J . F luid Mech. (2018) , v ol . 857 , pp . 216–238. c
 Cambr idge U niv ersit y Press 2018
doi:10.1017/jfm.2018.739
216
Pr opert ies of a sw eeping je t emitted fr om a
fluidic oscilla tor
Flor ian Ostermann 1 , † , Rene W os zidlo 1 , C . Na v id N a yeri 1
and C. Oliv er Pasc hereit 1
1 Hermann-Föttinger -Institut, T echnische Uni versität Berlin, Berlin 10623, German y
(Recei ved 29 January 2018; re vised 15 August 2018; accepted 9 September 2018;
first published online 19 October 2018)
This experimental study in vestigates the flo w field and properties of a sweeping jet
emitted from a fluidic oscillator into a quiescent en vironment. The aspect ratio of the
outlet throat is 1. Stereoscopic particle image v elocimetry is employed to measure the
velocity field plane-by-plane. Simultaneously acquired pressure measurements pro vide
a reference for phase correlating the indi vidual planes yielding three-dimensional,
time-resolved v elocity information. Lagrangian and Eulerian visualization techniques
illustrate the phase-a veraged flo w field. Circular head v ortices, similar to the starting
v ortex of a steady jet, are formed repetiti v ely when the jet is at its maximum
deflection. The quantitati ve jet properties are determined from instantaneous velocity
data using a cylindrical coordinate system that tak es into account the changing
deflection angle of the jet. The jet properties v ary throughout the oscillation c ycle.
The maximum jet velocity decays much f aster than that of a comparable steady jet
indicating a higher momentum transfer to the en vironment. The entrainment rate of
the spatially oscillating jet is lar ger than for a steady jet by a factor of 4. Most of
the mass flo w is entrained from the direction normal to the oscillation plane, which
is accompanied by a significant increase in jet depth compared to a steady jet. The
high entrainment rate results from the enlar ged contact area between jet and ambient
fluid due to the spatial oscillation. The jet’ s total force exceeds that of an idealized
steady jet by up to 30 %. The results are independent of the in vestigated oscillation
frequencies in the range from 5 to 20 Hz.
K ey words: flo w control, jets, mixing enhancement
1 . Introduc t ion
Properties of turb ulent jets hav e been researched for se veral decades because the y
represent a fundamental flo w field in fluid mechanics as well as being of importance
for v arious technical applications such as fuel injection and flo w control. Se veral
studies in vestigated the fundamental flo w field for axisymmetric and asymmetric
steady jets in a quiescent en vironment (some examples include Sforza, Steiger
& T rentacoste 1966 ; W ygnanski & Fiedler 1969 ; Zaman 1996 ). Specifically , the
jet’ s entrainment of surrounding fluid as an indicator for mixing performance is
of interest and focus of man y studies (e.g. Ricou & Spalding 1961 ; Faris 1963 ;
† Email address for correspondence: [email protected]
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 217
Krothapalli, Baganof f & Karamcheti 1981 ). The jet properties and the entrainment
change significantly for unsteady jets (Bremhorst 1979 ). T emporally unsteady jets (i.e.
pulsating jets) are jets with temporally changing jet properties (e.g. the supply rate).
Platzer , Simmons & Bremhorst ( 1978 ) re vealed that the entrainment of a pulsed jet
is significantly higher than that of a steady jet. Bremhorst & Hollis ( 1990 ) confirmed
this result and identify periodically created head v ortices that increase Reynolds
stresses thereby enhancing mixing performance.
Spatially oscillating jets (i.e. flapping jets or sweeping jets) are another group of
unsteady jets. These jets ha ve a constant supply rate; ho wev er , their exit direction
oscillates periodically . One tool to generate a spatially oscillating jet is provided
by fluidic oscillators. These de vices are able to generate an oscillating jet without
any mo ving parts in v olved, which makes them rob ust and attracti ve for technical
applications. They were de veloped in the Harry Diamond Laboratories in the 1950s,
initially with the intention for use as binary switches. In recent years, the interest
in fluidic oscillators has been rene wed due to their performance in flo w control (e.g.
Seele et al. 2009 ; Seifert et al. 2009 ; Schmidt et al. 2015 ; Whalen et al. 2015 ) as
well as mixing enhancement (Mi, Nathan & Luxton 2001 ; Lacarelle & Paschereit
2012 ). A comprehensi ve re view on spatially oscillating jets from fluidic oscillators
and their applications is pro vided by Gregory & T omac ( 2013 ).
Initial studies on spatially oscillating jets were performed by V iets ( 1975 ) and
Simmons, Platzer & Smith ( 1978 ). V iets ( 1975 ) in v estigated fluidic oscillators as
thrust ejector de vices. They sho wed that the spreading of the jet is significantly
enlar ged compared to steady jets. The same was found by Simmons et al. ( 1978 )
who analysed the flo w field of a spatially oscillating planar jet in co-flo w . They
also state that the velocity decay rate is greater than that of a steady jet. The
entrainment of spatially oscillating jets has been contro versial. Platzer et al. ( 1978 )
indicated that the entrainment of a spatially oscillating quasi-two-dimensional jet
is considerably higher than that of a comparable steady jet. In contrast, Srini v as,
V asude v an & Prabhu ( 1988 ) and Raman, Hailye & Rice ( 1993 ) ar gued that the
entrainment of the quasi-two-dimensional spatially oscillating jet is less than that of
a two-dimensional steady jet. These studies performed one-dimensional measurements
with hot-wire anemometry along the centre line of the jet at v arious distances
from the nozzle neglecting the direction of the flo w and potential three-dimensional
ef fects. The results were also discussed by Mi et al. ( 2001 ). They conducted
two-dimensional measurements with a direction-sensiti ve hot-wire system. Their
results confirmed that the entrainment of a quasi-two-dimensional spatially oscillating
jet is indeed higher and they contended that P latzer et al. ( 1978 ) ov erestimated
the entrainment due to neglecting three-dimensional ef fects. All these studies
in vestigated a quasi-tw o-dimensional oscillating jet. Ho we ver , most applications
in volv e oscillating jets with an aspect ratio of the order of 1, therefore requiring
essentially three-dimensional measurements.
W oszidlo et al. ( 2015 ) and Sieber et al. ( 2016 ) in v estigated qualitati vely the centre
plane flo w field of a spatially oscillating jet with a throat aspect ratio of 1. They
re vealed the e xistence of two alternating v ortices on either side of the flo w field.
Ostermann et al. ( 2015 a ) presented preliminary results on quantitati ve jet properties.
Their results indicate a greater velocity decay rate than a steady jet. Furthermore,
they conserv ati vely estimated the entrainment by determining an ef fecti v e jet depth
from assuming conserv ation of momentum. They suggested that the entrainment
is significantly higher than that of a steady jet. Ho we ver , their results are only
based on two-dimensional v elocity data without assessing the three-dimensional
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218 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
Mixing
chamber
y
(a) (b)
y
x
d h
l n l n
x
d h
Feedbac k channel

F IGURE 1 . (Colour online) T wo tested nozzle geometries. ( a ) The fluidic oscillator , and
( b ) the steady jet configuration. Denoted are the used coordinate origin, the hydraulic
diameter d h and the length of the outlet nozzle’ s di ver ging part l n .
flo w field. This shortcoming is addressed in the presented study that focuses on the
three-dimensional, time-resolved flo w field, jet properties, entrainment and forces of a
spatially oscillating jet emitted from one fluidic oscillator with unit aspect ratio. The
data presented in this study are also a vailable online in a repository (Ostermann et al.
2018 ) providing the three-dimensional flo w field for other numerical or experimental
studies to compare to.
2. Set-up and ins trument ation
Se veral methods for generating spatially oscillating jets e xist. In this study , a fluidic
oscillator equipped with two feedback channels emits the oscillating jet (figure 1 a ).
The basic principle of this type of oscillator was in v estigated and characterized in
v arious studies (Bob usch et al. 2013 ; W oszidlo et al. 2015 ; Sieber et al. 2016 ). The
jet’ s spatial oscillation is caused solely by the internal dynamics and the geometry .
The oscillating flo w field is self-induced and self-sustained.
In this study , the smallest cross-section of the fluidic oscillator outlet (i.e. the
nozzle throat) is 25 × 25 mm 2 that results in a hydraulic diameter d h of 25 mm.
The di ver gent part of the nozzle has a length l n = 1 . 1 d h and an opening angle of
± 50 ◦ . The coordinate system origin is located in the centre of the nozzle throat
at mid-depth of the oscillator . The oscillator is milled from acrylic glass. A co ver
plate seals the internal ca vities. The oscillator is equipped with pressure sensors
(HDO Series by Sensortechnics) for time-resolv ed pressure measurements inside the
oscillator . Their response time is faster than 100 µ s, which allo ws for the acquisition
of a time-resolved reference signal. A mass flo w controller (HFC-D-307 by T eledyne
Hastings Instruments) controls the amount of pressurized air supplied to the fluidic
oscillator . It is able to measure up to 200 kg h − 1 at a precision of better than 0.7 %
full scale. Do wnstream of the mass flo w controller , a portion of the air is di verted
through a seeding generator and then mer ged again with the main air flo w into the
oscillator figure 2 . That ensures that the air supply contains seeding particles without
additional mass flo w being added by the seeding generator . An additional seeding
generator adds particles to the en vironment. The fluidic oscillator is mounted on a
metal stand figure 2 . A wooden plate with dimensions of 1 . 2 × 1 . 2 m 2 (48 × 48 d 2
h )
surrounds the oscillator outlet to provide a solid boundary to the e xternal flo w field.
The supply mass flo w is used for determining the theoretical b ulk velocity based
on the assumption of a top-hat v elocity profile and ambient conditions (i.e. ambient
density ρ 0 ) at the throat of the oscillator ( 2.1 ). This assumption is reasonable because
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 219
Fluidic oscillator 1
2
3
4
5
PIV laser sheet
PIV cameras
3 3
2
1
4
5
Wa l l
T rav ersing sys tem
Pressurized
air
Mass flo w
controller
Seeding
g enerator

F IGURE 2 . (Colour online) The experimental set-up.
for the highest supply rate, a Mach number of 0.11 is estimated at the outlet throat.
Therefore, compressibility ef fects are neglected in this study .
U bulk = ˙ m supply
ρ 0 A outlet
. (2.1)
A stereoscopic particle image velocimetry (PIV) system measures flo w velocities
in the external flo w field. The system consists of a laser (Ever green 200 by Quantel)
with a maximum ener gy of 200 mJ and two cameras (pco.2000 by PCO A G) with a
resolution of 2000 × 2000 pix els. Each camera is equipped with a Scheimpflug adapter
and a 100 mm objecti ve by Canon. A synchronizer by ILA GmbH assures the timing
between the components of the measurement equipment. The laser sheet thickness
is approximately 3 mm. The measurement plane is spanned in the x – y direction
from x = 30 ( 1 . 2 d h ) to 350 mm ( 14 d h ) and from y = − 50 ( − 2 d h ) to 350 mm ( 14 d h ) .
It is note worthy that the y -direction captures only half of the flo w field. Ho we ver ,
the results are mirrored to the other half by considering the flo w field’ s symmetry
that is v alidated by the a v ailable negati ve y data. The fluidic oscillator and the w all
plate are mounted on a one-axis tra versing system that allo ws the complete set-up
to be mov ed in the z -direction. This enables the measurement of v arious planes
sequentially without requiring a ne w PIV calibration. The z -locations of the planes
are chosen in accordance to velocity gradients. The smallest distance between two
planes is 3 mm close to the centre plane and the lar gest distance is 28 mm when
farthest a way from the centre plane. The z -direction e xtends from z = − 15 ( − 0 . 6 d h )
to 138 mm ( 5 . 5 d h ) and consists of 22 planes. The z -direction e xtends to negati ve z
v alues to confirm symmetry in this direction. The pulse distance between the laser
pulses is adjusted for each plane and supply rate indi vidually to obtain an optimum in
resolv able velocities. It v aries from 20 to 400 µ s. A series of 6000 double images at
a sampling rate of 5 Hz is acquired for each indi vidual plane. This sampling rate is
smaller than the oscillation frequenc y . Therefore, phase av eraging is employed during
post-processing, which is discussed in more detail in § 3 . The sampling frequency
does not lock with the flo w field because the oscillation frequenc y fluctuates naturally
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220 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
y z
z
¥ r
x

F IGURE 3 . (Colour online) Coordinate systems used for analysing the flow field.
( a ) Cartesian coordinates, ( b ) cylindrical coordinates.
with a standard de viation of less than 5 % around its mean v alue. The double images
are post-processed by using PIVV iew3C v ersion 3.6 by PIVT ech. The final resolution
of the results with an analysing windo w ov erlap of 50 % is 120 × 146 vectors yielding
a spatial resolution of 2.8 mm (nine v ectors per d h ) in the x and y directions. Since it
is challenging to reliably determine the local uncertainty of stereo PIV measurements
for this highly unsteady flo w field, the mass flo w through a control volume within
the external flo w field is utilized as a global metric for uncertainty estimation of the
PIV measurements. The integrated mass flo w ov er the entire closed control volume
is ideally zero due to conserv ation of mass. In this study , the integrated total inflo w
into the control v olume dif fers less than 5 % from the integrated total outflo w out of
the control v olume figure 10 ov er the entire range of considered distances from the
nozzle (i.e. size of the control v olume). Since the inflo w and outflo w mainly originate
from dif ferent parts of the control v olume, this agreement can only be obtained from
accurate PIV measurements.
The PIV camera trigger signal (i.e. the time stamp for e very PIV v elocity field)
as well as the pressure signals from inside the oscillator are acquired simultaneously
through a cD A Q system by National Instruments at a sampling rate of 16 381 Hz
that is se veral orders of magnitude higher than the jet’ s oscillation frequencies. This
allo ws for the correlation of time stamps between the PIV snapshots and the pressure
signal inside the oscillator , which enables phase av eraging of the data and temporal
alignment of the indi vidual measurement planes (§ 3 ).
In addition to the oscillating jet, measurements are conducted on a steady jet for
comparison. This jet is emitted from a steady jet nozzle that is similar to the fluidic
oscillator b ut the feedback channels and part of the mixing chamber are omitted to
pre vent the spatial oscillation (figure 1 b ). Otherwise, all geometric properties are the
same including the nozzle diameter d h and the length of the di v erging nozzle l n . The
same stereoscopic PIV system is used for these measurements. Ho we ver , only cross-
sections at v arious distances from the nozzle (i.e. planes in y – z direction) are recorded.
3 . Data analysis
The jet properties of traditional steady jets are commonly described in global
Cartesian coordinates (figure 3 a ) or axisymmetric cylindrical coordinates oriented
along the flo w direction of the jet (i.e. only streamwise and radial coordinates). For
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 221
a spatially oscillating jet, neither of these coordinate systems is suitable because
they do not tak e into account the spatial mov ement of the jet. F or that reason, the
jet properties are in vestigated using a c ylindrical coordinate system (figure 3 b ) with
the jet being oriented in the radial direction. The origin of the coordinates is in the
centre of the outlet nozzle. Equations ( 3.1 )–( 3.2 ) transfer velocities and coordinates
from the Cartesian coordinate system to the cylindrical coordinate system. The
cylindrical coordinate system pro vides a more suitable comparison to con ventional
steady jets because r describes the jet’ s distance from the nozzle independently of
the instantaneous jet deflection angle:


x
y
z

 = 

r cos ψ
r sin ψ
z

 , (3.1)


u r
u ψ
u z

 = 

cos ψ sin ψ 0
− sin ψ cos ψ 0
0 0 1

 · 

u x
u y
u z

 . (3.2)
Se veral data processing steps are required to e xtract jet properties from the
sequentially measured two-dimensional v elocity fields. The general procedure is
illustrated in figure 4 . Depending on the quantity of interest, dif ferent steps are taken.
The top ro w describes the procedure to yield the time-resolved, three-dimensional
flo w field. The phase-a veraging process is based on a reference signal e xtracted
from inside the oscillator as described by Ostermann et al. ( 2015 b ). The dif ferential
pressure between the oscillator’ s feedback channels is used as the reference signal. A
Butterworth lo wpass filter with a cutoff frequenc y of twice the oscillation frequenc y
is applied forward and backw ard for additional improv ement in signal quality .
An autocorrelation of the signal with a signal fragment of approximately half an
oscillation period is used for identifying half period starting points. Since the reference
signal and PIV snapshots are acquired simultaneously , the half-period starting points
are mapped to the PIV snapshot time stamps, which enables the ensemble av eraging
of all snapshots within a phase angle windo w of 3 ◦ . Accounting for phase jitter or
weighting of snapshots according to their position inside the windo w is not employed
in fa v our of ha ving a larger amount of snapshots a v ailable, which allo ws for a
smaller phase angle windo w (on a verage 50 snapshots per phase angle windo w).
Ostermann et al. ( 2015 b ) v alidated that the deviation of structures within one phase
angle windo w is less than the signal noise of the PIV data. The phase-av eraged
results are phase aligned to a common period starting point by using the reference
signal. Thereby , all indi vidual planes are combined to one three-dimensional flo w
field which is mirrored in the y -direction with a 180 ◦ phase shift (i.e. the x – z plane
at y = 0) and in the z -direction without a phase shift (i.e. the x – y plane at z = 0). The
symmetry of the flo w field is v alidated by additional measurement planes. In order
to increase the spatial resolution in the z -direction, velocities in between the planes
are interpolated and smoothed by using a re gression procedure provided by Garcia
( 2010 ). This approach is based on discrete cosine transformations for regression and
a generalized cross-v alidation for adjusting the smoothing parameters.
The described phase-a veraging procedure cancels out stochastic noise isolating a
representati ve oscillation period, which is suitable for a qualitati ve in vestig ation of
flo w features. Ho we ver , the phase angle windo w size of 3 ◦ and possible meandering
of the jet makes in v estigating jet properties (e.g. maximum velocity , deflection angle
or jet dimensions) challenging because velocities are lo wered and the jet structures
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222 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
Pressure
data
DCT -PLS
regression
Mass flo w and
jet f orce
Jet
proper ties
3D flo w
field
3D jet
proper ties
e xtraction
Appl y
symmetry
Phase-
a v eraging
Meandering
cor rection
2D jet
proper ties
e xtraction
Mass flo w and
jet f orce
determination
2D 3C
PIV data

F IGURE 4 . Flow chart illustrating the data processing.
may be blurred. Therefore, the jet properties are extracted from the instantaneous data
for each plane indi vidually (figure 4 , second ro w). Meandering in the z -direction can
cause the jet to randomly de viate from its mean flo w direction. Therefore, a process is
applied to account for potential meandering by using the most probable v alue at each
plane for e very phase angle windo w instead of the mean value. The most probable
v alue is determined from a probability density fit based on a normal kernel function.
The determination of the phase angles for the instantaneous snapshots is similar to
the pre viously described phase-a veraging method of the three-dimensional flo w field.
The flo w field symmetry in z -direction is accounted for by mirroring the jet properties
at z = 0. The symmetry in y -direction requires a localization of the jet by identifying
the maximum velocity between one phase angle and its 180 ◦ counterpart for e very
r . The corresponding v alues at the point of maximum velocity are then mirrored at
y = 0 and if necessary phase shifted by 180 ◦ . This procedure yields the jet properties
as a function of the phase angle φ , the distance to the nozzle r and the PIV plane
z . In a last step, the three-dimensional properties are e xtracted by determining the
global v alues of all planes. Additional information is provided when discussing the
jet properties in § 4.2 .
The global quantities such as mass flo w and jet forces are determined in the same
manner except for the meandering correction and the application of the symmetry
(figure 4 , third ro w). The meandering correction is not performed because the
global quantity is independent of the position of the jet. The flo w field symmetry is
accounted for by adding the quantity of each phase angle with its 180 ◦ counterpart
(i.e. the y -symmetry) and doubling it (i.e. the z -symmetry). Additional details on the
determination of mass flo w and jet forces are discussed in § 4.3 .
4. Results
In the subsequent sections, the flo w field and jet properties of a spatially oscillating
jet issued into a quiescent en vironment are discussed. First, the three-dimensional,
phase-a veraged flo w field is examined qualitati vely in order to identify dominant flo w
structures. This global o vervie w educates the subsequent quantitati v e e valuation of jet
properties follo wed by the assessment of entrainment and jet forces. The objecti ve of
the presented material is to provide a foundational understanding of the flo w field and
properties of a spatially oscillating jet. It is noted that the parameter space in volv ed
with spatially oscillating jets is extensi ve and can certainly not be fully e xplored in
the current study .
It is anticipated that the flo w field of periodic jets is af fected by the oscillation
frequency and jet v elocity independently . Ho we ver , for the employed fluidic oscillator
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 223
0
10
f OSC (Hz)
20
0 20 000 40 000 60 000
10 20
U bulk ( m s -1 )
Re
30 40

F IGURE 5 . (Colour online) The oscillation frequency as a function of the supply rate. The
considered cases for the PIV measurements are marked by squares.
design, the jet velocity and oscillat ion frequency are coupled. Figure 5 sho ws the
oscillation frequency as a function of the supply rate. It is e vident that the oscillation
frequency is linearly dependent on the supply rate, which w as observed by se veral
other studies on similar fluidic oscillator designs operating in the incompressible
regime. The ef fect of the frequency is connected to the jet Strouhal number (e.g.
Choutapalli, Krothapalli & Arakeri 2009 ). The jet Strouhal number St is dependent
on the jet e xit velocity U b ulk , the oscillation frequency f osc and a characteristic length
scale d h ( 4.1 ). The length scale d h may be dependent on the particular oscillator
type or design that is utilized. Here, it is used as a representati ve scale for the
size of the oscillator . Considering the linear slope and the ne gligible of fset of the
oscillation frequency o v er the supply rate leav es a constant Strouhal number o ver
all supply rates. Therefore, it is not possible to change the Strouhal number in this
study . In fact, Schmidt et al. ( 2017 ) sho w that for this particular oscillator design the
Strouhal number is independent of oscillator size and working fluid as long as no
compressibility ef fects are present. That means changing the Strouhal number would
require changing the design (e.g. internal geometry) or including compressibility
ef fects, which is beyond the scope of this study .
St = f osc · d h
U bulk
= 0 . 015 . (4.1)
The jet Reynolds number is af fected by the supply rate. The Reynolds numbers
based on the hydraulic diameter of the e xit and the bulk v elocity are well within
the turb ulent regime of a pipe flo w (figure 5 ). Therefore, no sudden changes in the
internal boundary layer or internal dynamic are expected (W oszidlo et al. 2015 ).
The limited range of in vestigated Re ynolds number in combination with the constant
Strouhal number re veals that the normalized results of this study e xhibit the same
beha viour independent of the supply rate, which is confirmed by three dif ferent
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224 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
supply rates. For that reason, all results sho wn in the follo wing are extracted from
only one supply rate of U bulk = 19 m s − 1 , if not denoted otherwise. The corresponding
Reynolds number based on the h ydraulic exit diameter d h is 30 000.
4.1. General flow field
It is anticipated that the flo w field of a spatially oscillating jet includes the periodic
spatial oscillation as well as stochastic turb ulence. The phase-av eraging process
eliminates the stochastic turb ulence and potential small-scale flow features, which
enables a fundamental visualization and discussion of dominant flo w structures.
Figure 6 illustrates the three-dimensional flo w field for se veral phase angles φ o v er
half an oscillation period providing ini tial qualitativ e insight into the flo w field
characteristics. Figure 6 (left) depicts the backward finite time L yapunov e xponent
(FTLE). This Lagrangian analysis tool traces virtual particles through the flo w field in
time. It quantifies the attraction rate of streaklines meeting in almost one point. The
result is an intuiti ve representation of the flo w field due to its similarity to smoke or
ink visualizations. It enhances coherent structures such as v ortices and shear layers
in the flo w field. More information on the FTLE are provided by Haller ( 2001 ).
The supplementary material includes an animation of the FTLE (Movie_1, a v ailable
at https://doi.or g/10.1017/jfm.2018.739 ). Figure 6 (right) shows Eulerian quantities.
An isosurface of the v elocity magnitude delineates the time-dependent position of the
jet. An x – y slice through the v orticity component in the z -direction ω z is added at
z = 0, which highlights shear layers and the position of v ortices.
As anticipated, the most prominent flo w feature is the jet moving from side to side
spreading fluid ov er a lar ge area (figure 6 , A). The opening angle of the cov ered
area is ≈ 100 ◦ , which corresponds to the opening angle of the di ver ging part of
the nozzle. Ostermann et al. ( 2015 a ) suggest that the jet attaches to the walls of
the di ver ging part of the nozzle for the in vestig ated supply rates. Hence, the jet’ s
oscillation angle is independent of the supply rate in the current study . Note, that the
jet may not attach to the outlet walls for other supply rates or lar ger div er gent angles
of the nozzles. Furthermore, the jet’ s sweeping angle and pattern are dependent on
the oscillator design. Ho we ver , the influence of these parameters is be yond the scope
of this study .
When the jet switches to the sides, it trails a wak e of accelerated fluid. This
causes the shear layer on the trailing side to be stretched and the shear layer on the
leading side to be squeezed. Hence, the v orticity distribution is asymmetric around
the instantaneous position of the jet. The velocity gradients on the leading side are
expected to e xceed the gradients at the trailing side. This ef fect is also visible in
the FTLE of the deflected jet because it considers the temporal e v olution of the flo w
field. That is why the FTLE on the trailing side is smaller than that on the leading
side of the deflected jet (figure 6 , B). It is note worthy that the total time required
for the jet to switch from one side to the other decreases with the supply rate
due to the increasing oscillation frequency . Ho we ver , the phase-a veraged switching
speed 1ψ /1φ is independent of the supply rate, because the oscillation frequency is
linearly dependent on the supply rate.
When the jet is fully deflected, a circular head v ortex is created, which is clearly
visible in the FTLE and the local maximum in v orticity (figure 6 , C). For additional
confirmation and illustration, a v ortex tube follo wing the v orticity vectors starting
from the maximum of the Q -criterion (Jeong & Hussain 1995 ) in the x – y plane is
added in figure 6 (right). The two-dimensional footprint of this v ortex w as pre viously
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 225
C
-0.5 0
ø z · d h /U bulk
0.5
B
A
D
ƒ = 0 °
ƒ = 45 °
ƒ = 90 °
ƒ = 135 °

F IGURE 6 . (Colour online) The three-dimensional flo w field. Left: the backward finite
time L yapuno v exponent. Right: the normal v orticity ω z at z = 0, an isosurface of 0 . 35 U b ulk
and a tube indicating the dominant v ortex core. The annotations are referred to throughout
the text. Note that the top half of the boundary w all is omitted to provide an unobstructed
vie w .
observed by W oszidlo et al. ( 2015 ) and Sieber et al. ( 2016 ). Its creation mechanism
is suspected to be similar to that of the starting v ortex kno wn from transient straight
jets. Ho we ver , in this flo w field the v ortex is not only present when the jet is
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226 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
0 60 120 180 240
ƒ ( deg. )ƒ ( deg. )
300 360 0 60 120 180 240 300 360
4
8
12
(a) (b)
r/d h
¥ (deg.)
16
V or te x 1 V or te x 2
−90
−60
−30
0
30
60
90

F IGURE 7 . (Colour online) The position of the circular head vorte x centre at z = 0. The
solid lines are linear regression lines. ( a ) The distance to the nozzle. ( b ) The angular
position. V orte x 1 and v ortex 2 are the v ortices at either side of the flo w field.
initiated b ut repeats on either side despite the steady supply pressure. It is con vected
do wnstream where it causes local recirculation zones while the main jet mov es back
to the other side. Figure 7 sho ws the position of the two head v ortices as a function
of the oscillation phase angle. The v ortices are traced by observing the positions
of the v ortex le g footprints at z = 0. It is e vident that the angular positions ψ of
the v ortices remain constant. The angular position coincides with the maximum jet
deflection angle, which supports that the v ortices are created when the jet is fully
deflected. The v ortices are con vected do wnstream along a straight path aw ay from
the nozzle. The slope of d r / d φ is the con vection v elocity . Initially , the con vection
velocity is constant. F arther do wnstream, it decreases. The constant con vection v elocity
aligns with the jet being at its maximum deflection angle. Once the jet switches to
the opposite side, the con vection v elocity decreases. Considering the time for one
oscillation cycle, the initial con v ection velocity is approximately 0 . 3 U b ulk . This is
slo w compared to the head v ortices of pulsed jets. Choutapalli et al. ( 2009 ) identify
a con vection v elocity of 0 . 6 U max for the head v ortices of pulsed jets. Note that they
use the time-a veraged maximum v elocity that is smaller than the actual maximum
velocity of the jet. If this is taken into account, a con vection v elocity of 40 % of the
maximum velocity U max is obtained, which is considerably higher than the con v ection
velocity of the observed head v orte x of a spatially oscillating jet. It is note worthy ,
that due to the limited time the jet resides in its fully deflected state, the head v ortex
observed in the phase-a veraged flo w field is not followed by subsequent v ortices.
This may e xplain the smaller con v ecti ve speed.
4.2. J et pr operties
This section focuses on the local properties of the spatially oscillating jet which
include the jet’ s deflection angle, the maximum velocity magnitude and the jet
depth. The jet properties are calculated from instantaneous snapshots, corrected for
meandering, and phase a veraged thereafter § 3 . The maximum velocity magnitude
U max ( r , φ ) is defined as the maximum velocity magnitude of all measured planes for
each position r and for each phase angle φ . The local deflection angle θ jet ( r , φ ) is the
direction of the maximum velocity v ector for each recorded plane. The jet’ s depth
is represented by the extent in z -direction for the distance where the local maximum
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 227
0
0.5
1.0
1.5
2.0
−50
−25
0
25
U max
U max
50
60 120 180
ƒ (deg.)
U max /U bulk
œ jet (deg.)
œ jet
240 300 360

F IGURE 8 . (Colour online) The oscillating local maximum velocity U max and deflection
angle θ jet at r / d h = 2. The dashed lines indicate properties determined from the mirrored
dataset. Note that only e very tenth data point is mark ed.
velocity of each plane U max , z ( r , z , φ ) ⩾ 0 . 5 U max ( r , φ ) , which is a common threshold
for the discussion of the jet width (e.g. Schlichting & Gersten 2006 ). The same
definitions apply to the according steady jet that is added for comparison. Note that
the instantaneous jet width may also be e xtracted from each plane. Howe ver , due to
its sweeping motion, the jet forms a thin shear layer in the direction of motion while
trailing accelerated fluid behind it. This ef fect dilutes the meaning of the jet’ s width,
especially at lar ger distances from the nozzle. Therefore, the jet width does not of fer
any ph ysically conclusi ve quantity and is omitted here.
Spatially oscillating jets are characterized by their oscillation pattern and maximum
deflection angle. Figure 8 depicts the deflection angle θ jet and the maximum velocity
U max at r / d h = 2 as a function of the phase angle φ . Note that the properties in the
dashed line sections are extracted from the mirrored dataset. The temporal beha viour
of jet deflection angle and maximum velocity characterizes the oscillation pattern
that is dependent on this specific oscillator design. It is e vident in figure 8 that the
maximum deflection angle is approximately 45 ◦ which emphasizes the significantly
lar ger volume being af fected by the oscillating jet compared to a steady jet as shown
by W oszidlo et al. ( 2015 ). Note that the maximum deflection angle does not coincide
with the opening angle of the af fected v olume noted in § 4.1 (i.e. ≈ 100 ◦ ). That is
because the jet deflection angle is located at the point of maximum velocity and does
not take into account the outer shear layer and widening of the jet that yields a further
increase in af fected v olume. The oscillation pattern is characterized by long dwelling
times of the jet at its maximum deflection and short switching times. Furthermore,
figure 8 re veals that the maximum jet v elocity v aries by approximately ± 15 % of the
mean v alue. The time-resolved maximum jet v elocity reaches its lar gest v alues shortly
before the jet arri ves at its maximum deflection. That is also observed in figure 6 (D)
where a small portion of fluid is ahead of the neighbouring particles before the jet is
fully deflected. The maximum jet velocity reaches its minimum when the jet starts to
sweep to the opposite side. Note that the maximum jet v elocity is always lar ger than
the reference b ulk velocity , which is due to internal boundary layer and mixing layer
ef fects reducing the ef fecti ve size of the e xit area. W oszidlo et al. ( 2015 ) rev ealed that
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228 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
the dynamics inside a fluidic oscillator not only causes the jet to spatially oscillate
b ut also to temporally oscillate due to changes in the effecti ve outlet area for the
deflected jet and oscillating pressure losses. The observ ed oscillation pattern and
temporal oscillation of the jet properties are characteristic of the employed fluidic
oscillator (Ostermann et al. 2015 a ). It is note worth y that the temporal oscillation of
jet properties may af fect the presented results. Ho we ver , the amplitude of the temporal
oscillation is small compared to that caused by the spatial oscillation. Hence, it is
expected that the general trends are transferable to a spatially oscillating jet without
temporally oscillating jet properties. Furthermore, the deflection angle v ariation may
also ha ve an ef fect on the results. Howe ver , the in vestigation of dif ferent oscillation
patterns is beyond the scope of this fundamental study . Presumably , the general
trends for the jet properties sho wn in this study are expected to be applicable to
other oscillation patterns as well.
Figure 9 sho ws the jet properties a veraged o ver one oscillation period as a function
of the distance to the nozzle. Note that the coordinate r ∗ is used for representing the
distance to the nozzle ( 4.2 ). For this coordinate the length of the di ver ging nozzle l n is
subtracted from r because the jet is only fully exposed to the en vironment do wnstream
of r − l n = r ∗ = 0. For r < l n the jet is e nclosed which hinders the interaction with
the surrounding fluid figure 1 . Thus, the subtraction of l n allo ws for an objecti ve
comparison to data from the literature.
r ∗ = r − l n . (4.2)
Figure 9 ( a ) displays the velocity decay . For turb ulent axisymmetric steady jets, the
velocity decay of the centre line v elocity is proportional to 1 / r (Schlichting &
Gersten 2006 ). Hence, the v elocity decay rate may be in vestigated by e v aluating the
ratio between global maximum v elocity and the local centre line velocity (Quinn &
Militzer 1988 ). Ho we ver , defining a centre line v elocity for a spatially oscillating jet
may be misleading because of deflected and time-dependent jet centre lines. Instead,
the ratio between the global maximum velocity U max = max ( U max ( r ∗ )) and the local
maximum velocity U max ( r ∗ ) is used. In comparison, this pro vides an underestimation
of the velocity decay rate when the maximum v elocity is of f centre, which is the
case for square jets in the near field (Quinn 1992 ). This is likely the reason for the
considerable dif ference between the measured steady jet and the square jet from Quinn
& Militzer ( 1988 ) who used the con ventional definition of the centre line v elocity
(figure 9 a ). Compared to common steady jets, it is e vident that the maximum velocity
of the oscillating jet decays much faster in the near field without the presence of a
sustained potential core. Similar to steady jets, the v elocity decay rate of the sweeping
jet approaches a constant v alue do wnstream of r ∗ / d h > 6. Equation ( 4.3 ) describes
a linear function for the v elocity decay similar to Quinn & Militzer ( 1988 ) with K
being the velocity decay rate and C the virtual origin of the jet. The slope of the
linear trend K (i.e. the velocity decay rate) is approxima tely K = 0 . 26 for the spatially
oscillating jet. This is higher than the decay rate of steady jets which is K = 0 . 19 for
square jets and K = 0 . 17 for round jets (Quinn & Militzer 1988 ). The comparably
high velocity decay is indicati ve for a higher momentum transfer to the ambient fluid.
It is note worthy that for a comparison of the f ar field beha viour , the coordinate r ∗
should start from the respecti ve virtual origins C (W ygnanski & Fiedler 1969 ). The
virtual origin is not considered here because the data are limited to the near field of
the nozzles. Also, the discussion focuses on the rates at which the jet properties are
changing which are independent of the virtual origin.
U max
U max ( r ∗ ) = K  r ∗
d h
+ C  . (4.3)
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 229
0
1
2
3
4
U max /U max (r)
Jet depth /d h
02 4 6 8 1 0 1 2 1 4
1
2
3
4
5
6
2468 1 0
r * /d h r * /d h
12 14
Oscillating jet Square jet (Quinn & Militzer 1988)
Steady jet Theor . turb. axi. jet (Schlichting & Gers ten 2006)
(a) (b)

F IGURE 9 . (Colour online) Jet properties. ( a ) The maximum velocity as a function of the
distance from the nozzle r ∗ . ( b ) The jet depth as a function of r ∗ .
The oscillating jet depth is spreading significantly faster in the near field than
the depth of common steady jets (figure 9 b ). The shallo w increase in depth of the
measured steady jet close to the nozzle is e xplained by the uncon v entional nozzle
geometry (i.e. a long di ver gent outlet) and by the transition from a square to a
circular jet (Zaman 1996 ). Ho we ver , it compares well to similar data of a square jet
that were in vestigated by Quinn & Militzer ( 1988 ). F ollo wing the transition to an
axisymmetric jet (i.e. r ∗ / d h > 6), the measured steady jet approaches the theoretical
spreading rate for turb ulent axisymmetric jets (Schlichting & Gersten 2006 ). The rates
of oscillating and steady jet are particularly dif ferent in the near field, whereas these
dif ferences diminish in the far field. The lar ger jet depth suggests that the oscillating
jet has a high entrainment from the direction normal to the oscillation plane, which
is part of the discussion in the subsequent section.
4.3. Entrainment
The entrainment of a jet is an indication of its mixing potential. Entrainment is
caused by the acceleration of surrounding fluid due to the momentum of the jet. In
this study , the entrainment rate is defined from normalized quantities ( 4.4 ). Note that
the denominator defines the distance from the nozzle in an unobstructed en vironment.
Therefore, the distance r from the origin at the nozzle throat is of fset by l n that is
the enclosed length of the di ver gent section of the nozzle. This shift allo ws for a
more objecti ve comparison to traditional steady jets.
e = ∂ ( ˙ m / ˙ m supply )
∂ ( r ∗ / d h ) . (4.4)
The determination of the mass flo w as a function of distance is required for
quantifying the entrainment. Equation ( 4.5 ) defines the general continuity equation
for mass flo w in a control v olume enclosed by the surfaces S :
˙ m total = I S
ρ ( u · n ) d S = 0 . (4.5)
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230 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
Accordingly , the mass flo w is determined by integrating the flo w through control
surfaces. Con v entionally , the mass flo w of a jet is obtained by integrating in
Cartesian coordinates ov er a quasi-infinite cross-section placed normal to the flo w
direction ( 4.6 ):
˙ m y , z ( x , φ ) = ρ 0 Z z Z y
u x d y d z . (4.6)
Ho we ver , this approach is not suitable for analysing a spatially oscillating jet because
it does not account for the changes in the jet’ s tra vel length for dif ferent jet
deflections. Therefore, a c ylindrical volume (figure 3 b ) enclosed by four surf aces
is employed. The mass flo ws through all surfaces are determined indi vidually because
this allo ws us to distinguish between the sources of entrainment from dif ferent
directions (equations ( 4.7 )–( 4.10 )):
˙ m side ( r , φ ) = ρ 0 Z z max
− z max Z arccos ( l n / 2 )
− arccos ( l n / 2 )
u r r d ψ d z , (4.7)
˙ m base , 1 , 2 ( r , φ ) = ± ρ 0 Z r
l n Z arccos ( l n / 2 )
− arccos ( l n / 2 )
u z ( z = ± z max ) r d ψ d r , (4.8)
˙ m wall ( r , φ ) = − ρ 0 Z z max
− z max Z r
− r
u x  ψ = arccos l n
r  d r d z , (4.9)
˙ m total ( r , φ ) = ˙ m side + ˙ m base , 1 + ˙ m base , 2 + ˙ m wall = 0 . (4.10)
Note that ˙ m wall / ˙ m supply should be 1 due to the wall pre venting an y entrainment from
upstream of the jet’ s exit. Ho we ver , due to measurement constraints, reliable flo w field
data are only a v ailable slightly downstream of the w all at r ∗ = 0 . 5 d h . Therefore, the
corresponding plane is included in the interrogation ( 4.9 ). Moreo ver , the results are
not sho wn for r ∗ / d h < 2 because the control v olume would be too small to cov er the
complete jet throughout its oscillation.
It is possible to e v aluate in- and outflo w through the control surface by inte grating
positi ve and ne gati v e v alues of ( u · n ) in ( 4.5 ) separately . The in- and outflo w are
ov erestimated because v ortices such as the circular head vorte x (figure 6 , C) passing
through the surface as well as local turb ulence add to the in- and outflo w indi vidually
b ut cancel when added together . Despite these limitations, the dif ferentiation between
in- and outflo w allo ws us to identify flo w that would cancel out during the inte gration.
That is of particular interest because the c ylinder side includes the main outflow as
well as entrainment manifesting in inflo w from the sides.
Figure 10 sho ws the time-a veraged in-, out- and combined flo w for all surfaces
enclosing the cylindrical control v olume. Almost the complete outflow mo ves through
the cylinder side, which is e xpected because this is the main flo w direction. Some
additional outflo w through the wall surf ace is also noticeable. As mentioned, this is
likely an o verestimation caused by the circular head v ortex and turb ulence. The same
ov erestimation is e vident for the inflo w through the wall surf ace that is expected
to be constant at one (i.e. the supply mass flo w). These ef fects cancel out for the
combined flo w that remains constant at slightly lar ger le vels than the supply rate due
to the plane’ s distance from the nozzle. The outflo w through the c ylinder base is
negligible, which confirms that the extent of measured velocity planes in z -direction
is suf ficient to cov er the complete flo w field. The inflo w through the cylinder side
is indicati ve for entrainment from the sides that is e xpected to originate mostly
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 231
0 2468 1 0 1 2 1 4
2
4
6
8
10
12
|m
. |/m
.
supply
|m
. |/m
.
supply
02468 1 0 1 2 1 4
−8
−6
−4
−2
0
2
4
6
8 All surfaces
Cy linder side
Cy linder base
W all
Rang e of oscillating values
Inflo w
Outflo w
Combined flo w
02468 1 0 1 2 1 4
r * /d h
r * /d h r * /d h

F IGURE 1 0 . (Colour online) Breakdown of the mass flo w through the individual
cylinder surf aces.
from the areas of lar ge polar angles | ψ | close to the wall surface. Furthermore,
the in- and outflo w through the cylinder side is also b urdened by recirculation of
local v ortices and turbulence. Although these ef fects cancel out in the combined
flo w , any potential entrainment through this surf ace is also subtracted from the
outflo w , which leads to an underestimation of the total entrainment. For r ∗ / d h > 5,
the inflo w through the cylinder bases pro vides the lar gest source of inflo w . This
result infers that the most entrainment for a spatially oscillating jet originates from
the direction normal to the oscillation plane, which is consistent with the results for
jet depth (figure 9 b ). Hence, an increase in the nozzle’ s aspect ratio to yield a more
two-dimensional spatially oscillating jet w ould reduce this source of entrainment
relati ve to the o v erall entrainment. It is suspected that this is one reason for the
controv ersies re garding entrainment of spatially oscillating jets in earlier studies
(Platzer et al. 1978 ; Srini v as et al. 1988 ; Raman et al. 1993 ; Mi et al. 2001 ). These
studies used quasi-two-dimensional spatially oscillating jets at high aspect ratios (i.e.
aspect ratio > 7). The aspect ratio of the jet in this study is one, which renders a
direct comparison to the earlier results on spatially oscillating jets meaningless.
It is note worthy that the sum of the combined in- and outflo w through all surfaces
is approximately zero o ver a wide range of distances from the nozzle. Therefore, the
flo w field fulfils the continuity equation ( 4.5 ) which provides additional confidence
in the data quality . The shaded areas surrounding each line in figure 10 indicate the
range of oscillating v alues throughout one oscillation cycle. This range is comparably
lar ge for in- and outflow . The mass flo w is analysed for each individual snapshot and
phase a veraged thereafter figure 4 . These snapshots ha v e a considerable amount of
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232 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
0
2
4
6
8
10
12
14
e = 0.9
e = 1.0
2468
(x-l n ) d h, r * /d h
10 12
Car tesian cross-section
(in- and outflo w)
Car tesian cross-section
(outflo w onl y)
Rang e of possible values
Steady sq uare jet
Pulsed jet at St = 0.11
(Choutapalli, 2009)
Cy linder side
(in- and outflo w)
Sum of all cy linder sur faces
(outflo w onl y)
14
e = 0.9
e = 0.8
e = 0.2
e = 0.2
|m
. |/m
.
supply

F IGURE 1 1 . (Colour online) Entrainment range for the spatially oscillating jet.
stochastic turb ulence that induce such large fluctuation for the in- and outflo w . The
range of v alues for the combined flo w are more representati ve because turb ulence is
cancelled out during the integration. The combined mass flo w is mostly independent
of the phase angle and thus of the instantaneous position of the jet. Therefore, it may
be concluded that the significant oscillations in jet v elocity throughout one oscillation
period figure 8 are balanced by changes in jet width to yield quasi-steady mass flo w
characteristics.
Figure 10 delineates the mass flo w through all surfaces indi vidually . It is challenging
to extra ct the correct entrainment of the jet from these data. The sum of outflo w
through all surfaces certainly o verestimates the entrainment because it includes ef fects
such as recirculation from v ortices and turbulence that do not contrib ute to the overall
entrainment. In contrast, the combined flo w through the cylinder side underestimates
the total entrainment because local entrainment from areas close to the wall surfa ce is
subtracted throughout the integration ( 4.7 ). Therefore, the a vailable data and applied
methods only allo w the conclusion that the actual entrainment is in between these
two limits. The resulting range is illustrated in figure 11 . The annotated entrainment
e is based on the linear trend of the data points farthest a way from the nozzle. Note
that the present data only capture the near field entrainment. It is concei v able that
the entrainment rates e may change at greater distances from the nozzle. In order to
allo w a comparison to other studies, the mass flo ws for Cartesian cross-sections ( 4.6 )
are added as well. Note that the data of the Cartesian cross-sections are limited to
( x − l h )/ d h < 5 because parts of the jet do not go through the domain-limited cross-
section farther do wnstream. As expected, the entrainment obtained by inte gration ov er
Cartesian cross-sections e xceeds the results obtained in cylindrical coordinates due
to the jet’ s underestimated trav el distance from the nozzle when the jet is deflected.
Although omitted here, it may be possible to correct these data by introducing an
ef fecti ve distance from the nozzle based on an a verage deflection angle.
The comparison between the entrainment of the spatially oscillating jet and the
steady jet in figure 11 re veals that the entrainment rate e of the spatially oscillating
jet is increased by at least a factor of four compared to the entrainment rate of
a steady jet in the near field. This enhancement is e xpected to be a result of the
spatial oscillation that increases the contact area between jet and surrounding fluid
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 233
0
2
4
10 20 30
r * /d h = 2
r * /d h = 4
r * /d h = 6
40
U bulk ( m s -1 )
|m
. |/m
.
supply

F IGURE 1 2 . (Colour online) The combined mass flo w through the cylinder side as a
function of the supply rate.
in z -direction. It is note worthy that generally the entrainment rate of square jets is
slightly higher (i.e. e ≈ 0 . 3) than that measured in this study (Grinstein, Gutmark
& Parr 1995 ). This discrepanc y is a result of the uncon ventional nozzle geometry
(figure 1 b ). Ho we ver , the influence of the nozzle geometry and upstream ef fects are
negligible compared to the entrainment enhancement by unsteady jets (Bremhorst
1979 ). The entrainment rate of the spatially oscillating jet is also higher than that
of a pulsed jet at a Strouhal number of 0.11 that was assessed by Choutapalli
et al. ( 2009 ). Choutapalli et al. ( 2009 ) suspect that the creation of the head vorte x
causes the high initial entrainment rate of pulsed jets. This entrainment rate is of
the same order as the entrainment rate of the spatially oscillating jet. Ho we ver , with
increasing distance to the nozzle, the entrainment rate of the pulsed jet decreases to
the entrainment rate of a steady jet. In contrast, the entrainment rate of the spatially
oscillating jet remains constant throughout the range of examined distances. This
suggests that the high entrainment rate of the spatially oscillating jet is caused by the
increased entrainment from the direction normal to the oscillation plane instead of its
head v ortices. It is note worthy that the entrainment rate of a spatially oscillating jet
may decrease in the far field. Ho wev er , the initially high entrainment rate most likely
causes the spatially oscillating jet also to carry more mass flo w than the comparable
jets in the far field.
Figure 12 depicts the entrainment of the spatially oscillating jet at discrete positions
for v arious supply rates. It is e vident that the entrainment is not af fected by the supply
rate. Therefore, the jet Re ynolds number has no obvious ef fect on the entrainment
rate within the in vestigated Re ynolds numbers. Recalling that the oscillation frequency
increases with the supply rate, it is e vident that the oscillation frequency also does not
change the entrainment rate within the range of captured oscillation frequencies. This
is expected because the Strouhal number does not change with the supply rate. Hence,
it supports the statement at the beginning of § 4 that the linear coupling between
oscillation frequency and jet v elocity does not allo w for changing the Strouhal number
or the dynamic beha viour of the flo w field for the employed fluidic oscillator . Other
oscillator designs may therefore experience other results. Note that dif fering results
may also be e xpected in the sonic regime because the oscillation frequenc y stagnates
once the jet v elocity approaches sonic speed (V on Gosen et al. 2015 ).
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234 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
4.4. J et for ces
The oscillating jet acts with a certain force on the surrounding fluid. The magnitude
of the jet force acting on the fluid is of interest for se v eral applications such as flo w
control (i.e. determining the momentum coef ficient). It is challenging to measure the
jet force due to the spatial motion of the jet. Most studies that are employing the
momentum coef ficient use a force F bulk that is based on the assumption of ambient
conditions at the jet exit and the jet b ulk velocity U bulk in the e xit throat A outlet ( 4.11 ):
F bulk = ρ 0 A outlet U 2
bulk . (4.11)
Ho we ver , figure 9 ( a ) sho ws that the maximum velocity magnitude e xceeds the
b ulk outlet velocity . Therefore, the actual force is likely underestimated. Thrust
measurements with a one-component balance also underestimate the actual force
because this neglects the lateral component. This may be resolv ed by employing a
multi-component balance. Ho we ver , a suf ficiently lo w response time is required for
resolving the time-dependent lateral force component at high oscillation frequencies.
Here, the jet force F is determined from the instantaneous v elocity fields § 3 and
phase a veraged thereafter . The infinitesimal force d F acting on the fluid in normal
direction to the control surface is dependent on the local v elocity u ( 4.12 ):
d F = ρ u ( u · n ) d A . (4.12)
Spatially integrating the infinitesimal forces cancels out opposing forces. Ho we ver ,
they also need to be considered for the jet force magnitude. Therefore, the
infinitesimal force magnitude | d F | is considered, which is a function of the local
velocity magnitude acting in surface normal direction ( 4.13 )–( 4.14 ):
| d F | = | ρ u ( u · n ) | , (4.13)
= ρ U ( u · n ). (4.14)
The force magnitudes acting on the fluid are inte grated along the cylinder surf aces to
yield a total force magnitude F ( 4.15 )–( 4.17 ):
F side ( r , φ ) = ρ 0 Z z max
− z max Z arccos ( l n / 2 )
− arccos ( l n / 2 )
Uu r r d ψ d z , (4.15)
F base , 1 , 2 ( r , φ ) = ± ρ 0 Z r
l n Z arccos ( l n / 2 )
− arccos ( l n / 2 )
Uu z ( z = ± z max ) r d ψ d r , (4.16)
F wall ( r , φ ) = − ρ 0 Z z max
− z max Z r
− r
Uu x  ψ = arccos l n
r  d r d z . (4.17)
Analogous to the mass flo w determination, it is possible to distinguish between force
resulting from in- and outflo w by integrating only positi ve or ne gati ve v alues of ( u · n ) .
Note that the forces of in- and outflo w are ov erestimated due to v ortices and local
turb ulence that would cancel out in the combined flo w . Figure 13 sho ws the jet force
acting on the fluid along the cylinder surf aces. The forces are normalized by the
b ulk force ( 4.11 ). The outflo w through the cylinder side results in the dominant force,
which supports the selection of a c ylindrical control volume. It is constant for all
distances to the nozzle. The force resulting from the inflo w through the wall surf ace
(i.e. the supply mass flo w) is the corresponding opposite force. The inflo w through the
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 235
02 4 6 8 1 0 1 2 1 4
0.5
1.0
1.5
2.0
0 2 4 6 8 10 12 14
−2
−1
0
1
2 All surfaces
Cy linder side
Cy linder base
W all
Rang e of oscillating values
Inflo w
Outflo w
Combined flo w
0 2 4 6 8 10 12 14
|F|/F bulk
|F|/F bulk
r * /d h
r * /d h

F IGURE 1 3 . (Colour online) Force magnitude acting on the fluid inte grated along the
cylinder surf aces.
cylinder base (i.e. the entrainment) results in an additional force acting on the fluid.
The sum of time-a veraged forces from all surf aces is approximately zero, which is
consistent with the e xpected conservation of momentum and adds further confidence in
the data quality . The slight decrease in total force from all surfaces may be attrib uted
to a streamwise pressure gradient that is not assessed in this study .
Similar to the entrainment, it is not possible to determine the e xact force emitted by
the spatially oscillating jet. The forces obtained separately by in- and outflo w through
the cylinder side are ov erestimated due to turb ulence and local vortices. When
considering the combined flo w , the force created by the inflo w due to entrainment
from that direction is subtracted from the total force, which yields an underestimated
result. Hence, the range of possible v alues is bound by the force resulting from the
total outflo w through all surfaces and by the force resulting from the combined flo w
through the cylinder side. The resulting jet force is between 1.20 and 1.32 times
the idealized force F bulk . Thus, a momentum coef ficient determined from F bulk for a
spatially oscillating jet is underestimated. Similar to the entrainment, the normalized
jet force is independent of the supply rate.
The force acting on the fluid o ver the control surf ace oscillates throughout one
oscillation period. The shaded area in figure 13 illustrates the range of oscillating
v alues. It is e vident that at r ∗ / d h = 5, the force acting on the cylinder side surf ace
oscillates most. This is caused by changing con vection speeds that are a result of
the oscillating jet v elocity figure 8 . As the jet mov es from side to side, its exit
velocity decreases and then increases again later within the oscillation period. The
flo w emitted at the later instance ov ertakes the pre viously emitted flo w due to the
higher jet velocity . This behaviour results in a temporary increase in force o ver the
control surface follo wed by the opposite effect of a temporary force deficiency .
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236 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
5. Conc lusion
A spatially oscillating jet with an outlet throat aspect ratio of one is emitted from
a fluidic oscillator into a quiescent en vironment. The three-dimensional flo w field
is measured plane-by-plane employing a stereoscopic PIV system. Simultaneously
acquired time-resolved pressure signals from inside the nozzle enable to phase-a v erage
velocities and jet properties to be e v aluated. The phase-av eraged flo w field visualizes
the jet’ s spatial oscillation and emphasizes the spread of fluid ov er a large area.
Dominant flo w features include alternating circular head v ortices that are created
repetiti vely when the jet is fully deflected. The y are similar to the starting v ortex
kno wn from time-dependent straight jets. Hence, the jet injects increased vorticity into
the surrounding flo w field. This may be adv antageous for flo w control applications
that rely on mixing enhancement.
Quantitati ve jet properties are determined using a c ylindrical coordinate system.
The cylindrical coordinate system allo ws for an assessment of jet properties at
constant distances from the nozzle throat throughout one oscillation cycle. The jet’ s
properties are temporally oscillating, which is caused by the internal geometry of
the employed fluidic oscillators. It is anticipated that the general trends are not
af fected by the temporal oscillation because the amplitudes caused by the spatial
oscillating are significantly higher . Ne vertheless, future studies may pre vent the
temporal oscillation entirely for example, by using a mechanically turning steady jet
nozzle with constant output. Furthermore, this approach would allo w us to examine
the influence of jet angle v ariation on the fundamental observ ations made in this
study . For the in v estigated spatially oscillating jet, the jet’ s maximum v elocity decay
rate is considerably higher than that of a comparable steady jet accompanied by
a significant increase in jet depth. Both observ ations are indicati ve of a higher
momentum transfer to the quiescent en vironment and thus for a higher entrainment.
Conceptual constraints only allo w us to provide a range of possible entrainment
v alues for the spatially oscillating jet. Even within this range, the entrainment rate of
the spatially oscillating jet e xceeds the entrainment rate of a steady jet by at least a
factor of four . Most of the additional mass flo w is entrained from the direction normal
to the oscillation plane because of the enlar ged contact area between accelerated fluid
and quiescent en vironment. The benefit of this three-dimensional effect is e xpected to
be limited to small outlet aspect ratios. F or higher outlet aspect ratios, the contribution
of entrainment from the normal direction would decrease resulting in a decreased
ov erall entrainment. This ef fect is one reason for pre vious controv ersies re garding the
entrainment of spatially oscillating jets. In contrast, the oscillation frequenc y does
not ha ve an y obvious ef fects on the entrainment within the in v estigated range of
supply rates. This result supports the assumption that the Strouhal number accounts
for changes in the dynamic beha viour of the flo w field. Due to the coupling between
oscillation frequency and supply rate for the emplo yed fluidic oscillator , the Strouhal
number is constant for all supply rates and oscillation frequencies in this study . It is
left for future studies to analyse the ef fect of the Strouhal number .
The jet force of the spatially oscillating jet is sho wn to exceed the force of
an idealized steady jet with the same mass flo w by up to 30 %. This result may
be of particular interest for the momentum coef ficient that is generally used for
comparing dif ferent flo w control actuators. For flo w control studies, the momentum
coef ficient is often based on the idealized steady jet approximation. Measuring the
correct jet force is challenging because the lateral component of the instantaneous
jet force cancels out during one oscillation period. Ho we ver , it may be possible to
correct for the underestimation by considering the jet deflection angle and oscillation
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Pr opertie s of a s weepin g je t emitt ed fr om a fluidic oscilla tor 237
pattern. It should be noted that for many flo w control applications, these spatially
oscillating jets are commonly operated in the compressible flo w regime, which will
make the correct assessment of total jet force e ven more challenging. Here, numerical
approaches may provide a useful tool to confirm the presented results and extend the
scope of this work.
Supplementar y movie
A supplementary movie is a vailable at https://doi.or g/10.1017/jfm.2018.739 .
REFERENCES
B OBUSCH , B . C . , W OSZIDLO , R . , B E R G A D A , J . M . , N A Y E R I , C . N . N . & P ASCHEREIT , C . O .
2013 Experimental study of the internal flo w structures inside a fluidic oscillator . Exp. Fluids
54 (6), 1559.
B REMHORST , K . 1979 Unsteady subsonic turb ulent jets. In Recent Developments in Theor etical and
Experimental Fluid Mechanics , pp. 480–500. Springer .
B REMHORST , K . & H OLLIS , P . G . 1990 V elocity field of an axisymmetric pulsed, subsonic air jet.
AIAA J . 28 (12), 2043–2049.
C HOUT AP ALLI , I . , K RO THAP ALLI , A . & A RAKERI , J . H . 2009 An experimental study of an
axisymmetric turb ulent pulsed air jet. J. Fluid Mec h. 631 , 23–63.
F A R I S , G . N . 1963 Some entrainment properties of a turbulent axi-symmetric jet. T ech. Rep.
Mississippi State Uni versity Department of Aerophysics.
G ARCIA , D . 2010 A fast all-in-one method for automated post-processing of PIV data. Exp. Fluids
50 (5), 1247–1259.
G R E G O RY , J . & T O M A C , M . N . 2013 A revie w of fluidic oscillator de velopment. In 43r d AIAA
Fluid Dynamics Confer ence . AIAA.
G RINSTEIN , F. F . , G UTMARK , E . & P ARR , T . 1995 Near field dynamics of subsonic free square
jets. A computational and experimental study . Phys. Fluids 7 (6), 1483–1497.
H ALLER , G . 2001 Lagrangian structures and the rate of strain in a partition of tw o-dimensional
turb ulence. Phys. Fluids 13 (11), 3365–3385.
J EONG , J . & H USSAIN , F. 1995 On the identification of a v ortex. J . Fluid Mech. 285 , 69–94.
K R O T H A PA L L I , A . , B A GANOFF , D . & K ARA MCHETI , K . 1981 On the mixing of a rectangular jet.
J . Fluid Mech. 107 , 201–220.
L A CARELLE , A . & P ASCHEREIT , C . O . 2012 Increasing the passiv e scalar mixing quality of jets in
crossflo w with fluidics actuators. J. Engng Gas T urbines P ower 134 (2), 021503.
M I , J . , N A T H A N , G . J . & L U X T O N , R . E . 2001 Mixing characteristics of a flapping jet from a
self-exciting nozzle. Flow T urbul. Comb ust. 67 (1), 1–23.
O STERMANN , F. , W OSZIDLO , R . , N AY E R I , C . & P ASCHEREIT , C . O . 2015 a Experimental comparison
between the flo w field of two common fluidic oscillator designs. In 53r d AIAA Aer ospace
Sciences Meeting . AIAA.
O STERMANN , F. , W OSZIDLO , R . , N A Y E R I , C . N . & P ASCHEREIT , C . O . 2015 b Phase-averaging
methods for the natural flo wfield of a fluidic oscillator . AIAA J. 53 (8), 2359–2368.
O STERMANN , F. , W OSZIDLO , R . , N A YERI , C . N . & P ASCHEREIT , C . O . 2018 Experimental three-
dimensional velocity data of a sweeping jet from a fluidic oscillator . T echnische Uni versität
Berlin.
P LA TZER , M . F . , S I M M O N S , J . M . & B REMHORST , K . 1978 Entrainment characteristics of unsteady
subsonic jets. AIAA J . 16 (3), 282–284.
Q U I N N , W . R . 1992 Streamwise ev olution of a square jet cross section. AIAA J .
30
(12),
2852–2857
.
Q U I N N , W . R . & M ILITZER , J . 1988 Experimental and numerical study of a turb ulent free square
jet. Phys. Fluids 31 (5), 1017–1025.
R A M A N , G . , H A I LY E , M . & R I C E , E . J . 1993 Flip-flop jet nozzle e xtended to supersonic flo ws.
AIAA J . 31 (6), 1028–1035.
https://doi.org/10.1017/jfm.2018.739
Downloaded from https://www.cambridge.org/core . TU Berlin Universitaetsbibliothek, on 07 Feb 2019 at 08:01:17, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms .

238 F . Ost ermann, R. W oszidlo , C . N . N a yeri and C. O . P ascher eit
R I C O U , F. P . & S P ALDING , D . B . 1961 Measurements of entrainment by axisymmetrical turbulent
jets. J . Fluid Mech. 11 (1), 21–32.
S CHLICHTING , H . & G ERSTEN , K . 2006 Gr enzschicht-Theorie (German Edition) , 10th edn. Springer .
S C H M I D T , H . - J . , W OSZIDLO , R . , N A YERI , C . N . & P ASCHEREIT , C . O . 2015 Drag reduction on a
rectangular bluf f body with base flaps and fluidic oscillators. Exp. Fluids 56 (7).
S C H M I D T , H . J . , W OSZIDLO , R . , N A YERI , C . N . & P ASCHEREIT , C . O . 2017 Separation control
with fluidic oscillators in water . Exp. Fluids 58 (8), 106.
S EELE , R . , T E W E S , P . , W OSZIDLO , R . , M C V E I G H , M . A . , L U C A S , N . J . & W YGN ANSKI , I . J .
2009 Discrete sweeping jets as tools for impro ving the performance of the V -22. AIAA J.
Air cr aft 46 (6), 2098–2106.
S EIFER T , A . , S TA L N O V , O . , S PERBER , D . , A RW A T Z , G . , P ALEI , V . , D A V I D , S . , D AY A N , I . & F O N O ,
I . 2009 Large trucks drag reduction using acti v e flow control. In The Aer odynamics of Heavy
V ehicles II: T ruc ks, Buses, and T rains , pp. 115–133. Springer .
S FORZA , P . M . , S TEIGER , M . H . & T RENT A COSTE , N . 1966 Studies on three-dimensional viscous
jets. AIAA J . 4 (5), 800–806.
S I E B E R , M . , O STERMANN , F., W OSZIDLO , R . , O BERLEITHNER , K . & P ASCHEREIT , C . O . 2016
Lagrangian coherent structures in the flo w field of a fluidic oscillator . Phys. Rev . Fluids
1
(5), 050509.
S I M M O N S , J . M . , P LA TZER , M . F. & S M I T H , T. C . 1978 V elocity measurements in an oscillating
plane jet issuing into a moving air stream. J . Fluid Mech. 84 (1), 33–53.
S RINIV AS , T. , V ASUDEV AN , B . & P RABHU , A . 1988 Performance of fluidically controlled oscillating
jet. In T urb ulence Management and Relaminarisation (ed. H. W . Liepmann & R. Narasimha),
pp. 485–494. Springer .
V IETS , H . 1975 Flip-flop jet nozzle. AIAA J. 13 (10), 1375–1379.
V O N G OSEN , F. , O STERMANN , F., W OSZIDLO , R . , N AY E R I , C . N . & P ASCHEREIT , C . O . 2015
Experimental in vestigation of compressibility effects in a fluidic oscillator . In 53r d AIAA
Aer ospace Sciences Meeting . AIAA.
W HALEN , E . A . , L A C Y , D . S . , L I N , J . C . , A NDINO , M . Y . , W ASHBURN , A . E . , G RAFF , E . C . &
W YGN ANSKI , I . J . 2015 Performance enhancement of a full-scale vertical tail model equipped
with acti ve flo w control. In 53r d AIAA Aer ospace Sciences Meeting . AIAA.
W OSZIDLO , R . , O STERMANN , F. , N AY E R I , C . N . & P ASCHEREIT , C . O . 2015 The time-resolved
natural flo w field of a fluidic oscillator . Exp. Fluids 56 (6).
W YGN ANSKI , I . J . & F IEDLER , H . 1969 Some measurements in the self-preserving jet. J. Fluid
Mech. 38 (3), 577–612.
Z A M A N , K . B . M . Q . 1996 Axis switching and spreading of an asymmetric jet: the role of coherent
structure dynamics. J . Fluid Mech. 316 , 1–27.
https://doi.org/10.1017/jfm.2018.739
Downloaded from https://www.cambridge.org/core . TU Berlin Universitaetsbibliothek, on 07 Feb 2019 at 08:01:17, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms .

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