Some Observations on the Structure and Modeling of 3-D Turbulent Boundary Layers...
Transcript of Some Observations on the Structure and Modeling of 3-D Turbulent Boundary Layers...
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Some Observations on the Structure and Modeling of 3-D Turbulent
Boundary Layers and Separated Flow
Roger L. SimpsonTurbulence and Shear Flow Phenomena - 4
Williamsburg, VAJune 27, 2005
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Outline
• Some features of experimental results from low-speed flows
• Some computational insights• Some future research needs and tools• Cited references 1995-2005 plus earlier
review references
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Some 3-D Flows Examined• Wing/body junction
– Effects of Reynolds number– Effect of roughness
• Swept bump (Webster et al.)• Pressure-driven 3DTBL (Compton and Eaton)• ‘S-duct’ (Bruns et al.)• Channel flows with 3-D obstacles and separation• Axisymmetric bump with vortical separation• Prolate spheroid with crossflow separation• Compressor tip gap flow with leakage vortex• Current and future experiments
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Surface Vorticity Flux and Vorticity Equations
( )( ) ( ) ( ))/(/)/(2Re
4 LtUdUVdeCeLnUL
refrefnpnref
L
×+∇×=⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
∂
∂ω
DDt
Ur
r r r rωω ν ω= ⋅ ∇ + ∇ 2
Vorticity flux Pressure gradient Accelerating wall
Material derivative Vortex stretching Viscous diffusion
New vorticity from wall
Redistribution of vorticity within flow
Precise measurements needed from experiments
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X
Zω upstream
Chaotic horseshoevortices
See Simpson (2001), “JunctureFlows,” Ann. Rev. Fluid Mech.
3:2 elliptic noseNACA 0020 tail form “Rood” wing
zp
yW
w ∂∂
=∂∂
ρν 12
2
refUY
Streamwise vorticity flux
3-D smooth wall TBLoutside horseshoe vortex structure
Approach Reθ = 7300and 23,200.
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Webster, et al. 1996:Un/swept Bump
Internal layers begin near leading and trailing edges due to discontinuities
Compton & Eaton, 1997:Spanwise ∇PStreamwise Favorable ∇P
Strong skewing of flow with reductionin shear stress and TKE correlation
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Coherent Structures in a Skewed 3DTBL.
Large-scaled structuresthat entrain free-stream fluidmove in different directionsthan near wall vorticalstructures.
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Defines the statistically ergodiclength scale for every frequency and wavelength eddy within the flow (Ha and Simpson, 1993).
For example, the coherency γ2from the cross-spectra from sensor signals at span-wise locations ∆Z apart can be modeled by the equation:
γ2 = exp (-kz |∆Z|/Lγz(f))
where kz is a flow dependent decay constant and Lγz(f) is a length scale for each frequency eddy passing the 2 sensors.
Spatial Coherency and PhaseStation 5
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Station 5. Flow angle, flow gradient angle, shear stress angle calculated using two separate data sets in wall stress co-ordinates.
Tan-1(FA)= W/U
yUuv
yWvw
Nx
z
∂∂
−
∂∂
−==
/
/
εε
Ha and Simpson, 1993
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Confirmed Earlier Insights on 3-D TBL • Outer layer flow and inner layer flow from
different directions with different histories– lower coherencies than for 2-D flows– lower correlation between shearing stress and TKE
• Most cases are non-equilibrium flows• No universal law-of-the-wall mean velocity
profile exists – but may have semi-log U and flow angle variations with y for inner/outer overlap region for moderate skewing
• Shearing stress direction lags velocity gradient direction –non-isotropic eddy viscosity – no preferred co-ordinate system
• Less skewed flows easier to calculate
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No data for 3-D flowsat higher Reynoldsnumbers to developor test models
Momentum, continuity, &transport equations neededbecause of non-equilibriumnature of most 3-D flows
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Wing/Body Junction FlowU+ vs. y+ mean velocity profiles in local wall shear stress co-ordinates.
Stations 1 – 9, from top to bottom
Solid, approach Reθ = 5940;
Open, Reθ = 23,200.(Őlçmen et al., 1999)
Solid – wall stress; Open - FS
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Wing/Body Junction
W/Uτ in tunnel co-ordinateswith same legend.
Top, approach Reθ = 5940;
Bottom, Reθ = 23,200.
For 2 Reynolds numbers:
∂2(W/Uτ)/∂(y+)2 about the same for Stations 1- 6
∂2(W/Uτ)/∂(y+)2 for high Reθabout 2/3 of low Reθ forStations 7-9
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( ) ( )2
221
vvwuv
S−+−
= vs. y+ profiles near the wall throughout the flow for 890 < Reθ < 23200, Station 5.
Water tunnel, Fleming andSimpson (1997)
Wind tunnel, Őlçmen and Simpson (1995)Őlçmen et al. (1999)
v2 scales active stress producing motions
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Emerging Overlap Structure for High Reynolds Number 3-D Flows, Reθ = 23,200, Őlçmen et al. 1999
Semi-logarithmic variation of correlation coefficient for some triple products.Trend supported by DNW data for 2-D flows. Needs further data at higher Reθ.
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Emerging Overlap Structure for High Reynolds Number 3-D Flows, Reθ = 23,200, Őlçmen et al. 1999
Semi-logarithmic variation of correlation coefficient for some tripleproducts. Needs further data at higher Reynolds numbers.
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• No Law of the Wall for 3-D Flows.• Profiles show no effects of orientation for y>3k
yUτo/ν
U/U
τo
100 101 102 103 104
0
5
10
15
20
25
30
k=0.38mm, straight patternk=0.38mm, staggered patternk=0.76mm, straight patternk=0.76mm, staggered patternk=1.52mm, straight patternk=1.52mm, staggered patternsmooth wall
Station 1
k=1.52mm
k=0.38mm
k=0.76mm
yUτo/ν
U/U
τo
100 101 102 103 104
0
5
10
15
20
25
30
Station 3k=1.52mm
k=0.38mm
k=0.76mm
yUτo/ν
U/U
τo
100 101 102 103 104
0
5
10
15
20
25
30
Station 5
k=0.38mm
k=0.76mm
k=1.52mm
yUτo/ν
U/U
τo
100 101 102 103 104
0
5
10
15
20
25
30
Station 7k=1.52mm
k=0.76mmk=0.38mm
Rough Wall Wing/Body Junction (J. George and Simpson, AIAA 2002-0580)
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W Profiles Collapse at y> 3k
y/δ
W/U
e
10-3 10-2 10-1 100-0.3
-0.2
-0.1
0
0.1
0.2 k=0.38mm, straight patternk=0.38mm, staggered patternk=0.76mm, straight patternk=0.76mm, staggered patternk=1.52mm, straight patternk=1.52mm, staggered patternsmooth wall
Station 1
k=1.52mmk=0.38mm
k=0.76mm
y/δ
W/U
e
10-3 10-2 10-1 100-0.3
-0.2
-0.1
0
0.1
0.2
Station 3
k=1.52mm
k=0.38mm
k=0.76mm
y/δ
W/U
e
10-3 10-2 10-1 100-0.3
-0.2
-0.1
0
0.1
0.2
Station 5
k=0.38mm
k=0.76mm k=1.52mm
y/δ
W/U
e
10-3 10-2 10-1 100-0.3
-0.2
-0.1
0
0.1
0.2
Station 7k=0.76mm
k=0.38mm k=1.52mmMax W propagatesaway from the wallfaster for rougher
surface
BL thicknesses are all different
Rough Wall Wing/Body Junction (J. George and Simpson, AIAA 2002-0580)Same surface pressure gradient as smooth wall cases
Transport of streamwise vorticity andGrowth of boundary layer are similar
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y/δ
1/S
10-3 10-2 10-1 1000
0.25
0.5
0.75
1
1.25
1.5
1.75
2k=0.38mm, straight patternk=0.38mm, staggered patternk=0.76mm, straight patternk=0.76mm, staggered patternk=1.52mm, straight patternk=1.52mm, staggered patternsmooth wall
Station 1
k=1.52mmk=0.38mm
k=0.76mm
y/δ
1/S
10-3 10-2 10-1 1000
0.25
0.5
0.75
1
1.25
1.5
1.75
2
Station 3
k=1.52mm
k=0.38mm
k=0.76mm
y/δ
1/S
10-3 10-2 10-1 1000
0.25
0.5
0.75
1
1.25
1.5
1.75
2
Station 5k=0.38mm
k=0.76mm
k=1.52mm
y/δ
1/S
10-3 10-2 10-1 1000
0.25
0.5
0.75
1
1.25
1.5
1.75
2
Station 7
k=1.52mm
k=0.76mmk=0.38mm
( ) ( )2
221
v
vwuvS
−+−=
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Axisymmetric 3-D Bump (Byun and Simpson, 2004, 2005)
x,U
y,V
R=2H
z,W
ψ=0°
ψ=90°
ψ=180°
δ=H/2
refU
6.41δ Wind tunnel ceiling
H
j
i
k
zL,WL L
xL,UL L
yL,VL Lθ
ψ
r
i
j
k
The right-handed tunnel coordinates, (x,y,z)
The right-handed local coordinates, (xL,yL,zL) r : local radiusψ : yaw angle about y-axisθ : pitch angle about zL-axisyL : locally perpendicular to the surface
Measurements 0° ≤ ψ ≤ 90°
= 27.5m/s, Reθ ≈ 7300
At least 2 papers atTSFP- 4 discusscomputations of this case.Ma and Simpson discusswake flow experiments atTSFP- 4.
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Results - Normalized Mean Velocities , and Intermittency of UL in the Center PlaneU V
1
x/H
y/H
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.2
0.4
0.6
0.8
1
1.2
0=U
x/H ≈ 0.96 Mean backflow zone
downstream
downstream
Downstream from separationUpstream from separation
r/H=0.644
r/H=0.573
yL0+
Inte
rmitt
ency
,
101 102 103 1040
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0.5730.6440.7060.7810.8410.91
r/H
γ pu
L
yL0+
Inte
rmitt
ency
,
101 102 103 1040
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
0.9761.0441.1121.1791.2441.3131.3861.461.5321.6151.6921.769
r/H
γ pu
L
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Results – Nearest Wall Flow Field
RANS with quadratic eddy-viscosity model
Focus separation
00.5
11.5
2
0
0.5
1
1.5
-2
-1.5
-1
-0.5
0
1.781.651.531.401.271.141.020.890.760.640.510.380.250.130.00
→∇CP
Saddle separation
Pressure gradient contour, its vectors.line connecting vectors locally tangent to surface at yL0+ = 11
LLLL kWiU +
x/Hz/H
y/H
Uref
at x/H ≈ 1.2, z/H ≈ -0.7
at x/H ≈ 0.96 on the centerline
Mean backflow region
Saddle-focus separated flow extends up toyL0+ ≈ 340.
Separation line
→∇CP
1
Z
X
Y
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Results - TKE Contour and its Normalized Transport Vectors in the Center Plane
0.0460.0430.0400.0360.0330.0300.0260.0230.0200.0170.0130.0100.0070.0030.000
0.2TKE/Uref
2
x/H
y/H
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.2
0.4
0.6
0.8
1
1.2
≡2/2q )2/( 222 wvu ++TKE ≡
refrefqvqurefq UqjvqiuqUjViVUV222 /)(/)(/ +≡+≡
, normalized by Uref
TKE transport vector, qV
Their magnitudes show some unsteadiness and jitter of the instantaneous flow
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Results - TKE Contour and its Normalized Transport Vectors
0.2
x/H
z/H
0 0.5 1 1.5 2
-2
-1.5
-1
-0.5
0
0.2
0 0.5 1 1.5 2
-2
-1.5
-1
-0.5
0
yL0+ = 200yL0+ = 11
yL0+ = 578
locally tangent to the surface
qLV
Lines for visual aid of locally tangential mean velocity direction
4.50E-024.21E-023.91E-023.62E-023.33E-023.04E-022.74E-022.45E-022.16E-021.86E-021.57E-021.28E-029.86E-036.93E-034.00E-03
0.2
TKE/Uref2
x/H0 0.5 1 1.5 2
-2
-1.5
-1
-0.5
0
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Results – 1/S Parameter at r/H = 1.386
yL0+
1/S
100 101 102 103 1040
0.5
1
1.50102030405060708090
Yaw(deg)
very low correlation for 0° ≤ ψ ≤ 40°mean backflow region
2
22 )()(1
L
LL
v
vwuvS
−+−≡ Low A1 and Ruv for 0° ≤ ψ ≤ 40° due to the mean flow
angle, tan-1( ) variation with distance from the wall.The turbulent flow at different yL0+ from differentdirections is not correlated with turbulence at other yL0+.
LL UW /
2-D TBL level
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yL0+=90 yL0+=200 yL0+=261
yL0+=456
yL0+=261
yL0+=261
Results – Bimodal Velocity Probability Histograms in UL and WL
Bimodal regionyL0+ < 5000.841 ≤ r/H ≤ 1.7690° ≤ ψ ≤ 30°
yL0+=261
x/H
z/H
0 0.5 1 1.5 2
-2
-1.5
-1
-0.5
0
10
80
70
60
50
40
30
20
yaw angle
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Results – Flow Structures on Leeside of the Bump
x,U
H
z,W
ψ = 0°
ψ = 90°
i
k
ψ = 30°
y,V j
Uref
High TKE levelnear wall
Low Reynolds shearing stresses productionin mean backflow region, yL0+ ≤ 100
Mean backflow supplied by large eddies
Mean backflow supplied by flow from sides
Spanwise ejection(uL’ < 0, vL’ > 0, wL’ < 0)
Sweeping toward the center(uL’ > 0, vL’ < 0, wL’ > 0)
Mean backflow zone, yL0+ ≤ 350
Bimodal histogram zone, yL0+ < 500
Saddle separation
Focus separation
Large eddies
ψ = -30°
Focus separation
Reattachment downstreamNodal or Saddle point ?
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Conclusions
• A saddle type 3-D separation at x/H ≈ 0.96 on the centerline of bump.
• One focus separation on each side of bump at x/H ≈ 1.2 and z/H ≈ ±0.7.
• The large eddies and the flow from the bump side supply the mean backflow.
• The large eddies supply the intermittently forward flow in this mean backflow region.
• In the separation zones, the turbulent flow from different directions is decorrelated,
resulting in lower shearing stresses.
• Bimodal probability distributions of UL and WL appear in this region due to the unsteady
and low frequency meandering of the flow field.
• To get complete flow features over this bump, more measurements are needed for
the reattachment and separation regions downstream.
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Flowfield for 6:1 Prolate Spheroid at α = 20o
U∞
Solid lines are oilflowseparation lines. Dashed linesshow local minima in skin friction.(Wetzel et al., 1998).
Mean secondary flowstreamlines on leesideof crossflow separatedflow from 3DLDV data(Chesnakas and Simpson,1997)
Computations by othersUsing RANS,LES, DESAt least 2 papersat TSFP-4
ReL = 4.2 X 106
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Linear Cascade Model – Devenport et al., Va Tech
Fixed Blades
Moving endwall models casing
Vortex-generator pairs attached to moving endwallmodel IGV necklace vortices
• Large scale flow suited to rotor frame measurements.• Models relative motion of tip and casing and relative motion of vortical wakes and blades • Does not model axisymmetric effects and full IGV wake not important• Allows flow to be manipulated in ways not possible in actual turbomachine
Fixed bladesTip gap←region
Inflowregion
Tip-gap data by Tang, Tian,& Simpson (2003, 2004)
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Suction side data locations (Tian et al., 2004)
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LINEAR COMPRESSOR CASCADE RESEARCH
-2.2 -2.1 -2 -1.9 -1.8 -1.7 -1.6 -1.50.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24Y
/Ca
-2.2 -2.1 -2 -1.9 -1.8 -1.7 -1.6 -1.5
Z/Ca
blade tip
7U7P7B7C7SX1X4X2X5X3
Pressure Side
Blade Tip SeparationVortex
Tip LeakageVortex Suction Side
SP
The secondary mean velocity flow field in the tip gap and tip leakage vortex (x/Ca=0.42) in the separation-line coordinates (t/c=3.3%)
:UrefUref=24.5 m/s
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FA, FGA, and SSA plot for tip gap flow
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y+
1/S
101 102 1030
0.2
0.4
0.6
0.8
1
1.2uu1d2s3s4s5s6s7s8s9s
Suction side t/c=3.3%
1/S vs y+ from endwall along compressor blade suction side.(Tang and Simpson, 2004). Large reduction in 1/S due to large variation of flow angle with y and uncorrelated structures.
( ) ( )2
221
vvwuv
S−+−
=
-
yUuv
yWvw
Nx
z
∂∂
−
∂∂
−==
/
/
εε
y+
|Log
(-N
)|
100 101 102 103
10-1
100
101
102
c11u1b1d
|Log
N|
10-1
100
101
102
c11u1b1d
x/ca=0.00 t/c=1.65% Pressure to SuctionTop to Bottom
y+
|Log
(-N
)|
100 101 102 103
10-1
100
101
102
4u4p4b4c4s|L
ogN
|
10-1
100
101
102
4u4p4b4c4s
x/ca=0.12 t/c=1.65% Pressure to SuctionTop to Bottom
y+
|Log
(-N
)|
100 101 102 103
10-1
100
101
102
6u6p6b6c6s|L
ogN
|
10-1
100
101
102
6u6p6b6c6s
x/ca=0.27 t/c=1.65% Pressure to SuctionTop to Bottom
y+
|Log
(-N
)|
100 101 102 103
10-1
100
101
102
8u8p8b8c8s|L
ogN
|
10-1
100
101
102
8u8p8b8c8s
x/ca=0.65 t/c=1.65% Pressure to SuctionTop to Bottom
In Chord Coordinate System(Better data correlation than other coordinate systems)
Strongly Anisotropic Flow
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Some Results from Calculations• Full Reynolds stress model superior to algebraic stress model. (Iavocides)
• Nonlinear turbulent viscosity model superior to linear model. (Suga)
• Models with anisotropic dissipation perform better than those with isotropic dissipation. (Jongen)
• Near-wall region modeling critical to accurate description of 3-D flows.
• Reynolds stress models with wall functions are unsatisfactory. (Sotiropoulos)– near-wall turbulence closures must account for the anisotropy of the
Reynolds stresses.
• V2F model is the ‘best’ linear turbulent viscosity model. (Parneix)– An elliptic operator is used to model non-local effects of near-wall
turbulence.– Makes intrinsic and linear specific assumptions.– Good results by Wu and Squires (1998) for Swept Bump
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More Results from Calculations
• Unsteady RANS and DES can simulate 3-D flow features dominated by geometry with relatively simple turbulence models (Paik).
• LES important for separated flows with low frequency large-scale motions (Davidson)
• Stress transport and algebraic stress models preferable over eddy viscosity models (Cummings; Morrison)
• From DNS the directional ‘lag’ between the mean shear stress and the velocity gradient directions depends strongly on the velocity-pressure-gradient correlation. (Coleman et al.)
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Wavy Wall 3D TBL – Sadek & Simpson, 2005Waves of stream-wise vorticity produced by spanwise pressure gradients.
Floor BL data
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‘Comprehensive’ LDV Technologies
Linearly varying fringe patterns for resolving particle positions
Particle acceleration measurements
12
12 )()(tt
tftfddt
dfda DDD−−
==
2000 )(2
)()( ttattVxtx −+−+=vvvv
Second-order particle trajectory resolved to Kolmogorov length and time scales:
)( 2tfD)( 1tfD
'x
⎟⎟⎠
⎞⎜⎜⎝
⎛=
Blue
Green
ffgx'
Lowe and Simpson, TSFP-4
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RST Measurements• Navier-Stokes equations:
Multiply by u’, time-average:
Reynolds stress transport equations:
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– Obtain measurements of dissipation rate, acceleration/velocity fluctuation correlations to obtain velocity/pressure gradient correlation within flow field in laboratory flows
– Accomplished by measuring instantaneous position, velocity, and acceleration vectors within Kolmogorov scale (100-200 microns) measurement volume with single seed particles, current data rate 100KHz.
– Rate-of-strain tensor has not been measured on scales smaller than 5-7 times the Kolmogorov length scale.
Some Capabilities of Comprehensive LDV for High Reynolds Number 3-D Flow Research
iji
jji uuxpuua 2∇+∂∂
−= µρ
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Recommendations• Data for high Reynolds numbers 3-D flows, Reθ
> 105• Direct measurement of terms in transport
equations• Velocity pressure gradient correlation data to
develop models • Auto & cross-spectral data for coherency &
phase for large-scaled motions• Rate-of-strain tensor for dissipation rate and
enstrophy
• LES, URANS, DES calculations necessary to capture low frequency motions of separated flows that affect diffusion
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AcknowledgmentsThe completed work at Virginia Tech reported here has beensupported by the U.S. Office of Naval Research, Drs. L.P. Purtell,E. Rood, R. Joslin, and Ki-Han Kim, Program Managers.
K. Granlund, D. Hunter, and N. Varano contributed to the literature search and review.