Transcript A COMPUTATIONAL INVESTIGATION OF MEMS

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
• 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
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
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Previous Experimental Results
Riblet cross section.1
Experimental drag reduction for
riblets of various shapes and sizes.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
1
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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.
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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,
3 I.
D., Spalart, P. & Kim, J., 1987 ``Numerical simulations of turbulent spots in plane Poiseuille and boundary layer flow.” Phys. Fluids 30 (10) October.
Wygnanski, J. H. Haritonidis, and R. E. Kaplan, J. Fluid Mech. 92, 505 (1979)
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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
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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
6
Cantwell, Coles and Dimotakis from An Album of Fluid Motion, by Milton Van Dyke
Perry, Lim, and Teh from An Album of Fluid Motion, by Milton van Dyke
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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.
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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:
F(xs , t )= a o DUdt’+ bDU
t
DU =U ( xs ,t ) -Udesired (xs ,t )
• 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 133D. 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
8
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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
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.
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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
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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*.
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Results – Flat Wall
Enstrophy isosurfaces
showing spot growth.
Enstrophy isosurfaces
displayed at multiple
times to illustrate
spreading angle.
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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
Triangular
Riblets
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Results – Triangular Riblets (s/h = 3.86)
Flat wall
Triangular
Riblets
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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*
ZY Slice Comparison – Spanwise Damping Fins
Flat Wall
Damping Fins
s/h = 1.93
Damping Fins
s/h = 3.86
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ZY Slice Comparison – Real Fins
Flat Wall
Real Fins
s/h = 1.93
Real Fins
s/h = 3.86
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ZY Slice Comparison – Triangular Riblets
Flat Wall
Triangular
Riblets
s/h = 3.86
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Spreading Angle
Flat Wall
Triangular Riblets (s/h = 3.86)
Damping fins (s/h = 1.93)
Real fins (s/h = 1.93)
Damping fins (s/h = 3.86)
Real fins (s/h = 3.86)
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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
Greatest
extent
point farthest from the spanwise centerline
at whichspanwise
the quantity
(enstrophy or
vertical velocity) is ≥ the cutoff value.
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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).
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Spreading Angle – No Virtual Origin
Cutoff
Enstrophy = 0.864 δo*/U∞
Enstrophy = 0.971 δo*/U∞
V = 0.08 U∞
Average
Cutoff
Enstrophy = 0.864 δo*/U∞
Enstrophy = 0.971 δo*/U∞
V = 0.08 U∞
Average
Real Fins
s/h = 1.93
5.7
5.1
5.7
5.1
5.8
5.1
5.7
5.1
Damping Fins Damping Fins
s/h = 1.93
s/h = 3.86
2.5
4.9
2.2
4.7
2.8
4.8
2.5
4.8
Flat Wall
Real Fins,
s/h = 3.86
NA
6.2
6.1
6.2
Riblets
s/h = 3.86
5.1
5.1
5.3
5.2
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Spreading Angle – Virtual Origin
Flat Wall
Cutoff
*
Enstrophy = 0.864 δo /U∞
Enstrophy = 0.971 δo*/U∞
V = 0.08 U∞
Average
Cutoff
Enstrophy = 0.864 δo*/U∞
Enstrophy = 0.971 δo*/U∞
V = 0.08 U∞
Average
VO
Angle
26
6.8
31
7.0
21
6.4
26
6.7
Damping Fins
s/h = 1.93
VO
Angle
-20
1.9
-30
1.8
-129
1.5
-60
1.7
Real Fins
s/h = 1.93
VO
Angle
13.9
5.2
1.3
5.0
16.7
5.4
10.6
5.2
Damping Fins
s/h = 3.86
VO
Angle
21
5.6
26
5.6
30
5.8
26
5.7
Real Fins
s/h = 3.86
VO
Angle
NA
NA
41
7.3
13
6.7
27
7.0
Riblets
s/h = 3.86
VO
Angle
27.5
6.7
2.8
5.7
29.3
6.5
19.9
6.3
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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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