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DNS of Surface Textures to Control the Growth of Turbulent Spots

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. Presentation Outline. Introduction/motivation

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DNS of Surface Textures to Control the Growth of Turbulent Spots

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  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 • 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 The University of Texas at Austin – Computational Fluid Physics Laboratory

  4. Previous Experimental Results Riblet cross section.1 Experimental drag reduction for riblets of various shapes and sizes.1 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 The University of Texas at Austin – Computational Fluid Physics Laboratory

  5. Introduction: Turbulent Spots • 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. The University of Texas at Austin – Computational Fluid Physics Laboratory

  6. Boundary Layer Spots • 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 Front Tip 2 Henningson, D., Spalart, P. & Kim, J., 1987 ``Numerical simulations of turbulent spots in plane Poiseuille and boundary layer flow.” Phys. Fluids30 (10) October. 3I. Wygnanski, J. H. Haritonidis, and R. E. Kaplan, J. Fluid Mech. 92, 505 (1979) The University of Texas at Austin – Computational Fluid Physics Laboratory

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

  8. 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 The University of Texas at Austin – Computational Fluid Physics Laboratory

  9. Surface Textures + Spots • 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. The University of Texas at Austin – Computational Fluid Physics Laboratory

  10. Numerical Simulation and Force Field Method • 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: ( ) t ò = a + F x , t DUdt’ bDU s o ( ) ( ) x ,t x ,t =U DU -U s s desired • Method already validated for turbulent flow over flat plates and riblets8,9 and 2-D synthetic jet simulation10. 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 10C. Y. Lee and D. B. Goldstein, AIAA 2000-0406 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 s h • 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. The University of Texas at Austin – Computational Fluid Physics Laboratory

  13. Simulation Domain • 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 463.2δo*×18.5δo*×92.6δo* in the streamwise (x), wall-normal (y), and spanwise (z) directions respectively. • δo* is the (Blasius) boundary layer displacement thickness at the location of the perturbation. Y Z X The University of Texas at Austin – Computational Fluid Physics Laboratory

  14. Results – Overview • Flat wall. • Spanwise damping fins. • Real fins. • Triangular riblets. • ZY slice comparisons. • Spreading angle. • Note: Height (h) = 0.463δo* 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∞/δo*. The University of Texas at Austin – Computational Fluid Physics Laboratory

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  32. Spreading Angle • 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 δo*/U∞ and 0.971 δo*/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 The University of Texas at Austin – Computational Fluid Physics Laboratory

  33. Spreading Angle – Two Methods • 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). The University of Texas at Austin – Computational Fluid Physics Laboratory

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

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

  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 ReX The University of Texas at Austin – Computational Fluid Physics Laboratory

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