315 * An Experimental Study on the Characteristic of Mean Flow in Supersonic Boundary Layer Transition Shoji SAKAUE, Department of Aerospace Engineeri

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35 * An Experimental Study on the Characteristic of ean Flow in Supersonic Boundary Layer Transition Shoji SAKAUE, Department of Aerospace Engineering, Osaka Prefecture University ichio NISHIOKA, Department of Aerospace Engineering, Osaka Prefecture University (Received 3 September, 8; in revised form 9 arch, 9 To obtain a better understanding of the mechanism for supersonic boundary layer transition, we examine a ach.86 supersonic boundary layer along a small tunnel nozzle wall with rectangular cross section using Pitot-tube and quantitative schlieren optical system calibrated by wedge prism method. ean flow profiles in transition process are obtained by measuring distributions of density gradients. The results clearly show that near-wall density gradients start to increase at the beginning of transition, suggesting the occurrence and growth of disturbances which carry the mainstream fluid to the wall neighborhood and the near-wall fluid to the outer edge. It is also shown that inclined vortical structures our schlieren system visualizes are similar to the structures observed in supersonic turbulent boundary layers. Furthermore, the result obtained by the quantitative schlieren method indicates the transition to occur earlier compared with the corresponding obtained at the span center of the tunnel. It is suggested that the transition occurs near the nozzle corner region first and the turbulence is spread by a process of transverse contamination. (KEY WORDS: Supersonic boundary layer, Boundary layer transition, Quantitative schlieren method, Transverse contamination *599-853 E-mail: sakaue@aero.osakafu-u.ac.jp

36 Re = TS TS.3 ~ % e N TS e N N = e N TS TS TS Re = Re = 3,3 4-6 7-9 Coles.97 Re = 94 Re = 39 Re <. Re -4 x y z x = 3 mm 3 mm.7 mm x = 67 mm 8 mm x = 6 mm

37 (mm ach number y (mm - 4 6 8.5 8. (c 6 4..5 ach number Re θ. - 4 6 8 Re θ (mm. mm.8 mm Flash lamp Concave mirror Flash lamp controller Pulse generator irror Test section (c Re x irror Camera Concave mirror Knife-edge Camera controller.6 kpa9 K U x = 67 mm =.98U = 56 m/s x = 6 mm =.96U = 5 m/s Re = 574x = 67 mm~ 94 x = 6 mmx = 6 mm Coles Re. mm y. mm.8 mm x = 7 mm ~ 6 mm z = mm uy p/y = Pr = u u U 3 5.3 3 8 ns. mm f = mm 56 BP PC.86 mm.86 mm PC (

38 4 /y I f y y y f y fkd 6-8 K Gladstone -Dale.59 4 m 3 /kg = 67.4 nmd /fkd 7,8 y f y /y 6~8 3 3. 4 x = 7 mm ~ mm u y U.995 U x = 9 mm x = mm 5 Re 4 x = 9 mmre = 684 x mm u Van Driest 9 U c u / U c Tw T du A A U A T w T U ( u sin (3 w Reichardt inner layer profile Finley wake function 4 x y Re θ..5 U c x = 7mm...4.8...5 u/u x = 9mm...4.8. 3 5 5 5 u/u 5 x ln y y C e y Simulation results for laminar flow / y 3 y e...4.8. b y y 6 3 y 4 C C ln, =.4, C = 4.9, =, b =.33 u.6..5..5 x = 8mm...4.8. u/u x = mm u/u Simulation results for laminar flow 4 6 8 4 6 (4

39 3 6 x = mm ~ 6 mm Van Driest U c (4 x = 6 mm =.53 mm Re = 59 u c f c f Re 4 c f inc sin A c (5 f, Re inc Re w c f inc, Re inc 7 Karman-Schoenherr Blasius Uc + Uc + 6 x Van Driest U c (4 c 5 5 5 f inc 7.8 log Re 5. log Re inc inc / 4.6 Re f inc x = mm y + x = 4mm y + inc Uc + 5 5 5 Reichardt & Finley Uc + 6. U + c = y + U + c = κ ln y + + C x = mm (6 c (7 4 x = 9 mm 5 5 5 5 5 5 y + x = 6mm y + cf inc 6 5 4 3 mm mm mm Karman-Schoenherr Blasius 3mm 4mm 5mm 6mm 7mm 8mm 9mm 5 5 Reθ inc 7 Karman-Schoenherr(6 Blasius(7 Re = 684x = mmre = 448 x = 4 mmre = 98 x = 7 mm =.U = 58 m/s x = 6 mm =.86U = 49 m/s 3. 8 6 x = 6 mm 8 (c Pr = ( U f y y/ >.36y > mm ( /fkd (c y/ >.36 u (4 y mm y.5 mm

3. Quantitative schlieren. Simulation results for laminar flow Reichardt & Finley...8.. (c.8.8.6.6.6.4.4.4......5. ( y / δ..6.8.....4.6.8.. ρ / ρ u/u 8 x = 6 mm y (c u (4 3 4 5 6 7 8.... y (mm y (mm 9 4 /y 4.. y (mm. 8 9 3 4 5 6.. y (mm 4 /y 8 y mm 3.3 /y u/y (

3..8 Quantitative schlieren Simulation results for laminar flow.. x = mm.8 x = mm.8 x = 3mm y (mm.6.4 y (mm.6.4 y (mm.6.4... y (mm y (mm....8.6.4....5.4.8. x = 4mm. x = 5mm x = 6mm.4.8. y (mm x = 7mm x = 8mm x = 9mm. y (mm...8.6.4...5.4.8..4.8. y (mm y (mm...5....5.4.8..4.8...4.8...4.8...4.8. x y ˆ uˆ m ˆ uˆ y y uˆ u U, ˆ, m y/.3 8. y/.6 (8 9, 4 /y /y 9 y x = 9 mm x = mm ~ mm mm

3. Quantitative schlieren.5 3. y (mm..5 x = mm y (mm...5 x = mm y (mm.. x = mm. 3....4.6.8. (/mm. 3....4.6.8. (/mm. 3....4.6.8 (/mm y (mm.. x = 3mm y (mm.. x = 4mm y (mm.. x = 5mm....4.6.8 (/mm.....3.4.5 (/mm.....3.4.5 (/mm 3.4 4 x 9 mm 9 f y /y y mm 8 /y x = 9 mm /y =.336 3 kg/m 4 /y.43 3 kg/m 4 x.86 mm x 3 mm 6 x = mm =.9 mm y y x 9 mm 4 x 9 mm x 4 mm 9 x = 8 mm

33.. y (mm 4.. y (mm (c 3 8 9 3 4 5 6.. y (mm 3 v mm x 5 mm f y /fkd 8 x = 4 mm, 5 mm x = mm 5 mm 3 y ~ (c x 4 mm 5,6 (8 (8 (8 3 mm x 3 mm 3 x = 5 mm x = 8 mm (c x = 85 mm x = mm 4 y y / y / x.86 mm y x x = 9 mm Re = 684 x = mm Re = 448 / x = 4 mm x = 6 mm Re = 54

34 yρ' (mm y ρ' (mm δ / y.6.5.4.3.. x x = 9 mm x = 6 mm 8 4. 4 8 6...5 Linear growth Non-linear growth. 4 8 6 y δ/ Quantitative schlieren Simulation results for laminar flow Linear growth Non-linear growth 4 y / y TS 956788,,,, 5-39 (99. Asai,. Nishioka, Boundary layer transition triggered by hairpin eddies at subcritical Reynolds numbers, J. Fluid ech., 97, - (995. 3,,,,, 8, 4-45 (999. 4 J. Laufer, T. Vrebalovich, Stability and transition of a supersonic laminar boundary layer on an insulated flat plate, J. Fluid ech., 9, 57-99 (96. 5 J.. Kendall, Wind tunnel experiments relating to supersonic and hypersonic boundary-layer transition, AIAA J., 3, 9-99 (975. 6 P. Graziosi, G. L. Brown, Experiments on stability and

35 transition at ach 3, J. Fluid ech., 47, 83-4 (. 7 A. Thumm, W. Wolz, H. Fasel, Numerical simulation of spacially growing three-dimensional waves in compressible boundary layers, Laminar-Turbulent Transition, Springer, 33-38 (99. 8 C-L. Chang,. R. alik, Oblique-mode breakdown and secondary instability in supersonic boundary layers, J. Fluid ech., 73, 33-36 (994. 9 N. A. Adams, L. Kleiser, Subharmonic transition to turbulence in a flat-plate boundary layer at ach number 4.5, J. Fluid ech., 37, 3-335 (996. D. Coles, easurements of turbulent friction on a smooth flat plate in supersonic flow, J. Aero. Sciences,, 433-448 (954. E. Rechotko, Boundary layer instability, transition and control, AIAA paper 94- (994.,,, 5, 6-3 (996. 3 S. Sakaue,. Nishioka, On the Receptivity Process of Supersonic Laminar Boundary Layer, Laminar- Turbulent Transition, Springer-Verlag, 48-486 (. 4 S. Sakaue,. Nishioka, On the Receptivity of Supersonic Boundary Layer to Oscillating ach Waves, Proc. 4th Congress of the International Council of the Aeronautical Sciences, 44 (CD-RO (4. 5,,,,, 3, 47-56 (4. 6,,, 8, 39-47 (9. 7,,, 8, 4-48 (9. 8,,, 8, 49-56 (9. 9 E. R. Van Driest, Turbulent boundary layer in compressible fluids, J. Aero. Sci., 8, 45-6 (95. H. Reichardt, Complete representation of the turbulent velocity distribution in smooth pipe, Z. Angew ath., 3, 8-9 (95. T. Cebeci, P. Bradshaw, omentum Transfer in Boundary Layers, Hemisphere (997. S. E. Guarini, R. D. oser, K. Shariff, A. Wray, Direct numerical simulation of a supersonic turbulent boundary layer at ach.5, J. Fluid ech., 44, -33 (,. 3 A. J. Smits, J-P. Dussauge, Turbulent Shear layers in Supersonic Flow, AIP Press (996. 4 S. P. Pirozzoli, F. Grasso, T. B. Gatski, Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at =.5, Physics of Fluids, 6, 3, 53-545 (4. 5 E. F. Spina, A. J. Smits, Organized structures in a compressible, turbulent boundary layer, J. Fluid ech., 8, 86-9 (987. 6. W. Smith, A. J. Smits, Visualization of the structure of supersonic turbulent boundary layers, Experiments in Fluids, 8, 88-3 (995.

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