Numerical Analysis of the Behavior of Shock Wave in Spheroid Vessel

ABSTRACT Food processing utilizing underwater shock wave softens the food by breaking cells, and prevents loss of nutrients since there is little influence of heat. Moreover, it is also possible to extract a nutrient easily and reduce processing time. A device to generate a high intensity shock wave is required in order to process various kinds of food. The purposes of this research are to investigate the best condition to generate high intensity shock waves and to understand the behavior of converged shock wave. The capacitor electric discharge circuit was used as an underwater shock wave generating device. The waveform of discharge voltage and current were measured in order to search for the best condition of underwater discharge. It was confirmed that the larger charge voltage of capacitors become, the larger optimum electrodes interval become. Propagation and convergence of underwater shock wave was observed by numerical analysis.


INTRODUCTION
Eating habits become rich because the food processing technology develops.The conventional food processing are boil and burn, steam and so on for the improvement of safety and preservation.These are processing by heating.However there is loss of nutrient as a problem.
We propose food processing using underwater shock wave.The features of this technology are following.

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Nutrition is kept because the influence of heat is not almost caught.• Improvement of softening and extraction.The conventional method of generation of underwater shock wave is to utilize the underwater detonation of the explosive.But the fault of this method is following.

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Redundancy of a cycle time.

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Pollution of water by remains of the explosive.

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Legal restrictions.Therefore it proposes the utilization of the underwater shock wave generated by the electrical discharge of impulse large current.
The device to generate high intensity shock wave is required in order to process various kinds of food.The purposes are to investigate that optimum condition to generate high intensity shock wave and the behavior of converged shock wave.

THE IMPULSE LARGE CURRENT EQUIPMENT
The capacitor electric discharge circuit was manufactured as underwater shock wave generating equipment.The circuit diagram is shown in Fig. 1.Four oil capacitors (Made of Nichicon Corp. Capacitance: 25 [µF], Withstand voltage: 20 [kV]) were connected in parallel.After charging capacitors with 8-14 kV, underwater shock wave was generated by discharging between the electrodes installed underwater.Furthermore, the hemispheres of 20mm in the diameter (made of brass) were employed for the electrodes to obtain a semiequal electric field.Generally a spark occurs without going by way of corona discharge in semi-equal electric field. (1)2.DISCHARGE VESSEL 2.2.1.Vessel for shock wave convergence Fig. 2 was manufactured as vessel for shock wave convergence.The material is SUS, and the parts of isolation are polyacetal resin.The reflector plate is hemisphere of spheroid (Long radius = 103 [mm], Short radius = 93 [mm]).Discharge part and pressure measurement point are respectively located in primary focus and secondary focus.Electrodes interval is "d [mm]".At the time of experiment the inside of vessel is filled with water.

The metallic large container
At the time of experiment without pressure measurement the metallic large container was employed since spheroid vessel had low durability.Silicon rubber plate was bedded for isolation inside the container.

MEASUREMENT EXPERIMENT
"Charge voltage" and "Capacitance", "Electrodes interval", "Length of circuit cable" are considered as parameters to effect intensity of underwater shock wave.According to the former experiment (2) it was confirmed that optimum electrodes interval existed in every combination of "Charge voltage" and "Capacitance".In this research "Capacitance" was 100 [µF] and the purpose was to requested the optimum electrodes interval in each "Charge voltage".The influence was investigated which "Length of circuit cable" had on the intensity of underwater shock wave.Maximum discharge power [W] is defined as barometer of intensity of shock wave, because measurement of pressure of shock wave was mistaken.
Wave form was obtained by use of oscilloscope (Made of LeCroy).

Method of current measurement
Rogowski Current Transducer "CWT600" (Made of PEM [0.05 mV/A]) was employed.Fig. 4 shows condition of installation.The Rogowski coil was set up on high voltage cable between switch and electrodes.

Method of voltage measurement
High Voltage Probe "PPE 20 kV" (Made of LeCroy [1/1000]) was employed.Fig. 5 shows condition of installation.The probe was connected to the terminal of capacitor.

NUMERICAL ANALYSIS BY LS-DYNA
Numerical analysis of shock wave convergence phenomenon was run.Fig. 6 shows Numerical analysis model.The size of this model was same as Fig. 2. It was 2D model and the electrodes and its supporter were omitted for simplification.Since it is difficult to simulate discharge phenomenon, SEP (High explosive made by kayaku-Japan) was installed in primary focus.The purpose of this simulation is to recognize propagation and convergence of shock wave.Fig. 7 shows flow of numerical analysis.At first geometry data was created by use of SolidWorks (3D-CAD software produced by SolidWorks Japan).This geometry data was imported in HyperMesh (CAE software produced by Altair) and meshed.This FE data was imported in LS-DYNA 3D (CAE software produced by LSTC) and defined analysis condition.Fig. 8 shows Numerical analysis condition.

Rogowski coil
Integrator electronics   current and it resulted in arc electric discharge by discharge in air bubble.At the time of arc electric discharge the damped oscillation current flowed as Fig. 9 (a) and measured voltage V m was also damped oscillation which phases differed 90 degrees from discharge current I d .It was effect of inductance L = 6.63 [µH] included in measured circuit.Schematic of measured circuit and formula was shown in Fig. 10.

Optimum electrodes interval
Fig. 11 shows the relationship between electrodes interval d and maximum discharge current I max .Fig. 12 shows the relationship between d and maximum discharge power P max .Length of circuit cable was 3 × 2 [m].The larger d became, the smaller I max became from Fig. 11.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 V 0 there were d that P max became the largest from Fig. 12.The cause is the following.When d become large I max decreases, but discharge voltage V d increase because the impedance of between electrodes increases.As a conclusion it was confirmed that the larger V 0 became, the larger optimum electrodes interval became.

Length of circuit cable
Fig. 13 shows the relationship between length of circuit cable and P max and experimental condition.When cable length was short, P max was large from Fig. 13.The cause is the following.When cable length become long, inductance L increase, and intersection point of Figure 13 The relationship between length of circuit cable and maximum discharge power and experimental condition.Fig. 17 shows exceptional waveform of current.Fig. 18 shows property of exceptional waveform of current.This mode occurred unusually.When electrodes interval was large, it was easy to happen.Fig. 19 shows condition of two waveforms.These waveforms were same condition.It is seemed that the shift of mode happen when impedance R become large from any causes, and P max become large because energy is thrown in load efficiently in mode of critical damping.(4)

RESULT OF NUMERICAL ANALYSIS
Fig. 15 shows propagation and convergence of underwater shock wave.Secondary wave which reflected and converged by the reflector plate reached the secondary focus after first wave which generated in the primary focus reached the secondary focus from Fig. 15.
Fig. 16 shows the pressure variation of first wave and reflected wave above Y direction from center of ellipse.Pressure of reflected wave became maximum near secondary focus (Y = 45 [mm]) from Fig. 16.Fig. 17 shows the time history of pressure at secondary focus.The pressure of reflected wave was about 2.7 times larger than the pressure of first wave at secondary focus from Fig.

Figure 1
Figure 1 The circuit diagram of the impulse large current equipment.

Figure 2
Figure 2 Schematic and photograph of vessel for shock wave convergence.

Figure 3
Figure 3 Photograph and schematic of the metallic large container.

Figure 4 Figure 5
Figure 4 Condition of installation of Rogowski Current Transducer.

Figure 6
Figure 6 Numerical analysis model.

Figure 10
Figure 10 Schematic of measured circuit and formula.

Figure 11
Figure11The relationship between electrodes interval and maximum discharge current.

Figure 12
Figure12The relationship between electrodes interval and maximum discharge power.

Figure 14
Figure 14 Intersection point of discharge current and discharge voltage.

Figure 15
Figure 15 Typical waveform of current.

Figure 15a
Figure 15aPropagation and convergence of underwater shock wave.

Figure 16 Figure 16a
Figure 16 Property of typical waveform of current. 17 .

Figure 17a
Figure 17aThe relationship between time and pressure of shock wave.

Figure 18
Figure 18 Property of exceptional waveform of current.

Figure 19
Figure 19 Condition of two waveforms.
Figure 17 Exceptional waveform of current.