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1 NALTR-1390 TR-1390 ISSN UDC NAL TECHNICAL REPORT OF NATIONAL AEROSPACE LABORATORY TR-1390 e N NATIONAL AEROSPACE LABORATORY

2 ... 1 e N... 2 Orr-Sommerfeld... 2 T-S C-F... 3 N NACA

3 e N Takashi ATOBE and Kiyoshi YAMAMOTO Laminar-turbulent transitions of the boundary layer flow are predicted numerically using the SALLY-code based on the e N method. In order to validate the accuracy and applicability of this code, flow fields arround a wing model of the supersonic experimental aircraft being developed by the National Aerospace Laboratory, the NACA0015, a 2- dimensional wing model and a yawed circular cylinder were studied. Comparing these results with an experimental result and the wave propagation theory, it was found that the accuracy of this code is not sufficient, especially for 3-dimensional flow. Key words: laminar-turbulent transition, boundary layer, e N method, SALLY code e N SALLY NACA received 9 Jury 1999 Japan Science and Technology Corporation Fluid Science Research Center

4 e N e N NASA SALLY e N NACA0015 e N e N DNS e N Orr-Sommerfeld Orr-Sommerfeld DNS k x k y T-S

5 e N 3 UP up U U Ux 1 3 U 2 x 3 0 Px 1 u u u 1 x 1, x 2, x 3, t u 2 x 1, x 2, x 3, t, ux 3 1, x 2, x 3, t, t px 1, x 2, x 3, t x 1 x 2 x 3 Navier-Stokes u t u + U u+u U = grad p + R u, div u = R u = u x exp i ax + bx wt. Q = a + b, Q U = au + bu Orr- Tollmien-SchlichtingT- S Cross-FlowC-F C-F T-S C-F C-F abx 1 x 2 w w r w i i-1 u 3 U w Q u Q u U u = QR i u IV Q u + Q u. Sommerfeld N t t 0 A 0 t t c t t c A c N ln A c / A = t c w i dt. t 0 T-S C-F i O-S lna c /A 0 N e N N N Gaster

6 N U 1 U 2 C p C p NACA N N N N C p C p C p C p C p

7 e N 5 - -

8 N NN10 N N NACA0015 NACA0015 C p a C p C p 0 a U 0 NACA0015Cp R e U 0 a U m/s R e m/s a a m/ s

9 e N 7 NACA0015 U 0 20 m/s NACA0015 N 20m/s,30,40, 50 a N N a a

10 NACA0015 CFRP a x/ c 0.6 U 30 m/s 1200 HzU 40 m/s 2100 Hz N N U40 m/s N17 N 10N N

11 e N 9 17 N Itoh 1011 e N N U 0 50 D

12 N x/c N Itoh 11 x/c0.3 N 13 N e N SALLY NACA0015 N N SALLY 13x/c 0.3 N Itho 10 1W.S. Saric, Physical Description of Boundary-Layer Transition: Experimental Evidence, AGARD-R D. Arnal, Boudary Layer Transition:Predictions Based on Linear Theory, AGARD-R

13 e N 11 3H.L. Reed and W.S. Saric, Linear stability theory applied to boudary layers, Annu. Rev. Fluid Mech , pp A. Srokowski and S. Orszag, Mass Flow Requirements for LFC Wing Design, AIAA Paper , pp pp M. Gaster, A note on a relation between temporally-increasing and spatially-increasing disturbances in hydrodaynamic stability, J.F.M. 14 pt pp TR N. Itoh, Effect of wall and streamline curvatures on instability of 3-D boundary layers, in Lamiar-Turbulent TransitionSpringer, Berlin1995pp N. Itoh, Development of wedge-shaped disturbances originating from a point source in a three-dimensional boundary layer, Fluid Dyn. Res pp T. Cebeci and P. Bradshaw, Momentum Transfer in Boundary Layers, Hemisphere (1977), pp e N N U Navier-Stokes ru =. A.1 Du Dt = r DH Dt p+vdu. A.2 = - n H + nf. P r D A.3 F = / i u i + i u j + i u j j u i. A.4 Hru Pr / t 0u/w»u/w» Dy/Dx» Dy/Dz/» d/l 1 : L d p/ x xqy uwu x rxu + q rw + y rxu =. A.5 ru u x + rw x u q + ru u y rw x = y m u y. A.6 ru w x + rw x w q + ru w y + ruw x = x dp dq + y m w y.a.7 ru H x + rw x H q + ru H q = y u Pr H y + m Pr y u + w. A.8 y = x 3/ r e m e u e ƒhq, A.9 f = x / r e m e u e w e u e g hq, A.10

14 Cƒ + m ƒ ƒ+ m gƒ m g ƒ g + m ƒ = m g ƒ q ƒ g q, A.11 h = : ƒ = g = ƒ = g =, E = A.15 Cg + m g ƒ+ m gg + m c g c ƒ g + m g = m g g q g g q, A.12 h = h : ƒ = g = E = A.16 e ū e u e CE Pr + Cu e H ƒ ƒ + m e Pr g g + m E ƒ + m E g + m E = m g E A.13 q E g q, h = u e r e m e x ry, A.14 h ECcm 1 E H / H e, C rm / r e m e, c r e / r, m 1 /, m m + m + m ru w ru e u e x u e p e, m u e dw e dq, d rm e rm e dq, m w e u e, du e dq = w e= u s u e. A.17 p + ru s = const. u s A.18 Kerres Box method 12

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Flow Around a Circular Cylinder with Tangential Blowing near a Plane Boundary (2nd Report, A Study on Unsteady Characteristics) Shimpei OKAYASU, Kotar

Flow Around a Circular Cylinder with Tangential Blowing near a Plane Boundary (2nd Report, A Study on Unsteady Characteristics) Shimpei OKAYASU, Kotaro SATO*4, Toshihiko SHAKOUCHI and Okitsugu FURUYA Department