12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

INFLUENCE OF A CYLINDER INSTALLED UPSTREAM ON THE FLOWFIELD OF A TURBULENT JET

Srikar Yadala*, Girish K. Jankee, Eirik Æsøy, James R. Dawson & Nicholas A. WorthDepartment of Energy and Process Engineering
Norwegian University of Science and Technology
Trondheim N-7491, Norway∗ srikar.y.venkata@ntnu.no

ABSTRACTrying a portion of the total momentum. A second method is
to use geometrical features as a form of passive flow control.
These features can be a modified shape of the jet nozzle’s trailing edge (Longmire et al., 1992; Longmire & Duong, 1996) or
the use vortex generators (Reeder & Samimy, 1996). In thesecases, the amplification of secondary instabilities and corrugation of the primary vortical structures have been demonstrated.
The objective of the current research is to investigate andunderstand the influence of a cylinder installed upstream of thejet exit on the evolution of vortical structures and thereby thenear-field dynamics. In practical situations, jet flows are often
not well conditioned due to design constraints which can introduce disturbances that modify the flow in unexpected ways.
One such example is the study of acoustically forced flames byÆsøy et al. (2021a) which showed that vortex shedding fromupstream geometries can couple with acoustic oscillations tomodify the flame response. These findings were in fact the
motivation behind the current research efforts. As such, theuse of a cylinder is to replicate such scenarios in practical applications, albeit in a simplified manner.

The influence of a cylinder installed upstream of a roundjet’s exit plane on the dynamics of this flow field is investigated. Acoustic excitation is used to excite the flow at a particular frequency and phase-locked, high-resolution particle
image velocimetry is employed to obtain velocity data. The
cylinders have a marginal effect on the mean flow field. However, the circulation within the vortical flow structures reduces,which ultimately leads to a decrease in the strength of the fluctuating quantities. There is also evidence of the cylinders’ potential in increasing the three-dimensionality of the jet flow.
The results demonstrate that the vortex shedding in the cylinders’ wake modifies the boundary condition at the jet’s exit andthus, affects the shear layer and the jet flow field as a whole.

INTRODUCTION
Round jets that discharge into surrounding ambient fluid
have been studied extensively in the past decades. The interaction of the jet with the ambient fluid gives rise to a freeshear layer in the near field which is influenced by axisymmetric Kelvin-Helmholtz and helical instabilities (Crow & Champagne, 1971; Ho & Huerre, 1984). The Kelvin-Helmholtz (primary) instability waves yield regions of concentrated vorticity
that encircle the jet’s potential core and propagate downstream.
The secondary (helical) instabilities induce streamwise vorticity within the primary vortical structures and contribute to theireventual breakdown. There has been significant interest in manipulating the Kelvin-Helmholtz mechanism through the modification of the jet’s inlet boundary conditions (see for example Crow & Champagne, 1971; Ho & Huerre, 1984; Aydemir
et al., 2012). The aim of such research can be to better understand the fundamental response of the jet to certain input
conditions or to affect other aspects further downstream suchas turbulent statistics, mixing rate, jet noise and heat transfer
among others.
The majority of research efforts have focused on measuring the jet’s response to axisymmetric disturbances (forexample, Crow & Champagne, 1971; Aydemir et al., 2012).
Only a few studies have attempted to understand the impactof asymmetric forcing, which was summarised by Reynolds
et al. (2003). Asymmetric forcing can be achieved (for example) through transverse acoustic disturbances as demonstrated
recently by Worth et al. (2020) and Æsøy et al. (2021b). The
predominant effect in such cases is an inclination change insuccessive vortical structures and for some conditions, bifurcation of the jet into separated momentum streams each car-

EXPERIMENTAL SETUP AND MEASUREMENTSYSTEMSThe axisymmetric jet used by Aydemir et al. (2012) (alsoby Worth et al., 2020; Æsøy et al., 2021b) was modified andemployed in the current investigation. A schematic of the experimental set-up is shown in figure 1. The apparatus consistsof a 200 mm long cylindrical plenum chamber with an innerdiameter of 100 mm followed by a 350 mm long tube with an
inner diameter of 35 mm. The apparatus is completed by aconverging nozzle with a knife-edged exit to achieve a top-hat
exit velocity profile. The convergence ratio of the nozzle is12.25 : 1 along the streamwise direction and it has an exit diameter of D = 10 mm (used henceforth to non-dimensionalize
the spatial coordinates). The rate of air flow was regulatedwith a mass flow controller and fed into the facility below theplenum. As such, the bulk velocity of the jet was maintainedat Ub = 11 (±0.5) m s−1 for all tested cases and the Reynolds
number based on the jet’s exit diameter is ReD = 7483. Axisymmetric acoustic excitation was employed to ensure vortexstructure formation at select frequencies. To this effect, harmonic velocity oscillations at the nozzle’s exit were generated
by two diametrically opposed loudspeakers installed on theplenum chamber. A TTi 40 MHz waveform generator provided
monochromatic sinusoidal input signals at selected frequencies ( fe ) to drive the loudspeakers. The amplitude of these1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
=90º

x

Laser
=0º

r
PIV FOV xcNozzleCylinderMicrophones

Loudspeakers
Figure 2: Acoustic fluctuation at the jet’s exit plane(black curve) and PIV velocity measurement at x/D =
0.2 (green ’x’ in figure 3a) at different phases along theacoustic cycle (green markers).

Waveform
generator
Amplifier
Plenum chamber

Table 1: List of experimental conditions.

dC (mm)xC (mm)xC /dC

Figure 1: Schematic of the experimental set-up (not to

No cylinder-∞scale). Inset at the top-right corner shows the two PIV
planes captured.

2

70

35

6

104

17.3

6

70

11.7

10

87

8.7

Flow+seeding

acoustic velocity fluctuations (Ae = u′ ( fe )/Ub ) at the nozzle’s
exit was fixed using the multiple microphone method (Seybert & Ross, 1977) for which, pressure measurements at two
streamwise stations along the 350 mm long pipe were obtained
through Brüel & Kjær free-field 1/4′′ condenser microphones.
The coordinate system is defined as follows: x and r represent
the streamwise and radial directions respectively, with the origin being at the centre of the nozzle’s exit. The corresponding
velocity components are u and v respectively. For the caseswith a cylinder installed upstream, θ represents the azimuthal
angle, with θ = 0◦ being perpendicular to the cylinder’s length(see inset in figure 1).
Quantitative velocity measurements of the ensuing jet
flow were obtained through a low-speed planar particle image
velocimetry (PIV) system. The flow was seeded with olive
oil droplets that were produced using a Laskin nozzle and introduced into the air flow upstream of the plenum. Illumination of these oil droplets was achieved with a Litron Nano L
200 mJ dual-pulse Nd:YAG laser, whose beam was shaped intoa ≈ 1 mm thick light sheet. Imaging of the field-of-view (FOV)
was carried out using a LaVision Imager LX 16 MP camerafeaturing a 4904 × 3280 px2 sensor. The camera was equippedwith a Nikon-Nikkor 200 mm micro lens operated at f# = 8 andwas positioned normal to the imaging plane. The inspected
planes were along the x − r directions just above the nozzle
exit (dashed (green) rectangle in figure 1) and up to x/D ≈ 5 inorder to capture the developing shear layer. Synchronisation of
the laser pulses and camera timing was achieved using a LaVision PTU and the acquisition was at a sampling frequency of
1 Hz, in double-frame mode (∆t = 10 µs). Additionally, thePIV system was synchronised with the acoustic driving signal,
thereby achieving a phase-locked measurement at 12 equidistant phases along the driving signal for all test cases. For
each phase, 200 image pairs were captured. Image acquisition,
pre-processing and vector computations were performed using

LaVision DaVis 10 software suite. Cross-correlation for vector field computation was carried out with a final interrogation
window of 24 × 24 px2 with a relative overlap of 50%, which
resulted in a spatial resolution of 0.13 mm between vectors inboth x and r directions.
The PIV system was first employed to acquire quantitative velocity data of the jet flow field with no cylinder installed. The time-average vector field of the streamwise velocity u is presented in figure 3a. The velocity of the jet justdownstream of the exit at x/D = 0.2, r/D = 0 (green ’x’ in3a) is Ub = 11.03 m s−1 (henceforth used to normalise different quantities as necessary), which agrees well with the bulk
velocity set through the mass flow controller. The jet wasconditioned through an acoustic excitation at a frequency offe = 160 Hz, with an amplitude Ae = 0.2 at the nozzle’s exit
for all test cases. The corresponding Strouhal number basedon the jet’s exit diameter and bulk velocity is StD = 0.15. One
time period (Te ) of the imparted acoustic fluctuation, computed
using the multiple microphone method, is presented in figure
2. The velocity fluctuation measured at x/D = 0.2 at the different phases is also shown in the figure (solid green squares)
and is seen to agree well with the imparted acoustic fluctuation. It is worth noting that this no cylinder case serves as thereference against which the influence of the cylinders will becompared. Three cylinders with different diameters dC were
installed at various upstream locations in order to ascertain theeffect of such geometrical features on the jet’s dynamics. The
different test cases will henceforth be referred to by the ratio
xC /dC , where xC is the distance of the particular cylinder withrespect to the jet’s exit as illustrated in figure 1. The differ-2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 3: Statistical quantities. (a) Normalised u-velocity contour for the no cylinder (reference) case; (b) & (c) Normalised

u-velocity profiles at x/D = 4 with insets showing a zoomed-in view; (d) & (e) Normalised σu profiles at x/D = 4.
ent test cases are listed in table 1. Also, for the cases withcylinders installed, PIV measurements were acquired at two
different planes along the angular direction θ . The first plane
was perpendicular to the cylinder’s length while the second
was parallel to it. These planes are referred to by the angles
θ = 0◦ and θ = 90◦ respectively, in the rest of the document
and are shown in the inset in figure 1.

denced by the profiles of the standard deviation of the streamwise velocity (σu ) at x/D = 4, shown in figures 3d and e. A
general reduction in the strength of the fluctuations comparedto the reference case is observed for all cases with an upstream
cylinder. No clear trend is recognised in the jet core barring thegeneral reduction. In the shear layer region on the other hand(around r/D = ±0.5), the fluctuations seems to reduce withxC /dC as observed with the mean velocity. The maximum
reduction at this streamwise station again corresponds to thexC /dC = 8.7 case, with the change in the standard-deviation
profile’s maxima being a compelling ≈ 17% compared to thereference case. Finally, except the xC /dC = 35 test case, theσu profiles at the two measured planes agree well with one another for the different cases. The reason for this exception withthe xC /dC = 35 case cannot be ascertained with the available
data and will be investigated upon in the future.
The brief discussion until now clearly indicates that thecylinders have an impact on the jet flow field, especially on
the fluctuating quantities. These effects are investigated further through the phase-averaged velocity fields. The vorticity (ω) at the different phases were computed from the measured average velocity fields using a second-order central differences method and were normalised by multiplying with theratio D/Ub . Such a normalised vorticity field from the different test cases at t/Te = 0.75 along the acoustic cycle is presented in figure 4. Additionally, the swirl strength λci (Adrian
et al., 2000), also normalised with D/Ub , is employed to detect
vortical flow structures in the shear layer region. The resultsof these computations are superimposed on the presented vorticity fields as contour lines.
The initial development of the shear layer does not show
a significant difference in all the tested cases. It is observed to

RESULTS & DISCUSSION
Statistical quantities computed from the PIV acquisition
are presented in figure 3. The normalised u-velocity profile
along the radial direction at x/D = 4 for the different test
cases, at the two measured PIV planes, is presented in figures
3b and c respectively. Minor differences are observed at theedge of the jet, but this can be a result of the variable seeding density in this region and thus, can be discounted. Barring this, the streamwise velocity at the jet core is marginallylower when the cylinders are installed compared to the reference case, which is an artefact of the cylinder’s wake. The
reduction in velocity seems to scale with xC /dC (see insets infigures 3b & c). The change is negligible for the xC /dC = 35
test case and the maximum reduction is observed to be ≈ 5%of the reference case for xC /dC = 8.7. While the contracting nozzle seems to aid in recovering the velocity deficit in
the cylinder’s wake and regularise the flow at the jet’s exit toa great extent, the cylinders do leave a footprint on the mean
flow field, albeit very small. In the absence of such a contracting section, one can expect this effect to be significantly
amplified, depending on the upstream location of the cylinder.
While the mean velocity is affected marginally, the cylinders do impact the fluctuating quantities significantly as evi-3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 4: Phase-averaged vorticity distribution at t/Te = 0.75 along the acoustic velocity fluctuation cycle at the jet’s exit.
Contour lines represent vortical flow structures detected through swirl-strength criterion.

roll-up into vortical flow structures around x/D = 2.4. These
structures are a direct consequence of the acoustic excitation
being applied. Furthermore, these vortical structures are atabout the same streamwise station as in the reference case inboth the θ = 0◦ and θ = 90◦ planes when a cylinder is installed upstream. This observation implies that the timing of
the shear-layer roll up (and thereby the jet) is purely dictatedby the acoustic mode and the installed cylinder has no influence on either the timing or the symmetry of the jet.

the standard deviation maxima discussed previously.
The circulation Γ will now be used as a metric to quantify this reduction in vortical-structure strength better. To thiseffect, the circulation in the region enclosed by the dashed(black) rectangle in figure 4i is computed at each phase along
the acoustic cycle for every test case, according to equation 1.

Z Z

Γ(t) =|ω(x, r,t)| · drdx

(1)

x r

In the no cylinder case (figure 4a), a second vortical structure is observed around x/D = 4 which is the remnant of thesmaller structure at x/D ≈ 15 in the current snapshot, albeit
from the previous acoustic cycle. The exisstence of this second vortical structure is unsurprising, given the low Strouhal
number of the current acoustic excitation. It is well know thatthe jet’s preferred mode is in the range of 0.24 ≤ StD ≤ 0.64
(Crow & Champagne, 1971). In the current set-up, significant
jet response was observed in the range 0.3 ≤ StD ≤ 0.5 witha peak at StD = 0.33 (see Æsøy et al., 2021b). In comparison, the applied acoustic excitation at a Strouhal of StD = 0.15
is slightly less than half the peak value and as such, will be
the predominant mode only further downstream. This structure is also observed in the xC /dC = 35 and 17.3 cases atabout the same streamwise location. However, its size andstrength seems to diminish with xC /dC . In fact, in the lasttwo cases (xC /dC = 11.7 and 8.7), the swirl-strength criterion
does not even recognise the presence of a vortical structure.
This trend of reducing vorticity magnitude around x/D = 4
with the xC /dC ratio corroborates well with the reduction in

The cumulative sum of Γ(t) from each phase is then calculated
and used as a measure of the total circulation Γtot in the considered interrogation domain. The circulation within the vortical flow structures (Γvr ) present in the chosen domain is also
pertinent. This was achieved by masking the vorticity magnitude field with a threshold iso-vorticity contour that defines
the vortical structures’ boundary as done in previous research
efforts (Gharib et al., 1998; Aydemir et al., 2012). Througha sensitivity analysis, the appropriate threshold was found tobe ω · D/Ub > 1 which corresponds to about 20% of the peakvorticity within the selected interrogation domain. It is worth
noting that this threshold value is the same as that reported by
Aydemir et al. (2012) in their work. The computed circulation(both Γtot and Γvr ) is normalised by dividing with (Ub · D).
The evolution of circulation along the acoustic cycle forthe different cases is presented in figures 5a and b. In all cases
and in both PIV planes, the total circulation grows steadily
until t/Te = 0.42 beyond which, the rate of growth reduces a4

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

Figure 5: Normalised circulation (Γtot and Γvr ) along the acoustic cycle for the different cases in the region enclosed by

the dashed (black) rectangle in figure 4i. (a) θ = 0◦ plane; (b) θ = 90◦ plane; (c) and (d) Γtot and Γvr respectively, at
t/Te = 0.92.
little. The total circulation at the last phase along the acoustic
cycle (t/Te = 0.92) is plotted as a function of xC /dC in figure
5c to discern the impact of the cylinders. This particular phaseis chosen with the assumption that these values of circulation
will encompass all the flow dynamics within one acoustic cycle. While a specific scaling with xC /dC is not recognisable, it
is clear that the cylinders do influence the total circulation.
Akin to the total circulation, the circulation based on thevorticity within vortical structures too, shows a gradual increase until t/Te = 0.42. From here on and until t/Te = 0.67,
this component of circulation remains almost constant for all
test cases. Beyond this, the circulation is seen to increase once
again but at a lower rate. This feature is especially apparent
in the reference case and is attributed to the weaker vorticalstructure that was seen in the phase-averaged vorticity fields
close to x/D = 4 (see figure 4a). The cylinders installed upstream are seen to have a destructive effect on the vorticalstructures within the shear layer. This aspect is clearly noticeable in figure 5d where the circulation of the vortical structures
at t/Te = 0.92 as a function of xC /dC is plotted. The magnitude of Γvr is observed to diminish with this ratio, with thexC /dC = 8.7 test case demonstrating a reduction of about 25%
with respect to the reference case.
A reduction in Γtot with respect to xC /dC , synonymouswith Γvr , is expected but not observed. This discrepancy inthe current results can be attributed to two aspects. Firstly,
the computed vorticity fields were not treated with any spatial filters prior to the Γtot computation and as such, any background noise can impact the computed quantities. It is worth
noting that the threshold applied to compute Γvr acts as a filter of some sort, making the distinctions between the different
cases identifiable and trustworthy. Secondly, the observed discrepancy could be an attribute of the flow field, whereby thecylinders produce dynamics that are not synchronised with theacoustic cycle. These will therefore not be captured by thephase-locked measurement, but manifest as background vorticity in the different cases. These aspects will be investigatedfurther in future works. Nonetheless, the curtailment of thevortical structure circulation is consistent with the decrease in
the strength of fluctuations within the current jet flow field.
A decrease in the value of xC /dC essentially means the
dynamics in the cylinder’s wake that is perceived at the jet’s
exit plane is stronger. Thus, the fact that the decrease in different flow quantities is proportional to the ratio xC /dC implies
that the vortex shedding in the cylinder’s wake is responsible
for any modulations of the fluctuations in the jet flow field.
The vortices shed from the cylinders were not observed in anyof the acquired cases. This can be attributed to the contracting
nozzle which might be suppressing the vortical structure while
retaining the induced fluctuations. Thus, a direct interaction of
the shed vortices and the shear layer is discounted here. It is
more probable, that the fluctuations within the cylinder’s wake
seeps into and modifies the incoming boundary layer, thereby
affecting the shear-layer dynamics.
Finally, an interesting feature is brought to light when theΓvr computations at the two PIV planes are compared witheach other. As mentioned previously, the phase-averaged vorticity fields show that the cylinders do not impact the timing of
the shear-layer rolling up. Thus, these cylinders do not modify the axisymmetry of the round jet as was demonstrated tobe the case when the shape of the nozzle’s exit was changed(Longmire et al., 1992) or when tabs or vortex generators were
installed at the jet’s exit (Reeder & Samimy, 1996). However,the circulation magnitude at the two perpendicular planes dodiffer from one another in most cases with the cylinder. Thisobservation conveys that the cylinders do change the axisymmetry of the jet, albeit in a subtle manner.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022
CONCLUDING REMARKSREFERENCES

In this paper the dynamics of a round jet subject to acoustic forcing were studied, in the presence of a circular cylinder
located upstream of the jet exit. Cylinders of different diameters were installed at various upstream locations. Acoustic
excitation was used to condition the jet flow field at a particular frequency. Phase-locked, high spatial-resolution planar
PIV was employed to obtain quantitative velocity data in the
jet’s near field, especially in the developing shear layer. The
PIV measurements were acquired at two perpendicular planes
to discern the impact of the cylinders better.
The cylinders do not impact the mean flow field significantly. However, they diminish the strength of the vorticalflow structures within the shear layer. This manifests as a reduction in the circulation within the vortical structure and leads
to a decrease in the strength of the fluctuations within the flow
field. The diminishing effects on various flow quantities wasfound to be proportional to the ratio xC /dC which indicates thatthe vortex shedding in the cylinder’s wake interferes with theshear layer development and thus, the dynamics within the jet.
Furthermore, while the cylinders are not seen to modify thetiming of the shear layer rolling up (which is still dominatedby the imparted acoustic excitation), the circulation magnitude
at the two measured planes shows a difference which conveysthat the axisymmetry of the round jet might be broken resulting in a more three-dimensional flow field, albeit in a subtle
manner.
The observations made here may suggest that the cylinder modifies the inlet boundary condition of the jet. Thereby,
it manipulates the strength of the Kelvin-Helmholtz instability mechanism prevalent in the near-field of the jet. The subtle increase in the flow’s three dimensionality may also imply the cylinder impacting the secondary instabilities in theshear layer. These aspects will be investigated further in future works. A thorough parametric study is also necessary tobetter understand the trends observed here and to inspect if
there is any fixed scaling involved. Finally, while the effects of
the upstream cylinder on the jet flow are summarised here, themechanisms that lead to these effects are not clear yet. Better
insight into the mechanisms at play is of paramount importance and will be the focus of future research efforts.

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ACKNOWLEDGEMENT
The authors gratefully acknowledge financial support
from the European Research Council (ERC): Grant agreement677931 TAIAC.

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