8. 80 7. 76 15 2. 39 2. 98 8. 36 8. 36 8. 36 7. 16 16 1. 79 2. 09 3. 21 5. 67 5. 07 4.77 17 1. 72 2. 09 4. 03 5.97 5. 67 5. 37 18 1. 72 1. 79 5. 07 6. 86 6. 86 6. 27 19 1. 79 1. 79 3. 13 6. 86 5. 07 5. 07 j 21 6. 86 - - - - 19.40 22 6. 86 - - - - 20.00 23 6. 86 - - - - - 24 6. 86 - - - - 20.44 " O - o 25 30. 59 - - - - 31.56 S TABLE 13 HEAT TRANSFER DISTRIBUTIONS Ch x 104 e = 2o ° inches 0. .012 . 021 . 033 .040 .053 . 057 . 089 r mo couple No. 1 10. 50 11.93 12.09 10.74 10. 89 10. 44 10. 15 10.44 2 11. 34 12. 53 14. 17 11.93 11. 79 11. 04 11. 50 11. 34 4 7. 46 11. 34 11. 79 10.44 10.44 10. 15 10. 15 10.44 7 3. 87 6. 86 10. 74 10.74 10. 30 9. 85 9. 55 9. 70 8 3. 87 6. 94 10. 89 10.44 10. 14 10. 15 9. 85 9. 55 9 3. 58 4. 32 4 .4 8 5.97 8. 95 8. 36 8. 36 8. 21 10 2. 83 4.0 3 3. 88 4.03 8. 95 8. 80 8. 36 8. 36 11 2. 83 3. 58 3. 73 4. 18 9. 25 9. 10 8.95 8. 95 12 3. 51 3. 58 3. 88 5. 52 8. 80 8. 50 8. 21 8. 36 13 3. 06 4 .4 8 4. 18 3. 88 8. 65 8. 65 8. 21 8. 36 14 4. 18 5. 22 5. 22 4. 18 8. 50 8. 36 7. 76 8. 21 15 3. 66 4 .4 8 4. 18 3. 13 7. 91 7. 76 7.46 7. 61 16 3. 73 5. 07 5. 22 3. 58 5. 37 4. 77 4.9 2 5. 22 17 3. 51 4. 63 5. 07 3. 13 5. 22 5. 67 5. 37 5. 67 18 3. 58 4. 63 4 .4 8 2.98 6. 57 6.42 5.97 6. 86 19 3. 51 4. 55 4. 63 2.98 3. 73 5. 22 5. 15 5. 52 21 10. 67 - - - - - - 49.46 22 9. 55 - - - - - - 45.73 23 10. 97 - - - - - - 49. 31 24 9. 25 - - - - - - 42.00 j 25 66. 77 - - - - - - 55. 28 TABLE 14 DETERMINATION OF A FROM MEASURED SLOT PRESSURES Tx = 1060 °R e, degrees d*, inches Pz /Pp m 2 t 2, °R A z /A * A i/L s x 106 , : slugs /f t - s e c 20 0.010 0. 126 2.00 594 2.49 17. 9 .030 . 180 1.78 647 1. 50 37. 3 . 050 . 226 1. 63 689 1. 30 56. 0 . 070 . 287 1.46 742 1. 21 69. 1 | . 090 . 516 1.02 880 1. 16 56. 3 15 0. 010 0. 142 1.93 604 2. 26 15. 5 . 020 . 177 1. 79 647 1. 63 24. 1 | . 040 . 236 1. 60 700 1. 32 41. 3 . 050 . 275 1.49 732 1. 25 47. 7 . 060 . 305 1.42 753 1. 21 50. 1 ! . 070 . 389 1. 24 806 1. 18 42. 5 10 0. 010 0. 178 1. 78 647 2.03 12.4 | . 020 . 235 1. 60 700 1. 53 19. 3 . 030 . 306 1.42 753 1. 34 24.7 . 040 . 333 1. 38 774 1. 26 26. 1 ! . 050 . 284 1.47 742 1. 20 27.9 5 0. 005 0. 213 1. 66 689 2. 60 6. 1 .010 . 265 1. 52 720 1. 80 8. 9 .015 . 306 1.42 753 1. 53 vO 11.5 £ TABLE 15 DETERMINATION OF rfi BASED ON SONIC SLOT Tw = 1060 °R 6, d*. pp, rfi/L s x l 0 6 .4P , degrees inches m m Hg s lu g s /f t - s e c percent 0. 005 5. 16 3. 03 0. 22 . 010 4 .9 0 5.76 .43 . 015 4. 70 8. 28 .61 0.010 7. 30 8. 58 0. 61 . 020 6. 65 15. 62 1. 16 .030 5.75 20.27 1. 50 . 040 4. 65 21. 85 1. 62 0.010 9. 15 10. 75 0. 80 .020 8. 80 20. 68 1. 53 .030 8. 50 29.97 2. 22 .040 8. 14 38. 26 2. 83 . 050 7 .4 8 43 .9 4 3. 26 .060 6. 50 45. 82 3. 39 .070 4. 50 36.99 2.74 0.010 10. 28 12. 08 0.90 .020 10.00 23. 50 1. 74 . 030 9.79 34. 50 2. 56 .040 9. 50 44. 65 3. 31 .050 9. 10 53.47 3.91 .060 8. 60 60. 64 4.49 .070 8. 05 66. 24 4.91 .080 7. 30 68. 63 5. 08 .090 4. 30 4 5 .4 8 3. 37 TABLE 16 MEASURED MASS FLOW CALCULATIONS 8 , d*, L s , 6 p , i f i / L s x l 0 6 degrees____________inches___________ inches________ m m H g / sec_____s lu g s /f t - s e c 0. 008 7. 30 0. 1875 9. 58 . 014 6. 45 . 2240 12. 96 . 016 6. 45 . 2240 12. 96 0. 0055 6. 50 0 .2000 11. 48 . 006 1. 50 . 0812 20. 24 . 014 6 .0 0 . 2229 13. 86 . 021 5 .9 0 . 3524 22. 29 . 043 . 80 . 1340 62. 55 0. 005 6. 50 0. 1836 10. 54 . 010 6. 50 . 2275 13. 06 . 015 6. 50 . 3260 18. 72 . 018 1. 50 . 1070 26. 62 . 040 1. 55 . 2197 52. 89 . 060 1 .15 . 2278 73. 93 A P P E N D IC E S A P P E N D IX A M EASUREM ENT U N C ER TA IN TIES The s ilic o n e oil m a n o m e ter b oard angle w a s m e a s u r e d by a g u n n er1 s quadrant rea d a b le to 0. 1 m ill (90° arc = 1600 m ills ). The aft w ed ge w a s s e t through u s e of a m a c h in is t1 s b e v e l p ro tra cto r rea d a b le to 0. 1 d e g r ee . The gap s iz e w as s e t w ith a p r e c is io n fe e le r -g a u g e . T o in su r e that the gap did not c lo s e , tw o s m a ll b lo ck s w e r e fa b ric a te d for ea ch gap s iz e . It had b e e n found e a r ly in the p r o g r a m that the slo t c lo s e d slig h tly , 0. 002 inch, during the te s t. T h e se b lo ck s w e r e lo c a te d in the slo t at the outer ed ges of the span. N o slo t change co u ld be d e te c ted after ea ch run w hen the b lo ck s w e r e u sed . T he b lo c k s w e re m a ch in ed a c c u r a te ly to 0. 0 0 0 5 -in ch . It is e stim a te d , b a se d on r ep ea ted m e a s u r e m e n ts b e fo r e and after e a c h te s t during the en tire p ro g ra m , that any slo t w idth settin g w a s a ccu ra te to + 0. 0005 inch. A ctu a lly the r ep e a tib ility of the p r e s s u r e data w ould in d ica te ev en b e tter a ccu ra cy . The r o ll of the m o d e l, although not a v e r y c r it ic a l p a r a m e te r , w as ch eck ed b e fo r e each run w ith a leV el gauge. T h e rm a l c r e e p c o r r e c tio n s w e r e found to b e n e g lig ib le ,a t m o s t 0. 005 m m Hg, and w e r e th er e fo re not ap p lied to the data, 96 97 i s : T he stan d ard e r r o r a n a ly sis for the p ertin en t flow p a r a m e te r s a. M ach N um b er d M c o / M o0 = ° - 2 ( d P o 2 / P o 2 + d P o / P o ^ = 0 .2 (0. 2 / 7 0 + 2 0 / 1 2 0 0 )= 0.4% or M = 12. 34 + 0. 05 o o — b. R ey n o ld s N um b er R„ = D U x / U , e o o 0 0 0 0 CO d Rp / R e = d M / M + d p / p + 2 d T / T m m A m x m mi *00 CO CO ^ C O CO C O C O = 0 .0 0 4 + 0 . 0 0 5 / 0 . 3 6 7 + 0 .0 0 7 5 = 2 . 2% c. H eat F lu x * = (P m cm b) d T /d t d q / q = d ! 7 * + d ( p m cm b ) /p m cm b = 0 .5 /1 0 + 0 .0 2 5 = 7. 5% d. N u s s e lt N um b er Nu = q ( x / k) / (T 0 - Tw ) d N u /N u = d q / q + d (T Q- Tw ) / (T 0 - T w ) + d x / x = 0. 075 + 1 0 / 840 + 0 . 0 0 1 / 3 .5 8 = 8% 98 e. Stanton N um ber Ch = Nu / R ^ P r d C h / C h = d N u /N u + d R g ^ /R e ^ = 0 . 08 + 0 . 02 = 10% + d Pr / P r A PPEN D IX B MODEL CONSTRUCTION AND CALIBRATION C onstruction of the b a sic m od el stru ctu re, fr o m 321 sta in le s s steel, w as standard and req u ires no com m en t except to note that the aft wedge could be m o v e d in the s tr e a m w is e d irection to form a gap at the w e d g e /w e d g e junction, in addition, the aft w ed ge could be se t at variou s an gles of attack. T h e s e cap ab ilities elim in a ted the n eed for having sep arate aft w edges fo r the m any configurations in v e s t i gated. S e v e r a l experim en tal techniq ues h ave been developed fo r obtaining h e a t tran sfer rates in w ind tunnel testin g. The "th in-skin" or tra n sien t tem p eratu re m ethod is com m on ly used. The m ethod is obtained f r o m equating the heat tr a n sfe r r e d to the sk in , h (Taw - T), with the h e a t stored p er unit a r e a , p cb (d T /d t), in the skin of th ick n ess, b. The m o r e im portant assu m p tion inh erent in the "thin-skin" method i s that the h e a t conduction is a c r o s s the skin and none is alon g the skin, i. e. , the tem p era tu re is a ssu m e d to be uniform a c r o s s the sk in th ick n ess. In addition, the m a ter ia l p rop erties a re u sually a ssu m ed constant. E x p erim en tally, the method r eq u ir es that the m odel b e con stru cted with as thin a sk in as p ossib le to obtain a f a s t r esp o n se , but y et thick enough to m ain tain 99 100 stru ctu ral in tegrity. H oneycom b panels appeared to m e e t both r eq u irem en ts. A calib ration program of a honeycom b panel w as th erefo re initiated. Four te st pan els, each 3 x 3 x x / a in ch es, w e re m anufactured of type 321 sta in le ss steel. Two of the panels had cover sh eets of 0 .0 1 0 -in c h th ick n ess w hile the other two had sh eets of 0. 01 9 -in ch th ick n ess as the panel outside cover and 0. 01 0 -in ch th ick n ess as the panel in sid e cover sheet. In each of th e se two sets of p an els, one of the panels w as of honeycom b sandwich con stru ction with a c e ll c r o s s sectio n having a d im en sion of 0. 25-in ch and a web th ick n ess of 0. 0015-in ch . The second panel of each s e t did not have the h on ey com b, but the front and rea r sh eets w e re sep arated by 0. 25-in ch sp a c er s at each corn er. The honeycom b m a teria l w as a lso 321 sta in le ss steel. A slu g g ish ly flowing s ilv e r alloy, Staflo 7 6 l, w ith a low th erm al conductivity w as u sed as the brazing a lloy for the honeycom b to co v er sh eet jo in ts. E ach honeycom b c e ll w all contained sm a ll h o le s to provide p r e ssu r e r elief during the m anufacturing p r o c e s s and during testin g . In order to sp o t-w eld two th erm ocou p les (c h r o m e l/ alum el) to the rear face of the outside cover sh eet, each te s t panel had two sec tio n s rem o v ed fro m the back sheet. The opened sectio n in the honeycom b panel co n sisted of a 4 - c e ll cutout. 101 The h eat flux w a s obtained fr o m an oven having a m axim u m tem p eratu re capability of 2500 °R. A te st c o n sisted of raisin g the oven to a sp ecific tem p era tu re, rapidly in sertin g a te s t panel into the oven m anually (about 0. 2 second) and recording the tem p eratu re of the oven and that of the t e s t panel as a function of tim e on a strip chart reco rd er operating at a rate of about 5 in ch es per second. The tem p eratu re of the te s t panel w as record ed on a 75 °F to 200 °F type s c a le (6 inches) and the oven tem p eratu re on a 800 °F to 1700 °F type s c a le (6 in ch es). F or data reduction, the starting tim e w as taken at the point w here heating of the t e s t panel actually began after in sertio n into the oven. This point w as c le a r ly defined on the te s t panel tem p eratu re v e r s u s tim e tr a c e s . The slope of the tr a c e s 1. 5 secon d s after heating began w as defined as d T / dt, sin ce, during this tim e in terval, the data could be a ccu ra tely fitted by a straight lin e. Heating r a te s w e re then calcu lated through u se of the tra n sien t on e-d im en sio n a l heating rate to an infinite w all w h ere the heat is tran sm itted only in the direction norm al to the w all. F o r 321 sta in le ss ste e l the d en sity u sed was 501 l b / f t 3, and 0. 12 B T U / °F -lb w as u sed as the sp ecific heat. The p rogram w as initiated w ith testing of the set of test panels having 0 .0 1 0 -in c h th ick n ess for the outside cover sheet. The 102 hon eycom b panel of th is set began to take on perm anent w a v in ess on the outside cover sh eet after ten ex p o su res to tem p era tu res up to 2000°R and further testin g w as discontinued. The data fr o m te s ts of the s e t of panels having 0. 0 19-in ch th ick n ess for the outside cover sh eet w as red uced to heating ra tes. T em p eratu re r a te s w e re m e a su r ed 1 .5 secon d s after in sertio n of the te st panel into the oven; h ow ever, the data show ed that, had 2. 5 seco n d s b een ch osen for data reduction, the tem p eratu re rates would have b een identical. It should a lso be pointed out that both th erm o couples on a given te st panel gave id en tical r e su lts. F ig. B1 p r esen ts the c o rr e la tio n of m e a su r ed honeycom b panel heating ra tes again st heating ra tes m e a su r ed on the unsupported, 1 1 th in -sk in , " panel. It is se e n that the honeycom b la g s behind the " thin-skin" panel by a constant 7%, being attributed p r im a r ily to conduction lo s s to the honeycom b w eb s. Em bedding of the th erm ocoup le in a silv e r sold er ju st under the skin red uced th is lag som ew hat, but the d istortion to the su rface cau sed by the high tem p eratu re sold erin g p r o c e ss and subsequent m achining elim in ated th is m ethod of th erm ocou p le construction. It w as concluded that, for the sp ecific honeycom b configu ration tested , other ex p erim en ts u sing the sa m e configuration m ay be c o rrected to obtain the equivalent, unsupported, 1 1 thin-skin" heating rates by m u ltip lication of a factor equal to 1. 07, 103 T h e id e n tic a l h o n ey co m b p an el co n fig u ra tio n and m a n u fa ctu rin g p r o c e s s e s w e r e u s e d fo r the m o d e l p a n els. The s ta in le s s s t e e l p r e s s u r e tu b es, 0. 0 6 2 5 -in c h O. D. , w e r e s ilv e r s o ld e r e d into th e h o n ey co m b p a n el and the top s u r fa c e w a s p o lish e d at ea ch p r e s s u r e o r ific e lo ca tio n . AThermocouple Imbedded 1.07 Thin-Skin 0 o 2 3 4 qThin-Skin ,BTU/ft2_ sec 5 FIGURE BL CORRELATION OF HONEYCOMB PANEL HEAT TRANSFER DATA Honeycomb A PPENDIX C MASS FLOW CALCULATIONS DETERMINATION OF ifi BY SONIC THROAT CONSIDERATIONS C onsider the flo w of air isen tr o p ic a lly through an orifice a c r o ss w hich exists a p r e ssu r e ratio su fficien tly la r g e to in su re sonic conditions at th e m in im u m c r o s s - s e c t io n , then ,____ -rrrrrrrrr % o m p2 ^ 0. 528 Pl ifi* / A* = p * v * = p * N /y R T * /R T * = p 2 v 2 (A z / A*) but p* = px (2 j y + 1 ) ^ ^ T * = Tx ( 2 / y + 1) or for air : y ~ 1 .4 105 106 -V z and rft.*/ L s = 0. 01648 px d* Tj s lu g s / s e c - f t . px is the plateau p r e s s u r e , i. e. , the p r e ss u r e above the slot. F or Tj , the equilibrium w a ll tem p era tu re, Tw , is u sed in stea d of the fr e e str ea m , T 0. Tw is fe lt to be m o r e r ep resen ta tiv e of the actual gas tem p eratu re in th e sep arated reg io n c lo se to the slot. F o r px in m m Hg, d# in in c h e s, and Tw in °R, - 3 - 1 /? rfi*/ I js = 3. 825- 10 Pl d * T w /2 s lu g s /s e c - f t . The r e su lts of th e se ca lcu la tio n s are given in T able 15. In order to n on d im en sion alize the m a s s flow for graphical presen tation , the p a ra m eter ch o sen w as the boundary la y er m a ss d efect at the w e d g e /w e d g e junction without sep aration . F o r Tw / T q = 0 .5 6 , p 0 u e 6 * = 0 .5 3 2 -1 0 3 s lu g s / f t - s e c w h ile for Tw / T Q = 0 .2 8 , p e u e 5 * = 0. 27 8- 10 3 slu gs / ft -s e c . DETERMINATION OF A BY SLOT BACK PRESSURE The m a s s flow calcu lation s b a sed on p r e ss u r e m ea su rem en ts sligh tly below the son ic throat p ro ceed as fo llo w s : a. F o r a g iv e n aft-w ed ge angle, d2 for d* = 0 is known fro m the g eo m etry as d2 = 0. 054 sin (12 + Q / 2), (F ig . 5) fro m w hich the a r ea ratio is found fo r d* ^ 0 through A 2 / A* = 1 + d2 / d* 107 b. The p r e s s u r e s , p2 and px a r e known m e a s u r e d p r e s s u r e s s o that M 2 i s know n fr o m n o r m a l sh o ck r e la t io n s . Now rfi2 / L s = p 2 v 2 d 2 = p 2 v 2 d* or rfi2 / L s = 49. 9 p 2 M 2 d* —\ / R T 2^ , s lu g s / f t - s e c . T 2 / Tx is know n fr o m th e k n ow led ge of M 2 . rfi2 / L s = 6. 737- 10-3 p 2 M 2 d* • T 2 ^ , s l u g s / f t - s e c w h e r e p2 is in m m H g, d# i s in in c h e s and T 2 in °R. R e su lts of th e s e c a lc u la tio n s a re g iv e n in T a b le 14. E X P E R IM E N T A L D ETERM INATION OF rfi T he m e a s u r e m e n t of the m a s s flo w th rou gh the slo t at the w ed g e /w e d g e ju n ctio n w a s b a s e d on the fo llo w in g a n a ly s is . C o n sid er a la r g e r e s e r v o ir of v o lu m e , V r , the m a s s in th is v o lu m e i s : m = p V r , slu g s or s in c e p = p / R T m = V r p / RT . Now the tim e ra te of ch an ge of m , if the r e s e r v o ir is su dd en ly opened to a h ig h er p r e s s u r e , fo r a co n sta n t te m p e r a tu r e , is or dp ~ Ap = p2 - Pi > dt ~ At = t 2 - t x , so that 108 VR ^ = RT*! ^ P2 " Pi / 12 “ ^ • If tx is c h o s e n at z e r o and t id e n tifie d to be th e tim e in te r v a l o v er w h ich Ap is m e a s u r e d , then VR rfi = p _ , Ap, s l u g s / s e c . x\ J L i t V r and ifi/JL s = - — "■ Ap, slu g s / s e c - f t . -L »s 1 ^ T h is eq u ation n e g le c ts th e m a s s co n trib u tio n of the plum bing s y s t e m b e tw e en the s lo t and the tank. F o r Vp^ s _ < < th is is ju stifia b le . F o r th is in v e s tig a tio n Vp_ s _ = 0. 005 V R . With VR = 1 0 .4 ft 3 , T x = 5 4 0 °R, a n d t = 1 s e c , rh / L js = 3. 7 3 2 - 1 0 ”4 , s l u g s / s e c - f t s w h e r e Ap is in m m of Hg and L s in in c h e s . T ab le 16 p r e s e n ts the r e s u lt s of the c a lc u la tio n s. A PPEN D IX D SEPARATION PRESSURE RISE CORRELATION F ro m the theory of su p erso n ic flow, the rela tio n sh ip between the p r e ssu r e r i s e a cro ss the sep aration shock and the d eflectio n of the extern al str ea m lin e s m a y be g iv en by the lin e a r th eory for sm all d eflection an g les, - 1 = —^ ^ a , a : radians (D l) Pl (Mf - l / 2 ■ • • 2 3 • The te r m s of the expansion involving a , a , e tc . are n eg lected in Eq. (D l) for th is sim p lified a n a ly sis, although the second te r m , in a 2, m a y contribute as m u ch as 25% to the sep aration p r e ss u r e r ise for the com bin ation of M ach number before the sep aration and the la r g e s t sep aration angle of this investigation. In the follow ing a n a ly sis, the condition of incipient sep aration is defined as : - 1 = 0 for x = XtjT - 6 [ (D2) Pi HL XHL i. e. , in te r m s of the p r e ss u r e r ise , incipient sep aration is identified w ith z e r o p r e ssu r e r ise at one boundary layer th ick n ess in front of the hinge line. 109 110 N ow , at sep a ra tio n , th e a p p ro x im a tio n i s m a d e that a ~ 6^ / S - w h e r e I < < x is a c h a r a c t e r is t ic le n g th of th e boundary- la y e r se p a r a tio n sh o c k in te r a c tio n r eg io n , so that Eq. (D l) b e c o m e s 2 . - i/ ^ <D3) |E_1. fE - Ap_ L P l P l (M f - 1 ) /2 The unknow n in th e a b ove equation is th e len gth , I. To obtain an ad d ition al r e la tio n fo r I , th e boundary la y e r m o m en tu m equation is ev a lu a ted at the w a ll r e s u ltin g in dp i ^T w Pw v w n (D 4 ) ¥ ~ Tw ~ ¥ ‘t w f Ki - dfpw V g 1 (D 6> i a * P w w 1 w L 1 P w J r Pw v w " i s o that Ap ~ I 5* T ... Kj - 6 * ----------- 1 w L 1 J E quating E q s. (D3) and (D5) and so lv in g fo r (6 * / i ) y ie ld s : r m !? - 1 t ^ r Pw v w " l 5 f / i r M (D 6) s o that fr o m Eq. (D3) Ap Pi m i 2 r x i l l Pw Vw i ^ ,D7) [ ( M f - l ) R C l]% [ K2 pw J ( ] A t th is poin t th e unknown v a r ia tio n of p w vw o v e r a c h a r a c t e r is t ic le n g th m a y b e a p p ro x im a ted , h o w e v e r , it is apparent fr o m the o u tse t th at th is " fr e e -in te r a c tio n " c o n cep t, w ith Ill p w v w = 0, a p p lied to the r e s u lt s of th is in v e s tig a tio n f a ils to g iv e s a tis fa c to r y c o r r e la tio n . It is r e c a lle d that th e t e r m x/ Mf / [ (M f -1 ) R Sl ] is e s s e n t ia lly a c o n sta n t in th is in v e s tig a tio n , w h e r e a s ( A p /p x ) d e c r e a s e s w ith d e c r e a s in g fla p d e fle c tio n a n g le. T h e r e fo r e any c o r r e la t io n of p w v w and a c h a r a c t e r is t ic len g th w h ich y ie ld s z e r o for no m a s s tr a n s fe r at the slo t f a ils to c o r r e la t e the e x p e r im e n ta l data. A noth er c o n s id e r a tio n is th a t the c h a r a c t e r is t ic length w h en c o r r e la t e d to p w v w sh ou ld in c r e a s e w ith in c r e a s in g m a s s tr a n s fe r fo r a g iv e n fla p d e fle c tio n . T h e s e fa c to r s s u g g e s t that pw vw m a y be c o r r e la t e d to th e se p a r a tio n poin t x s . W ith th is a s su m p tio n Eq. (D7) m a y be w r itte n as - - - - - - - - - - - - - - -Ml- - - - - - - - - - - - - (1_ k 2 x s / 2 (D8) Pl [(M f -1 ) R e ] A x But Ap = 0 for x s = Xjjk s o that K2 = 1 / x ^ and Eq. (D8) thus b e c o m e s ^ -------------^ ---------- rr <d9) * [ (M f - i ) R e ] H L 1 F or > > 1, Eq. (D9) r e s u lt s in f i Pi [ ■ - y (D 10) 112 T h e e x p e r im e n ta l data of th is in v e stig a tio n are te s te d again st Eq. (DIO) in F ig . D l, r e su ltin g in g e n e r a lly good a g r e e m e n t and a con stan t of p ro p o rtio n a lity of 1 .7 . F o r no su c tio n at the slo t, i. e. , d* = 0, c o m p a r iso n is m ade w ith e x p e r im e n ta l data fr o m other s o u r c e s u tiliz in g Eq. (DIO). R e su lts of the c a lcu la tio n s a r e g iv en in F ig . D2. R e a lizin g the in h eren t in a c c u r a c y in obtaining the p r e s s u r e r is e r a tio a c r o s s the se p a r a tio n sh o ck and the other n e c e s s a r y flow p a r a m e te r s , the a g r e e m e n t is again s e e n to be good. 113 ! pi 9 , deg. 0-20 O - 15 □ - 10 R e ^ / i n = 7 .9 x l0 4 1.0 .8 .6 .4 .2 Apparent Uncertainty 0 0 .8 1.0 .2 A 6 rx , 2 ( |- ^ S ,2 *HL FIGURE Dl. TEST OF THE SEMI-EMPIRICAL PLATEAU PRESSURE EQUATION 114 1.2 - 1 .0 ~ .8 - .6 - 4 - .2 - A - Chapman,et. al. M(=2 Rei various (5) O-Townsend Mg-^IO R e ^ / m . ^ . e x I04 (29) O " Ginoux =2.1 R e ^ j/in .= 3 x I 0 4 (25) □ - Gulbran,et. al. M00=8 R e ^ /in .= 25x!04 (30) A - Present Inv. Ma>s l2.3 Reoo /in.= 7.9 x I04 [(M , - I) Re,] 1.2 Z ( I ~ 3 T > X HL FIGURE D2. T E ST OF THE SEMI-EMPIRICAL EQUATION FOR THE PLATEAU PRESSURE WITH d * = 0 FOR VARIOUS MACH AND REYNOLDS NUMBERS R E FE R E N C E S 116 R EFE R EN C E S 1. Libby, P. A ., F o x , H. , Sanator, R. J. , and D eC arlo, J. " T h e L am inar Boundary L ayer N ear the P lane of S ym m etry of a H ypersonic Inlet," JA S, I (D ecem b er 1963), 2732-2740. 2. Zakkay, Y. , B o s, A. , and Jen sen , Paul F . Jr. , " L a m in a r, T ran sition al and Turbulent F low with A d v erse P r e s s u r e G radient on a C o n e -F la re at M ach 10," O ffice of A ero sp a ce R esea rch , A R L 6 5 -253 (D ecem b er 1965). 3. W uerer, J. E. and Clayton, F. I. " F lo w Separation in High Speed F ligh t, A R eview of the S ta te -o f-th e -A r t, " D ouglas A ircraft Company, SM -46429 (A pril 1965). 4. C rocco, L. and L e e s, L. " A M ixing T heory for the Interaction B etw een D issip a tiv e F lo w s and N ea rly Isen trop ic S tr e a m s," JAS, XIX (O ctober 1952), 649-676. 5. Chapman, D. R. , Kuehn, D. M. , and L arson , H. K. " Investigation of Separated F low s in Su personic and Subsonic S trea m s with E m p h asis on the E ffect of T ra n sition, " NACA TN 3869 (1957). 6. E rd os, J. and P a ll one, F . " Shock-B oundary L ayer Interaction and Flow Separation, " P ro ceed in g s of the 1962 H eat T ran sfer and Fluid M echanics In stitu te, 1962, pp. 239-254. 7. Cook, J. C. " Separated S u p erson ic F lo w ," RAE TN 2879 (M arch 1963). 8. L ee s, L. and R e e v e s, B. L. " S u p erson ic Separated and R eattaching L am inar F lo w s: I. G en eral T heory and A pplication to A diabatic Boundary L ayer / Shock-W ave In tera ctio n s," AIAA J. , II (N ovem ber 1964), 1907-1920. 9. Tani, I. "On A pproxim ate Solution of the Boundary L ayer E quations," JAS, XXI (1954),487. 10. Cohen, C. B. and R eshotko, E. " S im ila r Solutions for the C o m p ressib le Lam inar Boundary L ayer with Heat T ra n sfer and P r e s s u r e G radient," NACA Rep. 1293 (1954). 117 11. Hankey, W. L. and C r o ss, E. J. "A pp roxim ate C losed F o rm Solutions for Supersonic L am inar Separated F lo w s ," AIAA J. , V (April 1967), 651-654. 12. Kaufman, L. G. , M eck ler, L. , H a rto filis, S. A ., and W e iss, D. " An Investigation of H yperson ic F low Separation and C ontrol C h a r a c te r istic s," Air F o r c e F light D ynam ics L aboratory, A F F D L -T R -6 4 -1 7 4 (January 1965). 13. S terrett, J. R. and E m ery , J. C. " E xten sion of Boundary L ayer Separation C riteria to a Mach Num ber of 6. 5 by U tilizing F la t P la tes and F orw ard F acin g S tep s," NASA TN D -6 1 8 (I960). 14. Bogdonoff, S. M. and V as, I. E. "Som e E x p erim en ts on H yp erson ic Separated F lo w s ," ARS J. , XXXII (O ctober 1952), 1564-1572. 15. M iller, D. S. , Hijm an, R. , and Childs, M. E. "M ach 8 to 22 Studies of F low Separation Due to D eflected Control S u rfa ce s," AIAA J. , XII (F eb ru ary 1964), 312-321. 16. S terrett, J. R. and H ollow ay, P. F . " On the E ffect of T ran sition on P a r a m e te rs Within a Separation R egion at H yp erson ic Speeds - - With E m p h asis on Heat T ra n sfer," ASME Sym p osiu m on F u lly Separated F lo w s, May 1 8 -2 0 , (1964), 15-26. 17. Holden, M. " S ep arated F low Studies at H yp erson ic Speeds, P art II, Two D im en sion al W edge Separated Flow S tu d ies," C ornell A eron autical L aboratory, Inc. (D ecem b er 1964). 18. T epe, F. R. , Brown, D. L. , Token, K. H. and H o elm er, W. " T h eoretical O perating R anges and C alibration R esu lts of the ARL T w enty-Inch H yperson ic Wind T unnel," ARL 63- 189 (O ctober 1963). 19. G regorek, G. M. and L ee, J. D. " D esig n P erfo rm a n ce and O perational C h a r a c ter istic s of the ARL T w enty-Inch H yperson ic Wind T unnel," A ero sp a ce R e se a rc h L a b o ra to ries, ARL 63-39 2 (August 1962). 118 20. G reg or ek, G. M. " Initial C alibrations and P erfo rm a n ce of the ARL T w enty-Inch H yp erson ic Wind Tunnel, 1 1 A ero sp a ce R e se a rc h L a b o ra to ries, ARL 62-393 (August 1962). 21. Brown, D. L. , Token, K. H. , H o elm er, W. , and T ep e, W. R. " Instrum entation and R ecording Equipm ent U sed in Conjunction w ith the ARL T w enty-Inch H yp erson ic Wind T unnel," A e ro sp a c e R e se a rc h L a b o ra to ries, ARL 63-189 (October 1963). 22. G oll, M. D. and L apenas, T. A. " O peration and M aintenance Instructions for Off A xis Double P a s s S ch lieren S y ste m ," A ero sp a ce R e se a r c h L a b o ra to ries, ARL 62-463 (N ovem ber 1963). 23. N eedham , D. A. and S tollery, J. L. " H y p erso n ic Studies of Incipient Separation and Separated F lo w s ," AGARD C onferen ce P ro ceed in g s No. 4 (May 1966), 111. 24. G ray, J. D. ARO, Inc. , Arnold A ir F o r c e Station, Tenn. , P riv a te C om m unication (Septem ber 1966). 25. Ginoux, J. J. " L am inar Separation in S u p erson ic F low , " von K arm an Institute for F luid D yn am ics, AD 612407 (O ctober 1964). 26. E ck ert, E. " Survey of Heat T ran sfer at High Speed, " WADC TR 54-70 (A pril 1954). 27. P e a r so n , L. W. " E ffe c ts of Slot Suction on Turbulent Boundary L ayer Separation ," AIAA P rep rin t No. 67-197 (January 1967). 28. H olden, M. " T h eo retica l and E xp erim en tal Studies of Separated F lo w s Induced by Shock-W ave Boundary L ayer In teraction ," AGARD C onferen ce P ro ceed in g s No. 4 (May 1966), pp. 147- 180. 29. Townsend, J. C. " E ffe c ts of L ead in g-E d ge B lun tness and Ram p D eflection Angle on L am inar B ou n d ary-L ayer Separation in H yp erson ic F lo w ," NASA TN D -3290 (F eb ru ary 1966). 119 30. Gulbran, C. E. , R ed ek er, E. , M iller, D. S. , and Strack, S. L. " H eating in R egion s of Interfering F lo w F ie ld s : Part I. T w o- and T h ree-D im en sio n a l L am in ar Interactions at M ach 8," A ir F o r c e F ligh t D ynam ics L ab oratory, A F F D L -T R -6 5 - 49 P a rt I (July 23, 1965) p. 34.

Asset Metadata

Creator Ball, Karlheinz Otto Willi (author)

Core Title An Experimental Investigation Of The Effect Of Mass Transfer On A Wedge Induced Laminar Separated Boundary Layer At Mach 12

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Philosophy

Degree Program Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, aerospace,OAI-PMH Harvest

Language English

Advisor Hickman, Roy S. (committee chair), Korkegi, Robert H. (committee member), Laufer, John (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-592917

Unique identifier UC11360876

Identifier 6805856.pdf (filename),usctheses-c18-592917 (legacy record id)

Legacy Identifier 6805856.pdf

Dmrecord 592917

Document Type Dissertation

Rights Ball, Karlheinz Otto Willi

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA