Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 9.3.3 - Velocity Fields and Void Fraction Measurements under Impinging Jets with Gas Entrainment
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00224
 Material Information
Title: 9.3.3 - Velocity Fields and Void Fraction Measurements under Impinging Jets with Gas Entrainment Experimental Methods for Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Danicu, D.
Kendil, F.Z.
Mishra, A.
Schmidtke, M.
Lucas, D.
Hampel, U.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: gas entrainment
particle image velocimetry
liquid velocity fields
simulation
 Notes
Abstract: Particle Image Velocimetry (PIV) is a powerful measurement technique, suitable for the study of complex flow fields encountered in single- or two-phase flow phenomena. Air entrainment is a widely studied phenomenon, which is encountered in multiple industrial applications, as well as in nature. Results from the successful application of PIV to both impinging region and recirculation zone are presented. Both instantaneous and time-averaged flow fields were obtained. The turbulent kinetic energy is estimated from the averaged velocity fields in the recirculation zone. Simulations of the phenomenon are performed with ANSYS-CFX. The turbulence was modelled using the k-epsilon model. Experimental results were compared with the simulation and showed good agreement.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00224
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 933-Danciu-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Velocity Fields under Impinging Jets with Gas Entrainment


Dana-V. Danciu1, Faiza Zidouni Kendil2, Avanish Mishra3, Martin Schmidtke1,
Dirk Lucas' and Uwe Hampel1

Forschungszentrum Dresden Rossendorf, Dresden 01314, Germany
2 Nuclear Research Center of Birine, Birine 17200, Algeria
3 Department of Mechanical Engineering and Mining Machinery Engineering, Indian School of Mines, Dhanbad 826004, India



Keywords: gas entrainment, particle image velocimetry, liquid velocity fields, simulation





Abstract

Particle Image Velocimetry (PIV) is a powerful measurement technique, suitable for the study of complex flow fields
encountered in single- or two-phase flow phenomena. Air entrainment is a widely studied phenomenon, which is encountered
in multiple industrial applications, as well as in nature. Results from the successful application of PIV to both impinging
region and recirculation zone are presented. Both instantaneous and time-averaged flow fields were obtained. The turbulent
kinetic energy is estimated from the averaged velocity fields in the recirculation zone. Simulations of the phenomenon are
performed with ANSYS-CFX. The turbulence was modelled using the k-epsilon model. Experimental results were compared
with the simulation and showed good agreement.


Introduction

Impinging liquid jets occur in different technical
applications, e.g. during filling a tank with liquid. One
prominent example from Nuclear Safety Research is
connected with the emergency core cooling (ECC) and it
may be activated during a loss of coolant accident (LOCA)
on a power plant. In some accident scenarios the cold water
is injected into the cold leg which is partially filled with hot
water and steam. For the integrity of the reactor pressure
vessel (RPV) sufficient mixing of cold and hot water needs
to be assured in order to avoid thermal shock. This is a
crucial issue especially for aged reactor pressure vessels. It
is known that gas entrainment in the jet region may enhance
liquid-liquid mixing due to bubble induced turbulence.
The interaction between the two phases in a bubbly flow is a
phenomenon not completely understood, that still needs to
be studied in detail. This particular flow is important not
only in the nuclear industry, but also in the chemical,
petroleum and medical industries. The turbulence
phenomena in bubbly flow regimes need to be better
understood for the improvement of predictions of the flow
behavior and the heat and momentum transfer
characteristics. A clear understanding of these physical
processes has a direct impact in developing and improving
many engineering systems. The study of the turbulence
structure in a two-phase bubbly flow is one of the problems
in which experimental, numerical and theoretical work is
being extensively done nowadays. It is considered that the
turbulence in two-phase flow has two different sources: one
is the turbulence generated in the continuous liquid phase,
and the other is the turbulence induced by the movement of
the bubbles in the flow.


Flow visualization measurement techniques have been used
over the years to study two-phase flows. They can provide
information at any point in the measurement zone. From
these, Particle Image Velocimetry (PIV) is the most
appropriate non-intrusive flow measurement technique that
yields a 2D velocity field. This technique is a very efficient
tool since it can obtain both qualitative and quantitative
spatial information about the studied flow. Transient
information is also available since a series of pictures of the
same area under study can be taken in a very short time. In
the past years, PIV has become a standard tool for fluid
mechanics studies. Reviews about PIV techniques have
been presented in [1], [4] [8]. With PIV, the velocity is
measured by recording the displacement of microscopically
small neutral density particles. The tracer particles are
embedded in the volume of the flow. They are illuminated
by two short light pulses fired with a known time separation.
The images appear with spacing proportional to the local
velocity vector. The problem is to track and extract the
velocity information quickly and accurately from the pattern.
Different tracking methods may be used to process the data.
Among these, techniques like cross-correlation [9], particle
tracking velocimetry, etc. are included. Recently, new
algorithms based on pattern recognition are becoming
popular; among them neural networks, genetic algorithms,
and fuzzy logic techniques seem to have good potential for
PTV [14].
Presently, much effort is spent to qualify Computational
Fluid Dynamics (CFD) codes to reliably predict the mixing
phenomenon that takes place under impinging jets and the
corresponding resulting thermal loads on the RPV walls.
For the validation of the CFD codes, experimental data with
high resolution in space and time are needed. Very little






Paper No


work has been published describing the use of PIV in the
investigation of air entrainment. However, some work has
been done regarding the investigation of dilute two-phase
flows. In this case, usually bubbles were injected in an
upward flow in a pipe ([10], [11]). As opposed to this flow,
in the case of air entrainment under plunging jets, large
amounts of bubbles are being created and carried downward
under the jet momentum. Rarefied plumes are present only
for low jet velocities. The aim of the presented work is to
provide a database with high spatial resolution needed for
modeling the turbulence of the liquid phase and for the
validation of CFD codes. Instantaneous and high accuracy
time-averaged velocity vector maps are obtained from the
processed experimental data. Comparisons between
experimental and simulation data show good agreement.

Experimental Facility

Air entrainment under plunging jets is a complex
phenomenon that has been studied over the years. Still,
despite extensive studies present in the literature ([2], [3],
[5]), the physics of the phenomenon is not completely
understood and there are still some unquantified parameters
that play an important role in the occurrence of air
entrainment. This experimental study aims for the liquid
velocity fields outside the bubble plume, as well as for the
jet velocities in single-phase flow.
The experimental setup was constructed to enable us to
conduct measurements of the interaction between the
entrained bubbles and the water in the pool. It consisted of a
flow system, an optical system and a data acquisition system.
These are described in detail next.
A schematic of the experimental setup is shown in Figure 1.
Water is being pumped out of the tank and reinjected back
in through a 16mm diameter smooth Plexiglas pipe used as
a nozzle. The outlet suction pipe is situated in the right back
corner of the tank and has a diameter of 2 cm. The jet is
impinging into a 300 mm x 300 mm x 500 mm rectangular
Plexiglas tank filled with deionized water. Air is being
entrained in the form of air bubbles of average size 4-5 mm
spherical-equivalent diameter. Sequences of the flow over
the centre vertical plane of the tank were recorded using a
CCD camera with a resolution of 1376 x 1040 pixel2 and a
maximum frequency of 5 Hz. To be able to follow the flow
correctly, the water was seeded with PMMA Rhodamine B
fluorescent particles with a density of 1.016 g/cm3 and
diameter of ca. 20 jim. The particles need to be small
enough to effectively follow the flow, and large enough to
reflect a sufficient amount of light to be detected by the
camera. Throughout the measurements, the tracer particles
were distributed homogeneously over the whole viewing
volume. Mixing was assured by the entrainment
phenomenon itself.
A twin Nd: YAG high-energy (400mJ) pulsed laser was used
as illumination source of the seeded flow, equipped with
sheet optics. The 532 nm frequency was selected for
illumination because it delivered the maximum power
output. The laser pulse width was 10 ts. The light sheet
optics provided by LaVision handles beam diameters of up
to 12 mm. The dimensions of the light sheet can be adjusted
by refocusing the light-sheet thickness as well as by
interchanging different divergent lenses. To ensure that only
the scattered laser light can reach the CCD of the camera


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

and that the unwanted background light is suppressed, a
high-pass optical filter was used with the camera. The
sequence recording is started with an internal trigger signal
and the incoming light is integrated on the CCD sensor and
read out as 12 bit data to the PC. The camera is operated in
the double frame/double exposure mode. Double frame
images can be evaluated using cross-correlation. The image
analysis is performed using DaVis 7.2 developed by
LaVision. The software has also the function of controlling
the signal system: timing of laser pulses, camera triggering
and data acquisition, triggering of external devices.


Double pulsed
Nd:YAG Laser


CCD Camera


1 st frame


2nd frame


-Nozzle


% MW Pump

t Laser sheet





t cross-correlation


image (double frame)


Figure 1: Schematic of the experimental setup.

Prior to the measurements, camera calibration was
performed. Camera parameters were determined using a set
of images with known world coordinates. Internal camera
parameters, like e.g. focal length or point distances, etc. can
also be computed through camera calibration. The
calibration was relatively non-complicated considering that
only one camera was used for recording the flow. A ruler
was placed in the measurement plane. Images of it were
taken to determine the pixel to mm ratio.
The experimental test matrix consists of four different jet
lengths chosen for testing: Ocm (single phase case), 5 cm,
7.5 cm and 10 cm. Also, for each jet length, six different
nozzle exit velocities were investigated, ranging from 1 m/s
to 2 m/s. The jet impact velocity is obtained assuming free
fall for the jet after leaving the nozzle:


v T = vo +2gLj


where vo is the velocity at the nozzle exit, Lj is the jet length
and g is the gravity.
For the given range of nozzle velocities the nozzle Reynolds
numbers are between 16 x 103 and 32 x 103. Since the






Paper No


critical Reynolds number for pipes is 2300, we obtained a
fully developed turbulence at the nozzle exit. We can also
assume, that turbulence is further generated in the hose,
which feeds the nozzle with water, because the critical Re
number is exceeded there, too. According to eq. 1, the
impact velocity of the jet, vj, is found between 1.4 m/s and
2.4 m/s.
Four different entrainment regimes are described in the
literature [5]. The "no entrainment" regime is found to be
present for the case of the submerged jet.
"incipient/intermittent entrainment" takes place in this setup
for jet velocities between 1.4 m/s and 1.55 m/s. For the rest
of the experimental matrix, the "continuous entrainment"
regime was established. With the chosen parameters, the
existence of all four entrainment regimes was assured.
In the case of single-phase measurements, for each
experimental condition, two different sequences were
recorded for two different laser pulse separations. For the jet
region, the proper difference was dt = 2 ms, whereas for the
recirculation zone dt = 20 ms was chosen. In the two-phase
cases, only the recirculation zone of the tank could be
quantified. The bubble plume obstructs the laser light and
particles and bubbles are overlapping so that a
quantification of the flow fields for both phases is quite
impossible.

System Limitations

The correct choice of seeding particles is critical to the
successful execution of PIV. A big variety of tracer particles
is available on the market. They satisfy even the most
difficult measurement requirements and are made of
materials like: nylon, polystyrene, titanium dioxide, glass,
etc. Tracer particles should be small enough to follow the
measured flow, but large enough to generate a strong
scattering signal. Standard particle sizes range from 1 itm to
100 ltm. Particle size, composition, density, shape and
concentration are important factors when selecting the tracer
particles. The ability of the particle to follow the flow
depends on the particle's geometric diameter and density. A
smaller diameter is associated with a higher frequency
response and a greater ability to follow rapid flow
fluctuations. To find the most appropriate particles for our
experiments, preliminary tests were carried out. It was
observed that polystyrene seeding particles ranging from 10
itm to 100 itm are not adequate. Even though the particles
followed the flow accurately, they had a rather short settling
time. Another problem is created by the bubbles present in
the light sheet. These reflect most of the light and create
shadows in the light sheet direction. The laser light is
obstructed by them and the tracer particles behind them are
not being illuminated properly. Even more, the light
reflected from the bubbles might also damage the CCD
sensor of the camera. For the implementation of PIV in
multiphase flow measurements, phase discrimination is
necessary. Therefore, fluorescent particles were chosen. The
fluorescent particles absorb some of the exciting discrete
light and emit, on the other hand, apart from the normal
reflection, light with a higher wavelength. For the
visualization of the flow, only the light emitted by the
particles at a higher wavelength is captured, by using a
high-pass optical filter in front of the CCD camera. Laser
induced fluorescence can be explained using the Stokes


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

relations that describe the relative phase of light reflected at
a boundary between materials of different refractive index.
The fluorescent particles used in these experiments were
coated with Rhodamine B. They emit light in the range of
550 nm and 710 nm, with an emission peak at 584 nm.
Even though the concentration of the tracer particles used in
the experiments is very small, their influence on the
interfacial area between the two phases can not be
completely foreclosed. Investigations on the influence of
impurities on bubble velocities were made by Clift et al.
(1978) and according to this work bubbles move faster
upwards in contaminated water than in pure water. The
velocity difference ranges up to 10 cm/s.

Processing Methods and Experimental Results

The sequences acquired for the different experimental
conditions were processed using DaVis 7.2 provided by
LaVision. Instantaneous as well as time-averaged velocities
were obtained from the recorded data. The results are used
to analyze the flow structure and the turbulence dissipation.
Considering that images were acquired in a double
frame/double exposure mode, cross-correlation mode was
chosen for data analysis. Each image of the recorded sets is
divided in so-called interrogation windows. The algorithm
computes the cross-correlation of all interrogation windows
between frame n and frame (n+1). This yields one velocity
vector for each interrogation window.
In the case of single-phase impinging experiments, as well
as for the two-phase flow experiments, the images were
divided into 32 x 32 pixel initial interrogation windows with
an overlap of 50% and a multi-pass iteration with
decreasing window size was applied. The resulting grid had,
thus, a size of 8 pixel. In this manner, the window shift is
improved and vectors are calculated more reliable in the
next steps. Also, using this method, the spatial resolution of
the vectors is improved and less erroneous vectors are
produced. Figure 2 contains an exemplification of the
selection of the area of interest (AOI) for a particular
recorded image and the coordinate system as well.


Jet axis


300
Free surface

24O
2(0
190
100"

no

100


32



Initial interrogation win
size 32 x 32 pixel with !
overlap 16 pixel grid





Tank wall


...... AOI
X axis
Figure 2: Example of the chosen AOI
spacing


Y axis


and initial grid


The AOI varies from one jet velocity to another, as a
function of the plume density. For the single phase flow, the






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


entire area from underneath the free surface is selected. Left
out of the AOI is the left side of the picture, corresponding
to the tank wall, as well as ca. 2 cm above the bottom of the
tank due to poor illumination. An example of the computed
velocity fields in the jet area (single phase flow) is presented
in Figure 3. The outlet velocity was 1 m/s. Figure 3a shows
the instantaneous vector fields for one image and Figure 3b
shows the time-averaged velocity fields over 40 s
measurement time.


a. b.
Figure 3: Example of instantaneous measured velocity
fields (a) and time-averaged velocity fields (b) for vo = 1
m/s and Lj = 0 cm.

The trend of the velocity on the jet centre line is presented
in Figure 4. In the immediate region under the free surface,
velocity gradients are high. After the first 5 cm, the velocity
decreases slowly and reaches very small values close to the
bottom of the tank. A difference of 2 cm/s between
simulation and experiments can be noted.


U = Ux+UY


where Ux and U- represent the time-averaged velocities
along the X- and Y-axis and are given by:
1N
Ux (x, y)= u,, (x, y) (3)
N -
1 N
UY (x, y)= N U,, (x, y) (4).
N -1
Figure 3a shows the turbulent behaviour of the phenomenon.
The velocity field has therefore an asymmetrical distribution.
It is also noticeable that the instantaneous velocity is locally
higher than the time-averaged velocity. On the other hand,
the time-averaged velocity fields are coherent and uniformly
distributed along the jet axial and radial direction.
The instantaneous and mean velocities are used to calculate
the fluctuating velocity, needed to further on calculate the
turbulent kinetic energy dissipation of the flow. The
fluctuating velocity is calculated as:
1N
U'= (U -U) (5)
N -i

whereas the averaged turbulent kinetic energy is calculated
as:

K=(U + 2) (6)

where Ux and U' represent the averaged components of
the fluctuating velocity along the axes.
In Figure 5 the turbulent kinetic energy for the same
velocity is presented.


* Experiments
3D simulation
2D simulation


0,30 0,25 0,20 0,15 0,10 0,05 0
Vertical distance from the bottom of the tank (m)
Figure 4: Vertical velocity component evolution on the jet
center line, averaged over time

In each processed image, information about each
instantaneous velocity vector, U, is contained. Each vector
consists of two components: u,(x, y) representing the
velocity along the X-axis and Uy(x, y) representing the
velocity along the Y-axis. The time-averaged velocity is
calculated as:


Figure 5: Example of the kinetic energy dissipation for
vo = 1 m/s and Lj = 0 cm.

The turbulence measurement is the combination of the
turbulence effect in the flow and the fluctuating velocity
components due to relative motion between the
measurement volume and the velocity gradients in the flow.
The shear layer surrounding the jet is a region of intense
velocity fluctuations (Figure 3a) with maximum values
located in the region of highest mean velocity gradients.
Similar to other complex turbulent flows, turbulence is
anisotropic with the relative magnitude of the normal
stresses changing along the flow. Large effects of flow
distortion on the turbulence structure can be noted. This


Paper No






Paper No


behaviour is associated with the interaction between normal
stresses and normal strains [17]. Also, turbulent diffusion
and dissipation are important in the balance of turbulent
kinetic energy.
In the case of two-phase flow (Lj > 0), only the recirculation
zone can be quantified by means of PIV (see Figure 2). Due
to the high amount of bubbles present in the plume and their
overlapping with particles, velocity measurements cannot be
carried out in the impingement zone. It must be mentioned,
that the size of the analyzed window from the recorded
images varies with the plume size. Nevertheless,
quantification of velocity fields in the outer region shows
the existence of one or two vortices in the 2D measurement
plane, as described in the literature. It is expected that these
improve and contribute to the transport of mass and energy
in the outer region. An example of the velocity field
distribution outside the jet region is presented in Figure 6.
Figure 6 presents the outer velocity fields for a jet length Lj
= 5 cm and two different nozzle velocities vo = 1 m/s
(Figure 6a) and vo = 2 m/s (Figure 6b).
p. I


\Jet ct
Jet center line


X(mm)

b.
Figure 6: Averaged outer velocity fields for Lj = 5 cm and
vo = 1 m/s (a) and vo = 2 m/s (b).

It was also observed, by analyzing single images of the
recorded sequences that even in the case of two-phase flow,


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

for vo < 1.5 m/s, the vortex in the upper region is not always
present. We assume the vortex to be induced by the rising
bubbles in the flow. However, for lower velocities, the
amount of bubbles is smaller, leading thus to a transient
behaviour of the flow field.

Measurement Accuracy

The global measurement accuracy in PIV is a combination
of a variety of aspects extending from the recording process
to the methods of evaluation [15]. The built-in errors of the
PIV technique limit the accuracy of the instantaneous
velocity vector fields. Various factors must be optimized in
order to obtain both high accuracy and high spatial
resolution measurements. Some of the factors have to be
taken into account before the data acquisition. In order to
attain a minimum error in estimating the displacement
correlation peak, the imaged particle size on the CCD sensor
of the camera has to be in the order of 1-2 pixel, as
described in the literature. The probability density function
(PDF) of a vector field can be computed in DaVis. The PDF
curve can be used to check the "peak locking" effect.
Acceptable values for the peak lock are between 0 (no peak
locking) and 0.1. The values of the peak lock in our
experiments were found to be maximum 0.01 and particle
sizes were in the range of 1-1.5 pixel. Another factor to be
taken into consideration at the recording stage is the tracer
particle concentration. The medium concentration of the
tracer particles is characterized by the fact that matching
pairs of particle images cannot be detected by visual
inspection of the recording. Also, large displacements of the
particles between exposures are desirable in order to achieve
high accuracy velocity estimates. The processing method is
another key factor in reducing the error of the measurements.
Cross-correlation was used with multi-pass processing and a
total number of 6 iterations with decreasing interrogation
window size. In this manner, the evaluation starts in the first
pass with the initial interrogation window size (32 x 32) and
a reference vector field is calculated. In the next pass, the
interrogation window is half the size of the initial one and
the vector calculated is used as best-choice image shift [7].
Thus, the window shift is improved and vectors are
computed more accurately in the following steps. This
method allows using a much smaller final interrogation
window size than it would be possible without adaptive
window shifting. In this way, the spatial resolution of the
vector field is improved and less erroneous vectors are
produced.
To calculate the overall error in the measurements, for each
experimental condition, three different sequences were
recorded. A standard deviation of 5 % was obtained for the
experimental obtained velocity fields. However, part of the
5 % difference between values are due to the errors
introduced by the instabilities of other components in the
setup, like for example fluctuations in the pump, error of the
flow meter.

CFD Simulation Approach

The numerical simulations were performed using
ANSYS-CFX 12.0, which is a commercial CFD package
that solves the Navier-Stokes equations via a finite volume
method and a coupled solver. The simulations were only





7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


done for single phase jet flow in three- and two-dimension
frame in order to estimate the effect of two dimension
approximation.
The continuity equation for liquid has the following form:


+ V.p = 0 (7)
dt
The momentum equation for computational domain in its
generalized form can be written as:


-p+ divpu = -grad(p) +
div[grad(u)]+ pg
diviu[grad(u)]+ pg


where g is the acceleration due to the gravity, p is the fluid
pressure, p and p are density and viscosity of the fluid,
respectively.

Turbulence Modeling. Since the liquid velocity exiting the
nozzle is relatively high, it is appropriate to simulate the
flow in the jetting system using a turbulent flow model. In
this case, every variable of the flow can be written as a
combination of its average and fluctuating component. For
example, the flow velocity variable, ), can be written in the
standard way as: ) = )average + )'. Inserting the
decomposed variables to instantaneous equations and
applying Reynolds averaging, yields a set of Reynolds
averaged conservation equations for mass and momentum,
as well as the turbulence kinetic energy, k, and its
dissipation rate e. For later convenience and dropping the
over-bar of the mean variables, the Reynolds averaged
equation can be written in the following generic transport
equation form:


-(pk) +- (pku,)=
at ax,

S\ +ILt k ]+Gk+Gb-pE-Yu+Sk




&t ax, aX, Uk aX,
2(9)
+C1 -(Gk + C3Gb)- C2p--+S,
k k

where:
Gk is the generation of turbulence kinetic energy due
to the mean velocity gradients;
Gb is the generation of turbulence kinetic energy due
to buoyancy;
YM represents the contribution of the fluctuating
dilatation in compressible turbulence to the overall
dissipation rate;
CIe, C2,, and C3, are constants;
Ok and o, are the turbulent Prandtl numbers for k and
o, respectively;
Sk and S, are user-defined source terms.

The turbulent (or eddy) viscosity, pt, is computed by


combining k and e as follows:


fr = pC k- (10)
where C, is a constant.
The model constants C1e, C2t, C,, Ok and o( have the
following default values:
C1i = 1.44; C2, = 1.92; C,= 0.99; Ok = 1.0; cy = 1.3.


Computational Methodology


Geometry and Grid Arrangement. A cylindrical tank
with a diameter of 15 cm is filled with water. The nozzle
diameter is 16 mm. Two and three dimensional simulations
were performed to highlight the effect of the two dimension
approximation on the results.

Two dimension Simulation Grid. To reduce the costs of
computation time, only a section of five degrees is used for
the simulation, as a 2D axisymmetric calculation (see Figure
7). The structured mesh has 75 cells for the total height of
the domain. For the radius of the water inlet, 7 uniform cells
are used and 30 cells for the opening. The grid is refined by
reducing the cell size near the impinging region, where the
flow behaviour has to be well captured.



















Figure 7: Grid arrangement in 2D simulation.

Three Dimension Simulation Grid. The symmetry of
the configuration allowed us to consider a quarter of domain
for the computation. The three dimensions computational
domain was meshed non-uniformly by the tetrahedral
scheme. Hence, the clustering was automatically made
towards the centerline of the water jet direction. Grid
contraction toward the free surface was required for
capturing liquid flows near the jet impingement.

Boundary Conditions. Four boundary conditions were
used to describe the flow field within the computational
domain:
For the water jet inlet: a fully developed pipe flow is
specified for liquid velocity and kinetic energy profiles.
These profiles were determined using an independent
calculation of a long pipe (0.5 m long and 16 mm inner
diameter).


Paper No







7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Top vessel boundary condition: a free slip wall
boundary condition is applied to yield the water to circulate
transversally toward the wall before flowing downward to
the outlet region.
The cylindrical vessel walls and bottom walls are
considered as no-slip wall boundary.
-The water outlet is an opening boundary with
hydrostatic pressure specification equal to pgh where h is
the height of the water vessel.



Comparison of the model results with experimental
data


The average velocity profiles are presented in Figure 8.
We can observe that the agreement between experiments
and simulations is very good for most of the axial positions.
However, a small difference between the 2D and 3D
simulation appears, but only in the upward flow, where the
velocities are very small.


Y=15cm from the bottom


-2D Simulation
3D Simulation
-- Experimental


-0,08 -0,04 0,00 0,04 0,08 0,12 0,16
Distance from the jet center line (m)


Y=25cm from the bottom


-0,2-


0,0-


0,2-
0
E
S0,4-
X
o
-

S0,6-
>

S0,8-


1,0-


1,2


- 2D Simulation
3D Simulation
-- Experimental


Y=10 cm from the bottom


2D Simulation
3D Simulation
Experimental


-0,08 -0,04 0,00 0,04 0,08
Distance from the center line (m)


0.12 0.16


-0,08 -0,04 0,00 0,04 0,08 0,12 0,16
Distance from the jet center line (m)


Y=20cm from the bottom


0,4-

0
o
S0,6-


S0,8-

1.0-


--2D Simulation
3D Simulation
-*- Experimental


Y=5cm from the bottom


2D Simulation
3D Simulation
-Experimental


-0,08 -0,04 0,00 0,04 0,08 0,12 0,16
Distance from the jet center line (m)


Figure 8: Average velocity profiles in radial direction.


-0,04 0,00 0,04 0,08
Distance from the jet center line (m)


012 0,1 The turbulence kinetic energy contour presented in Figure 9
highlights the jet core corresponding to a low turbulence at
the jet axis. Similar to the contour obtained from the
experiments (see Figure 5), the maximum of the turbulent


Paper No


- 0,4-
-
X,
o
0
0-
S0,6-
>
-
S 0,8-


-0,2-


0,0-


0,2-

E
0,4-


" 0,6-


S0,8-


1,0-


I I I I I I I






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


kinetic energy is located in the mixing layer around the jet
axis and in the impinging zone at the bottom wall of the
vessel.

k [m2s2]

2.49e-02



2.137e-02




1A25e.02




7.123 e-03


1.194 e-07


o,
0,01

0,02-
o
S0,03.

0,04.

0,05.


Y=20 cm from the bottom


2D calculation
- 3D calculation
--- Experimental


-0,09 -0,06 -0,03 0,00 0,03 0,06 0,09
Distance from the jet center line (m)


0,12 0,15


Y=15 cm from the bottom


Figure 9: Turbulent kinetic energy contour.


The radial distribution of the turbulent kinetic energy along
several lines situated at different axial positions is presented
in Figure 10. As it can be seen, the agreement between
experiments and simulations is quite good for most axial
position and the profiles are similar. The profile
corresponding to the position close to the jet outlet (25 cm
from the bottom) shows a good agreement with the
experiment. Also noticeable is a minimum of the turbulence
close to the jet exit, which corresponds to the jet core. We
can also state that the difference between the 2D and 3D
simulations is not big, so that the 2D approximation should
be an acceptable manner for performing more complicated
calculations, such as two-phase flow simulations, with an
acceptable CPU time.


0,00.

0 0,01.


S0,02.
o
. 0,03.

0,04-

o0,05


2D calculation
- 3D calculation
--- Experimental


-0,09 -0,06 -0,03 0,00 0,03 0,06 0,09 0,12 0,
Distance from the jet center line (m)


-0,01 -


Y=25 cm from the bottom


0,00-


E 0,01-

0,02-
C,
S0,03.

0,04.

0,05.


2D calculation
- 3D calculation
-*- Experimental


-0,09 -0,06 -0,03 0,00 0,03 0,06 0,09 0,12 0,15
Distance from the jet center line (m)


Y=10 cm from the bottom


2D calculation
- 3D calculation
-- Experimental


-0,09 -0,06 -0,03 0,00 0,03 0,06 0,09 0,12 0,15
Distance from the jet center line (m)


Paper No






Paper No


Y=5cm from the bottom


-
S0,01-

0,02-
-

0,03-

0,04-
20
S0,05-


2D calculation
- 3D calculation
--- Experimental


-0,09 -0,06 -0,03 0,00 0,03 0,06 0,09
Distance from the jet center line (m)


0.12 0.15


Figure 10: Turbulent kinetic energy profiles in radial
direction.

Conclusions

Experiments and simulations were carried out to study the
development of velocity fields under an impinging jet.
Experiments as well as simulations show that the axial
liquid velocities are damped with increasing penetration
depth. Also, the turbulent kinetic energy has a similar
behaviour. The radial profile was observed to be widened
around the jet axis with increasing penetration depth for
both axial velocities as well as turbulent kinetic energy.
Results obtained using PIV are in very good agreement with
the 2D and 3D simulations for the single phase flow. The
existence of a recirculation vortex was observed in the lower
region of the tank, near the wall.
In case of the two-phase flow, the existence of another
vortex was observed in the upper region of the tank, a few
centimetres under the free surface. Its appearance is due to
the rising bubbles from the plume.
The single-phase approach is the first step in describing the
velocity and turbulence fields developed under jet
impingement. The next step is the modeling of the
two-phase flow phenomenon and comparison of the data
with experimental results.


Acknowledgements

Special thanks go to Dr. Ralph Lindken, TU Delft,
Netherlands, and Christof Surmann, LaVision GmbH,
Germany, for their help and guidance in working with the
optical laser system.

References

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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

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