Numerical analysis of the behavior of shock wave in spheroid vessel

Yosuke Nishimura 　　 Naoki Kawaji Graduate School of Science and Technology

Kumamoto University, Japan

Index１． Background of research

２． Purpose of research

３． Method of experiment

４． Result of experiment ● Property of typical underwater discharge

● Relationship of electrodes interval d & Imax ・ Pmax

● Relationship of cable length & Pmax

● Exceptional discharge phenomenon

● Result of numerical analysis

５． Conclusion

● The explanation of the impulse large current equipment● Method of measurement● Numerical analysis

１． Background of research

The conventional food processing by heating

Eating habits become rich because the food processing technology develops.

The conventionalFood processing

Boil Burn Steam

Processing by heating

For the improvement of safety and preservation

However, as a problem

Loss of nutrientLoss of nutrient

・ Processing is momentary.

・ Energy saving

・ The influence of heat is not almost caught. 　→ Keeping of nutrition

・ Improvement of softening and extraction 　　　　　　　　　　

Food processing using underwater shock wave~New food processing technology~

２． Purpose of research

Method of generating underwater shock wave

Utilizing the underwater detonation of the explosive

As a fault・ Redundancy of a cycle time

・ Pollution of water by remains of the explosive・ Legal restrictions

Utilizing the underwater detonation of the explosive

As a fault・ Redundancy of a cycle time

・ Pollution of water by remains of the explosive・ Legal restrictions

The conventional method of generation Therefore

・・・It proposes the utilization of the underwater shock wave generated by the electrical discharge of impulse large current.

Purpose of research

The device to generate high intensity shock wave is required in order to process various kinds of food.

It is investigated that optimum condition to generate high intensity shock wave and the behavior of converged shock wave.

The purposes are following.

Maximum discharge power [W] is defined as barometer of intensity of shock wave, because measurement of pressure of shock wave was mistaken.

３． Method of experiment

● The explanation of the impulse large current equipment

● Method of measurement

● Numerical analysis

The circuit diagram of the impulse large current equipment

Oil capacitorOil capacitorMade of Nichicon Corp 　

Capacitance: 25μF

Withstand voltage: 20kV Charge part

The circuit diagram of the impulse large current equipment

The hemispheres were employed for the electrode to obtain a a semi-equal electric semi-equal electric fieldfield.

Made of brass 　　

20 mm

Generally a spark occurs without going by way of corona discharge.

Electrode interval Discharge part

Vessel for shock wave convergence

d [mm]Discharge part

Pressure measurement point

90[mm]

Reflector plate

Electrode

60[mm]

polyacetal resin

SUS

●● Property of Property of reflector platereflector plate

・ Shape is spheroid.・ Long radius is 103[mm].・ Short radius is 93[mm].

(Primary focus)(Primary focus)

(Secondary focus)(Secondary focus)

The vessel was filled with water at the time of experiment.

A pressure sensor was installed in secondary focus.

Metallic large container

Electrode

The metallic large container was employed at the time of experiment without the pressure measurement , since spheroid vessel has low durability.

Water

Silicon rubberfor isolation

Method of measurement

● Current measurement ● Voltage measurement

Rogowski Current Transducer

Model CWT600Manufacture

rPEM

Sensitivity 0.05 [mV/A]Peal current 120 [kA]Peak di/dt 40 [kA/μS]

HF(3dB) BW 10 [MHz]

High Voltage Probe Model PPE 20kV

Manufacturer LeCroyAttenuation 1000:1

Input resistance

100MΩ

Input capacitance

<3pF

System BW(-3dB)

100MHz typical

High voltage cable

Integrator electronics

Rogowski coil High voltage side

Grounded side

・ The voltage of capacitors was measured.

Flow of numerical analysis

At first geometry data was created by use of SolidWorksSolidWorks (3D-CAD software produced by SolidWorks JapanSolidWorks Japan).

This geometry data was imported in HyperMeshHyperMesh (CAE software produced by AltairAltair) and meshed.

This FE data was imported in LS-LS-DYNA 3DDYNA 3D (CAE software produced by LSTCLSTC) and defined analysis condition.

Method of numerical analysis (2D)

Air

SEP

Water

SUS

Calculation method

Equation of states

Euler:Euler: Air, Water , SEPLagrange:Lagrange: SUS

Mesh size1 x 1 x 1 (mm)

Ignition point(Primary focus) GRUNEISEN :GRUNEISEN : Water , SUS

LINEAR_POLYNOMIAL :LINEAR_POLYNOMIAL : AirJWL:JWL:SEP

The size of this model is the same as vessel for shock wave convergence. Since it is difficult to simulate discharge phenomenon, SEPSEP (High explosive made by kayaku-Japankayaku-Japan) is installed in primary focus. The purpose of this simulation is to recognize propagation and convergence of shock wave.

Secondary focus105 [mm]

103 [mm]

196[mm]

60 [mm]

90 [mm]

４． Result of experiment

● Property of typical underwater discharge ● Relationship of electrodes interval d & Imax

・ Pmax

● Relationship of cable length & Pmax ● Exceptional discharge phenomenon ● Result of numerical analysis

Property of typical underwater discharge

Charge voltage Vo [kV]

Capacitance[μF]

Electrode interval d [mm]

Cable length[m]

10 100 10 3×2

Property of typical underwater discharge

When high voltage was impressed between electrodes, the current of about 600[A] flowed through water.

The current of about 600[A]

Charge voltage Vo [kV]

Capacitance[μF]

Electrode interval d [mm]

Cable length[m]

10 100 10 3×2

It took 5~20[ms] from impression of high voltage to initiation of discharge, and charge voltage decreased gradually in the meantime.

The charge voltage before switching Vo was 10[kV], but the voltage of discharge initiation was 7.8[kV].

The voltage of discharge initiation

was 7.8[kV]

Property of typical underwater discharge

Initiation of discharge

Air bubbles are generated by current and it resulted in arc electric discharge by discharge in air bubble.

Charge voltage Vo [kV]

Capacitance[μF]

Electrode interval d [mm]

Cable length[m]

10 100 10 3×2

Damped oscillation current

Property of typical underwater discharge

Initiation of discharge

Air bubbles are generated by current and it resulted in arc electric discharge by discharge in air bubble.

Charge voltage Vo [kV]

Capacitance[μF]

Electrode interval d [mm]

Cable length[m]

10 100 10 3×2

Damped oscillation current

Phases differed 90 degrees.

It is effect of inductance L=6.63[μH] included in measured circuit.

dt

dILV

dt

dILRIV d

dd

dm

dVdt

dIL d

mV

Schematic of measured circuit and formulaSchematic of measured circuit and formula

Relationship of electrodes interval d & Imax ・ Pmax

Cable length[m]

3×2

Relationship of electrodes interval d & Imax ・ Pmax

The larger electrodes interval d became, the smaller maximum discharge current Imax became.

The cause is the following.

When d become large the impedance of between electrodes increases and the voltage of discharge initiation decreases.

Cable length[m]

3×2

Relationship of electrodes interval d & Imax ・ Pmax

The larger electrodes interval d became, the smaller maximum discharge current Imax became.

The cause is the following.

When d become large the impedance of between electrodes increases and the voltage of discharge initiation decreases.

In each charge voltage V0 there were d that Pmax became the largest.

When d become large Imax decreases, but discharge voltage Vd increase because the impedance of between electrodes increases.

The cause is the following.

The larger V0 become, the larger optimum electrodes interval become.

Cable length[m]

3×2

Relationship of cable length & Pmax

Charge voltage Vo

[kV]

Capacitance[μF]

Electrode interval d

[mm]10 100 10

When cable length was short, maximum discharge power Pmax was large.

When cable length become long, inductance L increase, and intersection point of Id & Vd becomes low, because Imax decreases and rising time of current become long.

The cause is the following.

Cable Length [m]

3×2 9×2

L [μH] 6.63 18.03

Exceptional discharge phenomenon●●Typical waveform of currentTypical waveform of current ●●Exceptional waveform of Exceptional waveform of

currentcurrent

Mode of waveform Damped Oscillation

Occurrence condition

R2 ＜ 4L/C

Maximum discharge power Pmax [MW] 59.8

Mode of waveform Critical damping

Occurrence condition

R2=4L/C

Maximum discharge power Pmax [MW] 121.3

Charge voltage Vo

[kV]

Capacitance[μF]

Electrode interval d

[mm]

Cable length [m]

14 100 14 3×2

Almost discharge was this mode.This mode occurred unusually. When electrode interval was large, it was easy to happen.

Exceptional discharge phenomenon●●Typical waveform of currentTypical waveform of current ●●Exceptional waveform of Exceptional waveform of

currentcurrent

Mode of waveform Damped Oscillation

Occurrence condition

R2 ＜ 4L/C

Maximum discharge power Pmax [MW] 59.8

Mode of waveform Critical damping

Occurrence condition

R2=4L/C

Maximum discharge power Pmax [MW] 121.3

Charge voltage Vo

[kV]

Capacitance[μF]

Electrode interval d

[mm]

Cable length [m]

14 100 14 3×2

Almost discharge was this mode.This mode occurred unusually. When electrode interval was large, it was easy to happen.

It is seemed that this shift happen when impedance R become large from any causes, and Pmax become large because energy is thrown in load efficiently in mode of critical damping.

Result of numerical analysis

0μs30μ

s60μ

s

90μs

120μs

(Primary focus)

Initiation

(Secondary focus)

Reflection

First wave reached secondary focus.

Reflected wave converged at secondary focus.

Graphs of pressure of shock wave (numerical analysis)

Graphs of pressure of shock wave (numerical analysis)

Y direction

Center of ellipse

Pressure of Reflected wave became maximum near secondary focus (Y=45[mm]).

Secondary focus

Graphs of pressure of shock wave (numerical analysis)

Y direction

Center of ellipse

Pressure of Reflected wave became maximum near secondary focus (Y=45[mm]).

Secondary focus

(Primary focus)

Initiation

(Secondary focus)The pressure of reflected wave

was about 2.7 times larger than the pressure of first wave at secondary focus.

Reflected wave

5 ． Conclusion

Conclusion• Property of typical underwater discharge was confirmed.• The larger electrodes interval d become, the smaller maximum

discharge current Imax become.

• The larger V0 become, the larger optimum electrodes interval become.

• When cable length is short, maximum discharge power Pmax is large.

• The shift of waveform happen when impedance R become large from any causes, and Pmax become large

• In the vessel for shock wave convergence pressure of reflected wave was about 2.7 times larger than the pressure of first wave at secondary focus.

Thank you for your attention!

Mode of waveform(a)R2 ＜ 4L/C (Damped oscillation)

(b)R2=4L/C (Critical damping)

(c)R2 ＞ 4L/C (Over damping)

ttL

R

L

Vi 0

0

0 sin2

exp

L

CR

2exp

V

V

0

r

LCf

21

t

L

R

L

tVi

2exp0

R

V

eR

VI p

00 74.02

ttL

R

L

Vi 0

0

0 sinh2

exp

Energy is thrown in load efficiently in mode of critical damping.

Optical observation No.

Voltage [kV]

Capacitor number

Capacitance[mF]

Energy [J ]

Electrode interval[mm]

1 17.5 2 50 7656 12.5

2 12.5 4 100 7813 12.5

3 15 4 100 11250 12.5

4 17.5 3 75 11484 12.5

Mechanism of dielectric breakdown

Dielectric breakdown theory of liquid

Electronic destruction Air bubble destruction

In this experiment

It is considered that they are air bubbles.

This shadow is air bubbles, air bubbles are generated by current and the “air bubble destruction” which results in the whole destruction for electric discharge in air bubbles is considered to be leading.

Pressure measurement

Schematic view