Activ e Separ ation Control By
Multiple Cooper ativ e Actuation
v orgelegt v on
Dipl. Ing.
Mar kus Blechschmidt
geb . in Dettelbach
v on der F akultät V - V er k ehrs- und Maschinensysteme
der T echnischen Univ ersität Berlin
zur Er langung des akademischen Grades
- Dr .-Ing.-
genehmigte Disser tation
Promotionsausschuss:
V orsitz ender : Prof . Dr .-Ing. Dieter P eitsch
Gutachter : Prof . Dr .-Ing. W olfgang Nitsche
Gutachter in: Dr . rer . nat. Karin Bauer
T ag der wissenschaftlichen A ussprache: 22.12.2016
Ber lin 2017

Abstract
This thesis aims at reducing the impulse and the required mass flo w needed in acti ve
separation control by pulsed actuation systems. The in vestigated strate gy to achie ve this is
based on the cooperati ve action of multiple ro ws of actuators positioned do wnstream of
each other . As sho wn by the analysis of PIV measurements in conjunction with pressure
measurements, the fluidic ro ws can be actuated such that the flo w structures (v ortices) they
produce are strengthened and stabilized by subsequent actuator ro ws while they propagate
do wnstream. This strategy w as applied to the reattachment of pressure induced separation
on a planar half dif fuser with v ariable step angle. A maximum reduction of
67%
in total
actuation momentum could be achie ved compared with a single ro w of actuators. The
authority requirements on the single actuator can be reduced by
89% c µ
, thus smaller and
lighter actuation de vices can be used to solve the flo w control problem in future. A mass
flo w reduction up to
21%
can be achie ved by using a non-optimized cooperati ve actuation
system. In future, a sa ving of approximately
30%
is estimated if the system parameters,
e.g. the duty c ycle or a control algorithm regarding to the propag ation velocities of the
v ortices, are fine tuned further . It is sho wn that this system is suitable to reattach the flo w
with less resources and therefore it is worth the additional ef fort.

Zusammenfassung
Diese Arbeit zielt darauf ab den Impuls und den Massenstrom eines gepulsten akti ven
Systems zur Beeinflussung abgelöster Strömungen zu v erringern. Um dieses Ziel zu
erreichen wurden mehrere Reihen v on Aktuatoren hintereinander in Strömungsrichtung
angeordnet. Mit Hilfe von PIV und Druckmessungen kann gezeigt werden, dass die
v erantwortlichen Strömungsstrukturen stabilisiert und v erstärkt werden. Dieses System
wurde dann auf einen Halbdif fuser übertragen, bei dem der Stufenwinkel stufenlos eingestellt
werden kann und somit eine Druck induzierte Ablösung erzeugt wird. Die kooperati ve
Aktuatorik erreicht hier eine Reduzierung des gesamten Impulsbeiwertes v on
67%
und
eine Reduzierung des Impulsbeiwertes beim Einzelaktuator v on bis zu
89%
. Damit
lassen sich in Zukunft kompaktere und leichtere Aktuatoren v erwenden oder verw orfene
Aktuator -K onzepte neu beleben. Der Massenstrom lässt sich mit einem nicht optimierten
System um
21%
reduzieren. Es wird angenommen, das bei einer weiteren Optimierung der
Aktuatorparameter , wie z.B. der Pulsweite oder durch die Installation eines Algorithmus der
den Phasenwinkel k ontrolliert, bis zu ca.
30%
eingespart werden können. Es wird gezeigt,
dass mit dieser Art der Strömungsbeeinflussung die Anforderungen an den benötigten
Massenstrom so wie an den Impulsbeiwert der Aktuatoren reduziert werden können. Mit
den erbrachten Einsparungen lässt sich der höhere Systemaufwand insgesamt durchaus
rechtfertigen.

Throughout the centuries
there were men who took first
steps down ne w roads ar med
with nothing b ut their own
vision.
(Rand, A yn)
Ac kno wledgments
The present thesis was de veloped as research associate at Airb us Group Innov ations in
cooperation with the Department of Aeronautics and Astronautics of the Berlin Uni versity
of T echnology . I ackno wledge the support and funding of this work recei ved through the
German national program LuFo 4. I want to especially thank Heribert Bieler from Airb us
Bremen for his support throughout the in vestigations.
First I want to e xpress my sincere thanks to my thesis supervisor , Prof. Dr .-Ing. Nitsche,
for his constant support and encouragement to carry out this work. The discussions, his
comments and editorial advices were helpful to find the o verall direction and essential to
finish this thesis.
It was al ways a pleasure to w ork with the people at the Department of Aeronautics
and Astronautics of the Berlin Uni versity of T echnology . Especially , I would lik e to thank
Marcel Staats and Dr . Matthias Bauer for their assistance and discussions during the wind
tunnel e xperiments.
I also thank my colleagues, W infried Kupk e and Roland W agner , for their technical
assistance and ar guments during my work at Airb us Group Innov ations. P articularly , I
would lik e to thank Rafael Knobling for his friendship and the sometimes heated, b ut
alw ays fruitful discussions we had in Ottobrunn.
I gratefully ackno wledge Dr . Karin Bauer for her support, the constructi ve contrib utions
and her management during my work in her team. It w as a pleasure to work with her on
dif ferent projects. I thank her for her engagement and for gi ving us the opportunity to b uild
up a reasonable lab .
On a personal note, I would like to thank my siblings for the great times we had and
will ha ve. They ne ver f ail in gi ving me the break I need. A special thank go out to my
parents for their lo ve and their unrestricted support throughout my life. P articularly , I
thank my wife, Angela, for her patience, encouragement and lov e. Her e xpertise and
contrib utions more than once sa ved my day .

Contents
1 Intr oduction 1
2 State of the Ar t 3
2 . 1 S e p a r a t i o n c o n t r o l .............................. 3
2 . 1 . 1 S e p a r a t i o n ............................. 3
2.1.2 Strate gies for separation control . . . . . . . . . . . . . . . . . . 4
2.2 Mechanism of periodic actuation . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Flo w control systems . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Influence of actuator parameters . . . . . . . . . . . . . . . . . . 9
2.2.3 Mechanism of shear layer entrainment . . . . . . . . . . . . . . . 12
2.2.4 Existing multiple actuation systems . . . . . . . . . . . . . . . . 14
2.3 Objecti ve and structure of this thesis . . . . . . . . . . . . . . . . . . . . 17
3 Experiments and Methods 21
3 . 1 T e s t f a c i l i t i e s ................................ 2 1
3 . 2 A c t u a t o r ................................... 2 3
3 . 3 M e a s u r e m e n t s e t u p ............................. 2 7
3.3.1 T raditional measurement techniques . . . . . . . . . . . . . . . . 28
3.3.2 P article Image V elocimetry (PIV) . . . . . . . . . . . . . . . . . 30
4 Ev aluation and T rac king 33
4.1 Flo w characterization and ke y parameters . . . . . . . . . . . . . . . . . 33
4.2 Alignment of multiple coherent structures in the flo w . . . . . . . . . . . 38
4.3 V orte x detection and tracking . . . . . . . . . . . . . . . . . . . . . . . . 39
5 In vestigations of V ortex Interaction 45
5.1 V orte x interaction without pressure gradient . . . . . . . . . . . . . . . . 45
5.1.1 Single v ortex propagation . . . . . . . . . . . . . . . . . . . . . 45
5.1.2 V orte x interaction . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2 V orte x interaction in half dif fuser . . . . . . . . . . . . . . . . . . . . . . 53
5.2.1 Basic flo w of half dif fuser . . . . . . . . . . . . . . . . . . . . . 53
5.2.2 Single v ortex influence . . . . . . . . . . . . . . . . . . . . . . . 55
5.2.3 Ef fect of pressure gradient on v ortex interaction . . . . . . . . . . 57
5.2.4 Comparison of single and cooperati v e actuation . . . . . . . . . . 61
6 Ev aluation of Cooperative Actuation 65
6.1 Benefits of vorte x interaction . . . . . . . . . . . . . . . . . . . . . . . . 65
6.1.1 Ef fect of v ortex interaction on flo w properties . . . . . . . . . . . 65
6.1.2 Momentum coef ficient reduction . . . . . . . . . . . . . . . . . . 67
i

Contents
6.1.3 Mass flo w reduction . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2 Outlook and future work . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7 Conc lusion 77
Bibliograph y 81
ii

List of Figures
2.1 Pressure induced separation on a curved surface [5] . . . . . . . . . . . . 4
2.2 Mechanism of high lift de vices . . . . . . . . . . . . . . . . . . . . . . . 5
2.3
Smoke flo w visualization at two dif ferent frequencies sho wing large v ortical
spanwise structures which are responsible for lar ge momentum transfer [
56
]
6
2.4 Classification of actuators (a) and distinction of periodic actuation (b) . . 7
2.5 Example of dif ferent actuator types . . . . . . . . . . . . . . . . . . . . . 8
2.6
Reattachment process at dif ferent blo wing angles at midspan of the dif fuser
step. The mean v elocity is subtracted from the vector fields. blue:
clockwise v ortex; red: counter-clockwise v ortex [33] . . . . . . . . . . . 11
2.7
Schematic dra w of a radial jet in cross flo w and the v orticity field of a
s l o t t e d j e t i n c r o s s fl o w ........................... 1 3
2.8 Shear layer and horseshoe v ortices of a jet in cross flo w [24] . . . . . . . 13
2.9 Schematic dra wing of the mechanism af fecting the reattachment process . 14
2.10 Flo w structures for v arious actuation modes [73] . . . . . . . . . . . . . . 15
2.11 Buildup for distrib uted flo w control at AoA α = 11 ◦ [ 7 2 ] ......... 1 6
2.12 Ov erall system ef ficienc y calculated with Equation 2.9 [82] . . . . . . . . 17
2.13 Schematic dra wing of v ortex mer ging by cooperati ve actuation . . . . . . 18
3.1 W ind tunnel O TN - L WK2 . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 W ind tunnel TUB - GSW (after [32]) . . . . . . . . . . . . . . . . . . . . 22
3.3 Section of used geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Geometry of the actuator . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.5 V elocity profiles of the actuator . . . . . . . . . . . . . . . . . . . . . . . 25
3.6 Correlation of continuity and hot wire v elocities . . . . . . . . . . . . . . 26
3.7 Characteristics of the actuator for the GWK at 100 Hz ........... 2 6
3 . 8 M e a s u r e m e n t C h a i n ............................. 2 7
3.9 Sketch of W all mounted pressure sensors, after [32] . . . . . . . . . . . . 29
3.10 Principle 2D/2C PIV Setup, after DLR [18] . . . . . . . . . . . . . . . . 30
4.1 Principle of phase a v eraging . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2
Assembled flo w field of two dimensional hot wire measurements (
1342
single measurement points) for dif ferent phase angles . . . . . . . . . . . 35
4.3
Cross correlation of two hot film sensor signals with characteristic time
delay ∆ t ( a f t e r [ 5 5 ] ) ............................ 3 6
4.4 V orticity and λ 2 criteria for the same flo w field with two v ortices . . . . . 37
4.5 Isosurfaces of blo wing with dif ferent phase shifts (red +2 m
s , blue − 2 m
s ) . 38
4.6
Example of real (left) and rele vant (middle) v elocities of one slice and the
fitted line of the RANSA C algorithm (right) . . . . . . . . . . . . . . . . 39
4.7 Single steps of v orte x detection . . . . . . . . . . . . . . . . . . . . . . . 40
iii

List of Figures
4.8
V orticity distrib ution around the center (red cross) of a nearly circular
s h a p e d v o r t e x ................................ 4 1
4.9 Edge detection for dif ferently shaped v ortices . . . . . . . . . . . . . . . 42
4.10
W orking principle (a,b) of tracking algorithm and o verall result of detection
a n d t r a c k i n g ................................. 4 3
5.1
Original hot film data and propagation v elocity of a V ortex at a v elocity
ratio V R = 1 . 5 and Re ynoldsnumber R e = 6 . 87 e 5 ............ 4 6
5.2 Dependencies of v orte x propagation velocity v conv ............. 4 7
5.3 Propagation ratio ov er v elocity ratio . . . . . . . . . . . . . . . . . . . . 47
5.4 T ime resolv ed PIV visualizations of single actuation on a flat plate . . . . 48
5.5
Comparison of computed v ortex propag ation velocity from hot film and
PIV data for v ∞ = 20 m
s and a v elocity ratio of V R = 2 . 5 ......... 4 8
5.6
Interaction of two co-rotating v ortices
Θ = 84 ◦
. (a) Appearance of first
v orte x
t = 0 ms
(b) Inducing second v orte x
t = 0 . 34 ms
(c) First v orte x is
pushed upwards
t = 0 . 68 ms
(d) Both v ortices interfering with each other
t = 1 . 36 ms ................................. 4 9
5.7
Destructi ve interaction of tw o co-rotating v ortices
Θ = 92 ◦
. (a) Appearance
of first v ortex
t = 0 ms
(b) Second actuator starts blo wing
t = 0 . 34 ms
(c) First v orte x resolves
t = 0 . 51 ms
(d) Second v orte x with less v orticity
t = 0 . 85 ms ................................. 5 0
5.8
Cooperati ve interaction of tw o co-rotating v ortices
Θ = 72 ◦
. (a) Appearance
of first v ortex
t = 0 ms
(b) First step of v orte x merging
t = 0 . 34 ms
(c) Bigger v orte x builds up
t = 0 . 51 ms
(d) Stronger v orte x propagates
do wnstream t = 0 . 85 ms .......................... 5 1
5.9
Comparison of the v orticity for dif ferent phase shifts. Counter -clockwise
rotating (red) and Clockwise rotating (blue) (a) Simultaneous blo wing of
two ro ws (b) Computed phase shift
Θ = 100 ◦
(c) Constructi ve interaction
for phase shift Θ = 89 ◦ (c) Destructi ve interaction at phase shift Θ = 150 ◦ 52
5.10
(a) Schematic separation conditions and positions of the pressure transducers.
(b) Pressure reco very o ver the step angles for the half dif fuser . . . . . . . 54
5.11
Flo w visualization of the half diffuser at a step angle
α step = 23 ◦
and
v ∞ = 20 m
s
. The positions of the inacti ve actuators (
v j et = 0 m
s
) are sho wn
relati vely to the separation. . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.12 Single v orte x after t = 0 . 34 ms and related vorte x pair after t = 4 . 2 ms . 55
5.13
V orticity , propagation ratio and direction of the v ortices propagation, which
emer gence for single actuation . . . . . . . . . . . . . . . . . . . . . . . 56
5.14
Flo w field, v orticity and propagation ratio for simultaneous blo wing. Phase
shift
Θ=0 ◦
, V elocity Ratio
V R = 2 . 4
, Step Reynoldsnumber
Re H =
174000 .................................... 5 7
5.15
Flo w field and vorticity for constructi ve interaction. Phase shift
Θ = 105 ◦
,
V elocity Ratio V R = 2 . 4 , Step Reynoldsnumber Re H = 174000 ..... 5 8
5.16
Sequence of v orte x merging process for
Θ = 105 ◦
at a step Re ynoldsnumber
of Re H = 174000 .............................. 5 9
5.17 V orticity and propagation ratio for a phase shift of Θ = 150 ◦ ....... 5 9
i v

List of Figures
5.18
Sequence of a destructi ve v orte x interaction for
Θ = 150 ◦
at a step
Re ynoldsnumber of Re H = 174000 .................... 6 0
5.19
Half dif fuser flow for an unactuated case at
v ∞ = 20 m
s
with the marked
lines where the normal v elocities are analyzed. The position are related to
the actuator slot positions . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.20
Normal v elocities for dif ferent actuation cases ov er period. (a-c) Single
actuation. (d-f) Simultaneous blo wing (
Θ=0 ◦
). (g-i) Constructi ve phase
shift ( Θ = 105 ◦ ) .............................. 6 2
6.1 Description and main findings of the RANSA C algorithm . . . . . . . . . 66
6.2
Comparison of v orticity (eddy viscosity) between cooperati ve actuation
and simultaneous blo wing . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.3
Pressure reco very
∆ c p
o ver dif ferent phase shifts
Θ
compared to single
actuation with ˙ m 1 = 0 . 0028 kg
s ....................... 6 8
6.4 Pressure reco very ∆ c p o ver dif ferent phase shifts Θ for ˙ m 3 = 0 . 003 kg
s . . 68
6.5
Comparison between cooperati ve actuation and single actuation (pink
dotted line) for dif ferent momentum coef ficients . . . . . . . . . . . . . . 69
6.6
Comparison of single actuation to cooperati ve actuation in relation to the
o verall momentum coef ficient c µ ...................... 7 0
6.7
V elocity profiles at certain distances for single actuation with a momentum
coef ficient of c µ, 1 = 0 . 22 % ......................... 7 1
6.8
V elocity profiles at certain distances for cooperati ve actuation with a
momentum coef ficient of c µ, 3 = 0 . 073 % .................. 7 2
6.9
V elocity profiles at certain distances for cooperati ve actuation with a
momentum coef ficient of c µ, 3 = 0 . 067 % .................. 7 2
6.10
Pressure reco very for single and cooperati ve actuation with re gard to the
o v e r a l l m a s s fl o w .............................. 7 3
6.11
The mer ging process of a system configuration where the second and third
ro w hav e a duty c ycle of
Λ 2 , 3 = 25 %
. The step angle is
α = 23 ◦
with an
incident flo w of u ∞ = 20 m
s ......................... 7 4
6.12
Estimated additional mass flo w savings at the same o verall momentum
coef ficient
c µ, 3
for dif ferent duty cycles
Λ
and dif ferent actuation concepts.
Duty c ycle lo wered for the 3rd ro w and the the other two ro ws still set to
50 %
(blue). Duty cycle lo wered for the 2nd and 3rd row , b ut still
50 %
for
the first (red). Duty cycle lo wered for all rows (black). . . . . . . . . . . 75
v

List of Figures
vi

Nomenc lature
Roman Letters
u, v , w v elocity components [ m
s ]
u 0 , v 0 , w 0 fluctuation v elocity components [ m
s ]
¯ u, ¯ v , ¯ w time a v erage velocity components [ m
s ]
˜ u, ˜ v , ˜ w median v elocity components [ m
s ]
h u i , h v i , h w i phase locked v elocity components [ m
s ]
c µ Momentum coef ficient [-]
c p Pressure coef ficent [-]
V R V elocity Ratio [-]
P R Propagation Ratio [-]
Re Rynoldsnumber [-]
F + Strouhalnumber [-]
f Frequenc y [ 1
s ]
f g Cuttof f Frequency [ 1
s ]
F s Sample frequenc y [ 1
s ]
˙ m Mass flo w [ k g
s ]
˙
V V olume flo w [ l
min ]
Ma Mach number [-]
T u Grade of turb ulence [%]
Gr eek Letters
α step Step angle [ ◦ ]
Θ Phase of e xcitation [ ◦ ]
ω V orticity [ 1
s ]
Λ Duty Cycle [ % ]
∆ Dif ference
∆ c p Pressure reco very [-]
σ Standard de viation
Φ Cross correlation, Phase angle [ ◦ ]
Subscript
1 , 2 , 3 number of actuator (ro w)
40 40 mm distance of two actuator
H Height
c Calibration
∞ refer to incident flo w
i control v ariable
j et refer to jet
vii

Nomenclature
LE Leading Edge
x refer to position
Abbr e viations
A Area
AFC Acti ve Flo w Control
AFM Aerodynamic Figure of Merit
AR Aspect ratio
CT A Constant T emperature Anemometer
CCD Char ged Coupled De vice
DEHS Di-Ethyl-He xyl-Sebacat
DSP Digital Signal Processing
ER Expansion Ratio
HF Hot Film
PID Proportional Inte gral Deri v ativ e
PIV P article Image V elocimetry
RMS Root Mean Square
TR-PIV T ime Resolv ed Particle Image V elocimetry
ZNMF Zero-Net-Mass-Flux
viii

1 Intr oduction
The wing design is a major topic for aircraft manufactures all o ver the w orld. Most of
the time an operating aircraft is in the flight phase called cruise . In this flight phase
the aircraft tra vels at high altitude and high subsonic speed. Since it spends most of
the time, especially on long distance routes, in this state, the wing is optimized for this
conditions. The cruise and induced drag as well as the fuel consumption are a fe w e xamples
of the engineering ef fort wing aerodynamicists are dealing with. Different systems are
employed lik e sophisticated wing tips, super critical airfoils or high-bypass engines to
enhance the aerodynamics. Despite the enormous ef fort to maximize the performance of
these wings, there are still some critical regions, especially in lo w speed flight conditions,
like the start and landing phase. In these specific flight phases the performance must be
enhanced by using high lift de vices. The common solution is to extend slats and flaps,
which are changing the geometry and therefore the aerodynamics of the wing. They enable
higher angle of attacks and thus higher lift coef ficients, before the flo w separates from
the wing. These de vices hav e been optimized ov er the years to enhance the performance.
Unfortunately the high lift de vices increase the ov erall system ef fort and increase weight.
Ne vertheless there are no alternati ves to date.
Although the optimization has been enhanced, mainly two re gions are still challenging.
Namely the leading edge of the outer wing and the pylon wing inte gration of the jet engines.
Due to the restricted space requirements, it is not possible to deplo y slats at these positions.
These are the locations, which are endangered to separate, due to the unco v ered leading
edge at angles of attack where the remaining wing is still in its working range.
Here, acti ve flo w control (AFC) systems can be deployed to solv e this issue. It is prov en
that AFC is capable of reattaching or at least delaying separated flo w [
57
,
71
]. Such a
system would increase the performance of the high lift de vices to wards higher angles of
attack. Up to date, there is no commercial airliner equipped with an acti v e flo w control
system.
Ho wev er , there is al ways a dra wback. An AFC system, capable of dealing with these
flo w conditions, requires a large amount of ener gy or mass flo w of pressurized air . This
mass flo w must be provided during the flight and is tak en either from the jet engine or an
additional pressure source. Both methods would lead to cutbacks. When, that the mass flow
is pro vided from the engine, a loss of performance is gi ven and using an e xternal pressure
source, additional weight is added to the aircraft. Moreov er , due to the restricted space
requirements, especially at the outer wing, smaller and lighter actuators are preferable.
The reattachment process by means of pulsed blo wing is mainly utilizing dynamic flo w
processes to increase the momentum within the separated area. This is done by supplying
high ener gy fluid by means of the mass flo w and to redistribute the fluid through the shear
layer caused by the separation. This redistrib uting is dri ven by coherent structures induced
by the pulsed blo wing into the flow . These coherent structures are primarily lar ge scale
v ortices. These vortices are depending on the e xcitation parameters, e.g the frequenc y ,
1

1 Introduction
duty c ycle or the angle of the jet. Especially the latter has an ef fect on the formation and
beha vior of the v ortices.
The aim of the present dissertation is to define ho w these vortices can be enhanced and
stabilized during their do wnstream propagation. Thereby the beha vior of two co-rotating
v ortices is systematically in vestigated during the interaction process. The dri ving parameter
to mer ge these v ortices is found using a non-intrusi v e measurement technique on a flat
plate. This kno wledge is then transferred to a half dif fuser , where a pressure induced
separation is pro vided. The influence of an adverse pressure gradient on the interaction
process has been e xamined successfully . Utilizing this mer ging ef f ect, the dynamic actuator
parameters can be reduced. An additional estimation of the mass flo w savings, achie v able
by the cooperati ve actuation, is pro vided.
This fundamental research of a ne w actuator concept represents a fresh approach to solve
flo w separation and thereby shows auspicious results. It also prepares the ground for further
in vestigations and de velopments.
2

2 State of the Ar t
Flo w separation describes the phenomena, when flo w detaches from a surface or wall
located in a stream. The origin of this behavior as well as the dif ferent mechanism to
o vercome this flo w e vent, are described in this section. The advantages and disadv antages
of se veral acti ve flo w control methods are sho wn and an ov ervie w of pulsed blowing is
gi ven. T o deepen the subject of pulsed blo wing, the mechanism of a jet in cross flo w and
the parameters to trigger this e vent are described.
The idea and no velty of multiple cooperati ve actuation are set in conte xt to existing acti ve
separation control methods. Moreo ver the necessity to perform basic in v estigations and
the aim of this thesis are described.
2.1 Separation contr ol
2.1.1 Separation
Separation of flo w occurs if a viscous fluid does not follow the body contour and is mainly
distinguished in geometry induced and pressure induced separation. Geometry induced
separation arises if flo w separates stationary on a fixed edge or an unsteady contour by
means of the mass inertia of the fluid. If the flo w detaches because of a positi v e pressure
gradient ∂ p
∂ x > 0 , it is called pressure induced separation as sho wn in Figure 2.1.
In this thesis a ne w method to reattach pressure induced separation is presented and
therefore the mechanism of this kind of separation is e xplained in the follo wing with
respect to an incompressible fluid. The boundary layer before the separation is marked as
turb ulent. The kinetic ener gy of a fluid is con verted into pressure by means of deceleration
of the flo w . This occurs, for e xample, at cross section expansion of a dif fuser , where
the static pressure is constantly increasing in flo w direction. This leads to a positi ve
pressure gradient in direction of flo w
∂ p
∂ x > 0
. The pressure gradient of the boundary
layer perpendicular to the flo w
∂ p
∂ y
can be ne glected. Referring to Prandtl’ s boundary layer
hypothesis the static pressure of the e xternal flo w is influencing the boundary layer and
therefore the deceleration of the flo w is directly linked to the boundary layer and leads
to a deceleration of the velocity gradient
( ∂ u
∂ y ) W
. W ith increasing pressure gradient the
deceleration of the v elocity is also increasing and by means of decreasing kinetic ener gy .
If the positi ve pressure gradient becomes too high the fluid is slo wed do wn to standstill
( ∂ u
∂ y ) W = 0
. At this point the wall shear stress also becomes zero
τ w = 0
and the fluid
separates from the contour . After this point a recirculation area b uilds up due the further
deceleration of the v elocity close to the wall. This deceleration results in the fluid flo wing
against the main flo w direction
( ∂ u
∂ y ) W < 0
. This recirculation area distract the flow a way
from the wall and a shear layer between recirculation area and e xternal flow is b uild up
3

2 State of the Art
Figure 2.1: Pressure induced separation on a curv ed surface [5]
(see Figure 2.1). The reattachment process is triggered by the de velopment of v ortices in
the free shear layer which leads to a momentum e xchange between the recirculation area
and the e xternal flo w . In case of a curved surf ace, e.g. a half dif fuser , the recirculation
area is bounded by the wall and therefore the separation is reattached because of the more
intense momentum transfer [8].
2.1.2 Strategies for separation contr ol
In fluid mechanics flo w control means changing the state of flo w by specific measures. The
comple xity and dynamic of the control system are determined by the state of the flo w . The
method of flo w control has to be coordinated with the the flow beha vior to maximize the
mechanism to reach a certain ef fect. Using the right flo w control method it is possible to
influence the flo w in a positi ve w ay , e.g. drag reduction or lift increase, which leads to an
economic adv antage.
The methods are principally distinguished in
passiv e
and
activ e
methods [
25
], where
passi ve methods do not require auxiliary po wer or a control loop, while acti ve de vices need
ener gy expenses. There are dif f erent passi ve methods to deal with separation. The physical
principles can be subdi vided as follo ws [32]
• Shear layer entrainment
• Momentum increase
• Influencing the pressure gradient ∂p
∂x
• Modifying the boundary layer profile ∂u
∂y
V ortex generators are an e xample for shear layer entrainment and can delay separation
locally . This is done by supplying high energy fluid to the separation prone area by
4

2.1 Separation control
(a) Schematic flow around slat and flap [2]
(b) Lift-to-drag ratio comparison of slat and flap [
67
]
Figure 2.2: Mechanism of high lift de vices
generating longitudinal v ortices [
45
]. These v ortex generators ha v e the disadv antage of
producing parasitic drag, e ven if the boundary layer is not separation prone. Switching
the boundary layer to turb ulent is another form of passi ve flo w control. Due to the higher
v elocity gradient, the turb ulent boundary layer is more resistance against separation[63].
Ho we ver , the most common standard of passi v e flo w control is to optimize the shape of the
airfoil. Hereby , the geometry of an airfoil is optimized during the design process to ensure
a less pronounced positi ve pressure gradient and therefore the flo w remains attached ov er a
longer distance [
71
,
50
]. It is also possible to supply energy to the separation prone flo w
by adding further elements to the airfoil geometry . These elements, normally slats and
flaps, supply energy from the surrounding flo w field, enhancing the lift to drag ratio as
sho wn in Figure 2.2 . Using flaps increases the curv ature of an airfoil and therefore the
circulation around the profile. The circulation then increases the lift by
∆ c l
. Hereby higher
lift coef ficients can be reached at the same angle of attack
α
compared to the baseline
without an y flap. On the other hand the higher curv ature also leads to an increase of the
pressure gradient which results in a higher load of the airfoil. Therefore the maximum lift
is reached at smaller angle of attack. The separation can then be pushed to higher angles of
attack by using a slotted flap. This slot supplies the separation prone boundary layer of the
suction side with ener gy from the pressure side of the airfoil. This effect can be enhanced
e ven further by using multiple slotted flaps.
Another way to reach a higher maximum lift at higher angles of attack is to install slats. The
pressure distrib ution is manipulated by the flo w through the slot between slat and airfoil in
such a way that the positi v e pressure gradient decreases. This ef fect delays separation to a
higher angle of attack and increases maximum lift
C l,max
. The buo yancy at lo wer angles
5

2 State of the Art
of attack is hardly af fected by the slats [74].
Acti ve flo w control af fects the velocity profile by injecting high ener gy fluid, sucking low
ener gy fluid or redirecting high ener gy fluid to the wall. The impulse of the flow is acti v ely
increased by these actuator systems, which are al ways supplied by an e xternal energy
source. The adv antages of these systems are that the flo w control can be adjusted to the
flo w conditions, and they can be turned on and of f, depending on whether they are needed
or not. The rele v ance of acti ve flo w control was sho wn by Ludwig Prandtl by implementing
a boundary layer suction on a circular c ylinder , delaying the separation of the cylinder
flo w [
60
]. In the late 1920s Bamber [
3
] in vestigated the ef fect of steady blo wing on the
lift-to-drag ratio. Furthermore the parameters of the slot were in vestigated. It was pro ven
that the lift-to-drag ratio of a con v entional two dimensional airfoil could be increased up
to
150 %
. W ith the definition of the momentum coefficient
C µ
by Poisson-Quinton an
ef fecti ve scaling parameter w as found. An extensi ve re vie w of the boundary layer control
with steady working actuator systems is gi v en by Lachmann [41].
Since the rele vance of momentum w as sho wn, Collins and Zelene vitz [
10
] demonstrated
that acoustic and therefore periodic e xcitation can increase the momentum near the surface
by transferring it from the free-stream. A lot of experiments were done later on, addressing
dif ferent issues of acoustic excitation [
87
,
1
,
53
]. Despite of the disadv antages of such
systems, e.g. comple xity and high amplitude of excitation, the ef fecti veness of pulsed
blo wing was sho wn. In a next step the e xcited mixing layer was e xamined [56, 34, 6, 35].
It is no w accepted that large v ortical, spanwise structures are the b uilding blocks of the
mixing layer and are responsible for the momentum transfer across its e xtent [
28
] (See
Figure 2.3). A detailed discussion of the mechanism of inciting the instabilities of a shear
layer is gi ven in section 2.2.3. Further in v estigations of periodic excitation are more
application oriented e.g. airfoils and high-lift configurations. The e xaminations range from
generic flaps [
54
], N A CA airfoils [
39
,
69
], trailing edge flaps without slot [
68
,
47
] to single
slotted flaps [
80
,
85
]. The focus of these e xaminations are the ef fect of the acti ve flo w
control on an o verall aerodynamic configuration with re gard to lift enhancement and drag
reduction.
The flo w reattachment method introduced in this thesis, is by means an acti ve flo w control
method and furthermore periodic actuation is used. Therefore the ne xt sections giv e an
o vervie w ov er the mechanism of periodic actuation.
Figure 2.3:
Smoke flo w visualization at two dif ferent frequencies sho wing lar ge vortical
spanwise structures which are responsible for lar ge momentum transfer [56]
6

2.2 Mechanism of periodic actuation
2.2 Mechanism of periodic actuation
2.2.1 Flow contr ol systems
Pro viding periodic excitation dif ferent designs of actuators can be used. There are
oscillating flaps, fle xible surfaces, rotating v alves, plasma, comb ustion dri ven and fluidic
actuators and mechanical v alves. An detailed and comprehensi ve o vervie w and comparison
of all kinds of actuators are gi ven by Cattafesta III & Sheplac [
7
]. A useful classification is
or ganizing the actuators by function.
Fluid injection or suction, in Figure 2.4(a) the fluidic part b uilt hereby the most common
type of actuators. W ithin the fluidic type the actuators hav e to be distinguished between
continuously and periodic working systems (Figure 2.4(b)). The periodic systems hav e
the adv antage of reducing the amount of ener gy needed to reattach the separated flo w
compared to continuously working actuators. The disadv antage, on the other hand, is that
the system becomes more comple x. In addition, the periodic systems are di vided into
oscillating blo wing and sucking, so called zero-net-mass-flux (ZNMF) [
88
] and pulsed
blo wing where the fluid is externally pro vided. The oscillating sucking and blo wing result
in a time a veraged jet abo ve the actuator slot which pro vided a positi ve momentum into
the flo w . This jet is called synthetic jet [
27
] (see Figure 2.5(a)). The synthetic jet sucks in
lo w momentum fluid from the boundary layer and blo ws the sucked in fluid back in the
flo w . Since there is no e xternal fluid supply this actuator has a time-av eraged net-mass-flux
of zero. The oscillation is generated electrically and is con verting electric po wer into fluid
po wer as a result. A lot of ef fort was put into the in vestig ations of synthetic jets to ov er
come the disadv antages of these actuators e.g. the limitation in frequencies [
61
], heat
de velopment and lo w momentum and velocity output [
76
]. An extensi ve o v ervie w on
synthetic jets and their application is gi ven by Glezer and Amitay [27].
A de vice which can generate high jet velocities is the pulsed comb ustion actuator (see
Figure 2.5(c)). The high momentum jet is produced by igniting a fuel oxidant mixture
[
16
] which triggers a detonation. This detonation causes a rapid pressure increase in the
(a) A type classification of flow control actuators [
7
]
(b) Classification of fluidic actuators for activ e flow
control [32]
Figure 2.4: Classification of actuators (a) and distinction of periodic actuation (b)
7

2 State of the Art
ca vity which then ejects the unb urned air through an orifice, b ut also emits the comb ustion
products. This possible compact design provides a high ener gy density with high jet
v elocities. Using auto-ignition by reflecting pressure wa v es and ca vity resonance [
16
]
the pulse repetition rate can be increased from
f ≈ 100 Hz
up to
f ≈ 1 kHz
[
13
]. The
dra wbacks of this type of actuation are that the emitted comb ustion products are e xtremely
hot and comb ustible material is required. Moreov er an additional engine process within
the wing or aircraft is not v ery desirable.
An actuator which o vercomes a dra wback all other ha ve, is the fluidic oscillator [
78
] or
fluidic actuator [
4
]. This de vice has no moving or electrical components and is therefore a
simple and rob ust de vice (see Figure 2.5(d)). The working principle was first patented in
1964 [
38
] and relies on the principle that a primary jet is switched between two stable states.
These actuators are sub-cate gorized in self-switching and external triggered de vices. The
e xternal trigger can be mechanical components [
15
], plasma actuators [
30
] or piezoelectric
benders [
29
]. The self-switching de vices can be divided in actuators with mass flo w
feedback and pressure feedback [
51
]. Other actuators follo wing the same principle as well
as the physical beha vior are explained in detail by Bauer [
4
]. Besides the adv antage that
no mo ving parts are in v olv ed, these actuators can provide high jet v elocities within a large
frequenc y range. On the other hand, an e xternal pressurized fluid supply is still necessary
and the amplitude and frequenc y are directly coupled for practical designs.
In order to reduce the de velopment ef fort for experiments, mechanical v alv es can be used.
(a) Synthetic jet with piezoceramic
diaphragm [7]
(b) Mechanical valv e [4]
(c) Resonant Detonation Actuator [16] (d) Fluidic oscillator with feedback loop [77]
Figure 2.5: Example of dif ferent actuator types
8

2.2 Mechanism of periodic actuation
These of f the shelf v alves operate with a plunger dri v en by a solenoid, opening and closing a
flo w channel (see Figure 2.5(b)). These de vices need pressurized air as an inlet and a slotted
actuator to work as an acti v e flo w control de vice [
57
]. The actuator normally transforms
the flo w from a round inlet to a slotted outlet (aspect ratio
>> 1
). The performance of the
system is gi ven by the v alve technique, where the switching time is dominating the duty
c ycle depending on the frequency . The amplitude is regulated by the mass flo w rate and is
also depending on the v alve technique. Fast switching solenoid v alves (e.g. Festo
TM
MHE )
keep the balance between amplitude and frequenc y . The duty c ycle and frequency are also
controllable o ver a wide range. The response of the jet velocity to the trigger signal is
depending on v arious factors like the chamber of the actuator and the length of the hoses
connecting the actuator with the v alve. Another often used actuator are the rotary v alv es
[
68
], which can pro vide high frequencies (up to
f = 1 kHz
) and high mass flo w rates. The
duty c ycle is fixed and therefore can not be v aried during an e xperiment. Since the flo w is
unidirectional from the inlet to the outlet, these actuators ha ve a positi v e net-mass-flux and
thereby belong to the injection type actuators. Periodic excitation is characterized by some
parameters. These can be di vided in physical and geometrical parameters. Physical ones
include the frequenc y , the duty c ycle and the amplitude and can also be called v ariable
parameters. The geometrical ones are related to the actuator and contain the shape and
the direction of the slot, b ut also the position of the actuator in the experiment. The flo w
conditions are commonly v aried in terms of the similarity parameters Mach number and
Re ynolds number . Nev ertheless the actuation system itself has to be in accordance with
the corresponding e xperiment and therefore the optimal exciting parameters can not be
directly transferred from one in vestigation to another [86].
2.2.2 Influence of actuator parameters
The physical parameters are also called v ariable parameters, because they can be v aried
during the e xperiments. Se veral parameters are used in acti ve flo w control and are presented
in a normalized form. Frequenc y is generally defined, analogously to the Strouhal number ,
as normalized frequenc y F + and gi ven in Equation 2.1.
F + = S t = f AF C · l r ef
u ∞
(2.1)
The frequenc y is normalized by the characteristic length
l r ef
and the incident v elocity
u ∞
.
In general, the distance between actuator and trailing edge of the model is used for
l r ef
.
Thereby the introduced v orte x structure refers to the length of the separation area of the
step or flap. This implies that, with a dimensionless frequenc y of
F + = 1
, the wa velength
of the generated oscillation correspond exact to the characteristic length of the model.
Sometimes the step height H or the diameter of a dif fuser D is also taken. Depending on the
normalized frequenc y the dif ferent scales of v ortex structures are generated. By increasing
the frequenc y the single v ortices are decreasing until no coherent vorte x structures can be
identified an ymore, when
F + = 10
[
26
]. W ith small excitation frequencies the coherent
v ortex struc tures are leading a periodic attachment of the free shear layer to the surface,
whilst with high frequencies the form of the model is changed by a v orte x layer ( trapped
vorticity [26]) which pre vent separation in the first place.
9

2 State of the Art
The duty c ycle describes the ratio between the time of blowing through the slot
τ
to the
length of the period
T = 1
f
of the actuator and is therefore linked to the frequenc y . In
Equation 2.2 the duty c ycle is gi ven as a percentage, where
Λ = 0 %
means no actuation
and
Λ = 100 %
is steady blo wing. In case of fast switching solenoid v alves it can be v aried
between
20 %
and
80 %
due to the response time of the v alve. Normally a duty cycle of
Λ = 50 % is used, which means the blo wing time and pause are equal.
Λ = τ
T · 100 (2.2)
The ne xt parameter , the velocity ratio
V R
is stated by Nagib et al.[
52
] to be the dominating
factor . It describes the ratio of the peak jet v elocity to the free stream velocity as gi ven in
Equation 2.3.
V R = u j et
u ∞
(2.3)
T o in vestig ate the influence of se v eral parameters Nagib et al. v aried the geometrical
actuator parameter by changing the width of a tangential blo wing jet. By doing so the y
were able to alter the momentum coef ficient and the velocity ratio independently of each
other . It has been sho wn that the acti v e flo w control performance is increasing the narro wer
the actuator slot, leading to the highest velocity ratio, whilst the momentum input is the
same.
The v elocity ratio depends on the actuator geometry and position, therefore this parameter
is not suf ficient to establish comparability between actuation concepts. Thus the introduced
momentum or the interference momentum is taken in form of the momentum coef ficient.
This coef ficient is a ratio of the interference momentum with regard to the momentum of
the incident flo w and is gi ven in the generalized form for steady blo wing in Equation 2.4.
c µ = J
q ∞ · A r ef
(2.4)
The momentum of incident flo w is giv en by the free stream dynamic pressure
q ∞
and a
reference area
A r ef
, e.g. the entry area of the wind tunnel [
79
] or the projected area of
the model [
4
]. The momentum introduced by the acti ve flo w system
J
can be gi ven as
˙ m · u j et
[
79
]. The time av eraged mean value of the jet v elocity
u j et
would lead to a f alse
result because the duty c ycle of a system would not be taken into account. Therefore the
RMS-v alue of the jet velocity , which rates the ef ficienc y of the blo wing, can be used [32]
and is gi ven in Equation 2.5.
u j et,RM S = r τ
T · e u 2
j et = 1
p τ
T
· u j et (2.5)
where
e u j et, ˙ m = ˙ m
ρ · A slot
· 100
Λ (2.6)
is the jet v elocity depending on the mass flo w , duty cycle and the area of the slot. W ith
Equation 2.5 the momentum coef ficient can be calculated analogously to the Equation for
steady blo wing.
c µ = ˙ m j et · u j et,RM S
q ∞ · A r ef
(2.7)
10

2.2 Mechanism of periodic actuation
Based on Equation 2.7 the momentum coef ficient can be determined with regard to the mass
flo w for e very single duty c ycle. Even though the momentum coef ficient
c µ
is commonly
used to quantify the amplitude of forcing, it is not consistently defined and therefore the
comparability is hardly gi ven and has to be e xamined carefully .
The geometrical parameters are usually hard factors and gi ven by the design of the actuators.
The main parameters are the shape of the slot, the jet angle with regard to the model surf ace
and also the position of the actuator slot relating to the separation. The shape of the slot
orifice is mostly distinguished between radial-symmetric and rectangular . Other shapes are
in vestigated by Sale wski et al. [
64
], e.g elliptic or square ape x, b ut only with small aspect
ratios (
<< 1 . 5
). The similarity between radial-symmetric and rectangular jets with a small
aspect ratio (
≈ 1
) are almost identical and discussed by Plesniak and Cusano [
58
]. Also the
jet cross section, the diameter for holes and the width of the rectangular slot are rele vant
for the separation control task since the mass flo w rate and the jet velocity depends on this
parameter . Therefore, the velocity ratio for a gi ven momentum coef ficient is determined.
The location of the AFC system is normally stated upstream of the time a v eraged detachment
line. T roshin and Seifert [
82
] demonstrate that the most ef fectiv e and ef ficient actuator
slot is close by , b ut upstream of the separation. Shmilovich and Y adlin [
72
] numerically
(a) Jet angle 30 ◦ , diffuser angle 23 ◦
(b) Jet angle 90 ◦ , diffuser angle 22 ◦
Figure 2.6:
Reattachment process at dif ferent blowing angles at midspan of the dif fuser
step. The mean velocity is subtracted from the v ector fields. blue: clockwise
v orte x; red: counter -clockwise v ortex [33]
11

2 State of the Art
in vestigated tw o dif ferent positions for ZNMF actuators on a simple hinge flap. The one
located upstream of the separation gains
79 %
more lift then the one located do wnstream.
Ho wev er , there are no reasons gi ven for this ef fect. Dif ferent experiments to e xamining
the actuator location, ranging from leading edge to trailing edge, high deflected flaps and
circular c ylinder , were done by W ygnanski [86].
The jet angle relati ve to the local surface influences the strength and characteristics of
the induced v ortices. Hecklau [
32
] in vestigated the impact of dif ferent jet angles on
the flo w structures. Dif ferent parameters, like duty c ycle, amplitude and mechanism of
reattachment are analyzed independently of each other . The mechanism of reattachment
can be distinguished with re gard to the jet angle. Using a perpendicular jet, the reattachment
process is triggered by the induced v ortices only . Due to the high penetration depth of
the jet, the v ortex structure becomes more complex as sho wn in Figure 2.6(b). Thus,
the reattachment is only initiated by the e xchange of fluid through the shear layer . The
adv antage of this angle is that only a small impulse is necessary to b uild up a v ortex and
therefore the duty c ycle can be kept small. Moreo ver , a high duty cycle can trigger a
separation by itself. A lo w jet angle, in contrast, has the adv antage by using an additional
ef fect, called the Coand
ˇ
a ef fect. This ef fect causes a flo w to wards the w all by means of the
attached jet flo w which further delays the separation. The dif ferent mechanisms of the jet
angle are sho wn in Figure 2.6.
The aim of this in vestigation is to enhance the fluid transferring v ortices and therefore it is
necessary to induce full de veloped v ortices as it happens with a
90 ◦
jet. On the other hand
the additional ef fect is also considered. Hence, for this experimentation a
45 ◦
jet angle
was chosen to combine the benefits of both.
2.2.3 Mechanism of shear la yer entrainment
The reattachment process is triggered by mainly two mechanisms, which are directly
increasing the momentum of the separation area and through shear layer entrainment. T o
understand the shear layer entrainment the mechanisms of a jet in cross flo w (JICF), which
are in vestigated elaborately in the recent years [
36
,
65
,
19
,
24
] are described. The jet is
superimposed by the cross flo w and is deflected in the direction of the flo w (see Figure
2.7). Depending on the v elocity ratio the penetration depth and the deflection of the jet
v ary . Fric [
23
] identified four dif ferent vorte x structures resulting from a radial jet in cross
flo w . These structures are sho wn in Figure 2.7(a) and are:
• Shear layer v ortices
• Counter -rotating v ortex pairs
• Horseshoe v ortices
• W ak e v ortices
W ith increasing aspect ratio of a rectangular slot (
>> 2
) the wall jet becomes quasi tw o
dimensional and forms a spanwise v orte x parallel to the slot, if superimposed with the
cross flo w (see 2.7(b)). At the edge of the slot counter -rotating streamwise v ortices are
formed. The influence on the spanwise v ortices on the rectangular jet decreases when the
length of the slot increases. The horseshoe vortices e xtend with the increasing slot length
and are dominated by two counter -rotating streamwise v ortices and are sho wn in Figure
12

2.2 Mechanism of periodic actuation
(a) Schematic drawing of the four types of v ortical
structure associated with the transverse jet[24]
(b) T wo dimensional vie w of a v ortex induced by a
rectangular slot in cross flo w .
Figure 2.7:
Schematic dra w of a radial jet in cross flo w and the v orticity field of a slotted
jet in cross flo w
2.8(a). The horseshoe vortices result from a positi v e pressure gradient through which the
boundary layer is separating, whereby the separation line depends on the velocity ratio. As
Plesniak and Cusano [
58
] ha ve sho wn, there are no wak e v ortices for a rectangle jet and
also the induced v ortices as well as the penetration depth is smaller compared to a radial
jet.
Jet penetration and the mixing process can be enhanced by use of pulsed blo wing. Recent
e xperiments ha ve sho wn that the jet penetration and the the spread can be maximized by
using periodic e xcitation [
70
,
46
,
20
]. The shear layer v ortices of a jet in cross flo w as
sho wn in Figure 2.8(b) can also be found during the blo wing phase of the pulsed actuation.
Ne vertheless these are too small to trigger a momentum transfer , which is necessary to
handle separation. Howe v er , by pulsed excitation lar ge-scale vortices are also induced,
which incite the instabilities of the shear layer .
Deploying a higher v elocity ratio
V R = u j et
u ∞ > 1
and a lo wer jet angle (e.g.
α j et = 45 ◦
)
two ef fects can be used to o vercome separation. W ith the lower jet angle the direct increase
of the momentum of the separation area is supported as kno wn for tangential blo wing.
The higher jet amplitude triggers the entrainment through shear layer . The jet separates at
the edge of the slot and a counter -rotating v ortex pair b uilds up [
44
]. The v ortex pair is
propagating do wnstream directly interacting with the shear layer of the separation. This
results in a high momentum transfer v ertical to the wall, implying a fluid entrainment
(a) Centreplane section sho wing two horseshoe
v ortices (indicated by arro ws) upstream of a jet
(b) Smoke streamlines entrained into the leading
edge of the jet
Figure 2.8: Shear layer and horseshoe v ortices of a jet in cross flo w [24]
13

2 State of the Art
Figure 2.9: Schematic dra wing of the mechanism af fecting the reattachment process
through the shear layer . Through this entrainment high ener gy fluid is transferred to the
wall whilst lo w ener gy fluid is transported aw ay . A schematic drawing of this process is
sho wn in Figure 2.9. The orientation of the jet determines the rotation and the symmetry
of the v orte x pair . Furthermore the mechanism of the separation control is depending on
the jet angle. A
90 ◦
jet related to the model surface, enhances the entrainment process
by producing lar ge-scale v ortices. The lo wer the jet angle the higher is the increase of
momentum in the separation area, because the jet adhere to the wall during the blo wing
phase.
The main objecti ve of this thesis is to enhance the mechanism of shear layer entrainment by
using a multiple cooperati ve system. In such a system the actuator slots must be deployed
do wnstream behind each other to maximize the mechanism of the single actuator .
2.2.4 Existing multiple actuation systems
The idea of a system containing se veral ro ws of actuators was numerically in vestigated
by Shmilo vich and Y adlin [
72
,
73
] on a simple hinge mo veable element. They “mounted”
fi ve synthetic jets at equal interv als within the flap, between the hinge line and a section
upstream of the trailing edge. The jet angle was rather lo w
α j et = 20 ◦
relati ve to the flap
surface. The flap was deflected to
δ f l ap = 25 ◦
, the angle of attack was set to
α = 11 ◦
at a
Mach number of
M a = 0 . 09
. The excitation of a single actuator w as sinusoidal with an
e xcitation frequency of
f = 217 Hz
. The momentum coefficient w as
c µ = 0 . 03
, resulting
in a v elocity ratio of
V R = 2 . 5
. The ov erall excitation pattern w as set to simultaneous
actuation of e very second port and with a phase shift of
Θ = 180 ◦
for the one in between
(see Figure 2.10 lo wer right). The location and numbers of the ports are sho wn in Figure
2.10. The first case is sho wn in the upper left illustration of Figure 2.10. There the first port
(port #1), located close to the hinge line where the separation originates, is acti ve with a
time-a v erage ov erall lift improv ement of
∆ C L = 0 . 65
. Mo ving the actuation do wnstream
a way from the separation line, the acti ve separation control becomes more and more
inef fecti ve. This is sho wn in Figure 2.11. Here the graph with the open circles sho ws a
single actuation of each port. The baseline results are included at the zero station. The lift
as well as the lift to drag ratio decreases with the distance from the separation line. The
flo w field of the single actuation of port #3 is depicted in the upper right illustration of
Figure 2.10. The largest lift increment can be achie ved if blo wing with all ports as sho wn
14

2.2 Mechanism of periodic actuation
the lo wer right illustration of Figure 2.10. In this case the lift increment (
∆ C L = 1 . 36
) is
nearly as high as this one of in viscid flo w , which is stated with
∆ C L = 1 . 66
. On the other
hand, with three actuators acti ve the lift can be enhanced to
∆ C L = 1 . 05
, which is
88 %
of
the lift gained with all ports acti ve. The ov erall results are sho wn in Figure 2.11. The filled
circles indicate the adapti ve actuation with e very port acti ve and the open squares that
e very other port is acti ve. The authors could sho w that the
∆ C L
and the
L/D
increases by
increasing the number of acti ve ports. The authors propose to proper ly place the single
actuator , which suggests that the distance between the actuator slots and the excitation
pattern ha v e a close relationship.
An important point are the e xcitation amplitude or , in the case of synthetic jets, the ener gy
consumption. This is set for all actuators as high as for the single actuation mode. This
means in consequence that, with se veral actuators acti ve, the total momentum coef ficient
(Equation 2.8)
c µ,n =
n
X
i =1
c µ,i (2.8)
(a) Single actuation with dif ferent locations. Acti ve actuators are gi ven by
the numbers.
(b) Combined actuation. Acti ve actuators are gi ven by the numbers.
Figure 2.10: Flo w structures for v arious actuation modes [73]
15

2 State of the Art
Figure 2.11: Buildup for distrib uted flo w control at AoA α = 11 ◦ [72]
is much higher than with a single actuator . The lift increment, howe ver , does not increase
in the same de gree. Since synthetic jets are used, no external mass flo w is required, but
an alternate current input v oltage. Therefore an actuator system with more actuators will
increase the ener gy consumption.
T roshin and Seifert [
82
] in vestigated e xperimentally the performance recov ery of a thick
turb ulent airfoil of a wind turbine by using a distrib uted closed-loop flo w control system.
In this e xperiment three ro ws of synthetic jet actuators were placed in equal interv als
behind each other with an jet angle
α j et = 30 ◦
relati ve to the surface. The e xcitation
frequenc y of the single actuator was
f = 1 . 35 kHz
with an amplitude of an a v erage peak
v elocity of
v j et ≈ 57 m
s
. This leads to a momentum coef ficient of
c µ ≈ 0 . 04
. The airfoil
was artificially tripped with “b ugs” to simulate the degradation of the wind turbine. The
e xperiments were ex ecuted with a Reynolds number of
Re = 0 . 5 × 10 6
. The excitation
pattern was similar to the numerical in vestig ation of Shmilovich and Y adlin and was set
to a phase shift of
Θ = 180 ◦
between the actuator ro ws. The ef ficienc y is e v aluated with
Equation 2.9, called aerodynamic figure of merit, where v alues of
AF M 3 > 1
mean that
it is ener gy ef ficient to introduce power to the actuators.
AF M 3 ≡ [( L − D ) · U ∞ ] C ontr ol led − 2 · P E lect
[( L − D ) · U ∞ ] B aseline
(2.9)
In Figure 2.12 the o verall system ef ficiency is sho wn with respect of the angle of attack.
It is demonstrated that the performance of a contaminated airfoil, intended for the root
section of a wind turbine blade, can be fully reco vered and its ener gy harvesting capability
is e xpected to be increased up to
60 %
using distrib uted acti ve flo w control ov er a narrow
incidence range [
82
]. Ho we ver , the authors state that a closed loop is necessary to be
ef ficient. In their in vestigation a single-input-single-output PID controller w as used in a
multiple-in-multiple-out configuration. The input was the estimated
C L
and the amplitude
of the actuator were controlled. The amplitude distrib utor was fed by the measured
separation location to maximize the ef ficiency . Ne vertheless the open loop case with high
po wer consumption did reach the best performance (see Figure 2.12).
Since both in vestigations uses lo w jet angle (Shmilovich et al.
α j et = 20 ◦
and T roshin et
al.
α j et = 30 ◦
) ob viously the acti ve separation control w orks best with high amplitudes,
because as Nagib et al. [
52
] states, the ef fecti v eness increases with increasing velocity
16

2.3 Objectiv e and structure of this thesis
Figure 2.12: Ov erall system ef ficiency calculated with Equation 2.9 [82]
ratio for tangential blo wing.
Since both of these systems reach considerable results, they are not using the entrainment
through shear layer in a cooperati ve w ay . T o reduce the energy , respecti vely the mass
flo w it is necessary to take the propagation v elocity and therefore the phase shift into
account. By doing so the v ortex can be amplified or maintained o ver a longer distance,
which increases the ef ficiency of such a system.
2.3 Objective and structure of this thesis
Pulsed actuation induces lar ge-scale v ortex structures, depending on jet angle, duty c ycle
and amplitude. These vortices trigger an e xchange of fluid through the shear layer to
reattach the separated re gion. The v orte x structures gro w with an increasing jet angle.
Hecklau [
32
] states that, with a lo w jet angle
α j et ≤ 30 ◦
, the induced v ortex triggers only
a short entrainment process vertical to the incident flo w . The flo w is then stabilized by the
fluid transfer caused by the attachment of the jet to the wall. Therefore, a higher duty cycle
with high amplitude is preferable, which in consequence increases the needed mass flo w .
A jet angle perpendicular to the wall can reduce the mass flo w by inducing an impulse
to the flo w . Here only the v ortex structure is responsible for the reattachment process.
In consequence the duty c ycle can be small (
Λ = 25 %
). Howe v er , a high duty cycle is
disturbing the flo w through building a fluid w all. Hence, the jet angle must be chosen by
the boundaries of the application. A lo w jet angle is classified as rob ust b ut mass flo w
costly , while with a higher jet angle the v ortex structures can be used to reduce the mass
flo w .
This kno wledge can be used to build up a system which tak es adv antage of both mechanisms,
the entrainment as well as the direct increase in momentum. T o increase the momentum
of the separated area a jet angle of
α j et = 45 ◦
is chosen, to hav e the jet adhere to the
wall b ut also inducing a proper vorte x. The objecti v e of this thesis is to reduce the energy ,
17

2 State of the Art
(a) Induced vorte x at actuator slot 1 (b) V ortex propagating with u conv do wnstream
(c) u j et of second actuator merge with the v ortex
(d) Strengthened and stabilized vorte x propagating
further do wnstream
Figure 2.13: Schematic dra wing of v ortex mer ging by cooperati ve actuation
respecti vely the mass flo w by using a cooperati v e ef fect, enhancing the entrainment through
the shear layer . Thereby , the responsible v ortex is enhanced o ver a certain distance and
the mass flo w of the single actuator can be reduced significantly . According to the saying,
the whole is grater then the sum of its parts, the o verall mass flo w is reduced by using this
cooperati ve ef fect.
T o enhance the v ortex se v eral parts must be considered. First a number of ro ws of actuators
must be located do wnstream of each other with a certain distance. Second the mass flo w
must be adaptable and sensored. Last b ut not least the e xcitation of the actuators must be
coordinated so that the v ortices mer ge with each other .
Figure 2.13 sho ws a schematic drawing of the mer ging process. A vorte x is induced by
pulsed blo wing of the first actuator (Figure 2.13(a)) and propagating do wnstream with the
propagation v elocity
u conv
(Figure 2.13(b)). When the vorte x reaches the second the slot,
the blo wing phase of this actuator starts, merging with propag ating v ortex (Figure 2.13(c)).
Thereby the v ortex is strengthened and stabilized. The now bigger v ortex propag ates
further to the ne xt slot (Figure 2.13(d)). Theoretically this process can be repeated more
often.
The theory is just as simple as challenging the practical implementation. One ke y to success
is a proper phase shift between the blo wing phases of the actuators. The phase shift
Θ
is
not only depending on the propagation v elocity of the v ortex and therefore the incident
flo w , but also from the distance of the actuator slots. Hence, an adaption of the wa ve length
formula can be used to estimate the necessary phase shift (See Equation 2.10).
Θ = d act · f act · 360 ◦
u conv
(2.10)
The mer ging and interaction of v ortices has been in vestig ated for dif ferent settings like a
counter -rotating v ortex pair [
12
,
14
] or co-rotating v ortices [
48
,
42
,
49
]. These in vestigations
address fundamental research or mer ging trailing edges of an aircraft. The propagation
v elocity is mostly opposite and fully b uilt up at the time of merging. In the case of
cooperating actuation, the aim is to merge the v ortex with a ne wly induced one. Ne vertheless,
the mer ging of two v ortices, generating at dif ferent times propagating in the same direction
18

2.3 Objectiv e and structure of this thesis
has not been in vestigated yet. Therefore it is necessary to in vestig ate the beha vior of such a
system. The results can then be taken to deplo y a cooperati ve actuation system to reattach
a pressure induced separation.
The main objecti ve is to reduce the mass flo w or , in the case of ZNMF actuators, to increase
the aerodynamic figure of merit (2.9), by maintaining the flo w attached to the surface.
Ho wev er , initially the merging parameter are in vestigated on a setup with no pressure
gradient. Thereby , the main focus is on the induced vortices and ho w they interact with
each other as well as the beha vior of the surrounding flo w . This has the adv antage, that
the boundary conditions remain the same and guarantee a direct comparability of dif ferent
phase shifts. The second step is to transfer the setup and the first results obtained to
a generic configuration, where a pressure gradient can be applied. This is done with a
half dif fuser where the separation line can be adjusted by changing the step angle
α step
.
This ensures that the flo wmechanics of the merging and therefore the reattachment of the
separation can be observ ed in isolation from changing boundary conditions like actuation
influenced changing of the pressure distrib ution. Here the changes of the merging process
are in vestigated, with the focus on the aerodynamic parameter . This is done in comparison
to simultaneous blo wing to highlight the adv antages of cooperati ve distrib ution.
F ollo wing on from that the mass flo w is reduced and v aried o ver a significant range of
phase shifts on the same setup. The ef ficiency of the system is rated with the pressure
reco very
∆ c p
. Mainly the parameter of momentum
c µ
and the phase shift are changed and
compared to a single acti ve ro w . W ith this configuration the potential of the distrib uted
actuation to reattach flo w with a lo wer velocity ratio and less mass flo w is pointed out.
In the follo wing section the measurement configurations, the used actuator system and
control unit as well as the measurement setup including traditional and imaging measurement
procedures are described. In section 4 the e v aluation and used methods are presented. The
flo wing section provides the interaction of v ortices without pressure gradient. First a look
at a single v orte x is described, follo wed by the mer ging process of v ortices on a flat plate.
This results are then transferred to an half dif fuser where a pressure induced separation
is deployed. The results of the interaction process is presented here. Subsequently a first
comparison between the single and the cooperati ve actuation is done. Section 6 provides
the benefits and discussion on the cooperati ve actuation with re gard to the parameters VR,
c µ
and mass flo w as well as a recommendation to future work. Finally the conclusion
completes this thesis.
19

2 State of the Art
20

3 Experiments and Methods
T w o dif ferent test facilities were used two e xamine the cooperati ve actuation system. T o
understand the process of interacting v ortices, the concept was first tested on a flat plate.
Then it was transferred tw o a half dif fuser , with an adjustable incline to generate a pressure
induced separation.
The mechanism of the cooperati ve actuation was systematically in v estigated by means of
dif ferent measurement techniques. The focus was on the laser optical in vestig ation with
P article Image V elocimetry (PIV), to get a better insight in the flo w beha vior .
In this section the realization of the cooperati ve actuation concept, the used actuator system,
the used measurement setup as well as both test facilities are presented.
3.1 T est facilities
The basic e xaminations were done at the L WK-2 located at Airb us Group Inno v ations in
Munich. This facility is a Göttinger type wind tunnel, as sho wn in Figure 3.1, for basic
subsonic measurements. The flo w velocity range is adjustable up to
v ∞ = 37 m
s
. This test
section has a length of
L = 0 . 6 m
and a square cross section of
h × b = 0 . 09 m 2
. The
grade of turb ulence is between
0 . 5 % ≤ T u ≤ 1 %
referring to the inlet of the closed
measurement test section. This test section also pro vides good optical access from the
ceiling as well as from the sides, to perform PIV measurements. In addition a 3D Cartesian
robot, mounted on the housing, enables exact flo w in vestigations by means of a hot wire
anemometer .
Three actuators are installed in the centre of the bottom plate of the test section. The first
actuator slot has a distance of
d LE = 0 . 3 m
, and the distance between the actuators is
d act = 0 . 04 m
. Here, fi ve hot film sensors were flush-mounted in between the ro ws and
additional twelv e hot film sensors were mounted behind the last ro w .
The in vestigations concerning the reattachment of the pressured induced separation were
done at he GSW located at the Department of Aeronautics and Astronautics of the Berlin
Institute of T echnology . This wind tunnel is sho wn in Figure 3.2 and is also b uilt as
Göttinger type, for subsonic in vestig ations. The flo w velocity can be controlled up to
v ∞ = 30 m
s
. Thanks to sie ves and rectifiers this wind tunnel has a lo w grade of turbulence
(
0 . 2 % ≤ T u ≤ 0 . 6 %
). This facility pro vides a cooling circuit, so that the temperature is
the same during the measurements. The incline step can be controlled with a step motion
control unit and is adjustable between
0 ◦ ≤ α step ≤ 25 ◦
. The section of measurements is
designed to ha v e optical access from abov e and from the side to allo w optical measurements
to take place. The positions of the hot wire anemometer are controlled by means of a 3D
Cartesian robot unit.
21

3 Experiments and Methods
Figure 3.1: W ind tunnel O TN - L WK2
The incoming cross section is gi ven by the section of measurements with
h 1 × b = 0 . 237 m 2
.
The length of the incline step is constant with
L step = 0 . 34 m
. This means that the step
height
H
and the outgoing cross section is a function of the step angle
α step
. The base plate
after the step is limiting the height
h 2
at the end of the test section. Therefore the e xpansion
ratio
E R = h 2
h 1
is adjustable through the step angle. The incoming height
h 1 = 0 . 395 m
,
the width of the section is
b = 0 . 6 m
and the height
h 2
for a step angle
α step = 23 ◦
results
in
h 2 = 0 . 53 m
. This leads to an expansion ratio of
E R = 1 . 34
with a step height of
H = 0 . 133 m .
The geometrical boundary conditions for the incline step are chosen too enable a specific
positioning of the separation for selecti ve step angles. The test section has secondary flo w ,
b ut in the middle section, where the in v estigations took place, these flo ws are negligible
[
32
]. F or these in vestig ations three ro ws with three actuators each were realized. A total of
40 %
of the width is co vered by the actuator slots. The actuators are flush-mounted to the
surface with a distance of
d LE = 0 . 034 m
to the leading edge. The follo wing ro ws ha ve a
distance of
d act = 0 . 04 m
. Between and after the centered actuators wall mounted pressure
transducers are implemented to monitor the pressure distrib ution and pressure reco very .
Figure 3.2: W ind tunnel TUB - GSW (after [32])
22

3.2 Actuator
3.2 Actuator
Pulsed blo wing through flush mounted slotted actuators has prov en to be suf ficient for acti ve
separation control. The slots are distinguished through a high aspect ratio transv ersely
to the incident flo w . This guarantees that a quasi two dimensional spanwise v orte x is
produced, interacting with the shear layer of the separation. Generally , for experimental
in vestigations the slotted actuators are dri ven by a f ast switching solenoid valv e. The
frequenc y and the duty cycle can be controlled, by means of a signal generator . The
amplitude is adjusted with a pressure re gulator and monitored with a v olume or mass flo w
meter .
This setup is suf ficient for the single actuator (ro w) setup. Ho we v er , ha ving se veral ro ws of
actuators each ro w needs its o wn setup. Furthermore, to adjust the phase shift of excitation
between the ro ws the signal generators hav e to communicate with each other . Therefore a
Digital Signal Processing (DSP) rapid prototyping system was used to be able to adjust all
parameters indi vidually but k eeping the dependence reg arding the phase shift
Θ
. W ith the
DSP it is also possible to control the amplitude by means of a PID control algorithm.
The cooperati ve actuation w as realized as sho wn in Figure 3.3. Here the setup for the GSW
is illustrated, b ut the insert, used in the L WK-2 is in principle the same. The dif ference
between the two inserts is the used measurement techniques between and after the centered
actuators. For the measurements on the flat plate hot film sensors are used, whereas on
the incline step pressure sensors were wall mounted, as seen in Figure 3.3. The distance
between the actuators is the nearest possible due to the fortifications to the insert. This
is done due to the dissipati v e beha vior of the vorte x. This ensures, that it is possible to
ha ve an ef fecti ve v ortex interaction. Ha ving this setup, a small addition has to be made
concerning the dimensionless frequenc y
F +
. The characteristic length
l r ef
between slot
and trailing edge of the model is changing with e very ro w and would therefore result in
three dif ferent Strouhalnumbers. An example is gi v en for the measurements done in the
GSW . W ith a distance of
d act = 40 mm
the dimensionless frequenc y is decreasing with
e very actuator ro w (see Equation 3.2). T o ha ve the same frequenc y for all actuator ro ws,
only the first one is set to a subharmonic of the characteristic length. The others are then
the result of Equation 2.1.
Figure 3.3: Section of used geometry
23

3 Experiments and Methods
F +
1 = 2 . 0
F +
2 = 1 . 7 (3.1)
F +
3 = 1 . 4
F or the cooperati v e actuation, generic slotted actuators are used within these in v estigations.
The actuator is sho wn in Figure 3.4 (a). The inlet is radially symmetrical, whereas the outlet
is rectangular . T wo important f actors ha v e to be taken into account. A sharp increase of the
v elocity at the beginning of the blo wing phase and a nearly rectangular velocity profile in
spanwise direction. The v olume of the actuator chamber is responsible for both beha viors.
A high v olume results in a rectangular v elocity profile, but reduces the increase at the
be ginning of the blo wing period. Therefore the chamber was adapted by e xperimental
in vestigations to meet both criteria. The compromise is illustrated in Figure 3.4 (b). It
pro vides also a high aspect ratio of
AR = 175
resulting in a slot length of
l act = 70 mm
and a slot width of
b act = 0 . 4 mm
. The jet angle of the actuator is set to
α j et = 45 ◦
. This
angle is an ideal combination of the two mechanisms to reattach the separated flo w . This
guarantees that reasonable v ortices are induced as well as the increase of momentum into
the detached area. These parameters are called geometrical parameters and most of them
may not be changed during the e xperiments.
The kno wledge of the velocity distrib ution along the slot, the introduced momentum and
the jet v elocity are important. Therefore the actuator is calibrated by means of hot wire
measurements. The actuator setup including the pressure regulator and the v olume flo w
meter has to be b uilt up outside of the wind tunnel. The hot wire is placed in the center
of the actuator slot width and mo ved in small steps by a tra verse along the slot. The hot
wire was positioned v ery close to the actuator slot (
< 0 . 5 mm
). The resulting v elocities are
normalized and the distrib ution is sho wn in Figure 3.5 (a) as an example. The slot profile is
nearly rectangular o ver the whole slot length, apart from the peak at the middle of the slot.
This is due to the radial symmetrical inlet. Ne vertheless this peak is smaller then
10 %
of
the mean v elocity and can be neglected.
In Figure 3.5 (b) the normalized v elocity ov er one period is illustrated. Additional
measurements of the pressure within the actuator chamber took place with a wall mounted
(a) Outside geometry (b) Inside geometry
Figure 3.4: Geometry of the actuator
24

3.2 Actuator
(a) Spanwise slot velocities
(b) T ime depending slot velocities with trigger signal
and pressure insight of the actuator
Figure 3.5: V elocity profiles of the actuator
transducer . As reference, the associated trigger signal is also plotted as a dashed line.
The signals are phase-a veraged o ver the period. The time delay of the rising edge of
the pressure and hot wire signal is due to the switching time of the solenoid v alve of
t sw itch ≈ 1 . 5 ms
. A sudden rise in pressure occurs when the v alve opens, resulting in a
steep rising edge of the v elocity . Then the actuator is nearly constantly blo wing o ver the
opening time of the v alve. Afterwards, when the v alve is closed, the remaining pressure
e v acuates the actuator chamber . The now accrued lo w pressure within the chamber result
in a small suction phase where the chamber is refilled. This is illustrated by the pressure
signal as well as the velocity peak behind the f alling edge of the signal. Since the hot wire
signal is unidirectional the v elocity is also positi ve, b ut together with the pressure signal
the statement is confirmed.
The jet v elocity of the actuator can only be obtained outside the wind tunnel. T o determine
the v elocity during the experiments a correlation between the permanent recorded v olume
flo w and the jet velocity has to be done. Again hot wire measurements took place with
an instantaneous measurement of the v olume flo w . Kno wing the area of the slot, which
is
A act = 28 mm 2
, the v elocity of the actuator at the slot plane can be computed with the
continuity condition (see Equation 3.2). Thereby the duty c ycle
Λ
has to be taken into
account. Utilizing the continuity condition means that it is only v alid for incompressible
flo ws, which means that the Mach number is smaller
M a < 0 . 3
. The velocities from the
hot wire measurements are a v eraged ov er the blowing phase angle Φ of the period.
v V ol = ˙
V
A act
· 100
Λ (3.2)
The result is sho wn in Figure 3.6 where the measured velocity is dra wn ov er the velocity
obtained from the continuity condition. The real v elocity is about
≈ 20 %
belo w the
computed v elocities. Ne vertheless a linear correlation can be found and therefore the jet
v elocity can be determined by means of the volume flo w meter v alues recorded during the
wind tunnel e xperiments.
This correlation can be used to compute the dif ferent velocity ratio
V R
as stated in Equation
2.3. T o compare the actuator with other e xperiments the root mean square of the v elocity
and the momentum coef ficient is established (see Equation 2.5 and 2.7). In Figure 3.7
(a) the dependenc y of
u RM S
on the mass flo w is shown. The mass flo w is instead of the
v olume flo w is taken to compensate the influence of the density . The velocity increases
25

3 Experiments and Methods
Figure 3.6: Correlation of continuity and hot wire v elocities
(a) Root Mean Square velocity o ver mass flo w (b) Momentum coefficient o ver mass flo w
Figure 3.7: Characteristics of the actuator for the GWK at 100 Hz
linearly with the introduced mass flo w . The duty cycle af fects the RMS velocity . A small
duty c ycle, here of
Λ = 25 %
, means that the solenoid v alve only opens for a quarter of the
period and the mass flo w rate decreases. Since the pressure is controlled by the pressure
re gulator , a lo wer duty cycle means a higher v elocity at the same mass flow compared
to a duty c ycle of
Λ = 50 %
. Since the mass flo w rate increases with the duty cycle, the
gradient of the RMS v elocity line decreases.
Utilizing the outcomes of correlation between the v olume flo w and the measured velocity
the momentum coef ficient can be computed in dependence of the duty cycle. This is done,
as an e xample, for the wind tunnel of the Berlin Institute of T echnology and illustrated on
the right hand side of Figure 3.7.
26

3.3 Measurement setup
3.3 Measurement setup
Figure 3.8 sho ws the schematic measurement chain used for all presented measurements.
Originating from the measurement PC, the dif ferent signals of the transducers are recorded
via the input channels. The regulating v ariables are transmitted to the corresponding
control units via the output channels. The data acquisition and the step angle control
are implemented in LabV iew . The signal generator implemented on the DSP is done in
Simulink and controlled by software pro vided by the manufacturers.
The parameters of the signal generator , the frequency
f
, duty cycle
Λ
and the phase shift
Θ
are controlled with the measurement PC and transmitted to the DSP . This unit produces
a rectangular trigger signal and transmit it to an amplifier , which pro vides the necessary
v oltage for the fast switching solenoid v alves. Simultaneously the trigger signal is sent
to the measurement PC. In addition the PID controller to adjust the v olume flo w is also
implemented on the DSP . The v olume flow is measured using the analogue-digital con v erter
of the DSP and the corresponding v oltage of the adjustment of the controller is sent to the
pressure re gulator . Therefore the e xcitation amplitude is controlled via the DSP system.
The complete pressure system consists of three identical ro ws with a pressure regulator ,
v olume flo w meter and a distributor when there are se veral actuators per ro w . This ensures
that e very actuator has the same amount of pressurized air and the desired v olume flo w is
constant, due to the DSP controller .
The dif ferent sensors to measure the static and transient measurement v alues (MV) are
recorded. The main parameters of the incident flo w (temperature, dynamic and total
pressure) as well as the v alues concerning the acti ve flo w control system (wall mounted
pressure sensors, hot wire, hot film and v olume flo w) are con verted by means of an
analogue-digital con verter . This data is then transmitted to the measurement PC. Beside
the monitoring the external re gulating v ariables can be controlled with the measurement
Figure 3.8: Measurement Chain
27

3 Experiments and Methods
PC. F or instance, the motion control unit to adjust the step angle or the position of the
tra v erse.
The used measurement techniques to analyze and e v aluate the reattachment process are
described in the follo wing sections.
3.3.1 T raditional measurement techniques
Dif ferent pressure transducer are used to measure the flo w of the wind tunnel. The dynamic
pressure
q ∞
is measured with a Prandtl tube, utilizing a dif ferential pressure transducer .
The ambient pressure of the surrounding is recei ved by means of a calibrated transducer .
Including the temperature the density
ρ ∞
can be computed utilizing the ideal gas equation,
presuming incompressibility . W ith the dynamic pressure and the density the inlet v elocity
can be computed with Equation 3.3
u ∞ = r 2 · q ∞
ρ ∞
(3.3)
Despite the ambient pressure, which is a total pressure transducer , all used pressure
sensors are dif ferential pressure transducers. All sensors are piezoresisti v e and calibrated,
transmitting a v oltage proportional to the pressure. The analogue signal is con verted with
an analogue-digital con verter and recorded for the e v aluation.
The static pressure at a position
x
of the insert is obtained by means of a wall mounted
pressure transducer . A sketch of such a setup is sho wn in Figure 3.9. The boundary layer
hypothesis states that the static pressure is constant throughout the boundary layer and thus
the static pressure of the flo w is measured with this setup. The connecting hose between
the transducer and the tube, connected with the wall, has to be short, to a v oid a damping
ef fect. Thus, it is guaranteed that the dynamic beha vior can be analyzed. The transducers
are mounted st the center of the surface of the insert at dif ferent locations (see Figure 3.3).
The output of all sensors are recorded simultaneously .
T o obtain the pressure coef ficient
c p
the transducer is connected to the static pressure
of the incident flo w
p stat
. The v oltage yielded by the sensor corresponds therefore to
the dif ference
∆ p = p x − p stat
. T aking the dynamic pressure into account, the pressure
coef ficient can be computed with Equation 3.4.
c p = p x − p stat
q ∞
(3.4)
T w o thermoelectric measurement procedures were used to analyze the beha vior of the
acti ve flo w control system. The hot wire technique allo ws to measure the a veraged as well
as the fluctuation ve locities of the flo w field. The general principle is to ov erheat a small
wire, bonded between two prongs, by means of a Wheatstone bridge. The o verheat ratio
is normally set to
≈ 1 . 7
abo ve of the incident flo w velocity . The resistance of the wire is
changing, due to the con vecti ve heat emission to the fluid . The bridge is regulating this
resistance by heating the wire. This method is called Constant T emperature Anemometer
(CT A). The heating v oltage is then used to measure the velocity . This relationship is gi ven
by King’ s la w . Equation 3.5 expresses the relationship between heating v oltage and flo w
28

3.3 Measurement setup
Figure 3.9: Sketch of W all mounted pressure sensors, after [32]
v elocity .
U 2 = A + B · u n (3.5)
The constants
A, B , n
are obtained by means of a calibration. A single hot wire is
unidirectional and therefore only one direction of velocity can be measured. T o obtain
more v elocity components, a 2D or 3D hot wire probe is used.The ef fort of the calibration
increases with the number of dimensions, due to the dependence of the wire on the direction.
Since this a matter of thermoelectric measurements, the temperature of the measured fluid
is an af fecting factor , which has to be taken into account. The dif ference of the calibration
temperature
T c
and the fluid temperature
T f
can be corrected with Equation 3.6 to obtain
the actual heating v oltage
U B
. Presumed is the knowledge of the senor temperature
T s
. A
more detailed insight of the method and the thermal balance of the wire is gi ven by Nitsche
& Brunn [55].
U 2
B = U 2
c · T s − T f
T s − T c
(3.6)
Another method used, also based on the constant temperature method, are hot film sensors.
The hot film sensors can be used to measure the fluid friction on surfaces in a flo w . In
principle, the local shear stress is measured with a heated flush-mounted surface sensor .
The sensor is electrically heated by means of a bridge, and the con vecti ve heat emission is
measured. This v alue is proportional to the wall shear stress. The measurement principle
is based on the Re ynolds analogy between heat transfer and shear stress. The wall shear
stress cannot be measured directly with this method, thereby the calibration is a important
issue. Since the hot film sensors used for the measurements are uncalibrated only a short
o vervie w is gi ven. A detailed ov ervie w is giv en by Nitsche & Brunn [55].
The relationship of the wall shear stress and the heating v oltage is again sho wn by an
empiric correlation as stated in Equation 3.5. As reference an appropriate measurement
system has to be used, as example a mechanical shear stress balance. This method is very
sensiti ve to temperature dif ferences of the fluid and the wall. T o protect the sensor from
the wall temperature as well as to pre vent the senor of heating the w all it is constructed on
29

3 Experiments and Methods
a PVC foil.
The uncalibrated hot film sensors are therefore not capable of measuring the shear stress.
Ne vertheless, the 22 hot film sensors mounted subsequently do wnstream are measured
simultaneously and thus a qualitati ve beha vior can be analyzed. Due to its high cutoff
frequenc y of f g = 50 kHz ev en high turbulence is measured.
3.3.2 P ar tic le Image V elocimetr y (PIV)
The particle image v elocimetry is an image based measurement procedure and therefore is
one of the non-intrusi ve measurements. The PIV captures the whole flo w field within one
plane during the considered measurement time. Three subsystems are mainly necessary
for a PIV measurement. T o visualize the flow field, tracers ha ve to be supplied to the flo w .
A light sheet with high intensity to illuminate the tracers and a camera for optical imaging
of these tracers.
The laser beam is extended to a quasi 2D plane in which the tracers are illuminated twice
by short laser pulses. T wo images are taken from the illuminated tracers within the lase
pulse within a short period of time
∆ t
. The correlation of these two images pro vides the
displacement of the particles within the plane. The v elocity is then computed with the
kno wn time delay
del tat
between the light pulses. If the time delay is adequate the particle
displacement is linear and the v elocity remains constant.
Figure 3.10 briefly sketches the principle PIV setup used in the GSW . The laser beam is
redirected and e xtended to a light sheet introduced through an optical access in the ceiling.
This light sheet illuminates the tracers supplied to the flo w twice. The lateral scattered light
by the tracer particles is recorded on two single frames on a digital camera. The optical
access for the camera is in the side wall of the test section. The output is directly transferred
to the memory of the computer .
T o obtain the v elocity out of the PIV recording the imagages are di vided into small areas,
called interrogation areas. The local displacement vector of the tw o images is determined
Figure 3.10: Principle 2D/2C PIV Setup, after DLR [18]
30

3.3 Measurement setup
with respect to the short time delay
∆ t
by means of the cross correlation function. This is
based on the assumption that the particles ha v e mov ed homogeneously between the two
light laser pulses.The v elocity vector is calculated on the bases of the kno wn time delay
and the magnification m of the images (see Equation 3.7).
~ u = ∆ ~ x
m · ∆ t (3.7)
The seeding tracer can be an y material reflecting or emitting light with a relati vly constant
particle size. The seeding normally used is Di-Ethyl-Hexyl-Sebacat (DEHS) which has a
a verage diameter of
d D E H S ≈ 1 µ m
. T o supply the seeding to the flow a Laskin-nozzle
can be used, where the seeding density and the size can be adjusted by a pressure regulator .
Generally the scattering of the light by the particles is a function of the ratio of the refracti ve
inde x of the particle to the surrounding medium, the size, shape and orientation [
62
]. In
cases of spherical shaped particles, which are lar ger then the wa velength of the light, Mie’ s
scattering theory can be applied. Another point concerning the tracer particles are the
density of seeding within the flo w . A high density can result in a speckle pattern, where the
single particles are hardly detected. In this case further post processing has to take place.
If the density is v ery lo w , it is referred to as particle tracking method. A homogeneous
density is preferred for PIV measurements.
As a light source to illuminate the seeding, lasers are commonly used due to their ability
to emit monochromatic light with a high ener gy density . The laser beam can be b undled,
redirected and e xtended to thin light sheets, illuminating the tracer particles without
chromatic abbre viations. Mostly double pulse lasers are used. The repetition rate per ca vity
of the laser beams gi ves the maximum sample frequencies. A detailed ov erview of the
working principle of a laser is gi v en by Raf fel et al. [
62
]. The light sheet is e xtended by at
least one c ylindrical lens to achie ve an appropriate thin light sheet. If a ND:Y A G laser is
used at least one additional lens has to be used to focus the light sheet.
Most common digital cameras are used for the optical imaging, which enable to obtain
an image pair with a short time delay up to
∆ t = 2 µ s
. The standard PIV cameras hav e a
Char ged Coupled De vice (CCD) chip and provides a sample rate of
F s = 10 Hz
re garding
the double frame capture mode. The rapid progress in chip technology and the peripherals
bring an increase in capabilities. No wadays, more and more high speed cameras are
used for time resolv ed PIV measurements (TR-PIV). These cameras are provided with a
Complementary Metal Oxide Semiconductor as an imaging sensor and enable a sampling
frequenc y up to
F s = 10 kHz
. The images are stored in an internal memory , which also
limits the maximum amount of single images.
Since a complete and detailed mathematical description is gi v en by W esterweel [
84
] only a
brief description is presented here. The obtained image pair is subdi vided into small areas,
the so called interrogation areas of the length
K × L
. The particle displacement of ev ery
interrogation area is determined with a discrete cross correlation of the intensity v alues
I 1
and I 2 of the particle images obtained at the times t 1 and t 2 .
R I I ( x, y ) =
K/ 2
X
i = − K/ 2
L/ 2
X
i = − L/ 2
I 1 ( i, j ) I 2 ( i + x, j + y ) (3.8)
The displacement v ector is gi ven by the displacement of the maximum correlation peak
R I I
. The cross correlation is capable of determining the displacement v ector within
± 0 . 5
31

3 Experiments and Methods
pix els. This can be impro ved by using an appropriate function lik e the three point Gauss
peakfit. The velocity v ector can be calculated, by means of the magnification and the
kno wn time delay between the image pair . T o identify false v ectors, se v eral filters are
commonly used. A brief description of the most important is gi ven. The Local Filter
calculates the dif ference of a velocity v ector and its neighboring v ectors. If the de viation is
too high it is marked as an outlier . The W indow Filter tak es the magnitude and direction of
all v elocity vectors and plot them in a scatter diagram. V ectors which are inside of a gi ven
area, are marked as v alid. The Signal-to Noise Filter is a filter which rates the quality of
the correlation peak. Correlation peaks, which fall belo w a certain v alue, are also marked
as outliers.
There are a lot of other factors, which ha ve to considered, to obtain a high quality PIV
measurement result. These factors as well as demanding methods to interpolate outliers
are gi ven by Raf fel et al.[62] and W esterweel[84].
32

4 Ev aluation and T rac king
T o obtain useful information from the e xperiments ke y parameters and dif ferent e valuation
methods are of great interest. In this part the focus will be on the ev aluation criteria to
rate the alignment of coherent structures in the flo w and a tracking algorithm to detect and
track v ortices in the flo w .
4.1 Flo w characterization and ke y parameter s
F or the e v aluation of the data acquired through the dif ferent measurement techniques,
mentioned in the section abo ve, to obtain the state of the flow in the wind tunnel and
the interaction of the jet and v ortices with the flo w , se veral methods and parameters are
kno wn. The instantaneous v elocity of a two dimensional measurement
u ( t )
and
v ( t )
is the
composition of the time depending mean v alue and the superimposed fluctuation velocity
[
55
]. This is sho wn in Eqaution 4.1 by the example of the v elocity component
u ( t )
, b ut is
also v alid in terms of a pressure signal and the uncalibrated hot film data.
u ( t ) = ¯ u + u 0 ( t ) (4.1)
whereby:
u ( t ) – instanteneous velocity ,
¯ u – mean v elocity ,
u 0 ( t ) – fluctuation part.
This decomposition is done with a temporally discrete signal, which means that the signal
consists of
n
single v alues obtained with a sampling frequency
F s
. The v alues are therefore
separated with the reciprocal of this frequenc y . Equation 4.2 sho ws the arithmetic mean
v alue obtained from the single values
u i
and the amount of v alues
n
. The mean v alue is
a location parameter and describes the a verage of a distrib ution. T o a void a dependenc y
of the mean v alue on the duration of the time interv al, the duration of the signal has to be
long enough, especially for periodic signals.
¯ u = 1
n
n
X
i =1
u i (4.2)
Another location parameter is the median (Equation 4.3). The definition considers the
median to be the 50th percentile of a distrib ution of numbers ranked in order of increase.
In other words, the median represents the central v alue of an ordered series of une ven
33

4 Evaluation and T racking
numbers or the a v erage of the two central v alues of an ordered series of e ven numbers [
21
].
The main dif ference to the mean v alue is the robustness ag ainst outliers.
˜ u = ( x n +1
2 , for n une ven
1
2  x n
2 + x n
2 +1  , for n e ven (4.3)
The parameter of the standard de viation
σ x
describes the scattering of random v ariables
around their e xpected v alue. In this case, it is the scattering of the measured v alues around
the mean v alue. The standard de viation refers to the fluctuation part of the signal and is
defined in Equation 4.4. This v alue is a measure of the intensity of the fluctuation, since
the fluctuation part is considered square.
σ u = p ¯
u 0 2 = v
u
u
t 1
n
n
X
i =1
( u i − ¯ u ) 2 (4.4)
The Root Mean Square (RMS) is the result of the square root of the squared o verall signal
and is referred to as the mean squared de viation (see Equation 4.5) [
55
]. Therefore, the
af fecting time av eraged effecti v e v alue can be obtained. In case of pulsed blowing the
RMS v alue sho ws the ef fecti ve v elocity induced by the jet o ver time. In the case of the hot
film sensors, when only the fluctuation part is measured, the RMS v alue is equal to the
standard de viation.
u RM S = v
u
u
t 1
n
n
X
i =1
u 2
i (4.5)
In cases where an instantaneous measuring of all flo w characteristics in a flo w field is
not possible, e.g. hot wire measurements, the phase av eraging is a possibility , at least for
periodic flo w structures (see Equation 4.6). The phase locked mean v alue is determined
from the single v alues obtained at a locked phase angle
Θ
of the signal. The number
N Θ
is
gi ven by the amount of phase angles for which a certain number of single v alues exist. A
reference signal has to be used to which the periodic signal is related. The frequency of the
reference signal determines thereby which periodic parts are admitted. Every periodic share
of the signal which are not in coherence with the reference frequenc y or their harmonics
are damped (see Figure 4.1).
h u i Θ = 1
N Θ
N Θ
X
i =1
u Θ ,i (4.6)
In the case of pulsed blo wing se veral single measurements can be related to a single
reference signal measured at the same time and assembled to a flo w field. As a result, the
periodic shares of a flo w field can be sho wn ov er one period. This is sho wn by way of
e xample of two dimensional hot wire measurements on a flat plate with periodic actuation
on a flat plate in Figure 4.2. In this case the fluctuation velocity of the flo w field is sho wn
to highlight the v orte x.
34

4.1 Flow characterization and k ey parameters
0 0.01 0.02 0.03
0
5
10
Time [s]
a.u.

Signal
Reference Signal

(a) Signal with reference signal ov er time (b) Phase av eraged signal ov er phase
Figure 4.1: Principle of phase a v eraging
(a) V ortex at phase angle Θ = 124 ◦
(b) V ortex at phase angle Θ = 179 ◦
(c) V ortex at phase angle Θ = 234 ◦
Figure 4.2:
Assembled flo w field of two dimensional hot wire measurements (
1342
single
measurement points) for dif ferent phase angles
35

4 Evaluation and T racking
Figure 4.3:
Cross correlation of two hot film sensor signals with characteristic time delay
∆ t (after [55])
T w o signals are compared in the time domain by using correlation functions, which e xamine
the similarities of the signals. The similarities of two dif ferent signals are detected by way
of cross correlation (see Equation 4.7). The amplitudes of the signals are multiplied and
inte grated taking into account an increasing time delay [55].
Φ τ = Z ∞
−∞
x ( t ) y ( t + τ ) dt (4.7)
F or the correlation of discrete time signals the sum function is used whereby
n ≡ t
and
k ≡ tau
. In Equation 4.8 the cross correlation is normed, which means that if for any k the
v alue is one, the signals are similar and for minus one the signals are in phase opposition.
Φ xy = P N
n =1 x n y n − k
q P N
i =1 x 2
i · P N
i =1 y 2
i − k
(4.8)
By amplifying similar and damping dissimilar parts, signal characteristics can be obtained
from the time delay . In the case of hot film measurements the propagation v elocity of a
flo w structure e.g. vorte x, can be calculated. Figure 4.3 sho ws a cross correlation for two
hot film sensors with pulsed actuation. W ith the kno wn distance of the sensors and the
obtained time delay
∆ t
, the propagation v elocity of the flo w structure can be calculated.
The parameter v orticity is a measure for strength of a v orte x within a velocity field and
is a significant v alue of fluid mechanics. It is a pseudo vector field describing the local
spinning of the flo w around a point. In other words, it is the tendenc y of a fluid flo w to
cause rotation. Mathematically the v orticity is defined as curl or rotation of a v ector field
~ v
and is sho wn for a two dimensional case in Equation 4.9.
~ ω = ∇ × ~ v =  ∂ v y
∂ x − ∂ v x
∂ y  ~ z (4.9)
Re garding PIV data, where the two dimensional v elocity vector field is e v enly spaced
and the v elocity data is disturbed by noise, a finite dif ference schema has to be applied to
36

4.1 Flow characterization and k ey parameters
(a) V orticity of a flo w field with clockwise (blue) and
counterclockwise (red) rotating v ortices
(b) λ 2 criteria for the flo w field depicted in (a)
Figure 4.4: V orticity and λ 2 criteria for the same flo w field with two v ortices
calculate the v orticity [
62
]. In this case the central dif ference schema is used, assuming
that the measurement uncertainties are independent of their neighbors. This assumption
is v alid, since the PIV images are not ov ersampled and ha ve a high image density with
small displacement gradients. Ne vertheless the v orticity field indicates the presence of
a v ortices, b ut tends to be v ery noisy , which makes the identification of v orte x centers
dif ficult. Moreov er , the vorticity also identifies shear stress as a v ortex as sho wn in Figure
4.4(a).
T o o vercome this, the
λ 2
operator is a useful method for the position estimation of v ortices
(see Figure 4.4(b)). Unfortunately the
λ 2
criteria does not pro vide any information about the
amplitude or direction of the v orte x itself. But once the position is kno wn other parameters
can be calculated to obtain the rele v ant information. T o detect v ortices, V ollmers [
83
]
stated that v ortices appear for non-real eigen v alues of the gradient tensor
G
(Equation
4.10).
G = d U
d x =  ∂ U
∂ X
∂ V
∂ X
∂ U
∂ Y
∂ V
∂ Y  (4.10)
T o separate v ortices from other patterns the discriminant
λ 2
of non-real eigen values is
calculated (Equation 4.11). V ortices are located at areas of negati ve λ 2 v alues.
λ 2 =  ∂ U
∂ X + ∂ V
∂ Y  2
− 4  ∂ U
∂ X · ∂ V
∂ Y − ∂ U
∂ Y · ∂ V
∂ X  (4.11)
The Equation 4.11 is restricted to two-dimensional flo w fields and can be e xtended for
three-dimensional v orte x detection if the full three-dimensional tensor is a v ailable. False
detection can occur at two-dimensional interpretation of flo ws if the ov erall flo w is highly
three-dimensional [62].
37

4 Evaluation and T racking
4.2 Alignment of m ultiple coherent structures in the
flo w
The interaction of v ortices induced at dif ferent times and locations can be seen as alignment
of multiple coherent structures. T o rate these structures se veral methods are used. One is
to look at the v ertical velocities with re gard to the incident flo w . A v ortex i s characterized
not only by its v orticity , b ut also by velocities v ertical to the flow .
In Figure 4.5(a) the simultaneous blo wing of three actuators are shown. Therefore three
nearly identical v ortices are induced propagating do wnstream. In the illustration on the
right hand side, the three actuators are cooperating with each other producing one big
v ortex. Since this data is obtained by a phase a veraging (Equation 4.6) the v ortex at the
end of the flo w field (
x ≈ 150 mm
) is the squeal of the v orte x induced in the front. The
v elocities gi v e a first hint of the ef fecti veness of the cooperati ve actuation. One might think
that the ef fecti veness is depending on the phase shift of blo wing. T o rate the alignment of
the structures the common computer vision algorithm RANSA C is used. This algorithm
is used for fitting a model to e xperimental data. T o o v ercome the drawback of the least
square method, where outliers are changing the fitted model, the data points are assessed
and therefore smoothed [
22
,
81
]. In this case the alignment of the footprints left by the
v ortices o ver time are rated by calculating the de viation from a linear fit. The outcomes
yields phase shifts Θ for best alignment.
The v ertical component of the velocity as sho wn in Figure 4.5 is e xtracted in slices as seen
in the illustration on the left hand side of Figure 4.6(a). T o obtain the rele v ant v elocities,
only those which are twice abov e the standard de viation are taken into account (see Figure
4.6, center). The illustration on the right hand side of Figure 4.6 sho ws the outcome of the
RANSA C algorithm. The sequel of the v ortex, caused by the phase a veraging as seen on
the lo wer right edge of the illustration, would falsify the result. Therefore, the algorithm
declares them as outliers, before fitting a linear line to the data. The square fitted error
for that linear line in cartesian coordinates is estimated and the mean v alue of the error is
taken as measure for the alignment. This means the better the alignment, the smaller the
estimated error . Since the a verage de viance of the velocity for small phase shift de viations
is only little, slices throughout the cross section of the v ortices are analyzed to v alidate the
results.
(a) V ertical velocities of simultaneous blo wing (b) V ertical velocities of cooperati ve blo wing
Figure 4.5: Isosurfaces of blo wing with dif ferent phase shifts (red +2 m
s , blue − 2 m
s )
38

4.3 V ortex detection and tracking
Figure 4.6:
Example of real (left) and rele v ant (middle) velocities of one slice and the fitted
line of the RANSA C algorithm (right)
The RANSA C algorithm can therefore be used to find the phase shifts which provides
the best alignment of separate induced v ortices o ver time. W ith the least de viation
the probability of constructi ve v orte x interaction, and therefore an amplification of the
mechanism of reattachment, is increasing. Ne vertheless it does not pro vide an y information
about the amplification and duration of v ortices or about the shear layer entrainment.
4.3 V or tex detection and trac king
The alignment of v ortices pro vide an estimation of the best phase shift, b ut to e v aluate the
physical beha vior of the flo w field the v ortices ha ve to be found and classified to wards their
impact on the reattachment process. There are a lot of detection methods, like
Lanbda 2
Method [
40
], Eigen vector Method [
75
] or Streamline Method [
59
] which are summarized
by Johnson and Hansen [31].
A simple b ut ef fecti ve method to identify the core center of a v ortex is presented by Holmén.
The idea is to identify the v ortex directly from the v elocity field information by looking at
the signs of the v elocity . The direction of the flo w around a center of rotation will ha ve
opposite signs on either side of the v ortex [
37
]. The search algorithm proceeds in sev eral
steps. The first step is to carry out a signum operation at e very point of the flo w field. T o
identify a v orte x, the four points around one point are selected and the sign of the v elocity
is considered. The point belongs to a vorte x center if the sum of the signs of the normal
v elocity of the two horizontal points and the sign of the tangential v elocities of the vertical
points is zero (see Equation 4.12 relating to Figure 4.7(a)).
Since this criteria is also true for shear stress another check has to be made. This is done
by considering only the signs of the normal v elocity of the left point and the tangential
v elocity of the upper point (see Equation 4.13). In this case the sum of the signs must not
be zero. Otherwise the considered point is discarded.
39

4 Evaluation and T racking
sig n ( v lef t ) + sig n ( v r ig ht ) + sig n ( u up ) + sig n ( u dow n ) = 0 (4.12)
and
sig n ( v lef t ) + sig n ( u up ) 6 = 0 (4.13)
This criteria usually finds se veral v orte x centers within one v ortex. In the case of v arious
centers, the Mean Shift algorithm finds the indi vidual center of the v orte x. The strength
of this algorithm is that the center of se veral v ortices in a flo w field can be found
simultaneously . In contrast to other clustering methods, there are no embedded assumptions
of the shape of the distrib ution or the number of clusters.
In general this algorithm treats the points as an empirical probability density function where
dense re gions correspond to the local maxima of the distrib ution. An iterati ve optimization
method, the gradient ascend method, is used on the local density until it con ver ges. Any
point associated with the stationary points of this method are considered as members of the
same cluster [
17
]. F or further and mathematical details refer to Cheng [
9
] and Comaniciu
and Meer [11].
In Figure 4.7(b) the detected core centers (marked as circles) and the center of the v ortex
(marked as star) are sho wn. It can be seen that the center found matches the real center
of this v ortex. But to be sure a last check is done. T o finally pass the detection method as
v ortex the center found has to match the
λ 2
criteria. Due to the speed and robustness of
this detection method it is suited for a lar ge amount of data as found by PIV recordings.
No w that the center is found, the dimensions of the vorte x can be computed using the
v orticity
ω
. The idea is that the vorticity around a v ortex center is follo wing a Gauss
distrib ution with the maximum located at the center . This assumption must be true for
the horizontal as well as for the v ertical part of the v ortex. In Figure 4.8 the v orticity of a
nearly circular shaped v ortex is sho wn in length (a) and height (b). The radius of a single
v ortex can no w be e xtracted using the corners of the vorticity distrib ution and with the
formula of the circle
f ( x ) = y m ± q r 2 − ( x − x m ) 2
the edges of the v orte x are gi v en. It
can be also seen in Figure 4.8 that e ven for this simple v ortex the base diameter of the
horizontal is slightly lar ger than for the v ertical distrib ution. This dif ference is greater for
comple x flo w conditions, like near w all v ortex pairs or v ortex interaction. The mismatch
(a) W orking principle of the
algorithm. The numbers
represent the sign of the
velocities. (after [37])
(b) Detected vorte x core centers
(circles) and result of MeanShift
algorithm (star)
(c)
λ 2
criteria for the v ortex
sho wn in Figure 4.7 (b)
Figure 4.7: Single steps of v orte x detection
40

4.3 V ortex detection and tracking
(a) Horizontel ω distribution (b) V ertical ω distribution
Figure 4.8:
V orticity distrib ution around the center (red cross) of a nearly circular shaped
v orte x
between the radii is handled using the ellipse formula sho wn in Equation 4.14.
 x − x m
r v  2
+  y − y m
r h  2
= 1 (4.14)
Ho wev er , most cases of vorte x expansion are co v ered v alidly (see Figure 4.9). Another
challenge is that v ortices mostly appear in pairs, or in the case of vorte x interaction at
least two v ortices are close together . Therefore, the v orticity distrib ution is not becoming
or crossing zero at the edges. Moreov er it is not always clear which v orticity belongs to
which v ortex, especially in the case of co-rotating v ortex pairs. Therefore starting from
the center in each direction only points higher than the standard de viation are taken into
account. This means that the real vorte x edge is not found, b ut the detected radii correspond
to
66 %
of the v orte x, referred to as the core radius of a v ortex. This is sho wn in both
illustrations of Figure 4.9, where the vorticity distrib ution expands be yond the detected
edges. Furthermore, the maximum of the vorticity distrib ution has often a small offset
related to the center . Since the of fset is small, the lo wer distance is taken in order to not
o verestimate the edges. This is sho wn for the horizontal line in illustration (b) of Figure
4.9. T aking the lar ger distance could cause an ov erlap in cases of nearby vortices. Since the
v orte x interaction is e v aluated, this would lead to false results, because tw o nearby v ortices
would ha ve the same bigger size, e ven if the y are not merged. Ha ving found the core radius
the points within can be e xtracted and analyzed with reg ard to the v ortex strength and flo w
beha vior .
The e valuation of v ortex interaction is based on the beha vior of the v ortices in respect to
the time. Therefore the v ortex must be tracked. Furthermore, all v ortices of the flo w field
time series must be determined and follo wed. This is done by computing the propagation
v elocity of the core center once a v ortex is detected. By means of the propagation v elocity
a search radius, in which the core center in the ne xt time step has to be found, is computed.
A safety factor of
1 . 5
is added to the computed search radius because of the influence of
the flo w field on the real vorte x propagation. Since the propagation velocity can not be
computed from the first flo w field an initial search radius has to be gi ven. If a v ortex core
center is found within the search radius in the next time step, the rotation of the v orticity
is checked. If they match, it is very lik ely that the v ortex is the same as detected in the
pre vious time step. T o be sure, the v ortex center of the further time step should be near
41

4 Evaluation and T racking
(a) V orticity and flow field with core radius edges
of a nearly circular shaped v ortex
(b) V orticity and flow field with core radius edges of a
elliptic shaped v ortex
Figure 4.9: Edge detection for dif ferently shaped vortices
the estimated place. T o estimate the ne w position of the v ortex center the strength and
direction of the propagation v elocity is used (see Equation 4.15).
 x
y  est
=  u
v  conv
· ∆ t  +  x
y  old
(4.15)
In Figure 4.10 (a) a v orte x with the search radius is sho wn wof fering an estimation where
the v orte x in the next time step should be. In Figure 4.10 (b) the next time frame is sho wn
with the v ortex center found. The estimation is only slightly higher than the actual core
center . The accuracy of the estimation is increasing with decreasing
∆ t
for two reasons.
First, the propagation v elocity is more precisely , on the other hand, the influence of the
flo w field on the vorte x is decreasing.
The o verall result of the detection and tracking algorithms is sho wn in Figure 4.10 (c).
There the v orte x with the core radius and tracked positions is sho wn. The v orte x properties,
obtained within the core radius, are stored and composed for each tracked v ortex. On the
basis of this data the strength, beha vior and changes during the e xistence of e very v ortex
are analyzed. Moreo ver the changes during the interaction of all v ortices can be monitored
o ver time.
42

4.3 V ortex detection and tracking
(a) V ortex with search radius and estimated
position of v ortex in the ne xt time frame (circle)
(b) Same v ortex in the ne xt time frame (red star).
The search radius and estimated position form
the prior time frame is also sho wn as working
principle of the tracking algorithm
(c) T racked v ortex with core radius after se veral time frames
Figure 4.10:
W orking principle (a,b) of tracking algorithm and o verall result of detection
and tracking
43

4 Evaluation and T racking
44

5 In vestigations of V or te x
Interaction
This sections presents the e valuation of the in vestig ation of merging v ortices without
pressure gradient. At first a single v ortex is in vestig ated with reg ard to the behavior and
propagation v elocity . Then the interaction of sev eral vortices induced at dif ferent time
steps are presented.
Afterwards, the results of the half dif fuser measurements are pro vided. In the beginning
the parameters and the base flo w of the diffuser are sho wn. Next the influence of a single
actuator ro w is presented. Then the ef fect of a pressure gradient on the mer ging of v ortices
induced from three actuator ro ws at different phase shifts is stated. At last a comparison of
single, distrib uted and cooperati ve actuation is done.
5.1 V or tex interaction without pressure gradient
5.1.1 Single v or te x pr opagation
The main idea is to amplify the reattachment process of pulsed blo wing by inducing a
second v ortex interacting with the arri ving v ortex. Kno wing the propagation velocity of
the v ortices induced by the pulsed blo wing is important to estimate the required time delay
for constructi ve interaction. Therefore, a single actuator was switched on at the flat plate of
the L WK-2 and measured with
22
uncalibrated hot film sensors simultaneously to obtain
se veral v elocity ratios at dif ferent Reynolds numbers.
In Figure 5.1 (a) the original data is plotted o ver time for all acti ve hot film sensors. The jet
v elocity is
v j et = 30 m
s
at an incident v elocity of
v ∞ = 20 m
s
, which leads to a velocity ratio
of
V R = 1 . 5
and a momentum coef ficient of
c µ = 0 . 12 %
. The dimensionless frequency
is
F + = 1 . 5
. The propagation of the v ortices is sho wn for three periods. Since the hot
film sensors are uncalibrated the amplitude does not say an ything about the strength of the
v orte x. Also two dif ferent types of hot film sensors are used. The more sensiti ve ones are
attached between the actuator ro ws, whilst the less sensitiv e are installed behind the last
actuator . T o ov ercome the intensity problem each signal is normed with its maximum and
only the fluctuation part is taken. Ne vertheless the cross correlation (Equation 4.8) has
been applied. Kno wing the distance of the sensors and the time delay , the cross correlation
can be computed and in Figure 5.1 (b) an example of the propag ation velocity is sho wn.
The parameters for the actuation are the same as on the left illustration. The red circles
indicate the analyzed v elocity and the dashed line is an exponential fit of the second order .
The propagation v elocity is considered v alid if the normed correlation coef ficient is at least
0.5. The propagation v elocity drops strongly to the velocity of the incident flo w within
45

5 In vestigations of V ortex Interaction
(a) T ime depending hot film signal at different
locations
(b) Computed propagation velocity and e xponential
fit
Figure 5.1:
Original hot film data and propagation v elocity of a V ortex at a v elocity ratio
V R = 1 . 5 and Reynoldsnumber Re = 6 . 87 e 5
the first
x = 16 mm
. Then the propagation v elocity of the vorte x decreases slightly ov er
the measured distance. It seems that the propagation velocity is link ed to the incident
flo w . Therefore, se veral measurements ha ve been tak en to in vestig ate the relation of jet
v elocity and incident flo w on the propagation v elocity . These measurements are sho wn
in Figure 5.2. The illustration on the left hand side sho ws the relation of the jet v elocity ,
decreasing from
V R = 2 . 3
to
V R = 1 . 0
at a constant Re ynoldsnumber of
Re = 6 . 87 e 5
.
V elocity ratios belo w 1 do not correlate suf ficiently to gi ve a clear statement about the
v ortex beha vior . The higher the jet velocity , the higher the propagation v elocity , but the
increase is small compared to the increase of the jet v elocity . Nev ertheless it has to be
mentioned that in this case, where the distance of the actuators is
d act = 40 mm
, the gap
between the propagation v elocities has to be considered.
The Re ynoldsnumber has a bigger influence on the propagation v elocity as sho wn in Figure
5.2(b). In the presented case, the jet velocity is held constant at
v j et = 40 m
s
. This means
not only a wider gap between the propagation v elocities, but also a change in the gradient
for the dif ferent Reynoldsnumbers. This leads to the assumption that the Reynoldnumber
has the lar gest influence on the v ortex propag ation, but the v elocity ratio also has a stronger
influence than Figure 5.2 (a) would presume. T o combine these two dependencies, the
propagation v elocity at a distance of
d 40 = 40 mm
was computed and put into relation
with the incident v elocity .
The propagation ratio
P R = v conv , 40
u ∞
is sho wn in Figure 5.3 (a) ov er the v elocity ratio. Since
the actuators ha v e a
40 mm
distance, the influence of the jet v elocity must be considered,
b ut the main dri ving parameter is the Reynoldsnumber . The influence of the jet velocity
increases linearly with the increase of the v elocity ratio. This means that a relationship can
be established to predict the propagation v elocity at the point of the second actuator . This
formula is gi ven by Equation 5.1. T o e xpand the prediction to other actuator distances a
factor
k 40 = 1 − 2 · d act
1 − 2 · d 40
is established. Since the jet influence is decreasing with increasing
distance, the gradient of the slope in Figure 5.3 is decreasing slightly . The factor therefore
decreases the influence of the jet v elocity as well as the slope. This assumption is v alid for
distances up to d act = 100 mm .
v conv ,act ≈ k 40 ·  1
6 · v j et + 3
4 · v ∞  (5.1)
46

5.1 V ortex interaction without pressure gradient
(a) Dependency of the propag ation velocity on the
velocity ratio
(b) Dependency of the propagation v elocity on the
Reynoldsnumber
Figure 5.2: Dependencies of v orte x propagation velocity v conv
The hot film sensors are unable to resolve the single v ortex, b ut sho w an increase in
amplitude o ver the hole blo wing phase. T o analyze the v ortex independently , time
depending PIV measurements are taken with a v elocity ratio of
V R = 2 . 4
, a momentum
coef ficient of
c µ = 0 . 3 %
with a sampling frequenc y of
F s = 6 kHz
. In Figure 5.4 (a) the
first appearance of a full v ortex is sho wn with core center and core radius. The vorticity
of the v orte x of the flo w field is also sho wn, where red marks counter -clockwise and blue
clockwise rotating v ortices. In Figure 5.4 (b) the same vorte x is shown, when reaching
the second actuator after an elapsed time of
∆ t = 1 . 7 ms
. The tracked positions are also
sho wn in this illustration.
It sho ws that the vorte x is not only propagating in streamwise direction, b ut also departs
from the surface during its propag ation. At this point a counter rotating v ortex starts to
b uild up, which is indicated by the clockwise rotating vorticity in front of the track ed v ortex.
Another point is that the v orticity and size of the v ortex are decreasing with distance and
time, due to its dissipati ve beha vior .
The tracking algorithm not only computes the core center and radius, b ut also determines
the propagation v elocity of the v ortex core. During the measurements ten v ortices are
recorded and the propagation v elocity is analyzed. The median v elocity of the ten v ortices
Figure 5.3: Propagation ratio o v er velocity ratio
47

5 In vestigations of V ortex Interaction
(a) V ortex with core radius and center after
emer gence
(b) Same v ortex of illustration (a) after a certain time
with tracked positions
Figure 5.4: T ime resolv ed PIV visualizations of single actuation on a flat plate
are taken and compared to the result of the hot film measurements, acquired under the
same conditions. Since these ten v ortices are not tracked at the same position and are
v arying in occurrence length, the velocities within a fi v e millimeter range are taken to
b uild the median. This is sho wn in Figure 5.5. The propagation v elocity of the v ortex
corresponds well with the v elocity computed from the hot film sensors and the computed
e xponential fit. The velocity predicted on the basis of Equation 5.1 w ould be under the
gi ven conditions
v conv , 40 ≈ 23 m
s
. The v elocity from the PIV measurements is at that point
v conv ,P I V = 20 . 5 m
s
. Although the prediction is ov erestimating the velocity slightly , it can
be used as a first hint. Kno wing the propagation v elocity , no w the phase shift between to
actuators is computed with Equation 2.10. In this case the phase shift is around
Θ ≈ 84 ◦
,
taking into account that the v orte x is fully built up ten millimeter behind the slot.
Figure 5.5:
Comparison of computed v ortex propag ation velocity from hot film and PIV
data for v ∞ = 20 m
s and a v elocity ratio of V R = 2 . 5
48

5.1 V ortex interaction without pressure gradient
5.1.2 V or tex interaction
Understanding the interactions of two co-rotating v ortices induced at dif ferent times is a
prerequisite to achie ve the main task of reattaching the flo w more ef ficiently . Therefore
the interaction of two v ortices is in v estigated at the L WK-2 for dif ferent phase shifts
Θ
by
means of PIV measurements. This was done at a v elocity ratio of
V R = 2 . 3
, a momentum
coef ficient of c µ = 0 . 3 % and Strouhalnumbers of F +
1 = 1 . 5 and F +
2 = 1 . 3 .
Using the correlated phase shift, computed on the basis of Equation 2.10, it turned out that
the v ortices are not mer ging suf ficiently . This is sho wn in Figure 5.6 (a-d). The first vorte x
induced from the first actuator reaches the second slot at
d act, 2 = 40 mm
in illustration (a).
This is considered as
t = 0 ms
of the interaction process. In illustration (b) the second
actuator starts to induce a v orte x at
t = 0 . 34 ms
. In this state the first v ortex is already
interfering with the ne w one. Furthermore the emergence of the ne w vorte x is af fected. In
the ne xt steps the ne w vorte x fully builds up and is pushing the first one a way . This process
withdra ws energy and therefore v orticity of both vortices. This is sho wn in illustration (c)
at a time step of
t = 0 . 68 ms
after the interaction process starts. This results in a co-rotating
v orte x pair interfering with each other , where only one vorte x with lo w v orticity remains
(d) at the end.
This destructi ve beha vior continues if the second v orte x is induced too late, as sho wn in
Figure 5.7 (a-d). In this case the phase shift is set to
Θ = 92 ◦
. Again, the appearance of
the first v orte x marks the beginning of the interaction process with
t = 0 ms
. In illustration
(b) at the be ginning of the second actuator blo wing, the first v ortex is at the point, where
the second v ortex is b uilding up. After
t = 0 . 51 ms
the uprising v elocity of v ortex tw o
(a) (b)
(c) (d)
Figure 5.6:
Interaction of two co-rotating v ortices
Θ = 84 ◦
. (a) Appearance of first v orte x
t = 0 ms
(b) Inducing second v orte x
t = 0 . 34 ms
(c) First v ortex is pushed
upwards
t = 0 . 68 ms
(d) Both v ortices interfering with each other
t = 1 . 36 ms
49

5 In vestigations of V ortex Interaction
(a) (b)
(c) (d)
Figure 5.7:
Destructi ve interaction of tw o co-rotating v ortices
Θ = 92 ◦
. (a) Appearance of
first v ortex
t = 0 ms
(b) Second actuator starts blo wing
t = 0 . 34 ms
(c) First
v orte x resolves t = 0 . 51 ms (d) Second v ortex with less v orticity t = 0 . 85 ms
is dissolving the first one completely (illustration c) and for a short time span no v ortex
is present at all. In the last illustration (d) the ongoing blo wing of the second actuator is
inducing a ne w , b ut significantly weaker v ortex.
Therefore the phase shift was lo wered so that the second actuator induces a v ortex before
the v orte x of the first actuator arri ves (see Figure 5.8 (a-d)). The optimal phase shift to
mer ge these two v ortices is found to be
Θ = 72 ◦
, which is
∆ t = 0 . 4 ms
earlier than
e xpected. After the first vorte x appeared at
t = 0 ms
in illustration (a) the second v ortex
starts to b uild up in front of this one. Illustration (b) sho ws, that the second vorte x uses the
v orticity of the first one to b uild up a bigger v ortex. After
t = 0 . 51 ms
this process is still
ongoing, e ven enhancing the v orticity further (c). In the last illustration (d) a bigger and
stronger v orte x emerges from this interaction process. Not only the v orte x is amplified, the
interaction time is also reduced, ha ving a less disturbing ef fect on the flow .
The special case of simultaneous blo wing results in two v ortices propagating do wnstream
hardly influencing each other . Ne vertheless, due to the turb ulence of the pre vious v orte x
the subsequent v orte x is losing strength more rapidly and disappearing earlier .
T o amplify the v orticity and duration of a v ortex, and thus the mechanism of reattachment,
it is necessary to induce the second v ortex before the first one appears. The mer ging
process is characterized by the ne wly created vorte x recei ving the v orticity of the incoming
v orte x. Using a constructi ve phase shift the duration of the mer ging is fast, with minimal
turb ulence in volv ed. The emer gence of the second directly underneath the vorte x to merge
with, repels the first one resulting in two turb ulent co-rotating vortices with weak er v orticity .
T o decompose the first one the second actuator must induce a v ortex shortly after the first
v ortex has passed the point of v ortex origin. In this case the direction of the normal
50

5.1 V ortex interaction without pressure gradient
(a) (b)
(c) (d)
Figure 5.8:
Cooperati ve interaction of tw o co-rotating v ortices
Θ = 72 ◦
. (a) Appearance
of first v orte x
t = 0 ms
(b) First step of v orte x merging
t = 0 . 34 ms
(c) Bigger
v ortex b uilds up
t = 0 . 51 ms
(d) Stronger v orte x propagates do wnstream
t = 0 . 85 ms
v elocities are opposed to each other . Nev ertheless the ongoing blowing of the actuator
results in a ne wly generated vorte x.
T o confirm the pre vious results under the conditions and the adaptions necessary for the
measurements carried out at the GSW , 2D hot wire measurements are done. A rele v ant
section of the middle plane was measured with an e xponential grid for better resolution
of the boundary layer . The 1342 single measurement points are phase a veraged with
Equation 4.6 to visualize the coherent structures of the flo w field. T o correspond with the
characteristic length of the setup, the dimensionless frequenc y of the first actuator ro w is
set to a subharmonic of
F + = 1
. This rsults in a Strouhalnumber of
F +
1 = 2
and therefore
for the second actuator ro w F +
2 = 1 . 7 . The velocity ratio was set to V R = 2 .
In Figure 5.9 (a) simultaneous blo wing is shown. There, two v ortices are propagating
simultaneous do wnstream until dissolving after
t = 0 . 32 ms
. Applying the Equations 2.10
and 5.1 the phase shift would be
Θ ≈ 100 ◦
. This is sho wn in Figure 5.9 (b). The path of the
first v orte x is interrupted before the v orticity of the second v ortex starts. It can be seen that
at period step
Φ = 175 ◦
two isosurf aces are on top of each other until the upper dissolves
a fe w steps later . This is in accordance with the measurement presented in Figure 5.6 (d)
where the pre vious vorte x is pushed upwards. If a vorte x emerges, from the second actuator
ro w before the first generated vorte x arriv es, the two v ortices are matching harmoniously
propagating the entire measured length (see Figure 5.9 (c)). At last a deconstructi ve phase
shift, similar to the measurements at the L WK-2 is sho wn in illustration (d). In this case,
the phase shift is set to
Θ = 150 ◦
. The first vorte x is terminated by the emergence of
the second v ortex, and as a consequent the second v ortex only lasts a short time before
51

5 In vestigations of V ortex Interaction
(a) Simultaneous blowing (b) Phase Shift Θ = 100 ◦
(c) Phase Shift Θ = 89 ◦ (d) Phase Shift Θ = 150 ◦
Figure 5.9:
Comparison of the v orticity for dif ferent phase shifts. Counter-clockwise
rotating (red) and Clockwise rotating (blue) (a) Simultaneous blo wing of two
ro ws (b) Computed phase shift
Θ = 100 ◦
(c) Constructi ve interaction for phase
shift Θ = 89 ◦ (c) Destructi ve interaction at phase shift Θ = 150 ◦
disappearing. Similar two the pre vious destructi ve case the ongoing blo wing generates a
ne w vorte x.
Interpreting these results to amplify or stabilize the reattachment process it is necessary
to mer ge the generated v ortices cle v erly . The mer ging process is designated combining
the v orticity of the v ortices. This can be done by inducing the second v ortex before the
pre viously induced vorte x arriv es in the appearance area of the ne w v ortex. If the second
v orte x is generated too early both vortices are propag ating do wnstream, hardly af fecting
each other . Like wise, inducing a vorte x too late also generates two do wnstream propagating
v ortices. Ne vertheless these tw o vortices are not as strong as a v ortex produced by a single
actuator . T w o considered cases sho w insuf ficient results. First, inducing the second vorte x
e xactly under the propagating v orte x. This leads to an repellent reaction of the v ortices,
withdra wing energy from both. The second e ven more destructi v e case is generating a ne w
v orte x right behind the propagating one. This can cause an annihilation of both vortices.
52

5.2 V ortex interaction in half dif fuser
5.2 V or tex interaction in half diffuser
5.2.1 Basic flow of half diffuser
The measurements re garding the reattachment of a pressured induced separation were
carried out in a half dif fuser with an adjustable step angle. T o analyze and e v aluate the
results of these measurements kno wing the basic flow parameters is important. Se v eral
parameters are important when dealing with flo w separation at an inclined step. There is
the step Re ynoldsnumber
Re H
, which uses the step height
H
as characteristic length. This
Re ynoldsnumber is therefore a function of the step angle α step . The flo w v elocity was set
to
v ∞ = 20 m
s
. W ith these v alues the step Reynoldnumber is between
1 . 59 e 5 ≤ RE H ≤
1 . 74 e 5
for the used step angles
21 ◦ ≤ α step ≤ 23 ◦
. This Reynoldnumbers are influencing
the shear layer of the separated flo w . In these cases the shear layer is dominated by the
turb ulent share, since the step Re ynoldsnumber is abov e R e H < 10 4 [43].
Another parameter is the condition of the boundary layer , which should be turb ulent
upstream of the step. In order to ensure that for all flo w conditions, the transition of the
boundary layer is forced with a carborundum at the be ginning of the wind tunnel inlet.
F ollo wing Schlic hting und Gersten [
66
], the form factor for a turb ulent boundary layer is
between
1 . 3 < H 12 < 1 . 4
. The form factor can be computed with the displacement height
δ 1 and the momentum thickness δ 2 .
H 12 = δ 1
δ 2
(5.2)
At a step Re ynoldnumber of
Re H = 174000
corresponding to a step angle
α = 23 ◦
, the
displacement height is
δ 1 = 1 . 35 mm
and the momentum thickness is
δ 2 = 1 . 007 mm
.
The boundary layer thickness in front of the step is
δ 99 = 9 . 46 mm
. The form factor of
H 12 = 1 . 35 pro ves therefore the fully turb ulent boundary layer .
In a half dif fuser the cross section is extended by the inclined step, whereby the static
pressure increases by con verting kinetic ener gy into pressure ener gy . The increase in
pressure is therefore a function of the e xpansion ratio
E R
of the half dif fuser and is
stated as pressure reco very
∆ c p
. The pressure reco very is measured by means of tw o wall
mounted pressure sensors, one before the step with a distance
x/L = − 0 . 6
and the second
right after the step with a spacing of
x/L = 1 . 5
. The positions are shown in Figure 5.10 (a)
in addition to the occurring flo w states for dif ferent step angles
α step
. In Figure 5.10 (b) the
pressure reco very is plotted ag ainst the step angle. The pressure recov ery increases linearly
until a step angle of
α step = 20 ◦
. The local separation bubble as sho wn in illustration (a)
arises at an angle of
α step = 17 ◦
, b ut is not measured by the pressure transducer , which is
still outside of the separation [
32
]. At
α step = 20 ◦
the pressure induced separation arises
and is increasing with an increasing step angle. This happens, when the pressure recov ery
∆ c p
drops in illustration (b). The do wnstream pressure transducer is no w located within the
area of recirculation. In this state, the pressure reco very tak es place o ver the free e v olving
e xtension of the separated flo w field. The separation position is thereby mo ving upstream
until it geometrically separates at the leading edge of the step at
α step = 24 ◦
. The bigger
the separation gets, the more the pressure reco very ∆ c p decreases.
Acti ve flo w control is supposed to reattach the flo w for these step angles of pressure
induced separation (
20 ◦ ≤ α step ≤ 23 ◦
). Ef fecti ve reattachment of the flo w to the surface
53

5 In vestigations of V ortex Interaction
(a) Schematic visualization of separation states and
positions of the pressure transducer (after [32])
(b) ∆ c p vs α step of the half dif fuser
Figure 5.10:
(a) Schematic separation conditions and positions of the pressure transducers.
(b) Pressure reco very o ver the step angles for the half dif fuser
leads to a pressure reco very of
∆ c p,max
as sho wn by the dotted line in illustration (b) on
the right. Therefore the value of
∆ c p
is a measure of the ef fectiv eness of the actuation for
the half dif fuser configuration.
Since most in vestigations took place at a step angle of
α step = 23 ◦
, this position as well
as the corresponding pressure reco very (
∆ c p = 0 . 43
) is marked in Figure 5.10 (b) by the
dashed lines. The marked area is the theoretical gain acti ve flo w control can achie v e. The
a v eraged velocity field with pressure induced separation is sho wn in Figure 5.11 including
the actuator insert with the position of the three actuators do wnstream. The scaling of
the abscissa is zero at the be ginning of the insert, which do not mark the be ginning of
the step, due to the round edge of the half dif fuser . The distance between the actuators
is
d act = 40 mm
. F or the step angle of
α step = 23 ◦
the a v eraged separation point lies
abo ve the first actuator slot. The redirection of the flo w is reduced and a recirculation
area is formed, whereby the pressure recov ery is decreasing. This flo w condition, with
the separation position upstream of the actuator , is a challenging configuration for the
actuation concept, b ut with certain parameters it is possible to reattach the flo w .
Figure 5.11:
Flo w visualization of the half dif fuser at a step angle
α step = 23 ◦
and
v ∞ =
20 m
s
. The positions of the inacti ve actuators (
v j et = 0 m
s
) are sho wn relati vely
to the separation.
54

5.2 V ortex interaction in half dif fuser
Since reasonably de veloped v ortices are essential for this in vestigation, and to use the full
capabilities of the PIV system, the total momentum coef ficient was set to
c µ, 3 ≈ 1 %
. The
results of the cooperati ve actuation are compared to the simultaneous blo wing. This is
done to sho w the benefit, which can be achie ved by a slight increase of the system ef fort
compared to the distrib uted actuation.
5.2.2 Single v or te x influence
Acti ve flo w control by means of pulsed blo wing generates coherent structures resulting
in a dynamic exchange and a transfer of fluid v ertical to the surface. Therefore not only
the increase in momentum in the recirculation area, b ut also the dynamic ef fects are used
to reattach the flo w . This increases the performance of the acti ve flo w control system. In
Figure 5.12 (a), the dominating v orte x structure is sho wn for the phase angle of
Φ = 100 ◦
.
The temporal distance between the rising edge of the trigger signal and the appearance
of the v ortex is
Φ = 85 ◦
. The v ortex is fully de veloped after
∆ t = 0 . 33 ms
. The
phase a v eraging, introduced in Equation 4.6, filters the phase independent and small scale
structures.
W ith the beginning of the blo wing phase, a v ortex is induced at the actuator slot, the
v orticity and strength of which depends on the jet angle [
32
]. In this case a jet angle
of
α j et = 45 ◦
is chosen, resulting in a positi ve rotating v ortex abo v e the jet. The jet is
redirected to the surface by another induced v ortex, directly supplying high ener gy fluid to
the recirculation area. Furthermore the vorte x structure is responsible for a fluid transfer
transv ersely to the main flo w .
In the illustration on the ride hand side of Figure 5.12 the counter rotating v ortex is sho wn.
This happens at a phase shift of
Φ = 190 ◦
. These two v ortices are b uilding a vorte x pair ,
transporting lo w energy fluid a way from the recirculation area. Meanwhile the velocity
component to wards the surface and the jet are transporting high ener gy fluid to the surface.
The v orticity of the v orte x pair ov er the propagating distance is sho wn in Figure 5.13 (a).
After the de velopment of the v orte x the vorticity increases within the ne xt three phase
(a) Counter-clockwise rotation v ortex shortly
after the emer gence
(b) Emergence of a related clockwise rotating v ortex
Figure 5.12: Single v orte x after t = 0 . 34 ms and related vorte x pair after t = 4 . 2 ms
55

5 In vestigations of V ortex Interaction
(a) V orticity of the vorte x pair ov er distance (b) Propagation ratio ( u conv
u ∞
) of the v ortex pair
(c) V elocity and direction of the vortices o ver distance
Figure 5.13:
V orticity , propagation ratio and direction of the v ortices propagation, which
emer gence for single actuation
steps to its maximum. W ith further propagating the v ortex is loosing strength, until it
disappears after
∆Φ = 175 ◦
. The counter rotating vorte x appears late at a phase angle
of
Φ = 190 ◦
with less v orticity . The vorticity then only decreases a little during the
propagation do wnstream until it disappears after
∆Φ = 165 ◦
. The propagation ratio
P R = ~ v conv
u ∞
o ver distance is sho wn in illustration (b) of Figure 5.13. W ith the appearance
of the v ortex the propag ation velocity increases up to
~ v conv = 1 . 2 · u ∞
and then decreases
to a v elocity around
~ v conv = 0 . 8 · u ∞
, which complies with the median propagation v elocity
of this v ortex. At the time the counter rotating v ortex is detected the v ortex propagation
accelerates up to
~ v conv = 1 . 65 · u ∞
until it disappears. Ne vertheless the counter rotating
v ortex propag ation velocity increases to the median v elocity , propagating with it until it
disappears.
T o understand the acceleration of the counter clockwise rotating v ortex Figure 5.13 (c) is
sho wn. There the position in the flo w field as well as the velocity is presented. The jet
angle
α j et = 45 ◦
at the be ginning of the v ortex propag ation is visible. The v orte x is then
steadily cast a way from the surf ace. The acceleration begins, when the v ortex is reaching
the end of the boundary layer , which is about
δ 99 ≈ 9 mm
. Furthermore, the appearance of
the clockwise rotating v orte x seems to enhance the propagation velocity as well.
56

5.2 V ortex interaction in half dif fuser
5.2.3 Effect of pressure gradient on v or tex interaction
The v orte x interaction with zero pressure gradient is presented in section 5.1.2. In this
section the v orte x interaction is in v estigated with the present of an adv erse pressure gradient,
obtained at the half dif fuser with an step angle of
α step = 23 ◦
. T o analyze the ef fect of the
phase shift, three representati ve actuation cases are considered.
The simultaneous blo wing is sho wn in Figure 5.14 (a), depicting three v ortices with core
radii and tracked positions. The v ortices are induced at the same time b ut are located
at dif ferent positions downstream. The core radii are increasing with the location of the
actuators do wnstream, but the v orticity , on the other hand, is decreasing. The vortices are
dissipating ener gy and thereby gro wing bigger in size. Apparently a vorte x is impeded if
another v orte x is follo wing and this ef fect is increasing with the number of vortices. The
reason for that, stems from the mechanism of reattaching the flo w by fluid entrainment
through the shear layer . Through interaction of the vortices with the separated shear
layer a momentum transfer v ertical to the incident flo w is generated. This momentum
transfer ensures an e xchange of fluid through the shear layer . Furthermore, the jet of
the actuator attaches to the surface directly increasing the momentum of the separated
area. Having se v eral vortices follo wing each other , the sequencing vorte x transports the
dispensed fluid of the jet located do wnstream away from the surf ace. Moreov er , the fluid
which is transported into the recirculation behind a v ortex, is contrary to the entrainment
of the follo wing one.
The v orticity of the core radius is obtained for e very single time step and sho wn in Figure
5.14 (b) o ver the distance
x
. The v ortices are numbered from the first time they are detected.
The a verage appearance distance of the single v ortex is about
90 mm
until it disappears.
(a) T racked positions with core radius for simultaneous blo wing
(b) V orticity over track ed location (c) Propagation Ratio vs. v ortex location
Figure 5.14:
Flo w field, vorticity and propag ation ratio for simultaneous blo wing. Phase
shift
Θ = 0 ◦
, V elocity Ratio
V R = 2 . 4
, Step Reynoldsnumber
Re H =
174000
57

5 In vestigations of V ortex Interaction
(a) T racked position and core radius for cooperati ve actuation
(b) V orticity vs tracked location (c) Propagation Ratio ov er tracked position
Figure 5.15:
Flo w field and vorticity for constructi ve interaction. Phase shift
Θ = 105 ◦
,
V elocity Ratio V R = 2 . 4 , Step Reynoldsnumber Re H = 174000
The v orticity is thereby decreasing rapidly within the first
60 mm
. The dissipati ve ef fect
of the v orte x influence on each other starts with the de v elopment of the v ortices. While
the first one has the highest v orticity , it is decreasing with e very ne xt v ortex. Ho wev er the
gradient of the v orticity loss is not changing due to this interaction. The propagation ratio
is similar to the single actuator ro w acti ve and sho wn in Figure 5.14 (c). The propagation
ratios increase up to
P R ≈ 1 . 2
and then decrease to the median ratio of
P R = 0 . 8
. All
the v ortices start to increase the propagation v elocity when leaving the boundary layer .
Although the v elocity ratio is smaller , the v ortices are propagating further do wnstream
compared to the single actuation.
The cooperati ve interaction, as sho wn in Figure 5.15 (a), is, ho we v er , more constructi v e.
The core radius as well as the v orticity are amplified by the mer ging process of the v ortices.
The tracked position suggests that the interaction between the arri ving v orte x and the
induced v ortex from the third act uator ro w is not mer ging perfectly (
x ≈ 120 mm
). The
transition at
70 mm ≤ x ≤ 90 mm
is smoother than at the location of the third actuator
ro w between
110 mm ≤ x ≤ 130 mm
. This is ev entually prov en by the v orticity sho wn
in Figure 5.15 (b). Whereas the first mer ging process resulted in an amplification of the
v orticity (
x ≈ 74 mm
), the second interaction (
x ≈ 120 mm
) do not gain a higher v orticity .
At least the v orticity is higher than for a single one and is still stabilizing the v ortex.
Ne vertheless, to understand the loss of v orticity , the mer ging process must be considered
more closely . Therefore a time series of the first vorte x interaction is sho wn in Figure
5.16 (a-f). In the illustration on the left, the vorte x arri ves after
∆ t = 0 . 42 ms
of its first
appearance. In illustration (b) the second actuator starts the blo wing phase after a phase
shift of
Θ = 105 ◦
. Since the jet is oriented
α j et = 45 ◦
, the v ortex arises about
5 mm
behind the slot location. The jet v elocity is redirected to wards the preceding v ortex and
58

5.2 V ortex interaction in half dif fuser
(a) T ime step t = 0 . 78 ms (b) T ime step t = 0 . 82 ms (c) T ime step t = 0 . 86 ms
(d) T ime step t = 0 . 91 ms (e) T ime step t = 0 . 95 ms (f) T ime step t = 1 . 00 ms
Figure 5.16:
Sequence of v orte x merging process for
Θ = 105 ◦
at a step Re ynoldsnumber
of Re H = 174000
simultaneously this v orte x is descending to wards the surf ace (see Figure 5.16 (c-d)). The
rotating v elocity is extended o ver the arri ving vorte x, forming one big stretched vorte x. In
the illustrations (e -f) a stronger circular shaped v ortex is propag ating further do wnstream.
The mer ging process happens within a time span of
∆ t ≈ 0 . 2 ms
. The necessity of
inducing a v orte x at the right time is important and depends on the propagation velocity of
the v orte x. The mer ging process is influencing not only the v orticity and core radius, b ut
also the propagation v elocity as sho wn in Figure 5.16 (c). Here the propagation ratio of
the v orte x
P R
is plotted o ver the v ortex location
x
. The initial propagation v elocity of the
mer ged v ortices is increased by
50 %
, compared to the initial propagation v elocity of the
first v ortex. As a result, the third actuator induces the v ortex a little to late and therefore
the mer ging process is impeded and less v orticity e volv es. At least the interaction is still
there, amplifying and stabilizing the v ortex. Ne v ertheless the second merging process can
be optimized and obtains an e ven higher impact on the separation, by adjusting the phase
shift Θ between the second and the third actuator ro w .
A constructi ve v orte x interaction takes place o ver certain phase shifts
Θ
, b ut inducing
(a) V orticity of a destructiv e phase shift ov er distance
(b) Propagation ratio for the destructi ve case in (a)
Figure 5.17: V orticity and propagation ratio for a phase shift of Θ = 150 ◦
59

5 In vestigations of V ortex Interaction
(a) T ime step t = 0 . 87 ms (b) T ime step t = 0 . 91 ms (c) T ime step t = 0 . 95 ms
(d) T ime step t = 1 . 00 ms (e) T ime step t = 1 . 04 ms (f) T ime step t = 1 . 09 ms
Figure 5.18:
Sequence of a destructi ve v ortex interaction for
Θ = 150 ◦
at a step
Re ynoldsnumber of Re H = 174000
a subsequent v orte x too late is dissolving the preceding v ortex. The vorticity of such a
destructi ve case is sho wn in Figure 5.17 (a). The first v orte x de velops normally until the
emer gence of the next v ortex, where the preceding one dissolv es. The ne wly generated
v orte x has 50 % less vorticity than the first one. When the third v orte x is induced, a small
o verlap occurs, b ut the vorticity is ag ain reduced about
50 %
. Ho wev er , the propagation
ratio, sho wn in illustration (b) of Figure 5.17, is hardly af fected by the destruction of the
v orte x.
A sequence of this progress is sho wn in Figure 5.18 (a-f). In illustrations (a-b),the vorte x is
propagating o v er the emerging area of the second v ortex. At the beginning of the blo wing
phase of the second actuator , the first vorte x is located right in front of that slot. Therefore,
the descending v elocity of the first v ortex is opposed to the ascending v elocity of the jet,
resulting in a complete destruction of this particular v orte x (Figure 5.18 (c-d)). Moreov er ,
the ne wly induced vorte x is impeded in its de v elopment, resulting in a weaker v orte x with
less v orticity . Although a small part of the preceded v orticity seems to be included in the
ne w one (illustration (e)), the vorticity is small compared to e ven the simultaneous blo wing.
Since the propagation v elocity is hardly changing during this interaction, the procedure is
repeated at the ne xt slot.
60

5.2 V ortex interaction in half dif fuser
5.2.4 Comparison of single and cooperative actuation
When reattaching a separated flo w by pulsed blo wing, it is important to increase the flo w
momentum in the separated area and refill it with high ener gy fluid. T o increase the wall
near momentum an entrainment through the shear layer has to take place in addition to the
direct input of the jet. This fluid transfer triggered by the coherent structures is visualized
by means of the v elocity perpendicular to the surface.
T o e xtract the normal velocities, lines perpendicular to the surf ace of the flo w field behind
e very actuator (
d n = 6 mm
) are taken and analyzed for e v ery measured phase angle. In
figure 5.19 these lines are sho wn in respect to the velocity magnitude of the pressure
induced separated flo w . The shear layer at the lines ha v e a height of
( y /H ) 1 ≈ 0 . 05
for
the first line,
( y /H ) 2 ≈ 0 . 95
for the second and
( y /H ) 3 ≈ 0 . 12
for the last. T o guarantee
the fluid transfer through the shear layer , the normal velocity must be abo ve these v alues.
The fluid transfer for dif ferent cases are sho wn in Figure 5.20 (a - i) in respect to one
actuation period. Each column illustrates the corresponding line in Figure 5.19. The first
case (Figure 5.20 (a-c)) is the single actuator ro w acti ve with a v elocity ratio
V R 2 . 9
. The
v ortex is induced at a phase angle of
Φ = 85 ◦
. The vorte x induces an upward v elocity
around the positi ve v elocity component of the v ortex responsible for the remo val of the
lo w energy fluid. The e xtension of this fluid transfer extends clearly abo ve the shear
layer . Meanwhile the descending v elocity is present o ver nearly the whole actuation
period, transferring high energy fluid into the separation area. F or the second location
at
x = 80 mm
the v orte x has extended, still transporting fluid through the shear layer .
Ho wev er , a region with no normal v elocities can be seen around the upward direction of
the v elocity . This region e xtends as sho wn in Figure 5.20 (c) at a location of (x = 120 mm).
Since a v elocity ratio of
V R = 2 . 9
is suf ficient to reattach flo w by itself, the entrainment
is still there, b ut decreasing with the location do wnstream.
In Figure 5.20 (d-f) simultaneous blo wing for the three lines is illustrated. Here the velocity
Figure 5.19:
Half dif fuser flo w for an unactuated case at
v ∞ = 20 m
s
with the marked lines
where the normal v elocities are analyzed. The position are related to the
actuator slot positions
61

5 In vestigations of V ortex Interaction
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
Figure 5.20:
Normal v elocities for dif ferent actuation cases ov er period. (a-c) Single
actuation. (d-f) Simultaneous blo wing (
Θ=0 ◦
). (g-i) Constructi v e phase
shift ( Θ = 105 ◦ )
ratio is
V R = 2 . 4
and therefore
21 %
less than for the single actuation. At the beginning of
the step in Figure 5.20 (a) the entrainment through shear layer is sho wn. The descending
v elocity of the v ortex is inducing a transfer of fluid to wards the surf ace, while the upward
direction is casting fluid a way . In the next illustration (e) the impeded transfer is depicted.
The first v orte x is weakened and the transfer is damped. The second v orte x is smaller than
the upstream one, hardly interacting with the shear layer at a height of
( y /H ) 2 ≈ 0 . 9
. The
transfer of fluid is getting worse with the location do wnstream (Figure 5.20(f)). The third
v ortex is e v en smaller , not triggering a fluid transfer through the shear layer . The whole
transfer is scattered, damping the entrainment process o ver the period.
The cooperati ve actuation for a phase shift of
Θ = 105 ◦
and a v elocity ratio
V R = 2 . 4
is sho wn in the illustration (g - i). Again at the first position the v ortex triggers an
entrainment, lasting nearly the whole period. The second location, as illustrated in (h),
sho ws the enhancing mechanism of cooperati ve interaction. The v ortex has mer ged and
strengthened inducing a higher transfer through the shear layer throughout he entire period.
This ef fect is ev en greater for the location further downstream (Figure 5.20 (i)). Both
directions of the normel v elocities of the vorte x are gro wing bigger ensuring an optimal
transfer all along the increasing shear layer height.
Due to the dif ferent velocity ratios between the single actuator ro w and the cases of
cooperati ve blo wing, a quantitati v e comparison is impossible. Ne vertheless, the qualitati ve
comparison sho ws that a constructi ve interaction is suitable to stabilize the entrainment
through shear layer , at least ov er the measured flo w field. Moreov er the fluid transfer is
62

5.2 V ortex interaction in half dif fuser
e ven stronger with less jet v elocity when the v ortices mer ge than for single blo wing. On
the other hand, it is sho wn that simultaneous blo wing impedes the entrainment by e vading
the fluid transfer through the simultaneous propagating v ortices. Furthermore, not only the
entrainment process is impeded, b ut also the formation of the v ortices itself.
63

5 In vestigations of V ortex Interaction
64

6 Ev aluation of Cooperative
Actuation
In this section the e v aluation and improv ement of the cooperati ve actuation are presented.
In the first part the results of the PIV measurements are sho wn. Since reasonably de veloped
v ortices are essential for this in vestigation, and to use the full capabilities of the PIV system,
the total momentum coef ficient was set to
c µ, 3 ≈ 1 %
. The results of the cooperati ve
actuation are compared to the simultaneous blo wing. This is done to show the benefit,
which is attainable by only a small increase of the system ef fort compared to the distrib uted
actuation.
The second part describes the impro vement with re gard to the required momentum
coef ficient to reattach the flo w . The savings for the single actuator as well as for the
cooperati ve actuation system are presented.
Then the potential sa ving of mass flo w is illustrated follo wed by a short discussion, an
outlook and an o vervie w of recommended future work.
6.1 Benefits of v or te x interaction
6.1.1 Effect of v or tex interaction on flo w pr oper ties
The phase shift
Θ
was v aried during the PIV measurement on the inclined step at the
half dif fuser to understand the behavior of the cooperati ve actuation. Moreov er , to gain
kno wledge about the robustness, a suf ficient se gment of phase shifts was measured. The
aim was to find the limits of constructi ve interaction. Therefore, the phase shift was v aried
in
∆Θ = 5 ◦
. W ith the results of the flat plate experiment and Equations 2.10 and 5.1 the
phase shift was computed to be
Θ = 99 ◦
. Ne vertheless the right assumption w as that the
adv erse pressure gradient slo ws do wn the propagation velocity . Confirmed by the first
results obtained during the measurement, the optimum phase shift was estimated to be
around
Θ = 120 ◦
. Therefore the phase shift was v aried around this v alue in one-de gree
steps. For the PIV measurements, the simultaneous blo wing is taken as reference to
illustrate the performance increase compared to the easiest setup.
The v arious cases of the PIV measurements at the half diffuse r hav e been analyzed by
means of the RANSA C algorithm as presented in section 4.2. The v ortex structures are
considered as aligned if the de viation function of the algorithm is minimal. From the PIV
flo w field ten slices in height, throughout the normal velocities of the v ortex, are tak en into
account to v alidate the result. Fi ve of the ten slices are sho wn in Figure 6.1 (a).
The illustration on the right of Figure 6.1 sho ws the result of the alignment of vortices
65

6 Evaluation of Cooperati v e Actuation
(a) Description of the single slices used for the
RANSA C algorithm
(b) Deviation of single layers and its mean v alue
resulting from RANSA C algorithm analysis versus
phase shift Θ
Figure 6.1: Description and main findings of the RANSA C algorithm
obtained with the RANSA C algorithm. The de velopment of the de viations sho ws a
minimum at a phase shift of
Θ = 105 ◦
. The dependence on
Θ
is confirmed in e very single
slice and has a minimum at the same phase shift. This result confirms the assumption that
the adv erse pressure gradient slo ws do wn the propagation velocity of the v ortex, b ut the
reduction is smaller than e xpected. Ne v ertheless the region from
90 ◦ ≤ Θ ≤ 130 ◦
sho ws
a reasonable alignment of the v ortices without too much de viation between the single slices.
Increasing the phase shift further , the alignment as well as the single de viation between
the slices are also increasing. This means that the outer v orte x region someho w aligns, b ut
the v orte x core is drifting further apart. The strong de viation with simultaneous blowing
(
Θ = 0
) is not surprising due to the fact that the v ortices are formed at the same time and
therefore the footprints can not be aligned.
The beha vior of the v ortex is analyzed using the detected and track ed core radius of all
in vestigated configurations. Mainly the v orticity as a measure of the rotation is e v aluated.
The outcome of the v ortex tracking is sho wn in Figure 6.2. The results are normalized
to the highest v orticity (eddy viscosity) calculated. Again, the best performance is at
phase shift
Θ = 105 ◦
with a gain of
∆ ω = 51 %
(
∆ µ τ = 57 %
). This is due to the
constructi ve mer ging process of the v ortices presented in Figure 5.16. The vorticity (eddy
viscosity) is enhanced by the fusion of two v ortices, which results in a higher vorticity
and, due to the the higher fluctuation, an enhancement of the eddy viscosity . Ne vertheless
the gain could be increased taking the modified propagation v elocity after the interaction
process into account. A constructi ve interaction can be considered for phase shifts between
95 ◦ ≤ Θ ≤ 115 ◦ .
A further increase of the phase shift results in an increase of the v orticity follo wed by a
sudden drop of v orticity or eddy viscosity respecti vely . After a short reco very of v orticity
(eddy viscosity) it drops back to a lo w v alue. These phases, between
115 ◦ ≤ Θ ≤ 125 ◦
,
will be referred to as the transition of v orte x merging. There, the location of the preceding
v orte x is abov e the point where the ne w v ortex is induced. Since the data is phase a v eraged,
no clear statement about the interaction can be made. Ho we ver , on the flat plate (Section
5.1.2) the corresponding phase shift to this state is
Θ = 84 ◦
. It has been observed that from
ten periods, at least two periods sho w some mer ging behavior . This leads to the assumption
that the v ortices sometimes mer ge and sometimes annihilate each other , depending on the
surrounding flo w state. According to which state happens more often, the phase av eraged
66

6.1 Benefits of vorte x interaction
Figure 6.2:
Comparison of v orticity (eddy viscosity) between cooperati ve actuation and
simultaneous blo wing
data sho w a merging or a destructi v e beha vior . Originating from Figure 6.2, it is plausible
that the interaction at
Θ = 118 ◦
occurs when the first v orte x is located right in the
45 ◦
jet
stream. Later the destructiv e part seems to outweigh the interaction process.
As sho wn in Figure 5.18, increasing the phase shift leads to an annihilation of one vorte x
and an impeded de velopment of the ne wly generated one. A further increase in phase shifts
would lead to the same or damped ef fect as stated for simultaneous blo wing, where the
v ortices are withdrawing ener gy of each other (see Figure 5.14(b)). The ef fect increases
the closer the v ortices are.
6.1.2 Momentum coefficient reduction
Since the aim is to reduce the needed momentum to reattach flo w , the velocity ratio
V R
and therefore the momentum coef ficient
c µ,n
, was lo wered. As demonstrated on the flat
plate in section 5.1.2, the propagation v elocity depends on the incident flo w velocity as
well as on the jet v elocity of the actuation. As sho wn in section 5.2.3 the pressure gradient
has an influence on the propagation v elocities of the v ortices. Therefore, the pressure
reco very
∆ c p
was measured for dif ferent phase shifts
Θ
and v elocity ratios
V R
. The phase
shift was v aried in two-de gree steps and the v elocity ratio was changed by adjusting the
mass flo w . The dotted line in the following Figur es sho ws the pressure recov ery necessary
to reattach the flo w of the separated half dif fuser . The step angle is
α step = 23 ◦
at a step
Re ynoldsnumber of
Re H = 174000
for the sho wn cases. All cooperati ve measurements
are compared to a single actuator ro w acti ve, capable to reattach the flo w . The velocity
ratio for the con ventional concept is
V R = 1 . 94
and the associated momentum coef ficient
is measured with c µ = 0 . 226 % .
In Figure 6.3 (a) the pressure reco very distrib ution for total
c µ, 3 = 0 . 042 %
is sho wn. The
black line is a fit to the measured data points to illustrate the beha vior in respect to the
phase shift. The ef fect on the separation is small, since the separated flo w has a pressure
reco very of
∆ c p = 0 . 43
. Furthermore no dependence on the phase shift is visible. The
67

6 Evaluation of Cooperati v e Actuation
(a) Cooperati ve actuation with o verall mass flo w of
˙ m 3 = 0 . 0018 kg
s
(b) Cooperati ve actuation with o verall mass flo w of
˙ m 3 = 0 . 003 kg
s
Figure 6.3:
Pressure reco very
∆ c p
o ver dif ferent phase shifts
Θ
compared to single
actuation with ˙ m 1 = 0 . 0028 kg
s
v elocity ratio of a single actuator is measured with
V R = 0 . 47
meaning that not only the
generated v orte x is dissipating rapidly , but also the induced momentum is limited. Since
there is no ef fect on the phase shift it is doubtful that the vortices interact at all.
In the illustration on the right hand side of Figure 6.3 the same v ariation of
Θ
is sho wn
for a total momentum coef ficient of
c µ, 3 = 0 . 117 %
. There the single measurement points
indicate a lo w dependence on the phase shift, but considering the fitted line the dependenc y
is insignificant. Moreov er , the pressure recov ery sho ws that for e v ery phase shift the flo w
separation is suppressed. This means that the momentum input of the three actuation ro ws
is suf ficient to reattach the flo w .
In Figure 6.4 the pressure reco very distrib ution is sho wn for a total momentum coef ficient
c µ, 3 = 0 . 075 %
. In this case the constructi ve interaction is capable of reaching the same
pressure reco very as the single actuation ro w depending on the phase shift. The measured
points indicate a broad re gion of suf ficient phase shifts
Θ
, where the cooperati ve actuation
is capable to reasonably reattach the separated flo w . This means that it is not necessary to
hit the optimum phase shift or that the momentum coef ficient can be reduced further with
more ef fort, e.g a phase shift controlled actuation. Looking at the v elocity ratio of the single
actuator of
V R = 0 . 64
and the associated single momentum coef ficient of
c µ = 0 . 026 %
,
Figure 6.4: Pressure reco very ∆ c p o ver dif ferent phase shifts Θ for ˙ m 3 = 0 . 003 kg
s
68

6.1 Benefits of vorte x interaction
Figure 6.5:
Comparison between cooperati ve actuation and single actuation (pink dotted
line) for dif ferent momentum coef ficients
these parameters are significantly lo wered ( ∆ V R = 66 % and ∆ c µ = 89 % ).
The main findings of pressure measurements are sho wn in Figure 6.5. The dotted line
at
∆ c p = 0 . 54
again is the pressure reco very of a single actuator ro w blo wing with
c µ, 1 = 0 . 226 %
for comparison. The other curves sho w the
∆ c p
for total momentum
coef ficients ov er the phase shift. These curves are the polynomials fitted lines of the
measurements for clarity . Blo wing with a
c µ, 3 = 0 . 042 %
does not af fect the separated flow
as discussed before. When the amplitude is increased to
c µ, 3 = 0 . 057 %
the separation
is delayed. Ho we ver , a phase dependence can be identified, with a maximum between
Θ = 100 ◦
and
Θ = 125 ◦
. This corresponds to the finding discussed in section 5.1.2.
Utilizing the cooperati ve ef fect has a positi ve influence on the separation. In this case the
v elocity ratio is
V R = 0 . 55
. Since the direct momentum increase in the detached area is
small due to the lo w velocity and mass flo w , the constructi ve mer ging of vortices must be
responsible for the delay of the separation. The lo west momentum coef ficient reaching the
same performance as the single ro w is
c µ, 3 = 0 . 075 %
as sho wn in Figure 6.4. The phase
dependenc y of the
∆ c p
v alue is larger than before. Again the maximum can be identified
between
Θ = 100 ◦
and
Θ = 125 ◦
. This could lead to the assumption that the momentum
coef ficient has no significant impact on the required phase shift. Ho we ver a look at the
measurement results sho ws that the maximum of the pressure recov ery is changing from
Θ = 130 ◦
for
c µ, 3 = 0 . 057 %
to
Θ = 108 ◦
for
c µ, 3 = 0 . 075 %
. This is comparable to the
results discussed in the section 5.1.2. Increasing the momentum coefficient e ven further
(
c µ, 3 = 0 . 117 %
) results in a higher maximum pressure reco very than the single ro w acti ve
and sho ws limited dependency on the phase shift. A further increase of c µ, 1 for the single
ro w shows that the maximum pressure reco very to be reached is about
∆ c p ≈ 0 . 55
. This
means with three ro ws acti ve an e ven higher ∆ c p is achie v ed.
In Figure 6.6 the pressure reco very at the optimal phase shift of all measured cases are
sho wn ov er the total momentum coef ficient. Furthermore the pressure recov ery for single
actuation is sho wn for comparison. The points are polynomial fitted, to estimate the
69

6 Evaluation of Cooperati v e Actuation
Figure 6.6:
Comparison of single actuation to cooperati ve actuation in relation to the
o verall momentum coef ficient c µ
beha vior of the pressure reco very with re gard to the ov erall momentum coef ficient. The
illustration sho ws that
c µ, 3 = 0 . 075 %
is the break e ven point with the single actuation. The
comparison of the the actuator concepts sho ws that the momentum coef ficient is reduced
o ver the whole measured
∆ c p
range. Ho wev er , as sho wn in the pre vious section, the phase
shift between actuators after a mer ging process is not optimal, and with further adjustments
the total momentum coef ficient could be decreased further . The illustration also sho ws that
a further increase of the momentum coef ficient does not increase the pressure recov ery
proportionally . Ne vertheless, a higher pressure reco very is achie ved with less c µ, 3 .
70

6.1 Benefits of vorte x interaction
6.1.3 Mass flow reduction
The v elocity ratio and the momentum coef ficient can be lo wered by means of cooperativ e
actuation as discussed in the pre vious sections. Since the momentum coef ficient is not
only af fected by the jet velocity , b ut also by the mass flo w , it is discussed in the following.
Considering Figure 6.6, the break e v en point is reached with a velocity ratio of
V R = 0 . 64
.
Ho we ver , the ov erall mass flo w consumption of all three actuator ro ws remains the same
as for the single actuation. Ne v ertheless the abov e illustration also sho ws the separation
is at least delayed that when the momentum coef ficient is smaller . Furthermore it is also
sho wn in Figure 4.6 that the cooperativ e actuation is not optimized due to the subsequent
mer ging processes.
In Figure 6.7 v elocity profiles at certain distances behind the actuators are sho wn for the
single actuation concept compared to the separated flo w . The positions are the same as
illustrated in Figure 5.19. The black circles depict the v elocity profile for the pressure
induced separation. The back flo w can be clearly distinguished, increasing with the location
do wnstream. W ith activ e flo w control the separation is reattached, resulting in a normal
v elocity profile. The illustration in the middle shows a surplus of v elocity . This is due to
the attached jet with a v elocity ratio of
V R = 2 . 2
. The needed mass flo w for reattaching
the flo w amounts to
˙ m = 2 . 8 · 10 − 3 kg
s
. The same effect is visible in Figure 6.8 for the
cooperati ve actuation with a v elocity ratio of
V R = 0 . 8
and a mass flo w for the single
actuator ro w of
˙ m = 0 . 9 · 10 − 3 kg
s
. Ho wev er , since three ro ws were acti ve the o verall
consumption stays the same. Nev ertheless the last illustration 6.9 sho ws a case with
15 %
less total mass flo w consumption. The profiles are still indicating an attached flo w , e v en if
it is smaller . The pressure recov ery is
5 %
lo wer than for the single actuation, which means
the flo w is delayed ef ficiently .
Therefore an estimation of the mass flo w savings w as done, taking all the measured pressure
Figure 6.7:
V elocity profiles at certain distances for single actuation with a momentum
coef ficient of c µ, 1 = 0 . 22 %
71

6 Evaluation of Cooperati v e Actuation
Figure 6.8:
V elocity profiles at certain distances for cooperati v e actuation with a
momentum coef ficient of c µ, 3 = 0 . 073 %
Figure 6.9:
V elocity profiles at certain distances for cooperati v e actuation with a
momentum coef ficient of c µ, 3 = 0 . 067 %
reco veries for the single as well as for the cooperati v e actuation into account. These were
used to estimate the potential mass flo w savings with re gard to the non-optimized system.
F or this, the measured points for the single actuation and the cooperati ve actuation are
indi vidually polynomial fitted as sho wn in figure 6.10(a). In the lo wer mass flow range the
single actuation requires less mass flo w than the cooperati ve actuation. This is due to the
higher impulse of the single actuator , having a higher influence on the flo w . Ho we v er , with a
certain mass flo w (
˙ m = 2 . 3 · 10 − 3 kg
s
) the cooperati ve actuation has a higher increase in
∆ c p
72

6.1 Benefits of vorte x interaction
(a) Comparison of mass flo w consumption for single
and cooperati ve actuation
(b) Massflow sa vings of the cooperativ e actuation at
the point of reattachment (Detailed vie w of (a))
Figure 6.10:
Pressure reco very for single and cooperati ve actuation with re gard to the
o verall massflo w
than the single actuation with less mass flo w consumption. Moreov er , the single actuation
saturates earlier than the cooperati ve one. Therefore the mass flo w sa ving was computed
for the highest measured pressure reco very of the single actuation (
˙ m 1 = 2 . 8 · 10 − 3 kg
s
)
with Equation 6.1.
∆ ˙ m (∆ c p ) =  1 − ˙ m 3 (∆ c p )
˙ m 1 (∆ c p )  · 100 (6.1)
As sho wn in figure 6.10(b) there is no measured point for the cooperativ e actuation equal to
the single actuation. Therefore, the fitted line was tak en for comparison (green arro w). The
mass flo w consumption for the single actuation to reattach the flo w is
˙ m 1 = 2 . 8 · 10 − 3 kg
s
.
The same
∆ c p
is estimated to be achie ved with
˙ m 3 = 2 . 44 · 10 − 3 kg
s
. This leads to a sa ving
of
∆ ˙ m (0 . 54) = 13 %
. Assumed that the single actuation concept would not saturate, the
mass flo w saving w ould further increase with higher
∆ c p
, because of the higher gradient
with re gard to the pressure reco very of the cooperati ve actuation concept. This means that
with higher separation tasks the cooperati ve concept re veals a higher mass flo w sa ving
potential. On the other hand, at a certain point the cooperati ve concept has a performance
increase compared to the single ro w concept.
Since the cooperati ve actuation is not optimized in terms of the phase shift nor the duty
c ycle, further savings can be e xpected. W ith a phase shift optimization a higher pressure
reco very could be achie v ed with less mass flo w . This would decrease the break e v en point
with the single actuation and therefore increase the mass flo w saving to reattach the flo w .
An e ven higher potential re veals the duty c ycle as explained in the follo wing.
The main ef fect of the cooperativ e actuation is the constructiv e interaction of vortices.
Only an impulse is needed to b uild up a v ortex at the be ginning of the blo wing phase,
this ef fect can be used to lower the mass flo w by reducing the duty c ycle
Λ
. In Figure
6.11(a-d) the mer ging process of such a setup is sho wn. Here the duty cycle of the second
and third ro w is set to
Λ 2 , 3 = 25 %
at a step Reynoldsnumber of
Re H = 174000
. The
v orte x is merging as sho wn before (see Figure 5.16), resulting in a higher vorticity . Hence,
this setup lo wers the mass flow to
∆ ˙ m ≈ 40 %
per actuator . Utilizing the kno wledge of
v ortex de velopment by cutting the duty c ycle back, results in an ov erall sa ving of
21 %
for the whole system (see Figure 6.12). On the other hand this takes only the entrainment
through shear layer into account, b ut the second mechanism, the increase of momentum,
73

6 Evaluation of Cooperati v e Actuation
(a) (b)
(c) (d)
Figure 6.11:
The mer ging process of a system configuration where the second and third
ro w hav e a duty c ycle of
Λ 2 , 3 = 25 %
. The step angle is
α = 23 ◦
with an
incident flo w of u ∞ = 20 m
s
is also af fected by the duty cycle. A Strouhalnumber of
F + = 2
with a v elocity ratio of
V R = 1 . 9
and a duty c ycle of
Λ = 50 %
results in an impulse of
~ p ≈ 3 . 8 · 10 − 4 Ns
per
period. The cooperativ e actuation with the same Strouhalnumber b ut with a velocity ratio
of
V R = 0 . 64
has an o ver all impulse of
P n
i ~ p i ≈ 1 . 3 · 10 − 4
. Ho wev er , the impulse is
reduced for the cooperati ve actuation by
66 %
. Cutting down the duty c ycle would result
in a further decrease of the impulse dispensed by the actuator system. This loss has then to
be compensated by the entrainment process.
Ne vertheless, this opportunity re veals a great potential for future w ork and de velopment of
the cooperati ve system. A few possibilities to optimize this system are presented in the
upcoming section.
74

6.2 Outlook and future work
6.2 Outlook and future w ork
Using the cooperati ve actuation it is possible to reduce the jet v elocity to belo w the velocity
of the incident flo w . Therefore electric actuator concepts e.g. synthetic jets, can be
reconsidered or at least lighter and smaller actuators can be de veloped. This is necessary at
locations with strong limitations concerning the space, like the outer wing section of an
aircraft. Furthermore, with lo wer requirements reg arding the mass flo w smaller pipes or
supply systems can be pro vided, cutting do wn the o verall mass of the acti v e flo w control
system.
The ne xt step to optimize this system would be, to further consider the enhancing ef fect
of the cooperati ve actuation. As sho wn abov e the duty cycle discloses a great potential
to auxiliary reduce the mass flo w . T o bring this system one step further the duty cycle
for all ro ws has to be reduced. Since this is also cutting do wn the second mechanism
of this system, an optimal equilibrium between the duty cycle and the direct increase
of momentum should be detected. Moreo v er , a redesign of the actuator slot regarding
the jet angle must be considered, since it has been presented by Hecklau ([
32
]) that a
higher jet angle supports the reduction of the duty cycle. Figure 6.12 indicates that such a
configuration lo wers the ov erall mass flo w to around ∆ ˙ m ≈ 31 % .
Further steps to e volv e the cooperate actuation must concern the
interaction of the vortices
to enhance the capability of such a system. Furthermore a
mass flow contr ol algorithm
should be established for additional sa vings. Last b ut not least the actuation system would
be more ef fecti ve if the a verage
detachment line
is sensed, gi ving the closest ro w the most
authority . An outlook o ver these impro vements are gi ven belo w .
As sho wn in section 5.1.2, the propagation velocity of a merged v ortex is increased by
the interaction. Thus, the successiv e interactions after the first merging process can be
optimized. An adjustment would increase the performance and the actuation parameters can
Figure 6.12:
Estimated additional mass flo w savings at the same o verall momentum
coef ficient
c µ, 3
for dif ferent duty cycles
Λ
and dif ferent actuation concepts.
Duty c ycle lo wered for the 3rd ro w and the the other two ro ws still set to
50 %
(blue). Duty c ycle lo wered for the 2nd and 3rd ro w , b ut still
50 %
for the first
(red). Duty cycle lo wered for all ro ws (black).
75

6 Evaluation of Cooperati v e Actuation
be further reduced. This adjustment of the phase shift
Θ
can be realized by implementing
a control algorithm concerning the propagation v elocity . The controlling can be done
with dif ferent sensors. Hot film sensors achie ve a high sampling rate and therefore a
high temporal solution, but the y are not practical in real world application, due to their
sensiti ve structure. Therefore wall mounted pressure sensors are preferable for a functional
sensor -actuator system. Such a b uildup would not only optimize the cooperati ve actuation
system, but is also independent from the flo w parameters. While the adverse pressure
gradient is af fecting the propagation velocity a change of the incident flo w as well as the
separation area would change the parameters of the system. A suf ficient control algorithm
is capable of handling these amendments. It is plausible that the actuator parameters, e.g.
the mass flo w , can be optimized, with an optimal phase shift, resulting in a more ef ficient
acti ve flo w control system.
Thinking about control algorithm, another optimization concerning the mass flo w could
be considered. In a real world application the mass flo w has to be provided from the jet
engines or an extra compressor , which results in a performance loss or additional weight.
W ith the pressure recov ery a simple b ut ef fecti ve method is presented to rate the state of
separation. Utilizing this, a control unit could optimize the mass flo w for a giv en flo w
condition ensuring that only a minimum is used to reattach the separation.
Concerning the results stated by T roshin and Seifert [
82
], the actuator nearest to the
separation is the most suf ficient one. W ith se veral ro ws this kno wledge can be used to
increase the performance of the cooperati ve actuation. The sensors of a phase shift control
unit can also be used to detect the a v erage detachment line gi ving the nearest actuator
ro w the most authority . For e xample, a pressure induced separation of a flap begins at the
trailing edge mo ving upstream with the flap deflection
δ
. Thus the authority of the single
actuator ro w is changing with the detachment line, still using the cooperati v e ef fect of all
ro ws to increase the performance. A change of the authority can be done by increasing the
duty c ycle of that ro w , if the abov e mentioned duty cycle reduction is deployed.
An adv antage of the cooperati ve actuation is the b uilt-in redundancy . Ha ving se veral ro ws
of actuators, a loss of one actuator can be compensated by increasing the authority of an
actuator in the abo ve or follo wing ro w . This would not e ven result in a higher mass flo w
consumption, if the phase shift is controlled as stated before. Howe ver , this means that the
actuators ha v e to be monitored reg arding their performance. This can be done for example,
by measuring the pressure inside of the actuators.
In the long run it would be preferable to ha ve an autonomous system, capable of controlling
independently the actuators, the phase shift, the mass flo w and the authority tow ards the
detachment line. Ho we ver , such a system increases the comple xity of the ov erall system,
b ut the adv antages would outweigh this drawback by ef fecti vely reducing the mass flo w ,
po wer consumption and the robustness of the single actuator .
76

7 Conc lusion
Much ef fort is put into the wing design of an aircraft by the manufacturers to optimize the
aerodynamics for the v arious phases of flight. Especially in lo w speed flight conditions,
like the tak e-of f and landing, the performance must be enhanced using high lift de vices.
At locations with limited space , it is nearly impossible to deploy slats. This positions are
predestined for the application of acti ve flo w control. Since these systems require energy , a
no vel system enhancing the mechanism of reattachment is needed. T o pro v e the feasibility
of this approach basic in vestigations were successfully performed.
The results of the e xaminations of a cooperati v e actuation sho w that it is possible to use the
ef fect of enhancing coherent structures induced by the activ e flo w control system to delay
the separation or reattach the flo w of a pressure induced separation. The velocity ratio
as well as the momentum coef ficient can be significantly lo wered compared to a single
actuation concept.
The two mechanisms of reattachment, direct increase of momentum in the separated area
and the entrainment through shear layer by induced v ortices, are closely considered. The
coherent structures are generated through pulsed blo wing and enhanced and stabilized with
further actuators located do wnstream. First the interaction process was in vestigated on a
flat plate. Later on the results were transferred to a half dif fuser , where a pressure induced
separation can be pro vided. Thereby it is pro v en that at least the entrainment through a
shear layer is used constructi vely by enhancing the induced coherent structures. Depending
on the delay between the excitation phase of the single actuator ro ws, the vortices are
mer ging, annihilating or not ef fecting each other .
Lar ge-scale v ortex structures are generated trough pulsed blo wing. Theses coherent
structures are propagating do wnstream, depending on the jet and the velocity of the
incident flo w . This initiates a fluid transfer through the shear layer , which transports lo w
ener gy fluid aw ay from the surface and high ener gy from the incident flo w into the detached
area. For a duty c ycle of
Λ = 50 %
the jet angle af fects the behavior of the jet. For jet
angle of
α j et = 45 ◦
the jet is attached to the surface, directly increasing the momentum of
the separated area.
The propagation v elocity mainly depends on the v elocity of the incident flo w , b ut especially
after the generation of a v orte x also on the chosen velocity ratio. After the formation of the
v orte x the propagation v elocity drops to a v alue slightly abo ve the incident flo w . Then it
decreases slo wly , while propagating do wnstream until it dissipates. Thus the vorte x mov es
a way from the surface throughout the boundary layer . By lea ving the boundary layer , the
propagation v elocity is rapidly increased, b ut the v orte x propagation v elocity increases as
fast as it v anishes.
The in vestigation of the mer ging process on a flat plate demonstrates the dependence of
constructi ve interaction on the phase shift of the e xcitation. It can be di vided into four
dif ferent processes. Inducing the subsequent vortices of the follo wing actuators too early
or too late results in se veral v ortices propagating do wnstream, b ut still af fecting each other .
77

7 Conclusion
Due to the opposite normal v elocity of the v ortices the entrainment process of each v ortex
is impeded by the follo wing one. Furthermore, the high energy fluid dispensed by the jet is
transported a way by the follo wing one. Utilizing the propagation velocity obtained from the
single actuator in vestigations, to induce the ne xt v ortex when the pre vious arri ves directly
at the slot location, results in a co-rotating v ortex pair interfering with each ot her . This
interaction dissipates ener gy , therefore only one weak v ortex survi ves. As a consequence,
the entrainment process is at least impeded and the reattachment process is mainly dri ven
by the jet dispensing high ener gy fluid. This means that the needed mass flo w must be
increased. If the v orte x arises after the pre vious v orte x is located right behind the actuator
slot, the v ortices are mostly annihilating each other . By the ongoing blo wing of the actuator
a ne w vorte x b uilds up, with less v orticity and therefore less impact on the entrainment
process. T o actually mer ge two co-rotating v ortices, the second one must be induced before
the preceding v orte x arri v es. Then the jet of the ne w one and the v orticity of the preceding
one ha v e a constructi ve ef fect on each other resulting in a bigger and stronger v orte x. An
additional adv antage is that the preceding vorte x is pushed down to the surf ace again.
This kno wledge is transferred to a half dif fuser with pressure induced separation. In this
in vestigation the step angle of the half dif fuser was set in a w ay to locate the av erage
separation line upstream the first actuator . By doing so a more challenging case was chosen
to sho w the effecti veness of the multiple cooperati ve actuation. The adv erse pressure
gradient of the separation is af fecting the propagation velocity of the v ortex. First of all
the v elocity of propagation is slo wed down. Furthermore the v ortex casts a way from the
surface more rapidly leading to a shorter duration of the v ortex. The merging process itself
seems relati vely independent of the pressure gradient, e ven if the phase of e xcitation has
to be adjusted. Another point is that the constructi ve interaction process accelerates the
v orte x propagation so that the phase shift between subsequent actuators should be adjusted
after a mer ging process. By v arying the phase shift and analyzing the vorticity the dif ferent
interaction processes can be restricted. A constructi v e interaction takes place for phase
shifts, where the v orte x built up in front of the arri ving one and the v orticity is enhanced.
Inducing the v ortex later leads to a state called transition of mer ging. In this state the
v ortices sometimes mer ge and sometimes don’t. Depending, which is happening more
often the rate of v orticity is lo wer or higher . If the phase shift of excitation is increased
further , the vortices are annihilating each other .
The state of flo w in the half dif fuser can be rated with the pressure recov ery
∆ c p
. The
static pressure increases as a function of the angle of the inclined step
α step
, by con verting
kinetic ener gy into into pressure ener gy . This happens until the flow cannot follo w the
surface an ymore and detaches. The static pressure decreases within the separated area.
This beha vior can be measured by means of a pressure transducer , before and after the step.
The dif ference between these sensors yields the pressure recov ery . Acti ve flo w control is
supposed to suppress the separation, with a certain set of parameters. The con v entional
system, consisting of a single actuator or a ro w of se veral adjacent actuators, needs a high
v elocity ratio and a suf ficient amount of mass flo w . Cooperati ve actuation is supposed to
reduce the v elocity ratio by utilizing constructi v e interaction between the actuator ro ws. As
sho wn in section 6.1.2, the velocity ratio is reduced by
∆ V R = 66 %
and the momentum
coef ficient of the single actuator by
∆ c µ = 89 %
. The ov erall system sa ving is measured
with the total momentum coef ficient taking all ro ws into account. Compared to a single
ro w the gain is still up to 66 % .
78

Ne vertheless the mass flo w required to reattach the flo w remains the same. But looking at
Figure 6.10 and 6.9, the cooperati ve actuation is supposed to cut do wn these requirements.
Therefore the potential mass flo w savings are estimated. It is very likely that the cooperati v e
actuation can reduce the required mass flo w up to
∆ ˙ m ≈ 10 %
. It should be recalled that
the system is not optimized re garding the phase shift or the velocity ratio. Since the system
aims at enhancing or at least stabilizing the v orte x responsible for the entrainment through
shear layer , the duty cycle of the second and third ro w was set to
Λ 2 , 3 = 25 %
. The PIV
measurements sho w that through the merging process the v ortex is still enhanced. Such
an adjustment leads to an o verall sa ving of
∆ ˙ m = 21 %
. Other authors showed that the
reattachment process can be triggered by only using the entrainment through shear layer .
Utilizing this, all actuator ro ws can be set to a duty cycle of
Λ 1 , 2 , 3 = 25 %
, which would
lead to a sa ving of
∆ ˙ m = 31 %
. Howe ver , a redesign of the actuator slot re garding the
jet angle should be considered. It is also shown that the mer ging process influences the
propagation v elocity of the v ortex and therefore the related phase shift. A control algorithm
would be capable to deal with that issue, by adjusting the phase shift indi vidually . That
would lead to further sa vings reg arding the mass flo w .
Additional positi ve side ef fects of the cooperati ve actuation are the b uilt in redundancy and
the possibility to react to the separation indi vidually . This basic in vestig ation of this ne w
actuation concept sho ws promising results for future applications and creates the conditions
for further in vestigations and de velopments to bring this system to mark et maturity .
79

7 Conclusion
80

Bib liograph y
[1]
K. K. Ahuja, R. R. Whipke y , and G. S. Jones. Control of turb ulent boundary layer
flo ws by sound. AIAA paper , 726:1983, 1983.
[2] J. D. Anderson. Fundamentals of Aer odynamics . McGra w-Hill, Inc, 1991.
[3]
M. J. Bamber . W ind-tunnel tests on airfoil boundary layer contr ol using a
bac kwar d-opening slot . National Advisory Committee for Aeronautics, 1932.
[4]
M. Bauer . Design and application of a fluidic actuator system for high lift flow
contr ol . PhD thesis, T echnische Uni versität Berlin, 2015.
[5] J. J. Bertin and M. L. Smith. Aer odynamics for engineers . Prentice-Hall, 1979.
[6]
F . K. Bro wand and C. M. Ho. The mixing layer -an example of quasi tw o-dimensional
turb ulence. J ournal de Mecanique Theorique et Appliquee Supplement , 1:99–120,
1983.
[7]
L. N. Cattafesta III and M. Sheplak. Actuators for acti ve flo w control. Annual Revie w
of Fluid Mec hanics , 43:247–272, 2011.
[8]
D. R. Chapman, D. M. Kuehn, and H. K. Larson. In vestig ation of separated flo ws in
supersonic and subsonic streams with emphasis on the ef fect of transition. 1958.
[9]
Y . Cheng. Mean shift, mode seeking, and clustering. P attern Analysis and Mac hine
Intelligence , IEEE T r ansactions on , 17(8):790–799, 1995.
[10]
F . G. Collins and J. Zelene vitz. Influence of sound upon separated flow o ver wings.
AIAA journal , 13(3):408–410, 1975.
[11]
D. Comaniciu and P . Meer . Mean shift: A rob ust approach to ward feature
space analysis. P attern Analysis and Mac hine Intelligence , IEEE T ransactions
on , 24(5):603–619, 2002.
[12]
L. Cortelezzi and A. R. Karagozian. On the formation of the counter -rotating v ortex
pair in transv erse jets. J ournal of Fluid Mechanics , 446:347–373, 2001.
[13]
T . Crittenden, B. W arta, and A. Glezer . Characterization of comb ustion po wered
actuators for flo w control. AIAA paper , 2864:2006, 2006.
[14]
S. C. Cro w . Stability theory for a pair of trailing v ortices. AIAA journal ,
8(12):2172–2179, 1970.
[15]
D. E. Culle y . V ariable frequency di verter actuation for flo w control. In 3r d AIAA
Flow Contr ol Confer ence , page 3034, 2006.
[16]
A. D. Cutler , B. T . Beck, J. A. W ilkes, J. P . Drummond, D. W . Alderfer , and P . M.
Danehy . Dev elopment of a pulsed combustion actuator for high-speed flo w control.
AIAA paper , 1084:2005, 2005.
81

Bibliography
[17]
K. G. Derpanis. Mean shift clustering. Lectur e Notes. http://www . cse . yorku. ca/˜
kosta/CompV is_Notes/mean_shift. pdf , 2005.
[18]
DLR. Pricipal-PIV -Setup.
http://www.dlr.de/as/en/Portaldata/5/
Resources/images/abteilungen/abt_ev/artikel/PIV_img1_xl.
jpg , 2016. [Online; accessed 20-March-2016].
[19]
A. Eroglu and R. E. Breidenthal. Structure, penetration, and mixing of pulsed jets in
crossflo w . AIAA journal , 39(3):417–423, 2001.
[20]
A. Eroglu and R. E. Breidenthal. Structure, penetration, and mixing of pulsed jets in
crossflo w . AIAA journal , 39(3):417–423, 2001.
[21]
European Union. Commission regulation (ec) no 796/2002. Official J ournal of the
Eur opean Communities , L128:22, 2002.
[22]
M. A. Fischler and R. C. Bolles. Random sample consensus: a paradigm for
model fitting with applications to image analysis and automated cartography .
Communications of the A CM , 24(6):381–395, 1981.
[23]
T . F . Fric and A. Roshk o. Structure in the near field of the transverse jet. In 7th
Symposium on T urb ulent Shear Flows, V olume 1 , volume 1, page 6, 1989.
[24]
T .F . Fric and A. Roshko. V ortical structure in the wak e of a transverse jet. J ournal of
Fluid Mec hanics , 279:1–47, 1994.
[25]
M. Gad-el Hak. Modern de v elopments in flo w control. Applied Mec hanics Re views ,
49(7):365–379, 1996.
[26]
A. Glezer . Some aspects of aerodynamic flo w control using synthetic-jet actuation.
Philosophical T ransactions of the Royal Society of London A: Mathematical, Physical
and Engineering Sciences , 369(1940):1476–1494, 2011.
[27]
A. Glezer and M. Amitay . Synthetic jets. Annual Revie w of Fluid Mechanics ,
34(1):503–529, 2002.
[28]
D. Greenblatt and I. J. W ygnanski. The control of flo w separation by periodic
e xcitation. Pr ogr ess in Aer ospace Sciences , 36(7):487–545, 2000.
[29]
J. W . Gregory , E. P . Gnanamanickam, J. P . Sulli v an, S. Raghu, and D. Fello w .
V ariable-frequenc y fluidic oscillator dri v en by piezoelectric de vices. In AIAA J ournal,
43r d AIAA Aer ospace Sciences Meeting & Exhibit Reno, NV , 2005.
[30]
J. W . Gregory , J. C. Ruotolo, A. R. Byerley , and T . E. McLaughlin. Switching
beha vior of a plasma-fluidic actuator . AIAA paper , 785:2007, 2007.
[31] C. D. Hansen and C. R. Johnson. V isualization handbook . Academic Press, 2011.
[32]
M. Hecklau. Experimente zur aktiven Strömungsbeeinflussung in einer
V er dichterkaskade mit pulsier enden W andstrahlen . PhD thesis, T echnische Uni versität
Berlin, 2012.
[33]
M. Hecklau and W . Salazar , D. P .and Nitsche. Influence of the actuator jet angle on
the reattachment process with pulsed e xcitation. In New Results in Numerical and
Experimental Fluid Mec hanics VIII , pages 143–150. Springer , 2013.
82

Bibliography
[34]
C. Ho and L. Huang. Subharmonics and v orte x merging in mixing layers. J ournal of
Fluid Mec hanics , 119:443–473, 1982.
[35]
C. Ho and P . Huerre. Perturbed free shear layers. Annual Re view of Fluid Mec hanics ,
16(1):365–422, 1984.
[36]
J. D. Hodges, Z. D. Little, Craig P . Fernandes, G. Natsui, and J. S. Kapat. The
ef fect of inclination angle on turbulent quantities of a single ro w of cylindrical jets in
crossflo w . In 51st AIAA/SAE/ASEE J oint Pr opulsion Confer ence , page 4198, 2015.
[37]
V . Holmén. Methods for v ortex identification. Masterâ ˘
A ´
Zs Theses in Mathematical
Sciences , 2012.
[38] B. M. Horton. Fluid-operated system, February 25 1964. US Patent 3,122,165.
[39]
F . Hsiao, J. Shyu, and C. Liu. Control of wall-separated flo w by internal acoustic
e xcitation. AIAA journal , 28(8):1440–1446, 1990.
[40]
J. Jeong and F . Hussain. On the identification of a vorte x. J ournal of fluid mechanics ,
285:69–94, 1995.
[41]
G. V . Lachmann. Boundary layer and flow contr ol: its principles and application .
Else vier , 2014.
[42]
S. Le Dizes and A. V erg a. V iscous interactions of two co-rotating v ortices before
mer ging. J ournal of Fluid Mechanics , 467:389–410, 2002.
[43]
A. Leder . Abgelöste Strömung en Physikalische Grundla gen . Grundlagen und
F ortschritte der Ingenieurwissenschaften. V ie weg+T eubner V erlag, 1992.
[44]
M. A. Leschziner and S. Lardeau. Simulation of slot and round synthetic jets in
the conte xt of boundary-layer separation control. Philosophical T ransactions of
the Royal Society of London A: Mathematical, Physical and Engineering Sciences ,
369(1940):1495–1512, 2011.
[45]
J. Lin, F . Ho ward, and G. Selby . T urbulent flo w separation control through passi v e
techniques. In Shear Flow Confer ence , pages –. American Institute of Aeronautics
and Astronautics, March 1989.
[46]
R.T . M’closke y , J.M. King, L. Cortelezzi, and A.R. Karagozian. The acti vely
controlled jet in crossflo w . J ournal of Fluid Mec hanics , 452:325–335, 2002.
[47]
L. P . Melton, C. S. Y ao, and A. Seifert. Acti v e control of separation from the flap of
a supercritical airfoil. AIAA journal , 44(1):34–41, 2006.
[48]
P . Meunier , U. Ehrenstein, T . Le weke, and M. Rossi. A mer ging criterion
for two-dimensional co-rotating v ortices. Physics of Fluids (1994-pr esent) ,
14(8):2757–2766, 2002.
[49]
P . Meunier and T . Le weke. Three-dimensional instability during vorte x merging.
Physics of Fluids (1994-pr esent) , 13(10):2747–2750, 2001.
[50]
W . Mokhtar . A numerical parametric study of high-lift lo w reynolds number airfoils.
In Aer ospace Sciences Meetings , pages –. American Institute of Aeronautics and
Astronautics, January 2005.
[51] N. M. Morris. An intr oduction to fluid logic . McGraw-Hill, 1973.
83

Bibliography
[52]
H. Nagib, J. Kiedaisch, P . Reinhard, and B. Demanett. Control techniques for
flo ws with large separated re gions: A ne w look at scaling parameters. AIAA paper ,
2857:2006, 2006.
[53]
M. Nishioka, M. Asai, and S. Y oshida. Control of flo w separation by acoustic
e xcitation. AIAA journal , 28(11):1909–1915, 1990.
[54]
B. Nishri and I. W ygnanski. Ef fects of periodic excitation on turb ulent flo w separation
from a flap. AIAA journal , 36(4):547–556, 1998.
[55]
W . Nitsche and A. Brunn. Strömungsmesstec hnik . Springer , 2. auflage edition, 2006.
[56]
D. Oster , I. W ygnanski, B. Dziomba, and H. Fiedler . On the ef fect of initial conditions
on the two dimensional turb ulent mixing layer . In H. Fiedler , editor , Structur e and
Mec hanisms of T urb ulence I , v olume 75 of Lectur e Notes in Physics , pages 48–64.
Springer Berlin Heidelber g, 1978.
[57]
R. Petz and W . Nitsche. Acti ve separation control on the flap of a tw o-dimensional
generic high-lift configuration. J ournal of Air cr aft , 44:865–874, 2007.
[58]
M. W . Plesniak and D. M. Cusano. Scalar mixing in a confined rectangular jet in
crossflo w . J ournal of Fluid Mechanics , 524:1–45, 2005.
[59]
F . H. Post, B. Ma, D. C. Banks, H. Pagendarm, et al. Selecti ve visualization of
v ortices in hydrodynamic flo ws. In V isualization’98. Pr oceedings , pages 419–422.
IEEE, 1998.
[60]
L. Prandtl. Er gebnisse der aer odynamisc hen V ersuc hsanstalt zu Göttingen , v olume 3.
Uni versitätsv erlag Göttingen, 2009.
[61]
A. Qayoum, V . Gupta, P . K. Panigrahi, and K. Muralidhar . Influence of amplitude
and frequenc y modulation on flo w created by a synthetic jet actuator . Sensors and
Actuators A: Physical , 162(1):36–50, 2010.
[62]
M. Raf fel, C. E. W illert, J. K ompenhans, et al. P article imag e velocimetry: a pr actical
guide . Springer , 2013.
[63]
H. Reed and W . Saric. T ransition mechanisms for transport aircraft. In Fluid
Dynamics and Co-located Confer ences , pages –. American Institute of Aeronautics
and Astronautics, June 2008.
[64]
M. Sale wski, D. Stankovic, L. Fuchs, and E. Gutmark. Coherent structures in circular
and non-circular jets in crossflo w . In 44th AIAA Aer ospace Sciences Meeting and
Exhibit , pages 2006–907, 2006.
[65]
R. Sau and K. Mahesh. Optimization of pulsed jets in crossflow . J ournal of Fluid
Mec hanics , 653:365–390, 2010.
[66]
H. Schlichting and K. Gersten. Boundary-layer theory . Springer Science & Business
Media, 2000.
[67]
H. Schlichting and E. T ruckenbrodt. Aer odynamik des Flugzeuges . Springer Berlin,
Heidelber g, 1969.
[68]
A. Seifert, T . Bachar , D. K oss, M. Shepshelo vich, and I. W ygnanskil. Oscillatory
blo wing: a tool to delay boundary-layer separation. AIAA journal , 31(11):2052–2060,
1993.
84

Bibliography
[69]
A. Seifert and L. G. P ack. Oscillatory excitation of unsteady ressible flo ws ov er
airfoils at flight re ynolds numbers. 1999.
[70]
S. R. Shapiro, J. King, R. T . M’Closke y , and A. R. Karagozian. Optimization of
controlled jets in crossflo w . AIAA journal , 44(6):1292–1298, 2006.
[71]
M. Shioka wa, K. Matsushima, and K. Nakahashi. Design and aerodynamics of lift
enhancement control for a single element airfoil. In 43r d AIAA Aer ospace Sciences
Meeting and Exhibit , page 2005, 2005.
[72]
A. Shmilo vich and Y . Y adlin. Flo w control for the systematic b uildup of high-lift
systems. J ournal of Air craft , 45(5):1680–1688, 2008.
[73]
A. Shmilo vich and Y . Y adlin. Flo w control techniques for transport aircraft. AIAA
J ournal , 49(3):489–502, 2011.
[74] A. M. O. Smith. High-lift aerodynamics. J ournal of Air craft , 12(6):501–530, 1975.
[75]
D. Sujudi and R. Haimes. Identification of swirling flo w in 3d vector fields. T echnical
report, T echnical report, Department of Aeronautics and Astronautics, MIT , 1995.
AIAA P aper 95-1715, 1995.
[76]
F . T erno y , J. Dandois, F . Da vid, and M. Pruvost. Overvie w of onera actuators for
acti ve flo w control. Aer ospaceLab , pages p–1, 2013.
[77]
V . T esa ˇ
r, C. Hung, and W . B. Zimmerman. No-moving-part h ybrid-synthetic jet
actuator . Sensors and Actuator s A: Physical , 125(2):159–169, 2006.
[78]
V . T esa ˇ
r, S. Zhong, and F . Rasheed. Ne w fluidic-oscillator concept for flo w-separation
control. AIAA journal , 51(2):397–405, 2012.
[79]
F . Thomas. Untersuc hungen über die Erhöhung des A uftriebes von T r agflüg eln mittels
Gr enzsc hichtbeeinflussung dur ch A usblasen . DFL-Bericht. Dt. F orschungsanstalt f.
Luft- u. Raumfahrt e.V ., 1962.
[80]
F . T inapp. Aktive K ontr olle der Strömungsablösung an einer
Hoc hauftriebs-K onfiguration . PhD thesis, T echnische Uni versität Berlin,
2001.
[81]
P . H. S. T orr and A. Zisserman. MLESA C: A ne w rob ust estimator with application to
estimating image geometry . J ournal of Computer V ision and Imag e Understanding ,
78(1):138–156, 2000.
[82]
V . T roshin and A. Seifert. Performance reco very of a thick turb ulent airfoil using a
distrib uted closed-loop flo w control system. Experiments in fluids , 54(1):1–19, 2013.
[83]
H. V ollmers. Detection of v ortices and quantitati ve e v aluation of their main
parameters from e xperimental velocity data. Measur ement Science and T echnology ,
12(8):1199, 2001.
[84]
J. W esterweel. Digital particle imag e velocimetry: theory and application . TU Delft,
Delft Uni versity of T echnology , 1993.
[85]
J. W ild, G. W ichmann, F . Haucke, I. Peltzer , and P . Scholz. Large scale separation
flo w control experiments within the german flo w control network. In 47th AIAA
Aer ospace Sciences Meeting , page 530, 2009.
85

Bibliography
[86]
I. W ygnanski. The v ariables af fecting the control of separation by periodic e xcitation.
In Fluid Dynamics and Co-located Confer ences , pages –. American Institute of
Aeronautics and Astronautics, June 2004.
[87]
K. Zaman, A. Bar -Se ver , and S.M. Mangalam. Ef fect of acoustic excitation on the
flo w ov er a lo w-re airfoil. J ournal of Fluid Mechanics , 182:127–148, 1987.
[88]
P . Zhang, J. W ang, and L. Feng. Re vie w of zero-net-mass-flux jet and its application
in separation flo w control. Science in China Series E: T echnolo gical Sciences ,
51(9):1315–1344, 2008.
86

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