AERODYNAMIC DIAGNOSIS & DESIGN BASED ON LOCAL DYNAMICS

1. AERODYNAMIC DIAGNOSIS & DESIGN BASED ON LOCAL DYNAMICS J. Z. Wu The University of Tennessee Space Institute Tullahoma, TN 37388 State Key Laboratory for Turbulence and Complex System at Peking University, Beijing 100871, China June 2004

2. Collaborators of Presented studies • UTSI: J. M. Wu, C. Lo, F. L. Zhu • PKU: Y. B. Luo • USTC: L. Y. Zhuang, X. Y. Lu, L. Bao • BUAA: S. Zhou, Q. S. Li, M. Guo • THU: Z. H. Xu

3. 1. Introduction • The target functions or performance indices of various aerodynamic designs are integrated quantities. The integrand cannot not directly reflect the local flow structures (e.g., vortices, shock waves, flow separation) that have key contribution to the performance, and the local dynamic mechanisms by which these structures are produced at body surface (including flexible surface), since the latter exist only in differential governing equations in the form of space-time derivatives.

4. Example: Conventional force formula in a diagnosis domain （ : external boundary of diagnosis domain, which can be equal to or smaller than the boundary of experimental or computational domain) （Total force is independent of the size of  ; when shrinksto body surface the two formulas are the same）

5. Lack of a complete physical chain to trace the integrated performance back to the key local flow structures and their roots • Flow visualization (experimentally or numerically) can reveal all structures in the flow field, but cannot pinpoint exactly what structures have key net contribution to the performance and how • Optimal design does not have precise and clear target/constraint • Our goal: recover the lost linkage between global performance and local dynamics

6. 2. Local DynamicsTheory 2-1. General Principle • Mathematic Tool: Generalize the integration by parts to multiple variables: identities for derivative moment transformations (DMT) to recast conventional integral formulas • External-flow problems: A set of unified DMT formulas for total force and moment • Internal-flow problems: flexible treatment based on the performance indices (e.g., radial DMT on cross sections for circular pipe flow)

7. 2-2. DMT Total Force • 3-D viscous compressible flow with constant . Notations: : inside the fluid is vorticity diffusion flux across  (VDF); on body surface is boundary vorticity flux (BVF, vorticity-production rate)

8. Total force = moment of vorticity diffusion + that of BVF due to tangent acceleration + that of VDF across ：

9. Moment of vorticity diffusion can be split to inviscid terms • Irrotational & barotropic flow： • Non-accelerating body in compressible potential flow is force-free.

10. 2-3. A Theoretical Unification •   : reduces to vorticity moment theory (J. C. Wu 1981） •  shrinks to body surface: reduces to boundary vorticity-flux theory (J. Z. Wu 1987） • Arbitrary : permits various local dynamic diagnoses that form a complete physical picture

11. 3. Vorticity Moment Theory •   :n (=2,3) –dimensional space，incompressible flow， • All classic incompressible steady & unsteady force and moment formulas can be recovered (starting vortex has to be included. In 3-D all vorticity tubes form loops)

12. For thin vorticity loop, total force is proportional to the rate of change of vector area spanned by the loop 3-D Kutta-Joukowski formula

13. Applied to insect flight by Sun & Wu (2002）

15. 4. Boundary Vorticity-Flux Theory •  shrinks to body surface: Arbitrary comp. & incomp. Flows, closed & open body-surface integrals. Let be the BVF caused by pressure and shear stress, n=3:

16. 4-1. 2-D airfoil diagnosis & design （s : counterclockwise arc-length）

17. Origin of moment: mid-chord. BVF favorable for the lift： • BVF of opposite sign produces negative lift and leads to earlier separation and drag increase

18. p-caused BVF over NACA0012：

19. A qualitative observation

20. Naturally leads to supercritical airfoil

21. K. Yamamoto & O. Inoue, AIAA 95-1650

22. Improved design of VR-12 • Goal: Increase Clmax and delay stall • Take BVF as the target function • Simple parametric optimization based on potential-flow theory • N-S scheme (J. C. Wu & C. M. Wang) to check performance of new airfoil

23. Case 1

28. Case 2

31. 4-2. Local Dynamics of Thrust & Drag in Fish Swimming • Identify the local regions of fish body that produce net thrust and drag (an ongoing project)

32. 白斑狗鱼S-type start：t=0.06s，tail moving up Vorticity field Pressure field

33. BVF Diagnosis，t=0.06s T is produced in the region after x=-0.25

34. t=0.1s，tail moving down with large amplitude Vorticity field Pressure field

35. BVF diagnosis, t=0.1s T generated after x=-0.25

36. 4-3. Cracks on an Inducing Fan of an Axial Pump: p-distribution

37. BVF distribution

38. 4-4. Slender Delta Wing • ＝ 76°，＝ 20°，Re = 50,000，2nd order，k- model

39. x/c = 0.55

40. Streamwise BVF on upper surface

41. Streamwise BVF on lower surface

42. BVF diagnosis: the net contribution to the lift from upper and lower surfaces are -24%和124％ • Normal force comes from LE vortices due to boundary-layer separation at LE. Lifting x-vorticity is from the BL at lower surface, but BL at upper surface has opposite x-vorticity • Blocking the LE separation of BL at upper surface may enhance lift, say by a small fin

43. Idealized numerical experiment: turn the flow near LE that will separate to along LE

44. 控制后的上表面流向BVF分布

45. Sectional lift in terms of BVF: Upper surface

46. Sectional lift in terms of BVF: Lower surface After control, the net contribution to lift of upper and lower surface becomes -17% & 117％

47. Normal Force due to Control Increased by 30％

48. 5. Finite-Domain Diagnosis 5-1. Incompressible Flow Over 2-D Cylinder（r =1）at Re =500

49. BVF Diagnosis（shrinks to body surface） ：