DNS of Surface Textures to Control the Growth of Turbulent Spots

James Strand and David Goldstein

The University of Texas at AustinDepartment of Aerospace Engineering

Sponsored by AFOSR through grant FA 9550-05-1-0176

Presentation Outline

• Introduction/motivation• Review of numerical method• Adapting the code for a boundary layer• Surface textures examined• Results• Conclusions

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Introduction: Riblets

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• 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

Previous Experimental Results

Experimental drag reduction for riblets of various shapes and sizes.1

Riblet cross section.1

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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

Introduction: Turbulent Spots

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• 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.

Boundary Layer Spots

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• 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

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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

ReX = 100,000 ReX = 200,000

ReX = 400,000

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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 Dyke6 Perry, Lim, and Teh from An Album of Fluid Motion, by Milton van Dyke

Surface Textures + Spots

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• 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.

Numerical Simulation and Force Field Method

F x ts o

t

, UUdt’

U x xs desired sU U,t ,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.354-3669 D. B. Goldstein, R. Handler and L. Sirovich, J. Fluid Mech., 302, pp.333-37610C. Y. Lee and D. B. Goldstein, AIAA 2000-0406

• Method already validated for turbulent flow over flat plates and riblets8,9 and 2-D synthetic jet simulation10.

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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

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Surface Textures Examined

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• 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

Simulation Domain

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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 463.2δo*×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.

Results – Overview

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• 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*.

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Results – Flat Wall

Enstrophy isosurfaces displayed at multiple times to illustrate spreading angle.

Enstrophy isosurfaces showing spot growth.

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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.

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Results – Spanwise Damping Fins (s/h = 1.93)

Flat wall

Damping fins

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Results – Spanwise Damping Fins (s/h = 1.93)

Flat wall

Damping fins

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Results – Spanwise Damping Fins (s/h = 3.86)

Flat wall

Damping fins

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Results – Spanwise Damping Fins (s/h = 3.86)

Flat wall

Damping fins

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Results – Real Fins (s/h = 1.93)

Flat wall

Real fins

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Results – Real Fins (s/h = 1.93)

Flat wall

Real fins

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Results – Real Fins (s/h = 3.86)

Flat wall

Real fins

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Results – Real Fins (s/h = 3.86)

Flat wall

Real fins

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Results – Triangular Riblets (s/h = 3.86)

Flat wall

TriangularRiblets

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Results – Triangular Riblets (s/h = 3.86)

Flat wall

Triangular Riblets

Flat Wall

Real Fins

h = 0.463 δo*

s = 0.965 δo*

Damping Fins

h = 0.463 δo*

s = 1.930 δo*

ZY Slice Comparison

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Flat Wall

Damping Fins

s/h = 1.93

Damping Fins

s/h = 3.86

ZY Slice Comparison – Spanwise Damping Fins

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Flat Wall

Real Fins

s/h = 1.93

Real Fins

s/h = 3.86

ZY Slice Comparison – Real Fins

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Flat Wall

Triangular

ZY Slice Comparison – Triangular Riblets

Riblets

s/h = 3.86

Spreading Angle

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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)

Spreading Angle

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• 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

Spreading Angle – Two Methods

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• 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).

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Spreading Angle – No Virtual Origin

Cutoff Flat Wall Real Fins s/h = 1.93

Real Fins, s/h = 3.86

Enstrophy = 0.864 δo*/U∞ 5.7 5.1 NA Enstrophy = 0.971 δo*/U∞ 5.7 5.1 6.2

V = 0.08 U∞ 5.8 5.1 6.1 Average 5.7 5.1 6.2

Cutoff Damping Fins

s/h = 1.93 Damping Fins

s/h = 3.86 Riblets

s/h = 3.86

Enstrophy = 0.864 δo*/U∞ 2.5 4.9 5.1 Enstrophy = 0.971 δo*/U∞ 2.2 4.7 5.1

V = 0.08 U∞ 2.8 4.8 5.3 Average 2.5 4.8 5.2

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Spreading Angle – Virtual Origin

Flat Wall Real Fins s/h = 1.93

Real Fins s/h = 3.86 Cutoff

VO Angle VO Angle VO Angle Enstrophy = 0.864 δo

*/U∞ 26 6.8 13.9 5.2 NA NA Enstrophy = 0.971 δo

*/U∞ 31 7.0 1.3 5.0 41 7.3 V = 0.08 U∞ 21 6.4 16.7 5.4 13 6.7

Average 26 6.7 10.6 5.2 27 7.0 Damping Fins

s/h = 1.93 Damping Fins

s/h = 3.86 Riblets

s/h = 3.86 Cutoff VO Angle VO Angle VO Angle

Enstrophy = 0.864 δo*/U∞ -20 1.9 21 5.6 27.5 6.7

Enstrophy = 0.971 δo*/U∞ -30 1.8 26 5.6 2.8 5.7

V = 0.08 U∞ -129 1.5 30 5.8 29.3 6.5 Average -60 1.7 26 5.7 19.9 6.3

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

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