1. Experimental and Numerical Investigation of Controlled, Small-Scale Motions in a Turbulent Shear Layer
Bojan Vukasinovic, Ari Glezer
Woodruff School of Mechanical Engineering
Georgia Institute of Technology
Zvi Rusak
Department of Mechanical, Aerospace, and Nuclear Engineering
Rensselaer Polytechnic Institute

2. Controlled Vorticity Manipulation
single-stream shear layer U0
shear
layer
backward-facing step
Interaction with baseline flow through the free stream

3. Controlled Vorticity Manipulation
single-stream shear layer
initial interaction region U0
shear
layer
vorticity source
backward-facing step
Interaction with baseline flow through the free stream
Vorticity source (e.g., synthetic jet actuator)
High-frequency vorticity ejection
Actuation frequency can be varied

4. Controlled Vorticity Manipulation
single-stream shear layer
initial interaction region U0
shear
layer
vorticity source
backward-facing step
Interaction with baseline flow through the free stream
Vorticity source (e.g., synthetic jet actuator)
High-frequency vorticity ejection
Actuation frequency can be varied
Vortex circulation is adjustable
Wall shear stress and turbulent production are altered

5. Vorticity Source
f = 500 Hz (Uj = 20 m/s)
f = 1000 Hz (Uj = 30 m/s)
f = 2000 Hz (Uj = 30 m/s)
0.2H
f = 0
180 0
180 0
180
Control actuators generate synthetic jets into the cross flow
Nominal jets issued at f = 2000 Hz (St ~ 7)
Jets can be synthetisized from 2000 to 200 Hz with decreasing Uj

6. High-Frequency (Dissipative) Control
uncontrolled U0 ln
controlled U0
high-frequency
actuation
Lre-em >> ln
Stabilized Shear Layer
(Stanek’s Model)
Emergence of Inviscid Instability
INCREASED DECREASED
production, dissipation
HF Domain I II
III
Region I: HF Actuation increased dissipation and turbulent production leads to modification of the time-averaged baseline.
Region II: Stabilized Shear Layer suppression of fundamental coherent vortices formation, reduced turbulent production and dissipation.
Region III: Re-emergence of Inviscid Instability at a lower frequency.

7. Experimental Facility
Closed-loop, low-speed wind tunnel; free stream turbulence intensity ~ 0.5%
test section
10”  16”  52”
synthetic jets
Flow-diagnostics H x U0 y
Particle image velocimetry (PIV)
Hot-wire anemometry (HWA)
trip wire

8. Theoretical Tools I Mathematical Model
2-D, unsteady, incompressible viscous flow
Navier-Stokes equations in vorticity and stream function formulation

9. Theoretical Tools II | ψ ω x/H | ψ x/H δ
Linear temporal and spatial stability studies; natural frequency ωn along base shear layer
Second-order stability analysis; the flow linear frequency response; ;
perturbation’s amplitude
shape function
periodic in time and space
0< ω < 2ωn,max
ω > 2ωn,max | ψ ω
x/H | ψ
x/H δ

10. Theoretical Tools III
Nonlinear parabolic stability equations (NPSE); nonlinear interaction between M+1 modes
2M+1 parabolic equations
Integrated numerically
Linear
Non Linear

11. The Unforced (Baseline) Flow
measurement domain
shear layer evolution y x
PIV
0.5H
HWA
2.5H
-0.5H
-0.5H
H = 50.8 mm
q0 ~ 0.35 mm
Reqo ~ 470
ReH ~ 43,000
0.5
y/H
-0.5 1 2
x/H

12. Computed Baseline Flow
Experimental baseline flow conditions matched within measurement domain
y/H
x/H b 1
x/H 2
-0.5
y/H
0.5 a
y/H
x/H c
Full computational domain:
Extended spatial domain
Reduced temporal domain

13. The Unforced (Baseline) Flow
EXPERIMENTAL:
disturbance amplification
ANALYTICAL:
most amplified frequency
-0.2
y/H
0.5
1.0
x/H
300 Hz
200 Hz
100 Hz
50 Hz
● local stability theory
The local natural frequency decreases along the expanding shear layer
Agreement with experimental results of most amplified frequencies

14. Continuous High-frequency Actuation
momentum coefficient Cm= rUj2bj/(rU02H)
phase average
ensemble average
0.25
Cm = 4  10-3
0.5
y/H
-0.25
-0.5
0.25
26  10-3
0.5
y/H
-0.25
-0.5
0.25
51  10-3
0.5
-0.5
y/H
-0.25
0.25
0.5
0.75 1 2
x/H
x/H

15. Continuous High-Frequency Actuation
f = 2000 Hz
Cm = 26  10-3
ensemble average
phase averaged 1 2
x/H
0.5
-0.5
y/H
0.25
0.5
0.75
-0.25
f = 100
f = 140
f = 180
f = 220
f = 260
f = 300
f = 340
f = 20
f = 60
x/bj 15 12
y/bj
Temporal and spatial alteration of the BL vorticity
CCW vortex displaced and accelerated around CW vortex
f = 2000 Hz
Cm= rUj2bj/(rU02H) = 4, 26, 51, 69  10-3

16. Characterization of the Forced Shear Layer: Mean Flow
Cm103
x/H = 0.1
–○– 0
–■– 4
–▲– 26
–♦– 51
momentum thickness
x/q0
q/q0
0.5
1.0
weak forcing (Cm = 4  10-3) does not alter the baseline flow
b and q increase with Cm
2.0

17. Characterization of the Forced Shear Layer: Natural Frequency
EXPERIMENTAL:
disturbance amplification
ANALYTICAL:
most amplified frequency
300 Hz
Cm = 4  10-3
x/H
fn [Hz]
Cm103
26  10-3
–♦– 0
–▲– 26
51  10-3
Local natural frequency lowered by the actuation
Relates to the shear layer thickening

18. NPSE Computed Flows MODE 6 ACTUATION NO ACTUATION StH = 0.97 m = 2
NPSE calculation (6 modes are used): vorticity perturbations field is presented
In the “natural” case (a), the low-frequency mode dominates
In the “actuated” case (b) of increased amplitude of mode 6, high frequency mode dominates

19. Reynolds Stresses
0.1
0.5
1.0
2.0
Cm103
y/H
-0.5
x/H
x/H
x/H
x/H
x/H

20. Turbulent Kinetic Energy
Cm103
0.5
Cm = 0
–○– 0
–■– 4
–▲– 26
–♦– 51
y/H
-0.5
0.5
4  10-3
y/H
-0.5
0.5
26  10-3
y/H
-0.5
0.5
51  10-3
y/H
-0.5 1 2
x/H
x/H

21. Energy Transfer: StH = 7.36 cross-over frequency fc fc x/H
0.2
-0.2
y/H
Cm = 4  10-3
x/H
0.2
-0.2
y/H
26  10-3
Cm = 4  10-3
0.2
-0.2
y/H
51  10-3
0.2
-0.2
y/H
69  10-3
Cm = 51  10-3
0.5
1.0
x/H

22. Turbulent Dissipation Rate: StH = 7.36
25 mm
Cm = 51  10-3
Cm = 0
0.5
x/H
-0.25
0.25
y/H
Actuation leads to an order of magnitude increase in turbulent dissipation rate in the near field

23. Turbulent Dissipation Profiles
StH = 7.36
0.3
-0.3
y/H
x/H = 0.05
0.1
0.2
0.3
-0.3
y/H
0.3
0.4
0.5
104
5103
e* = eH2/(3nU02)
104
5103
e* = eH2/(3nU02)
104
5103
e* = eH2/(3nU02)
Baseline flow: dissipation peak in the near-wall region. Controlled flow: much broader peak with an order of magnitude higher amplitude
As the flow evolves, dissipation enhancement is reduced and becomes comparable to the unforced flow
The controlled flow exhibits enhanced dissipation at shear layer edges

24. Experimental TKE Profiles
–○– 0
–▲– 26
Cm103
x/H=0.1
x/H=0.25
x/H=0.5
EXPERIMENTS
fd = 2000 Hz

25. Experimental and NPSE TKE Profiles
–○– 0
–▲– 26
Cm103
x/H=0.1
x/H=0.25
x/H=0.5
EXPERIMENTS
fd = 2000 Hz I II II
x/H=0.25
x/H=0.50
x/H=0.75
fd = 300 Hz
NPSE I I II
I – small-scale structures dominate
II – peak energy lowered and energy is broadened (thicker shear layer)

26. Regions of HF Influence
EXPERIMENTAL
momentum thickness
EXPERIMENTAL
cross-section integrated TKE
–○– 0
–▲– 26
Cm103
III I II
ANALYTICAL
natural frequency
Region I - actuation increases TKE
Region II – actuation spreads TKE and reduces its peak in the thickened shear layer
Region III - low frequency mode re-emerges

27. Cross-sectional Integrated TKE
EXPERIMENTAL
fd = 2000 Hz
–○– 0
–▲– 26
Cm103
III I II I II
III
NPSE
fd = 300 Hz

28. LI/q0 < x/θ0 < LII/q0
High-Frequency Control
uncontrolled U0 ln
controlled U0
high-frequency
actuation
Lre-em >> ln
Stabilized Shear Layer
Emergence of Inviscid Instability
INCREASED DECREASED
production, dissipation
HF Domain I II
III
Li = func(Cm, fd) LI
LII
LIII
0 < x/θ0 < LI/q0
LI/q0 < x/θ0 < LII/q0
x/θ0 > LII/q0
Under HF actuation, three regions of shear layer are found

29. Conclusions
Direct small-scale manipulation of the BFS shear layer is investigated experimentally and numerically.
Continuous high-frequency actuation is effected by interaction of a small-scale vortex train with the shear layer.
Stability analysis suggests that high-frequency actuation is characterized by fd > 2fn,max.
High-frequency actuation modifies the base shear layer:
Region I:
much thicker shear layer and significantly lower natural frequencies
increase in both TKE production and dissipation
“stabilized” flow to fundamental instability
Region II:
thicker shear layer and lower natural frequencies
suppressed peak of TKE and spread of energy in the thicker shear layer
Region III:
Energy of high-frequency actuation is dissipated
No significant alteration of shear layer thickness and natural frequencies
Re-emergence of inviscid instability, but at lower frequency and spatially delayed

30. Discussion: High-Frequency Excitation
The possible mechanism:
- high-frequency excitation of mode M modifies the mean flow through the zero mode changes
- the modified mean flow interacts with the low frequency modes (ω1, ω2,…, 2ωn,max) to redistribute their energy and lower it
M & conj(M)  0  0 & & conj(1)  modified 1;
 0 & & conj(2)  modified 2; …
- As the strength of mode M decreases along the shear layer its effect decreases and low-frequency modes reappear but at lower natural frequencies