Study on Behavior of Underwater Shock Wave in Enclosed Vessel

Transcription

1 OS-03-3 The 1th International Symposium on Fluid Control, Measurement and Visualization November18-3, 013, Nara, Japan FLUCOME013 Study on Behavior of Underwater Shock Wave in Enclosed Vessel Y. Seki 1, H. Fukuoka, *, Y. Miyafuji 3, H. Iyama 4, and S. Itoh 5 1 Advanced Mechanical Engineering Course, Nara National College of Technology, Nara, Japan Department of Mechanical Engineering, Nara National College of Technology, Nara, Japan 3 Technical Support Section, Okinawa National College of Technology, Okinawa, Japan 4 Department of Mechanical and Intelligent Systems Engineering, Kumamoto National College of Technology, Kumamoto, Japan 5 Okinawa National Colloege of Technology, Okinawa, Japan *Corresponding author, fukuoka@mech.nara-k.ac.jp ABSTRACT We are developing a food processing system by using the underwater shock wave. The effect of a underwater shock wave on the pressure in the vessel is the important factor for the food processing system. The purpose of this study is to research the behavior of the underwater shock wave in the enclosed vessel to investigate the influence of the contour and volume of the elliptical vessel on the pressure. In this research, we used the elliptical shape for the vessel and the explosive was used to generate the shock wave. Numerical calculations were carried out by using LS-DYNA. The ratio of the length of the major axis to minor axis of the elliptical and elliptical volume were changed, as main parameters. As a result, the underwater shock wave generated at the first focal point of the elliptical vessel was converged at the second focal point. At the same time, the pressure was increased by the converged underwater shock wave at the focal point in the all elliptical vessels. The peak of the pressure at the focal point was determined by the contour and the volume of the elliptical vessel. Keywords: Underwater, Shock wave, Explosion, Supersonic flow, CFD 1. INTRODUCTION Presently in Japan, the reduction of the consumption of a rice attracted attention as a problem. In this situation, a rice-powder is used instead of a flour when food made from flour is produced. The rice-powder is that the grain of the rice is powderized. It is evident that the consumption of the rice is increased by substituting the rice-powder for flour. However, there are two disadvantages in case that the rice-powder is manufactured. First, the methods of manufacturing the rice-powder needed various processes. Thus, the conventional methods waste much cost and time. Second, the quality of the rice-powder is degraded by using conventional methods because the grain of the rice is heated in case that it is crushed. Itoh et al. proposed a new method to manufacture the rice-powder. This method uses a converged underwater shock wave generated by the underwater discharge [1]. On using this method, the rice-powder can be manufactured without heating because the rice-powder is crushed in a moment by spall-fracture generated by a shock wave. Moreover this method can reduce the process of manufacturing the rice-powder. Therefore, the high quality rice-powder can be made with low cost. In addition, the underwater shock wave focusing phenomena are studied. Takayama et al. research the behavior of the underwater shock wave which is generated in the elliptical vessel to investigate the shock wave focusing phenomena in the water []. As a result, the underwater shock wave generated at 1

2 the first focal point of the elliptical vessel is converged at the second focal point of the elliptical vessel. Moreover, the momentum high pressure is generated by the converged shock wave at the second focal point. In our previous research, the behavior of the underwater shock wave was observed by high-speed camera in the elliptical vessel [3]. As a result, the velocity of the underwater shock wave is estimated. However the influence of the contour and the volume of the elliptical vessel on the pressure has not been investigated. This influence is the important to crush the grain of the rice but it is extremely difficult to change the contour and volume of the elliptical vessel in the experiment. Therefore, the purpose of this study is to investigate the influence of the contour and volume of the elliptical vessel on the pressure by using numerical calculations. The numerical simulations were carried out using LS-DYNA finite element code. For simplicity of the numerical analysis, the underwater shock wave generated by the underwater discharge is replaced with the underwater shock wave generated by the underwater explosion.. NUMERICAL PROCEDURE AND BOUNDARY CONDITION In the numerical calculations, the ALE method is used. The ALE method combines the Lagragian and Eulerian techniques to adopt the fluid and the structual dynamic. In this paper, Eulerian techniques are used to analyze the fluid dynamics. Figure 1 shows the numerical calculation model in this research. The shape of the numerical calculation model is the elliptical. In the elliptical vessel, it is composed the explosive and water. The explosive and water are adopted Jones-Wilkins-Lee (JWL) EOS and Mie-Gruneisen EOS, respectively. The Mie-Gruneisen EOS is shown in Eq. (1) [4]. P = ρ 0 C μ [1+ (1- Γ 0 ) μ- a μ ] μ [1-(S 1-1)μ-S μ+1 -S μ 3 +(Γ 0+αμ)E (1) 3 (μ+1) ] Where E is the internal energy per unit volume, C is the intercept of the us-up curve, Г0 is the Mie-Gruneisen gamma, and α is the first-order volume correction to Г0. The constants C, S1, S, S3, Г0, and α are all input parameters. In this research, the parameters are used, as shown in Table 1 [4]. Table 1: Parameters of Mie-Gruneisen of state for water Material ρ0 [kg/m3] C [m/s] S1 Γ0 Water The JWL EOS is shown in Eq. () [5]. P = A [1- ω ] exp(-r VR 1 V)+B [1- ω ] exp(-r 1 VR V)+ ωe V () Where A, B, R1, R, and ω are material constants by experiment, E is the internal energy per unit volume, and V is the initial relative volume. In this research, the parameters are used, as shown in Table [5].

3 Table : Parameters of JWL equation of state for SEP Explosive A [GPa] B [GPa] R1 R ω SEP The boundary conditions for the wall of the elliptical vessel and central axis are adopted the non-slip wall and the axial-symmetry, respectively. As shown in Fig. 1, L is the distance between origin point and first focal point of the elliptical vessel and it is calculated by Eq. (3). Dl and Ds represent the length of the major and minor axes, and the shape of the elliptical vessel is determined by Dl and Ds. The Dl /Ds are changed for 1.05, 1.14, 1.5, 1.37, 1.47, 1.59 and 1.8. In all shapes, the typical volume of the elliptical vessel V1 = 1.61 x 10 6 mm 3 is fixed exept for the investigation of the influence of the volume of the elliptical vessel on the flow and the pressure. The ratio of the volume V/V1 is changed for 1.00,.00 and 3.00, where V is the volume of the elliptical vessel. In all calculations, the explosive and its volume is adopted as SEP and 7.85 x 10 3 mm 3, respectively, to correspond to electrostatic energy U = 4.9 kj [3]. All calculations are carried out by using mesh density NE =.15 element / mm. L Dl D (3) s Figure 1: Numerical calculation model 3. RESULTS AND DISCUSSION 3.1 Element refinement A tri-quad mixed mesh is used in this numerical calculation. Tests are conducted in case of the Dl /Ds = 1.05 to select suitable mesh density NE, which can exactly capture the shock wave generated by the explosion. The pressures generated by the shock waves are compared for the four NE = 0.137, 0.54,.15 and 8.54 element / mm. The values of the pressure generated by the first shock wave passing is recorded at Pm (X = 9.5, Y = 35.7) for Dl /Ds = Figure shows relation between NE and the value of the maximum pressure generated by the first shock wave at Pm. The pressure is increased by increasing the NE and then the value of the pressure remain practically constant. We thus conclude that 3

4 0.08 Pressure [GPa] x10 3 Figure : Relation between NE and pressure for Dl /Ds = 1.05 at Pm the NE.15 is capable of capturing the shock wave and the resolution must be sufficient. In this research, NE =.15 is adopted to reduce the calculation time. 3. Effect of the contour of the elliptical vessel on the flow and the pressure Figures 3(a) ~ (f) show the pressure contours for Dl /Ds = The explosive is set at bottom of the elliptical vessel. The time shown in each figure denotes the elapsed time from the moment of the explosion. Figure 3(a) shows the spherical shock wave generated by the sudden explosion. Figure 3(b) shows that the spherical shock wave reflects from the left and right side of the wall. In Fig. 3(c), the head of the shock wave arrives at the upper wall. At the same time, the shock wave reflected from the wall propagates toward the focal point. It is seen from Fig. 3(d), the shock wave reflected from the wall is just before convergence around the focal point. Figure 3(e) shows that the shock wave is converged and the converged shock wave is on a point. Then, the converged shock wave spreads again in the elliptical vessel. Moreover, the low-pressure area is appeared around the focal point, as shown in Fig. 3(f). This is because the converged shock wave is spreading. The shock wave generated at the first focal point is converged on the second focal point in case of Dl /Ds = For the investigation of the influence of the contour of the elliptical shape on the behavior of the underwater shock wave, the pressure contours for Dl /Ds = 1.59 are shown in Figs 4(a) ~ (f). Figure 4(a) shows the spherical shock wave in the elliptical vessel. This is the same phenomenon as Dl /Ds = Figure 4(b) demonstrates that the shock wave reflected from the left and right side of the wall is intersected at the central axis. Moreover, the shape of the reflected shock wave is linear. Figure 4(c) shows that the head of the shock wave arrives at the upper wall. Then, the shock wave is converged around the focal point and the converged shock wave is not on a point, as shown in Fig. 4(d). In other words, the shock wave is converged in a large area. This is because the shape of the reflected shock wave forms straight. In Fig. 4(e), the converged shock wave spreads in the elliptical vessel again. And it is seen from Fig. 4(f) that the shock wave is converged again around the focal point. This second convergence is appeared in all shapes. The high-pressure area at the moment which the shock wave is converged became larger in case that the shape of the elliptical vessel is elongated. Next, for the quantitative investigation of the contour of the elliptical vessel on the pressure, the pressure fluctuations are shown in Fig. 5. Fig. 5 illustrates the pressure variations at each focal point for same conditions as for Figs. 3 and 4. There are three pressure rises in case of Dl /Ds = Three pressure rises are appeared at t = 5.8, 99.4 and 180μs, respectively. The first pressure rise at t = 5.8μs is because the head of the shock wave passes through the focal point. The second pressure rise at t = 99.4μs is because the shock wave is converged at the focal point. The third pressure rise at t = 180μs is because the secondary shock wave [6] which appears N E 4

5 (a) t = 5.8μs (b) t = 5.8μs (c) t = 64.4μs (d) t = 94.6μs (e) t = 99.4μs (f) t = 111μs Figure 3: Pressure contour variations for Dl /Ds = 1.05 (a) t = 0.μs (b) t = 73.8μs (c) t = 111μs (d) t = 14μs (e) t = 131μs (f) t = 138μs Figure 4: Pressure contour variations for Dl /Ds = 1.59 around the focal point passes through the focal point. The cause of the shock wave generation is sudden spreading the converged shock wave. In case of Dl /Ds = 1.59, three pressure rises are also appeared at t = 95.4, 14 and 138μs, respectively. The first pressure rise at t = 95.4μs is slight pressure rise. This is because the distance between the first focal point and the second focal point is increased by increasing Dl /Ds. Therefore, the head of the shock wave is attenuated. The second pressure rise at t = 14μs is the same phenomenon as the second pressure rise in case of Dl /Ds = The third pressure rise at t = 138μs is because the expansion shock wave which moves toward the focal point is converged at the focal point. In case of the Dl /Ds = 1.05 and 1.59, the maximum pressure is appeared at t = 99.4 and 138μs, and the value of the pressure is reached at 3.05 and 0.674GPa, respectively. In case of Dl /Ds = 1.59, the maximum pressure is lower than in case of Dl /Ds = This is because the area of the pressure distribution at the time when the shock wave converged at the focal point became larger as Dl /Ds is increased. However there are two peaks which are reached over 0.5GPa by converged shock wave and the second converged shock wave at t = 14 and 138μs, respectively. 5

6 Figure 5: Pressure variations at each focal point for Dl /Ds = 1.05 and Pressure [GPa] 3 1 First peak pressure Second peak pressure D l /D s Figure 6: Relation between pressure and Dl /Ds at focal point In order to explain the influence of the contour of the elliptical on the pressure at the focal point, the relation between the maximum pressure at focal point and Dl /Ds is shown in Fig. 6. In this figure, the circle and square symbols represent the first peak of the pressure which is appeared by converged shock wave and the second peak of the pressure which is appeared by second converged shock wave, respectively. Figure 6 shows that the first peak of the pressure is decreased as Dl /Ds is increased. On increasing the Dl /Ds, the area of the pressure distribution at the moment which the shock wave is converged became larger. Moreover, the second peak of the pressure is decreased on increasing Dl /Ds except for Dl /Ds= Relation between the volume of the elliptical vessel and the pressure As mentioned above, the Dl /Ds is considered to be one of the important factors in the peak value of the pressure. For the investigation of the influence of the volume of the elliptical vessel on peak of the pressure, the volume of the elliptical vessel is changed. Figure 7 shows the relation between the first peak of the pressure and V /V1, where V and V1 are the volume of the elliptical vessel and the typical volume of the elliptical vessel, respectively. In this figure the circle, square and diamond symbols represent the Dl /Ds = 1.05, 1.5 and 1.59, respectively. The first peak of the pressure is decreased on 6

7 First peak of the pressure [GPa] D l /D s = 1.05 D l /D s = 1.5 D l /D s = V / V 1 Figure 7: Relation between V/V1 and first peak of the pressure increasing the V/V1 except for Dl /Ds = On increasing the volume of the elliptical vessel, the sum of the distances from wall of the elliptical vessel to those two focal point is increased. Therefore, the shock wave converged at the focal point is attenuated. 4. CONCLUSIONS The behavior of the underwater shock wave in the enclosed vessel is numerically studied by using LS-DYNA finite element code to investigate the influence of the contour and volume of the elliptical vessel on the pressure. The parameters of the calculations are the ratio of the length of the major axis to minor axis of the elliptical vessel and the ratio of the volume of the elliptical vessel. The conclusions are summarized as follows: (1) The shock wave generated at the first focal point converges on the second focal point for all shapes. () The pressure generated at the second focal point for Dl /Ds = 1.05 is the highest of all Dl /Ds. (3) There are two peaks of the pressure at the focal point in case of all shapes and the two peaks reaches over the 1.00GPa in case of Dl /Ds = (4) The pressure generated by the converged shock wave at the focal point decreases as Dl /Ds increased. (5) The first peak of the pressure decreases on increasing the volume of the elliptical vessel. REFERENCES [1] K. Naha, K. Shimojima, Y. Miyafuji, S. Itoh, Design and Development of Pressure Vessel for Improvement of Manufacturing rice-powder Efficiency using Underwater Shock wave, Proceeding of the ASME 01 Pressure Vessels & Piping Conference, PVP , 01. [] K. Takayama, T. Obara, K. Saito, N. Hameshima, Focusing of Underwater Shock Waves and the Mechanism of High Pressure Generation, Transactions of the Japan Society of Mechanical Engineers Series B, 56, pp , [3] O. Higa, R. Matsubara, K. Higa, Y. Miyafuji, T. Gushi, Y. Omine, K. Naha, K. Shimojima, H. Fukuoka, H. Maehara, S. Tanaka, T. Matsui, S. Itoh, Mechanical of the Shock Wave Generation and Energy Efficiency by Underwater Discharge, The International Journal of Multiphysics, 6, pp.89-98, 01. [4] J. Kim, H. Shin, Application of the ALE technique for underwater explosion analysis of a submarine liquefied oxygen tank, Ocean Engineering, 35, pp.81-8,

8 [5] Y. Kim, I. Tomoaki, S. Itoh, Microstructual, crystal structure and electrical characteristics of shock-consolidated GaO3 ZnO bulk, Power Technology, 08, pp , 011. [6] S.M. Liang, J.S. Wang, H. Chen, Numerical study of spherical blast-wave propagation and reflection, Shock Waves, 1, pp.59-68, 00. 8