Global Skin Friction Diagnostics Based on Surface Mass-Transfer Visualizations

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1 Global Skin Friction Diagnostics Based on Surface Mass-Transfer Visualizations Tianshu Liu & S. Woodiga Western Michigan University, Kalamazoo, MI J. Gregory The Ohio State University, Columbus, OH J. Sullivan Purdue University, W. Lafayette, IN

2 Objective To explore the feasibility of global skin friction diagnostic based on surface mass-transfer visualizations Current State (1) Global luminescent oil-film skin friction meter (2) Global skin friction diagnostics based on surface heat-transfer/temperature visualizations

3 The Specific Question Came from an Image Pyrene PSP image on a 75-deg delta wing in a large wing tunnel at ONERA (Bouvier, Le Sant & Merienne 2001) The pattern results from sublimation of Pyrene PSP Question: How to extract a skin friction field from this image?

4 The Issues in Global Skin Friction Diagnostics Based on Mass-Transfer Visualizations (1) There is no explicit analytical solution for the relation between surface species density, mass flux and skin friction vector. (2) It was not recognized that it should be solved globally as an inverse problem.

5 Asymptotic Form of Binary Mass Diffusion Equation at Wall where i Skin friction vector (to be determined) Surface density of species 1 (measurable) Surface mass flux (measurable) Relevant Quantities: 0 X / F i 1w i i i 1w w 12 w X X m D t m D F w 3 1 w 12 w 1 ) X / ( D m / 1 1

6 Snapshot Solution in a Short Interval or Window F t i 1w,s / X i 0 where F t D T w 12 m 1w,s D 12 T 2 X m i 1w,s X i Projection onto Image Plane Projected skin friction vector where ˆ h ji j h ji F j i / X define the directions of the coordinate curves on a surface i

7 Generic Optical Flow Equation for Skin Friction in Mass-Transfer Visualizations G ˆ j g / x j 0 g PSP Visualization I / I G g Iref / I 00 0 ref Sublimation Visualization with Changing Density g I / I ref G g 1 Sublimation Visualization with Changing Thickness g I / I ref G g

8 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 & ˆ ( ˆ 1,ˆ 2 G are measured and known, ) can be obtained by solving the E-L equation.

9 Uncertainty Analysis and Intrinsic Limitation The relative error in skin friction calculation: (1) When ˆ / ˆ N the error blows up (2) The Lagrange multiplier must be as small as possible. which imposes an intrinsic limitation on this method Consequences: ˆ ˆ g ˆ ˆ ˆ g G ˆ ˆ N T 0 N N g 0 0

10 Unsteady Measurements with Fast PSP Visualization Quasi-steady solution: Superposition ˆ j ˆ j,s ˆ' j G1 ˆ j,s g s / x j 0 where G 1 gs g00 Variation for unsteady effect: t G2 ˆ' j g s / x j 0 where G ˆ 2 g k1 g k j,s( g k1 / 2 ) / x j

11 Circular Impinging Nitrogen Jet Visualized with PSP PSP: Ru(phen) in GE RTV 118 UV for illumination CCD camera with long-pass filter 75 microns Mylar D 2 mm U o 50 m / Re s 3 D UoD / H / D 6

12 Normal Impinging Nitrogen Jet Normalized PSP Intensity Distribution Normalized skin friction field

13 Transverse Distributions of Skin Friction Magnitude for Normal Impinging Jet

14 75-deg Oblique Impinging Jet Normalized PSP Intensity Distribution Normalized skin friction field

15 Transverse Distributions of Skin Friction Magnitude for 75-dge Oblique Impinging Jet

16 Dual Colliding Impinging Nitrogen Jets Visualized with PSP PSP: Ru(phen) in GE RTV 118 UV for illumination CCD camera with long-pass filter 75 microns Mylar D 5.18 mm o 30 H 29.5mm U = 4.14 m/s

17 PSP Intensity Images at Different Offsets

18 Skin Friction Vector and Magnitude Fields

19 Skin Friction Lines

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

21 Quasi-Steady and Variation Fields at 0 s Quasi-steady field Variation field associated with unsteady effect (~ 10%)

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

23 Sublimation Visualization with Pyrene PSP on a 75-deg Delta Wing (ONERA) Sublimation image Extracted skin friction field

24 Sublimation Visualization with Acenaphthene in Shock-BL Interaction at Mach 6 (VKI) (S. Zemsch 1996, M. Carbonaro 1994) Sublimation image Extracted skin friction field

25 Conclusions Global skin friction diagnostics is feasible based on surface mass-transfer visualizations. In particular, it is possible for unsteady skin friction diagnostics with fast PSP. The intrinsic limitation is that this method has large error when the intensity gradient is zero. It is incorporated into the unified framework of physics-based optical flow method for global velocity and skin friction diagnostics.

Analytical Methods for Determination of Heat Transfer Fields from TSP Measurements in Hypersonic Tunnels

Analytical Methods for Determination of Heat Transfer Fields from TSP Measurements in Hyersonic Tunnels Tianshu Liu, Z. Cai & J. Lai Western Michigan University, Kalamazoo, MI 49008 J. Rubal & J. P. Sullivan