Proceedings of AJK2011-FED
The ASME-JSME-KSME Joint Fluids Engineering Conference 2011 (AJK2011-FED)
July 24 - 29, 2011, Hamamatsu, Japan

AJK2011-16010
EFFECT OF REYNOLDS NUMBER ON THE TURBULENT FLOW STRUCTURE IN
THE NEAR-WALL REGION OF AN IMPINGING ROUND JET
Khaled J. Hammad
Dantec Dynamics Inc.
Holtsville, NY, USA

ABSTRACTTime-Resolved Particle Image Velocimetry was used to
study the effect of the Reynolds number on the turbulent flow
structure of a submerged water jet impinging normally on asmooth and flat surface. A fully developed turbulent jet and asemi-confinedflow
configuration
ensuredproperly
characterized boundary conditions allowing for straightforward
assessment of turbulence models and numerical schemes. The
Reynolds number based on jet mean exit velocity was 5,000,
10,030 and 15,050 while the pipe-to-plate separation distance
was fixed at two diameters. Turbulent velocity fields arepresented using Reynolds decomposition into mean andfluctuating
components
while
ProperOrthogonal
Decomposition (POD) analysis identified the most energetic
coherent structures in the stagnation and wall-jet regions.
NOMENCLATURE
D
H
L
Re
Uc
Ub
u, v

Pipe internal diameter (m)Pipe-to-plate separation distance (m)Pipe length (m)Reynolds number ( U b D  )Mean centerline velocity at the pipe exit (m/s)
Pipe bulk velocity (m/s)
Normalized mean axial and radial velocities
U U c ,V U c ui, viu , v 

Instantaneous axial and radial velocity (m/s)
Normalized axial and radial RMS velocities

Greek Symbols



Kinematic viscosity of jet fluid (m2/s)

Subscriptsb

Ivana Milanovic
University of Hartford
West Hartford, CT, USA

c
j
p
r
x

Centerline
Jet
Pipe
RadialAxial

INTRODUCTION
Jet impingement is used in many technologically important
applications such as cooling/heating, drying, mixing andchemical vapor deposition (CVD) processes. Figure 1
illustrates three distinct regions that may be observed in an
impinging jet: (1) the ‘free’ jet, where the flow does not feelthe presence of the wall and the surrounding fluid is entrained
into the jet; (2) the impingement or stagnation region, where
the wall imposes pressure gradients changing the direction of
streamlines from the axial to the radial, and (3) the wall-jet
region where a complete deflection of the jet is accomplishedwhile the region is characterized by strong shear and velocity
fluctuation levels much higher than in an ordinary boundary
layer.
Impinging jets have been extensively studied with focus on
the flow, heat/mass transfer characteristics, and turbulencemodeling. Comprehensive reviews of impinging jet research
are provided by Martin [1], Downs et al. [2], Jambunathan etal. [3], Viskanta [4], Polat [5], Webb et al. [6] and Garimella[7]. Spatial topology of a round impinging jet issuing from along pipe at a high Reynolds number was investigated in large
eddy simulations (LES) of Hadziabdic and Hanjalic [8] at Re =20,000 and separation distance H/D = 2 and in a snapshot
Proper Orthogonal Decomposition (POD) study of Hammad
and Milanovic [9] at Re = 16,000 with separation distances
between 1 and 8D. The aforementioned works revealed
interesting time and spatial dynamics of the vortical structures
and their imprints on the wall.

Bulk

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Copyright © 2011 by ASME

nozzlediameter ratio of the tube, L/D = 112, assured fully developed
turbulent flow conditions at the outlet. The resulting Dplate/D
ratio is 16.

fully developed jet

free jetwall jetimpingement region

FIGURE 1. IMPINGING JET SCHEMATIC

Shear layer instability near the nozzle lip at moderate andhigh Reynolds numbers results in the formation of large
vortical structures. This instability is controlled by theprocesses taking place at two different length scales: (1) the
momentum thickness of the boundary layer at the nozzle lip,
critical to the initial development of the shear layer, and (2) the
jet diameter, D, which becomes important further downstream.
Recent studies [8-9] highlighted the influence of vorticalstructures on flow and heat transfer characteristics andemphasized the need for further research focusing on jet-wallinteractions. The present work used time-resolved PIV (TRPIV) measurements to study the effect of the Reynolds number
on the flow field resulting from a submerged water jet
impinging normally on a smooth and flat surface. The selected
flow configuration, inflow and boundary conditions allow forstraightforward assessment of turbulence models and numerical
schemes. Statistically averaged mean and RMS velocities arereported with emphasis on the near-wall region. POD analysisof the TR-PIV data was used to gain insight into the mostenergetic coherent structures of the turbulent flow field. The
experimental setup and test procedure used in this investigation
are presented below.
EXPERIMENTAL SETUP
Figure 2 illustrates the experimental setup for the PIV
measurements. A closed-loop system is composed of the test
section, pump, and the pipe mount. The rectangular andimpingement plate are made of smooth finish, clear cast acrylic
with the impingement plate diameter Dplate = 101.6 mm,
thickness of 12.7 mm and tank height Htank = 279.4 mm.
The jet was produced using a submerged verticalprecision type 304 stainless steel tube placed on the cylinder
centerline with an inner diameter D = 6.35 mm, length L =711.2 mm and wall thickness 0.381 mm. The length-to-

FIGURE 2. EXPERIMENTAL SETUPx
Hr

FIGURE 3. TEST SECTION AND COORDINATE SYSTEMAs shown in Fig. 2, after impinging the circular plate theflow leaves the test section through the bottom of therectangular tank. As shown in Fig. 3, the separation distance
between the pipe outlet and the cylindrical impingement plateis denoted by H. The origin of the cylindrical r,x coordinate
system coincides with the stagnation point. The x-axis ispointing away from the impingement plate in the verticaldirection. The r coordinate is measured along the bottom
circular plate.
Measurements were performed at a fixed pipe-to-plate
separation distance, H/D = 2. Volumetric flow rates of 1.827 ×
10-5 m3/s (0.29 GPM), 3.591 × 10-5 m3/s (0.57 GPM) and 5.229
× 10-5 m3/s (0.83 GPM) were used, resulting in pipe bulk
velocity, Ub, of 0.58, 1.13 and 1.68 m/s, respectively. The
kinematic viscosities of the working fluid, DI water at 34, 35
and 36C, were 7.33 × 10-7, 7.18 × 10-7 and 6.97 × 10-7 m2/s.
The Reynolds number, Re, based on jet mean exit velocity was
5,000, 10,030 and 15,050.

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Copyright © 2011 by ASMEPIV SYSTEM AND DATA PROCESSINGA DANTEC DYNAMICS two-dimensional TR-PIV
system was used to measure the flow field along each rx planeof interest. The system consisted of synchronization hardware
for controlling the laser and camera, and software running on a
Windows-based platform for data acquisition, management andpost-analysis. The light source was a New-Wave Research
Pegasus® dual-head, diode-pumped Nd:YLF laser system.
Each laser head had operating range between 1 and 10,000
pulses per second. When fired at 1 kHz, the resulting per-cavity
energy at 527 nm is 10 mJ. A Phantom® v210, 1Mpx highspeed camera capable of taking more than 2,000 frames-persecond (fps) at full 1280 x 800 pixel resolution was used. The
CMOS camera has an active pixel size of 20 microns with 8and 12-bit pixel depth.
The Nd:YLF laser was fired at a frequency of 100 Hz,
yielding 200 pulses of green (527-nm wavelength) 1.5 mm
beams, each having a typical duration of about 180 ns. Lightsheet forming optics mounted at the exit portal of the laser
system generated a thin, focusable light sheet by means of aseries of spherical and cylindrical lenses. A vertical divergent
light sheet was used to illuminate the full extent of themeasurement region within the cylindrical tank. The verticallight sheet was aligned to pass through the center of the pipe.
The thickness of the light sheet at the imaging plane was 1 mm.
The spatial location of the illumination system was fixed during
all the tests. The CMOS camera was placed perpendicular tothe laser sheet. The lens used was a Nikon Micro-Nikkor 105mm.
To eliminate image contamination or saturation due to highintensity reflections near the metal surfaces, fluorescentpolystyrene particles were used as the tracer. The particles
fluoresced when illuminated by the green laser light. A highpass color filter was then used to discriminate particle
fluorescence from surface reflections and other Mie-type of
scattering. The average diameter of the fluorescent particles
was 15 m with the density of 1.05 g/cm3. The latter value wasclose to the water density (0.994 g/cm3); hence the particles
were nearly neutrally buoyant in the measurement region.
For the present set of measurements, a high-accuracy
multi-pass adaptive cross-correlation technique was used toevaluate the velocity field determined from each pair of particle
images. A high sub-pixel accuracy independent of correlation
peak shape was achieved and further minimized displacement
estimate errors [10].
The final interrogation area, IA, was 16  16 pixels with
50% overlap in both the horizontal and vertical directions. An
initial IA of 128 × 128 pixels was sequentially reduced to thefinal IA. A dynamic second-order accurate method was used tospatially offset the two IA’s during each subsequent iteration
cycle by the displacement calculated from previous steps.
During each iteration cycle, checks on the correlation’s signalto-noise, as well as a local comparison of vector attributes withthe median value of 3  3 neighbors were applied to validate
and remove outliers. To remove spurious vectors, a minimum

peak height ratio (between the 1st and 2nd peak) of 1.2 wasselected, thereby enforcing more stringent conditions on peakidentification for the subsequent determination of vectors.
Three thousand PIV realizations at a sampling rate of 100
Hz were obtained for all test cases and used to evaluate themean and RMS flow field information presented here.
The focus of the current work was to investigate the flow
structure close to the impingement region. Therefore, theresults correspond to a 1D × 5D rectangular sub-region situatedabove the impingement wall. The final IA was 16 × 16 pixels
for all test cases. Each obtained vector represented the spatial
average over a 0.59 × 0.59 × 1 mm volume. Each obtained
vector map corresponded to 21 vectors along the x direction
and 110 along the r direction, a total of 2,310 vectors.
The pipe exit region was also analyzed to investigate theexit flow conditions 0.1D from the nozzle. The centerline axial
velocity, Uc, was measured for all pipe-to-plate distances, andsubsequently used to normalize reported flow field data.
Measured Uc values were 0.90, 1.63 and 2.37 m/s for Re =5,000, 10,030 and 15,050, respectively.
REYNOLDS DECOMPOSITION
The mean velocity is given by the following equation:
U

1 N
 ui
N i 1(1)where ui is measured instantaneous velocity and N is thenumber of PIV data sets. Both the radial and axial componentsof the mean velocity are calculated using Eq. (1). The
fluctuating velocities are obtained after evaluating the mean
velocity. Normal and shear Reynolds stresses are calculatedusing the following equations:
1 N
 (ui  U )2
N i 1
1 Nv 2   (vi  V ) 2
N i 1u 2 

(2)

Normalized axial, u   u 2 , and radial, v  v2 , RMS
velocity components are calculated and used for data
presentation.
Figures 4 and 5 illustrate radial profiles of the mean and
RMS velocities 0.1D away from the nozzle. While all velocities
are normalized by the centerline axial velocity at the pipe exit,
Uc, the axial and radial distances are normalized by the pipe
diameter, D. The radial profiles of the mean axial (u), andradial (v) velocity, measured for Re = 5,000, 10,030 and
15,050, are given in Fig. 4. All shown velocity distributions
obtained in the nozzle region, clearly demonstrate flow
symmetry. Furthermore, normalized profiles collapse indicating
fully developed pipe conditions. A comparison of axial profiles
with expected fully developed pipe conditions as approximatedby the empirical Power law, u  1  2r D  , is also given in
1n3

Copyright © 2011 by ASME

Fig. 4. Good correlation with experimental data is achieved forthe 1/6th power low velocity profile (n = 6).

1

u(r), v(r)0.8

u(r), Re15u(r), Re10u(r), Re5v(r), Re15v(r), Re10v(r), Re5
Power law

0.6

0.4

0.2

center of the annular shear layer where the velocity fluctuations
are appreciably stronger than those found in the jet core.
The variation of the mean axial velocity, uc, along thestagnation line, r = 0, is shown in Fig. 6. Curves for all three
Reynolds numbers collapse. In the vicinity of x = 1, centerline
velocity is dropping gradually, mainly due to the turbulent
shear stresses. However, as the jet moves further downstream, x< 0.5, proximity to the plate results in a more rapid jet
deceleration and centerline velocity decay.

1

0.8

0
-0.5

0

r

0.5

0.6

1

Re15
Re10
Re5

uc

-1

0.4

FIGURE 4. RADIAL TIME-AVERAGED VELOCITY PROFILESAT X = 0.1
0.2
0.15

u'(r), Re15
u'(r), Re10
u'(r), Re5v'(r), Re15v'(r), Re10v'(r), Re5

u'(r), v'(r)

0.1

0

0
0

r

0.5

1

x

1.5

2

FIGURE 6. MEAN AXIAL VELOCITY DECAY
ALONG STAGNATION LINE

0.05

-0.5

0

0.5

FIGURE 5. RADIAL RMS PROFILES AT X = 0.1

The radial profiles of RMS velocities, u  and v , areshown in Fig. 5. Close to the nozzle, v values are generally
low and do not vary much across the jet. However,u  distribution experiences substantial changes with two
distinct peaks ( u   0.075, r  0.45 D ) appearing at the edge ofthe jet due to the development of the turbulent shear layer.
Noticeably different RMS value components confirm theanisotropy of the Reynolds normal stresses. Furthermore,variations across the jet core (region defined by r  0.3 ) arerather small with a local centerline turbulence intensity  0.04 , or uCL U c U b   0.05 . This is in good agreementuCL
with the expected value of about 4.7% for the Reynolds
number of 15,050. The location r  0.45 can be considered the

Figures 7 and 8 provide a global view of the mean velocity
field and RMS velocities in the impingement and the wall-jet
regions for Reynolds numbers 15,050 and 5,000, respectively.
Interaction of the fully developed turbulent jet with the nonstagnant ambient fluid results in radial spreading of the annular
shear layer. As the jet approaches the plate, rapid flow
deceleration and shear layer growth are observed for x < 0.5.
The presence of a stagnation zone leads to an overall radial
deflection of the incoming flow and the formation of a wall-jet.
In the wall-jet region, mean velocity contours indicate strong
gradients reflecting the flow undergoing a deflection
accompanied by acceleration, followed by a radial spreading of
the wall-jet and deceleration.
Significant radial RMS velocities are visible only in thewall-jet region, 1  r  3 . This is expected due to the axial
nature of the flow in the ‘free’ jet. The impacted region is ofapproximately the same length and somewhat wider for lower
Reynolds numbers. Axial RMS velocity in the jet shear layer isstronger than in the jet core or ambient fluid. The annular shear
layer grows radially by entrainment. However, a complete
inward penetration for this separation distance is not achieved
here due to the short separation distance. Complete inward
penetration of the jet shear layer, or lack of it, significantly
impacts the characteristics of momentum and heat transfer rates
in the impingement and the wall-jet regions.

4

Copyright © 2011 by ASMEU   u1

u2

 u11

 
u 1
 u N    M1
 v1
 
 1
 vM

u12


uM2
v12


vM1

 u1N   uMN 
 v1N  
 vM1 (3)

The autocovariance matrix is created:C = U T U(4)And the eigenvalue problem is solved:
 i =  i Ai
CA

(5)

The solutions are arranged:        (6)The eigenvalue corresponding to a spatial mode, n ,represents the fraction of turbulent kinetic energy associatedwith the mode.
FIGURE 7. MEAN AND RMS VELOCITIES FOR RE = 15,050

POD spatial modes are now found:
N

A u

n

A u

n

i
n

 i  nN1

i
n

n 1

, i  1,....NWith POD modes arranged as:   1  2   N 
POD coefficients ai can be found for the snapshot n as:ai   i una n  Ψ T un
A snapshot (fluctuating part) can be reconstructed as:

(7)

(8)
(9)
(10)

N

u n   ain i  Ψa n

(11)

i 1

FIGURE 8. MEAN AND RMS VELOCITIES FOR RE = 5,000

POD APPROACH
Snapshot POD has been applied to 2D PIV data sets in amanner similar to that used by Meyer et al. [11]. The zeromode represents the mean velocity field. Fluctuating parts ofvelocity components for the N snapshots and M positions arearranged as follows:

Coherent structures can carry a substantial percentage ofthe total turbulent energy. A POD mode represents a coherent
structure only if it contains a dominant percentage of energy.
POD does not require any prior information on the flow andcaptures the most energetic components with just a few modes.
It is used both as an advanced processing method to reveal themain energetic features by eliminating the low energy motions
and as a means to construct low-dimensional dynamical modelsof coherent structures.
Turbulent energy distribution for the first 1,000 modes ofeach configuration is presented in Fig. 9. The rate of decay of
the POD spectrum is an indication of the complexity of theflow. Flatter spectrum curves suggest a more complex flowwhere a larger number of modes contribute significantly to theturbulent energy.

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Turbulent energy content (%)

8

6

Re5
Re10
Re15

4

2

0
0
10

10

1

Mode number

10

2

10

3

FIGURE 9. POD MODAL ENERGY DISTRIBUTION

The energy content of the ten dominant POD modes islisted in Table 1. POD modes 1-10 contain 38.63%, 40.78%
and 41.62% of turbulent energy in the cases Re = 5,000,
10,030, and 15,050, respectively. The overall modal
distribution is almost identical for Re = 10,030, and 15,050.
The most significant POD mode, number one, in the case of Re= 5,000, displays a substantially lower energy content
compared to those of Re = 10,030 and 15,050.
TABLE 1. MODAL ENERGY DISTRIBUTION
FOR MODES 1-10
Re
Mode

5,000

10,03015,050

1
2
3
4
5
6
7
8
9
10

5.25%
5.14%
4.55%
4.45%
4.01%
3.61%
3.17%
3.11%
2.83%
2.51%

6.80%
5.51%
4.79%
4.64%
4.20%
3.77%
3.19%
2.78%
2.74%
2.36%

6.79%
5.73%
5.08%
4.58%
4.33%
3.81%
3.53%
2.80%
2.56%
2.41%

1‐10

38.63%

40.78%

41.62%The spatial flow characteristics of POD modes 1-10 are
shown in Figs. 10 and 11 for Reynolds numbers of 5,000 and
15,050, respectively. The selected modes represent flow
structures that contain substantial turbulent energy, 38.63% and41.62%, as indicated in Table 1. For the given separation
distance, H/D = 2, large scale flow structures are mainlypresent within the jet shear layer and above the impingement
wall, outside of the stagnation region, r  0.5 .

The POD modes reveal the existence of vortical structures,developing in the mixing region, that stretch and acquire astrong radial component when they approach the impingement
plate. The generation of these vortices is due to the KelvinHelmholtz instability within the jet shear layer. The vorticalstructures existing in the jet shear layer are more prominent in
the case of Re = 5,000, as clearly seen in the first two POD
modes shown in Figure 10. However, vortical structures above
the impingement plate seem to be the dominant features in thecase of Re = 15,050, as shown in Figure 11.
The modes shown also confirm the findings of the LES
study [8] which investigated the vortical structures and heattransfer in a round impinging jet for H/D = 2 and Re = 20,000.
The interaction of large scale structures emanating from the jet
shear layer with the wall-jet was found to lead to unsteadyseparation and the creation of distinct wall-attached vortices.
The outward radial motion eventually breaks up these wallattached vortices due to strong stretching resulting in theirdetachment and entrainment into the wall-jet. It was concluded
that the breakup of the wall-attached vortices leads to theenhancement of the local momentum and heat transfer rates andpotentially the appearance of a secondary Nusselt number peak[8]. In the current study, the wall-attached vortices form in ther  1 region, for all modes and Reynolds numbers shown.

CONCLUSIONS
Time-Resolved PIV (TR-PIV) measurements were used to
study the flow field resulting from a submerged water jet
impinging normally on a smooth and flat surface. The jet issued
from a long pipe that ensured fully developed turbulent flow
conditions at the outlet. A semi-confined setting provided
properly characterized flow boundary conditions. The
Reynolds numbers based on jet mean exit velocity were 5,000,
10,030 and 15,050. The pipe-to-plate separation was 2D.
Statistically averaged mean and RMS velocities are reportedwith a special emphasis on the near-wall region. For the studied
small separation distances, H/D = 2, the core region of the axial
jet is not influenced by the jet shear layer, resulting instagnation region turbulence characteristics similar to the
inflow conditions.
POD analysis of the TR-PIV data was used to gain insight
into the most energetic coherent structures of the turbulent flow
field. The snapshot POD was applied to an ensemble of 3,000
instantaneous PIV measurements that captured the flow field of
the stagnation and wall-jet regions. Modes 1-10 were found tocontain 39%, 41%, and 42% of the turbulent energy for Re =5,000, 10,030 and 15,050, respectively. POD spatial
distributions reveal that vortices along the impingement wall,outside of the stagnation region, were most prominent,
especially in the Re = 15,050 case. The vortices forming in thejet shear layer were more prominent for Re = 5,000.

6

Copyright © 2011 by ASMEFIGURE 10. POD SPATIAL MODES 1-10 FOR RE = 5,000;
CONTOURS OF VELOCITY MAGNITUDE

FIGURE 11. POD SPATIAL MODES 1-10 FOR RE=15,050;
CONTOURS OF VELOCITY MAGNITUDE

7

Copyright © 2011 by ASMEACKNOWLEDGEMENTS
The authors are grateful to Mr. Craig Goulbourne for his
assistance with the experiment setup.
REFERENCES[1] Martin, H, 1977. ‘Heat and Mass Transfer Between
Impinging Gas Jets and Solid Surfaces,’ Adv. Heat
Transfer, 13, pp. 1-60.
[2] Downs, S. J., and James, E. H., 1987. ‘Jet Impingement
Heat Transfer – A Literature Survey,’ ASME Paper No. 87H-35, ASME, NY.
[3] Jambunathan, K., Lai, E., Moss, M. A., and Button, B. L.,
1992. ‘A Review of Heat Transfer Data for Single Circular
Jet Impingement,’ Int. J. Heat and Fluid Flow, 13, pp. 106115.
[4] Viskanta, R., 1993. ‘Heat Transfer to Impinging Isothermal
Gas and Flame Jets,’ Exp. Term. Fluid Sci., 6, pp. 111-34.
[5] Polat, S., 1993. ‘Heat and Mass Transfer in Impingement
Drying,’ Drying Technol., 11, pp. 1147-1176.
[6] Webb, B., and Ma, C.-F., 1995. ‘Single-Phase Liquid Jet
Impingement Heat Transfer,’ Adv. Heat Transfer., 26, pp.
105-134.
[7] Garimella, S. V., 1999. ‘Heat Transfer and Flow Fields in
Confined Jet Impingement,’ Chapter 7, Ann. Rev. Heat
Transfer, 11, pp. 413-494.
[8] Hadziabdic, M., and Hanjalic, K., 2008. ‘Vortical
Structures and Heat Transfer in a Round Impinging Jet,’ J.
Fluid Mech., 596, pp. 221-260.
[9] Hammad, K., and Milanovic, I.M., 2009. ‘A POD Study ofan Impinging Jet Flow Field,’ ASME FEDSM09
conference, paper FEDSM09-78398, August 2-6, Vail,Colorado.
[10] Westergaard, C.H., Madsen, B.B., Marassi, M., andTomasini, E.P., 2003. ‘Accuracy of PIV Signals in Theory
and Practice,’ 5th International Symposium on Particle
Image Velocimetry, Busan, Korea, September 22-24, Paper
3301.
[11] Meyer, K. E., Pedersen, J. M., Özcan, O., 2007, ‘A
Turbulent Jet in Crossflow Analyzed with Proper
Orthogonal Decomposition,’ J. Fluid Mech., 583, pp. 199227.

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