The Numerical Analysis and Experiment of Shock Processing for Bouef

The Numerical Analysis and Experiment of Shock Processing for Bouef

Graduate School of Science and Technology, Kumamoto 　 University

YAMASHITA 　 Yusuke

Shock wave and condensed matter research centerShock wave and condensed matter research center

Contents

• Introduction

• Objectives

• Calculation of parameter

• Experimental Results

• Numerical Analysis

• Conclusion & Future Works


• Heat Treatment • High-pressure Treatment　　

In the processing method used for the food processing, there are chiefly heat-treatment and high-pressure processing.

There are few changes of the nutrient New physical properties Short processing timeVery low energy consumption

Introduction

Shock processing for foods


Electric detonator

Detonation fuse

Cage

Food

Water

• The explosive and the high voltage electrical discharge are investigated as the high-pressure source.

• The food is processed in water to propagate the shock wave.

Introduction


＜ Problems ＞Strength

Shape

Reflection of shock wave etc..

It is necessary to develop an appropriate food processing vessel where these are considered

Practical use of the shock processing

Objectives

Trial and error experimentation can cause damage to the device

→ We focused Numerical analysis for design

• Calculation of numerical analysis parameter of beef

[Measurement experiment]

• Evaluation of accuracy of numerical analysis[Numerical analysis for pressure comparison]


Many parameters for the numerical analysis are need for pressure vessel material and various foods

Objectives

Calculation of numerical analysis parameter


Necessary parameter in numerical analysis

using shock wave

Hugoniot equation of state in foods

Calculation by impedance matching method

At the interface of known material A and unknown B, the incidence shock wave velocity and the transmitted shock wave velocity when the shock wave spreads to the interface are necessary, to be measured

Reflected shock wave

Up

P

Up

P

A B A B

Transmitted shock wave

Incident shock wave


Us = C0 + s ・ up

P = ρ0 ・ Us ・ up

Shockwave pass on the interface of A and

B

Generation of reflection wave and transmitted

wave

B and C denote hugoniot points driven in

unknowns

Impedance matching method

This experiment measured the incident and the transmitted shock wave velocity at the interface of known material PMMA and unknown beef.

The velocity of unknown material calculated by thickness of the beef divided by transit time of the shock wave in beef.


5mm

50m

m50

mm

t m

m

Electric Detonator

SEP （ 50g ）

PVC （ VP30 ）

Beef

PMMA block

Streak slit

Detonation Fuse No. t [mm]

1 50

2 50

3 30

4 30

5 10

6 10

Experimental Condition

The shock wave pressure is changed by changing thickness t of the PMMA block

Closed chamberTarget

Window

Flash generator


Shooting Procedure (Shadow Graph Method)

IMACON468

HADLAND PHOTONICS

interframe times 10ns to 1ms in 10ns steps independently variable, number of channels framing:4 streak:1

The experiments were carried out using the high-velocity image converter camera, flash generator and the explosive experimental facilities.

The streak photograph of shock wave


PMMA

PMMA

Beef(5mm)

Measurement point

shock wave

• The incident shockwave is obtained by plot of shockwave motion.• Penetration shock wave is invisible in beef. • The average velocity was assumed to be a transmitted shock wave

velocity

Experimental Results 　（ 1 ）The result of experimental number 1( t=50 mm)

40μs

Image processing

Photo of incident shock wave

Photo of transmitted shock wave

2.9

3

3.1

3.2

3.3

3.4

0 2 4 6 8Time　(μ s)

Vel

ocity

　(mm

/μs)

Experimental number 2 (t = 50 mm)


Curve fitting method

cttBAtBAy )exp(1)exp(1 2211

Incident shockwave velocity Us

(PMMA-Beef)

• To calculate the incidence shock wave velocity, the function was approximated to this plot point by using the curve fitting method.

• Shockwave velocity of interface PMMA-beef is about 2.93km/s.

• Transmitted shockwave velocity is the 2.34km/s.

- 40

- 30

- 20

- 10

0

10

20

30

40

0 5 10 15 20 25 30[μ s]

[mm]

Incidentshock　wave

Transmittedshock　wave

Experimental Results 　（ 2 ）

Incident shock wave: Us

Transmitted shock wave: U’s


Experimental

Number

PMMA Gap

t[mm]

PMMA-beef 界面

Incident velocity

Us (PMMA)[km/s]

PMMA-beef 界面

Transmitted velocity

Us'[km/s]

1 50 2.8576 2.2063

2 50 2.9256 2.3447

3 30 3.1528 2.8259

4 30 3.1647 2.6709

5 10 3.7688 3.4551

6 10 3.8158 3.5704


Other experimental results

Hugoniot equation of state

Us=C0+s ・ upC0 = 1843.8 [m/s] s = 0.547


NumberPMMA

Gap t[mm]

Us’(beef)[km/s]

Up[km/s]

P[Gpa]

1 50 2.2063 0.7933 1.8904

2 50 2.3447 0.9614 2.4346

3 30 2.8259 1.4939 4.5593

4 30 2.6709 1.5631 4.5088

5 10 3.4551 3.0410 11.3473

6 10 3.5704 3.1347 12.0876

Us=s*up+C0

y　=　0.547x　+　1.8438

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5

up　[km/ s]

Us　

[km

/s]



Numerical Analysis Model of pressure comparison

• The pressure comparison model of the numerical analysis was written by using hugoniot data obtained from the experimental results.

• As shown in this figure, the beef is placed underwater. Another is surrounded by air. Then, a high explosive is exploded.

• We compare pressure of the beef in air with that in water.

• Each size is as following slide.

　 ρ　[kg/m3]C0　

[m/s] s Γ0

Beef 1.08 1843.8 0.547 1.0

ρ: initial density of the mediumC0, s : Constant of materialΓ0 : Grüneisen coefficient


Numerical Analysis

Numerical analysis Parameter of beef[Mie-Grüneisen Parameter]

Model of pressure comparison

SEP

SUS

beef

Air

Water10

0mm

100m

m

60m

m

200mm

SEP

SUS

beef

Water

Water

100m

m10

0mm

60m

m

200mm

Air-beef-Water Water-beef-Water


Numerical Analysis

• Calculation method 　： Euler : Explosive (SEP), Water , Beef, SUS , Air

• Equation of state 　　　　　　： JWL equation : Explosive (SEP)

Grüneisen equation : SUS, Beef, Water, Air

• Mesh size 　　　　　　　　　　　　　　　　　　： 1 x 1 x 1 [mm] 　 element number:31000

• Initial condition 　　　　　　　： Initial particle velocity : 1711 [m/s]

The other analysis conditions

V

eVR

VRBVR

VRAPJWL

)exp(1)exp(1 2

21

1

(1)

es

cP 00

02

200

21

)1(

V: 0 (initial density of the explosive)/ (gas density of the detonation)PJWL: pressure e: specific internal energyA, B, R1, R2: JWL parameter

η: 1− 0 (initial density of the medium)/ (density)P: pressure e: specific internal energyc0, s: Constants of material 0: Grüneisen coefficient

The model was analyzed using LS-DYNA.

Result of Numerical analysis


Air-beef-Water

Result of Numerical analysis


Water-beef-Water

The comparing pressure value


beef

Measurement point (90mm)

Measurement point (40mm)

Measurement point

Each pressure history point is as follows.


The comparing of peak pressure

The pressure history by time in the beef (Water)

A pressure value has a difference in the surface (90mm) of beef.

It is higher among the water.

Therefore, as for shock processing of beef, underwater is better.

Distance[mm] 　

Air[MPa]

Water [MPa]

40 140 140

90 15 60

The pressure history by time in the beef (Air)

Pressure of beef (Air) Pressure of beef (Water)

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100

Time　(μ s)

Pre

ssur

e　(M

Pa)

40mm50mm60mm70mm80mm90mm

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100

Time　(μ s)

Pre

ssur

e　(M

pa)

40mm50mm60mm70mm80mm90mm

The comparing pressure value

Conclusion 　


• The parameter of the numerical analysis of the beef was obtained by using the impedance match method from a result of the optical observation. Us=C0+s ・ up 　（ C0 = 1843.8 [m/s] , S = 0.547 ）

• The process of the spread of the shock wave was analyzed• In the food processing using shock wave, the load pressure value was able

to be obtained

• The parameter of the numerical analysis of the beef was obtained by using the impedance match method from a result of the optical observation. Us=C0+s ・ up 　（ C0 = 1843.8 [m/s] , S = 0.547 ）

• The process of the spread of the shock wave was analyzed• In the food processing using shock wave, the load pressure value was able

to be obtained

Us=s*up+C0

y　=　0.547x　+　1.8438R2　=　0.977

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5

up　[km/ s]

Us　[km

/s]

P=ρ *Us*up

y　=　0.5639x2　+　2.0574xR2　=　0.999

0

4

8

12

16

0 0.5 1 1.5 2 2.5 3 3.5up　[km/ s]

P　[G

Pa]


Conclusion 　

Future works

• Accurate calculation of equation of state

Accurate measurement of shock wave velocity

Appropriate parameter of beef

Experiment for beef’s parameter evaluation

For experiment, pressure value is measured by strain gage in SUS.Numerical analysis parameter will evaluate after comparing to experimental value and numerical analysis.

Shock wave and condensed matter research centerShock wave and condensed matter research centerTherefore, we will experiment like this in the Therefore, we will experiment like this in the

future (and evaluate the parameter). future (and evaluate the parameter).

Conclusion 　 Future Works

Experiment for beef’s parameter evaluation

Detonation　fuse

Beef （ 20×20×5 ）

SUS （ φ20 ）

Water

Measurement point

The Numerical Analysis and Experiment of Shock Processing for Bouef

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