Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 3.7.1 - Jet and Conduit Flow Induced by Underwater Explosion in a Straight Tube
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 Material Information
Title: 3.7.1 - Jet and Conduit Flow Induced by Underwater Explosion in a Straight Tube Interfacial Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Zhu, Y.
Sun, M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: underwater explosion
jet
bubble
 Notes
Abstract: For better understanding of bubble dynamics in a confined situation, a study on jet and conduit flow induced by a wire explosion underwater in a straight tube is carried out in this paper. Experimentally, high-speed video camera is employed to record the flow field directly. Limited numerical simulations are also performed to analyze some typical phenomena. A complex flow pattern including bubble expansion, collapse, jet formation and interactions between bubble and free surface are extensively revealed and interpreted. It is found that the water jet is mainly induced by a strong rarefaction following shock-surface interaction. The speed of the jet is strongly related to initial curvature of the water surface where gathering energy effect applies. This study also reveals two typical collapse modes of explosion bubble, where one is broken up by air penetrating upper water layer and flushing into the bubble, and the other undergoes a similar process as that of RM instability without direct interaction of atmosphere and the bubble.
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: VID00094
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 371-Zhu-ICMF2010.pdf

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


Jet and Conduit Flow Induced by Underwater Explosion in a Straight Tube


Y.Zhu and M. Sun

Center for Interdisciplinary Research, Tohoku University, Sendai, 9808578, Japan
yjzhu@iswi.cir.tohoku.ac.jp and sun@cir.tohoku.ac.jp
Keywords: underwater-explosion, jet, bubble




Abstract

For better understanding of bubble dynamics in a confined situation, a study on jet and conduit flow induced by a
wire explosion underwater in a straight tube is carried out in this paper. Experimentally, high-speed video camera is
employed to record the flow field directly. Limited numerical simulations are also performed to analyze some typical
phenomena. A complex flow pattern including bubble expansion, collapse, jet formation and interactions between
bubble and free surface are extensively revealed and interpreted. It is found that the water jet is mainly induced by
a strong rarefaction following shock-surface interaction. The speed of the jet is strongly related to initial curvature
of the water surface where gathering energy effect applies. This study also reveals two typical collapse modes of
explosion bubble, where one is broken up by air penetrating upper water layer and flushing into the bubble, and the
other undergoes a similar process as that of RM instability without direct interaction of atmosphere and the bubble.


Introduction

A sudden expansion of high pressure gas bubble in liq-
uid will send out a pressure wave propagating outwards,
accompanied by a series of bubble evolution processes
such as expansion, shrinking, deformation or collapse.
As in water this is often referred as an underwater ex-
plosion, which has been continuously and widely inves-
tigated for about a century. When this explosion occurs
in a confined tube with a free surface, the liquid in be-
tween can be accelerated towards the free surface and
a jet may arise. Taking advantage of the kinetic energy
carried by a slim liquid column, the jet can be used as a
mass-delivery, cutting or breaking tool in many aspects.
One of the typical applications for mass-delivery
might be the bubble jet technology run by certain types
of ink jet printer (e.g. Canon and HP). Usually, a tad
of ink in ejector is quickly heated by a film resistor and
vaporized to be a vapor bubble which then squeezes the
liquid ink out of the open head. Lots of researches have
been done to understand and to improve the performance
or controllability of ejection process[Asai (1992); Hong
(2004); Lindemann (2004)]. In recent years, potential
applications of this sort of bubble-driven pulsed jet in
biology and medicine have been proposed by some re-
searchers and have drawn plenty of interest and atten-
tion. Water jet induced by a high energy pulsed laser
was found a suitable instrument for surgical dissection
[Nakagawa (2002); Tomohiro (2004)], where less side


damage on surrounding tissues comparing to the conven-
tional rigid knives and laser scalpel has been reported.
Similar technique was also brought up for drag deliv-
ery in endovascular treatment of thrombi and cerebral
embolisms [Hirano (2001, 2002)] which seems able to
reduce therapeutic time and to enhance the medicine ef-
ficiency. Regardless of the specific geometry of the con-
tainers and how the initial bubbles are generated, above-
mentioned jet flows experience the very similar dynam-
ical process. And a study on this basic process may pro-
vides better understandings on the complex appears in
the varied applications.
On the other hand, though liquid jet can be easily pro-
duced with current technology and the required parame-
ters for above applications have been technically achiev-
able, the mechanism of the jet production in a confined
situation as well as the dynamics of the supporting flow
remains unclear. Existing researches have mainly fo-
cused on the global effects such as jet amount and ve-
locity, penetration depth or the surgical results instead
of the dynamical details. Present study, hence, attempts
to acquire more information about the latter.
To be feasible in both experiment and numerical sim-
ulation, we use wire explosions to deposit the energy in
water and setup the initial bubble. A straight rectangular
tube is adopted as present test section which gives the
simplest confined situation. It is prepared to develop a
nearly two-dimensional flow pattern so that we may get
better inside views. Complicated flow patterns including







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


Side view A:


Spark trigger
F_


N P





10/1_mm1

Side view- B:


N 5 mm


Driver circuit
Exploding wire
(copper D = 0 05 mm)


Figure 1: Experimental setup


bubble expansion and destruction, and jet formation are
experimentally revealed and discussed. Numerical sim-
ulations are also performed in order to extend the under-
standings, though they are somewhat limited due to the
sophisticated physics of wire explosion.


Experimental setup

Present experimental setup is designed to produce a two-
dimensional flow situation. As illustrated in Fig. 1,
a transparent plexiglass tube with rectangular cross-
section is taken as the test section. It is 200mm in total
length and 5mm thick, whereas the width can be either
10mm or 15mm. For installation of two electrodes (P
and N), two aligned small holes are drilled on frontal and
back sidewalls at 75mm from bottom along center line
(view A in Fig. 1). In practice before test, the electrodes
must be taken off first to load exploding wire by welding.
The exploding wire, which is of copper and 0.05mm
thick (diameter) 5mm long in current study (view B in
Fig. 1), will then be passed into the tube through the
holes, and locked and sealed by two electrodes. We use
discharge of high voltage capacitors to explode the wire,
and detailed driver circuit has been scratched in Fig. 1.
High-speed video camera is then employed to screen the
conduit flow.
Ideally, above arrangement allows a 2-D considera-
tion if boundary effects are negligible. To check the real
configuration of the bubble generated by current setup,
we pretested a wire explosion under water with free
boundary (no side walls) and a sequent result is shown in
Fig. 2. The bubble boundary appears quite thin compar-
ing to the bubble diameter, which confirms the previous
2-D assumption.


Figure 2: a 2-D bubble induced by wire explosion in
water (free boundary)


Numerical considerations

Numerically, the problem is simulated with a two-
dimensional two-phase FVM solver based on quadrilat-
eral grid. The treatment of multi-phase in this solver is
essentially VOF, but it differs from traditional ones in
two mains. First, the direction of interface is conserv-
atively tracked, and a new interface is reconstructed by
both volume fraction and interface direction. Secondly,
flow around interface is separately solved inter-cells and
inner-cells, where the former employs master-slave ap-
proach and the latter follows a dynamical relaxation be-
tween phases. One may refer to paper [Sun (2009)] for
details if interested.
The EOS adopted in present study are Clapeyron
equation for gas and Tait's equation for liquid. However,
following Tait's equation pressure of water under strong
relaxation may become highly negative which should
turn to cavitations in reality. To fixup this problem, we
consider water phase an equilibrium blend of liquid wa-
ter and vapor. The state dependence of it will then be
governed by following relations,


p = B(p/p) + (A B)
p = p,RT/W,
P = p(l () + Pv,0
pe = p,(l w) e, + p0 -
p = p,s(T), when 0 < < 1


Where, subscript v denotes vapor and w denotes liq-
uid water, and p is the volume of vapor, e, and e, are
internal energies which may include latent heat with the
form e = Cv T + co. Basically, as total density and
internal energy are known, pressure, temperature, and
volume fraction can be solved through above relations.
Note that when p = 1 or p = 0, relation (5) becomes
invalid.
Sound speed must be estimated during calcu-
lation. For the equilibrated liquid-vapor blend,







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


the compressibility-averaged formula is adopted [Iga
(2004)], which writes,

1 0 1-
+ 2 (6)
pC2 Pv C2 Pw Cw 2
This study also takes into account viscosity and heat
transfer. The transport coefficients simply take p
01(1 + 2 ).'. .)pl + gpg [Iga (2004)] and k lki +
(1+2 .'. )k, respectively, where subscript I denotes the
liquid phase and g the gas phase.

Results and discussion

Experimental results
Experiments of underwater explosion in a rectangular
tube are conducted. We here are interested in how the
explosion bubble expands, deforms and finally breaks
through the water surface, as well as how the jet arises
from the original surface. A typical image of the devel-
opment of conduit flow is shown in Fig. 3 (frame time
is marked in bottom of each image in micro second).
The tube width D = 10mm and exploding wire locates
around 10mm below surface. Total consumed energy
can be roughly estimated by E CU2 5J though
only a small portion of it contributes to the flow.
The load of energy pulse on exploding wire produces
an extremely high temperature which vaporizes and ion-
izes the copper wire immediately as well as some water
in vicinity. These hot materials (or plasma) produces the
initial luminous bubble as can be observed in frame 2
and 3 of Fig. 3. At the same time, a blast wave is gen-
erated and propagating in water. When it hits the free
surface, it reflects as a rarefaction wave downward. The
rarefaction tends to lift the water, and thus a jet starts to
build up from free surface whose tip moves at a speed
about 35m/s. Along with the bubble growth, pressure
and temperature in bubble keep decreasing. The flash
quenches soon because the ions turn to recombined and
vapors are condensed. This process reduces bubble pres-
sure seriously by consuming gas phase substances. The
actual ingredients of bubble materials is hard to deter-
mine, and we only concern the dynamical part. Never-
theless, there is always gas (not vapor) remaining, which
is evident in an extra tests on deep water explosion.
As being over expanded, the bubble starts to pull back
up-moving water, whereas the water jet still keeps lift-
ing due to the inertia. Stretched by the two, the water
layer on the jet shoulder is greatly thinned. Since the
water along sidewalls moves at the lowest speed, the
breakup of the top surface starts from this part of water.
Air above with about atmosphere pressure then blows in,
creating a pair of bubbly regions which can be observed
in Fig. 3 (frame 4 8). The two bubbly regions develop


DZlIOn


R _
I owl
ri-"-


ii Lid I~


Figure 3: Wire explosion in a 10mm wide tube, total
energy 5J, explosion depth 10mm


quickly and fiercely towards main bubble. In frame 5,
the whole side regions have been corrupted. This is ac-
tually a process of local fragmentation, where dominant
phase switches from liquid to gas. The over-expanded
bubble then sucks in fragments of water and air from
above, which destroys the bubble thoroughly.
The water jet appears in Fig. 3 is featured by a sharp
spire. It's essentially a result of gathering energy ef-
fect of the curved surface. Capillarity along wall counts
for the curvature. We then test a wider tube so that the
curved part of surface will be relatively smaller. The
tube width D = 15mm, and the explosion depth and en-
ergy input are same as former case (10mm, 5J). Results
are presented in Fig. 4. Similar structures and evolution
history can be found. The sudden relaxation on surface







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


D=15mm


I iL


i 1


i I


I 4


Figure 4: Wire explosion in a 15mm wide tube, total
energy 5J, explosion depth 10mm


induces speed in surface normal direction. For a concave
surface the liquid tends to converge. In the barely com-
pressible liquid, converging flow causes accumulation of
kinetic energy, whereby speed at the curved surface will
build up and a jet comes into being. The larger the sur-
face curvature is, the stronger jet it will produce. In this
case, the curvature near sidewalls is much larger than
other region. Therefore, despite of the whole rising jet
column, two small peaks develop from two sides (frame
2- 5) and emerge as one later in frame 6. With more liq-
uid on top of bubble and with a flatter surface in current
case, the jet is launched at a much lower speed (around
20m/s) than former case.
In above two cases, the explosion position is rela-
tively shallow beneath water surface and the energy is


Figure 5: Wire explosion in a 15mm wide tube, total
energy 4J, explosion depth 15mm


relatively large, thereby a final breakup of water column
between bubble and atmosphere takes place. When en-
ergy comes lower or the explosion goes deeper, the in-
duced flow and collapse of bubble may switch to another
mode, as illustrated by Fig. 5 where tube width 15mm,
explosion depth 15mm and total energy 4J. The forma-
tion of jet keeps similar to that of Fig. 4 except that the
jet speed is even lower (8m/s). Main difference appears
in the evolution of explosion bubble. It first expands as
usual, then pressed by the water column on top the bub-
ble undergoes a similar process as that of RM instability
without local fragmentation of water nor breakthrough
of upper air into the bubble. From frame 5, top surface
of the bubble turns to move downward and sticks out to
be a small blunt jet in bubble. The small jet finally hits


I I











the lower bubble surface splitting the whole bubble into
two.


Numerical analysis

Two dimensional numerical simulations are performed
to analyze typical phenomena observed in experiments.
Only two phases are considered for qualitative compar-
ison. Besides water phase, the atmosphere and bubble
material are all set as air.
The calculation domain is a 15 x 180 tube with vis-
cous sidewalls, open top and closed bottom. Explosion
is initialized with a tiny bubble of condensed air. Fig. 6
shows the results (density), where (a) employs a flat sur-
face and (b) a curved one. Other conditions are same.
These results are not quite comparable to real case for
two reason. First, the solid boundary condition is not
quite valid for plexiglass to water considering their close
sound impedance; and second the physics of wire explo-
sion (e.g. recombination and condensation of material)
is not effectively included. For the first reason, as can be
seen in Fig. 6, after a strong reflected shock sweeps over
the flow field, very serious cavitation occurs below bub-
ble and a jet builds up inside the bubble which is much
obvious than the real case (Fig. 3 and Fig. 4). For the
second reason, an explosion bubble that drives compara-
ble speed of jet always goes over-expanded very late and
the water column above may sustain much longer than
that in real test.
Nevertheless, there are still some typical features re-
flected by numerical results in Fig. 6. With a flat surface,
the bubble can grow faster and the jet turns out blunt and
much shorter. On the contrary, explosion under a curved
surface builds up a long sharp jet as we have observed
in experiment. For collapse of bubble, it is of interest to
note that case (a) follows a very similar regime as real-
ity where violent fragmentation occurs, whereas (b) only
shows a very peaceful blow-up collapse. Since the over-
expanded situation is a main cause of local fragmenta-
tion and the violent breakup, the more expanded bub-
ble in (a) than that in (b) may explain the more realistic
breakup regime of (a).

Conclusions

A study on the jet and conduit flow induced by under-
water wire explosion in a rectangular tube is carried
out. Experimentally the bubble evolution and interac-
tions with free surface are revealed by high-speed video
camera. Preliminary numerical simulations are also per-
formed to analyze some typical phenomena appear in
experiments. It is found that,
1. A two-dimensional conduit flow situation is par-
tially reached in experiment, especially for the explosion


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


bubble. But for the water surface and jet it is not quite
successful due to capillarity on boundary.
2. Rarefaction generated by shock-surface interaction
induces a water jet in conduit. In liquid the gathering
energy effect is significant, hence the speed of the jet is
strongly related to initial curvature of the water surface.
Larger concave curvature results in faster jet.
3. Wire explosion underwater generates a hot plasma
bubble first. It is then cooled and rarefied along with the
expansion as well as recombination and condensation of
the bubble materials. Two modes of conduit flow are
observed. When explosion energy is high and position
is shallow beneath water surface, the bubble goes highly
over-expanded and upper air can penetrate the water col-
umn between bubble and atmosphere which creates a vi-
olent breakup phenomenon. However, when energy is
low or the explosion occurs deep enough, there won't
be a fierce breakthrough of air into the bubble and the
bubble will undergoes a similar process as that of RM
instability.

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


Iga Y., Nohml N., Goto A. and Ikohagi T., Numerical
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(a) Flat surface


Figure 6: numerical results of jet flow induced by un-
derwater explosion (density)




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