4TH INTERNATIONAL CONFERENCE ON EXPERIMENTAL FLUID MECHANICS
Beijing, China, August 12-15, 2014

Experimental Investigation of Jet Impingement by Stereo PIV
Hua Wang1*, Gӧkhan Ergin1
1. Dantec Dynamics A/S, Skovlunde, Denmark* Corresponding author: hwg@dantecdynamics.com

Abstract
Impinging jets have been studied extensively thanks to their potential in obtaining high convective heattransfer rates in various applications that require intensive heating or cooling. As a first step, a better
understanding of the flow field is essential in order to reveal the mechanisms for the enhanced heat transfer
rates. For this purpose, a stereo PIV experiment has been performed on a jet impinging on a flat plate at room
temperature with a moderate Reynolds number (Re=4000). The three-component velocity field is measured in
the center plane of the jet using a Stereoscopic PIV system. Finally, a proper orthogonal decomposition (POD)
analysis is performed, revealing the modes involved in the process. The POD analysis indicates that thevortical structures sweeping over the flat surface may be the reason for increased convective heat transfer fromthe surface.
1. Introduction
Impinging jets on a plane surface are frequently used for intensive heating or cooling in various applications[1]. The reason is that impinging jets are known to produce some of the highest Nusselt numbers using
single-phase convection in the vicinity of the stagnation/impinging point [2]. As a result, numerous studies
have been conducted to reveal the heat transfer characteristics of impinging jets under various conditions, andone of the earliest experimental studies is reported in Reference 3. A summary of generic correlations,
including many parameters for both single jets and multiple jet arrays, can be found in Reference 4.
Realizing that the essence of heat transfer enhancement lies in the flow field and turbulent fluid motion, somerecent works have focused on measuring both the mean and fluctuating velocities, aiming to provide more
information about both the mean flow and turbulence characteristics [1]. Early research used ConstantTemperature Anemometry (CTA) or Laser Doppler Anemometry (LDA) to measure the fluctuating velocity
components point by point [5]. Recently Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry(PTV) methods are more frequently applied, for simultaneous measurement of 2- or 3-component velocity
fields in a plane or in a volume [6-7].
Although numerous velocity measurements have been reported, at various experimental conditions, mostmeasurements are performed to obtain 2-components of the velocity. In order to get a better understanding of
the three-dimensional flow field, the acquisition of 3rd velocity component is quite important. Stereoscopic
PIV is one of the PIV techniques, which can measure three velocity components in a plane (2D3C) at the sametime, based on the principle of parallax [8]. Compared with Volumetric PIV (3D3C), it is much less complex,
while still capable of providing 3D information about the flow. In the present work, Stereoscopic PIV
measurements are performed on an impinging jet, aiming to unveil detailed information about the flow field. In
particular, all of the three velocity components measured in the jet center plane will be presented and analyzed
in depth. In addition, a Proper Orthogonal Decomposition (POD) analysis is performed to produce a deeper
insight into the flow field dynamics. This has been proved to be a powerful and elegant method to extract thedominant features from the flow field [9].
2. Experimental Setup and data processing
2.1 Flow rig
Figure 1 illustrates the impinging jet flow rig and the stereoscopic imaging setup. The continuous air jet was
produced using a blower-type fan, situated well upstream of the nozzle exit. The flow passes through aconverging section before the nozzle exit with an internal diameter of D=30mm. Dimensions of the converging
section and the nozzle is also given in Figure1 in terms of the nozzle diameter, D. A screen was installed
upstream of the converging section to break down larger turbulent structures in the flow. It was observed that

4TH INTERNATIONAL CONFERENCE ON EXPERIMENTAL FLUID MECHANICS
Beijing, China, August 12-15, 2014

the jet studied in this measurement was not fully developed at the exit of the nozzle, but rather had anear-top-hat profile.
The jet impinged perpendicularly to the center of a square, flat metal plate, with a planar dimension of 10D x
10D, and situated 2.7 D away from the nozzle exit. An orthogonal coordinate system is defined with its origin
at the center of the jet exit, is shown in Figure 1. The y-axis is measured along the jet axis and is taken as
positive in the jet mean flow direction. The x- and z- coordinate is measured along the jet exit plane.

Figure 1 Flow rig and Stereo PIV set up

2.2 Measurement setup
A Dantec Dynamics PIV system is used for the velocity measurements, comprising a DualPower 65-15
Nd:YAG twin cavity laser (max. power per pulse 65 mJ, max. trigger rate15 Hz), two FlowSense EO CCD
cameras (2046 x 2046 pixels2, 12 bit) two Nikkor 60 mm lenses, a Timerbox for the synchronization and
DynamicStudio software to control the whole measurement. The angle between the two cameras was set to be
90° and the cameras were symmetric with the z-axis (shown in Figure 1), to achieve the best stereoscopic
reconstruction accuracy. Each of the cameras was mounted onto a special mechanical mount to enforce theScheimpflug condition and thereby achieve well-focused particle images in the whole field of view. The
aperture of each lens was set to be f/8 for sufficient SNR for stereo PIV processing. A narrow band pass filter
was mounted in front of each camera lens to remove the ambient light. The overlapped Field of View wasapproximately 100 x 100 mm2, resulting an image resolution of 70 µm per pixel.
Light sheet optics was mounted at the laser exit to generate a diverging light sheet, passing the center of the jet
through x-axis. The light sheet had a width less than 1 mm. The tracer particles were µm-sized olive oil
droplets, generated from a liquid atomizer. These droplets were injected into the flow well upstream of thenozzle to ensure uniform seeding with negligible influence on the jet flow downstream.
Double frame images were acquired with pulse separation time of 120 µs and a frequency of 9 Hz. This pulse
separation resulted a particle displacement in the jet potential core area as approximately 10 pixels, which ismostly accepted for PIV processing. In total, 1000 image pairs were recorded for statistical analysis.
Each camera was calibrated by capturing still images of a dot-pattern target (100 x 100 mm2) at seven differentz positions (from –3 mm to 3 mm, with 1 mm intervals). The calibration was performed using a 3rd-orderpolynomial mode [10] and the reprojection error for each camera view was approximately 0.7 pixels.
2.3 Data processing
Adaptive PIV processing routine in DynamicStudio was used to process each image pair. The algorithm is an
iterative and adaptive cross-correlation based displacement estimator combined with window shifting, window
deformation, and sub-pixel analysis. It iteratively adjusts the size and the shape of the individual interrogation
areas (IAs) during processing in order to adapt to local seeding densities and flow gradients. The iteration
process started with an IA size 64 x 64 (pixel2), and ended with an IA size 16 x 16 pixel2. The grid step size was4TH INTERNATIONAL CONFERENCE ON EXPERIMENTAL FLUID MECHANICS
Beijing, China, August 12-15, 2014

set to be 8 x 8, which resulted an overlap of 50%. 15 iterations were carried out for each image pair to achievesufficient valid vectors; and after each iteration the universal outlier detection [11] was applied in aneighborhood of 5 x 5 vectors.
As the stereoscopic vector reconstruction is very sensitive to measurement errors originating from the 2D2C
vector maps from each camera view, sufficient smoothing is often applied before reconstruction. One way ofsmoothing vector map ensembles is a flow reconstruction using high-energy POD modes with physicalmeaning, and excluding low-energy POD modes that represent noise. For this purpose, a modal analysis andflow reconstruction is performed using POD. This was followed by another round of universal outlier detection
with a neighborhood of 9 x 9 vectors. Then stereo reconstruction was performed, based on the calibration
performed previously. Thanks to this process routine, measurement noise was largely reduced and a statisticalanalysis based on these 1000 stereo PIV dataset can be performed.
3. Results and analysis
3.1 Mean and fluctuation of the velocity field
Figure 2, 3, and 4 give the radial profiles of the mean velocity components; v, u, and w respectively. All of theshown velocities are scaled by the mean jet exit velocity – Vj = 2.25 m/s. The Reynolds number based on themean jet velocity and the nozzle diameter is computed as Re = 4,000. In Figure 2, the velocity profiles at y/D =0.2 and y/D = 1 show that the jet is still in the developing stage, tending to have a top-hat profile. Inside the jet,the vertical velocity (V) first decreases slowly as the jet moving away from the nozzle, with a slowly increasing
deceleration rate. The influence of the plate on the jet velocity is only obvious when the jet is approaching thewall: from y/D = 2 to y/D = 2.6, the velocity is decreased more than 60%.
Different from the trend shown inside the jet, the velocity increases as the measurement line approaching theimpinging plate in the area 1<|x/D|<0.5. This is mainly due to the expansion of the jet, in both the jet exit
region and impinging region. When |x/D|>1, the vertical velocity is effectively zero, although further awayfrom the jet axis, there is small negative vertical velocity near the impinging plate, indicating the rebounce ofthe jet. All of these phenomena agree well with earlier measurements [2].

Figure 2 Radial profiles of mean vertical velocity (V) at various distances between the pipe exit and the plate

As can be seen in Figure 3, the radial velocity is effectively very small when y/D<2. Nonetheless, themagnitude of radial velocity still increases slightly as the jet moving away from the nozzle, due to the jet
expansion. When the jet reaches the plate, the radial velocity increases dramatically, due to the flow turningaway from the stagnation point. The magnitude of the radial velocity near the plate (y/D = 2.6) first increases
due to the lateral expansion of the jet, until x/D = 0.6; and then the radial velocity profile decreases, indicating
an interaction between the impinging jet and the surrounded air. This also agrees with earlier measurements[2].

4TH INTERNATIONAL CONFERENCE ON EXPERIMENTAL FLUID MECHANICS
Beijing, China, August 12-15, 2014

Figure 3 Radial profiles of mean horizontal velocity (U) at various distances between the pipe exit and the plate

As seen in Figure 4, and as expected in the centerplane, the out-of-plane velocity (W) is effectively very small
in the entire measurement domain.

Figure 4 Radial profiles of mean out of plane velocity (W) at various distances between the pipe exit and the plate

Figure 5-7 show the standard deviation (std) of each velocity component at various positions – also scaled by
the mean jet exit velocity Vj. The results show similar standard deviation developing trend along all three
directions. Inside the jet (|x/D|≤0.5), the std of each velocity component first increase as the jet moving awayfrom the nozzle, and then decrease when the jet is approaching the plate, due to the stagnation of the flow. At
the edge of the jet, it shows max. std for all three velocity components at different y positions, except where thejet approaches the plate. When |x/D|>1.2, the std of all of the velocity components increases in all of the three
direction, indicating again the interaction process between the jet and the ambient air. The trend shown here isin good agreement with previous study [2].
It has to be mentioned that although the out-of-plane velocity is effectively very small in the whole field of
measurement, its std profile is similar to the std of the other two velocity components. In other words, although
the mean crossflow in the centerplane is very small, the measured turbulent fluctuations in this direction havethe same order of magnitude and spatial distribution. Additionally, this results of W’ presents a monotonic
increasing as further away from the jet axis, in the jet impact region, while the fluctuation of other two velocity
components are approximately constant outside of the jet (y/D = 2.6). The importance of stereoscopic
measurement presents itself here: as a result of the third velocity component measurement, the total turbulencekinetic energy computation is more accurate.

4TH INTERNATIONAL CONFERENCE ON EXPERIMENTAL FLUID MECHANICS
Beijing, China, August 12-15, 2014

Figure 5 Radial profiles of the standard deviation of vertical velocity (V’) at various distances between the pipe exit andthe plateFigure 6 Radial profiles of the standard deviation of horizontal velocity (U’) at various distances between the pipe exit
and the plate

Figure 7 Radial profiles of the standard deviation of out-of-plane velocity (W’) at various distances between the pipe exit
and the plate

Figure 8 shows the turbulent kinetic energy k spatial distribution, which is defined as:
k=(U’2+V’2+W’2)/2(1)

High level of turbulence is only observed in the region where jet is mixed with ambient air. In the stagnationarea, the turbulence level is effectively very low, due to the presence of the wall in this region. In the region
above the stagnation area, the turbulence level is slightly higher, which is the result of ambient air entrainment
into the jet. Above all, the strongest turbulence is observed 0.2 diameters from the plate and around 1.8
diameters away from the jet centerline. This indicates a strong interaction between the wall jet and ambient air.

4TH INTERNATIONAL CONFERENCE ON EXPERIMENTAL FLUID MECHANICS
Beijing, China, August 12-15, 2014

According to the results of std of different velocity components at different radial profiles (Figure 5-7), the U’
and V’ are approximately constant outside of the jet, but W’ is monotonically increasing in this area. This
indicates the start of tangential expansion of the jet.

Figure 8 Turbulence kinetic energy distribution

3.2 POD analysis
POD analysis has been performed to expose the high-energy modes in the flow. First a convergence analysis isperformed. The POD analysis At first, PODs for different ensemble sizes taken from the same data set were
calculated and analyzed with regard to the first 100 modes, to determine the influence of sample size on the
turbulent energy distribution. The results indicate a convergence of the spectra once the ensemble size exceeds
800 samples. Consequently, 1000 samples acquired in this study are enough to reveal the dynamics of the flow.
Figure 9 shows the eigen-value spectra of the PODs for the acquired flow field in terms of energy fraction(Figure 9 (a)) and cumulative energy content (Figure 9 (b)). The spectrum exhibits a monotonic decrease of
turbulent energy with increasing mode number, indicating no dominance of any periodic elements. In addition,
both of the energy fraction plot and the cumulative energy plot show that a considerable number of modes are
required to significantly contribute to the total turbulent energy of the flow, although 50% of the fluctuatingenergy is contained in the first 16 modes.

(a)4TH INTERNATIONAL CONFERENCE ON EXPERIMENTAL FLUID MECHANICS
Beijing, China, August 12-15, 2014(b)
Figure 9 POD eigen-value spectra for the investigated flow field

Figure 10 shows the spatial projection of the POD basis function for the first 6 modes in the jet center plane.
Both the colors and the length of the vectors indicate the velocity magnitude, which is calculated from all
three measured velocity components. Nonetheless, it has to be mentioned that the magnitude of out-of-plane
velocity (W) is effectively very small in all of the POD modes, and could be considered negligible.
The projection of the first mode shows the mean flow field (Figure 10 (a)). No large vortex structure has
been observed here, although large recirculation zone has been reported by [12]. This is primarily because
this measurement was focused on the near-field (-2<x/D<2), where wall reflection effects are mostsignificant.
However, various vortex structures can be observed from the projection of higher POD mode numbers. In
the region before the jet impinges onto the plate, vortex pairs are can be clearly observed in the second andthe third modes. In the followed two modes, the dominant coherent structures are found to be where the jet
expands. As the modes number increasing, the dominant vortex is moving from the jet edge to far field,
indicating a spatial turbulent energy transfer process: the turbulence is originally brought by the jet to themeasurement field. Upstream of the impinging, the turbulence is concentrated on the jet edge, where thevortex ring exists. Here is also where air is entrained into the jet by this vortex. During the impinging, theturbulence is moving along the plate as the jet expanding. Afterwards. The turbulence is transmitted to theambient.
In addition, a sweeping vortex structure can be observed at each side of the jet from mode 2 to mode 6. In
fact, this structure can be also observed in many other lower energy modes, although not presented here. The
existence of these structures at different modes proves that the interaction between the impinging jet and the
air has a very wide turbulence scale range. This might be also related with the increased convective heattransfer from the surface.

4TH INTERNATIONAL CONFERENCE ON EXPERIMENTAL FLUID MECHANICS
Beijing, China, August 12-15, 2014

Figure 10 shows the POD projection of each of the first six modes. The first one shows the mean flow field, which
contributes slightly more than10% of the total energy

4. Conclusions
The focus of the current study was to investigate the flow field from an impinging jet using stereo PIV
measurement. The 3 dimensional velocity field results from an impinging jet of moderate Reynolds numberof 4000 is reported at the jet center plane.
The analysis of the time-mean flow field reveals that out of plane velocity is effectively very small, although
its fluctuation presents the same developing trend as other two velocity components: the fluctuation of all

4TH INTERNATIONAL CONFERENCE ON EXPERIMENTAL FLUID MECHANICS
Beijing, China, August 12-15, 2014

three velocity components are larger in the jet edge and near-plate region, where strong interaction between
the jet and the ambient happens.
The velocity field was also analyzed by POD, allowing for a detailed insight into the fluid dynamic processes
Various modes involved in the process are presented. The results indicate that the vortical structures sweeping
over the flat surface may be the reason for increased convective heat transfer from the surface.
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Experiments in Fluids 36, 946-958[2] Fairweather, M. & Hargrave, G. K. 2002 Experimental investigation of an axisymmetric, impinging
turbulent jet. 1. Velocity field. Experiments in Fluids 33, 464-471[3] Gardon, R. & Akfirat, J. C. 1965 The role of turbulence in determine the heat transfer characteristics ofimpinging jets. Int. J. Heat Mass Transfer 8, 1261-1272[4] Martin, H. 1977 Heat and mass transfer between impinging gas jets and solid surfaces. Advances in heattransfer 13, 1-60
[5] Cooper, D., Jackson, D. C., Launder B. E. and Liao G. X. 1993 Impinging jet studies for turbulencemodel assessment – I. Flow-field experiments. Int. J. Heat mass Transfer 36 (10), 2675-2684[6] Fairweather, M. & Hargrave, G. K. 2001 DPIV measurements in axisymmetric, impinging turbulent jets.
In Processing of the 4th International Symposium on Particle Image Velocimetry, Gottingen, Germany,
September 2001
[7] Bilsky, A, Heinz, O., Ilyushin, B., Kaipov, P. & Markovich, D. 2002 PIV measurements with conditional
sampling in axisymmetric impinging jet. In: Processing of the 11th International Symposium on Applicationsof laser Techniques to Fluid Mechanics, Lisbon, Portugal[8] Adrian, R. J., & Westerweel, J. 2010 Particle image velocimetry. Cambridge University Press.
[9] Schulz, S., Schueren, S. & Wolfersdorf, J. 2014 A particle image velocimetry based investigation of theflow field in an oblique jet impingement configuration. Journal of Turbomachinery 136, 051009-1[10] Soloff, S. M., Adrian, R. J. & Liu, Z. C. 1997 Distortion compensation for generalized stereoscopic
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turbulent jet. In: Processing of the 10th Symposium on Turbulent Shear Flows 2, Pennsylvania State
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