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Experimental Comparison between the Flow Field of
Two Common Fluidic Oscillator Designs
F. Ostermann∗
Technische Universität Berlin, Berlin, 10623, Germany
R. Woszidlo†
The University of Kansas, Lawrence, KS 66045, USA
C.N. Nayeri‡and C.O. Paschereit§
Technische Universität Berlin, Berlin, 10623, Germany
The time-resolved internal and external flow field of two common oscillator designs with
equal outlet diameters are acquired by employing PIV measurements and phase-averaging
the results. The investigation of the flow fields and pressure measurements reveals the
same underlying oscillation mechanism for both designs. The curved oscillator does not
incorporate the change of the internal dynamics as observed for the angled oscillator. The
oscillation frequency is similar and solely depends on the geometry-specific total volume
transported through the feedback channels. The different mixing chamber geometry of the
curved oscillator requires a larger recirculation bubble for the jet to attach to the other wall
and prevents the reverse flow through the feedback channels which is found in the angled
oscillator. Separation bubbles inside the corners of the angled oscillator are avoided by
the streamlined feedback channel geometry of the curved oscillator. The required supply
pressure infers a superior general performance of the curved oscillator in terms of energy
requirements. Contrary to the angled oscillator, the curved oscillator’s jet attaches to
the walls of the outlet nozzle’s diverging part which causes a higher maximum deflection
angle and a different oscillation pattern in the external flow field. The distribution of
fluid in the external flow field reveals significant differences between the designs. Similar
characteristic vortices are identified in both flow fields. The curved oscillator yields slightly
more entrainment than the angled oscillator. The entrainment is affected little by maximum
deflection angle and oscillation pattern.
I. Introduction
Fluidic
oscillators, also known as sweeping jet actuators or flip-flop nozzles, are able to generate an
oscillating jet by being supplied with a steady pressure source. The basic principle is illustrated in Fig. 1
for two common designs. The air enters through the inlet nozzle and forms a jet which attaches to one of
the walls in the mixing chamber due to the Coanda effect. Upstream of the outlet nozzle, some fluid is
separated into the feedback channels and interacts with the jet downstream the inlet causing the jet to flip to
opposite side of the mixing chamber. Then, the process re-initiates. Thus, this oscillation is self-induced
and self-sustained. These oscillator designs incorporate two feedback channels. It is noteworthy that other
designs, including designs with only one or no feedback channels exist. A comprehensive overview over various
fluidic oscillator designs and their applications is given by Gregory & Tomac.
1
Fluidic oscillators are very
reliable because they do not require any moving parts. Therefore, they are attractive for various applications,
such as windshield washer, shower heads, or Jacuzzi nozzles.
2
Besides these applications from everyday life,
∗PhD Student, Hermann-Föttinger-Institut, AIAA Student Member.
†Visiting Assistant Professor, Aerospace Engineering, AIAA Member.
‡Research Associate, Hermann-Föttinger-Institut, AIAA Member.
§Professor, Chair of Fluid Dynamics, Hermann-Föttinger-Institut, AIAA Associate Fellow.
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fluidic oscillators are also subject of research in active flow control. They have been proven beneficial in
a wide field of applications, for example combustion
3,4
, noise
5,6
, drag
7,8
, and separation control
9–11
. In
many studies, one of the two designs shown in Fig. 1 is employed. In this study, the one on the left side will
be referred to as "curved fluidic oscillator" (Fig. 1, left) and the other as "angled fluidic oscillator" (Fig. 1,
right). A number of studies employed the curved oscillator design
2,6,12,13
and others used the angled oscillator
design
8,11,14,15
. Despite the proven performance of both oscillators, it remains uncertain which design yields
a better performance for particular applications. Furthermore, information on the flow fields are limited
because the naturally oscillating flow field makes it challenging to acquire time-resolved data. Vatsa et al.
16
compared both oscillator designs experimentally and numerically. The lack of time-resolved data made a
detailed analysis of the jet’s properties challenging and a general statement regarding the influence of the
geometries problematic. Bobusch et al.
17
revealed the influence of some geometry parameters on the flow field
numerically. Ostermann et al.
18
introduced phase-averaging methods for the flow fields of fluidic oscillators.
One of these methods is used to acquire time-resolved data from the curved and angled oscillator’s flow
field experimentally. Gaertlein et al.
19
successfully employed this method for phase-averaging the angled
oscillator’s flow field. In this study the flow fields of both oscillator designs are analyzed and compared. The
internal dynamics are evaluated and the instantaneous jet properties in the external flow field are examined.
Curved Fluidic Oscillator2Angled Fluidic Oscillator 19
FBC
FBC
MC
MC
inlet outlet inlet
outlet
Figure 1. Two common fluidic oscillators (FBC: feedback channel, MC: mixing chamber).
II. Experimental Setup and Instrumentation
1
2
3
4
5
1fluidic oscillator
2pressure sensors
3regulated air supply
4PIV laser
5PIV camera
Figure 2. Sketch of the experimental
setup.
Two fluidic oscillator designs are investigated in this study
(Fig. 1). Compared to most applications, the oscillators are scaled-
up in order to lower the oscillation frequency and to improve the
access to the internal flow field. The comparability between the
designs is ensured by scaling both oscillators to the same outlet
nozzle diameter. The oscillators are machined from acrylic glass
(PMMA) with a constant cavity depth of
25 mm
which yields an
outlet area of
Aoutlet
= 25
×25 mm2
. The use of transparent acrylic
glass allows optical access for PIV measurements. Both oscillators
are investigated sequentially with the same setup illustrated in
Fig. 2. One oscillator is mounted on a metal stand and emits its
jet into quiescent air and into an unobstructed environment. Up-
stream of the oscillator a settling chamber absorbs high-frequency
pressure fluctuations. Furthermore, a honeycomb is installed in-
side the plenum of each oscillator to provide homogenous inflow
conditions. The oscillator is supplied by pressurized air with a
maximum pressure of
16 bar
. The supply rate is controlled by a
massflow controller allowing a massflow up to
28 g/s
with an ac-
curacy of
0.6 %
full scale. In order to allow a comparison to other
studies, the theoretical outlet velocity
Uoutlet
, representing the
supply rate, is given. It is determined by considering the continuity
equation in the outlet nozzle (Eq. 1). The area
Aoutlet
is the outlet
nozzle’s smallest cross-sectional area,
ρ0
is the ambient density.
Throughout the study, all figures are created by evaluating the
flow field for
Uoutlet
=
19 m/s
. If not stated otherwise, the findings
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are independent of the supply rate within the investigated range.
Uoutlet =˙msupply
Aoutletρ0
(1)
Pressure taps located inside the oscillators are used to acquire a reference signal for phase-averaging. The
pressure taps are optimized using the dynamic response of tubes calculation
20
and located along the oscillators’
axis of symmetry and inside the feedback channels. The positions are chosen in consideration of previous
studies.
19,21
Additional pressure taps inside the settling chamber provide time-resolved information regarding
the supply pressure. Pressure sensors of the HDO Series by Sensortechnics with an adequate range and
a maximum response time of
0.1 ms
between extreme values are installed. Particle image velocity (PIV)
measurements are conducted to survey the oscillator’s internal and external flow field. A mono high-speed
PIV system is employed. Aerosol seeding particles are mixed into the pressurized air in the settling chamber
upstream the oscillator. No additional massflow is added by seeding the air because the seeding generator is
fed by air separated downstream the massflow controller. The PIV system is capable of acquiring snapshots
with a maximum resolution of 1024
×
1024 pixels at a sampling rate of
5000 Hz
. Throughout the study, a
constant sampling rate of
1500 Hz
is chosen as a compromise between recorded periods and snapshots per
period. This sampling rate is several orders higher than the expected oscillation frequency (
fosc
=
O
(
10 Hz
)).
The geometry inside the oscillators yields an inhomogeneous illumination of the internal flow field which
makes PIV measurements challenging. Hence, the position of the laser source is altered three times so that all
regions are illuminated adequately. The resulting flow fields are phase-averaged, phase-aligned and merged.
A similar approach is chosen for the external flow field. In order to increase the spatial resolution, several
regions of the external flow field are acquired sequentially with a high resolution and merged afterward.
The overlapping regions are fitted to provide a smooth transition between the individual regions. Velocity
deviations within the overlap region are less than
5 %
of the outlet velocity. The PIV measurements provide a
resolution of approximately
2 mm
. The data acquisition of pressure and PIV data is executed simultaneously
as described by Ostermann et al.18
III. Data Analysis
In order to investigate the time-resolved flow field while neglecting stochastic effects, the flow fields are
phase-averaged. Ostermann et al.
18
describe a detailed method for phase-averaging the data of a fluidic
oscillator’s naturally oscillating flow field by using a reference signal. In this study, a reference signal extracted
from pressure signals is used for phase-averaging the internal and external flow field of both oscillators. The
following steps summarize the phase-averaging procedure:
1.
Pressure signals from the feedback channels are found to be the best choice for a reference signal for the
angled oscillator. For the curved oscillator, pressure signals from the mixing chamber yield the most
suitable reference signal. These choices are made based on best signal quality. In order to increase the
oscillation amplitude the difference between the signals of two symmetrically positioned pressure taps is
used as the reference signal.
2.
The signal quality is further improved by applying a low pass filter forward and backward to avoid
a phase lag. The signal is autocorrelated by using a signal’s fragment with a size of a half to one
oscillation period.
3.
The sign change of the correlation coefficient marks half an oscillation period. The corresponding phase
angles for every PIV snapshot are determined by evenly distributing the phase angles between these
half oscillation periods.
4.
All snapshots are averaged within a phase angle window of
3°
. This window size is optimized by
minimizing the RMS value.
18
The chosen window size yields an average of 91 snapshots per phase angle
window. The results converge for more than 50 snapshots per window.
5.
The individual flow fields, sequentially acquired with PIV, are phase aligned by comparing the appropriate
reference signals and merged afterward. The overlapping regions are replaced by a weighted average
between appropriate regions providing a smooth transition.
The autocorrelation does not provide a physically based period starting point. Therefore, the results of the
individual oscillators need to be phase aligned to a common period starting point.
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IV. Results
The flow field of fluidic oscillators is characterized by the oscillation frequency. Therefore, a first general
overview is achieved by evaluating the frequency to supply rate dependence. Figure 3 shows the oscillation
frequency as a function of the supply rate for the two oscillator designs. The supply rate is represented by
the theoretical outlet velocity
Uoutlet
. For comparability to other studies, the supplied massflow
˙m
and the
Reynolds number based on the hydraulic diameter of the outlet nozzle
dh
are added as well. According to
the Reynolds number, the flow is well within the turbulent regime of a pipe flow. It is evident that both
oscillators are characterized by a linear dependence of the oscillation frequency on the supply rate. It is
noteworthy that the oscillation frequency of both oscillators is approximately equal although the internal
geometries differ. A minimum required supply rate to emit an oscillating jet was not noticed for either design.
For supply rates higher than
Uoutlet
=
23 m/s
the angled oscillator’s frequency deviates from the curved
oscillator with a smaller slope. Gaertlein et al.
19
identify this deviation to be caused by a change in the
internal dynamics due to increasing turbulence of the jet. It is evident that this change is directly linked to
the geometry of the angled oscillator because it does not occur for the curved oscillator.
0 5 10 15 20 25 30 35
0
10
20
Uoutlet (m/s)
fosc (Hz)
curved oscillator
angled oscillator
0 5 10 15 20 25
˙m(g/s)
0 10 20 30 40 50 60
Re (-) ·103
Figure 3. The jet’s oscillation frequency vs. supply rate for b oth oscillator designs.
A. Internal Flow Field
The frequency behaviors indicate a similar oscillation dynamic for both oscillator designs (Fig. 3). In this
section, the detailed dynamics are analyzed and compared by investigating the time-resolved internal flow
field. As a first step, a common period starting point has to be characterized. Most definitions are directly
linked to a particular oscillator design and depend on the flow field of interest. Because the internal flow field
is available in this study, the sign change of the deflection angle in the outlet nozzle from negative to positive
is defined as the period starting point
φ
=
0°
. This definition makes a comparison between oscillator designs
possible because it is linked to a position of the jet.
Figure 4 illustrates the internal flow field for half an oscillation period. The coordinates are normalized
by the hydraulic diameter of the outlet nozzle (
dh
=
25 mm
). It is evident that the general behavior is
similar for both designs. The jet enters from the left into the mixing chamber. There, it attaches to the
lower wall and stagnates at the converging part of the outlet nozzle (Fig. 4,
φ
=
60°
). Some fluid is diverted
into the feedback channel inlets. A recirculation bubble forms and pushes the jet to the other side (Fig. 4,
φ
=
120°
). It is noteworthy that in the curved oscillator no initial recirculation bubble is present (Fig. 4,
φ
=
0°
). However, it is created by the low momentum flow from the feedback channel which drains in between
the main jet and the wall. Gaertlein et al.
19
identify this growth of the recirculation bubble as the driving
mechanism for the angled oscillator. They show that the oscillation frequency solely depends on the time
required to transport a geometry-specific, total volume through the feedback channel which is independent
of the supply rate. Figure 5 (left) validates this statement for both designs by integrating the volume flow
through the lower feedback channel per oscillation period. It is approximately constant for both oscillators
which confirms that both are governed by the same oscillation mechanism. In Fig. 5 (right), the time-resolved
volume flow
Q
is shown. For the angled oscillator, a negative volume flow through the feedback channels
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is present which delays the switching of the jet and increases pressure losses. Gaertlein et al.
19
suggest an
increase in the distance between the mixing chamber’s inlet wedges to avoid this effect. The distance between
these wedges is larger in the curved oscillator successfully avoiding the reversed flow in the feedback channel
(Fig. 5, right). Furthermore, this prevents the vortices in the feedback channel outlets which are caused
by the reversed flow (Fig. 4,
φ
=
0°
). The
25 %
larger distance between the walls of the mixing chamber
increases the required size of the recirculation bubble for pushing the jet to the other side. Therefore, more
volume needs to be transported through the feedback channels, which is evident in Fig. 5 (left). Both effects,
the avoided reversed flow and larger required recirculation bubble, balance each other and lead to a similar
oscillation frequency for both designs (Fig. 3). The recirculation bubble growth needs more time which leads
to a seeming phase difference between the flow fields of the angled and curved oscillator (Fig. 4,
φ
=
60°
).
The temporal difference is recovered by the curved oscillator’s flow field at
φ
=
120°
. This observation implies
that the time scales of the oscillation process differ and depend on the geometry although the underlying
oscillation mechanism is the same.
0 10 20 30 40
0
100
200
Uoutlet (m/s)
volume per cycle (cm3)
0 90 180 270 360
0
2000
4000
φ(deg.)
Q(cm3/s)
curved oscillator angled oscillator linear regression
Figure 5. Left: Total volume transported through the lower feedback channel per period. Right: Time-resolved
volume flow through the lower feedback channel. Every 10th data point marked.
An apparent difference between the oscillators’ geometry are the feedback channels. Gaertlein et al.
19
suggest streamlined feedback channels in order to avoid separation around the sharp corners. The rectangular
design of the angled oscillator causes separation in the channel inlets and outlets (Fig. 4,
φ
=
120°
). The
curved oscillator comprises a streamlined feedback channel which successfully avoids the separation at its
outlet. However, at the feedback channel inlet a separation bubble is still evident (Fig. 4,
φ
=
120°
). Therefore,
possible design improvements may address a different feedback channel inlet geometry for the curved oscillator.
Another difference between the geometries is the converging part of the outlet nozzle. The angled
oscillator’s converging outlet nozzle consists of two walls with an angle of
60°
to the line of symmetry. In
contrast, the converging outlet nozzle of the curved oscillator incorporates rounded walls which are tangential
to the outlet. The recirculation bubble fits into these rounded walls and causes several other vortices inside
the feedback channels (Fig. 4,
φ
=
120°
). Contrary to the recirculation bubble of the angled oscillator, this
bubble is larger and lasts longer. This may increase the deflection of the curved oscillator’s jet to higher
angles.
The aforementioned differences do not only affect the flow field but also influence the overall performance of
the oscillators. In order to compare the performance between both designs, the supply pressure is investigated.
In Fig. 6 the time-averaged (left) and time-resolved (right) differential supply pressure, measured inside
the settling chamber, are shown. For all supply rates, the required supply pressure is higher for the angled
oscillator. This infers a higher pressure loss and hence an inferior performance of the angled oscillator in
terms of energy requirements. The time-resolved supply pressure reveals that the oscillation frequency affects
the flow field far upstream. This is caused by a fluctuating pressure loss inside the oscillators. The maximum
pressure loss coincides with the stagnation of the jet at the converging walls of the outlet nozzle (Fig. 4,
φ≈120°
). The oscillation amplitude of the supply pressure for the curved oscillator is higher than for
the angled oscillator which implies higher oscillation amplitudes of the jet properties. In this study, the
investigated jet properties include massflow, jet width and deflection angle. In the internal flow field the
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0 10 20 30 40
0
1000
2000
3000
Uoutlet (m/s)
psupply (Pa)
0 60 120 180 240 300 360
500
600
700
800
φ(deg.)
psupply (Pa)
curved oscillator angled oscillator range of oscillation values
Figure 6. Left: Time-averaged supply pressure as a function of the outlet velocity. Every 2nd data point
marked. Right: Time-resolved required supply pressure for both oscillator designs. Every 10th data point
marked.
massflow is calculated by assuming a two dimensional jet profile and multiplying the massflow per unit depth
by the cavity depth. Boundary layer effects are neglected in this assumption. However, this calculation
yields a reasonable qualitative time-dependent massflow. The deflection angle is determined by evaluating
the direction of the velocity vectors with highest magnitude. The jet width is defined as the span of all
velocity vectors with a magnitude of
50 %
of the maximum local velocity. Figure 7 shows the time-resolved jet
properties in the outlet nozzle. As anticipated, the massflow through the oscillator changes and its amplitudes
are higher for the curved oscillator. It is evident that the minimum massflow approximately coincides with
the maximum pressure loss for both oscillators. In contrast, the maximum massflow does not coincide with
the minimum pressure loss for the angled oscillator. It is suspected that the change of massflow is not only
a result of the oscillatory pressure loss but also a change of the effective outlet area.
19,21
When the jet is
deflected, the effective outlet area for the jet is smaller. This is also evident for the jet width. The jet width
reaches its maximum when the jet has no deflection. These changes are accompanied by respective oscillations
in jet velocity and momentum. The oscillating jet properties impact the dynamics of the external flow field
which may affect the performance for certain applications. It is also noteworthy that the deflection angle of
the curved oscillator at the outlet is smaller than for the angled oscillator. This is caused by the different
geometry of the outlet nozzles’ converging part. However, the discussion in the following section indicates
that the maximum deflection angle of the curved oscillator’s jet is larger in the external flow field due to the
jet attaching to the diverging nozzle walls.
0 60 120 180 240 300 360
0.6
0.8
1
φ(deg.)
w/dh
0 60 120 180 240 300 360
−40
0
40
θjet (deg.)
0 60 120 180 240 300 360
0.8
0.9
1
1.1
1.2
˙m/ ˙m
, massflow
, jet width
, deflection angle
Figure 7. Oscillating jet properties in the outlet nozzle of the curved oscillator (red) and angled oscillator
(blue). Every 10th data point marked.
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B. External Flow Fields
The investigation of the internal flow field reveals that the jet properties of both oscillator designs are not
constant. This has a significant effect on the external flow field which is examined in this section. At first the
general external flow field is inspected. Afterward, the time-resolved and time-averaged jet properties are
investigated in detail. The determination of the external jet properties is based on a transformation to a polar
coordinate system with its origin in the center of the outlet nozzle. The jet properties are evaluated along the
radial distance
r
. This approach accounts for the jet’s deflection instead of considering a constant distance
x
.
φ= 0◦
φ= 0◦
0 5 10 15 20
x/dh
φ= 60◦
0 5 10 15 20
x/dh
φ= 120◦
0 5 10 15 20
x/dh
φ= 180◦
0 5 10 15 20
x/dh
φ= 60◦
φ= 120◦
φ= 180◦
0 0.3 0.6 0.9 1.2 1.5
U/Uoutlet
Figure 8. The external flow fields of the curved (top) and angled oscillator (bottom).
The time-resolved external flow field is visualized for the curved and angled oscillator design in Fig. 8.
It is apparent that the flow fields differ substantially between the designs caused by different oscillation
patterns. The curved oscillator’s jet has a long dwelling time in its maximum deflection which generates a
high concentration of fluid at this state. In contrast, the angled oscillator’s jet has more balanced dwelling
times, yielding a more homogenous distribution. This is validated in Fig. 9 by evaluating the time-averaged
flow field. The massflow is linearly dependent on the local velocity. Thus, the time-averaged velocity is a
quantity to compare the distribution of fluid. Furthermore, the time-averaged velocity field shows the affected
region of the emitted jet. It is evident that the curved oscillator concentrates the fluid at the maximum
deflection of the jet. This leads to the aforementioned inhomogeneous distribution of fluid but also extends
the affected region. In contrast, the angled oscillator has a homogenous distribution of fluid while affecting
a smaller region. This difference may have an effect on certain applications which require a homogenous
distribution of fluid.
The larger affected region of the curved oscillator is caused by the jet’s maximum deflection angle. In
Fig. 10 the maximum deflection angle is evaluated as a function of the supply rate. The deflection angle is
examined at a radial distance of
r/dh
= 3 by determining the direction of the velocity vector with the local
maximum magnitude. This approach takes a possible curvature of the jet into account. The dependence on
the supply rate reveals a constant maximum deflection angle for the curved oscillator. This indicates a similar
oscillation pattern for all supply rates. In contrast, the maximum deflection angle of the angled oscillator’s
jet is dependent on the supply rate above a threshold supply rate. The deflection angle rapidly decreases
for
Uoutlet >23 m/s
which is accompanied by the aforementioned change in the frequency behavior (Fig. 3).
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curved oscillator
0 10 20
x/dh
angled oscillator
0 10 20
x/dh
0
0.1
0.2
0.3
0.4
0.5
U
Uoutlet
Figure 9. Time-averaged external flow field.
0 5 10 15 20 25 30 35 40
0
20
40
Uoutlet (m/s)
maximum deflection angle (deg.)
curved oscillator
angled oscillator
Figure 10. Maximum deflection angle at r/dh= 3.
Gaertlein et al.
19
suggest this effect to be caused by increasing turbulence of the jet and changes in the
internal dynamics. However, the oscillation pattern is unaffected by these changes. Figure 10 further reveals
that the maximum deflection angle of the curved oscillator’s jet is higher than that of the angled oscillator for
all supply rates. This is contrary to the maximum deflection angle in the outlet nozzle (Fig. 7). There, the
angled oscillator’s jet achieves larger deflection angles. This discrepancy between the curved oscillator’s jet
deflection angle in the internal and external field is caused by the diverging part of the nozzle. The curved
oscillator’s nozzle has an opening angle of
100°
. The jet attaches to the walls of the nozzle’s diverging part.
This increases the maximum deflection angle to the geometry given ±50°. The diverging part of the angled
oscillator has an opening angle of
125°
. This is too large for the jet to attach to the walls. Therefore, the
angled oscillator’s maximum deflection angle is not increased and hence smaller than that of the curved
oscillator. Bobusch et al.
17
reveal that the diverging part of the nozzle has no significant influence on the
external flow field for the angled oscillator. However, it is shown that a smaller opening angle cause the jet to
attach to the walls and may be used to increase the maximum deflection to higher angles.
The diverging part of the nozzle does not only affect the deflection angle but also the external flow field’s
oscillation pattern. The oscillation pattern is best described by the time-resolved deflection angle. In Fig. 11
the time-resolved deflection angle θ(top) and its time derivative, the angular velocity (bottom), at a radial
distance of
r/dh
= 3 are shown. The oscillation pattern of both jets exhibit significant differences. The
curved oscillator’s jet has long dwelling times (i.e.,
50 %
of the period time) in its maximum deflection and
rapid changes of the deflection angle in between. This is caused by the aforementioned Coanda effect at the
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−40
−20
0
20
40
θjet (deg.)
0 30 60 90 120 150 180 210 240 270 300 330 360
0
0.5
1
1.5
φ(deg.)
|∂θjet /∂ φ|( - )
Figure 11. Time resolved deflection angle at r/dh= 3 for the curved (red) and angled oscillator (blue).
diverging walls of the outlet nozzle. The attachment of the jet to the outlet nozzle walls imposes a force
delaying the jet’s flipping. The jet’s angular velocity is dominated by two extremes. The angular velocity
magnitude has its maximum when the jet flips to the other side. Two other local maxima are also apparent.
These are caused by the attachment process to the outlet nozzle’s diverging walls which yields a further
increase in deflection angle to its maximum. The resulting time-averaged flow field is thereby dominated by
the jet’s presence in the deflected state (Fig. 9). The angled oscillator’s pattern is not affected by the diverging
part of the nozzle. The maximum deflection angle is reached during an overshoot which was identified by
Gaertlein et al.
19
(
φ
=
90°
). The duration of the overshoot is relatively short before the jet dwells around a
smaller deflection angle. In fact, the dwelling time of the angled oscillator is not characterized by a constant
deflection angle but rather by small angular velocities (e.g.,
φ
= 90 to
135°
). Overall, the angular velocity of
the jet is smaller than that of the curved oscillator. Therefore, this jet describes a smoother movement which
causes a more homogeneous distribution of fluid in the external flow field (Fig. 9).
0246810
x/dh
0246810
x/dh
curved
oscillator
angled
oscillator
Figure 12. Vortex in the external flow field in comparison to a flow visualisation.8
A more detailed analysis of the time-resolved external flow field reveals two symmetrical, distinct vortices
at the outer edge of the affected region (Fig. 12). It is suspected that the reason for the fluidic oscillator’s
effectiveness in flow control applications are these vortices which are bent in streamwise direction by a
freestream.
8
In both external flow fields these two vortices are present. The vortex is created in the jet’s
shear layer when it reaches its maximum deflection angle. Consequently, the vortices do not coexist but are
created alternately. The vortex convects downstream and vanishes when the jet switches to the other side.
Therefore, it is suspected that its intensity is higher in the curved oscillator’s flow field due to the jet’s longer
dwelling times in its deflected state.
Beside the jets’ oscillation patterns, their instantaneous properties are of interest for applications. Figure
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0 5 10 15 20
0
0.5
1
1.5
r/dh
Umax/Uoutlet
0 2 4 6 8 10
0
2
4
6
8
r/dh
w/dh
curved oscillator angled oscillator range of oscillation values
Figure 13. The maximum jet velocity and jet width as a function of the radial distance to the nozzle. Every
30th data point marked.
13 (left) shows the jets’ time-averaged local maximum velocity magnitude and their oscillation amplitudes
as a function of radial distance. The supply rate dependency of the time-averaged maximum velocity is
approximately similar for both oscillators. Furthermore, it is apparent that the maximum velocity close
to the nozzle is higher than the theoretical outlet velocity. This is caused by boundary layer effects which
reduces the effective outlet area. Recall that the theoretical outlet velocity is based on the geometric outlet
area. Despite the commonalities, it is evident that the oscillation amplitude is higher for the curved oscillator.
That is anticipated because the amplitudes of the jet properties in the internal field are also higher. This
may have an effect on applications of fluidic oscillators because of the changing jet properties in the external
flow field such as locally and temporally changing momentum coefficients. In Fig. 13 (right) the jet width as
a function of the radial distance
r
is illustrated. The jet width is defined as the normal distance of velocities
whose magnitudes are higher than
50 %
of the local maximum velocity. The jet width is also approximately
similar for both oscillators close to the nozzle. Compared to non-oscillating jets (e.g., Zaman
22
), the jet
width increases significantly faster. That is caused by the jet’s motion. During the motion, the trailing air
adds to the jet width. This is also evident in an increasing amplitude of the oscillatory jet width. Especially
for the curved oscillator, the jet’s movement causes large amplitudes because it incorporates long dwelling
times when no substantial trailing exist and short switching time with a large trailing effect. The mean jet
width decreases for higher radial distances because here the maximum velocity concentrates at the maximum
deflection angle and the trailing’s magnitude is small. The high jet width of both oscillators accompanied by
a rapid decrease in the maximum velocity indicate high entrainment.
0 5 10 15 20
0
5
10
15
r/dh
˙m/ ˙msupply
0 10 20 30 40
0
2
4
6
8
10
r/dh= 3
r/dh= 10
Uoutlet (m/s)
˙m/ ˙msupply
curved oscillator angled oscillator range of oscillation values
Figure 14. Left: The massflow as a function of radial distance from the nozzle. Every 30th data point is
marked. Right: The massflow as a function of the supply rate for two radial distances.
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In the present study only two dimensional flow fields are measured and evaluated. The absence of
information in the third dimension allows only the determination of massflow per unit depth. However, this
shortcoming is alleviated by introducing an effective jet depth which is calculated by taking the conservation
of momentum into account. This conservative approach allows the investigation of entrainment without
the third dimension available. More detailed information on this approach are given by Gaertlein et al.
19
.
Figure 14 (left) shows the massflow as a function of the radial distance. It is evident that both oscillators’
entrainment rate is approximately linear and considerably higher than that of a freejet (e.g., Zaman
23
).
The entrainment and its amplitude of the curved oscillator’s jet are slightly higher than that of the angled
oscillator. It is suspected that the curved oscillator’s jet has more quiescent air surrounding it at its maximum
deflection due to longer dwelling times. Figure 14 (right) shows that the entrainment rate is independent of
the supply rate for the curved oscillator. Therefore, it is also independent on the oscillation frequency. The
angled oscillator’s entrainment undergoes a slight decrease for high supply rates caused by the decreasing
maximum deflection angle. However, compared to the rapid reduction of the maximum deflection angle,
the change in the entrainment rate is rather small. Overall, the entrainment rate of both sweeping jets is
higher than for a steady jet and reveals only minor dependencies on the design. However, certain applications
requiring high entrainment need to consider the differing fluid distribution of the oscillators as well.
V. Conclusion
This study successfully identifies commonalities and differences between the two oscillator designs.
Depending on the application, these differences may be advantageous or disadvantageous and one of both
oscillators may be favored. Both devices incorporate the same oscillation mechanism and yield similar
oscillation frequencies. The oscillation frequency solely depends on the time to transport a geometry-specific
volume through the feedback channels. This volume feeds into a recirculation bubble which pushes the jet to
the opposite wall of the mixing chamber. The geometric differences between the designs and their effects
on the flow field are investigated in detail. The curved oscillator has a larger distance between the inlet
wedges of the mixing chamber. This prevents reversed flow in the feedback channel which is observed for the
angled oscillator. Furthermore, the streamlined feedback channel geometry of the curved oscillator minimizes
separation in the channel’s corners. However, additional optimization of the geometry may further improve
the flow through the channels. It is shown that the curved oscillator is more effective in terms of energy
requirements. The required supply pressure for a given massflow is reduced by
20 %
compared to the angled
oscillator. Despite the lower mean pressure loss, the amplitudes of the time-dependent pressure loss are larger
for the curved oscillator which is also accompanied by stronger oscillations in the jets’ properties.
The investigation of the external flow field reveals considerable differences in the oscillation pattern. These
differences are caused by the oscillators’ diverging nozzles. For the curved oscillator, the opening angle is
smaller which causes the jet to attach to either side of the nozzle’s walls. This increases the jet’s maximum
deflection angle and induces longer dwelling times at that position. Therefore, this oscillation pattern yields
an inhomogeneous distribution of fluid in the external flow field. In contrast, the diverging nozzle of the
angled oscillator, incorporating a higher opening angle, is shown to have no effect on the jet. Thus, the
angled oscillator’s jet has smaller deflection angles with shorter dwelling times at the maximum deflection
which yields a more homogeneous distribution of fluid. Depending on the application, the curved oscillator is
favorable for high deflection angles and consequently large affected areas. For a homogenous distribution of
fluid, the angled oscillator may be a better choice. In terms of maximizing the entrainment, both oscillators
reveal a similar result. The entrainment of sweeping jets is comparably high to the entrainment of steady jets.
Neither the oscillation pattern, nor the deflection angle is found to significantly influence the entrainment.
Overall, a superior design for all applications is not found in this study. However, the curved oscillator
reveals properties such as reduced pressure loss and larger (supply rate independent) deflections angles, which
may be favored in some applications.
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