16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
Phase-Locked 3D3C-MRV Measurements in a Bi-stable Fluidic Oscillator
Florian Wassermann1,*, Daniel Hecker1, Bernd Jung2, Michael Markl3
and Sven Grundmann1
1: Center of Smart Interfaces, Technische Universität Darmstadt, Germany
2: Dept. of Radiology & Medical Physics, University Medical Center Freiburg, Germany
3: Dept. of Radiology and Biomedical Engineering, Northwestern University Chicago, USA
* Correspondent author: wassermann@csi.tu-darmstadt.de
Abstract In this work the phase-resolved internal flow of a bi-stable fluidic oscillator was
measured using phase-locked 3D3C-MRV, also termed as 4D-MRV. A bi-stable fluidic oscillator
converts a continuous inlet-mass flow into a jet alternating between two outlet channels and, as a
consequence provides an unsteady, periodic flow. Since data acquisition of a single time step in a
3D volume can take up to several minutes, only a small portion of data is acquired per period cycle,
i.e. the acquisition of the entire data set is segmented over many cycles of the periodic process. By
this technique a phase-resolved velocity field is created. However, the procedure requires triggering
to the periodic nature of the flow. Therefore, triggering the MR scanner precisely on each flow
cycle is one of the key issues discussed in this manuscript.
A triggering system was developed, based on a piezo-element pressure transducer, providing a
reliable signal despite the harsh magnetic and electro-magnetic environment inside an MR scanner.
The obtained 4D-MRV data are compared to data measured using Laser-Doppler anemometry and
good agreement between the results is found.
Subsequently, the validated 4D-MRV data is analyzed and the fluid-mechanic features and
processes inside the fluidic oscillator are investigated and described and a detailed description of the
internal jet-switching mechanism is provided.
1. Introduction
Fluidic oscillators are devices generating an oscillating flow when supplied with a constant flow
rate. They are termed differently throughout the literature. The most common terms are ”oscillatory
blowing actuator”, ”sweeping jets”, ”flip flop jet nozzle” or ”fluidic diverter”. One of the most
valuable features of fluidic oscillators is, that they do not consist of moving parts and that their
oscillation frequency can be controlled by adjusting the flow rate. Fluidic oscillators have gained
much interest in many disciplines of fluid mechanics. In the field of active flow control for instance,
a pulsating jet can be far more effective and efficient than a continuous jet. Seifert et al. [15] report
that oscillations introduced to the flow excite large-scale structures inside the boundary layer, which
enable the flow to withstand adverse pressure gradients without flow separation. In Seifert et al.
[16] a method is described which decreases the size of the recirculation zone behind a truck trailer,
using an array of oscillating actuators. A drag reduction of up to 20% is possible. A drag reduction
and lift enhancement of 60%, caused by an array of fluidic oscillators installed on the suction side
of the airfoil of a Bell-Boeing V-22 were achieved by Seele et al. [14]. Other applications of fluidic
oscillators are e.g. discussed in Raman et al. [12] for jet-thrust vectoring or in Guyot et al. [8] for an
active-combustion control in bluff-body burners.
The basic feature of the oscillators discussed in this work is the Coanda effect. In his patent Coanda
[3] describes an experimental setup which shows a fluidic jet attaching to a wall installed in the
vicinity of the jet exit. The jet entrains fluid particles, generating a low pressure region around the
jet. A wall within this low pressure region causes the jet to deflect and to attach to this wall.
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
Fig. 1 a) describes a generic fluidic-oscillator model which was first investigated by Spyropoulos
[17]. The main components are the two control ports, the two Coanda walls, the splitter and the two
outlets. The space upstream the splitter and between the two Coanda walls can be termed as
interaction cavity ([18]). The fluid enters the oscillator from the left. Due to the above described
Coanda effect the fluid jet attaches to one of the two walls, which is in this example Coanda wall A.
As a consequence a low pressure region develops in control port A drawing fluid out of the port
into the jet. This state of the fluidic oscillator is stable. If the control ports A and B are connected
with each other by a feedback tube as sketched in Fig. 1 b) the low pressure region at port A draws
fluid through that tube from control port B. This leads to a pressure gradient which pulls the jet
toward control port B and consequently to Coanda wall B. As a result of the side change of the jet, a
low pressure region now develops at control port B creating a reversed pressure gradient between
both control ports, causing the jet to switch back to Coanda wall A. A full cycle is now completed
and the process restarts. This self-sustained oscillation and the fact that without feed-back tube each
state is stable justifies the term bi-stable oscillator.
Figure 1: Basic oscillator model after Spyropoulos [17]
A first parameter study of a simple bi-stable fluidic oscillator under subsonic flow conditions was
conducted by Viets [19]. He found out that the frequency of the jet oscillation increases with
increasing flow rate and decreases with increasing feedback tube length. Raman et al. [13] add the
feedback-tube diameter as parameter: the oscillation frequency increases with increasing diameter.
Further studies visualizing the internal flow of fluidic oscillators of different geometry and features
were i.e. conducted by Yang et al. [20] or Gregory et al. [6]. Despite the long tradition of
investigations in this field there are no comprehensive visualizations of the flow field inside the
actuator available helping to understand the oscillatory process in detail.
The primary measurement technique used in this investigation is the 4D magnetic resonance
velocimetry (4D-MRV), which was originally developed for the diagnostic of the human
cardiovascular system [10]. On the basis of modern phase contrast imaging (PCI) procedures which
acquire three-dimensional three-component (3D3C) velocity data for stationary flows ([9]), the 4Dmethod is able to capture phase-resolved 3D phase contrast images. Hereby the traditional 3D data
acquisition scheme is extended by a fourth dimension: the time. The main requirement is that the
investigated flow may be unsteady but has to be periodic. Since data acquisition of a single time
step in a 3D volume can take up to several minutes, only a small portion (a few k-space lines) of
data is acquired per period cycle, i.e. the acquisition of the entire data set is segmented over many
cycles of the periodic process. Since segmented time-resolved acquisition collects data over many
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cycles (in in-vivo imaging typically over several heartbeats) and merges the information into a
single cycle, effects such as a varying cycle length (in in-vivo imaging varying heart rates) are
averaged out. However, the procedure requires triggering to the periodic nature of the flow. The
result is a four-dimensional velocity matrix with three spatial and one temporal dimension.
The procedure requires triggering to the periodic nature of the flow. In case of the cardiovascular
imaging an electrocardiogram (ECG) marks the beginning of a new heart cycle which in turn
triggers the scanner. Canstein et al. [2], for example, have used this method to compare the flow in
the thoracic aorta of a human volunteer and a replica manufactured using rapid prototyping. The
flow through the replica is supplied by providing a pulsatile flow. The 4D-MRV measurement was
triggered on the periodic operation of the pump.
In mechanical engineering sciences this method first has been applied by Elkins et al. [4], who
investigated a model of an internal gas-turbine blade cooling channel. This flow was unsteady due
to strong turbulence but not periodic and consequently, no system for an in-situ flow triggering was
implemented. A comprehensive review of MRV for engineering applications can be found in Elkins
and Alley [5].
2. Experimental Setup
2.1 Flow Apparatus
A flow supply system similar to the one described in Grundmann et al. [7] was used. Deionized
water with a Gadolinium-based contrast agent was used as medium.
An important modification to the previous system is the added immersion heater with a thermostat
which controls the temperature of the water. The water temperature can be held constant on a
certain level. This allows adjusting the Reynolds number by modifying the viscosity as well as with
the flow rate and helps preventing Reynolds number drifts at constant flow rates due to temperature
drifts. The temperature, pressure and flow rate are monitored. A Labview program with an
implemented PID controller controls either the flow rate or the Reynolds number at fixed
temperatures.
Figure 2: Cross-sectional view of the CAD model of the oscillator, assembled with upstream flow
straightener and downstream plenum and outlet nozzle.
2.2 Fluidic Oscillator
The design of the fluidic oscillator was taken from Arwatz et al. [1] and the geometry was kindly
provided by Prof. Avi Seifert. This actuator has the same working principle as described above and
as depicted in Fig. 1. The actuator was scaled in order to suit the experimental limitations.
Fig. 2 shows a cross-sectional view of the CAD model of the assembled oscillator setup as used in
the experiments. The supply tube, with an inner diameter of 25.4 mm, is connected to the inlet port
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
with a flow straightener removing large scale vortices, emerging from the curvature of the supply
tubing. The cross-section is then transformed from circular to quadratic, resulting in an inlet crosssectional area of 21x21 mm2. A downstream converging nozzle accelerates the fluid towards the
throat, with a minimum cross-sectional area of 7.85x21 mm2 creating a jet of rectangular crosssection with an almost uniform velocity profile that enters the interaction cavity farther
downstream.
As described above the investigated bi-stable fluidic oscillator consists of two control ports and two
outlets. A connection for the integration of a pressure transducer is implemented into one of the
control ports. All necessary modifications were made symmetrically in both control ports. All
components on the side of the pressure sensor are subscribed with an index A and on the other side
with an index B.
Downstream of the oscillator’s outlets the fluid enters a plenum with the dimensions in x, y, z of
200x80x38 mm3. Then a nozzle reduces the rectangular cross-section of the plenum to the circular
shape of the tube leading back to the water tank.
The flow straightener, actuator and outlet nozzle are made of PA using direct-laser sintering. The
plenum was manufactured of PMMA. All parts were joined using PVC bolts and sealed with Orings.
2.3 In-situ pressure signal and triggering procedure
For the 4D-MRV measurements it is necessary to trigger the MRI scanner precisely on the periodic
flow. The scanner can process an electrocardiogram signal or a TTL signal. In this work unsteady
pressure measurements seemed most appropriate for this purpose. Several types of pressure
transducers and installation positions were considered and tested.
Due to the strong magnetic field and issues with electro-magnetic compatibility inside the MR
scanner not all measuring principles are worth considering. Another requirement is avoiding parts
of of metal to not impair the quality of the MR signal. Considering these difficulties a pressure
sensor based on a piezo-electric foil was chosen. The basis is a transparent film made of highpolarized polyvenylidenfluorid (PVDF) in which an electric charge accumulates in response to
externally applied forces. With metallic coatings of a few hundred Angstrom thicknesses on the
lower and upper side, the electric potential can be measured (Nitsche et al. [11]). The sensor is only
able to measure dynamic effects and provides an output voltage proportional to the applied force in
the range from -5 to 5 V.
Figure 3: Assembly of the sensor setup with sensor plug, grommet and mounting.
Three possible locations for the pressure sensor were tested: 1) on the Coanda wall, 2) in the middle
of the feedback tube and 3) at a control port. The sensor position 3) directly at a control port was
chosen. Fig. 2 shows the pressure port location.
The sensor setup was developed and built by Mirow Systemtechnik GmbH according to the
requirements from the experimental setup. The PVDF foil and the charge-amplifier electronics were
integrated into a small plug as shown in Fig. 3.
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The pressure signal has to be filtered and analyzed in real time to generate the triggering signal for
each flow cycle individually. Fig. 4 shows the components needed for the triggering process. The
signal from the pressure sensor is low-pass filtered (LP-filter) with a Kemo Benchmaster 8.07 8pole Bessel dual channel filter/amplifier. The cut-off frequency for each measurement is listed in
Table 1 and the slope was 48 dB/octave for all cases. Fig. 5 shows two pressure signals: in blue the
unfiltered sensor signal and in green the low-pass filtered signal. The unfiltered pressure signal
shows strong noise induced by the operating MRI scanner. The frequency spectrum of this signal
reveals a fundamental frequency of 192 Hz and higher harmonics. The low-pass filtered pressure
signal in green is suitable for further processing; nevertheless this signal shows a significant phaselag from the filtering process corresponding to about 100-200ms. This phase-lag does not pose a
problem, since it is a constant offset and can be removed in the postprocessing.
Figure 4: Schematic of the triggering process and components.
Figure 5: Raw, unfiltered pressure signal and filtered pressure signal, with resulting phase shift.
The filtered pressure signal is then sampled by a National Instruments Real-Time PXI-1031 DC
system, equipped with a NI PXI-8106 embedded controller card and a NI PXI-6259 multifunctional
DAQ card, running under the LabVIEW Realtime operating system. The signal is sampled every
10ms and a high-pulse of 15ms duration is generated when the pressure signal crosses the zero Volt
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
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threshold on a negative slope. The TTL triggering signal is fed into the MRI scanner through a
RCA jack.
2.4 4D-MRV procedure
Phase Contrast Imaging is a widely used method for medical examinations of blood and tissue
movement. Three-dimensional and three-component velocity vectors are the result (3D3C-MRV).
The 4D-MRV procedure is an advanced 3D3C-method, which subdivides the 3D-velocity encoding
into equidistant time steps for an underlying cycle.
Prior to a 4D-MRV scan a fixed scan-cycle duration (SD) according to the periodic flow has to be
chosen. This duration is then subdivided into a number of equal phase steps (PS) representing the
phase-slots of the phase-averaging process, yielding a temporal resolution of TRes. Once triggered, a
single scan of this predetermined duration (SD) starts. In each scan different parts of k-space are
acquired and afterwards composed to PS phase-averaged velocity fields. In the case that the
duration of the flow-cycles varies, there may be some flow cycles that are not fully covered by the
scan-cycle duration (SD), which leads to imprecise temporal positioning of the phase-slots in the
flow cycle. This results in increased standard deviation of the data and affects the last phase-slots
more than the first. Other flow cycles may be too short for the duration of a scan. This also results
in imprecise positioning of the phase-slots in the flow cycle. Flow cycles too short for one whole
scan cause the next trigger signal to arrive before the current scan is completed. This, of course,
leads to an interruption of the scanning process until the next trigger signal arrives. This
interruption elongates the total acquisition time (TAT). Choosing the fixed scan-cycle duration is an
important decision that strongly affects the quality of the data. It is necessary to accept the frequent
occurrence of such interruptions and the elongation of the scanning procedure. The thereby captured
too short flow cycles compensate the occurrence of the too long flow cycles, which results in
increased standard deviation for the last phase slots but allows for capturing a whole 360° flow
cycle.
A Siemens Trio Tim System with a 3 Tesla strong main magnetic field was used. The maximum
resolvable velocity is given by the velocity encoding value VENC≤10 m/s that is chosen
individually for each experiment. The VENC should be chosen to cover the whole velocity range in
the field of view to avoid aliasing errors but as low as possible since the signal-to-noise-ratio (SNR)
is proportional to the magnitude of the VENC.
For each complete experiment two separate measurements have to be conducted: first a flow-on
scan with the 4D-MRV procedure is performed. Afterwards a flow-off scan is conducted with the
identical procedure. With the flow-off scan background phase shifts due to eddy currents and
system imperfections can be compensated.
In order to reduce the acquisition time a GRAPPA-sequence (Generalized Auto-calibrated Partially
Parallel Acquisition) was used for selected measurements. In the GRAPPA-sequence a number of
phase-encoding steps are bypassed and the missing k-space data is filled with synthetic echoes. This
procedure reduces the total acquisition time (TAT) for one full three-dimensional 4D-MRV
measurement by about two-thirds. However, penalties concerning the SNR have to be considered as
shown below.
Another option to immensely reduce the TAT is to scan only a two-dimensional slice of finite thickness. Especially this is valuable for two-dimensional flows. The benefit of significantly reduced
TAT can be used for increasing the number of phase steps (PS) to increase the temporal resolution
or to improve SNR by averaging multiple scans. The SNR improves with √n, where n is the
number of conducted scans. Two 2D measurements have been conducted in this work.
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Figure 6: Frequency-Reynolds number map for the three feedback tube configurations.
Table 1: Flow conditions and model configurations of all experiments.
2.5. Measurement series
In preliminary experiments the oscillation frequencies of the fluidic oscillator were determined
from unsteady pressure measurements for three different feed-back tubes as a function of the
Reynolds number. The Reynolds number Re = (ubulk D h)/ν is built with the bulk velocity ubulk in the
smallest cross section of the actuators’ throat and the hydraulic diameter at this position and the
fluids kinematic viscosity ν. The feed-back tubes had different lengths l and different inner
diameters d. Due to the constant water temperature the Reynolds number is a function of the flow
rate only. Fig. 6 shows the oscillation frequencies for each feedback-tube configuration.
The black hollow circles in Fig. 6 mark five different combinations of feedback-tube geometry and
Reynolds numbers measured using the 4D-MRV technique. These cases were chosen for reasons of
comparability: cases 1 and 2 have the same Reynolds number but different frequencies due to
different feedback-tube geometry. Cases 1 and 5 have similar frequencies but different Reynolds
numbers and feedback-tube geometry as well as cases 3 and 4.
Table 1 displays the parameters of all conducted measurements. No. stands for the serial number of
a measurement configuration. In the following all results are referred to this table by the serial
number MX, for X = 1..8. l × d defines the feedback-tube geometry and filter describes the cut-off
frequency of the analog low-pass filter.
The flow conditions are defined by the flow rate V, the Reynolds number Re and the water
temperature T. The MR settings are the velocity encoding value VENC, the spatial resolution (xyz)
for 3D measurements and yz-layer) for 2D measurements, the total scanning duration TAT of a
single flow-on or flow-off scan (the value in brackets gives the number of scans that were
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averaged), the temporal resolution Tres, the phase steps per cycle PS, the scan-cycle duration SD and
the phase error on a single velocity vector σvel.
Figure 7: Measurement positions of the LDA measurements.
3. Discussion
3.1 Validation of 4D-MRV data
For validating the MRV data Laser-Doppler-Anemometry (LDA) measurements have been
conducted. A Dantec Dynamics Flow Explorer module with a Dantec Dynamics BSA F60
processor was used for acquiring the LDA data. An integrated synchronization option allows to
trigger the LDA system on the TTL-pulse of the triggering system and to obtain phase-averaged
velocity data as with the 4D-MRV sequence. Titanium dioxide was used as a seeding. The LDA
measurements were taken inside the plenum that was built of PMMA for this purpose. The data was
taken along a line of 12 points with 5mm spacing. The points are 18mm downstream of the outlets
of the oscillator and at half the channel height in z-direction, as shown in Fig. 7.
The comparison of 4D-MRV data with LDA data were made for case M3 of Table 1.The results are
shown in Fig. 8. Subfigures 8(a) and 8(b) show the velocity data along 55mm of the line as defined
in Fig. 7 across outlet B for the phase angle Φ = 270° and across outlet A for the phase angel Φ =
90°. Subfigures 8(c) and 8(d) show the velocity data at fixed positions: (c) y=-17.5mm near outlet B
and (d) y=22.5mm near outlet A. These two diagrams show the phase averaged data as a function of
the phase angel of the flow cycle. The results of Fig. 8 show very good agreement, both in space
(Figs. 8(a) and 8(b)) and in time (Figs. 8(c) and 8(d)). Differences in the resolution of the data
resulting from the different measurement techniques are the spatial resolution of the LDA data,
which was chosen lower than of the MRV data and the temporal resolution of the LDA data, which
could easily be increased much higher than for MRV. All diagrams are in good agreement
concerning the development of the velocity data in time and space and concerning the magnitudes
of the velocity. Both techniques precisely capture the periodic oscillation of the exiting jet with all
details.
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Lisbon, Portugal, 09-12 July, 2012
(a)
Velocity downstream of outlet B for Φ =
270° along the line x=18mm and z=0
(b)
Velocity downstream of outlet B at
(x=18mm, y=-17.5mm, z=0mm) as a
function fot he phase angle
(d)
(c)
Velocity downstream of outlet A for Φ =
90° along the line x=18mm and z=0
Velocity downstream of outlet A at
(x=18mm, y=22.5mm, z=0mm) as a function
fot he phase angle
Figure 8: Comparison of velocity data from LDA and MRV measurements.
3.2 Jet switching mechanism
In the following the jet switching process is analyzed by investigating the flow inside the oscillator
and the control ports. First the switching process is segmented into different sections using a
measurement with high temporal resolution, namely M5. Fig. 9 shows two-dimensional x-velocity
contours in the center plane (xy-layer, z=0) for a half-cycle of the periodic flow. Each plot shows
the velocity field of one of 25 phase angles of the cycle and therefore is labeled in alphabetic order.
The time between two consecutive plots is the repetition time of M5 TR = 84.8ms. All velocities
are normalized with the bulk velocity ubulk = 4 m/s in the throat. The contour plots were smoothed
by averaging five slices along the z-axis in between −2.4mm ≤ z ≤ 2.4mm.
The plots (a) to (q) of Fig. 9 represent one half-cycle of the flow beginning with phase angle φ =
57.6° and ending with φ = 273.6°. The series of plots starts with the jet fully attached to Coanda
wall A (a). A little later, in plot (c) the jet in outlet A and the recirculation in outlet B are fully
developed. Starting from plot (d) the jet is detaching from Coanda wall A. The detachment begins
on the Coanda wall shortly downstream of the junction to control port A. This separation no. 1
grows in size and thickness until plot (l). Then, the recirculation in outlet B starts to collapse in plot
(j) and significantly decreases in plots (k) and (l). On its way down to Coanda wall B the jet is just
in the middle of the interaction cavity and the jet is splitted in two parts exiting through both outlets
as shown in plot (m).
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Figure 9: Internal jet switching process for measurement M5.
In plot (n) the jet has quickly arrived at Coanda wall B within just one phase-step. After the jet has
flipped the first separation bubble on Coanda wall A is growing and a second recirculation bubble
advances at the splitter near exit A in plot (o). In plot (p) both separation bubbles merge to a single,
large recirculation zone filling the whole channel. The state shown in plot (n) is the mirrored
version of plot (a), indicating that one half-cycle is completed. The rest of the cycle (not shown
here) is identical to the above described series of events. The description of the jet switching
process goes along with the theories in the literature.
In this manuscript the jet switching mechanism is defined to be a composition of three different
phases: At first a stay phase occurs, during which the jet is attached to one wall and is staying
locally fixed. During this phase the recirculation develops, by merging of the two developing
recirculation bubbles. In Fig. 9 these phase is represented by the plots (a) to (c).
Secondly a detachment phase from the wall can be observed. The detachment starts with a slow and
slight movement of the jet away from Coanda wall and ends with the advancement of the jet to the
center of the interaction cavity pointing directly on the leading edge of the splitter. Plots (d) to (l)
correspond to this description. Finally the influence of the opposing Coanda wall prevails and,
hence, the jet moves towards this wall. This phase can be termed attachment phase and occurs
between plots (n) and (o).
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4. Conclusions
In this investigation the internal flow of a bi-stable fluidic oscillator was analyzed using the phaseaveraged measurement procedure 4D-MRV. It is the first time that this measurement procedure is
applied for periodic flow phenomena that are not driven and forced by pulsatile flow rate. A MR
compatible experimental setup was developed allowing triggering of the scanning procedure on a
pressure signal measured inside the flow, inside the scanner. A purpose built piezo-foil pressure
sensor was capable of operating reliably in the harsh environment inside an MR scanner and
capable of measuring a pressure signal without impairing the quality of the MRV data.
The fluidic oscillator geometry was taken from Arwatz et al. [1] and kindly provided by Avi Seifert.
It was modified in size to suit the requirements of the measurement procedure: water as operation
fluid, spatial resolution, oscillation frequency and the available range of the flow rate. The
oscillation frequency was varied depending on the feedback tube length and diameter, and the flow
rate was varied. Both effects on the oscillation procedure were analyzed using the data of eight
different measurements.
The acquired MRV data are in good agreement with LDA measurements which were conducted to
verify the validity of the 4D-MRV data.
Essential contributions to the understanding of the fluidic-oscillator flow could be made and new
insights into the processes composing the flow cycle in such devices were obtained. The flow cycle
could be divided into three phases: the stay phase, the detachment phase and the attachment phase.
Further analysis and interpretation of the data are currently conducted and will complete the here
described experimental procedure and results.
Acknowledgments
The authors gratefully acknowledge the support of Professor Avi Seifert who provided us with the
geometry of a reliably working fluidic oscillator.
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