Characterization, Manipulation And Control

of the Turbulent Boundary Layer For Aero-

Optical Applications

AFOSR Grant: FA9550-12-1-0060

Program manager: Dr. Douglas Smith

Stanislav Gordeyev, University of Notre Dame

and

Beverley McKeon, California Institute of Technology

Graduate students: Adam Smith, Matthew Kemnetz, Rebecca Rought, Theresa Saxton-Fox

2014AFOSR Flow Interactions & Control Portfolio Review

29-31 July 2014, Arlington, VI

Courtesy of Mike Paschal

http://www.airliners.net/search/photo.search?id=1075413

Aero-Optical Effects: Wavefront Aberrations

due to the flow around Aircraft and Beam.

Aberration Environment for Propagation from an

Airborne Laser Platform

'1 GDKn

Index of refraction n(x,t) is dependent

on local density fluctuations

Degree of aberrations – Optical Path Length (OPL) 2

1

),(),( 0

s

s

dstsntsOPL

Optical Path Difference (OPD) –

spatial mean subtracted ),(),(),( txOPLtxOPLtxOPD

KGD = 2.27x10-4 m3/kg – Gladstone-

Dale constant

Both Laser DE Weapons and Laser Free-Space Communication depend being able to

“FOCUS” (high intensity) a Laser on a distant “target.”

22

0

rmsOPD

eI

ISRFar-Field Intensity (Strehl Ratio) - Large-Aperture Approximation

where OPDrms – spatial root-mean-square of OPD

Boundary Layers: Motivation Traditional turret-based systems create unacceptably large aero-

optical distortions at high transonic and supersonic speeds, as well

additional unsteady forces, an increased radar cross-section, noise etc.

Surface mounted phased laser arrays or beam directors enclosed in a

sealed cavity, only contend with the boundary layer over the aperture

Objective

Demand for high-speed and secure free-space link between aircraft and

ground/aircraft/satellite for military and commercial applications.

Turbulent field near aircraft distorts the laser beam – aero-optical effects.

Combined with atmospheric distortions, they are main limiting factors for

free-space communication links (intensity drop-outs).

Better understanding of instantaneous dynamics of BL large-scale structures,

relation to intensity drop-outs and develop passive flow control strategies.

Passive Flow Control

for Boundary Layers

Assuming p‟ is negligible and using

Extended Strong Reynolds Analogy (ESRA),

2

2

22

)()1(

)()(

U

yUMr

T

T

U

yuy rmsrms

dyyyKOPD rmsGDrms )()(2 222

Sutton (1969)

Ways to mitigate aero-optical distortions:

1. Reduce rms by

- reducing urms and/or U(y)

- by cooling the wall, T < 0

2. Reduce the structure size, (y)

3. Reduce extent of optically-active region

Two approaches are investigated:

o Disrupt large-scale structure with Large-Eddy

Break-Up (LEBU) devices.

o Manipulate density field via wall

cooling/heating

l

δ0h h1

h2h

s

b) Multi LEBU c) Tandem LEBU

δ0 δ0

x

y

z

FLOW

t

Tapered Leading & Trailing Edges

a) Single LEBU

δ0

U(y)

Cf reductions persist

for O(100δ)

Zero Angle of Attack

Device wake

U(y)

LEBU DeviceIncoming Turbulent Boundary LayerLEBU-

Modified TBL

Flow visualization from Corke, et al. (1979)

Large-Eddy Break-Up Devices • Thin flat plate(s) or small airfoil shapes

mounted parallel to wall within TBL – Coarse version of mesh

grids/honeycombs

• Late 1970s – 80s found reductions in Cf for distances on order of 100δ downstream

– Extent of reduction dependent on configuration

• Possible mechanisms for Cf reduction – Reduction of TBL intermittency & large

scales, (wall-normal and streamwise) – Wake/Plate effects:

• Reduced wall-normal velocity fluctuations • Redistribution of TKE (reduce production

below LEBU device)

Baseline LEBU-Modified

Flow-visualization of LEBU-modified

TBL. Corke, et al. (1979)

LEBU modify BL large-scale structure,

which was shown to cause aero-optical

problems

Previous Results: Single LEBU

1. LEBU devices induce wake deficit on TBL

flow, significant reduction in RMS velocity

below LEBU device.

2. Increase in RMS velocity above LEBU:

increased production from local increase in

dU/dy

3. Spectral analysis shows significant

reduction of large-scale structures in LEBU

wake

Smith (2013) AIAA Paper 2013-0718

)()(~)( yUyuy rmsrms

Reduction in OPDrms:

Single LEBU

For h = 0.6δ LEBU,

>30% reduction over ~3δ

1. LEBU suppresses low-frequency (large scale) structures in the TBL, leading to substantial reductions in

OPDrms. (~30%)

2. Wavefront spectra showed after suppression of large scales (relatively close to LEBU), peak location of

spectra recovers towards baseline spectral peak location.

l = 1.6d, x = 1.6d

Effect of LEBU type LEBU

Configuration l/δ h1/δ h2/δ s/δ

Single 1.6 0.6 - -

1.6 0.5 - -

1.6 0.9 0.6 -

Multi 1.6 0.8 0.5 -

1.6 0.6 0.3 -

Tandem 1.6 0.6 - 4.0

1.6 0.6 - 8.0

EXPERIMENTAL OBJECTIVES:

1. Extension of streamwise measurement

region from 6δ to 10δ

2. Wavefront measurements of multiple-

element LEBU devices

(b) Multi LEBUs (Vertically Stacked)

(c ) Tandem LEBUs (Horizontally

Spaced)

Single

Multi

Tandem

Single LEBU: OPDrms Data Maximum reduction in

OPDrms of > 30% for

Single LEBU

Results are in good agreement

with previous wavefront

measurements.

The h = 0.5δ, and h = 0.6δ

cases are similar, but h = 0.6δ

shows a slightly longer

streamwise extent of reduction

and a „slower‟ recovery

towards the baseline value.

> 30% reduction in OPDrms for

streamwise distance of approx. 4δ

Both Single LEBU devices

show recovery towards

baseline for x/δ > 6

Smith (2013) AIAA Paper 2013-0718

l = 1.6δ

Multi LEBU: OPDrms Results

Maximum reduction in

OPDrms of ≈ 40% for

Multi LEBUs

Multi LEBU Devices:

Step back towards screens and

honeycombs for turbulence control.

Two-element Multi LEBUs with 0.3δ

spacing tested at different heights.

Configuration with h1 = 0.6δ, h2 =

0.3δ gave largest reductions in

OPDrms

Sustained reductions (h1 = 0.6δ, h2 = 0.3δ):

>30% for approx. 7δ, >35% for approx. 4δ

l = 1.6δ

Tandem LEBU: OPDrms Results

Maximum reduction in

OPDrms of > 40% for

Tandem LEBUs

The best OPD reduction among all tested LEBUs.

Wider wake, less device drag by placing second

LEBU element in wake of the first.

Nonlinear interaction between wakes.

Sustained reductions (s = 8δ):

>30% for approx. 9δ, >35% for approx. 7δ

l = 1.6δ

For quantitative comparison, define the ratio

Plotting surfaces of Cθ gives a more detailed picture of the streamwise

development of LEBU wavefront spectra:

LEBUs: Spectral Analysis

LEBU

Baseline

ˆ ,, 1

ˆ ,

x StC x St

x St

d

d

d

dd

d

Reduction in high-frequency (i.e. small scale) content

as x increases

Peak recovering to

baseline location.

Suppression of large-scale TBL

scale structures (Stδ < 1)

Effect diminishes as x increases.

Optical reduction: Spectral Features

Strong initial suppression of low-f

(large-scale) structures.

s = 8δ tandem LEBU shows the most

significant broad-band reductions in

wavefront spectra.

Increase in high-frequency content

just downstream of multi LEBU

Significant suppression of low-f

(large-scale) structures

h1 = 0.6δ, h2 = 0.3δ multi LEBU

shows the most significant broad-

band reductions in wavefront

spectra.

Modest reduction in high-frequency

Suppression of low-f (large-scale)

structures

Spectrum peak location shows

recovery towards TBL peak location

(Stδ = 1) approaching 10δ

For all LEBUs, spectrum peak location shows recovery towards

TBL peak location (Stδ = 1) approaching 10δ.

Single LEBU: Wake Recovery

Estimate is in good agreement with direct measurements.

Assuming that at each x-location the peak frequency corresponds

to a dominant structure size γ, it can be estimated by

Shift from high-to-low frequency suggests streamwise growth of

this structure size – result of LEBU wake deficit.

Estimating the wake-deficit half-width:

Peak

Peak

U

f Std

d

1

2 2 Peakb x

Std

d

Smith (2013) AIAA Paper 2013-0718

Linking Equation Analysis

Λρ for canonical BL Λρ ~ Λx Experiments

Single LEBU

(h = 0.6δ) 10% 22% 30%

Multi LEBU

(h1 = 0.6δ, h2 = 0.3δ) 15% 30% 35%

Tandem LEBU

(s = 8δ) 16% 28% 40%

Streamwise correlation lenghts, Λx, were computed from hot-wire velocity data.

Λρ = Λρ (canonical BL) * Λx /Λx (canonical BL)

Implies non-linear relationship between streamwise and wall-normal correlations.

1/2

2

2

0

( ) ( )rmsrms

yU y u y yOPD d

U

d d

Reduction in OPDrms

Single LEBU Parametric Studies

18

• Long-LEBU (l = 4δ) reductions comparable to results for Tandem-LEBU (AIAA-2014-0321) Tandem vs. Long Single LEBUs:

>> Both produce strong wakes which disrupt TBL equilibrium for long distances downstream

>> Cf reductions monotonically increased with LEBU length in parametric studies by Savill & Mumford (1988), but due to

increased wetted surface area, no further studies (no net drag reduction) -> Tandem LEBUs did give net drag reductions.

>> For Aero-optic mitigation, we may wish to accept a small drag penalty and use long, single LEBU devices.

a) Single LEBU

h/δ 0.3 0.5 0.6 0.8 1.0

l/δ

0.8 ■ ■ ◊ ◊ ■

1.0 ■ ■ ■ ■ ■

1.6 ■ ■ ◊ ◊ ■

3.0 ■ ■ ■ ■

4.0 ■ ■ ■ ■

Increasing length

Maximum OPDrms Reduction

Length of Sustained OPDrms Reduction > 20%

Increasing length

Optimal height for all lengths:

h/δ ≈ 0.5 – 0.6

LEBU devices: Summary Single

Multi Tandem

~40% reduction

LEBUs were shown to be simple and cost-

efficient devices to mitigate BL aero-optical

effects.

Optimal LEBU AO Configuration

Single LEBU, l = 4δ, h = 0.6δ

Sustained reductions >30% over 9δ

Tandem LEBU, l = 1.6δ, h = 0.6δ, s = 8.0δ.

Sustained reductions >35% over 7δ

Comparison of Wavefront and Velocity

Measurements

Able to pick out features of recovering LEBU

wake flow from wavefront spectra

Changes to Λρ(y) must be accounted for to

obtain accurate predictions

Estimations of Λρ(y) from streamwise correlations

of wavefront and velocity measurements do not

to consistently yield estimates that are in good

agreement with wavefront measured levels of

OPDrms reduction.

Reduction in density fluctuations

l = 1.6δ

Wall-Temperature Effects: theory dyyyKOPD rmsGDrms )()(2 222

-linking equation

2/12

2

2

1

4*

T

TCM

T

TCMAOPD

SL

rms d

Neglecting pressure fluctuations and using Extended Strong Reynolds Analogy,

Wall Cooling

2/12

22211

MT

TC

MT

TC

OP

Drm

s /

OP

Drm

s,

T=

0

• Wall cooling is another effective way to reduce

aero-optical BL distortions.

• Experiments agree quite well with theory.

Model

60% reduction!

Den

sity

Flu

ctuat

ion P

rofi

les

Density fluctuations are

significantly suppressed

in the near-wall region

by partial wall cooling.

y+

Cress, 2014

New Experimental Approaches

Heating the boundary layer allows to study aero-optical effects at low subsonic speed

Wall-heating circumvents aero-optic „invisibility‟ problem in incompressible flow

Systematic studies of instantaneous aero-optical structure at subsonic and transonic

speeds to find effective strategies to mitigate aero-optical effects

thermal image of the heated boundary-layer plate, Caltech

For positive T, expression for OPDrms can be further simplified as,

T

TDMAOPD

SL

rms

2*d

Caltech Malley Probe Setup Advantages:

• Simultaneous PIV and Malley probe data

• Extends results into incompressible flow

Flow Conditions:

Malley probe

beams

PIV light

sheet

Malley Probe Spectra

ΔT

Incompressible flow regime with heat addition:

o Spectrum similar to that of compressible flow

o Spectrum amplitude increases with T

Simultaneous PIV and Malley Probe

Malley probe

PIV snapshot at t = 0.08 sec

Time of PIV snapshot

θ1

θ2

Vectors shown:

Malley probe locations drawn in θ1 θ2

The change in sign in 1 at about 0.08

seconds in the Malley probe plot lines up in

time with the center of the vortex at 0.3 y/d

passing through the first beam.

Link between the passage of structures in

the PIV images and the deviation of the

Malley probe beams.

Aero-Optical Measurements

of Low-Re BL To date, comparison between experiments and simulations has been limited by

substantial differences in Reynolds numbers between experiments and simulations:

CFD

White & Visbal

Reθ = 1426

Experiment

Gordeyev, et al. (USAFA)

Reθ = 12,000 – 90,000

Experiment

Gordeyev, et al. (ND)

Reθ = 18,000 – 27,000

CFD

Wang & Wang

Reθ = 3550

Reθ 0 5,000 10,000 15,000 20,000 25,000

Also, there is a need to validate the model for OPDrms at low Re

Increasing Reθ

Consistent with increasing

inertial sub-range

f (-2/3) roll-off from Kolmogorov-type arguments

Aero-Optical Spectra for Low-Re BL

AIAA Paper 2014-2491

3/5

83.01ˆˆ

d

dd

St

StSt peakfit

Original empirical

spectral model

Spectral roll-off term

Assumed to take form

inspired by Tatarski‟s

modification of

Kolmogorov‟s atmospheric

wavefront spectrum to

account for inner scale

dissipative structures.

Empirically determined

that,

f(Reθ) ≈ 1.6Reθ(0.22)

fGDrms CMKTOPD 22.00 d

Heated wall wavefront data collected in wind tunnels at Notre Dame and Caltech

• M = 0.03 – 0.4, Reθ = 1,700 – 20,000

Very good agreement between experimental data

and new model equation - was proven to be valid for Reθ > 4,000

2

Reexp

d

f

St

Comparison Between Experimental and

Model Spectra

For individual cases, there is

good agreement between

spectral model and

experimental data over a large

range of Reynolds numbers

(~2k – 20k, or order of

magnitude)

AIAA Paper 2014-2491

2

3/5Re

exp83.01

ˆˆ

d

d

dd

f

St

St

StSt peakfit

Summary Parametric studies of different LEBUs geometries in subsonic BL were performed.

Sustained reduction (~40% ) of OPDrms for several BL thicknesses were shown.

Analysis of deflection angle spectra lead to optical measurements of the wake evolution.

Modest heating/cooling of the boundary layer wall allows to modify the density field in BL without

modifying velocity structure.

Wall-heating circumvents aero-optic „invisibility‟ problem in incompressible flow

- study BL structures at low subsonic speeds using sensitive non-intrusive optical sensors.

- study different BL regions by selectively “tagging” with passive temperature “markers”.

- direct measurements of convective speeds at different BL regions.

- direct comparison with CFD predictions at low Re-range.

Models for OPDrms and spectra, originally derived for high-Re TBLs,

were shown to work down to Reθ = 4,000.

Future Work

Simultaneous optical-velocity measurements

Measurements of density structure for LEBU-modified BL

Correlation between instantaneous OPD and the instantaneous BL thickness

Ability to optically measure instantaneous BL thickness ?

Instantaneous version of Strong Reynolds Analogy ?

Extend OPD models to modified and instantaneous BL

Publications 1. J.A. Cress, S. Gordeyev and E.J. Jumper, “ Aero-Optical Measurements in a Subsonic, Turbulent Boundary

Layer with Non-Adiabatic Walls", submitted to Physics of Fluids, 2014.

2. S. Gordeyev, A. E. Smith, J.A. Cress and E.J. Jumper, “ Experimental studies of aero-optical properties of

subsonic turbulent boundary layers", Journal of Fluid Mechanics, 740, pp. 214-253, 2014.

3. A.E. Smith; S. Gordeyev; E.J. Jumper. Recent measurements of aero-optical effects caused by subsonic

boundary layers. Opt. Eng. 52 (7), 071404, 2013.

Several more journal articles are currently in preparation.

Conference papers

1. D.J. Wittich III, M. Paul, H. Ahmed, A. Ahmed, A.E. Smith and S. Gordeyev, “Aero-Optic Characterization of

Supersonic Boundary Layers in the Trisonic Gasdynamic Facility”, AIAA Paper 2014-2356.

2. A.E. Smith, S, Gordeyev, T. Saxton-Fox and B. McKeon, “Subsonic Boundary-Layer Wavefront Spectra for a

Range of Reynolds Numbers”, AIAA Paper 2014-2491.

3. A.E. Smith, S. Gordeyev, H. Ahmed, A. Ahmed, D.J. Wittich III and M. Paul, “Shack-Hartmann Wavefront

Measurements of Supersonic Turbulent Boundary Layers in the TGF”, AIAA Paper 2014-2493.

4. A. Smith and S. Gordeyev, “Aero-Optical Mitigation of Turbulent Boundary Layers Using Large-Eddy Break-

Up Devices”, AIAA Paper 2014-0321.

5. A. Smith and S. Gordeyev, “The Effects of Wall Cooling on Aero-Optical Aberrations Caused by Subsonic

Turbulent Boundary Layers”, AIAA Paper 2013-3133.

6. A. Smith and S. Gordeyev, “Evaluation of Passive Boundary Layer Flow Control Methods for Aero-Optic

Mitigation”, AIAA Paper 2013-0718.

Hessert Transonic Wind Tunnel

31

Hessert Transonic Wind Tunnel

University of Notre Dame

Indraft Tunnel

Present Study: Mach = 0.4

Cross-section: 10 cm × 9.9 cm

Section length: 165 cm

h1δ

l

x

Δ

Malley Probe

Beams

Return MirrorOptical Window

Multi-LEBU

Device

LEBU

Device

δh

Adjustable Height,

Embedded LEBU

Supports

h2

(a) (b)

Inlet Contraction

(150:1)

Boundary Layer Optical

Measurement Section

Diffuser

Plenum & Pumps

Passive Flow Control Mounted in

Tunnel Walls

Experimental Setup

Malley Probe Wavefront Sensor

2-Beams (Deflection angle & Uc)

Analog position sensing devices

(PSDs)

Sample rate up to 200 kHz for 10 sec

OPD reconstructed via Frozen Flow

Assumption;

LASER

SOURCEBEAM

CUBE

SPATIAL

FILTER

BEAM

SPLITTER

PSDS TB

L 1

FLOW

RETURN

MIRROR

Δ

TB

L 2

32

,OPDOPDOPD2

21

2DBL SBL, BASELINE

rmsrms

T

rmsw

.ˆˆˆ2

21

2

,SBL BASELINEDBLTfff

w

Wittich, et al. (2007) AIAA Conf. Proc., Cress (2010) Ph.D. Thesis

Assuming statistical independence of TBL

statistics:

LEBU

Configuration l/δ h1/δ h2/δ s/δ

Single 1.6 0.6 - -

1.6 0.5 - -

1.6 0.9 0.6 -

Multi 1.6 0.8 0.5 -

1.6 0.6 0.3 -

Tandem 1.6 0.6 - 4.0

1.6 0.6 - 8.0

0

, , , ,

t

COPD x z t U x z d

Partially-Cooled Wall 2/1

2

102

2

101

4* ),(),(

T

TxxCM

T

TxxCMAOPD

SL

rms d

Details: AIAA-2013-3133

Decreasing the aircraft skin temperature upstream of

the laser beam could greatly increase the far-field

laser intensity.

Near aperture cooling is more efficient as it requires

less T.

Reduction 60%

Reduction 80%

OP

Drm

s(

T)O

PD

rms(

T

=0

)

OP

Drm

s(

T)O

PD

rms(

T

=0)

-T

OP

TIM

AL/(

T*

M2)

Rcool = Cooled Length / Full Length

FLOW

Single Boundary Layer (SBL) Modification

Un-Modified

Boundary Layer

Cooling-Modified

Boundary Layer

Return

Mirror

TBL 1

TBL 2

Cooled Wall

To Malley Probe Optics

Single BL Modification Modify only 1 TBL and remove effect of un-

modified TBL using statistical scaling relation:

For wall cooling, we have

observed significant reductions

in OPDrms of TBLs.

SBL wall cooling experiments, applying scaling

results in extracting a small signal from a large

signal:

TBL Wall Cooling Single vs Double Boundary Layer Modification Experiments

34 Smith & Gordeyev (2013) AIAA Paper 2013-3133

2SBL,22SBL,1DBL OPDOPDOPD rmsrmsrms

Small OPDrms

Large OPDrms

Necessary to perform DBL wall cooling experiments (both

walls modified) to verify SBL results and reduce uncertainty.

TBL Wall Cooling Single vs Double Boundary Layer Modification Experiments

• SBL and DBL measurements are in

good agreement

• DBL measurements still show

broadband effect in spectra

(i.e. ΔT is a scalar multiplier)

TBL 1

TBL 2

FLOW

To Malley Probe Optics

Cooling-Modified

Boundary Layer

Cooling-Modified

Boundary Layer

Symmetrically

Modified TBLs

Double Boundary Layer (DBL) Modification

Return

Mirror

Cooled Wall

Cooled Wall

*OPDrms from Icing-corrupted spectra removed from plot for

clarity