AEDC-TR ry. R. W. Rhudy ARO, Inc. March This document has been approved for public release and sale; its distribution is unlimited.

Transcription

1 AEC-TR ry #CAJ RSj INVESTIGATIN F LAMINAR BUNARY-LAYER SEPARATIN N A FLAT-PLATE-RAMP CMBINATIN WITH AN WITHUT MASS REMVAL AT MACH NUMBERS 6, 8, AN 10 R. W. Rhudy AR, Inc. March 1970 This dcument has been apprved fr public release and sale; its distributin is unlimited. VN KÄRMÄN GAS YNAMICS FACILITY ARNL ENGINEERING EVELPMENT CENTER AIR FRCE SYSTEMS CMMAN ARNL AIR FRCE STATIN, TENNESSEE

2 NTICES When U. S. Gvernment drawings specificatins, r ther data are used fr any purpse ther than a definitely related Gvernment prcurement peratin, the Gvernment thereby incurs n respnsibility nr any bligatin whatsever, and the fact that the Gvernment may have frmulated, furnished, r in any way supplied the said drawings, specificatins, r ther data, is nt t be regarded by implicatin r therwise, r in any manner licensing the hlder r any ther persn r crpratin, r cnveying any rights r permissin t manufacture, use, r sell any patented inventin that may in any way be related theret. Qualified users may btain cpies f this reprt frm the efense cumentatin Center. References t named cmmercial prducts in this reprt are nt t be cnsidered in any sense as an endrsement f the prduct by ihe United States Air Frce r the Gvernment. \

3 AEC-TR INVESTIGATIN F LAMINAR BUNARY-LAYER SEPARATIN N A FLAT-PLATE-RAMP CMBINATIN WITH AN WITHUT MASS REMVAL AT MACH NUMBERS 6, 8, AN 10 R. W. Rhudy AR, Inc. This dcument has been apprved fr public release and sale; its distributin is unlimited.

4 AECTR FREWR The wrk reprted was dne at the request f the Air Frce Flight ynamics Labratry (AFFL), FLight Mechanics ivisin, Air Frce Systems Cmmand (AFSC), under Prgram Element 62201F, Prject 133'6. b The results f the tests presented were btained by AR, Inc. (a subsidiary f Sverdrup & Parcel and Assciates, Inc.), cntract peratr f the Arnld Engineering evelpment Center (AEC), AFSC, Arnld Air Frce Statin, Tennessee, under Cntract F C The tests were cnducted frm July 11, 1965, t April 18, 1969, under AR Prject N. VT0611, and the manuscript was submitted fr publicatin n August 8, The authr wishes t acknwledge the cntributins f Mr. J.. Gray, wh supplied the theretical calculatins presented herein. This technical reprt has been reviewed and is apprved. Eugene C. Fletcher Ry R. Cry, Jr. Lt Clnel, USAF Clnel, USAF AF Representative, VKF irectr f Test irectrate f Test li

5 AEC-TR ABSTRACT An experimental investigatin f laminar bundary-layer separatin induced by a trailing edge ramp n a flat plate was cnducted at Mach numbers f 6, 8, and 10. The tests were cnducted ver a range f Reynlds numbers. Lngitudinal and spanwise surface pressure distributins, pitt pressure prfiles, and shadwgraph pictures were used t investigate the tw-dimensinality f the flw and the effects f mdel gemetry, angle f attack, Reynlds number, ramp angle, and mass remval frm the separatin regin. ata are presented t shw that laminar, tw-dimensinal bundary-layer reattachment, nt limited by mdel gemetry, was btained. These data are cmpared t the integral-mment thery f Lees and Reeves as mdified by Klineberg. It is als shwn that a separatin regin can be reduced r even eliminated by remving mass at the hinge line. in

6 AEC-TR CNTENTS Page ABSTRACT iii NMENCLATURE vii I. INTRUCTIN 1 II. APPARATUS 2.1 Wind Tunnels Mdel Instrumentatin 6 III. PRCEURE 6 IV. RESULTS AN ISCUSSIN 4.1 Tw-imensinality f the Flw Effects f Pitch Extent f Laminar Flw Reattachment Pressure Rise Ramp Angle Effect Influence f Mass Bleed 36 V. CNCLUING REMARKS 43 REFERENCES 44 ILLUSTRATINS Figure 1. Mdel etails a. imensins 3 b. Mdel Installed in Hypersnic Tunnel 4 2. Instrumentatin Lcatins 5 3. Flat-Plate Crrelatin at M^ = 8, Re,,, = 0. 5 x 10" 6, ft" Tw-imensinality f Flw at M Wi = M a = 6, Re v =0.38xl0 6 x c a. Chrdwise Pressure istributin b. Spanwise Pressure istributin 11 c. Mach Number Prfiles at x/x c = Tw-imensinality f Flw at M w. = M = 8, Re x =0.38xl0 6 a. Chrdwise Pressure istributin 13 b. Spanwise Pressure istributin 14 c. Mach Number Prfiles at x/x c =

7 AEC-TR Figure Page 6. Tw-imensinality f Flw at M Wi = M x =10, Re Xc = 0.38 x 10 6 a. Chrdwise Pressure istributin 16 b. Spanwise Pressure istributin Mdel Pitch Effect n Pressure istributin at M w. = 4. 5, Re Xc = x 10 6 a. Chrdwise istributins 19 b. Spanwise istributins 20 Mdel Pitch Effect n Pressure istributin at M w. = 6, Re 'i Xc = x 10 6 a. Chrdwise istributin 21 b. Spanwise istributin Effect f Reynlds Number Change at M Wi = M,,, = 6 a. Centerline Pressure istributin 23 b. Change in Interactin Length 24 c. Shadwgraphs at 0 = 11 deg 25 d. Mach Number Prfiles Effect f Reynlds Number Change at M WjL = M^ = 8 a. Centerline Pressure istributin 27 b. Change in Interactin Length 28 c. Shadwgraph at Re Xc = 0.38 x 10 6, 0 = 11 deg.. 29 d. Mach Number Prfiles Effect f Reynlds Number Change at M Wi = M m = 10 a. Centerline Pressure istributin 31 b. Change in Interactin Length 32 c. Shadwgraph at Re Xc = 0.19 x 10 6, 0=11 deg Effect f Ramp Angle Change n Centerline Pressure istributin at M Wi = M,,, = 10 a. Re x =0.38xl b. Re x = 0.75 x Effect f Mass Remval n Separatin at M w^ = 4. 5, Re x = 1.06 x x c 14. Effect f Mass Remval n Separatin at M w. = 6 a. Re x = 1.0 x b. Re x = 1.5xl Effect f Mass Remval n Separatin at M w - = M s = 8 a. Re Y x = 0.75 x 10 6 ( 40 c b. Re Xc = 1.0xl vi

8 AEC-TR Figure Page 16. Effect f Mass Remval n Interactin Length at M w. =8 42 'i TABLES I. Test Cnditins 7 II. Test Summary 7 APPENIX - Inviscid Wedge Curves 45 NMENCLATURE b Flat-plate semi-span, in. C Chapman-Rubesin viscsity factr, (T/T w )(/u w //Lt) C Pressure cefficient (p - p^/q,,, d Bleed slt pening in streamwise directin, in. r ft h Ttal enthalpy, Btu-lb" 1 -^" 1 M Mach number p Static pressure, psia r psfa q ynamic pressure, psia Re Unit Reynlds number, in. r ft"-*- S Ttal enthalpy functin, (h^/h^ - 1) T Temperature, R u Velcity, ft-sec"* W B Weight flw bleed per unit span, p c d T w -1 / 2, lb-ft^-sec -1 WT Theretical weight flw per unit span in laminar bundary layer at x c, Q f & pjjij^dy, lb-ft _1 -sec -1 x Streamwise surface distance measured frm leading edge, in. y Vertical height measured nrmal t surface, in. Vll

9 AEC-TR z Spanwise distance frm mdel centerline, in. a^i Angle between flat plate and free stream, deg 6 Bundary-lay er thickness, in. 0 Angle between ramp and flat plate, deg 0 S Angle between blique shck wave and flat plate, deg ju ynamic viscsity, lb-sec-ft~ 2 p ensity, lb-ft" 3 X Hypersnic viscus interactin parameter, <i [C./(Rex) Wi ] 1/2 SUBSCRIPTS b Mdel base value c Value at ramp leading edge i Lcal inviscid value L Lcal cnditins within the bundary layer NB Value with n bleed Value at start f interactin t Tunnel stilling chamber cnditins w Mdel wall cnditins x Value based n length x «> Free-stream cnditins Vlll

10 AEC-TR SECTIN I INTRUCTIN An experimental study was cnducted t investigate the effects f mass remval (bleed) n tw-dimensinal, laminar bundary-layer separatin. The test prgram, supprted by the Air Frce Flight ynamics Labratry, was undertaken t determine the feasibility f increasing hypersnic cntrl surface effectiveness by reducing the extent f separatin caused by a deflected cntrl surface. The prgram was expected t verify and extend, ver a wider range f Mach numbers and Reynlds numbers, the mass bleed studies f Ball (Ref. 1). The primary criteria fr these tests were that the flw be: (1) laminar thrugh re attachment, (2) tw-dimensinal ver a finite span each side f the mdel centerline, and (3) the reattachment lcatin must nt be limited by the ramp length. In rder t prvide infrmatin that the abve criteria culd be met, extensive "n bleed" tests were cnducted at Mach numbers 6, 8, and 10 and several Reynlds numbers. Because the results in Ref. 2 shwed that large ramp angles wuld prbably trigger transitin during flw reattachment, the tests were cnducted using a nminal ramp angle f 10 deg. uring these initial tests, data were btained t check the feasibility f pitching the mdel t btain a Mach number lwer than free stream n the plate. Checks were als made early in the tests, with the mdel unpitched, t determine if the separatin extent culd be reduced by venting the separatin regin t the mdel base pressure. A mdel supprt failure during mdel injectin at M a = 6 made further testing at this time impractical. Because f the failure, very little data were btained with mass bleed; hwever, the grundwrk has been dne fr future investigatin f this cncept. The tests were run at free-stream Mach numbers f 6, 8, and 10 and Reynlds numbers, based n the length frm the leading edge t hinge line, frm x 10^ t 1. 5 x 10^. ata, sme f which were with side plates installed n the mdel, were btained fr pitch angles frm 0 t 18 deg and with ramp angles f zer and apprximately 10 deg. Tests were made with slt penings f and in. at M = 8.

11 AEC-TR SECTIN II APPARATUS 2.1 WIN TUNNELS The tunnels (Gas ynamic Wind Tunnels, Hypersnic (B) and (C)) are cntinuus, clsed-circuit, variable density wind tunnels with axisymmetric cntured nzzles and 50-in.-diam test sectins. Tunnel B was perated at a nminal Mach number f 6 r 8 at stagnatin pressures frm 27 t 110 and frm 90 t 420 psia, respectively, at stagnatin temperatures up t 1280 R. Tunnel C was perated at a nminal Mach number f 10 at stagnatin pressure frm 210 t 840 psia at 1900 R stagnatin temperature. The mdel may be injected int the tunnels fr a test run and then retracted fr mdel cling r mdel changes withut interrupting the tunnel flw. 2.2 MEL The mdel, furnished by AFFL, (Fig. 1) was a sharp leading-edge flat plate with a hinged trailing-edge ramp. The hinge prvided fr ramp angles frm 0 t 30 deg, althugh tests were cnducted nly at zer and apprximately 10 deg. A full-span channel extending (internally) frm just ahead f the hinge line ( in.) t the base f the mdel prvided fr mass remval, i. e., "bleed. " Sharp-lip inserts were used in the entrance f the channel t vary the full-span slt pening frm 0 t in., in the streamwise directin. Because early data indicated that the extent f bundary-layer separatin was limited by ramp length, an extensin was built by VKF t lengthen the ramp frm 4. 5 t 9. 0 in. All subsequent tests were run with this extensin in place. The base f the mdel was shielded frm the supprt yke by a fairing plate extending dwnstream frm the mdel, Fig. 1. Lwer surface side plates were an integral part f the mdel supprt. The built-in angle between the axis f the yke and the upper surface (25 deg), alng with the ther munting equipment, prvided fr upper surface pitch angles frm 0 t 30 deg with respect t the free-stream flw. An additinal fairing plate was added t the lwer surface f the yke during testing in an attempt t reduce tunnel chking presumed t be caused by.the strng bw wave ahead f the yke.

12 AEC-TR L Ramp Hinge Line TTT-i NJU ^(Sym) I (b) V >-->. ii A 1A 30 deg 45 deg 0.75-» **j~ (x ) c Remveable Side Plates 4.50» Slt Insert Fairing lates All imensins in 0,50 Inches - Nt t Scale Surface istances etail A Bleed Slt Entrance a. imensins Fig. 1 Mdel etails

13 AECTR Alignment f the mdel in pitch was within ±0. 1 deg; hwever, because f the clutch face n the yke, the mdel was rlled deg. This small rll angle, when cmbined with angle f attack, created a slight leading-edge yaw (less than deg). Remvable side plates (Fig. 1), which extended frm near the leading edge f the flat plate t the trailing edge f the ramp (a set fr bth ramp lengths), were munted n the utbard edge f the plate during sme f the tests. The mdel was instrumented with surface pressure taps (0.062-in. I) as shwn in Fig. 2. In additin t the centerline rw n the flat plate, tw clsely spaced rifice rws were lcated 4 in. tward n side and 7 in. tward the ther side t prvide a detailed check f the lngitudinal pressure distributin ff axis. Three spanwise rws, at x/x c = 0. 5, and 0. 89, were als prvided fr checking the pressure variatin in a lateral directin. Three thermcuples, munted in pressure rifices, were used t mnitr the plate surface temperature. b. Mdel Installed in Hypersnic Tunnel Fig. 1 Cncluded

14 1 U1 -a er ~ 8 ii + z/b -z/b v, I, III IV x/x Rw' Tap' I * x/ * c z/b ±0.012 Rw Tap A/ / c z/b II III ' ' ' ' i ' IV V * VI * > m Surface Thermcuple b = Semi- span ~ 10 In. x r " lstance frm L.E. t c Hinge Line In. 1 ' < Fig. 2 Instrumentatin Lcatins

15 AEC-TR INSTRUMENTATIN Mdel pressures were measured in Tunnel B with 1-psid transducers n the frward plate and 15-psid transducers n the ramp. In Tunnel C, 1- and 15-psid transducers were switched in and ut f the system autmatically t allw measuring t the best precisin. All transducers were referenced t near vacuum. Frm repeat calibratins, the estimated Tunnel B pressure measurement precisin was ±0.001 psi r ±0. 5 percent, whichever was greater, fr the 1-psid transducer and ± psi r ±0. 5 percent, whichever was greater, fr the 15-psid transducers. The estimated Tunnel C precisin was ± psi r ±0. 5 percent, whichever was greater. The precisin f the temperature measurements, using Chrmel -Alumel thermcuples, was ±2 F r ±0. 5 percent, whichever was greater. The pitt pressure measurements were made with a in.- high val prbe cnnected t a 15-psid transducer. The prbe drive allwed the prbe t travel nrmal t the surface f the ramp with an estimated precisin f ±0.001 in. in the y directin. The estimated precisin f the prbe pressure was ± psi r ±0.5 percent, whichever was greater. Mdel flw field shadwgraphs were btained during all tests. SECTIN III PRCEURE The tests were cnducted at nminal free-stream Mach numbers f 6, 8, and 10 with Reynlds numbers, based n the length t the hinge line, frm x 10 t 1. 5 x 10. The test cnditins are shwn in Table I. The lcal flw cnditins when the mdel was pitched were btained frm the curves in the Appendix. These curves were calculated frm the infrmatin cntained in Ref. 3. A cmplete test summary is shwn in Table II.

16 AEC-TR TABLE I TEST CNITINS Nminal MÄ 6!H. psiu Tl, 'R H0j,x -. -6, If r.c 0 's 54 S. SL l.u B 00 :u S 198 :21c !J0U 9. f! !M TABLE II TEST SUMMARY a. Surface Pressure istributins Nminal MW] Nminal M Rexc x dcg *M. deg b. Pitt Pressure Surveys Ramp Length, x/x«. d. in. Side Plates 4.4 U 0.4C rr , 1 0..^S 10 -f.. i ff C4 1 li c 0C2 ar.j 0. I 5 rf 0 1.5, S 0 n li ff 6 1.5, ff 5. B ff , 1.0, l.s 0 ff 8 1.5, G2 ff S 1.5 I C 125 f-: 6 1U r. ne tiff C 1 5, 0.75, r, ff a n ff ff 8 1.5, 0.75, ff l : 0 n a l.c C.0C2, 0 12J rt B :n.b ff B 0.38, 0.75 n n and 0:f , 1. 5 S (1 0 n , 0.38, n , 0.38, 0.75 u n Hump, x/xc =2.0 0 = 11.0 dcg d = 0 «M = 0 3*w M. ' H XL. x 10-6 x/xc Wb Side Plates ,10 4 Cn and ff ff C and CW i ff 8.0 B and ± n and ff ? 0, ±0.4, -0.7 ff , -0.4 f-:

17 AEC-TR The bundary -layer pitt pressure data were taken at tw streamwise psitins n the ramp (x/x c = 1.47 and 1. 84) and several (z/b = 0, ±0.4, and 0. 7) spanwise lcatins by surveying nrmal t the surface f the ramp. The measurements were used alng with a measured ramp surface static pressure, which was assumed cnstant thrugh the bundary layer, t calculate the lcal Mach number. Selected data were repeated with the side plates installed. The frward plate temperature, which was mnitred during all tests, in general was near an equilibrium cnditin being T^ at Mach number 6, T t at Mach number 8, and T t at Mach number 10. SECTIN IV RESULTS AN ISCUSSIN 4.1 TW-IMENSINALITY F THE FLW In rder t demnstrate that a laminar, tw-dimensinal separatin that was nt influenced by the mdel gemetry limitatins culd be btained, the initial investigatins were cnducted with mass bleed channel sealed. ata were als btained with the ramp at zer deflectin fr reference purpses. The flat-plate pressure is shwn in Fig. 3 in terms f the variatin in the rati f measured pressure t the inviscid wedge pressure (btained frm curves in the Appendix) as a functin f the hypersnic viscus interactin parameter, x. These data were btained at several angles f attack at a fixed free-stream unit Reynlds number (Re,, = 0. 5 x 10^ ft"*). The data agree reasnably well with the weak interactin frmula f Ref. 4. An indicatin f the tw-dimensinality f the flw ver the plate with a deflected ramp is shwn in Figs. 4 thrugh 6. The pressure distributins fr M W j = 6 (Fig. 4a) shw a prnunced discrepancy between the centerline data and that frm the ff-centerline rws, especially with the side plates remved. This discrepancy is mst prnunced in the regin f the maximum pressure gradient. The spanwise pressure distributins (Fig. 4b) als shw this variatin in pressure between centerline and the ff centerline. Frm these figures, it appears that the upstream influence f the ramp, i. e., the start f the pressure rise, was less ff centerline than n. The ramp bundary-layer prfiles (Fig. 4c) indicate that reattachment ccured earlier utbard f the centerline (z/b = 0) because higher Mach numbers were measured clse t the ramp surface. This is cnsistent with a reductin in upstream influence. 8

18 AEC-TR There was little change in the prfiles with the side plates remved. The chice f static pressure used fr data reductin was the reasn that sme f the curves d nt g t a Mach number rati f zer in the recirculatin regin. The prper static pressure wuld nly shift the curves t the left r right and wuld nt change the verall trend a - 6 (leg a u - 10 deg y Sym a, deg M % rr^r QP A / c 9^ - 18 deg P/P - - H Wi - 8 M Wi - (Ref. 4 4)-v s&* r^?>* <Kef. 4) 1 1 i i 1 i X Fig. 3 Flat-Plate Crrelatin at M^ = 8, Re^ = i~6 f-l When all f the data are cnsidered, the flw appears t be twdimensinal n the centerline, but nly fr a small span n each side, e. g., z/b «±0.1. This is based n the fact that (1) the centerline data were unaffected by the remval f the side plates, and (2) they agree well with the VKF calculatins based n the integral-mment thery f Ref. 5 as mdified in Ref. 4 <S W = 0). The discrepancy between thery and experiment n the dwnstream part f the ramp is discussed in detail in Sectin 4. 4

19 Sym z/b Side Plates Pc/P» 0 ff ff 1.21 C -0.7 ff n 1.18 a 0.4 n n Thery M - 6, Re = 0.5 x 10 6 ft" > m 2.5 p/p J22a x/x a. Chrdwise Pressure istributin Fig. 4 Tw-imensinality f Flw at M W = M M = 6, Re e = 0.38 x 10*

20 AEC-TR Sym Side Plates p p «ff 1.21 n 1.18 Thery M = 6, Re = 0.5 x 10 6 ft -1, Ö = 11 deg P/P, P/P, 2.0 h 8 x/x =0.72 c P/P, x/x = z/b 8 8 I i b. Spnwise Pressure istributin Fig. 4 Cntinued 11

21 t y, in ^ Sym z/b A -0.7 <* 10 6 ft" 1, H =6, Re = 0.5 x c 'n 0-11 deg (9A CA 0 A n A A A PA A A A A a A A Side Plates ff A A A P*/P» " " - > a a p Side Plates n PyP» " 3-15 i i 1 1 ) *l/ M «Ö Q a p a p > m n c. Mach Number Prfiles at x/x e = 1.47 Fig. 4 Cncluded

22 4.S Sym z/b Side Plates P /p - 0 ff 1.41 a 0.4 ff 1.41 c -0.7 ff n 1.43 a 0.4 n 1.43 n -0.7 n 1.43 Thery , Re 0.5 x 10 6 ft -1, Ö - 11 deg 3.0 P/P 2.5 W > m n a. Chrdwise Pressure istributin Fig. 5 Tw-imensinality f Flw at M W) - M M - 8, Re* e = 0.38 x 10 6

23 AEC-TR Sym Side Plates p ^<*> ff 1.41 a n 1.43 Thery M = 8, Re = 0.5 x 10 6 ft" 1, 6 = 11 deg 2.0 i P/P 1 r x/x c i i p/p. x/x c = _, 9 i! i t. iii iii p/p ) Q x/x^ c =0.50 A i z/b b. Spanwise Pressure istributin Fig. 5 Cntinued

24 Ui 0.6 y, in. Sym z/b A _ ca Re = 0.5 x 10 6 ft = 11 deg M ' A A C A A A A Side Plates ff * P/P» = 455 \ 0!tP C» as S n S S - _ja 3A C ca A ca A l A c. Mach Number Prfiles at x/x c 1.47 A A Fig. 5 Cncluded A C A A A cp Side Plates n P /P r W = J M T ]_, /M 00 A A > m n * H

25 AEC-TR _ P/P a. Chrdwise Pressure istributin Fig. 6 Tw-imensinality f Flw at M W = M^ = 10, Re x<. = 0.38 x

26 AECTR Sy Side Plates P</P, n Thery 1.95 M M - 10, Re M = 0.5 x 10 6 ft -1, 9-11 deg P/P^ > ( 1 A x/x c p/p x/x c > P/P x/x i Thery 1 «/ I * \ ,6 0.8 z/b b. Spanwise Pressure istributin Fig. 6 Cncluded 17

27 AEC-TR The spanwise pressure distributins fr M w. = 8 (Figs. 5a and b) shw better agreement ver a wider span, with the side paltes n, than the M w j = 6 data. When the side plates were remved, the relatively gd agreement with thery fr the flat-plate prtin became wrse, and the spanwise variatins were amplified. The Mach number prfiles (Fig. 5c) als indicate that the flw was mre nearly the same fr a wider span with the side plates n than with them remved. Therefre, because f the clser agreement with thery and the imprved spanwise unifrmity, the data with side plates n are cnsidered t be mre nearly tw-dimensinal. The pressure distributins fr M w^ = 10 (Fig. 6) shw very gd agreement between the centerline and the ff-centerline rws, and the spanwise data are unifrm t z/b ^ ±0. 6. These data were taken nly with the side plates n. While there is sme disagreement with the thery n the flat-plate prtin f the mdel, these data are cnsidered t be tw-dimensinal because f the unifrm spanwise distributins. In summary, it appears that tw-dimensinal flw was btained: (1) at M W i = 6 with and withut side plates, (2) at M w^ = 8 with side plates but nt withut, and (3) at M w. = 10 with side plates, n data being btained withut. iscrepancies between thery and experiment, especially n the dwnstream prtin f the ramp, were bserved at all Mach numbers. The magnitude f these discrepancies increased as Mach number increased. 4.2 EFFECTS F PITCH In rder t investigate the effects f mdel attitude n the crrelatin f the separatin extent with lcal flw cnditins, the mdel was pitched at free-stream Mach numbers f 6 and 8 such that M w^ = 4. 5 in each case. The stilling chamber pressure and temperature were adjusted, using the curves in the Appendix, t prvide the same Reynlds number (Rexc = x 10^) n the flat plate. The data btained in this manner are presented in Fig. 7, and they shw large differences between the pressure distributins at the tw Mach numbers, bth in the upstream influence and in the ramp pressure gradient. Unfrtunately, n data were btained in a pitched attitude bth with and withut end plates at the same lcal cnditins. The data at M,,, = 6 were btained with the side plates n; hwever, data at a lwer Reynlds number (but at a m = 0) as well as at a higher Reynlds number with the mdel pitched, indicated that there was little change when the side plates were remved. The data at M^ = 8 fr z/b =0.4 agree with the centerline data, and the spanwise distributins are unifrm fr a large span; 18

28 AEC-TR therefre, these data are cnsidered t be tw-dimensinal. The shadwgraphs at M^ 8 shw that the bundary layer was, at least, transitinal during reattachment. Because f the side plates, the state f the bundary layer was indeterminate at M_ = 6. *.u 3.5 M Sym < z/b Side Plates 8» ff ff ff n n n Re x 10" 6 ft 1 p /p e - 10 deg p/p u n 0 a 0 a 0 a r- 10 deg 1.0 Iflmnm x/x a. Chrdwise istributins Fig. 7 Mdel Pitch Effect n Pressure istributin at M w = 4.5, Re x = 0.75 x

29 AEC-TR Sym c Side Plates 8 ff 6 n Re_ x 10" 6 ft -1 p /p» P/P l.u. 9» 10 deg. > x/x c \ i! 8 1 i A <» P/P x/x c. n. 1, a. 4?? 1 5 p^p x/x c k_r_ l. _n l_ -n l i i Ö ft z/b b. Spanwis istributin* Fig. 7 Cncluded ata which were btained at M w^ = 6 and which were mre likely t have been laminar during reattachment are presented in Fig. 8. These results are als in disagreement with each ther t a similar degree, as shwn at M w. =4.5. It is nted that at bth Mach numbers the smallest upstream extent f interactin existed when the flat-plate pressure rati, PQ/P,,,* was the greatest. Since utflw frm the mixing zne wuld be expected t increase with an increase in p 0 /Pa, and thereby reduce the upstream extent, it is cncluded that even thugh lcal Mach number and Reynlds number are matched, valid laminar separatin data prbably cannt be btained by pitching a flat-plateramp cmbinatin t lwer appreciably the lcal Mach number. 20

30 t p/p 3.0 Sym 2.0 _6 - = 10 deg Side Plates Re x 10~ 6 C M ft_1 z/b P 0 /P a 8 0 ff , ff ff ~ 6 0 ff n ff ff ^ 6 0 Thery jr a 'a » Jg c B* f> /a - deg /a a < 0 Qr > bcjlr" l 1 '^- T-"" x/x n a. Chrdwise istributin Fig. 8 Mdel Pitch Effect n Pressure istributin at M w i 6, Re, «

31 AEC-TR Sym * Side Plates ff ff Thery Re M x IP" 6 ft" 1 P 0 /P, = 10 deg P/P X/x c =0.89 " " 8 8" p/p -/x c = L.t ] f 1 ) 0 0 i 1 1 -,_l,-_ L_ - i P/P x/x z/b b. Spanwise istributin Fig. 8 Cncluded 22

32 AETR EXTENT F LAMINAR FLW The data presented in Fig. 9 were used t judge if the bundary layer was laminar thrugh reattachment at M = M Wi = 6. As seen in Figs. 9a and b, the beginning f the interactin regin mved upstream as Reynlds number increased; hwever, the rate f change was less than indicated by the thery. It has been shwn (Refs. 2, 6, 7, and 8) that the extent f upstream influence shuld increase as Reynlds number is increased if the bundary layer is laminar thrugh reattachment. While nne f the flat-plate centerline pressure distributins (Fig. 9a) agree exactly with the thery f Lees and Reeves, Ref. 5 as mdified in Ref. 4, the lwest Reynlds number data are the clsest. Fr cmparisn t the present data n the ramp, data frm Ref. 6 are presented in Fig. 9a fr a slightly different ramp angle and a lwer Reynlds number. These data n the ramp shw gd agreement with the thery, althugh the upstream interactin extent (als shwn in Fig. 9b) is smewhat less than predicted. ata frm K and Kubta (Ref. 7) are shwn in Fig. 9b t have relatively gd agreement with the thery Re_ x 10-6 Sym 6, dcg *<: S A Lewis (Rel. 6) Thry Thery Thery 3 0 i^* P/P a. Centerline Pressure istributin Fig. 9 Effect f Reynlds Number Change at M w. = M =6 23

33 AECTR-69-19? 1.0 Sym 6, deg A Ref. 7 ^X^ 0.8 h Ref. 6 >^ "" Thery >^ ^ Thery ^X^ ^"' 0.6 h c 0.4 V- - n 0.2 L_ III Re x 10 x c 2.0 b. Change in Interactin Length Fig. 9 Cntinued 24

34 AEC-TR c. Shadwgraphs at 9 = 11 deg Fig. 9 Cntinued 25

35 t y, in. 0.6 Sym x/x c m Slid Symbls with w Side Plates m z/b = 0, 6-11 deg % ^ B 0.1 _ - Re X c = 0.38 x 106 B a _L- B m m - a a R % = a a - n ff i 1 1 a B Q] V 1 V M d. Mach Number Prfiles Fig. 9 Cncluded n a

36 AETR The shadwgraph pictures (Fig. 9c) indicate that the bundary layer was laminar thrugh reattachment fr the lwest Reynlds number and, at least, transitinal fr the higher Reynlds numbers. Mach number' prfiles n the ramp fr tw lcatins are presented in Fig. 9d and shw that the recirculatin regin was smaller at higher Reynlds number, i. e., reattachment ccurred earlier. This als indicates that the bundary layer was at least transitinal at reattachment fr the higher Reynlds numbers. As stated befre, the chice f static pressure used fr data reductin was the reasn that sme f the curves d nt g t a Mach number rati f zer in the recirculatin regin. The pressure data fr M Wi = 8 and 10 were taken with the side plates installed, and shadwgraphs were btained with them remved at nly the lwest Reynlds number. The data (Figs. 10 and 11) shw the same general trends as fr M Wi = 6. nly the lwest Reynlds number at M Wi = 8 was judged t be laminar thrugh reattachment. This is true fr bth ramp angles tested, as indicated in Fig. 10b. The M Wi = 10 data (Fig. 11) indicate, as based n the variatin f the upstream extent with Reynlds number increase, that the reattaching bundary layer was laminar fr all ramp angles fr the tw lwest Reynlds numbers and prbably fr the highest (Re Xc = x 10 6 ). The reattachment pressure distributin is, as in all previus data, very different frm the thery. x 10 Sym Thery 0.75 Thery > - 11 dag Sid Plates n P/P a. Centerline Pressure istributin Fig. 10 Effect f Reynlds Number Change at M W = M^ = 8 27

37 AEC-TR Sym A Q, deg Thery 11.0 Thery 0.6 c I I J L_ Re 6 x x 10 c b. Change in Interactin Length Fig. 10 Cntinued

38 AECTR c. Shadwgraph f Re Xc = 0.38 x = 11 deg Fig. 10 Cntinued 29

39 0.6 y, in. 0.5 _ Sym x/ X c n am % Slid Symbl with Side Plates m z/b = 0, e = 11 deg m <m (9 a 9 m> n t m> % e CP «m m f> Re = 0.38 x 10 6 J 6 x c i 1 I a» i «0 d «Ö 3 «B 5 «a «> a «a «a a f?> 0 A J$P Re x 10 6 *0 x c _ P n «jj 00 M L /M c d. Mach Number Prfile» Fig. 10 Cncluded

40 AEC-TR P/P,. u Re x 10" 6 n Sym x c p c/p ^^«^^ 0.19 Thery i 0.38 Thery 0.75 Thery u A = 11 deg 8* A / Side Plates n a /. Q / / 6 / / *// / / y tiy rp j ^s^ 1.0 ^ -1»«""""""""^ V- 11 deg 1«=: i x/x Centerline Pressure istributin Fig. 11 Effect f Reynlds Number Change at M w. = M M = 10 31

41 AEC-TR Sym 0, deg 9.5 a _-_ 9.5 Thery _ Thery Thery 0.6 x - x c s*s I J I L Re x 10 x c 2.0 b. Change in Interactin Length Fig. 11 Cntinued 32

42 AEC.TR c. Shadwgraph at Re x 0.19 x 10 6, 6 = lldeg Fig. 11 Cncluded 33

43 AEC-TR REATTACHMENT PRESSURE RISE As pinted ut in previus discussins, the pressure gradient n the ramp was in all cases larger than that predicted by thery. In general, this is cnsidered t be an indicatin f nnlaminar reattachment. Hwever, there appears t be enugh evidence frm the upstream extent data and the shadwgraphs t indicate that the reattaching bundary layer was laminar, at least at the lwest Reynlds number. The present data with the lng ramp are cnsidered t be free f gemetry limitatins because the theretical reattachment pint is well upstream f the trailing edge f the ramp. It remains, then, t determine the cause f this discrepancy. ther investigatrs have btained data which in mst cases, when the reattachment has been shwn t be laminar, agree reasnably well with the thery f Lees and Reeves. The thery has nt previusly been extended t the higher Mach numbers f the present test. If, hwever, there were sme fallacy in the thery at the higher Mach number, it wuld still leave the disagreement at Mach number 6 unexplained because ther authrs, Ref. 5 fr instance, have btained better agreement at this Mach number. It is, f curse, pertinent t nte that the theretical results presented here are fr the case f S w = 0, which is relatively far remved frm the actual test cnditins investigated. Perhaps the mst remarkable fact derived frm the cmparisns f thery and experiment is the general agreement fund upstream f the ramp despite the significant differences bserved n the ramp. There is ne majr difference between the present wrk and that f Refs. 4, 6, 7, and 8. The maximum flat-plate length t the hinge line, x c, f previus wrk was 5 in., whereas the present mdel was 9 in. Lewis (Ref. 6) fund n change in either the upstream influence r the reattachment pressure rise fr lengths f x c = 2, 3, and 5 in. at cnstant Reynlds number. Hwever, the aspect ratis, x c /2b, fr these lengths were 1. 5, 1.33, and 0. 8, respectively. The aspect rati f the present mdel was 2. 22, greater than that fr even the shrtest flat-plate length f Ref. 6. An investigatin f the effects f flat-plate length and/r aspect rati was planned fr the present study and in fact was being started when the mdel failure ccurred. It was felt that the pressure rise n the ramp may be a functin f the flat-plate length even thugh the bundary layer remains laminar thrugh reattachment. There is still the pssibility, especially at M Wi = 6, that transitin at r even dwnstream f reattachment caused the unusual pressure rise n the ramp. Further wrk is needed t reslve these questins. 34

44 AEC-TR RAMP ANGLE EFFECT As pinted ut by ther authrs, Ref. 7 fr instance, the extent f the upstream influence f the ramp is sensitive t small variatins in angle f attack. Figure 12 shws a similar sensitivity t a small change in ramp angle. An increase f 1. 5 deg in ramp angle at M w. = 10 caused a measurable increase in the extent f the upstream interactin and in particular the maximum pressure rati btained n the ramp. As in previus figures, this pressure rise was greater than that predicted by thery Sym 6, deg P /P a Thery Thery »- = 10, Re = 0.5 x 10 6 ft" 1 00 Side Plates n 0 Q 3.5 P/P x/x a. Re x = 0.38 x 10 6 C Fig. 12 Effect f Ramp Angle Change n Centerline Pressure istributin at M WI = M =10 35

45 AEC-TR Sym 6, deg V p «> Thery Thery M m - 10, Ite = 1.0 x 10 6 ft Side Plates n 9 a Ö P-'P 2.S b. Re x = 0.75 x 10 6 Fig. 12 Cncluded 4.6 INFLUENCE F MASS BLEE As stated in Sectin I, nly a limited amunt f data was btained with the mass-remval slt pen. These data were btained befre the extensin was added t the ramp, and therefre, the reattachment was prbably frced t ccur further upstream than it wuld have with the lng ramp (at least in the n-bleed case with the mdel pitched). Figure 13 shws that with the mdel pitched t btain a lcal Mach number f 4. 5, a bleed-slt inlet size f nly in. (area = in. 2 ) remved all f the separatin. These data are, as indicated in the shadwgraphs, at least transitinal during reattachment. The data btained 36

46 AEC-TR fr M w (Fig. 14) shw that the increase in upstream interactin (ver that at M Wi = 4. 5, but at the same Re Xc ) required a larger slt inlet area in rder t remve all f the separatin. The upstream influence withut bleed in Figs. 14a and b remained apprximately the same when the Reynlds number was increased; therefre, these data are als cnsidered t be transitinal at reattachment. As in the case f the M wi = 4. 5 data, when the separatin was cmpletely remved, a pressure rati f less than 1. 0 was btained well upstream f the inlet t the bleed slt. 4.0 d. 0 d in d in. 3.5 Sym d in. P /P V P c M - 8, Re x 10 6 ft" 1, 9-10 deg 3.0 p/p $ \ 10 deg x/x Fig. 13 Effect f Mss Remval n Separatin at M w, = 4.5, Re x = 1.06 x

47 AECTR Sym d, in. d - 0 P /P P»./P M - 8, Re - e 0.88 X 10 6 ft -1, d in. P/Pn e - 10 deg a a a a 0^ G a 2.0 _ G _ - S T 10 deg 1.0 x&h*nncp\. i r^ h 1 i i x/x a. Re x = 1.0 x 10 6 x c Fig. 14 Effect f Mass Remval n Separatin atm W = 6 38

48 AEC-TR d = in. d in. P/P 3.5 _ Sym d, in. P / P =» P b /P» M «, = 8 ' Re = 1-34 X 1C 6 **" 1 ' e8^*> 0-10 deg cpö <* C <* n a y-10 deg x/x b. Re x = 1.5 x 10 6 Fig. 14 Cncluded 39

49 AEC-TR The data btained with the mdel at zer pitch (Fig. 15) appears, at least in the shadwgraph picture at the lwer Reynlds number, t be laminar at reattachment. The separatin regin apparently was nt cmpletely remved at either Reynlds number, even with the slt pened t in. (area = in. *), because a very slight pressure rise was present upstream f the slt (instead f the drp belw a rati f 1.0 as seen frm the previus figures). These data suggest that the gap (bleed) area required t eliminate the upstream interactin increases with an increase in Mach number. 4.5 d - 0 d in. Sym d, in. P /p» V p» /s M - 8, Re x 10 6 ft" 1, 6 «= 10 deg p/p " a a a 0 «0 - n^ ^ B* v- 10 deg 1.0 L -T-" 1? x/x_ a. Re x = 0.75 x 10 6 Fig. 15 Effect f Mass Remval n Separatin at M w. = M^ = 8 40

50 AEC-TR d in. d In. P/P Sym d, In. P-/P v p» <* M a> - 8, Re x 10 6 ft" 1, 9-10 deg G 0 B a n G 1.5 ^ v- 10 deg ^ flfawfw*^0 i "T"" A 1 i i b. Re x = 1.0 x 10«Fig. 15 Cncluded 41

51 AEC-TR Ball (Ref. 1) has btained mass bleed data at several Mach numbers (M Wi = 5. 3, 6.5, 6.7, and 8. 0) but with the mdel pitched at M w These data were als all at different Reynlds numbers (Re x ). A cmparisn f the present data at Mwj = M,,, = 8 t thse f Ball at M wi = 8, M,,, = 12 is shwn in Fig. 16. The weight flw was calculated in the same manner as Ref. 1, i. e., using the static pressure at the hinge line and the wall temperature as the supply cnditins and by assuming snic flw at the slt inlet. The present data n the left curve f Fig. 16 were extraplated t btain the amunt f weight flw bleed needed fr the "incipient" separatin. The weight flw was ratied t the theretical weight flw in a laminar bundary layer n an adiabatic flat plate f length x c. The theretical value was calculated by integrating the velcity and density prfiles (insulated plate, Prandtl number = 0. 75) btained frm the results in Ref. 9. This weight flw rati is shwn in the right curve f Fig. 16 as a functin f the rati f the interactin length with bleed t that with n bleed. In this frm, the present data and that f Ref. 1 appear t give a reasnable crrelatin with nly slight Reynlds number dependence. It shuld be remembered, hwever, that the present data are prbably transitinal at the higher Reynlds number and may be adversely affected by the shrt ramp at bth Reynlds numbers. The data f Ref. 1 were taken with the mdel pitched, and the ramp was, in fact, shrter with respect t the flat plate (x/x c = 1.43) than the present investigatins * B x 10 3 lb-ft" 1 -sec" 1 V W T Fig. 16 Effect f Mass Remval n Interactin Length at M w. = 8 42

52 AECTR SECTIN V CNCLUING REMARKS Results f this investigatin shw that tw-dimensinal, ramp induced, laminar bundary-layer separatins were btained fr Mach numbers 6, 8, and 10 at Re Xc = x The Mach number -6 data were fund t be tw-dimensinal either with r withut side plates; the Mach number 8 and 10 data were nly judged tw-dimensinal with side plates (n Mach number 10 data were btained withut side plates). The bundary layer was prbably laminar thrugh reattachment at R e x = c x 10 r belw fr all three Mach numbers; hwever, there remains sme questin regarding the Mach number 6 data relative t that f ther investigatins. At M,, = 10, a small change in the ramp angle (1 deg) was shwn t give a large variatin in bth the upstream interactin and in the verall ramp pressure rise. The data btained during this investigatin shw large variatins in the extent f upstream interactin and in the ramp pressure gradient between tw sets f data btained at the same lcal Mach number and Reynlds number but at different free-stream cnditins. It was fund that, even when lcal cnditins were matched, valid separatin data culd nt be btained by pitching the mdel t btain a lwer Mach number. Frm the limited amunt f data btained, it was fund that the separatin induced by a 10-deg ramp angle at Mach numbers 4. 5 and 6 n a pitched flat plate was cmpletely eliminated by remving mass frm the separatin regin. In the case f the unpitched plate-ramp cmbinatin at M s = 8, the data indicated that the separatin culd have been eliminated by remving between 20 t 25 percent f the theretical weight flw in a laminar bundary layer n a flat plate f length x c. Because f the mdel failure during the tests, much f the investigatin remains incmplete. ther investigatrs have als left several majr pints unreslved either because the flw in their experiments was nt examined in sufficient detail fr tw-dimensinality, r checked clsely fr laminar flw at reattachment, r was nt clearly free f gemetry limitatins. While quite a bit f data has been published n bundary-layer separatin with mass remval, insufficient data are available t btain a cmprehensive understanding f the factrs invlved. The majr pints which require further investigatin are (1) the validity f the separatin data btained with a flat-plate-ramp cmbinatin 43

53 AEC-TR pitched in rder t btain lwer than free-stream lcal Mach numbers, (2) the effect f mass bleed n tw-dimensinal, laminar bundarylayer separatin that is nt limited by mdel gemetry, (3) the cause f the discrepancy between the pressure gradient n the ramp btained during the present tests and that predicted by adiabatic, integralmment separatin thery, and (4) the effects f flat-plate length and/r aspect rati n the cmplete pressure distributin, particularly at Mach number 6. REFERENCES 1. Ball, K.. W. "Effects f Flap Length and Slt Suctin n Laminar Bundary Layers. " AIAA Paper 69-36, January Gray, J.. "Investigatin f the Effect f Flare and Ramp Angle n the Upstream Influence f Laminar and Transitinal Reattaching Flws frm Mach 3 t 7. " AEC-TR (A645840), January Ames Research Staff. "Equatins, Tables, and Charts fr Cmpressible Flw. " NASA Reprt 1135, Klineberg, J. M. "Thery f Laminar Viscus-Inviscid Interactins in Supersnic Flw. " Ph.. Thesis, Califrnia Institute f Technlgy, Lees, L. and Reeves, B. L. "Supersnic Separated and Reattaching Laminar Flws: I. General Thery and Applicatins t Adiabatic Bundary Layer/Shck-Wave Interactins. " AIAA Jurnal, Nvember Lewis, J. E. "Experimental Investigatin f Supersnic Laminar, Tw imensinal Bundary Layer Separatin in a Cmpressin Crner with and withut Cling. " Ph.. Thesis, Califrnia Institute f Technlgy, K,. R. S. and Kubta, T. "Supersnic Laminar Bundary Layer alng a Tw-imensinal Adiabatic Curved Ramp. " AIAA Paper Ginux, J. J. "Supersnic Separated Flws ver Wedges and Flares with Emphasis n a Methd f etecting Transitin. " ARL , January Van riest, E. R. "investigatin f Laminar Bundary Layer in Cmpressible Fluids Using the Crcc Methd. " NACA TN 2597, January

54 AEC-TR APPENIX INVISCI WEGE CURVES 45

55 AEC-TR g. deg Fig. 1-1 Wedge Shck Wave Angle 47

56 AEC-TR a M, deg Fig. 1-2 Wedge Surface Mach Number 48

57 AEC-TR ~ a M, deg 32. UM = 0 t 30 deg Fig. 1-3 Wedge Surface Pressure Cefficient 49

58 / AEC-TR M / / /8 / Al / Ay i W MM r 0.4 /yy ^^ b. au = 0 t 15 deg Fig. 1-3 Cncluded 50

59 AEC-TR /l / / Pw/ P «32 24 f i See Fig. I-4b I / / / 8 16 S.*r ^>S* I a M, cleg a. am = 0 t 30 deg Fig. 1-4 Wedge Surface Pressure Rati 51

60 / AEC-TR b. an = 0 t 15 deg Fig. 1-4 Cncluded 52

61 AEC-TR T /T 3 _ 22 a. aw = 0 t 30 deg Fig. 1-5 Wedge Surface Temperature Rati 53

62 AEC-TR II ~ - / _ / / x v' v" V >r ^/"^ ^"" ^ 1 1 1, a M, deg b. a M = 0 t 15 deg Fig. 1-5 Cncluded 54

63 AEC-TR Re^./Re^ percent' ashed prtin f curves indicates \ y 0.6 regin where rati is apprximate \ \ because f linear viscsity relatin. V v Crss curves indicate percent errr in. v rati based n T Wi /T fr average T^ \ \ 0.5 I ver Re range. \ I I 1 I \ i^ a M' deg Fig. 1-6 Wedge Reynlds Number Rati 10 55

64 UNCLASSIFIE SecurityClassUicatin CUMENT CNTRL ATA -R& (Security classificatin t title, bdy f abstract and indexing anntatin must be entered when the verall reprt Is clsattled) I. RIGINATING ACTIVITY (Crprate authr) Arnld Engineering evelpment Center AR, Inc., perating Cntractr Arnld Air Frce Statin, Tennessee «. REPRT SECURITY CLASSIFICATIN UNCLASSIFIE 2b. GRUP 3. REPRT TITLE INVESTIGATIN F LAMINAR BUNARY-LAYER SEPARATIN N A FLAT-PLATE- RAMP CMBINATIN WITH AN WITHUT MASS REMVAL AT MACH NUMBERS 6, 8, AN ESCRIPTIVE NTES (Type l reprt and Inclusive dates) July 11, 1965 t April 18, Final Reprt B. AUTHR(S) (First name, middle Initial, last name) R. W. Rhudy, AR, Inc. N/A 6. REPRT ATE March 1970 «.. CNTRACT R GRANT N. F C-0001 b. PRJECT N. 1«300 Prgram Element 62201F 7a. TTAL N. F PAGES 63»a. RIGINATR'S REPRT NUMBER(S) 7b. N. F REFS AEC-TR b. THER REPRT NISI (Any ther numbers that may be assigned this reprt) N/A ISTRIBUTIN STATEMENT This dcument has been apprved fr public release and sale; its distributin is unlimited. II- SUPPLEMENTARY NTES Available in C, 12. SPNSRING MILITARY ACTIVITY Arnld Engineering evelpment Center, Air Frce Systems Cmmand, Arnld AF Statin, Tennessee ABSTRACT An experimental investigatin f laminar bundary-layer separatin induced by a trailing edge ramp n a flat plate was cnducted at Mach numbers f 6, 8, and 10. The tests were cnducted ver a range f Reynlds numbers. Lngitudinal and spanwise surface pressure distributins, pitt pressure prfiles, and shadwgraph pictures were used t investigate the tw-dimensinality f the flw and the effects f mdel gemetry, angle f attack, Reynlds number, ramp angle, and mass remval frm the separatin regin. ata are presented t shw that laminar, tw-dimensinal bundary-layer reattachment, nt limited by mdel gemetry, was btained. These data are cmpared t the integralmment thery f Lees and Reeves as mdified by Klineberg. It is als shwn that a separatin regin can be reduced r even eliminated by remving mass at the hinge line. FRM I NV UNCLASSIFIE Security Classificatin

65 UNCLASSIFIE Security Classificatin KEY WRS LINK C bundary-layer separatin laminar bundary layer trailing edges ramps flat plate mdels tw-dimensinal flw hypersnic flw APBC IdAriTMM UNCLASSIFIE Security Classificatin