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

THE TURBULENT SHEAR STRESS AND TURBULENT HEAT FLUX OFTWO PARALLEL PLANE JETS WITH PERIODIC VORTEX SHEDDING

Soichiro Hiromasa
Shumpei Hara
Department of Mechanical Engineering
Department of Mechanical Science Engineering
Doshisha University
Doshisha University
1-3 Tatara Miyakodani, Kyotanabe-shi, Kyoto, Japan, 1-3 Tatara Miyakodani, Kyotanabe-shi, Kyoto, Japan,
ctwg0515@mail4.doshisha.ac.jp
shhara@mail.doshisha.ac.jp

Kyoji Inaoka
Department of Mechanical and System Engineering
Doshisha University
1-3 Tatara Miyakodani, Kyotanabe-shi, Kyoto, Japan,
kinaoka@mail.doshisha.ac.jp

ABSTRACT

be studied and evaluated upon.
The purpose of the present study is to measure the turbulent velocity and turbulent heat ﬂux of two parallel plane
jets using simultaneous particle imaging velocimetry (PIV)
and two-color laser induced ﬂuorescence (LIF) method. By
evaluating vector values and scalar values, quantitative insighton turbulent velocity and turbulent heat ﬂux for jets with orwithout a periodic vortex shedding phenomenon is presented.

The turbulent velocity and heat ﬂux of two parallel plane
jets with a periodic vortex shedding phenomenon were experimentally investigated using simultaneous particle imaging velocimetry and two-color laser induced ﬂuorescence. In the upstream regions, the incoming jet feeds the recirculation zone,
causing the temperature to stay constant, leading to small turbulent heat ﬂux. For jets with a nozzle distance ratio of 1.4, thevortex shedding phenomenon suppresses the inner shear layers, causing both Reynolds shear stress and turbulent heat ﬂux
within this region to become smaller in comparison to two parallel plane jets without a periodic vortex shedding. However,these vortices also stimulate the outer shear layers, causing turbulent statistics to spread greater in the transverse direction.

EXPERIMENT APPARATUS AND PROCEDURE
The ﬂow system is shown in Fig. 1, done in an acrylic
water tank (800×500×1000 mm3 ). Two side plates along thenozzle were used to retain the two-dimensionality of the jet
and two rectangular exits were placed parallel to each other.
Each exit had a width of w = 3 mm and length l = 60 mm (anaspect ratio of 20). The distance between the two nozzles wered = 4.2 mm and d = 6.0 mm for case 1 and case 2 respectively,
shown in the schematic view of the test section in Fig. 2. A
Cartesian coordinate system was established, with its origin
located at the center of the two nozzles with the vertical direction the x-axis and the horizontal direction the y-axis, with the
x component velocity and y component velocity noted as u andv. The exit Reynolds number (Re0 ≡ U0 w/ν) were 810 and
890 for case 1 and case 2, U0 being the average exit u velocity
and ν the kinematic viscosity of water. The development of
two parallel plane jets can be divided into 3 regions (Miller andComings, 1960). The converging region (region A) consistsof a recirculation zone bordered by the two jets which continues until where the two jets meet at the centerline known as
the merging point (mp). The region between mp and where thetwo jets form a velocity distribution of a single jet (combined
point, cp) is the merging region (region B), and any region
downstream of this point is considered the combined region(region C). A 10 degree temperature difference was also implemented between the jet exit and surrounding ﬂuid.
The measurement system used for the simultaneous PIV
and two-color LIF measurements is shown in Fig. 3. A laser
with a wavelength of 488 nm was used, and the emitted beam
was adjusted using multiple mirrors and made into a 2 mm

INTRODUCTION
Thermal pollution caused by thermal discharge fromplants and stack gas ravage the ecosystem, and turbulent diffusion from jets shines light in ways to lessen the damage
caused. One way to improve turbulent diffusion in jets is
by using two parallel plane jets. Tanaka (1970, 1974) experimented by changing the distance ratio between jets andcompared the results to a single jet, concluding that two parallel plane jets had active diffusion characteristics, while also
stating that the distance ratio d/w (d being the distance between the two jets and w being the width of each jet) affects
the ﬂow ﬁeld greatly, with different phenomenon occurring between the jets according to the distance ratio. Bunderson andSmith (2005) reported vortices forming and wavering within
the recirculation zone, while Anderson et al. (2003) reported
a vortex shedding phenomenon occurring when the distanceratio is between 0.6 and 1.4, which was conﬁrmed by Mondal et al. (2016) through numerical simulation. The effectsof the vortex shedding phenomenon upon vector values havebeen studied upon, yet scalar values such as temperature havebeen paid little attention. Throughout inspection of previous
studies, signs indicate active turbulent diffusion in two parallel
plane jets and values. However, in order to fully incorporate
two parallel plane jets into industrial usage, heat transfer must1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
The time-averaged transverse turbulent heat ﬂux for bothcases are shown in Fig. 7. Values are made dimensionless using U0 and ∆T0 , which are the exit velocity and the temperature difference between the jet exit and surrounding ﬂuid. In
both cases, region A showed little turbulent heat ﬂux, not inalignment with observations for Reynolds shear stress. The
discrepancy is that Reynolds shear stress is a product of two
velocity vectors while turbulent heat ﬂux is a product of a velocity vector and a temperature scalar. As shown in Fig. 5,high temperature ﬂuids keeps on recirculating within region A
from the incoming jet and is able to retain a constant temperature, resulting in small turbulent heat ﬂux. In region B andregion C, the time-varying component of temperature (t ′ ) becomes larger as heat is not constantly fed into the region, causing an increase in turbulent heat ﬂux. Transverse turbulence isalso a cause, as the merging of the two jets causes v′ to becomelarger, leading to greater turbulent heat ﬂux when compared toregion A. A difference that can be seen between the two cases
is that case 1 shows a greater spread in turbulent heat ﬂux whencompared to case 2, which will be discussed later on.

laser sheet using a pinhole and a cylindrical lens. From one
side of the water tank, PIV measurements were obtained usinga CCD camera (800 fps, pixel resolution of 640 × 480 pixels, spatial resolution of 0.166 mm/pixel), to track the 50 µ m
nylon particles dispersed throughout the tank. Two-color LIF
measurements were made using Rhodamine B (RhB) and Rhodamine 110 (Rh110) circulating throughout the ﬂow system.
Two CMOS cameras with a pixel resolution of 564 × 480 pixels and a spatial resolution of 0.166 mm/pixel were used at
400 fps for LIF measurements. A dichroic mirror was used toobtain identical areas of measurements for the two LIF cameras, placed at the opposite side of the tank from the PIV camera. Filters were used for each CMOS cameras to allow different wavelengths to enter each camera. Wavelengths between
495 nm and 530 nm were allowed to enter the CMOS camera for Rh110 measurements, and wavelengths above 570 nm
entered cameras for RhB measurements. Simultaneous measurements were conducted for 15 seconds, and calculations to
obtain temperature values were done using methods used by
Sakakibara and Adrian (1999). A calibration test was donein a test-cell by taking a sample of the RhB and Rh110 solution and heating up the solution from 25 degrees to 35 degrees.
A second degree calibration curve was obtained from the ﬂuorescence ratio of two LIF images taken at every 0.5◦ C andthe solution’s temperature obtained by a thermocouple, measurement errors related to calibration not expected to exceed
5.3%/◦ C.

Instantaneous and Phase Averaged Statistics
To grasp the differences in ﬂow structures between thetwo cases, the instantaneous velocity streamlines for case 1
and case 2 are shown in Fig. 8. For either case, two vortices
are present within the recirculation zone, but their location andmovement differ between cases. For case 1, counter rotating
vortices are present in the top left and bottom right of the recirculation zone, while being aligned next to each other at times
for case 2, similar to the ﬁndings of previous research (Mondal et al., 2016). To conﬁrm a periodic vortex shedding forcase 1, the Fast Fourier Transform (FFT) was performed withv′ at (x/w, y/w) = (mp, 0.5 (d/w)) = (1.3, 0.7), where neither
the streamwise nor transverse velocity is dominant. A peakfrequency of f = 15.6 Hz was obtained and converted into a
Strouhal number St (≡ fd/U0 ) = 0.33, in line with results previous experimental results (Anderson et al., 2003). Althoughvortices were shed at times for case 2, FFT showed no periodic
vortex shedding frequency.
Using this frequency, phase averaging was carried out andfour phases within a time period were created for case 1. The
streamlines of the phase averaged results are shown in Fig. 9,with results similar to the instantaneous results. Vortices wereshown to not align with each other and vortices are shown tooscillate one after another. The ﬁrst phase in Fig. 9 (a) shows
the vortex on the right downstream while the vortex on the left
is forming. Figure 9 (b) has a vortex forming on the right being
shed while a vortex on the left is developing. Afterwards, thevortex on the right begins to form while the vortex on the left
moves downstream in Fig. 9 (c). Finally, the vortex on the rightenlarges and the vortex on the left is shed in Fig. 9 (d). It must
be noted that just past the merging point along the jet centerline
at x/w = 1.9, the jet is seen to waver in the transverse direction
in a periodic fashion. A peak frequency of f = 15.6 Hz was at
this point as well, showing that the periodic vortex shedding
plays a key role in the jet wavering in downstream regions.

RESULTS AND DISCUSSION
Time Averaged Statistics
The velocity ﬁeld of the two cases are shown in Fig. 4,
with lines at the merging point (mp) and combined point (cp)for each case. The mp and cp were located at x/w = 1.3 andx/w = 5.0 for case 1 and x/w = 2.0 and x/w = 5.9 for case 2.
With the locations of the mp for case 1 and case 2 being similar to the points found in previous studies (Lee et al. (2018),
Wang et al. (2015)), it is safe to assume that the mp moves
downstream along with the distance ratio.
Temperature differences between the jet and surrounding
ﬂuid are shown in Fig. 5, made dimensionless with the temperature difference between the jet exit and surrounding ﬂuid.
For both cases, the recirculation zone has a constant temperature distribution regardless of the backwards ﬂow. Due to theﬂuids in the recirculation zone being supplied by the incoming
high temperature jets, the average temperature remains constant. The temperature begins to decline in the streamwise direction and transverse direction in Region B for both cases,
as entrainment of the surrounding ﬂuid causes the temperature
difference to become smaller.
Figure 6 shows the dimensionless mean Reynolds shear
stress for either case, with the black dotted lines representing
the shear layers. These shear layers were determined as locations with at least 2 percent of the maximum Reynolds shear
stress of the entire ﬁeld of measurement. Inner shear layers
are caused by the interaction between the individual jets whilemerging, and with the mp being located closer for case 1, themerging of the jets occurs more upstream, leading to smaller
inner shear layers. When comparing the Reynolds shear stressalong the mp for each case, peak values in the inner shear layers were found to be approximately 2.5 times that of the peakvalues of the outer shear layers for both cases. Although thereis turbulent mixing occurring with the surrounding ﬂuid in theouter shear layers, the merging of the jets produces higher turbulence, hence taking a larger value.

Totaled Turbulent Statistics
The total magnitude of Reynolds shear stress across eachcross section for inner and outer shear layers are plotted inFig. 10, with areas of each shear layer determined as previously mentioned. The total amount of Reynolds shear stressin the inner shear region for each cross-section is plotted inFig. 10 (a), showing that both cases show similar trends, tak-2

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan, July 19–22, 2022
Table 1. Half width slopes based off Reynolds shear stress,
turbulent heat ﬂux and values of transport spreading coefﬁcient.

ing a peak value at the mp and declining rapidly afterwards.
The effects of the periodic vortex shedding becomes evident
in the outer shear layers, plotted in Fig. 10 (b). Similar trends
are apparent in region (A), with the increase in total Reynolds
shear stress coming to a halt once past the mp. In the instance of case 2, Reynolds shear stress totals decrease until
x/w = 4.6 where the total values begin to increase again. However, for case 1, Reynolds shear stress totals decrease only up
until x/w = 2.0, where these values begin to increase again.
The periodic vortex shedding for case 1 plays a key role indestabilizing the outer shear layers (Mondal et al. 2016), as
the vortex shedding creates a periodic wavering at x/w = 1.9,
leading to the destabilization of the outer shear layers. This
destabilization allows for greater momentum transfer to occur
in downstream regions when compared to case 2.
Similar to the total Reynolds shear stress, the total turbulent heat ﬂux values in the shear layers showed signs of
the effects of the periodic vortex shedding as well, shown in
Fig. 11. In the inner shear layers shown in Fig. 11 (a), similar
turbulent heat ﬂux totals are shown until x/w = 2.0. From thispoint where turbulent heat ﬂux becomes relatively constant forcase 1. For case 2, total turbulent heat ﬂux values continue
to increase until x/w = 2.8 where turbulent heat ﬂux becomes
relatively constant. In both cases, turbulent heat ﬂux becomes
smaller as the shear layers shrinks in size, starting at x/w = 3.1
for case 1 and x/w = 3.9 for case 2. When observing the outer
shear layers in Fig. 11 (b), the inclination of total turbulent heatﬂux remains relatively constant in the downstream regions forcase 1. However, case 2 shows turbulent heat ﬂux rise rapidly
until x/w = 3.9 where its slope becomes relatively smaller. The
constant destabilization of the outer shear regions for case 1
causes the transverse direction velocity ﬂuctuations to spread
as well, hence greater total values.
To address how the turbulent statistics spread, the slopesof the half widths of Reynolds shear stress (C1u′ v′ ) and turbulent heat ﬂux (C1v′ t ′ ) were obtained using equation (1) andequation (2).
bu′ v′ /w = C1u′ v′ (x/w +C2u′ v′ )(1)

bv′ t ′ /w = C1v′ t ′ (x/w +C2v′ t ′ )(2)

C1u′ v′

C1v′ t ′CT

Case 1

0.33

0.22

0.67

Case 2

0.27

0.12

0.44

lent heat ﬂux in comparison to Reynolds shear stress is greaterfor jets with a periodic vortex shedding.

CONCLUSION
Simultaneous PIV and two-color LIF were used to measure the turbulent velocity and turbulent heat ﬂux of two parallel plane jets with different distance ratios. Jets with a periodic
vortex shedding phenomenon were found to repress the inner
shear layers while also stimulating outer shear layers. These
effects are evident when comparing turbulent statistics to jets
without a periodic vortex shedding, as the inner shear layers
had smaller total Reynolds shear stress and turbulent heat ﬂux.
On the other hand, outer shear layers showed these jets to havehigher total turbulent statistics. The half width slopes of turbulent statistics also showed that jets with a periodic vortex
shedding have a greater rate of spreading when compared tojets without a periodic vortex shedding.

REFERENCES
Anderson, E. A., Snyder D. O. & Christensen, J. 2003 Periodic
ﬂow between low aspect ratio parallel jets. Journal of Fluids
Engineering 125 (2), 389–392.
Bunderson, N.E. & Smith 2005 Passive mixing control ofplane parallel jets. Experiments in Fluids 39, 66–74.
Jenkins, P.E., Goldschmidt V.W. 1973 Mean temperature andvelocity in a plane turbulent jet. Journal of Fluids Engineering 95 (4), 581–584.
Lee, Saya & Hassan, Yassin A. 2018 Experimental study of
ﬂow structures near the merging point of two parallel plane
jets using piv and pod. International Journal of Heat andMass Transfer 116, 871–888.
Miller, D.R., Comings E.W. 1960 Force-momentum ﬁelds in adual-jet ﬂow. Journal of Fluid Mechanics 7 (2), 237–256.
Mondal, T., Das M. K. & Guha, A. 2016 Periodic vortex shedding phenomenon for various separation distances between
two parallel plane jets. International Journal of Heat andMass Transfer 99, 579–588.
Sakakibara, J. & Adrian, R.J. 1999 Whole ﬁeld measurementsof temperature in water using two-color laser induced ﬂuorescence. Experiments in Fluids 26, 7–15.
Tanaka, Eiichi 1970 The interference of two-dimensional parallel jets : 1st report, experiments on dual jet. Bulletin of
JSME 13, 272–280.
Tanaka, Eiichi 1974 The interference of two-dimensional parallel jets : 2nd report, experiments on the combined ﬂow of
dual jet. Bulletin of JSME 17 (109), 920–927.
Wang, Huhu, Lee, Saya, Hassan, Yassin A. & Ruggles,
Arthur Elwood 2016 Laser-doppler measurements of the
turbulent mixing of two rectangular water jets impinging ona stationary pool. International Journal of Heat and Mass
Transfer 92, 206–227.

Locations where Reynolds shear stress and turbulent heatﬂux reached half the value of their local maximum values(bu′ v′ /w and bv′ t ′ /w) were plotted using experimental data andlinear approximation was used to obtain the slope of the half
widths in the downstream direction (C2u′ v′ , C2v′ t ′ being experimental constants). The slopes for both statistics are listed inTable 1, where the spreading of Reynolds shear stress and turbulent heat ﬂux is found to be greater for case 1. To compare the spreading of Reynolds shear stress and turbulent heattransfer, a transport spreading coefﬁcient CT, similar to the
spreading coefﬁcient that compared velocity half width slopes
and temperature half width slopes (Jenkins and Goldschmidt,
1973) were obtained as shown in equation (3), with results
listed in Table 1.
CT = C1v′ t ′ /C1u′ v′

Case

(3)

Through examination of C1u′ v′ and C1v′ t ′ , the spread of
Reynolds shear stress and turbulent heat ﬂux is greater forcase 1. With the periodic vortex shedding, a periodic disruption of the outer shear layers leads to a greater spread in turbulent statistics. The transfer coefﬁcient CT shows that in bothcases, the spread of Reynolds shear stress is greater than the
spread of turbulent heat ﬂux. Also, the spreading rate of turbu-

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

Figure 2. Schematic diagram of the ﬂow ﬁeld of twoparallel plane jets.

Figure 1. Flow system used throughout the experiment.

Figure 3.

Figure 4.

Simultaneous PIV and two-color LIF measurement system.

Dimensionless mean streamwise velocity for (a) case 1 and (b) case 2.

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

Figure 5.

Dimensionless temperature differences between jet and surrounding ﬂuid for (a) case 1 and (b) case 2.

Figure 6. Dimensionless mean Reynolds shear stress for both cases with contour lines around shear layers for (a) case 1 and (b) case 2.

Figure 7.

Dimensionless mean turbulent heat ﬂux for both cases with contour lines around shear layers for (a) case 1 and (b) case 2.

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

Figure 8.

Instantaneous streamlines of the upstream region for (a) case 1 and (b) case 2.

Figure 9. Phase averaged streamlines for case 1 within a time duration of T divided into four phases at (a) t = T/4, (b) t = 2T/4,(c) t = 3T/4 and (d) t = 4T/4.

Figure 11. Total turbulent heat ﬂux across each cross-sectionfor (a) inner shear layers and (b) outer shear layers.

Figure 10. Total Reynolds shear stress across each crosssection for (a) inner shear layers and (b) outer shear layers.

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