Seventh International Conference on CFD in the Minerals and Process Industries
CSIRO, Melbourne, Australia
9-11 December 2009
SIMULATION OF FLOW THROUGH ABRASIVE WATER JET NOZZLE USING
COMPUTATIONAL FLUID DYNAMICS
Abhinav Bhaskar
CSIRO Minerals, Clayton, Victoria 3169, AUSTRALIA
Department of Mechanical & Manufacturing,
abhinavbhaskar@gmail.com
MIT,Manipal,India
ABSTRACT
The present work is a compilation of efforts to gain a
fundamental knowledge of the ultra-high velocity dynamic
characteristics such as the velocity distribution, pressure
distribution, turbulence intensity and kinetic energy of
an abrasive water jet system. . This knowledge can help
enhance the AWJ technology, understanding the kerfs
formation or cutting process and modeling the various
cutting performance measures that are required for
process control and optimization. For this purpose, CFD
analysis is found to be a viable approach because direct
measurements of particle velocities and visualizations
of particle trajectories are very difficult for the ultrahigh
speed and small dimensions involved.
The development of a theoretical approach to the
evaluation of turbulent flow and particle dynamic
properties in the nozzle is attractive because of difficulties
associated with direct measurements in nozzles of high
flow speed and small dimensions. Axis symmetric
simulations have been performed with the help of
commercial code (fluent 6.3), using the standard k-e
turbulence model. One way coupling was considered
in the simulations, which means that the effect of the
presence of the dispersed solid phase on the liquid phase
was not considered. The abrasive water jet nozzle was
modeled using a co-ordinate measuring machine and
feeding the co-ordinates into gambit. The predictions have
been compared with available experimental and theoretical
results published by other investigators. This modeling
technique will assist in the nozzle design of premixed
abrasive water-jet systems and the prediction of water jet
cutting performance. The turbulence characteristics can
be used to empower the manufacturing industries with an
optimum cutting speed and maximize nozzle life.
NOMENCLATURE
Drag coefficient
Inlet diameter of nozzle
Outlet diameter of nozzle
Particle diameter
Drag correction factor
Turbulent kinetic energy
Average depth of kerf
[km = 0.5(kmax + kmin)]
Maximum depth of kerf
Minimum depth of kerf
kmax
kmin
Copyright © 2009 CSIRO Australia
essential for improving nozzle design, as well as for
modelling, evaluating and improving AWJ cutting
performance. However, this work has proved to be
complicated. For example, the water-particle
interaction in the mixing unit is extremely intricate
while the ultra high velocity and small nozzle and
particle dimensions make the investigation of the jet
and particle behaviour difficult. Nevertheless, some
important investigations have been reported on
understanding the AWJ dynamic characteristics for
relatively low velocity AWJs and for particular jet
cutting status through theoretical and experimental
studies as well as CFD simulation. However,
research on ultra-high pressure jets and abrasive
water jets to arrive at a comprehensive
understanding of the jet properties has received very
little attention.
MODEL DESCRIPTION
The nozzle used for the experiment was a tungsten
carbide nozzle. After the co-ordinates
were measured the inside profile was generated
using gambit. The profile so generated was
composed of three steps. The solid modelling
composed of generation of frustum of cones and
definition of base radius at appropriate z-co-
ordinates. The next step was to mesh the inside
profile so generated and exporting the profile to
fluent. The gambit models of the inside profile have
been shown below.
Figure 1
RESEARCH METHODOLOGY
Steps involved
The first step for the process was to measure the co-
ordinates of the nozzle using the CMM. The objective of
the procedure was to generate the internal profile of the
nozzle. The probe of the nozzle was inserted and x and y
co-ordinate of the nozzle was measured at different z co-
ordinates. The initial results of the measurement have been
put up in the form of an excel file. Few of the co-0rdinates
have been put in the form of a table and are displayed
below.
Co-ordiantes of Nozzle
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Nozzle dimensions
The following table shows the dimensions of the abrasive
nozzle which has been modelled .
Minimum diameter of nozzle 0.9 mm
Maximum diameter of nozzle 10.12 mm
Length of the nozzle
22.498 mm
Literature Review
A turbulent K-ε model was found to be accurate enough
for this problem. The lift force and the virtual mass force
can usually be neglected in the calculations, as they give a
minor contribution to the solution with respect to the other
terms. The inter-phase momentum transfer term is very
important and it is modeled via the drag coefficient, CD.
For the multiphase model the drag correlations
implemented in FLUENT 6 apply to particles falling
in a still fluid. One of them has been tested in this
work (Syamlal-Obrien). It is well known that drag
coefficients measured for single particles in still fluids
do not necessarily apply to particles in a turbulent fluid.
Therefore, the effect of a correction to take into account
the increase in the drag coefficient due to liquid turbulence
would have to be considered (Magelli et al., 1987 and
1990; Brucato et al., 1998; Pinelli et al., 2001). Nowadays
the Magelly correction is not available in this lab, and will
be added in future papers.
For the Discrete phase model it is possible to
define a non spherical coefficients of the particles Φ=
where
same volume as the particle, and
is the actual surface
area of the particle, which increases the value of the drag
coefficient CD. This coefficient has been established in
an iterative way to satisfy the experimental results and a
value of 0.07 has been obtained. Therefore considering
that the real non spherical coefficient is 0.7 we conclude
that a correction of f = 1/10 it is necessary.
Boundary Conditions
The various boundary conditions and specifications used
for the analysis of the given problem have been listed
below:
Model Description
3D
Steady
Standard
k-epsilon
turbulence model
Wall
Standard Wall
Treatment
Functions
Heat Transfer
Enabled
Table 3:Model Description
Space
Time
Viscous
Table 2 Nozzle Dimensions
is the surface area of a sphere having the
Zones
Solid
mixture flow
Wall
Exit pressure
Inlet pressure
Default-interior
2
3
4
5
6
8
Solid
Fluid
Wall
Pressure-outlet
Pressure-inlet
Interior
Copyright © 2009 CSIRO Australia
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Velocity magnitude
Figure 4
The colour indicates the velocity of the fluid inside the
nozzle at every point.
Minimum velocity = 0 m/sec
Maximum velocity = 273 m/sec
Turbulent Kinetic Energy
Figure 5
Maximum turbulent kinetic energy = 184 m2/s2
Minimum turbulent kinetic energy = 0.125 m2/s2
The turbulent kinetic energy reaches its maximum to
184m2/sec2. We can clearly make out that the turbulent
kinetic energy has its maxima at the slant faces and
maximum at the face just before the exit. The K.E has its
minimum of 0.125m2/sec2.
Turbulent Intensity
Copyright © 2009 CSIRO Australia
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by using these results.
REFERENCES
Brucato, A., Grisafi, F., Montante, G., “Particle drag
coefficients in turbulent fluids”, Chem. Eng.
Sci., 53, 3295–3314, 1998.
Cokljat, D., Slack, M., Vasquez, S.A., Bakker, A.,
Montante, G., “Reynolds-Stress Model for
Eulerian Multiphase”, submitted, Progress in
Computational Fluid Dynamics, 2004.
Fajner, D., Magelli, F., Nocentini, M., Pasquali,
G., “Solids concentration profiles in a
mechanically stirred and staged column slurry reactor”.
Chem. Eng. Res. Des., 63, 235-
240, 1985.
Magelli, F., Fajner, D., Nocentini, G., Pasquali, G., “Solid
concentration profiles in slurry
reactors stirred with multiple impellers: recent results”,
Engineering Foundation Conference-
Mixing XI, New England College, Henniker N.H., USA,
1987.
Magelli, F., Fajner, D., Nocentini, M., Pasquali, G., “Solid
distribution in vessels stirred
with multiple impellers”, Chem. Eng. Sci., 45, 3, 615-625,
1990.
Montante, G., Micale, G., Magelli, F., Brucato,
A., „Experiments and CFD predictions Of
solid particle distribution in a vessel agitated with four
pitched blade turbines“, Chemical
Engineering Research and Design, 79, 8, 1005-1010,
2001.
Montante, G., Magelli F., „Modelling of solid distribution
in stirred tanks: analysis of
simulation strategies and comparison with experimental
data.“ Accepted to International
Journal of Computational Fluid Dynamics, 2004.
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