Extraction of Skin Friction Fields from Surface Flow Visualizations as an Inverse Problem

Transcription

1 Extraction of Skin Friction Fields from Surface Flow Visualizations as an Inverse Problem Tianshu Liu Department of Mechanical & Aerospace Engineering Western Michigan University, Kalamazoo, MI 49008

2 Objective To extract high-resolution skin friction fields from surface flow visualization images by using a unified approach of optical flow Global luminescent oil-film (GLOF) visualization Surface heat transfer visualization with TSP Surface mass transfer visualization with PSP & sublimating coatings in air and dye in water

3 Global Luminescent Oil-Film (GLOF) Method Oil Film Thickness (h) Surface in Object Space Luminescent Intensity (g) Image Plane

4 Equivalent Skin Friction: 2 3 i i i 2 1 a 3 g g x p x,g ),x x ( f Pressure Gradient and Gravity Terms: f x ) / g ˆ ( t / g j j ) 2 / g( H ˆ o ji i j Thin-Oil Equation for GLOF is Recast into Optical Flow Equation

5 Variational Formulation The functional with a smoothness constraint: J( ˆ ) g / t g ˆ f dx1dx2 ˆ 1 ˆ 2 dx1dx2 The Euler-Lagrange equations: g g t 2 g ˆ f ˆ 0 where the Neumann condition ˆ /n 0 From two successive images, a snapshot solution is obtained. Superposition or averaging of snapshot solutions

6 Typical Experimental Setup for GLOF Method Low-AR Wing with NACA0012 Airfoil Section Dow Corning silicone oil with oil-based UV dye

7 Low-Aspect-Ratio Wing The Upper Surface at AoA = 18 deg Typical Luminescent Oil Image Skin Friction Vectors

8 Low-Aspect-Ratio Wing Topological Analysis Based on the Poincare-Bendixson Index Formula # N # S 1 ( # Z # Z ) / 2 1

9 Topological Change Caused by a Roughness Strip along the Leading Edge at AoA = 18 deg # N # S 1 ( # Z # Z ) / 2 2

10 Square Cylinder Junction Flow Experimental Setup Typical Luminescent Oil Image Local Re: Re = Square Size: 51 by 51 mm

11 Square Cylinder Junction Flow Skin Friction Vectors Skin Friction Magnitude (fusion of 300 snapshot solutions)

12 Square Cylinder Junction Flow Skin Friction Lines

13 65 o Delta Wing Typical Luminescent Oil Image Skin Friction Lines Secondary separation line Reattachment line AoA = 13 deg (Re c = 300,000) AoA = 13 deg

14 65 o Delta Wing Vortex Bursting AoA = 15 deg AoA = 20 deg

15 Double-Delta Wing The Evolution of Skin Friction Topology as AoA is Changed at Nominal Zero Yaw 3 nodes 3 saddles AoA = 0 deg AoA = 16 deg

16 Double-Delta Wing The Evolution of Skin Friction Topology as AoA is Changed at Yaw Angle of 6 deg 2 nodes 2 saddles 2 nodes 2 saddles AoA = 16 deg AoA = 24 deg

17 Skin Friction Field Mapped onto Surface of a Wing-Body Junction GLOF Intensity Distribution Surface Mesh (240,372 grid points)

18 Five Views of Wing-Body Junction from at Different Positions

19 Reconstructed Skin Friction Field on Surface of a Wing-Body Junction for AoA = 6 deg # N # S 6 6 # N # S 0

20 Surface Heat and Mass Transfer Visualizations with TSP, PSP and Sublimating Coatings From the asymptotic forms of the energy transport equation and the mass transport equation at wall, the projected equation on the image plane is obtained: G ˆ j g / x j 0

21 Variational Formulation The functional with a smoothness constraint: J( ˆ ) G ˆ g dx1 dx2 ˆ 1 ˆ 2 dx1 dx2 The Euler-Lagrange equations: 2 G ˆ g g ˆ 0 where the Neumann condition ˆ /n 0 If g & G are measured and known, ˆ ( ˆ 1,ˆ 2 ) can be obtained by solving the E-L equation.

22 Normal Impinging Air Jets with TSP

23 Normal Impinging Nitrogen Jet with PSP Normalized skin friction field PSP Intensity Ratio

24 Oscillating Impinging Nitrogen Jets at 9.4 khz Visualized with Fast PSP (Gregory et al. 2007) 0 s 20 s 40 s

25 Unsteady Skin Friction Fields Reconstructed by Superposition of Quasi-Steady and Variation Fields 0 s 20 s 40 s

26 Sublimation Visualization with Pyrene PSP on a 75-deg Delta Wing (Bouvier, Le Sant & Merienne 2001 ONERA)

27 Sublimation Visualization with Chemical on a Flat Plate in Shock/Boundary-Layer Interaction over a Fin at Mach 6 at AoA of 40 deg (Zemsch & Carbonaro VKI, 1995)

28 Surface Luminescent Dye Visualization on a 65-deg Delta Wing in Water Tunnel AoA = 10 deg, Re c = 40,000

29 Surface Luminescent Dye Visualization on a 76/40-deg Double Delta Wing in Water Tunnel AoA = 10 deg, Re c = 40,000

30 Conclusions Global skin friction diagnostics is feasible based on surface flow visualizations with luminescent oil, TSP, PSP, sublimating coatings, and dye. It is incorporated into a unified framework of physics-based optical flow method in image processing.

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