PIV and electrodiffusion diagnostics of ﬂow ﬁeld, wall shear stress and [610136]

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PIV and electrodiffusion diagnostics of ﬂow ﬁeld, wall shear stress and [610136]

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PIV and electrodiffusion diagnostics of ﬂow ﬁeld, wall shear stress and
mass transfer beneath three round submerged impinging jets
Kodjovi Sodjavia, Brice Montagnéa, Pierre Bragançaa, Amina Meslemb,⇑, Paul Byrneb, Cédric Degouetc,
Vaclav Sobolika
aLaSIE, University of La Rochelle, Pôle Sciences et Technologie, avenue Michel Crépeau, 17042 La Rochelle, France
bLGCGM EA3913, Equipe Matériaux et Thermo-Rhéologie, Université Européenne de Bretagne, Université Rennes 1, IUT de Rennes, 3 rue du Clos Courtel, BP 90422, 35704
Rennes Cedex 7, France
cLaVision, Anna-Vandenhoeck-Ring 19, D-37081 Goettingen, Germany
article info
Article history:Received 5 May 2015Received in revised form 1 October 2015
Accepted 5 October 2015
Available online 13 October 2015
Keywords:
Impinging round jetTime-resolved tomographic PIVElectrodiffusionVelocity ﬁeldWall shear rateMass transferabstract
This paper reports on measurements of velocities, wall shear rates and mass transfer in an impinging
round jet issued from a round nozzle. The effect of the nozzle shape on transfer phenomena was inves-
tigated. A round oriﬁce perforated either on a ﬂat plate (RO/P) or on a hemispherical surface (RO/H) was
compared to a reference convergent nozzle (CONV). All the nozzles have the same exit diameter D. The
exit volumetric ﬂow rate was also conserved and led to the same Reynolds number based on the exit bulkvelocity, Re
b= 5620. The nozzle-to-wall distance was constant and equal to 2 D.
The Particle Image Velocimetry technique (PIV) was used to capture the jet ﬂow ﬁeld. The limitations of
the PIV technique in the vicinity of the target disk are addressed by using the electrodiffusion technique(ED) to obtain the wall shear rate distribution. The ED technique was extended for the measurement of
local mass transfer distribution and global mass transfer on the target disk.
The whole velocity ﬁeld, wall shear rates and mass transfer in the three impinging round jets were
compared. It was shown that at constant volumetric ﬂow rate, the use of an oriﬁce nozzle not only
improves wall shear rate, but also increases local and global mass transfer. The global mass transfer on
a target disk of a 3.2 Ddiameter is 25% and 31% higher for RO/H and RO/P nozzles, respectively, compared
to the reference CONV nozzle.
The oriﬁce nozzles generate narrower exit proﬁles relatively to the convergent nozzle. The vena con-
tracta effect in oriﬁce jets, more intense with RO/P than with RO/H, generates an increase of the exit cen-
terline velocity. The hemispherical surface of RO/H nozzle stretches the ﬂow at the exit and somewhatattenuates the vena contracta effect. The characteristic scale representation of the data conﬁrms the origin
of the observed differences between the three jets.
A link between the wall shear stress and the mass transfer is revealed. The wall shear rate and the mass
transfer are in a close relationship with the near ﬁeld ﬂow features, themselves affected by the nozzle
geometry. Time-resolved tomographic PIV technique reveals that the wall shear rate ﬂuctuation is related
to the dynamics of the jet coherent structures.
The instantaneous PIV ﬁelds indicates the formation of secondary vortices in the region where a sec-
ondary peak in local mass transfer emerges. The level of this secondary peak is sensitive to the nozzle
shape. The higher is the jet acceleration, the more intense is the level of the secondary peak.
/C2112015 Elsevier Inc. All rights reserved.
1. Introduction
A ﬂuid ﬂow released against a surface can transfer large
amounts of mass or thermal energy between the surface and the
ﬂuid. Enhanced heat and mass transfer for industrial devices relyessentially on impinging jet management. It provides an effective
and ﬂexible way for heat and mass transfer adjustment. A
thorough research, beginning with contributions of Gardon et al.
[1–3] , concerned the heat and mass transfer in impinging jets, and
an early observation has been made in [2]about the importance
of jet turbulence in heat transfer processes. It was shown that some
seemingly anomalous heat transfer phenomena can be explained
as effects of the turbulence occurring in jets. Turbulence is
http://dx.doi.org/10.1016/j.expthermﬂusci.2015.10.004
0894-1777/ /C2112015 Elsevier Inc. All rights reserved.⇑Corresponding author.
E-mail address: amina.meslem@univ-rennes1.fr (A. Meslem).Experimental Thermal and Fluid Science 70 (2016) 417–436
Contents lists available at ScienceDirect
Experimental Thermal and Fluid Science
journal homepage: www.else vier.com/locate/etfs

generated by the jet itself and by external disturbances and varies
signiﬁcantly with the nozzle shape, the upstream conditions and
the position within the jet. One decade after the observation of
Gardon and Akrifat [2], Popiel and Boguslawski [4]claimed that
nozzle exit conﬁguration is the most important factor affecting
the heat and mass transfer. Despite these ﬁrst very signiﬁcant
indications, there are only a few studies dedicated to heat and
mass transfer dependency on nozzle geometry. This section ﬁrst
reviews the literature regarding heat and mass transfers using
impinging jets and presents the objectives of the study.
1.1. Heat transfer in impinging jets
Lee et al. [5]compared three round oriﬁce nozzles with an exit
jet Reynolds numbers in a range from 10,000 to 30,000 and nozzle-
to-plate spacing Hin a range from 2 Dto 10 D, where Dis the exit
nozzle diameter. The oriﬁces were square-edged, standard-edged
and sharp-edged. The square-edged oriﬁce is straight hole with
straight-through edges (90 /C176corners at the hole). The standard
edged oriﬁce has square edged corners at the entrance, and bevel
edges at the outlet. The sharp-edged oriﬁce is beveled through
the entire thickness of the hole (with an angle of 45 /C176relative to
the axis normal to the oriﬁce plate). In the stagnation region, the
sharp-edged oriﬁce jet produces signiﬁcantly higher heat transfer
rates than either the standard-edged oriﬁce jet or square-edged
oriﬁce jet. The effect of nozzle exit conﬁguration on the stagnation
point heat transfer is more sensible at shorter nozzle-to-plate
spacing.The literature reveals that for high exit Reynolds numbers and
low nozzle-to-wall distances, two peaks are present on the radial
distributions of local Nusselt number Nu, produced by circular
impinging jets. The ﬁrst peak corresponds to the maximum of heat
transfer rate and occurs approximately at the nozzle radius. In
some investigations [5–8] , the location of the ﬁrst peak is observed
from r= 0.5 Dtor= 0.7 DforH<4D. This peak is attributed to the
high turbulence intensity at the nozzle edge and to the direct
impingement of large toroïdal Kelvin–Helmholtz (K–H) vortices
originated in the mixing region.
The secondary peak occurs at the radial distance from the stag-
nation point ranging from 1.2 Dto 2.5 D[5,7–9] . The second peak is
either attributed to the transition from laminar to turbulent
boundary layer in the wall jet region [3]or to the unsteady separa-
tion of the induced secondary vortices that form near the wall
under primary K–H vortices [10]. Carlomagno and Andrea [11] give
in their recent review of impinging jets a comprehensive descrip-
tion of secondary vortex dynamics. With increasing exit Reynolds
number, the location of the secondary peak of Numoves outwards
from the stagnation point and the peak height increases [5].
1.2. Wall shear stress and mass transfer in impinging jets
Whereas numerous papers were published on the Nusselt num-
berNudistributions generated by impinging jets, only a few stud-
ies were dedicated to the analysis of the corresponding wall shear
ratecdistributions [6,12–14] . Comparison of available data of Nu
andcreveals similarities in their distributions and in the numberNomenclature
A hydrodynamic parameter, m/C01s/C01
C bulk concentration of active ions, mol/m3
D nozzle jet exit nominal diameter
D⁄characteristic jet exit diameter, m
Dc diffusion coefﬁcient of active ions, m2/s
F Faraday constant, 96,485 C/mol
f#lens aperture
f vortex shedding frequency, Hz
H nozzle-to-plate axial distance, m
I limiting diffusion current, A
j ﬂux of active ions, mol/s
k coefﬁcient of mass transfer, k=I/SelnFc, m/s
Nu Nusselt number
n number of electrons involved in the electrochemical
reaction
Q reconstruction quality
Q0 volumetric ﬂow rate, m3/s
R electrode radius, m
r radial distance measured from stagnation point, m
Re Reynolds number based on the exit maximum velocity
and characteristic diameter, Re=W0D⁄/m
Reb Reynolds number based on the exit bulk velocity and
nominal diameter, Reb=WbD/m
Reh Reynolds number based on the exit maximum velocity
and the initial momentum thickness, Reh=W0h/m
Sc Schmidt number, Sc=m/D
Sel active surface of the electrode, m2
Sh Sherwood number based on the nominal diameter,
Sh=kD/Dc
Sh⁄Sherwood number based on the characteristic diameter,
Sh=kD⁄/Dc
Sth Strouhal number, Sth=fh/W0Ste external excitation Strouhal number, Ste=fD/W0
t time, s
U velocity in xdirection (normal velocity), m/s
V velocity in ydirection (spanwise velocity), m/s
Vr radial velocity, m/s
W velocity in zdirection (streamwise velocity), m/s
W0 exit maximum velocity, m/s
Wb exit mean or bulk velocity, m/s
(X,Y,Z) system of coordinates attached to the nozzle, m
Z⁄axis normal to target wall with origin on the target wall,
Z⁄=H/C0Z(m)
c wall shear rate, s/C01
cMES corrected wall shear rate, s/C01
k2 vortex detection criterion, s/C02
l dynamic viscosity, Pa s
q density, kg/m
s wall shear stress, s=lc,P a
s0ﬂuctuation of wall shear stress, Pa
m kinematic viscosity, m2/s
e discharge coefﬁcient
xr radial vorticity component obtained by TPIV, s/C01
xh azimuthal vorticity component obtained by TPIV, s/C01
xz axial vorticity component obtained by TPIV, s/C01
xY azimuthal vorticity component obtained by 2D classical
PIV, s/C01
h initial shear layer momentum thickness
D vector spacing
Subscripts
avg space average value
S stagnation point
c centerline value418 K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436

and the radial locations of their peaks. For high Reynolds number
equal to 41,600 and H<4D, two peaks are evident in c(or in wall
shear stress s=l/C1c) distribution [13]. Similarly to Nu-distribution
[5–8] , the ﬁrst peak in c-distribution appears at the distance from
the stagnation point ranging from r= 0.56 Dtor= 0.74 D, while the
second peak is located at r= 1.9 D[13,15] . The fact that peak loca-
tions in c-distribution are closely matching with those of Nu-
distribution suggests that the wall shear stress and the local heat
transfer are closely linked.
If the round impinging jet is a well-documented ﬂow for the
kinematic and the heat transfer behaviors, the literature review
reveals a lack of information on local mass transfer process in such
a ﬂow. The available few studies devoted to this subject have
mainly used the electrochemical limiting diffusion current tech-
nique. Vallis et al. [16] used this method to study the radial distri-
bution of mass transfer coefﬁcient produced by a convergent
impinging jet for exit Reynolds numbers ranging between 5000
and 30,000 and for a nozzle to plate distance ranging from 5 Dto
20D. The stagnation point mass transfer was found to be an increas-
ing function of the exit Reynolds number and decreasing function of
nozzle to plate distance. Based on the same technique, Kataoka et al.
[12] performed measurements of local mass transfer for impinging
convergent nozzle jet with an exit Reynolds number ranging from
4000 to 15,000 and a nozzle-to-plate distance ranging from 2 Dto
10D. The authors observed that the stagnation point mass transfer
reaches a maximum when the nozzle-to-wall distance was equal
to 6Dand noted that the mass transfer is enhanced owing to the
velocity turbulence in the momentum boundary layer. Chin and
Tsang [17] used the electrodiffusion method for the local mass
transfer measurement from an impinging jet to the stagnation
region on a circular disk electrode. The authors give the variation
of the limiting current density as a function of the dimensionless
electrode radius R/Dwithin a range from 0.02 to 3. It was found that
forR/Dfrom 0.1 to 1.0 for turbulent nozzle ﬂow and from 0.1 to 0.5
for laminar nozzle ﬂow, the electrode has a ‘‘uniform accessibility”
to the diffusion ions. Beyond this uniform accessibility region the
mass transfer rate was found to be a decreasing function of the lat-
eral coordinate.
The connection of the heat or mass transfer phenomena with
the large-scale structures which develop in the free jet region or
with the subsequent ﬂow dynamics in the stagnation and wall
jet regions is now recognized [7,10,18,19] . Therefore, the control
of large-scale structures in impinging jets is a key element in the
strategy of heat and mass transfer optimization and control. The
passive control based on nozzle geometry modiﬁcations is particu-
larly attractive because of easy implementation in industrial
applications.
Kristiawan et al. [20] have compared the performance of the
cross-shaped oriﬁce nozzle impingement jet with the reference
convergent nozzle in terms of stagnation point mass transfer. They
calculated mass transfer rate in the impingement region from the
measured wall shear rate in the vicinity of the stagnation point
under the assumption of uniform thickness of hydrodynamic and
concentration boundary layer.
Meslem et al. [21] have compared a round plate oriﬁce jet to a
reference convergent nozzle jet in terms of wall shear rate and
stagnation point mass transfer at a very low exit Reynolds num-
ber of 1360. The same method as in [20] has been used in [21] for
stagnation mass transfer calculation. It was concluded that the
oriﬁce jet enhances signiﬁcantly the stagnation mass transfer
compared to the reference convergent jet. The mass transfer dis-
tribution on the target and the global mass transfer were not
measured in the previous study. Hence, the global performance
of the oriﬁce jet relatively to the convergent jet remains
unproven.1.3. Objectives
The present investigation is the continuation of a previous
study [21]. It is considered herein a turbulent case with an exit
Reynolds number of 5620 rather than the very low exit Reynolds
number of 1360 considered in [23]. In our previous study, only
the stagnation mass transfer has been provided and has been
deduced from the slope of the radial wall shear rate distribution
[20,21] . In the present study, the radial mass transfer distribution
and the global mass transfer is measured directly. A round plate
oriﬁce, a reference convergent nozzle and an innovative geometry,
i.e., a round oriﬁce perforated on a hemispherical surface are con-
sidered to drive the jet ﬂow. According to our literature review, the
hemispherical nozzle has never been used for impinging jet gener-
ation. The hemispherical surface which is supporting the roundoriﬁce considered in the present study is intended to increase the
stretching of the shear layer at the jet exit, supposing to create a
more efﬁcient jet dynamics for wall skin friction and mass transfer
enhancement.
The study is conducted at constant exit area and constant volu-
metric ﬂow rate for the three jets. This speciﬁc choice is related to
the aimed Heating, Ventilation and Air Conditioning (HVAC) appli-
cation, and speciﬁcally to the Personalized Ventilation aspect [22].
For other applications where the energy conservation is required,
further investigations should be conducted at the same power
input. The ﬂow exit conﬁguration and the downstream ﬂow char-
acteristics are investigated along with the resulting mass transfer
distribution at the vicinity of the target plate. The nozzle-to-wall
distance is kept constant at H=2Dwith D= 7.8 mm for each noz-
zle. This particular distance was selected considering that it corre-
sponds approximately to the ﬁrst half of the potential core length
of a round free jet [23], where the K–H toroïdal vortices are well
formed and are still well deﬁned at the target placed at this
distance.
The wall shear stress and the mass transfer on the target plate
are measured using the electrodiffusion method (ED), the same
method as we have used before in [20,21] for wall shear stress
measurements. The electrodiffusion method (ED) is based on the
measurement of the limiting diffusion current ( I) on a working
electrode (probe) and is presented in detail in Section 2.3. In the
present study, this method is extended for local and global mass
transfer measurements. Phares et al. [14] made a critical survey
of different techniques used for the measurements of wall shear
stress and concluded that the ED method provides the greatest
accuracy of any indirect method. To our knowledge, Kataoka
et al. [6]were the ﬁrst to introduce this technique for the measure-
ment of wall skin friction generated by an impinging jet. This
method provides information on the wall shear rates whereasthe velocity ﬁeld is captured using Particle Image Velocimetry
(PIV). Both techniques (ED and PIV) are complementary as the
PIV fails at the vicinity of the wall due to the laser scattering by
the solid surface.
Particle Image Velocimetry (PIV) is used in this study to cap-
ture velocity ﬁelds in the free and the near wall jet regions of
the impinging jet. Recall that velocity ﬁelds in impinging jet ﬂow
have been measured for the ﬁrst time by Landreth and Adrian
[24]. Two PIV techniques were used in the present study: (i)
the classical 2D PIV providing high spatial resolution in a plane,
allowing the investigation of the mean ﬂow ﬁelds in the three
jets; (ii) the time-resolved tomographic PIV applied in the refer-
ence case (CONV nozzle) allowing a 3D vision of the ﬂow.
Although the spatial resolution is lower compare to the 2D clas-
sical PIV, the dynamic of the coherent ﬂow structures of the con-
vergent jet is captured and related to the wall shear rate
ﬂuctuation.K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436 419

The following is structured within two main sections. Section 2
presents the employed experimental procedures and Section 3is
dedicated to results analysis.
2. Experimental procedures
2.1. Experimental setup and geometry of nozzles
The experiments are conducted in a liquid–liquid jet impinging
orthogonally onto a wall. A schematic diagram of its generation in
a reservoir is shown in Fig. 1 a. A gear pump (Ismatec with a GJ-N23
head) draws the liquid from a reservoir and delivers it to a nozzle.
The liquid jet issued from the nozzle impinges a circular target disk
provided with six electrodes ( Fig. 1 b) which serve as the probes for
electrodiffusion measurements. The temperature of liquid is con-
trolled by a cooling coil within ±0.2 /C176C.
The nozzle is screwed to a 200 mm length stainless steel tube
with inner and outer diameters of 15 and 20 mm, respectively. A
honeycomb manufactured of a 7 mm thick disk by drilling 17 holes
with a diameter of 2 mm was ﬁtted in the tube inlet. The nozzle
assembly was located in a support which allowed vertical move-
ment for accurate alignment of the nozzle axis with the electrodes
center. The reservoir was placed on a sliding compound table
(Proxxon KT 150) which allowed movement in the axial and trans-
verse direction relative to the nozzle with a precision of 0.05 mm.
The target was manufactured of a Plexiglas disk with a diameter
of 100 mm and a thickness of 17 mm by ﬁrst drilling holes to insert
the electrodes. The platinum foil with a diameter of 50 mm and a
thickness of 50 lm(Fig. 1 b) was assembled centrally with the disk
using Neoprene glue. Holes with a diameter 0.7 mm were drilledthrough the platinum foil as a continuation of the holes in the disk.
The electrodes were manufactured of a 0.5 mm platinum wire
which was coated electrophoretically using a deposit of a poly-
meric paint. After soldering the connection cables, the electrodes
were glued with an epoxy resin into the disk, so that the tops of
the platinum wires just projected above the platinum foil. The
wires were then rubbed down ﬂush with the surface of the plat-
inum foil using progressively ﬁner grades of emery paper. The last
emery paper had a grit size of 10
lm. The whole surface was then
polished using a ﬁne dental paste. The resulting surface roughness
was about 0.11 lm which is much less than the Nernst diffusion
layer thickness estimated at 10 lm. Before each series of test, the
electrode surfaces were polished and rinsed with distilled water.Nickel sheets introduced in the reservoir with an area of 0.15 m2
was used as the auxiliary electrode (anode). The area of the nickel
sheets was 76 times superior to the platinum disk area. To measure
only the phenomena which happen on the measuring electrode
(cathode), the area of the auxiliary electrode (anode) should be
large enough. Measured currents in our experiments did not
change if the anode area was slightly varied which was the proof
of the sufﬁciency of anode area.
The test ﬂuid was an aqueous solution of 5 mol/m3potassium
ferricyanide, 25 mol/m3potassium ferrocyanide and 1.5% mass
potassium sulfate as supporting electrolyte. The solution had a
density q= 1006 kg/m3, kinematic viscosity m= 1.06 /C110/C06m2/s
and diffusivity DC= 7.5 /C110/C010m2/s at 20 /C176C. The resulting Schmidt
number was 1410.
In this study, three round nozzles ( Fig. 2 ) having the same exit
diameter D= 7.8 mm are compared: a convergent nozzle (CONV in
Fig. 2 a), a round oriﬁce perforated on a ﬂat plate (RO/P in Fig. 2 b)
and a round oriﬁce perforated on a hemisphere (RO/H in Fig. 2 c).
For RO/H ( Fig. 2 c), the considered diameter Dcorresponds to the
projection on the plane of the curved oriﬁce. The diameter corre-
sponding to the curved free area of RO/H is equal to 8.0 mm. The
ﬂat and the curved oriﬁces (RO/P and RO/H, respectively) had the
same thickness e= 0.5 mm ( Fig. 2 b and c). A convergent nozzle
(Fig. 2 a) had a conical shape with an area contraction 4:1 on a
length of 17 mm.
The exit Reynolds number based on the diameter Dand the jet
bulk velocity Wb(Wb=4Q0/pD2= 0.77 m/s) was Reb= 5620. The
distance Hbetween the jet exit and the target wall was kept
constant, H=2D, for all the measurements. The coordinate system
(r,Y,Z) attached to the nozzle is shown in Fig. 3 . As sketched in this
ﬁgure, the ﬂow ﬁeld may be divided into several regions. In the
neighborhood of the stagnation point S, the ﬂow spreads in radial
directions parallel to the wall. The development of the impinging
jet ﬂow ﬁeld near the wall is typically divided in two regions:
the stagnation region associated with the turning of the mean ﬂow,
r/D< 1, and the radial wall jet region, r/D>1 .
2.2. PIV measurements
2.2.1. Classical 2D PIV Measurements
Flow analysis has been carried out using PIV measurements.
The PIV system, from the manufacturer Dantec, includes a Quantel
BigSky 200 mJ double-pulsed Nd:Yag laser and a FlowSense EO
12 3 4 56
Platinum disc φ503.4 3.4 3.9 5 55BP AP5 10
6 platinum electrodes φ0.5(a)(b)
Fig. 1. (a) Diagram of apparatus: 1. target disk with electrodes, 2. tube with nozzle and honeycomb, 3. pump, 4. reservoir, 5. compound table, 6. nozzle holder , 7. cooling coil,
8. laser source with laser sheet in the mild plane of the nozzle, 9. FlowSense EO camera and (b) target disk with electrodes row: 1–6 electrodes /0.5 mm. APand BPare the
limits of stagnation point displacement.420 K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436

(CCD) camera of 2048 /C22048 pixels resolution with pixel size of
7.4/C27.4lm2. The total ﬁeld of view is about 2 D/C26Dto cover free
and wall jet regions ( Fig. 3 ) with an average resolution of 35.6 pix-
els/mm. The light sheet optics produces a laser sheet of less than
1 mm in thickness. The maximum acquisition frequency of the
PIV system is 15 Hz which is lower than the shear layer frequency
of considered jets. The seeding particles are glass hollow spheres of
9–13lm in diameter and 1.1 g/cm3in density. For each experi-
ment, 500 couples of images are acquired. The recordings are ana-
lyzed through two different windows using DynamicStudio Dantec
software. Firstly, the velocity distribution in the total ﬁeld of view
(2D/C26D) is calculated using an adaptive multi-grid correlation
algorithm [25] handling the window distortion and sub-pixel win-
dow displacement (128 /C2128, 64 /C264, and 32 /C232 pixels) and
50% overlapping. The resulted spatial resolution is 0.11 D/C20.11 D.
Secondly, to get a better resolution of velocity vectors in the
radial wall jet region ( Fig. 3 ) the same algorithm is used with a ﬁnal
grid composed of 8 /C264 pixels interrogation windows and 50%
overlapping. Hence, in the radial wall jet region the spatialresolution is 0.03 D/C20.23 D. The prediction–correction validation
method of multi-grid algorithm identiﬁed on average less than1% erroneous velocity vectors, which are replaced using a bilinear
interpolation scheme. For all the experiments, the uncertainty of
the measurement due to displacement error was estimated using
the theoretical analysis of Westerweel [26]. When adding the glo-
bal bias errors, the total uncertainty is estimated to be in the range
of 2–3.5% outside the boundary layer. The uncertainty rises near
the impinging plate due to laser scattering, so that the boundary
layer is not accessible using PIV technique. This difﬁculty is
bypassed using another measurement technique, which is the elec-
trodiffusion (ED) method described in Section 2.3.
2.2.2. Time-resolved tomographic PIV measurement
To get three-dimensional jet velocity ﬁelds and its dynamics,
the time-resolved tomographic particle image velocimetry tech-
nique (TPIV) is used. This technique provides a spatial resolution
fourteen times lower compared to the classical 2D PIV. However,
its use allows the analysis of the possible link between the jet
CONV (b) RO / P
φ26φ15φ 7.8
3017 2 1
φ7.8 φ26φ15 φ211.6 0.5
5
171
2 3
φ7.8
φ15.2
φ19.4
φ22.4RO / H
0.5 2
12φ15
φ20 (c) (a)
Fig. 2. Sketch of nozzles: (a) 1 – convergent nozzle (CONV), 2 – tube; (b) 1– Round Oriﬁce on Plate (RO/P), 2 – tube, 3 – sleeve nut; (c) 1 – Round Oriﬁce on Hemispher e (RO/
H), 2 – tube.
Impingement region
X, r
WU
Z*
rZY Round nozzle
Free jet region
Radial wall jet
region D
Deflection region
δH
UmaxSWb
Fig. 3. Schematic description of round impinging jet on a ﬂat plate and associated system coordinates. The stagnation point is designated by S.K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436 421

dynamics and the wall shear rate ﬂuctuation. For brevity, the TPIV
measurements are given for the convergent reference jet and the
conclusions are extensible to the other considered two jets.
The TPIV system consisted of high-repetition rate laser and
three high-speed CMOS cameras (Phantom V9.1, 1600 /C212
00 pixel2, 12 bit) equipped with Nikon objectives of 105 mm focal
length. The sketch of the experimental setup is shown in Fig. 4 .
Two cameras were arranged in fowardscatter orientation with
an angle approximately 20 /C176relative to the normal of the viewing
face of the light volume. The third camera was oriented normal
to the viewing face of the light volume. Scheimpﬂug adapters were
used to align the mid-plane of the illuminated area with the focal
plane and the lens apertures were ﬁxed to f#= 16. The test ﬂuid
was seeded with titandioxide ﬁlled polyamide12 ﬁne powder par-
ticles of 20 lm mean diameter. The illumination was provided by a
pulsed, dual-cavity Nd:YLF laser with a power of 2 /C210 mJ. A beam
expander (volume optics of LaVision), composed of two cylindrical
lenses and a rectangular aperture, was used to generate a rectangu-
lar light volume. In order to increase the light, a mirror was
inserted at the bottom of the reservoir to reﬂect the laser beam
back to the measurement volume. The effective measurement vol-
ume was 2 D/C26D/C25Dwith an average resolution of 29.75 pixels/
mm. The particle image density was approximately 0.04 particles/
pixel. The imaging system was calibrated by the two-level spatial
target (Type 7 target in the LaVision Software). In each of the
two calibration planes, a third order polynomial ﬁt was used to
determine the transformation matrix which matched the viewing
planes of the three cameras with an accuracy of approximately
0.18 pixels.
A number of 866 couples of images were recorded at a fre-
quency of 1000 Hz with laser time interval dt¼250ls:
Prior to the particle volume reconstruction, the original images
were preprocessed to improve the reconstruction process. The
main images preprocessing steps were described by Hain et al.
[27]. A sliding minimum was subtracted from the images to reduce
the background noise. A constant background due to laser
reﬂecting or dirty Plexiglas was removed through an algorithmicmask, thus increasing the number of zero voxels. The particle
image intensities were normalized by local image intensity, lead-
ing to similar particle intensity magnitude for the three cameras.
Gaussian smoothing by 3 /C23 kernel was also applied. A geometric
mask was used to deﬁne the boundaries of the calculated region.
The 3D particle positions within the volume were reconstructed
using seven iterations of the Fast Multiplicative Algebraic Recon-
struction Technique (Fast MART) algorithm provided by the LaVi-
sion software Davis 8.2.1. The volume was discretized with
520/C21544 /C21188 voxels and a pixel to voxel ratio of 1. The vol-
ume self-calibration [28] showed an initial particle based calibra-
tion error of up to 2–3 pixels. After self-calibration correction the
errors are reduced to below 0.2 pixels. At the present particle
image density and number of cameras, the reconstruction quality
Qis recognized to be above 0.75 [29,30] . In this condition, the
reconstruction should be assumed to be sufﬁciently accurate [30].
The vector ﬁelds were obtained by performing multi-pass direct
cross-correlation using a ﬁnal interrogation volume of
64/C264/C264 voxels (0.28 D/C20.28 D/C20.28 D) and 75% overlap
between adjacent interrogation boxes. The resulting vector spacing
in each 3D velocity distribution is 0.07 D. The spatio-temporal noisy
ﬂuctuations were reduced by using a second order polynomial ﬁl-
ter over a kernel size of 5 grid nodes in space and 5 steps in time
[7]. The spatial resolution of the ﬁltered data remained equal to
0.28 Dwhereas the temporal resolution was reduced to 4 m s. The
corresponding frequency of 250 Hz was approximatively ﬁve times
greater than the vortex shedding frequency (53 Hz) of the studied
jet ﬂow.
The local mass conservation principle was used in numerous
studies [7,31,32] to estimate the random velocity error in tomo-
graphic PIV measurements. In fact, when the ﬂow is incompress-
ible, the divergence of the 3 Dvelocity ﬁelds should be zero.
However, this is not the case when there are measurement errors
and numerical truncation in the spatial discretization. When a sec-
ond order central difference scheme is used to calculate the veloc-
ity gradients, assuming uniform vector spacing D, and uniform
3PEGASUS-PIV
12
2456
77
7
Fig. 4. Schematic of the experimental setup of tomographic PIV: 1. laser head, 2. mirror, 3. beam expander with rectangular slit, 4. target disk, 5. tube with n ozzle, 6. nozzle
holder, 7. phantom V9.1 cameras, 8. laser beam.422 K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436

random error in all directions, the velocity gradient error is given
by:
d@u0
i
@xi/C18/C19
¼ﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ
3
2D2s
dðuȚð 1Ț
where d@u0
i
@xi/C16/C17
is the RMS ﬂuctuation divergence and d(u) the random
error.
In this study the mean random error was found to be around
0.44 pixel, corresponding approximatively to 4.9% of the stream-
wise velocity in the free jet region. A random error varying
between 0.60 and 0.42 pixel were reported by Atkinson et al.
[31] and Buchner et al. [32] in turbulent boundary layer. The mean
error of this measurement is in the same order of magnitude.
2.3. Electrodiffusion technique for wall shear rate and mass transfer
measurements
2.3.1. Wall shear rate
The electrodiffusion method (ED) for wall shear rate measure-
ment consists in using a working electrode ﬂush-mounted on the
wall to measure the limiting diffusion current. This technique
was extensively described in Kristiawan et al. [20], El Hassan
et al. [18] and Meslem et al. [21]. Thus, only a brief summary will
be given here. The method is based on electrochemical redox reac-
tion whose rate is very fast but the electric current is limited by the
convective mass transfer on the measuring electrode (probe). For
the total current through a circular electrode in a viscosimetric
ﬂow with a uniform wall-shear rate cMES, the formula correspond-
ing to the Leveque’s equivalent equation for heat transfer was
established by Reiss et al. [33] and is given by:
I¼0:884p
31=3Cð4=3ȚnFCc1=3
MESD2=3
CR5=3ð2Ț
where Cis the bulk concentration, DCthe diffusion coefﬁcient
of active species, Fthe Faraday constant, nthe number
of electrons involved in the electrochemical reaction
Fe CNðȚ3/C0
6țe/C0() Fe CNðȚ4/C0
6/C16/C17
,Rthe radius of the electrode and
Cthe gamma function.
Eq.(2)was used to calculate the wall shear rate from the mea-
sured limiting diffusion currents for steady and quasi-steady ﬂows.
In practice the ﬂows studied are often unsteady. Therefore, the wall
shear rate measured using Eq. (2)do not take into account the
unsteady nature of the diffusion boundary layer on the working
electrode. This inertia effect acts as a ﬁlter and lead to an underes-
timation of the measured current ﬂuctuations. A corresponding
correction based on the dynamic theory of the electrodiffusion
shear stress probe was proposed by Sobolik et al. [34]:
c¼cMES1ț0:45D/C01=3
CR2=3c/C05=3
MESdcMES
dt/C20/C21
ð3Ț
where cMESis the wall shear rate calculated from measured currents
using Eq. (2).
Let us recall that the basic assumptions for the derivation of the
Leveque relationship (Eq. (2)) is that the probe is in a ﬂow with
parallel streamlines and uniform wall-shear rate c. In the case of
impinging jet, the streamlines in the wall vicinity spread radially
from the stagnation point S(Figs. 3 and 5 ) and the wall-shear rate
increases with r. Kristiawan et al. [20] have determined the draw-
backs of application of this equation in the stagnation region for an
electrode having a radius R= 0.25 mm. At a radial distance
r= 1 mm from the stagnation point S, the authors have found
2.1% error in wall shear rate. Taking into account the others param-
eters which can affect the wall shear rate, Meslem et al. [21] con-clude that the error on the wall shear rate using Eq. (2)is less than
5% for rP1m m .
2.3.2. Mass transfer
As outlined before, the ED method is extended in the present
study to local and global mass transfer measurements.
The limiting diffusion current is controlled by the transfer of
active species to the working electrode. Under the assumption that
the transfer resistance on the auxiliary electrode is negligible in
comparison with that on the working electrode, the coefﬁcient of
mass transfer can be calculated using the following relation:
k¼j
SelC¼I
SelnFCð4Ț
where j¼RR
Sel/C0DC@C
@z/C3/C0/C1
z/C3¼0dsis the ﬂux of the active ions, Selis the
active surface of the working electrode.
The Sherwood number is then deﬁned by:
Sh¼kD
DCð5Ț
Local and instantaneous wall shear rate and mass transfer were
acquired separately. During the local wall shear rate measure-
ments, the platinum wires worked as the cathode and the platinum
disk ( Fig. 1 b) with the nickel sheets as the anode. During the local
and global mass transfer measurements the platinum wires and
the platinum disk worked as the cathode and the nickel sheets as
the anode. In this case, the platinum disk was maintained at the
same potential as the worked electrodes; whereas the platinum
disk was used to measure the global mass transfer, the platinum
wires were used to measure the local mass transfer.
2.3.3. Measurements procedure
Local and instantaneous wall shear rate and mass transfer were
acquired separately using the electrodiffusion method (ED)
described above in Sections 2.3.2 and 2.3.3 . The radial distributions
of the wall shear rate and local mass transfer were obtained by
moving the stagnation point Shorizontally in the range limited
by the points APand BPon the target shown in Fig. 1 b. Forty three
displacements of the stagnation point with a step of 0.5 mm were
performed to well capture the details of wall shear rate and local
mass transfer proﬁles. Thereby, several values of the two quantities
(wall shear rate and local mass transfer) measured by different
electrodes at similar radial distances from the stagnation point
were obtained.
The electrodes were calibrated before and after every series of
measurements using a transient voltage step [35]. The result of this
calibration, i.e. the Cottrell coefﬁcient, which is proportional to
(CSelD1/2), had a variation of about ±4%. The estimated errors were
±8% and ±4% for the wall shear rate and the Sherwood number
respectively.
3. Results and discussion
3.1. Mean ﬂow characteristics
Table 1 gives the initial conditions of the three studied ﬂows. To
take into account the vena contracta effect, which takes place in the
oriﬁce jet, additional parameters based on the characteristic jet
diameter D⁄were introduced. The characteristic diameter is
deﬁned as follows [36]:
D/C3¼Dﬃﬃﬃep
ð6Ț
where e=Wb/W0is the discharge coefﬁcient.
The obtained discharge coefﬁcients are 0.94, 0.72 and 0.64 for
the CONV, RO/H and RO/P nozzle, respectively. A value of 0.61 isK. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436 423

usually adopted for a sharp-edged oriﬁce [36]. In the case of an
impinging jet issued from multiple sharp-edged oriﬁces Geers
et al. [37] used a value of 0.71.
To normalize the data presented in this section, two groups of
parameters were considered. The ﬁrst group includes the nominal
diameter D, the jet bulk velocity Wband the corresponding Rey-
nolds number Reb,and refers to ‘‘ﬁrst normalization”. The second
group comprises the characteristic diameter D⁄, the jet maximum
velocity W0and the corresponding Reynolds number Re, and refers
to ‘‘second normalization”.
Fig. 5 presents the mean velocity ﬁeld of each round jet from
classical 2D PIV measurements, superimposed to the correspond-ing contours of the azimuthal vorticity in the longitudinal plane.
On the bottom of this ﬁgure, a zoom on the recirculation region
is given for each jet in the window 0 6r/D61 and 1.5 6Z/D62.0.
The entire ﬁelds ( Fig. 5 a1, b1, and c1) clearly show that the free
jet region is more contracted in RO/H and RO/P cases ( Fig. 5 b1, c1)
than in CONV case ( Fig. 5 a1). From a detailed comparison of the
oriﬁce jets, it can be concluded that the RO/P nozzle generates
greater contraction than RO/H nozzle. As shown in Fig. 5 a2, b2
and c2, the contracted free jet region leads to a contracted deﬂec-
tion region.
For an axial position Z, the extent of the radial jet expansion in
the free jet region is deﬁned by the jet thickness r0.1, which is the
Z/Dr/D
012-3-2-1012-500 -250 0 250 500RO / P
Z/Dr/D
012-3-2-1012-500 -250 0 250 500RO / H
Z/Dr/D
012-3-2-1012-500 -250 0250 500CONV
Z/Dr/D
1.5 2011m/s
Z/Dr/D
1.5 2011m/s
Z/Dr/D
1.5 2011m/s
Fig. 5. Mean vector ﬁeld ðWe Z!țUer!Țand azimuthal vorticity xY¼@U
@Z/C0@W
@r/C0/C1contours (color map) in longitudinal plane Y= 0 of impinging jet – data from classical 2D PIV: (a)
convergent nozzle (CONV), (b) Round Oriﬁce on Hemisphere (RO/H), (c) Round Oriﬁce on Plane (RO/P); (1) entire ﬁeld, (2) zoom on deﬂection region.
Table 1
Initial conditions of the three studied ﬂows.
Nozzle W0(m/s)W0
WbUmaxðȚPeak
WbD⁄(mm) Re¼W0D/C3
mh0(mm) f(Hz) Sth=fh0/W0
CONV 0.82 1.06 0.93 7.6 5850 0.192 53 0.012
RO/H 1.07 1.38 1.20 6.6 6680 0.168 66 0.010
RO/P 1.21 1.57 1.35 6.2 7100 0.163 76 0.010424 K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436

radial position in the jet where the axial velocity Wtakes the value
0.1Wc;Wcis the centerline velocity at the same axial position Z.
The streamwise evolution of the normalized jet thickness, r0.1/D,
is plotted in Fig. 6 for each jet. As expected, the convergent jet is
more expanded than the oriﬁce jets ( Fig. 6 a). The comparison of
the two oriﬁce jets conﬁrms that the RO/H nozzle attenuates the
vena contracta effect, which characterizes oriﬁce jets. When using
the second normalization and considering the characteristic diam-
eter D⁄as characteristic length ( Fig. 6 b), the jet thickness of all
three considered jets collapse well in the free jet region for Z/
D⁄61.5. In this normalization, the nozzle to plate distance Htakes
different values as a function of the level of vena contracta effect;
that is H= 2.1 D⁄, 2.4 D⁄and 2.5 D⁄for the CONV, RO/H and RO/P
nozzle jets, respectively. Near the wall, for Z/D⁄> 1.5, the jet thick-
ness shows a different trend for the three jets due to different val-ues of H/D
⁄; closer is the wall, faster is the jet deﬂection, leading to
different jet thicknesses r0.1/D⁄.
Streamwise mean velocity changes along the jet centerline is
given in Fig. 7 . As evidenced by Fig. 7 a, the axial velocity achieves
zero at the stagnation point S. The value of jet bulk velocity Wb
reported in this ﬁgure highlights, when compared to the maximum
centerline velocity W0, the level of ﬂow acceleration in each jet.
The most accelerated ﬂow is given by RO/P nozzle, followed by
RO/H nozzle and then CONV nozzle (see also Table 1 where the val-
ues of W0/Wbare provided). When the maximum velocity W0and
the corresponding characteristic diameter D⁄are used as normal-
ized parameters for each jet ( Fig. 7 b), the velocity decay W/W0is
correlated to H/D⁄as was the case for the jet thickness r0.1/D⁄
(Fig. 6 b). However, if the origin of the jet axis is positioned onthe target wall ( Fig. 7 c), the damping effect exerted by the wall
is almost similar for the three jets, leading to nearly identical
velocity changes.
The differences in jet contraction are visible also on the stream-
wise velocity proﬁles ( Fig. 8 a1 and b1), and on transverse velocity
proﬁles as well ( Fig. 8 c1).
In the free jet region, at Z= 1.7 D(Fig. 8 b), axial velocity proﬁle
exhibits an ‘‘M shape” whereas at Z= 0.5 D(Fig. 8 a) the proﬁle is
ﬂat. Hence, ﬂow acceleration in the outer edge of the shear layer
is a result of jet/wall interaction. Before impinging the wall, the
jet accelerates in the outer edge ( Fig. 8 b1) and decelerates on the
axis as visible on streamwise velocity changes along the jet center-
line ( Fig. 7 a).
Considering the same positions ( Z= 1.7 Dand Z= 0.5 D), the sec-
ond normalization is applied to the data of Fig. 8 a1, b1 and c1, and
the results are plotted in Fig. 8 a2, b2 and c2. Near the jet exit at
Z= 0.5 D, the proﬁles collapse well. However, when approaching
the wall at Z= 1.7 D, a noticeable difference in magnitude of axial
velocity ( Fig. 8 b2) and radial velocity ( Fig. 8 c2) is visible between
the three jets, due, as pointed before, to different nozzle-to-plate
distances H/D⁄.
InFig. 8 a3, axial velocity proﬁles at Z/D⁄= 0.5 (i.e. at Z= 0.49 D,
0.42 D, 0.40 Dfor CONV, RO/H and RO/P, respectively) are plotted
using the second normalization. As for Z/D= 0.5 ( Fig. 8 a2), the pro-
ﬁles collapse well, meaning that apart the vena contracta effect, the
jet exit velocity proﬁles are similar for the three jets.
To compare jets proﬁles before jet impingement at the same
relative distance from the target wall, additional proﬁles were
extracted at constant Z⁄/D⁄equal to 0.3, that is for Z= 1.71 D,
0.40.50.60.70.80.91.01.1
0.0 0.5 1.0 1.5 2.0CONV
RO/H
RO/P
0.40.50.60.70.80.91.01.11.2
0 . 00 . 51 . 01 . 52 . 02 . 5CONV
RO/H
RO/P
(a) (b)
Fig. 6. Growth of the jet thickness; (a) using the ﬁrst normalization; (b) using the second normalization.
0.00.40.81.2
0 . 00 . 51 . 01 . 52 . 0CONV
CONV-TPIV
RO/H
RO/P SWb= 0.77 m/s
0.00.30.50.81.0
0.0 0.5 1.0 1.5 2.0 2.5CONV
RO/H
RO/P
0.00.30.50.81.0
0.0 0.5 1.0 1.5 2.0 2.5CONV
RO/H
RO/P
(a) (c) (b)
Fig. 7. Streamwise mean velocity changes along the jet centerline; (a) with dimensional velocities; (b) using the second normalization; (c) using the secon d normalization
and the origin of the jet axis positioned on the target wall.K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436 425

1.75 D, 1.76 Dfor CONV, RO/H and RO/P, respectively ( Fig. 8 b3 and
c3). In this case, almost no difference appeared between the three
jets, meaning that the jet scales W0and D⁄taking into account jet
acceleration and jet contraction introduced by the round nozzle
shape, are sufﬁcient to model ﬂow modiﬁcation. This should
remain valid as long as H/D⁄values are close, which is the case
in the present study ( H/D⁄vary from 2.1 to 2.5).
As outlined earlier, time-resolved tomographic PIV (TPIV)
measurements were performed in the convergent reference jet to
capture the jet ﬂow dynamics. The validation of the TPIV measure-
ments consists in their comparison in Figs. 7 a and 8a1, b1, c1 to
those obtained with the 2D PIV. While rather good agreement
between axial mean velocity proﬁles was observed in the jet core
region ( Figs. 7 a and 8a1), discrepancies appeared in the shear layerand ﬂow deﬂection regions. At axial position Z= 1.7 D, where the
ﬂow defects radially and creates a strong gradient region owing
to the presence of the target wall, this discrepancy is about 18%.
This could be attributed to the difference of the spatial resolution
between the two measurement techniques. Indeed, the 2D PIV
measurements were obtained with a spatial resolution of
0.11 D/C20.11 D/C20.13 D(the third direction corresponds to the
1 mm thickness of the laser) while the spatial resolution of the
3D PIV was 0.28 D/C20.28 D/C20.28 D, which is fourteen times greater
than that in 2D PIV measurements. Hence, in the regions of strong
gradients, the 3D PIV leads to an underestimation of velocities dueto their spatial integration. Anyway, comparisons are satisfactory,
which gives conﬁdence in the tomographic PIV used in the present
study.1 1 1
Fig. 8. Streamwise velocity proﬁles (a, b) and transverse velocity proﬁles (c) at different locations: (1) with dimensional velocities; (2) using the secon d normalization at Z/D
constant; (3) using the second normalization at Z/D⁄constant (a3) or at Z⁄/D⁄constant (b3, c3).426 K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436

Fig. 9 gives the changes of maximum velocity Umaxalong the
wall. The peak level of Umaxis also linked to the jet acceleration
level. However, the curves have similar shapes and the position
of the peak of Umax,r= 0.95 D, seems to be insensitive to the con-
traction level of the jet ﬂow ( Fig. 9 a). When Umaxis normalized
byW0(Fig. 9 b), radial distributions of the maximum velocity in
the wall jet region collapse into a single curve. The comparison
of the obtained dimensionless distributions to those of round jets
from the literature [15,38,39] at a same normalized nozzle-to-
plate distance, H/D= 2, suggests a possible effect of jet exit Rey-
nolds number on the level of Umax/W0. However, the radial position
of the peak value remains almost unchanged with different values
of Reynolds number and different round nozzle geometries. In fact,
the round nozzle in [15,39] is a long pipe and a convergent nozzle
connected to a short pipe in [38].
3.2. Unsteady ﬂow characteristics
Prior to the analysis of the statistical properties of wall shear
rate and mass transfer, the unsteady features of the ﬂows were
conducted based on electrodiffusion signals. These signals giveinformation on the unsteady futures of impinging jet at the target
which are expected to be related to the jet dynamics in its free
region before impinging the wall. In the case of the reference con-
vergent jet, we seek this possible link by the comparison of domi-
nant frequencies in TPIV and ED signals.
Fig. 10 provides the power spectra of electrodiffusion signals
plotted against the non-dimensional frequency given by the Strou-
hal number Sth. The Strouhal number is deﬁned using the jet max-
imum velocity W0and the jet initial momentum thickness h0
(Table 1 ) obtained for each jet using the mean streamwise velocity
proﬁle at Z/D= 0.25. The power spectra were obtained by discrete
Fourier transform of the electrodiffusion time-series signals. For
clarity of representation, every spectrum is shifted two decades
downwards with respect to the previous one.
For the radial location in the range r=/C00.4D–1D, the spectra are
displayed a hump centered on Sth= 0.012 for CONV nozzle jet, and
onSth= 0.010 for RO/H and RO/P nozzle jets. The corresponding
frequencies are reported in Table 1 .
In our previous work [21] that considered two of the nozzles of
the present study at a lower Reynolds number Reb= 1360, the nor-
malized characteristic frequency of the wall shear stress ﬂuctua-0.20.40.60.811.2
0.5 1 1.5 2 2.5 3 3.5CONV
RO / H
RO / P
0.20.40.60.811.2
0.5 1 1.5 2 2.5 3 3.5Sengupta and Sarkar [38], Re = 13300, H = 2D
Tummers et al. [15], Re=23000, H = 2D
Xu and Hangan [39], Re= 23000, H = 2D
Present study,
Re = 5620, H = 2DCONV
RO / H
RO / P
(a) (b)
Fig. 9. Radial distribution of maximum radial velocity above the wall. (a) Dimensional values; (b) dimensionless values and comparison to the literature – t he round nozzle in
[15,39] is a pipe and in [38] a convergent connected to a short pipe.
1.E+001.E+011.E+021.E+031.E+041.E+051.E+061.E+071.E+081.E+091.E+101.E+111.E+121.E+131.E+14
0.001 0.01 0.1PSD
Stθ= fθ0/ W0r= -0 . 4 Dr= 0 . 5 Dr= 1 . 0 Dr= 1 . 6 Dr= 2 . 2 Dr= 2 . 9 D
0.0120.0120.012
1.E+001.E+011.E+021.E+031.E+041.E+051.E+061.E+071.E+081.E+091.E+101.E+111.E+121.E+131.E+14
0.001 0.01 0.1PSD
Stθ= fθ0/ W0r= -0 . 4 Dr= 0 . 5 Dr= 1 . 0 Dr= 1 . 6 Dr = 2.9 D
0.0100.0100.010r = 2.2 D
0.0100.0100.010
1.E+001.E+011.E+021.E+031.E+041.E+051.E+061.E+071.E+081.E+091.E+101.E+111.E+121.E+131.E+14
0.001 0.01 0.1PSD
Stθ= fθ0/ W0r= -0 . 4 Dr= 0 . 5 Dr= 1 . 0 Dr= 1 . 6 Dr= 2 . 2 Dr= 2 . 9 D
0.0100.0100.010CONV RO / H RO / P
Fig. 10. Power spectra of wall shear rate signals at different radial locations of the three jets – every spectrum is shifted two decades downwards with respect to the previous.
The vertical dashed line indicates the normalized characteristic frequency.K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436 427

tions was 0.023 and 0.014 for the CONV nozzle and the RO/P noz-
zle, respectively. At the higher Reynolds number Reb= 5620 con-
sidered here, the normalized characteristic frequency is 0.012 for
the CONV nozzle and 0.010 for the RO/P nozzle. Although normal-
ized characteristic frequencies values obtained in both studies falls
in the range 0.009–0.023 given in the literature [40], they seem
Reynolds number dependent and the dependency seems more
important for the convergent nozzle compare to oriﬁce nozzle.
Husain and Hussain [41] observed for a given nozzle a decrease
of the normalized characteristic frequency with increasing the
shear layer Reynolds number Reh.
In our case, Reh= 39 in CONV and 42 in RO/P for Reb= 1360 to be
compared to Reh= 148 in CONV and 185 in RO/P for Reb= 5620.
Hence, the increase of Rehis more important for RO/P (4.4 times)
compared to RO/H (3.8 times) which could explain the differencein the changes of the corresponding St
h.
The frequencies captured using the power spectra of the elec-
trodiffusion signals are conﬁrmed by the autocorrelation proﬁles
displayed in Fig. 11 aa tr=1D. As it is well known, the autocorrela-
tion and power spectrum have an inverse spreading relationship
since both of these functions are Fourier transform pairs and the
autocorrelation shifts out the strongest underlying event [42].
Fig. 11 b compares for the CONV nozzle jet, the autocorrelation
coefﬁcient from ED to the one from TPIV. The TPIV signal is the
time evolution of the transverse jet velocity Uat the position
Z/D= 1.7 and r/D= 0.6. One can note that the two signals exhibit
a same period. As it will be shown later on, the captured frequency
corresponds to shedding phenomenon of the toroidal Kelvin–
Helmholtz (K–H) structures.
The presence of the shedding frequency of K–H vortices in the
ED signal is related to the imprint of these vortices on the target.Hence, the fundamental frequency in the ED signal for each jet
(Fig. 10 ) corresponds to the trace of the K–H vortices on the target.
In a free round jet [43], the K–H vortices become three-
dimensional after one or multiple pairing, and eventually break
down at the end of the jet potential core which extends to 5–6 D
[23]. In the present study, the target plate was placed at a distance
H=2D, where the structures were still well organized and no pair-
ing took place. Beginning with the location r=1.6D, the shedding
frequency completely disappears for the three jets, meaning that
the K–H vortices were far above the wall or they were already bro-
ken and destroyed.
The three-dimensional ﬂow organization of the CONV nozzle jet
is given in Fig. 12 . This ﬁgure gives a temporal sequence of iso-
surfaces of azimuthal vorticity xhD/W0= 2.5 labeled ‘‘1” and ‘‘2”.
The time interval between the displayed snapshots is DtW0/
D= 0.32. The three dimensional behavior generated by the ﬂow
defection near the target is visualized by the iso-surface of axial
vorticity xZD/W0= ± 1.1.
Vortex structures are often identiﬁed from experimental veloc-
ity ﬁelds using the vorticity. However, the vorticity is not always
convenient for this purpose as it cannot distinguish between pure
shearing motion and swirling motion. A more pertinent method for
vortex identiﬁcation is the k2-criterion based on the eigenvalues of
the velocity gradient matrix. It uses the local pressure minimum
criterion in the center of a vortex [44]. This method was applied
to the velocity ﬁelds of Fig. 12 and the results are given in
Fig. 13 . This ﬁgure also includes the contours of axial velocity W
along with velocity ﬁeld on the vertical plane X/D= 0 and radial
velocity Vron the horizontal plane Z/D= 1.9. The K–H structure
labeled ‘‘3” identiﬁed by the k2-criterion in Fig. 13 is not clearly
identiﬁed by the vorticity contour in Fig. 12 .
-0.8-0.400.40.81.2
-0.08 -0.04 0 0.04 0.08t [s]Electrodiffusion – CONV
Electrodiffusion – RO/HElectrodiffusion – RO/P
-101
0 0.01 0.02 0.03
-0.8-0.400.40.81.2
-0.08 -0.04 0 0.04 0.08t [s]Electrodiffusion – CONV
TPIV – CONV
(a) (b)
Fig. 11. (a) Autocorrelation coefﬁcient of the wall shear rate ﬂuctuation at r/D= 1.0 in the three jets; (b) comparison to autocorrelation of the transverse velocity ﬂuctuation
atr/D= 0.6 and Z/D= 1.7 in the case of convergent jet.
Fig. 12. Time sequence instantaneous iso-surfaces of azimuthal vorticity xhD/W0= 2.5 (white), axial vorticity xZD/W0=/C01.1 (cyan) and 1.1 (purple) and axial velocity
W= 0.7 (m/s) (red), superimposed to the Z–Yprojection of velocity vector on the plane X/D= 0 – the time interval between the displayed snapshots is DtW0/D= 0.32. (For
interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)428 K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436

Figs. 12 and 13 provide 3D view on the development of K–H
instabilities in the initial shear layer, their roll-up and pinch-off
and the advection of the resulting azimuthally coherent ring vor-
tices. These vortices were shed between Z/D= 0.9 and 1.4
(Fig. 13 ) at a fundamental frequency of 53 Hz. As mentioned above,
this frequency is equal to that captured on the target using the
electrodiffusion method. In the impinging region the ring vortices
are still circular and less distorted until they strike the target. After
the impact, as they are advected, they stretch in the radial direc-
tion, distort and break into small chips. As shown in Fig. 14 provid-
ing a 2D view of the ﬁrst snapshot from Fig. 13 , the resulting
vortices are very close to the wall at r/D= 1.2 and beginning with
r/D= 1.5, they draw far apart the wall. This observation is in agree-
ment with the absence of periodicity in the wall shear rate signal at
r/D= 1.6 ( Fig. 10 ).
When the K–H vortices approached the wall, they stretched and
their diameter increased ( Figs. 12 and 13 ). The instantaneous
imprint of the K–H vortices on the target, is visible in Fig. 15 which
gives the X–Ypresentation of the iso-lines k2D2=W2
0¼/C01:0a t
Z/D= 1.8 (i.e., at 1.6 mm from the target), along with iso-colors of
radial velocity Vrand projection of velocity vectors on the plane
X–Y. Popiel and Trass [45] using the smoke-wire ﬂow visualization
technique have shown that at nozzle-to-plate separation H/D= 1.2,
the toroidal vortices of the circular jet reached the plate at a radiusr= 0.7 D–0.9 D, which is consistent with the present results
(Fig. 15 ).
3.3. Statistical properties of wall shear rate and mass transfer
The radial distributions of the mean value of wall shear rate c
(Eq. (7)) and its RMSﬃﬃﬃﬃﬃﬃ
c02q
are plotted in Fig. 16 for the three con-
sidered nozzles. The maximum value of mean wall shear rate is
equal to 9850 s/C01, 14,670 s/C01and 17,380 s/C01for the CONV, RO/H
and RO/P nozzle jet, respectively. Hence, the maximum of cis noz-
zle geometry dependent and is higher for the oriﬁce jets than for
the convergent jet at a Reynolds number of 5620. This observation
conﬁrms the previous one made at a Reynolds number of 1360
[21]. Contrary to our expectation, the hemispherical oriﬁce nozzle
RO/H reduces somewhat cmaxlevel. That is probably because the
curved surface already converge the ﬂow at the exit and so reduces
the vena contracta effect. Anyway, this ﬁnding is interesting for
applications where wall-friction modulation is required. The cur-
vature of the plate supporting the exhaust oriﬁce may be modiﬁedto achieve a given level of local friction without changing the vol-
umetric ﬂow rate of the injected ﬂuid.
Fig. 17 a clearly shows the effect of nozzle geometry on the posi-
tion of the maximum value
cmax. It appears at r= 0.7 Dfor the CONV
nozzle jet, and at r= 0.58 Dand 0.55 Din the RO/H and RO/P nozzle
jet, respectively. These locations are close to the values 0.6 D–0.74 D
reported in the literature [12–14] for the round impinging jets
when H<4D. Thus, the ﬁrst peak of cdoes not coincide with the
peak of Umax(Fig. 9 ). The ﬁrst peak of cis located in the growth
region of Umax.
Fig. 17 a also highlights in the stagnation region the changing of
thec-slope with the nozzle geometry. According to the method
based on the assumption of uniform thickness of hydrodynamic
and concentration boundary layer [20,21] , the stagnation mass
transfer (Eq. (8)) deduced from the slope of the radial wall shear
rate distribution (Eq. (7)) should be higher for oriﬁce jets compared
to the reference convergent jet. This is consistent with our previous
observations made at very low Reynolds number Reb= 1360 [21].
Fig. 13. Time sequence of iso-surface of k2D2=W2
0¼/C01:0 (white), iso-contour of axial velocity Won the vertical plane X/D= 0, iso-contour of radial velocity Vrat the vicinity
of the plate Z/D= 1.9, and Z–Yprojection of velocity vector. The time instants and order are the same as in Fig. 12 .
Fig. 14. View in the vertical plane X/D= 0 of the ﬁrst instant from Fig. 13 – iso-lines
ofk2D2=W2
0¼/C01:0, iso-colors of the transverse velocity Vrand velocity vector ﬁeld
in the plane. (For interpretation of the references to color in this ﬁgure legend, thereader is referred to the web version of this article.)K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436 429

The stagnation mass transfer deduced from this indirect method
will be compared further downstream to their direct measure-
ments using the extend ED method proposed in the present study.
c¼@u=@zjz¼0¼A/C2r ð7Ț
Sh¼kD
DC¼1
31=3Cð4=3ȚA
DC/C18/C191=3
D ð8Ț
The wall shear rate falls sharply beyond its maximum ( Fig. 17 a)
and then the decrease rate slows down in the region r= 1.1 D–1.8 D;
the slowing down is more pronounced in oriﬁce jets. As shown in
Figs. 12 and 13 , this region is dominated by a complex interaction
between vortices issued from the breaking of the primary K–H vor-
tices and the target wall. Hence, the difference between the con-
vergent jet and the oriﬁce jets regarding wall shear rate
distribution is logically related to differences in vortex dynamics
in the vicinity of the target wall. The radial distributions of the
RMS of cnormalized by its maximum value ( Fig. 16 ) are reported
inFig. 17 b. Whereas the RMS distribution of the convergent jet
exhibits one sharp peak located at 1.1 D, the oriﬁce nozzle jets show
a plateau ranging approximately from 0.8 Dto 1.7 D. This difference
seems to be linked to the slope changing of cdistribution in the
same region ( Fig. 17 a). Another interesting observation is the shift
between the peak location of mean wall shear rate ( Fig. 17 a) and
its ﬂuctuations ( Fig. 17 b). In the case of the convergent jet, our nor-
malized data c/cmaxandﬃﬃﬃﬃﬃﬃ
c02q/C30ﬃﬃﬃﬃﬃﬃ
c02q
maxﬁt very well to those of
Alekseenko et al. [46] also obtained by electrodiffusion technique.
The authors provided both normalized mean wall shear rate and itsRMS for a similar case than ours, i.e., a convergent nozzle jet at a
Reynolds number Re=6 7 0 0 a n da n o z z l e t o p l a t e d i s t a n c e H/D=2 .
This comparison reinforces our ﬁndings regarding the shape of
distribution of cand its RMS. Quantitative levels were not
compared since it was not possible to trace the information on
dimensional values of Alekseenko et al. due to the lack of informa-
tion on their cmaxandﬃﬃﬃﬃﬃﬃ
c02q
maxvalues.
To move forward on the analysis of mean wall shear rate and its
RMS distributions, the second normalization is applied ( Fig. 17 a0
and b0) and comparison is made with the data of the literature
[13,20,47] . All authors consider the nominal nozzle diameter Das
a characteristic length scale of the jet and did not give the corre-
sponding value of the characteristic diameter D⁄. Anyway, in these
studies the nozzle is either a convergent [13] or a pipe [47] for
which the vena contracta effect is relatively low compared to the
oriﬁce nozzle.
In another work [13] of Alekseenko et al. at a higher Reynolds
number Re= 41,600, both mean wall shear rate and its RMS for a
convergent nozzle jet at a nozzle to plate distance H/D= 2 were
provided and the given information were sufﬁcient to apply to
them the normalization considered in Fig. 17 a0and b0.
The normalized mean skin friction distributions ( Fig. 17 a0) are
similar for our three jets except at radial distance beyond
r/D⁄= 1.4. In this region there is a slope change for oriﬁce jets
reﬂecting a birth of a second peak. The measurements of
Alekseenko and Markovich [13] and Tummers et al. [47] that were
performed at high Reynolds numbers are in good agreement with
our results for r/D⁄< 1.4. Further downstream, the appearance of
a high second peak supports the idea that the slope change in
Fig. 15. Time sequence of instantaneous iso-lines of k2D2=W2
0¼/C01:0 (white), iso-contours of radial velocity Vrand X–Yprojection of velocity vector at X/D= 1.8. The time
interval between the displayed snapshots is DtW0/D= 0.42.
06001200180024003000
0400080001200016000
0400080001200016000
0123RO / H
)s('12 −γ
06001200180024003000
)s('12 −γ
0123
D/r D/rD/r06001200180024003000
0400080001200016000
0123RO / P)s(1−γ
)s('12 −γ)s(1−γ)s(1−γ
Fig. 16. Wall shear rate and its RMS values as a function of normalized radial distance from the stagnation point.430 K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436

the skin friction distribution is Re-dependent. Indeed, as shown in
Table 1 , in the present study at a constant Reb,Reis greater in
oriﬁce jets than in convergent jet due to the vena contracta effect
and the corresponding jet acceleration.
Fig. 17 b0compares in the second normalization form, the distri-
butions of skin friction ﬂuctuations in the three considered jets.
Among the data sources used for previous comparisons made in
Fig. 17 a0, only Ref. [13] provides the wall shear rate ﬂuctuations.
The data of Ref. [13] were obtained for a convergent nozzle at
Re= 41,600 and H/D= 2. Although the level and the position of nor-
malized maximum ﬂuctuation are different than ours for CONV
nozzle jet explored at lower Reynolds number ( Re= 5850), the dis-
tributions are similar in shape. Considering together, data from Ref.
[46] atRe= 6700 ( Fig. 17 b) and data from Ref. [13] atRe= 41,600
(Fig. 17 b0), differences in the distribution of normalized skin fric-
tion ﬂuctuation in the convergent jet of Alekseenko et al. are surely
due to Reynolds number level.
Considering our own results, the most noticeable feature
evidenced by Fig. 17 b0is the particular ﬂat distribution and the
lower ﬂuctuation values in oriﬁce jets compared to those of a con-
vergent jet.A similar trend is visible in velocity ﬂuctuations near the target
wall at Z⁄/D⁄= 0.3 ( Fig. 18 a) and at Z⁄/D⁄= 0.2 ( Fig. 18 b). At posi-
tions lower than Z⁄/D⁄= 0.2, our PIV measurements are question-
able due to the laser light scattering on the wall. Velocity
ﬂuctuations at Z⁄/D= 0.04 obtained by Vejrazka et al. [48] using
hot wire anemometry in a circular convergent impinging jet
(Re= 10,000 and H/D= 2) with or without external excitation are
included in Fig. 18 b for comparison. In the natural convergent
impinging jet ( Ste= 0), the distribution of radial velocity ﬂuctuation
near the target wall present a peak around Z/D= 1. This peak
becomes sharper when the jet is excited at normalized frequency
Ste= 0.74, whereas a plateau instead of local sharp peak appears
at a normalized excitation frequency of Ste= 2.14. In this case,
the plateau in velocity ﬂuctuation is similar to the ones in the pre-
sent study obtained for oriﬁce jets. The authors observed that Kel-
vin–Helmholtz vortices produced in the jet at normalized
excitation frequency Ste=0.74 are large and regular, and while
approaching the wall, they increase the near wall ﬂow ﬂuctuations.
For normalized excitation frequency Ste= 2.14, Kelvin–Helmholtz
vortices become small and disorganized that attenuate the near-
wall ﬂow ﬂuctuations. In this case, the contribution of coherentFig. 17. Radial distributions of normalized mean wall-shear rate (a, a0) and of the corresponding mean square root (b, b0) – comparison with available literature data.K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436 431

vortices at the wall are similar to that of stochastic small scale ﬂuc-
tuating motion and lead to a plateau in velocity turbulent
distribution.
Similar conclusions were drawn by Alekseenko et al. [46] con-
cerning the effect of impinging jet excitation on transfer phenom-
ena at the target wall. The authors observed that jet excitation at
the most probable frequency (natural frequency) of the corre-sponding natural jet, enhances the coherence of the large vortices
and increases the skin friction ﬂuctuation with a maximum located
around radial position r= 1.1 D. By progressively suppressing the
large scale vortices in the previous excited jet, using different con-
centrations of air bubbles introduced in the jet, they observed a
strong local decrease of the skin friction ﬂuctuation and the
appearance of a plateau, instead of a local sharp peak in its radial
distribution ranging from 1 Dto 2.5 D. On the other hand, when
the jet without air bubbles is excited at frequencies exceeding
the natural jet frequency, a similar plateau in the same region is
also observed.
Based on the previous observations made in the literature about
the link between coherent structures organization in the jet and
the resulting radial distributions of wall shear stress [13] and the
near-wall velocity ﬂuctuations [48], it could be advanced that in
oriﬁce nozzle jets, coherent vortices are smaller and less regular
than in the convergent jet, leading to their rapid breakdown on
the target and to a plateau-type distribution and lower values of
wall shear stress ﬂuctuations ( Fig. 17 b and b
0).
In our previous work [21] on convergent and oriﬁce impinging
jets at the very low Reynolds number of 1360, such a difference incoherent structure organization in the two types of jets has been
observed without making the link with near-wall ﬂuctuations.
Fig. 19 shows the radial distribution of the local Sherwood num-
ber ( Sh) for the three considered jets. Similarly to what we
observed for the wall shear rate c, the maximum value of the local
Shis nozzle geometry dependent and is equal to 1042, 1241 and
1392 for the CONV, RO/H and RO/P nozzle jet, respectively. Themaximum Sherwood number Shis then 19% and 34% higher for
RO/H and RO/P nozzles compare to the CONV nozzle. Given that
the maximum value of Shcorresponds to the maximum mass
transfer, the present results demonstrate that the use of an oriﬁce
nozzle not only improves wall shear rate, but also increases the
level of maximum mass transfer, which let assume that the latter
is correlated to the former. The maximum of Shoccurs near the
nozzle edge, approximately at r= 0.55 D, 0.45 Dand 0.35 Dfor the
CONV, RO/H and RO/P nozzle jet, respectively. Hence, the ﬁrst peak
ofShis shifted from the stagnation point, as was also observed by
Kataoka et al. [12] in the core jet region of their convergent imping-
ing jet. The authors explained that the mass transfer is very sensi-
tive to the velocity turbulence which is still low on the jet axis in
the potential core region and increases near the nozzle edge. In
Vallis et al. investigation [16], the peak of Shfor nozzle-to-plate
distance in the range 5 D–20Dappears on the stagnation point. It
is expected here that the core jet region is already consumed at
5D, a position from which the turbulence rises on the jet axis. In
numerous studies of heat transfer, as in Lee and Lee [49] and
Colucci and Viskanta [50] investigations, the same behavior was
observed for the Nusselt number ( Nu) distribution: the maximumFig. 18. Radial distributions of normalized velocity ﬂuctuation: (a) at Z⁄/D⁄= 0.3; (b) at Z⁄/D⁄= 0.2 – comparison with the data of Vejrazka et al. [48].
040080012001600
0 1 2 3Sh CONV
D/rD/r D/r040080012001600
0 1 2 3Sh RO / H
040080012001600
0 1 2 3Sh RO / P
Fig. 19. Local Sherwood number as a function of normalized radial distance from the stagnation point.432 K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436

ofNuin the core jet region is shifted from the stagnation point,
whereas in the jet transition region and downstream the maxi-
mum of Nuappears at the stagnation point.
Fig. 19 highlights for the three jets what we might call ‘‘ the birth
of Sh secondary peak ”. The secondary peak in Shdistribution is more
pronounced in oriﬁce jets. It appears approximately at r=2Dfor
the CONV nozzle jet, and at r= 1.7 Dfor the oriﬁce jets.
As evidenced in Fig. 20 , the ﬁrst peak in Shdistributions appears
in the region where the K–H vortices strike the target (see also
Fig. 15 ) and its secondary peak emerges at the position where
appear counter-rotating vortices on instantaneous vorticity ﬁeld;
the secondary vortices are designated by an arrow in Fig. 20 a.
The secondary counter-rotating vortices are present in both con-
vergent jet ( Fig. 20 , left) and oriﬁce jet ( Fig. 20 , right). For brevity,
only the oriﬁce jet from RO/H nozzle is presented, because theRO/P case is similar.
If we advance the similarity between the secondary peak of Sh
and the secondary peak of Nu, the observation made above is con-
sistent with that of Hadziabdic and Hanjalic [10]. From their LES
simulation of a round impinging jet, the authors observed that
the secondary peak in Nu, (pertinent only for small H/Dand high
Reynolds numbers) is caused by the reattachment of the recircula-
tion bubble and by the associated turbulence production, as well asthe subsequent strong advection. The conclusions of Hadziabdic
and Hanjalic [10] are consistent with those of Carlomagno and
Andrea [11] and Dairay et al. [51], who give in their recent works
a comprehensive description of secondary vortex dynamics in
impinging jets.
Similarly to what was done previously for the skin friction
(Fig. 17 ), the Sherwood number is normalized using the two groups
of parameters and the results are compared to the available litera-
ture data ( Fig. 21 ). When the Sherwood number is normalized
using the characteristic scales ( Fig. 21 a), the proﬁles of the three
jets collapse onto a single curve indicating that the jet contraction
scales W
0and D⁄are sufﬁcient to model the difference on mass
transfer introduced by the nozzle shape. The comparison of mass
transfer results of the present study with the available literature
data [52] obtained for convergent and oriﬁce nozzles ( Fig. 21 b) is
made using nominal scales, because the authors do not provide
the characteristic scales of their jets. Although maximum values
and their positions in the two studies are almost identical in each
type of jet, the overall agreement is less satisfactory. The origin of
this difference could be attributed to the bulk Reynolds number Reb
nearly four times greater in [52] than in the present study.
One important quantity which has received considerable atten-
tion is the stagnation Sherwood number. In this study, the value of
00.51
0 0.5 1 1.5 2 2.500.51
0 0.5 1 1.5 2 2.5(b)(b)(c)(c)(a) (a)
(d) (d)
Fig. 20. CONV nozzle jet (left) and RO/H nozzle jet (right): (a) instantaneous vorticity ﬁeld xY¼@U
@Z/C0@W
@X/C0/C1D
W0– arrows indicate secondary vortices on the target; (b) c/cmax; (c)ﬃﬃﬃﬃﬃﬃ
c02q
=ﬃﬃﬃﬃﬃﬃ
c02q
max; (d) Sh/Shmax.
00.250.50.751
01234CONV
RO / P
RO / H4
4.0 .05
.05 .0Re*
ScSh
*/Dr r00.511.5
01234CONV
RO / P
RO / H
D/ReScSh
bPopiel and Boguslawski (1986), Reb=20000 , H/D = 2
Circular orifice Convergent nozzlePresent study
Reb = 5620
H/D = 2
(a) (b)
Fig. 21. Normalized local Sherwood number distributions: (a) ﬁrst normalization; (b) second normalization – comparison to the literature.K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436 433

the stagnation Sherwood number is also nozzle geometry depen-
dent ( Fig. 19 ). It is equal to 900, 1053 and 1154 for the CONV,
RO/H and RO/P nozzle jet, respectively.
The stagnation Sherwood number can be also obtained from
wall shear rate distribution as described in Kristiawan et al. [20]
and Meslem et al. [21] and recalled above (see Eqs. (7) and (8) ).
As shown in Fig. 22 , the wall shear rates were ﬁtted according to
Eq.(7), with a linear dependence law in the stagnation region.
The corresponding slope is equal to the hydrodynamic parameter
A. The values of the stagnation Sherwood number calculated from
the hydrodynamic parameter Ausing Eq. (8)is equal to 897, 1038
and 1140 for the CONV, RO/H and RO/P nozzle jet, respectively.
These values are very close to those obtained by the direct mea-
surement procedure ( Fig. 19 ).
Chin and Tsang [17] proposed an empirical equation (Eq. (9)) for
the stagnation Sherwood number in the case of a turbulent straight
pipe impinging jet with a Reynolds number ranging from 4000 to
16,000 and a nozzle-to-plate distance H/Dranging from 0.2 to 6.
Sh¼1:12Re1=2Sc1=3gðScȚH=DðȚ/C00:057ð9Ț
where g(Sc) is equal to 0.992.By extrapolating Eq. (9)to the parameters of the present study,
we obtain a value of 898. Although the ﬂow ﬁelds of a convergent
jet and a pipe jet at a same Reynolds number could be different, the
fact that our results are very close to the literature ones validates
our measurements.
The normalized stagnation mass transfer coefﬁcients, the ones
obtained in the present study and in [21], are compared in Table 2
with the theoretical value of Shadlesky [53]. The deviation of our
data relatively to the theoretical value falls in the range from 2%
to 13%, which is quite satisfactory.
Assuming the axial symmetry of the jets, the average Sherwood
number Shavgcan be obtained from the local Sherwood number as
follows:
ShavgðrȚ¼2
r2Zr
0ShðqȚ/C2qdq ð10Ț
For each jet, Fig. 23 a gives the best curve ﬁt of the local Sher-
wood number and in Fig. 23 b, the radial distribution of the corre-
sponding average value Shavgis plotted. The ﬁtted curves were
obtained using a cubic spline interpolation. Fig. 23 illustrates the
mass transfer enhancement by the oriﬁce jets not only locally
(Fig. 23 a) but also globally in the disk area ranging from 0 to
3.5D(Fig. 23 b). This trend was conﬁrmed by direct measurement
of the global Sherwood number obtained from the limiting diffu-
sion current through the platinum disk of 3.2 D(Fig. 1 b). The
obtained values are 495, 618 and 650 for the CONV, RO/H and
RO/P nozzle jet, respectively. Their comparison to the correspond-
ing integrated values 571, 648 and 680 obtained using Eq. (10) for
r= 3.2 D(Fig. 23 b), reveals a difference of 15% for the convergent
nozzle jet and 5% for the oriﬁce nozzle jets. Eq. (10) assumes an
axial symmetry of the jet mean ﬂow. This hypothesis seems to
be less true for the convergent nozzle jet than for the oriﬁce nozzle
jets. Fig. 24 showing the iso-contours of time-averaged axial veloc-025005000750010000
0 0.01 0.02 0.03
r(m)CONV
)s(1−γ)s(1−γ)s(1−γA=2335810 (s-1m-1)
0400080001200016000
0 0.01 0.02 0.03
r(m)RO/HA=3499430 (s-1m-1)
0400080001200016000
0 0.01 0.02 0.03
r(m)RO/PA=4632780 (s-1m-1)
Fig. 22. Determination of hydrodynamic parameter Afrom the wall shear rate proﬁles.
Table 2
Normalized stagnation mass transfer coefﬁcient Sh/C3
0=ðRe0:5SC0:5Ț, comparison with
data of Ref. [21] and the theoretical value of Ref. [53].
H/D=1 H/D=2 H/D=3
CONV – present study – 0.63 –
RO/P – present study – 0.60 –RO/H – present study – 0.60 –CONV – [21] 0.61 0.63 0.66
RO/P – [21] 0.63 0.61 0.60
Theoretical value [53] 0.585 0.585 0.585
040080012001600
01234CONV
RO / H
RO / P
Dr/040080012001600
0 1234CONV
RO / H
RO / P
avgSh
Dr/00.250.50.751
01234CONV
RO / H
RO / P45.0.0*
ReScShavg
*/Dr
(b) (a) (c)Sh
Fig. 23. Curve ﬁt of local Sherwood number distribution (a), calculated average Sherwood number (b) and calculated average Sherwood number in the second norm alization
form (c).434 K. Sodjavi et al. / Experimental Thermal and Fluid Science 70 (2016) 417–436

ity of the convergent jet in the Y–Xplane at Z/D= 1.8 (i.e. 1.6 mm
above the target), conﬁrms a defect in ﬂow symmetry near the tar-
get that could explain the 15% difference between measured and
calculated global Sherwood number.
4. Conclusion
Three round impinging jets with exit nominal Reynolds number
of 5620 and nozzle-to-wall distance of 2 D, have been compared in
the present study. A round oriﬁce perforated either on a ﬂat plate
(RO/P) or on a hemispherical surface (RO/H), is compared to a ref-
erence convergent nozzle (CONV). In each jet, Particle Image
Velocimetry (PIV) and electrodiffusion technique (ED) were used
to produce a data set on the ﬂow ﬁeld, the wall shear rate, and
mass transfer, respectively. The study is conducted at constant exit
area and volumetric ﬂow rate for the three jets. This speciﬁc choice
is related to the aimed Heating, Ventilation and Air Conditioning
application, and speciﬁcally to the Personalized Ventilation aspect.
The instantaneous velocity ﬁelds indicated the formation of
small secondary vortices above the impingement plate, under pri-
mary Kelvin–Helmholtz (K–H) in the region r= 1.5 D–2D, which is
consistent with the literature. Consequently, beginning with
r=1.5D, the structures issued from the breaking of the primary
K–H structures draw far apart the wall.
It was also shown that the wall shear rate ﬂuctuation is related
to the dynamics of the jet coherent structures. The shedding fre-
quency of the K–H vortices revealed by time-resolved tomographic
PIV, applied to the reference convergent jet (CONV), is present inthe ED signals for r< 1.6 D. At farther radial positions, the shedding
frequency completely disappears from the ED signals whatever the
jet considered, because the coherent structures are far above the
wall or they are destroyed.
Jet mean ﬁeld analysis reveals that the level of maximum veloc-
ity in the wall jet region is as high as the ﬂow is accelerated at the
jet exit. The jet acceleration was shown to be more intense in the
oriﬁce jets than in the convergent jet due to the vena contracta
effect. However, the curved surface supporting the oriﬁce stretches
the ﬂow at the exit, and reduces the vena contracta effect. This
leads to a lower wall friction than in the case of the ﬂat oriﬁce. This
ﬁnding is interesting for applications where wall-friction modula-
tion control is required without changing the volumetric ﬂow rate
of the injected ﬂuid.
It was shown that the use of an oriﬁce nozzle not only improves
wall shear rate, but also increases local and global mass transfer,
which let assume that the latter is correlated to the former. At a
constant volumetric ﬂow rate and exit nozzle area, the global masstransfer on a target disk of 3.2 Din diameter is 25% and 31% respec-
tively higher for RO/H and RO/P nozzles compare to the reference
CONV nozzle. As for local mass transfer, the local Sherwood num-
ber distributions indicate a gain of 19% and 34% with RO/H and RO/
P nozzles compare to the CONV nozzle. Also, the distribution of the
local Sherwood number exhibited a secondary peak in the wall
region where secondary vortices appear. The level of this sec-
ondary peak is sensitive to the nozzle shape. The higher is the
acceleration, the more intense is the level of the secondary peak.
The last main conclusion concerns the consequence of the
choice of normalization parameters in data analysis. While large
differences appear in nominal scale representations between the
three jets, in both their statistical ﬂow properties and their transfer
processes, the use of characteristic scale representation clariﬁes
these differences.
Acknowledgment
This work was supported by the Grants of the French National
Agency of Research, project ‘‘FLUBAT”, ANR-12-VBDU-0010.
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