1. DNS of Surface Textures to Control the Growth of Turbulent Spots James Strand and David Goldstein The University of Texas at Austin Department of Aerospace Engineering Sponsored by AFOSR through grant FA 9550-05-1-0176

2. Presentation Outline Introduction/motivation Review of numerical method Adapting the code for a boundary layer Surface textures examined Results Conclusions The University of Texas at Austin – Computational Fluid Physics Laboratory

3. Introduction: Riblets The University of Texas at Austin – Computational Fluid Physics Laboratory Correctly sized riblets reduce turbulent viscous drag ~5-10%. Not used often because of retro-fitting costs, UV degradation, paint/adhesion, small net effects… Work by damping near-wall spanwise fluctuations. Large riblets stop working due to secondary flows, and can increase drag

4. Previous Experimental Results Experimental drag reduction for riblets of various shapes and sizes. 1 Riblet cross section. 1 The University of Texas at Austin – Computational Fluid Physics Laboratory 1 Bruse, M., Bechert, D. W., van der Hoeven, J. G. Th., Hage, W. and Hoppe, G., “Experiments with Conventional and with Novel Adjustable Drag-Reducting Surfaces”, from Near-Wall Turbulent Flows, Elsevier Science Publishers B. V., 1993

5. Introduction: Turbulent Spots The University of Texas at Austin – Computational Fluid Physics Laboratory Boundary layer transition occurs through growth and spreading of turbulent spots. Spot development and universal shape is mostly insensitive to initial perturbation. Re-laminarization occurs in the wake of the spots Flow inside the spots has characteristics of fully turbulent flow.

6. Boundary Layer Spots The University of Texas at Austin – Computational Fluid Physics Laboratory Boundary layer spots take on an arrowhead shape pointing downstream. 2,3 Front tip of the spot propagates downstream at ~0.9U ∞ Rear edge moves at ~0.5U ∞ Spanwise spreading angle is ~10º with zero pressure gradient 2 Henningson, D., Spalart, P. & Kim, J., 1987 ``Numerical simulations of turbulent spots in plane Poiseuille and boundary layer flow.” Phys. Fluids 30 (10) October. 3 I. Wygnanski, J. H. Haritonidis, and R. E. Kaplan, J. Fluid Mech. 92, 505 (1979) Front Tip

7. The University of Texas at Austin – Computational Fluid Physics Laboratory Turbulent Spots – Flow Visualization Visualization of a turbulent spot using smoke in air at different Reynolds numbers. 4 4 R. E. Falco from An Album of Fluid Motion, by Milton Van Dyke Re X = 100,000 Re X = 200,000 Re X = 400,000

8. The University of Texas at Austin – Computational Fluid Physics Laboratory Turbulent Spots – Flow Visualization Turbulent spot over a flat plate. Flow is visualized with aluminum flakes in water. Reynolds number based on distance from the leading edge is 200,000 in the center of the spot. 5 Cross section of a turbulent spot taken normal to the flow. Visualized by smoke in a wind tunnel. 6 5 Cantwell, Coles and Dimotakis from An Album of Fluid Motion, by Milton Van Dyke 6 Perry, Lim, and Teh from An Album of Fluid Motion, by Milton van Dyke

9. Surface Textures + Spots The University of Texas at Austin – Computational Fluid Physics Laboratory If surface textures can constrain spanwise spreading of spots, turbulent transition might be delayed, leading to significant drag reduction. DNS to investigate the effect of surface textures on spot growth and spreading. Goal: Interfere with turbulent spot growth to postpone transition, and thus reduce drag.

10. Numerical Simulation and Force Field Method  Fxt s o t,     U  Udt’   UU xx s desired s UU UU,t Spectral-DNS method initially developed by Kim et al. 7 for turbulent channel flow. Incompressible flow, periodic domain and grid clustering in the direction normal to the wall. Surface textures defined with the force field method: 7 J. Kim, P. Moin and R. Moser, J. Fluid Mech. 177, pp 133- 8 D. B. Goldstein, R. Handler and L. Sirovich, J. Comp. Phys. 105, pp.354-366 9 D. B. Goldstein, R. Handler and L. Sirovich, J. Fluid Mech., 302, pp.333-376 10 C. Y. Lee and D. B. Goldstein, AIAA 2000-0406 Method already validated for turbulent flow over flat plates and riblets 8,9 and 2-D synthetic jet simulation 10. The University of Texas at Austin – Computational Fluid Physics Laboratory

11. Adapting the Code: Suction Wall and Buffer Zone Top wall is slip but no-through-flow Blasius profile has small but finite vertical velocity even far from plate Suction wall is used so that boundary layer grows properly Suction wall forces vertical velocity from Blasius solution The University of Texas at Austin – Computational Fluid Physics Laboratory

12. Surface Textures Examined The University of Texas at Austin – Computational Fluid Physics Laboratory Three textures examined: Triangular riblets Real fins Spanwise-damping fins Triangular riblets and real fins are solid, no-slip surfaces, created with the immersed boundary method. They force all three components of velocity to zero. Spanwise-damping fins occupy the same physical space as real fins, but apply the immersed boundary forces only in the spanwise direction. They force only the spanwise velocity to zero. Relevant parameters for all three textures are height, h, and spacing, s. h s

13. Simulation Domain The University of Texas at Austin – Computational Fluid Physics Laboratory X Y Z Domain is periodic in the spanwise direction. Perturbation is a quarter-sphere shaped solid body, created with the immersed boundary method, which appears briefly and then is removed. Domain was 463.2δ o * ×18.5δ o * ×92.6δ o * in the streamwise (x), wall-normal (y), and spanwise (z) directions respectively. δ o * is the (Blasius) boundary layer displacement thickness at the location of the perturbation.

14. Results – Overview The University of Texas at Austin – Computational Fluid Physics Laboratory Flat wall. Spanwise damping fins. Real fins. Triangular riblets. ZY slice comparisons. Spreading angle. Note: Height (h) = 0.463δ o * for all textures examined. Spacing to height ratio (s/h) is listed for each case. Spots are shown with isosurfaces of enstrophy at the value 0.756 U ∞ /δ o *.

15. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Flat Wall Enstrophy isosurfaces displayed at multiple times to illustrate spreading angle. Enstrophy isosurfaces showing spot growth.

16. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Flat Wall Side view of spot at t = 277.9 δ o * /U ∞ Cross section of spot as it moves through a zy plane 360 δ o * from the leading edge of the plate.

17. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Spanwise Damping Fins (s/h = 1.93) Flat wall Damping fins

18. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Spanwise Damping Fins (s/h = 1.93) Flat wall Damping fins

19. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Spanwise Damping Fins (s/h = 3.86) Flat wall Damping fins

20. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Spanwise Damping Fins (s/h = 3.86) Flat wall Damping fins

21. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Real Fins (s/h = 1.93) Flat wall Real fins

22. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Real Fins (s/h = 1.93) Flat wall Real fins

23. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Real Fins (s/h = 3.86) Flat wall Real fins

24. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Real Fins (s/h = 3.86) Flat wall Real fins

25. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Triangular Riblets (s/h = 3.86) Flat wall Triangular Riblets

26. The University of Texas at Austin – Computational Fluid Physics Laboratory Results – Triangular Riblets (s/h = 3.86) Flat wall Triangular Riblets

27. Flat Wall Real Fins h = 0.463 δ o * s = 0.965 δ o * Damping Fins h = 0.463 δ o * s = 1.930 δ o * ZY Slice Comparison

28. The University of Texas at Austin – Computational Fluid Physics Laboratory Flat Wall Damping Fins s/h = 1.93 Damping Fins s/h = 3.86 ZY Slice Comparison – Spanwise Damping Fins

29. The University of Texas at Austin – Computational Fluid Physics Laboratory Flat Wall Real Fins s/h = 1.93 Real Fins s/h = 3.86 ZY Slice Comparison – Real Fins

30. The University of Texas at Austin – Computational Fluid Physics Laboratory Flat Wall Triangular ZY Slice Comparison – Triangular Riblets Riblets s/h = 3.86

31. Spreading Angle The University of Texas at Austin – Computational Fluid Physics Laboratory Flat Wall Triangular Riblets (s/h = 3.86) Real fins (s/h = 3.86) Damping fins (s/h = 3.86) Real fins (s/h = 1.93) Damping fins (s/h = 1.93)

32. Spreading Angle The University of Texas at Austin – Computational Fluid Physics Laboratory Specific cutoff values of enstrophy and vertical velocity define boundaries of the spot. Separate spreading angle calculated for each cutoff value. Two cutoffs for enstrophy: 0.864 δ o * /U ∞ and 0.971 δ o * /U ∞ One cutoff for vertical velocity: 0.08 U ∞ Point of greatest spanwise extent (for a given cutoff value) is defined as the point farthest from the spanwise centerline at which the quantity (enstrophy or vertical velocity) is ≥ the cutoff value. Greatest spanwise extent

33. Spreading Angle – Two Methods The University of Texas at Austin – Computational Fluid Physics Laboratory Plot magnitude of greatest spanwise extent vs. streamwise location of the point of greatest spanwise extent. In first method, a linear trendline is forced to pass through the origin (the center of the quarter-sphere perturbation. In second method, the trendline is not forced through the origin, and a virtual origin is calculated. For both methods, spreading angle = arctan(slope of trendline).

34. The University of Texas at Austin – Computational Fluid Physics Laboratory Spreading Angle – No Virtual Origin

35. The University of Texas at Austin – Computational Fluid Physics Laboratory Spreading Angle – Virtual Origin

36. Conclusions Most closely spaced real fins (s/h = 1.93) reduce spreading angle by 11%-23% of the flat wall value, depending on method of calculation. Similarly spaced damping fins reduce spreading angle 56%-74%. Riblets (s/h = 3.86) reduce spreading angle 7%-10%. Optimal riblets for turbulent drag reduction have s/h ≈ 1.0 - 1.5 Further reduction in spreading angle may be possible with more closely spaced fins and riblets. Fin and riblet height should be further optimized. Higher resolution runs should be performed. Longer domains may be studied, to investigate spot behaviour at higher values of Re X The University of Texas at Austin – Computational Fluid Physics Laboratory