@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Mechanical Engineering, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Sun, Yung-chiun"@en ; dcterms:issued "2011-11-16T17:23:55Z"@en, "1961"@en ; vivo:relatedDegree "Master of Applied Science - MASc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """When a thin delta wing with high leading-edge sweep is placed at incidence in a stream, the fluid separates from the surface at the leading edges and coils up to form a pair of symmetrically placed vortices above the upper surface of the wing. This flow pattern is stable up to high incidence, but at extreme high incidence, the stable vortex core appears to burst or rapidly diffuse. The present research was done as part of a general program to study the vortex bursting phenomenon about sharp-edged delta wings. The aim was to determine the bursting position at different angles of attack and the effect on the wing performance. It was found that the bursting occurs first downstream of the trailing edge and then moves rapidly upstream with increasing incidence. The wing stalls when the bursting point occurs at a position upstream of the wing's trailing edge. The pressure distributions on a sharp-edged rectangular wing were also measured in the present research and the overall normal force coefficient was obtained by the graphical integration of surface pressures. It was found from the pressure distributions that the flow pattern changes from one type to another in the range from ∝= 10° to ∝= 15°. The overall normal force coefficient reaches its first maximum value at 17° incidence."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/39067?expand=metadata"@en ; skos:note "EXPERIMENTAL INVESTIGATION OF THE FLOW FIELD ABOUT SHARP-EDGED DELTA AND RECTANGULAR WINGS by YUNG-CHIUN SUN B . S c , N a t i o n a l Taiwan U n i v e r s i t y , 1957 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.A, Sc. i n the Department of Mechanical Engineering We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard The U n i v e r s i t y of B r i t i s h Columbia December I961 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y • a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n permission. Department The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date - 11 -ABSTRACT. When a t h i n delta wing with high leading-edge sweep i s placed at incidence i n a stream, the f l u i d separates from the surface at the leading edges and c o i l s up to form a pair of symmetrically placed vortices above the upper surface of the wing. This flow pattern i s stable up to high incidence, but at extreme high incidence, the stable vortex core appears to burst or rapidly d i f f u s e . The present research was done as part of a general program to study the vortex bursting phenomenon about sharp-edged delta wings. The aim was to determine the\"bursting position at d i f f e r e n t angles of attack and the e f f e c t on the wing performance. I t was found that the bursting oocurs f i r s t downstream of the t r a i l i n g edge and then moves rapidly upstream with increasing incidence. The wing s t a l l s when the bursting point occurs at a position upstream of the wing's t r a i l i n g edge. The pressure d i s t r i b u t i o n s on a sharp-edged rectangular wing were also measured i n the present research and the o v e r a l l normal force c o e f f i c i e n t was obtained by the graphical integration of surface pressures. I t was found from the pressure d i s t r i b u t i o n s that the flow pattern changes from one type to another i n the range from <=>(,= 10° to o(= 15°. The o v e r a l l normal force c o e f f i c i e n t reaches its f i r s t maximum value at 17° incidence. i i i -CONTENTS . . ~ Page. INTRODUCTION .' . . . . 1 HISTORICAL BACKGROUND AND CURRENT THEORIES . . . . . . . . . . . k TEST FACILITIES AND APPARATUS .13 MEASUREMENT TECHNIQUES . . . . . . . . . . 17 TEST RESULTS - 19 DISCUSSION OF TEST RESULTS . . . . . . . 24 CONCLUSIONS vi-^fv* 31 RECOMMENDATIONS • • * 32 REFERENCES 33 ILLUSTRATIONS 36 - i v -ILLUSTRATIONS Fig u r e Number 1. WIND TUNNEL AERODYNAMIC OUTLINE 2. SKETCH OF MODELS I AND I I 3. SKETCH OF MODEL I I I k. SKETCH OF MODELS IV, V, VI AND VII.. 5. SKETCH OF MODEL V I I I 6. SKETCH OF MODELS IX, X AND XI 7. SKETCH OF MODEL X I I ' 8. SKETCH OF PROBES 9. TRAVERSING APPARATUS 10. POSITION OF VORTEX CORE MEASURED WITH VORTOMETER MODELS I AND I I 11. VORTEX CORE POSITION FOR FLAT DELTA WINGS 12. TIP VORTEX CORE ABOUT MODEL I I I AT 15° ANGLE OF ATTACK, 13. VORTEX SYSTEM ABOUT MODEL V I I I AT 10° ANGLE OF ATTACK Ik, SPANWISE PRESSURE DISTRIBUTIONS AT STATION 1 MODEL .IX 15. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 2 MODEL IX 16. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 3 MODEL IX 17. SPANWISE PRESSURE DISTRIBUTIONS AT STATION k MODEL IX 18. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL IX 19. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 6 MODEL IX 20. \"SPANWISE PRESSURE DISTRIBUTIONS AT STATION 7 MODEL IX 21. VARIATION OF SECTIONAL NORMAL FORCE COEFFICIENT C w WITH x INCIDENCE MODEL IX. 22. CHORDWISE VARIATION OF C H MODEL IX 23. VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C N WITH INCIDENCE MODEL IX ILLUSTRATIONS CONTINUED Fi g u r e Number 2k. SPANWISE PRESSURE DISTRIBUTIONS MODEL IX (COMPARISON WITH RESULTS OF BROWN AND MICHAEL, MANGLER AND SMITH) . 25. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 1 MODEL X. 26. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL X 27. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 7 MODEL X 28. SPANWISE PRESSURE DISTRIBUTIONS AT. STATION 9 MODEL X .'. 29. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 10 MODEL X 30. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 11 MODEL X 31. VARIATION OF SECTIONAL NORMAL FORCE COEFFICIENT C w WITH :INCIDENCE MODEL X 32* CHORDWISE VARIATION OF C N MODEL X 33, VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C N WITH INCIDENCE MODEL X . 3k.' . SPANWISE PRESSURE:DISTRIBUTIONS AT STATION 1 MODEL XI 35. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 2 MODEL XI 36. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 3 MODEL XI 37. SPANWISE PRESSURE DISTRIBUTIONS AT STATION k MODEL XI . 38... SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL XI 39. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 6 MODEL XI kO. SPANWISE PRESSURE DISTRIBUTIONS AT STATION 7 MODEL XI kl. VARIATION OF SECTIONAL NORMAL FORCE COEFFICIENT C N x WITH INCIDENCE MODEL XI k2. CHORDWISE VARIATION OF C w MODEL XI k3. VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C N WITH . INCIDENCE MODEL XI - v i ILLUSTRATIONS CONTINUED Fig u r e Number kh. . COMPARISON BETWEEN EXPERIMENTS AND THEORIES FOR NORMAL FORCE COEFFICIENTS OF DELTA WINGS 45. SPANWISE VARIATION OF C p AT STATION 1 MODEL X I I k-6. SPANWISE VARIATION OF C p AT STATION 2 MODEL X I I hf. SPANWISE VARIATION OF C p AT STATION 3 MODEL X I I kQ. SPANWISE VARIATION; OF C p AT STATION k MODEL X I I 1+9. SPANWISE VARIATION OF Cp AT STATION 5 MODEL X I I 50. SPANWISE VARIATION OF C p AT STATION 6 MODEL X I I 51. SPANWISE VARIATION OF C p AT STATION 1^ . i n . FROM L.E. MODEL X I I 52. PRESSURE DISTRIBUTIONS ON THE UPPER SURFACE OF MODEL X I I AT 10° ANGLE OF ATTACK 53. VARIATION OF SECTIONAL NORMAL FORGE COEFFICIENT C„ WITH x INCIDENCE, MODEL X I I $k. CHORDWISE VARIATION OF C w MODEL X I I 55. VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C N WITH INCIDENCE MODEL X I I 56. COMPARISON BETWEEN EXPERIMENTS AND THEORIES FOR NORMAL FORCE CHARACTERISTICS OF A = 2 RECTANGULAR WINGS 57- VARIATION OF VORTEX BREAKDOWN-POSITIONS WITH INCIDENCE MODEL IX 58. VARIATION OF VORTEX BREAKDOWN POSITIONS WITH INCIDENCE MODEL X. 59. VARIATION OF VORTEX BREAKDOWN POSITIONS WITH INCIDENCE MODEL XI 60. VARIATION OF VORTEX BREAKDOWN POSITIONS WITH SWEEP 61. VARIATION OF LIFT COEFFICIENT C L WITH INCIDENCE MODELS IX,X AND XI - v i i -ACKNOWLEDGMENT The author wishes t o acknowledge the advice and encouragement given by Dr. G. V. Parkinson who supervised the research. He a l s o wishes to thank the Mechanical Engineering Department f o r the extensive use of the U n i v e r s i t y of B r i t i s h Columbia wind t u n n e l . F i n a n c i a l a s s i s t a n c e was re c e i v e d from the Defence Research Board of Canada. - v i i i SYMBOLS Aspect r a t i o Span ( t r a i l i n g edge) Root chord .; P - P~ Pressure c o e f f i c i e n t ir.pu: S t a t i c pressure S t a t i c pressure i n the undisturbed stream Density Free stream v e l o c i t y Pressure c o e f f i c i e n t at zero incidence = C - C P P lower upper 2 s L o c a l normal f o r c e c o e f f i c i e n t . / L o c a l semi-span Normal f o r c e L i f t f o r c e ,c> O v e r a l l normal f o r c e c o e f f i c i e n t = - * N 6 Cf-L i f t c o e f f i c i e n t Wing area C a r t e s i a n co-ordinates x measured chordwise y measured spanwise SYMBOLS CONTINUED Angle of a t t a c k Leading edge sweepback Serai apex angle of d e l t a wings = t a n ^ 3 = cot A EXPERIMENTAL INVESTIGATION OF THE FLOW FIELD ABOUT SHARP-EDGED DELTA AND RECTANGULAR WINGS INTRODUCTION . During the nineteen f o r t i e s , i t was recognized that sweepback could appreciably delay the transonic drag r i s e on. a i r c r a f t wings. Also i n the lower supersonic regime, the wave drag could be reduced i f the l i f t i n g surface were kept inside the Mach cone. I t was also known that the drag of high speed a i r f o i l s is•proportional to the square of t h e i r thickness. Under these considerations, th i n swept wings and t h i n delta wings were developed for high speed a i r c r a f t . Although t h i s class of - l i f t i n g surfaces has excellent high speed performance ch a r a c t e r i s t i c s , i t s low speed behavior, important for taking off and landing, poses serious problems. In order to f i n d out what the r e a l flow f i e l d around t h i s class of wings looks l i k e and the reason for poor low speed performance, many investigators have studied t h i s problem by experimental or theoretical methods. Observations show that, when th i n wings with high leading-edge sweep are placed at.incidence i n a stream, the f l u i d separates from the surface along l i n e s near the leading edges and c o i l s up to form pairs of symmetrically placed vortices above the upper surface of the wing. This flow pattern, which has been found by many investigators, has a stable char-acter even at high incidence and gives higher l i f t than would resu l t from a flow pattern without leading edge separation. I t i s also found that the - 2 -f l o w i s not s e n s i t i v e t o Mach number and i n consequence many i n v e s t i g a t i o n s of t h i s type of f l o w may be -performed i n the low speed wind tun n e l or water : t u n n e l . When a c e r t a i n high incidence i s reached, the s t a b l e vortex core appears t o b u r s t or r a p i d l y d i f f u s e at some di s t a n c e downstream. As-incidence i s i n c r e a s e d the b u r s t moves forward towards the apex. The p o s i t i o n along the vortex at which b u r s t i n g occurs depends p r i m a r i l y on a combination of the angle of sweepback of the l e a d i n g edge and the incidence of the wing. For l a r g e angles of sweepback and low incidence the b u r s t occurs i n the vortex downstream of\"the wing, but w i t h an increase of incidence or a decrease of e f f e c t i v e sweepback the b u r s t moves upstream t o a p o s i t i o n above the surface of the wing. Observation of the b u r s t i n g process r e v e a l s t h a t i t i n v o l v e s r a p i d d e c e l e r a t i o n of the f l u i d moving along the a x i s of the vortex f o l l o w e d by what appears t o be s p i r a l l i n g of the vortex core be-f o r e the f l o w becomes completely i r r e g u l a r . This phenomenon i s not f u l l y understood so f a r and i t i s s t i l l the subject of much t h e o r e t i c a l and ex-perimental research. The f i r s t p a r t of the present research was done as part of a general program t o study the l e a d i n g edge separation and vortex b u r s t i n g phenomenon f o r sharp-edged d e l t a wings. The aim was t o determine t h e , b u r s t i n g p o s i t i o n at d i f f e r e n t angles of a t t a c k on.three h a l f model d e l t a wings and the e f f e c t of vortex b u r s t i n g on the surface pressure d i s t r i b u t i o n . Normal f o r c e c o e f f i c i e n t s on the 65°, 70° and 75° l e a d i n g edge sweepback models were worked out by the g r a p h i c a l i n t e g r a t i o n of surface pressures. Vortometers ware used t o l o c a t e the s t a b l e vortex core. The data were then c o r r e l a t e d w i t h r e s u l t s from other sources. I t d i d not prove easy to i n t e r p r e t ana-l y t i c a l l y a l l the f e a t u r e s of the f l o w f i e l d and t o c o n s t r u c t a s a t i s f a c t o r y . theory f o r the f l o w . Recent developments i n a i r c r a f t and m i s s i l e s f o r high speed f l i g h t have r e s u l t e d i n a tren d toward u s i n g t h i n a i r f o i l s of short span among which r e c t a n g u l a r wings pla y an important r o l e . Consequently, i t i s necessary t o understand the f l o w p a t t e r n s about t h i s k i n d of wing both ax hi g h speed and low speed. When a t h i n r e c t a n g u l a r wing i s set at &• small.angle of a t t a c k i n a uniform stream, the f l o w remains attached t o the wing surface so th a t a l l the shed v o r t i c i t y l i e s i n a sheet which contains the wing planform and proceeds t o r o l l up g r a d u a l l y ' a f t e r l e a v i n g the wing t r a i l i n g edge. As the angle of a t t a c k i s i n c r e a s e d , the si d e edges become more oblique t o the f r e e stream, the f l u i d can no longer n e g o t i a t e the l8o° t u r n at the side edges and side^edge s e p a r a t i o n occurs, g i v i n g r i s e to two a d d i t i o n a l • v o r t e x sheets which b e g i n t o r o l l up even ahead of the wing t r a i l i n g edge. F i n a l l y at s t i l l higher angles of a t t a c k , the f l o w separates from the l e a d i n g edge, •. g i v i n g r i s e t o v o r t i c e s whose axes are e s s e n t i a l l y normal t o the f r e e stream d i r e c t i o n . The angles o f a t t a c k at which the fo r e g o i n g phenomena occur and the r a t e of r o l l i n g up and shedding depend on the aspect r a t i o of the wing and the sharpness of i t . In the second part\" of the present research an i n v e s t i g a t i o n i s made of the flow p a t t e r n and pressure d i s t r i b u t i o n on a sharp-edged r e c t a n g u l a r wing at low speed. The main o b j e c t i v e was t o o b t a i n the vor t e x system.about the wing a t 10° angle of a t t a c k by u s i n g a vortometer. Surface pressure d i s t r i b u t i o n s were measured from the pressure taps on the wing and the over-a l l normal force, c o e f f i c i e n t was obtained by the g r a p h i c a l i n t e g r a t i o n of surface pressures. The data were c o r r e l a t e d w i t h other a v a i l a b l e data.and theory. - 4 -HISTORICAL BACKGROUND AND CURRENT THEORIES The f l o w f i e l d about d e l t a wings has been i n v e s t i g a t e d by many experimenters over the l a s t f i f t e e n y e a r s . I n the f i r s t few years, they d i s c o v e r e d the n o n - l i n e a r property of l i f t and moment curves by means of wind t u n n e l balance measurements. In order t o i n t e r p r e t t h i s n o n - l i n e a r i t y , a number of experimental s t u d i e s have been performed t o l o c a t e vortex cores and t o f i n d the d i r e c t i o n of f l o w w i t h i n the i n n e r core of the boundary l a y e r by u s i n g d i f f e r e n t techniques such as t u f t g r i d , vortometer, vapor screen, lamp-black and china c l a y c o a t i n g s . Recently a t t e n t i o n has been drawn t o the phenomenon of vortex b u r s t i n g which occurs when a c e r t a i n incidence i s reached and which may have d e t r i m e n t a l e f f e c t s . A b r i e f summary of the experimental work i s given i n the f o l l o w i n g paragraphs. In 19^ 7> Anderson 1 i n v e s t i g a t e d the low speed c h a r a c t e r i s t i c s of a l a r g e - s c a l e t r i a n g u l a r wing w i t h symmetrical double wedge s e c t i o n . He found t h a t there are two types of f l o w over the wing; smooth fl o w at low angle of a t t a c k and f l o w w i t h s e p a r a t i o n o f f the sharp l e a d i n g edge at h i g h angle of a t t a c k . The t r a n s i t i o n from one type of f l o w t o the other was i n d i c a t e d by breaks i n the f o r c e and moment curves, which occurred at d i f f e r e n t values of angle of a t t a c k , depending upon the wing c o n f i g u r a t i o n . A f t e r t e s t i n g s i x plane d e l t a wings i n 19^8, Berndt a l s o found that both the l i f t and moment curves show a t y p i c a l n o n - l i n e a r form. The l i f t curve slope has one value at low angle of a t t a c k ( 32° and 29° incidence, respectively^ For ordinary subsonic a i r f o i l s s t a l l i s due to separation of flow on the upper surface. Separation f i r s t occurs at the t r a i l i n g edge and then moves forward with incidence. When the point of separation moves close to the leading edge, the a i r f o i l s t a l l s . For sharp-edged delta wings, flow separates-at the leading edge, even at very low angle of attack and i t i s clear from the l i f t curves that the separation does not cause the wing s t a l l but rather gives a higher l i f t than the wing without separation. Therefore, separation i s not the reason for s t a l l on sharp-edged delta wings. Probably the reason i s the st r u c t u r a l change of the vortex system or vortex bursting i n the flow f i e l d . Bursting, which occurs downstream of the t r a i l i n g edge at small angle of attack, moves upstream towards the apex with incidence and causes the wing s t a l l . For Model IX, see Figures 6l and 57 • The wing .s t a l l s at 3^° incidence for which bursting occurs at 6C$ c r. This suggests that the wing s t a l l s when the bursting point reaches a position upstream of the t r a i l i n g edge. The same phenomenon was found on Model X, as shown i n Figures 6l and 58, and Model XI, as . shown i n Figures 6l and 59-Comparison between the present test results and theories f o r normal force c o e f f i c i e n t of these three wings i s shown i n Figure kk. I t i s seen that the experimental results are lower than the t h e o r e t i c a l r e s u l t s . Some experimental results from other sources are shown i n the figure f o r comparison. - 27 -RECTANGULAR WINGS Spanwise pressure d i s t r i b u t i o n s show that' the average Cp on the upper,surface of the wing increases r a p i d l y w i t h incidence t o a maximum value and then, drops g r a d u a l l y w i t h i n c r e a s i n g i n c i d e n c e . For example, at s t a t i o n ' 6 of Model X I I , the average C increases from -0.3 at <=< = 5° \"to -0.7 at <=«£_ = 10° and then drops tor-0.5 at o< = 20°. When the incidence i n c r e a s e s again, the average C^ drops g r a d u a l l y to -0.45 at °^-= 30° and almost remains constant t h e r e . On the lower s u r f a c e , the average inc r e a s e s c o n t i n u o u s l y from +0.1 at oC = 5° \"to +0.6 at &<. = 30°. The same behavior was found at other s t a t i o n s . I t was found that the d i f f e r e n c e of C between s t a t i o n s i s • P n o t i c e a b l e at lower angle of a t t a c k . S t a t i o n s near the t r a i l i n g edge give a smaller reading. At higher angle of a t t a c k , Cp on the upper surface i s almost the same at a l l s t a t i o n s . :For'example, Cp i s around -0.6 at a l l s t a t i o n s at o< = 20°. At =< = 10° and oC = 15°, a s u c t i o n peak near the wing t i p was found which i s caused by the side edge s e p a r a t i o n . For angles of a t t a c k more than 15°, no evidences of t i p v o r t e x core were found from the pressure d i s t r i b u t i o n s . F i g ure 53 shows the v a r i a t i o n of l o c a l normal f o r c e w i t h incidence at each s t a t i o n . I t was found t h a t the shapes of the curves are the same; They a l l increase w i t h incidence t o a maximum , value and then decrease a l i t t l e b i t and then r i s e again. For given angle of a t t a c k , s t a t i o n 6 gives the l a r g e s t l o c a l normal f o r c e c o e f f i c i e n t . C^x f o r ..other s t a t i o n s decreases p r o g r e s s i v e l y as the t r a i l i n g edge i s approached. The maximum qccurs at d i f f e r e n t angles at d i f f e r e n t s t a t i o n s . , C J J reaches i t s maximum at o£ - ne-at s t a t i o n 6, but at oC = 19° at s t a t i o n 1. The. maximum occurs at other s t a t i o n s i n the range from.; c< = 11° t o o< = 19°. For angles of a t t a c k greater than 25°, the normal f o r c e increases again w i t h incidence at a l l - 2b -stations. I t can be imagined that Cjj - w i l l reach a maximum at o( = 90° and the curves f o r stations 1 and 6 w i l l meet there. From the o v e r a l l normal force curve, i t i s seen that C,T = Cm at c*C = 17° (see Figure 55) • - N INmax 23 I t i s known that forc< = 90° i s about 1.20 f o r a f l a t , plate of A = 2. Reference to the chordwise va r i a t i o n of C-^ (see Figure 5*0 shows . 0 that the character of v a r i a t i o n for °C = 15 i s di f f e r e n t from that f o r o< - 10°. For o< less than 10°, concave upward curves were obtained, but for o£ larger than 15°, a l l the \"curves are concave downward. This suggests that the flow pattern changes from one type to another i n the range from .cx£ = 10° to oC = 15°« Preliminary vortometer tests indicate that there i s a stable t i p vortex core about the wing t i p and a vortex core at the leading edge at 10° incidence. Therefore, the flow pattern about the rectangular wing i s dominated by a t i p vortex core and a leading edge vortex core above the wing. These vortex cores produce the high suction at the wing t i p and the leading edge as seen on the pressure d i s t r i b u t i o n curves. When angles of attack exceed • 15° the leading edge vortex passes downstream with the free stream, producing an unsteady flow pattern with vortex shedding i n the' manner of flow past a b l u f f body. The vortex core at the wing t i p also changes i t s structure at high angle of attack. This unstable flow pattern does not produce high suction peaks around the leading edge and wing t i p as shown on the pressure d i s t r i b u t i o n curves f o r angles of attack above 20°. Comparison of the o v e r a l l normal force c o e f f i c i e n t with the results\" of other Investigators indicates very good agreement 'for angles of attack less than 15°> but disagreement at high angles of attack (see Figure 56). Discrepancies are. due to the d i f f e r e n t a i r f o i l sections of the experimental models. The theory of Sacks and Nielsen does not show close agreement for - 29 -angles of a t t a c k greater than 14°, because they d i d not consider the l e a d i n g edge se p a r a t i o n on the. wing-. They a l s o d i d not analyze the unstable f l o w p a t t e r n at extremely high angles of attack.,.. VORTEX BURSTING . -Vortex b u r s t i n g , which occurs at high angles of a t t a c k , was known as a sudden s t r u c t u r a l change of the vo r t e x core. For a given l e a d i n g edge sweep d e l t a wing, the b u r s t i n g p o s i t i o n depends on the angle of a t t a c k * From F i g u r e s 57, 58 and 59, i t was noted t h a t the b u r s t i n g p o s i t i o n i s very s e n s i t i v e t o angle of a t t a c k when b u r s t i n g occurs around the t r a i l i n g edge. On the three models, the b u r s t i n g p o s i t i o n moves q u i c k l y forward to 50$ c r and g r a d u a l l y moves again towards the apex, w i t h i n c r e a s i n g i n c i d e n c e . No e f f e c t of Reynolds number i s n o t i c e a b l e i n the range of Re = 7-l6 x 10^ t o 9\"i5 x 10-*. Leading edge sweep i s another important parameter of b u r s t i n g p o s i t i o n . For 75° l e a d i n g edge sweep, b u r s t i n g occurs at the t r a i l i n g edge at c< = 33°, but i t occurs there at o ( = 21° on 65° l e a d i n g edge sweep wings. The p l o t of l e a d i n g edge sweep against °< at which b u r s t i n g occurs at the t r a i l i n g edge i s a s t r a i g h t l i n e (see Figure 6o). This curve i s i d e n t i c a l w i t h E l l e ' s r e s u l t s obtained by smoke t e s t . Compar-i s o n between the present t e s t r e s u l t s and other a v a i l a b l e data i s shown i n F i g u r e s 57 and 59* For Model XI, 'Lambourne and Bryer showed t h a t the b u r s t i n g occurs a t the t r a i l i n g edge at l6.5° incidence by smoke t e s t , but the present t e s t gave a value of 21°, which i s i d e n t i c a l w i t h E l l e 1 s r e s u l t . For incidence g r e a t e r than 22°, t h e i r r e s u l t s are i n good agreement w i t h the present t e s t s . For Model IX, the d i f f e r e n c e between E l l e ' s r e s u l t s o and the present t e s t s i s of the order 1.5 • The reason f o r and the a c t u a l mechanism of vortex b u r s t i n g have not yet been found. Based on the a v a i l a b l e experimental data, i t i s reasonable t o speculate that b u r s t i n g occurs: 1 . due t o the disturbance produced at the t r a i l i n g edge, t r a i l i n g edge e f f e c t . . 2. ' due to a. f o r c e unbalance on the vortex system at high i n c i d e n c e . - 31 -CONCLUSIONS From the i n t e r p r e t a t i o n of the data which have been presented, the f o l l o w i n g conclusions are drawn: 1. The vor t e x b u r s t i n g occurs f i r s t downstream of the t r a i l i n g edge and then moves r a p i d l y upstream w i t h i n c r e a s i n g i n c i d e n c e . 2. At a given angle of a t t a c k , the p o s i t i o n of vortex b u r s t i n g depends on the angle of sweep. For higher l e a d i n g edge sweep wings, b u r s t i n g occurs f u r t h e r downstream. 3« The p o s i t i o n of vortex b u r s t i n g i s not s e n s i t i v e to Reynolds number. ' ' k. The vor t e x b u r s t i n g makes the surface s u c t i o n peak much f l a t t e r than t h a t produced by a concentrated vortex core. 5. The ' forward movement of the b u r s t i n g p o i n t i s the reason f o r s t a l l . The wing s t a l l s when the b u r s t i n g occurs at a p o s i t i o n upstream of the t r a i l i n g edge. 6. The f l o w p a t t e r n about the sharp-edged r e c t a n g u l a r wings o . o changes from one type to another i n the range from ©(. = 10 t o °< = 15 . \" 7» This change s h i f t s the center of pressure backward, 8. This change a l s o causes the wing s t a l l . - 32 -RECOMMENDATIONS The f o l l o w i n g recommendations are made f o r f u t u r e i n v e s t i g a t i o n s : 1. In order to understand the vortex b u r s t i n g phenomenon, i t i s necessary t o measure the t o t a l head, s t a t i c pressure and the f l o w d i r e c t i o n a t v a r i ous s t a t i o n s along the vortex core r i g h t up t o the b u r s t i n g p o i n t . 2. For the purpose of c a r r y i n g out the t e s t s i n ( l . ) new measurement techniques must be developed. 3. The e f f e c t of t r a i l i n g edge r e q u i r e s some d e t a i l e d i n v e s t i g a t i o n . h. The f l o w f i e l d around the corners of the re c t a n g u l a r wing a l s o r e q u i r e s d e t a i l e d measurement. - 33 -REFERENCES 1. Anderson, A. E. An i n v e s t i g a t i o n a t low speed of a l a r g e - s c a l e t r i a n g u l a r wing of aspect r a t i o two, ~~ NACA RM A7F06 . 19^ 7 2. Berndt, S. B. • Three component measurement and f l o w i n v e s t i g a t i o n of plane d e l t a wings a t low speeds and' zero yaw. K.T.H. Aero. TN 4 1949. 3. B i r d , J . D. and R i l e y , D. R. Some experiments on v i s u a l i z a t i o n of fl o w f i e l d s behilnd low- a s p e c t - r a t i o wings by means'of a \" t u f t g r i d . NACA TN 2674 May 1952. 4. Ornberg, T. A. A. note on the f l o w around d e l t a wings. K.T.H. Aero. TN No.\" 38, 1954. 5. F i n k , P. T. and T a y l o r , J . T. Spme- low speed experiments w i t h 20 degree d e l t a wings. ''•Imperial College Rep.\" F. M. 2339 Sept., 1955. 6. J a s z l i c s , . 1. and T r i l l i n g , L. An experimental study of the,f l o w f i e l d about swept and d e l t a wings w i t h sharp 'leading edges. ~~ 0SR- TN-58-6 October, 1957. \" 7. E l l e , B. J . An i n v e s t i g a t i o n at low speed of the flow-near the apex of t h i n delta.wings w i t h sharp l e a d i n g edges. ARC F. M. 2629 January7 1958. 8. Marsden, D. J . , Simpson, R. W. and R a i n b i r d , W. J . An i n v e s t i g a t i o n i n t o the f l o w over d e l t a wings at low speeds w i t h l e a d i n g edge s e p a r a t i o n . The College of Aeronautics Report No. 114 February, 1958.. 9. Peckham, D. H. •Low-speed wind tun n e l t e s t s on a s e r i e s of uncambered slender pointed wings w i t h sharp edges. R.A.E. Report Aero. 2613 December, 1958. 10. Weber, J . • ,• • Some e f f e c t s of f l o w s e p a r a t i o n on slender d e l t a wings. R.A.E. Tech.' Note \"No. Aero 2425. ' ~~' November, 1955 11. Lambourne, N. C. and Bryer, D. J . The b u r s t i n g of leading-edge v o r t i c e s -Some observations and d i s c u s s i o n of the phenomenon A.R.C.- R.M. 3085 A p r i l , 1961.. - 3^ -12. Harvey, J . K. An a l y s i s of vor t e x breakdown phenomenon, Pa r t I I Im p e r i a l College of; Science and Technology Report 103 September, i960. 13- Legendre, R. Vortex formation a t the l e a d i n g edge, of. an a i r f o i l . C.R. Acad. S c i . P a r i s , 23^, 12, September, 1956. Ik. Brown, C. E. and Mi c h a e l , W. H. J r . E f f e c t of leading-edge s e p a r a t i o n on the l i f t of a d e l t a wing. J.A.S. V o l . 21, No.' 10, P 609, October, 195^. ' 15. Mangier, K. W. and Smith, J . H. B. A theory of slender d e l t a wings w i t h l e a d i n g edge s e p a r a t i o n . Proc. Roy. Soc, London (A) 251,1265, pp 200-217 May, 1959 16. Jones, R. T. Pr o p e r t i e s of l o w - a s p e c t - r a t i o pointed wings at;speeds below and above the speed of.sound. NACA Report No. 835, I945. 17. Squire, H. B. A n a l y s i s of the vor t e x breakdown phenomenon, P a r t I . Im p e r i a l College of Science and Technology . Report No. 102 i960. 18. Jones, J . P. The breakdown of v o r t i c e s i n separated f l o w . U. S.A. A. Report No\".' lh-0 ~ \" J u l y , i960. \"\" \" 19. B o l l a y , W. • . ' A no n - l i n e a r wing theory and i t s a p p l i c a t i o n to r e c t a n g u l a r wings of small aspect r a t i o . • Z. Angew Math. Mech, Bd. 19, February, 1939* 20. Gersten, K. Non-linear a i r f o i l theory f o r r e c t a n g u l a r wings i n compressible f l o w . NASA RE 3-2-59W Feburary 1959-21. Sacks, A. H. and N i e l s e n , J . N. An a n a l y t i c a l study of the low speed aerodynamics of s t r a i g h t and swept wings w i t h f l o w s e p a r a t i o n . VIDYA, Report No. \"38, -January I961.' 22. Hopkins, E. J . and Sorensen, N. E. A device f o r vortex core measurements. J . A. S. V o l . 23/ No.\" k, pp 396-398 A p r i l , 1956. 23. Hoerner, S. F. F l u i d dynamic drag, p. 3 -l6. P u b l i s h e d by the author, 1958* TABLE I P o s i t i o n of Pressure Taps on Models IX, X, XI and X I I . Model IX Model XI — S t a t i o n x/.cr 1 .9375 2 .8125 3 .6875 4 .6oko i 5 .5210 6 .4375 7 .3540 S t a t i o n x / c r 1 • 9375 2 .8125 3 .6875 4 .6o4o 5 .5210 6 .^375 : 7 •35+0 Model X Model. X I I S t a t i o n x / c r S t a t i o n x / c r 1 .936 1 .866 2 • 914 2 .727 •3 .87 3 .636 4 .83 4 • 5^ 5 5 .786 5 .364 6 . .744 6 .182 7 8 .700 .658 9 • 573 10 .486 11 .402 TURNING THIRD POWER FOURTH PIP7H VASES DIP7USSR SECTION l>IPPUSEIi DIPP'JSKR SECTI Yd 53.50' PIUIUE 1 WIND TUMEL AERODTJAXIC G:v:i I'.IE - 3 8 4 ~~! A J 1\" - SXE^H DP KPDEL I I I - 39 -- 40 -24\" • PIRURE 4b - SKETCH OP MODELS IV, V, VI AMD VI I 11\"-- i 1 1/4\" y SECTION A-A 11\" - 41 -FIGURE 5 - SKETCH OP MODEL VIII - 4 2 -STATIONS MODEL IX 1/4 14° SECTION A-A STATIONS MODEL X - 4 3 -STATIONS PIS'JHE 6b - SKETCH OP MODELS IX, X AND XI STATIONS 1 ? 3 4 r — * 1 n J 0 0 —I 11\"_ y v///////z^/y/^/^^ 14° SECTION A-A PI GUPS 7 - SI'ET'CH OP XII I'D 4 3-(a) h i ' 1*\" ! CYLINDER (b) FIGURE 8 - SKETCH OF PROBES - 4 6 -FIGURE 9 - TRAVERSE APPARATUS - 4 7 FIGURE 10 - POSITION OP VORTEX CORE MEASURED WITH VORTOMETER MODEL I AND I I - 4 8 -0.4 O PUBLISHED DATA © PRESENT TESTS MODEL I a = 10? 15? 22.5° LEGENDRE BROWN & MICHAEL MANGLER & SMITH 0.5 0.6 0.7 0.8 0.9 y/s FIGURE 11 - VORTEX POSITION FOR PLAT DELTA WINGS 1.0 - 5 0 -TRAILING EDGE H 2 LEADING EDGE -6 8 i n . 10 ROOT CHORD FIGURE 13 - VORTEX SYSTEM ABOUT MODEL V I I I AT 10° ANGLE OF ATTACK +0.4 1.0 0.8 0.6 0.4 0.2 0 y / e FIGURE 14 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 1 MODEL IX -1.50 +0.75 U 1 1 1 1 1 1.0 0.8 0 o6 0.4 0.2 0 y/s FIGURE 15 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 2 MODEL IX - 5 3 1.0 0.8 0.6 0.4 0.2 0 y/s FIGURE 16a - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 3 MODEL IX UPPER SURFACE - 5 4 -FIGURE 16b - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 3 MODEL IX LOWER SURFACE FICURE 17a - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 4 MODEL IX UP?:O< 'CT.JKJ'ACK - 5 6 -FIGURE 17b - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 4 MODEL IX LOWER SURFACE y / s FIGURE 18 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL IX - 58 --3.0 + 1.0 | I I | ; . 1.0 0.8 0o6 0 e4 0.2 0. y / s FIGURE 19 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 6 MODEL IX FIGURE 21 - VARIATION OF SECTIONAL NORMAL FORCE . . COEFFICIENT C„ WITH INCIDENCE MODEL IX MODEL IX - 63 -- 2 . 5 ._ BROWN & MICHAEL _ MANGLER & SMITH PRESENT TESTS FIGURE 24 - SPANWISE PRESSURE DISTRIBUTIONS MODEL IX ( COMPARISON WITH RESULTS OP BROWN AND . MICHAEL, MANGLER AND SMITH ) - 6 4 -- 65 -•1.50 1.0 0.8 0.6 0.4 0.2 0 y / s FIGURE 26 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL X - 66 -3.0 1.0 0.8 0.6 0.4 0.2 0 y / s FIGURE 28 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 9 MODEL X 3.0 30° FIGURE 29 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 10 MODEL X FIGURE 30 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 11 MODEL X 1.75 1.50 1.25 1.00 0.75 0° 10 c 20° 30° a 40 c 50< FIGURE 33 - VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C N WITH INCIDENCE MODEL X - 74 FIGURE 35 - SPAIWISE PRESSURE DISTRIBUTIONS AT STATION 2 MODEL XI 2.00 1.0 0.8 0.6 0.4 0.2 0 y / s FIGURE 36 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 3 MODEL XI 76 -3.0 2.5 1.0 0.8 0.6 0.4 0.2 0 y / s FIGURE 38 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 5 MODEL XI - 7 8 -. -3.0 1«0 0.8 0.6 0.4 0.2 0 y / s FIGURE 39 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 6 MODEL XI - 7 9 -1.0 0.8 0.6 0.4 0.2 0 y / s FIGURE 40 - SPANWISE PRESSURE DISTRIBUTIONS AT STATION 7 MODEL XI - 80 -3.0 2.5 - 81 -- 82 1.75 1.50 - 8 3 — 18 16 14 12 °N/K 2 10 8 O 9 9 A 4-e JONES BROWN & MICHAEL MANGLER & SMITH PRESENT TESTS MODEL IX MODEL X MODEL XI DATA PROM REP. 15 PINK & TAYLOR p = 10° MICHAEL p = 10°,M =1.9 LAMPERT p = 7.5°, M = 1.46 MICHAEL p = 7. LAMPERT p = 12°, M = 1.46 MICHAEL p = 10°, M = 1.9 V 0.2 0.4 0.6 0.8 1.0 1.2 1.4 a/K FIGURE 44 - COMPARISON BETWEEN EXPERIMENTS AND THEORIES FOR NORMAL FORCE COEFFICIENTS OF DELTA WINGS .0.3 -0.6 -0.4 -0.2 +0.2 +0.4 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 C y/s FIGURE 45a - SPANWISE VARIATION OP C ? AT STATION 1 MODEL X I I -0.8 -0.6 -0.4 *0.2 +0.2 +0,4 1.0 0.9 0.8 0.7 0.6 0.5 y / s 0.4 0.3 0.2 0.1 FIGURE 45b - SPANWISE VARIATION OF C AT STATION 1 MODEL X I I P ( a - 10°, 20°, 30° ) 0 00 FIGURE 46a - SPANWISE VARIATION 0? C AT STATION\" 2 MODEL X I I P FIGURE 46b - SPANWISE VARIATION OF C AT STATION 2 MODEL X I I P ( «!== 10°, 20°, 30° ) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 \" 0.3 0.2 0.1 y/s 0 FIGURE 47a - SPANWISE VARIATION OF C AT STATION 3 MODEL X I I I P ( a = 5°, 15°, 25° ) -0.8 +0,6 1.0 0.9 0.8 0,7 0.6 0.5 0.4 0.3 0.2 0.1 0 y/s 1 vo ro FIGURE 49a - SPANWISE VARIATION OF C AT STATION 5 MODEL X I I . P 1 ( a = 5°, 15°, 25° ) FIGURE 49b - SPANWISE VARIATION OF C AT STATION 5 MODEL X I I P ( a = 10°, 20°, 30° ) - 99 FIGURE 55 - VARIATION OF OVERALL NORMAL FORCE COEFFICIENT C„ WITH INCIDENCE MODEL X I I - i o i -- 102 -20 28° 30° 32° 34° 36° 38° o ANGLE OP ATTACK -40° 42'° FIGURE 57-~ VARIATION OF VOPTEX R^FAIGDCWN. POSITIONS WITH INCIDENCE HOTEL-J7. -.103 -100 60 40 20 ol • ELLE V 0 PRESENT TESTS >^ i > *» ?6° 28° 30° 32° 34° 36° 38° 40° « ANGLE OP ATTACK . PICUPE 58 ~ VARIATION OF VORTEX BREAKDOWN POSITIONS WITH INCIDENCE MCDEL X - 104 -FIGURE 59 - VARIATION OF VOHTFX BREAKDOWN POSITIONS WITH INCIDENCE MODEL XI FIGURE 61 - VARIATION OF LIFT COEFFICIENT C T h WITH INCIDENCE MODELS I X , X AND XI "@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0105700"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Mechanical Engineering"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Experimental investigation of the flow field about sharp-edged delta and rectangular wings"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/39067"@en .