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Application of shock wave research to geophysics
Journal of Materials Processing Technology 85 (1999) 4 – 10
Application of shock wave research to geophysics K. Takayama a,*, O. Onodera a, T. Saito b a b
Tohoku Uni6ersity, Institute of Fluid Science, Shock Wa6e Research Center, 2 -1 -1 Katahira, Aoba-ku, Sendai 980 -77, Japan Shock Wa6e Research Center, Institute of Fluid Science, Tohoku Uni6ersity Nihon Silicon Graphics Cray K.K., Tohoku, Japan
Abstract This is a report describing an ambitious application of shock wave research to volcanology. In the explosive eruption of a volcano, a shock wave or a blast wave is created, which as it propagates, exhibits characteristics related to the nature of the pressure release at the mouth of the volcano. Hence, it was decided that it would be worthwhile to measure its overpressure in situ via a pressure transducer installed at a point not very far away from its mouth and then to use the measured data to validate a numerical scheme which, to identify the initial energy release of the eruption, was constructed for shock wave propagation over the three-dimensional geometry. The Shock Wave Research Center, Institute of Fluid Science, Tohoku University began a project in 1995 to study the shock wave dynamics of volcanic eruption, by measuring the time variation of blast wave overpressures in situ at Mount Aso near Kumamoto. This paper describes the preparation of the overpressure measurement, still awaiting an eruption, and the result of a three-dimensional fine numerical simulation, which is ready to be compared with the measured data. © 1999 Published by Elsevier Science S.A. All rights reserved. Keywords: Volcanic eruption; Blast wave; Pressure measurement; Pressure transducer
1. Introduction In general, shock waves produced by explosions induce high speed flows and are traditionally called blast waves. Large scale blast waves created by nature are those generated at the explosive eruption of a volcano. The time variation of blast wave overpressures possibly appearing at eruption will be recorded by the installation of a pressure transducer at the mouth of Mount Aso Nakadake. The results of a finite difference numerical scheme are compared with the expected overpressure data. This is an interdisciplinary project between shock wave dynamics and volcanology with the aim of understanding the mechanism of volcanic eruptions, from the shock wave dynamic point of view, as a large scale explosion. When energy is released in a very short period of time, a shock or blast wave is formed, whose overpressures are intimately affected by the gas dynamic process of the pressure release at the volcano mouth and that of wave interactions in the volcano shaft [1 – 3]. Therefore, it is considered that the time history of the blast wave * Corresponding author. Fax: [email protected]
+81
22
2277390;
e-mail:
overpressure produced at the volcanic eruption can provide a clue to understanding its dynamic mechanism. In the field of volcanology, the overpressures of the blast wave are traditionally monitored by using microphones which have very low frequency responses suited to measuring mostly very weak atmospheric pressure variation at a relatively distant location from the volcano. Its frequency response is usually of the order of tens of Hertz, so that these microphones cannot detect such steep overpressures of blast waves, whose rise time is typically less than 1 ms. In the Shock Wave Research Center (SWRC), a pressure transducer suited for this project was designed and manufactured. The pressure transducer, which uses a PVDF piezofilm as the pressure sensitive material, was calibrated and installed at the edge of the crater of Mount Aso Nakadake. The pressure transducer can quantitatively measure high frequency pressure variations [4]. For comparison with the measured result, three-dimensional numerical simulations of blast wave propagations induced by possible eruptions of Mount Aso Nakadake are also carried out at the SWRC [5,6], taking its topographical three-dimensional geometry into account. To initiate the eruption numerically, both a point source explosion model and a shock tube model
0924-0136/99/$ – see front matter © 1999 Published by Elsevier Science S.A. All rights reserved. PII S0924-0136(98)00244-1
K. Takayama et al. / Journal of Materials Processing Technology 85 (1999) 4–10
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Fig. 1. PVDF pressure transducer. Fig. 3. Transmission of measured data.
are assumed as eruption models [7,8]. The quantitative comparison between the measured overpressure history and the numerical results obtained from these eruption models provided not only the validation of the eruption model, but also the mechanism of the pressure release at the volcanic mouth.
2. Installation of a pressure transducer at Mount Aso Nakadake Mount Aso Nakadake, 1238 m high, the world’s largest active volcano located very close to modern civilization, is one of the tourist attractions of Kyushu. Although this volcano is not necessarily ideally suited
to the measurement of blast waves occurring during its eruption, its crater lake is continuously monitored by two TV cameras, each of which is installed in a concrete bunker built at the edge of its crater and hanging over the lake. The size of the actual eruption site is expected to be about 10 m in diameter, while the diameter of the crater is approximately 200 m. The exact position of the eruption is readily identified visually from the live TV image. This information becomes particularly useful when setting up the initial and boundary conditions for numerical simulations of the eruption. The bunker is equipped with an electric power supply for the TV camera and other purposes. The TV signals are converted into optical signals and transmitted to the Volcano Museum located at about 4 km
Fig. 2. Installation of the PVDF pressure transducer (right) and signal converter (left).
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K. Takayama et al. / Journal of Materials Processing Technology 85 (1999) 4–10
Fig. 4. Contour lines.
from the crater. Here, the images from the TV cameras are displayed on monitor screens. It should again be emphasized that the visual and correct identification of the volcanic mouth inside such a large crater is the most important merit of Mount Aso. A pressure transducer is installed in one of the bunkers which is relatively easy to reach from the Volcano Museum at the side of the TV camera called the A-camera.
2.1. Pressure transducer Blast-wave overpressures are generally measured by low frequency microphones and thus far, to the best of the authors’ knowledge, no pressure transducers commonly used for shock wave research have been applied to the measurement of blast wave overpressures. However, during the eruption of Mount Unzen Hugen, a blast meter was used for the first time to detect the impulse of the blast waves. A blast meter is a kind of useful detector which records the deformation of a metal plate exposed to the overpressures of blast waves commonly caused by explosions. Hence, it measures the impulse of blast waves and usually consists of a lead plate with various thicknesses and a metal holder facing the center of the explosion. The lead plate is so soft that it is readily deformable by the blast waves. Blast wave peak overpressures can be deducted from its deformation. Blast meters were first used in volcanology during the Mount Unzen Hugen eruption [9]. This method is often used in the field testing of large scale explosions, but is unknown in the volcanology field tests, since it is believed that significant differences exists between blast waves created by the explosion of explosives and during volcanic eruptions. In particular, they have very a different time history of energy release. The blast meters were usually calibrated by exposing them to a known amount of TNT exploded at various distances in order to determine the relationship between the deformation of lead plates and the overpressure history loaded onto them. Studies are necessary to determine whether the blast meter is a reliable means of measuring the blast wave created by volcanic eruptions.
A blast meter was placed on the north-east slope of Unzen Hugendake at 2.7 km from the eruption center and noticeable deformation was indeed found immediately after the second eruption of June 8, 1991. Later, from this dent the peak overpressure of the blast wave was estimated to be approximately 0.3 atm. The blast meter was also calibrated by the dynamic loading shock waves of known strength emitted from a shock tube [9]. The three-dimensional numerical simulation of the second eruption on June 8 of Mount Unzen Hugen was carried out by taking the real ground geometry into consideration. The result showed a peak overpressure of 0.5 atm at the same location [5]. The measured overpressure was found to be significantly different from that predicted by the point explosion theory. Hence, this implies that the effect of the topography should not be neglected in estimating the overpressure. It also indicates that measurement of the time variation of the blast wave overpressure in situ is important. Consequently, it is necessary to use a pressure transducer with a high frequency response in order to compensate for the shortcomings of low frequency microphones or blast meters. Fig. 1 shows a pressure transducer designed for the current study [10] and manufactured in the machine shop of the Institute of Fluid Science, Tohoku University. The pressure sensitive material is piezo film (Polyvinylidenefluoride, Solvay) 20 mm in diameter and 0.024 mm in thickness is placed in a stainless steel housing, as shown in Fig. 1. The film is so thin that a very high frequency response is obtained. Frequency responses of up to 10 MHz were possible in the underwater shock wave study and frequencies ranging from 1–0.1 MHz were reported for gases, whereas where piezoceramics were used as the pressure sensitive material, the frequency response is known to be as good as this PVDF pressure transducer. Being so thin however, its sensitivity is not very high, so that in order to secure relatively higher output signals against weak blast wave loading, the use of a larger pressure sensitive area is nearly compulsory According to the manufacturer’s nominal value of the charge production per the stress
K. Takayama et al. / Journal of Materials Processing Technology 85 (1999) 4–10
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Fig. 5. Process of determining contour lines on computer.
loaded on the film, its pressure sensitive area is determined to be 20 mm in diameter., since the maximum overpressure of the blast waves which occurred during the last 10 years was estimated to be 0.4 MPa when evaluated at the position of the A-camera. Hence, the Mach number of the blast wave corresponding to this overpressure value is about 2.0 in air. This is a very strong shock wave. The film was tightly sandwiched between a stainless steel diaphragm 0.5 mm thick and another metal rod whose end surface was well polished and supported the film. The diameter of this diaphragm was approximately 50 mm. The metal rod, insulated from the stainless steel housing, became the electrode and was connected to a BNC terminal, while the housing itself was grounded. The output voltage signal was then transformed proportionally to the overpressure loaded onto it. Although the structure of this pressure transducer is straightforward, care must be taken in its manufacture. To secure a very tight contact between the film surface and the metal surfaces, the assemblage of these components was carried out under a vacuum environment. This is to prevent layers or pockets of air being trapped between these contact surfaces [4,10]. The entire housing of this pressure transducer is sealed with an O-ring in a container of 70 mm diameter and is accommodated in the end of a stainless steel pipe 30 mm in diameter and 1 m in length. This assemblage was located beside the TV camera facing towards the crater, as shown in Fig. 2. The position of the pressure transducer was so fixed that, knowing the angle between the direction of the blast wave propagation and the face normal of the pressure transduced from the relative position of the spot of the eruption detected from the TV camera image, its output signal would be correctly re-evaluated from this geometrical information. It should be mentioned that the pressure transducer is continuously exposed to a very corrosive environment, the atmosphere being filled with rich sulfur dioxide and other corrosive gases. The inside of the pressure transducer therefore, was carefully sealed from the atmosphere. However,
in the spring of 1997, 1 year after its installation, the pressure transducer was recovered for the firs time and replaced with a second one. Outwardly, the transducer appeared very badly corroded, but no sign of corrosion was found inside the transducer accommodated in the stainless steel pipe. However, a loose connection of the electrode was discovered. This is probably the result of minor shaking over the course of the year, presumably due to wind and underground volcanic activity. The pressure transducer was calibrated by explosing it to spherical shock waves produced by 10 mg lead azide pellets.
2.2. Transmission of measured signals The electrical signal from the pressure transducer is converted to a light signal by means of an electro/optical signal converter. The TV signal was also thus converted and transmitted through an optical-fiber cable to the Volcano Museum about 4 km from the volcanic crater. This conversion prevented electrical noise which otherwise caused interference during the transmission of electrical signals through cables when eruptions take place. Fig. 3 shows a schematic diagram of the signal transmission. At the Volcano Museum, the optical signal was reconverted to the electrical signal and recorded by the transient recorder (Iwatsu DM2350). The data were then transferred to a personal computer (Apple PowerBook 150) through GPIB interface (National Institute GPIB-SCSI/MacA) and stored on the hard disk. The transient recorder could store data at the sampling rate of 1–2 ms per word for approximately 1–2 s. This measuring system was adjusted to be triggered automatically upon any signal exceeding the threshold pressure value. These measuring and data acquisition systems were remotely controlable. The personal computer installed at the Volcano Museum was linked to that at the Shock Wave Research Center in Sendai, via the NTT telephone network using modems (Microcom V.34 ESII). The network communications software, ARA (apple remote access) and Timbuktu Pro (Falcom), are used to link these personal computers.
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Fig. 6. Three dimensional view from the east of Mount Aso, displayed on computer.
It takes about 10 s to transmit the measured data from Mount Aso to Sendai at approximately 1600 km distance, with a transmission rate of, in most cases, 26.4 kbyte s − 1. The time intervals of each eruption are expected to be much longer than 10 s, so the present data transmission rate is sufficiently long to rest the system for the next eruption when Mount Aso produces more frequent eruptions. Although the system must be maintained once or twice a year, it is basically fully automated and waiting for eruptions to occur. The PVDF piezofilm is reported to lose its sensitivity if heated over about 400 K. It is well known that during eruptions, the crater lake disappears and its dry basin sometimes becomes red hot. Hence, the temperature of the pressure transducer may exceed this critical temperature, due to radiation from the crater basin. To protect the system from this risk, proper methods of reducing the temperature of the pressure transducer, such as water-cooling of the stainless steel housing, are now being considered. Another concern is for the long term degradation of the sensitivity of the piezofilm due to leakage of charges. The effect can be compensated for by changing the circuit constants. This sensitivity degradation however, was not observed when the pressure transducer was inspected 1 year after its installation.
Fig. 7. Time variation of overpressure at the A-camera location.
3. Numerical simulations of blast wave generated by Mount Aso eruptions Before starting the numerical simulation of blast wave propagation over Mount Aso Nakadake, it was decided that the three-dimensional geometry of its topography should be stored on a supercomputer. It has not been an easy task to convert the contour lines of, for example scaled topographical maps issued by the Geographical Survey Institute (Ministry of Construction) into the numerical memory. A system of conversion of contour lines of a ground geometry into its corresponding numerical grid system was established in the Shock Wave Research Center. Three-dimensional numerical grids were then constructed for Mount Aso and finite difference numerical simulations were carried out over these three-dimensional meshes by using a finite volume method [11].
3.1. Grid generation of the ground shape A 1:5,000 scaled map of Mount Aso issued by the Geographical Survey Institute (Ministry of Construction) was used initially. First, the marks and other unnecessary information on the map, except the contour lines, were erased by hand. A scanner (Canon Pixcel Jet) was then used to read the processed map and
Fig. 8. Overpressure distribution on the ground surface 0.95 s after the explosion.
K. Takayama et al. / Journal of Materials Processing Technology 85 (1999) 4–10
Fig. 9. 3-D representations of the jet flow and the induced blast wave.
the digitized data was stored on the hard disk of a personal computer (Macintosh Quadra800). Fig. 4 shows the original map and its processed contour line map. In previous work, the contour lines were read manually by using a digitizer. This was a tedious task and took several days to process; for example, it took 4 – 5 days to digitize a piece of 1:25000 scaled map of the Sakurajima. In the current study, a newly developed system could handle the contour lines in such a way that they could be digitized almost automatically. The scanned map consists of pixels with 256 different grey levels. Those pixels representing contour lines have higher grey levels and the background pixels have lower grey levels. The algorithm of reading contour lines recognizes first the difference between these grey levels, as shown in Fig. 5 as follows. An arbitrary point on a contour line is chosen by a computer mouse. Then, another point in the vicinity of the first point in the tracing direction is chosen, Fig. 5(a). This initiates the automatic tracing of the contour line. The grey levels of pixels around the first point are compared in the selected direction as in Fig. 5(b). The pixel having the highest grey level is chosen as the point on the same contour line and its position is recorded, as seen in Fig. 5(c). The grey level of the chosen pixel is reset to zero in order to avoid any confusion which may occur in tracing the next point, Fig. 5(d). In principle, a contour line is traced automatically, repeating the previous process. In some cases, when the contour lines are not clearly identified, such as in cases of obscured lines and merging lines, which represent steep or overhanging cliffs on the maps, the searching process is interrupted. The process must then be restarted manually by indicating the next point on the contour line.
3.2. Numerical simulations The basic equations of the numerical simulations are the three dimensional nonstationary Euler equations. These are solved by a finite volume method, with second order accuracy in both space and time [5,6,12].
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The calculated area ranges for 1350 m from east to west and for 2000 m from south to north, as shown in Fig. 6. The number of grid points used on the ground surface is 270 and 400, respectively. In the vertical direction, 65 grid points are used in order to calculate blast wave propagation above the ground surface. Fig. 6 shows an aerial view from the east. The mouth of Aso-Nakadake is seen on the right hand side of Fig. 6 and an arrow indicates the location of the A-camera and pressure transducer. The eruption model was similar to a point explosion in which the finite volume of high pressure and high temperature air is suddenly released at a specified eruption point. The pressure and temperature are 400 MPa and 1200 K, respectively. The volume of the energy source in the current simulation was set at 10 ×10×8 m. The total energy of this eruption model is chosen just to produce the shock Mach number of 2.0 at the location where the pressure transducer was set. Its total energy corresponds to that of 154 t of TNT. This model appears to be too simple to represent an actual volcanic eruption, but in order to validate the usefulness of the present scheme, it would be worth using as the first step in a series of numerical simulations. Fig. 7 shows the numerical pressure history at the A-camera location. The ordinate is the overpressure of the blast wave in MPa and the abscissa is the time in seconds. In Fig. 7, a shock wave of Mach number 1.98 arrives 0.13 s after the eruption. The pressure history appears to be somewhat similar to one predicted by a point source explosion over a flat ground surface. However, its fine structure shows irregular pressure variations which clearly indicate the surrounding topography. The pressure history is strongly affected by the eruption model. One of the objectives of the numerical simulations is to determine the eruption model. If, for specified initial conditions and eruption model, the numerical result agrees with the measured pressure history, not only the initial condition but also the assumed eruption model would be acceptable. Fig. 8 shows the numerical pressure distribution at the A-camera location at 0.95 s after the eruption. Unlike explosions on flat ground, local reflections and diffractions of shock waves over the three-dimensional geometry are readily seen. Depending upon the incidence angles of blast waves with the ground geometry, the pattern of their reflected blast waves would be either Mach reflection or regular reflection. Regions behind the Mach stems would show higher pressures than those in the regular reflections. In particular, inside the inner wall of the crater, the blast wave would reflect from its vertical cliff and create a high pressure. However, in the analytical survey of reflected shock wave in three-dimensional geometry, its three-dimensional characteristics are not yet clear-cut. A more realistic eruption model may be the shocktube model in which a foreign gas at high temperature
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and pressure is released suddenly from a vertical shaft [13 – 15]. Fig. 9 gives one of the numerical results obtained with such an eruption model [16].
4. Conclusions Preparation of overpressure measurements of blast waves possibly produced by eruptions of Mount Aso Nakadake and their corresponding numerical simulation is described. At present, this project is still waiting for an eruption; the preparation for numerical simulations aiming to compare their result with that of the overpressure measurement are complete. This project is based upon the premise that the mechanism of volcanic eruptions is a result of nonstationary energy release on a gigantic scale, which is in principle represented by the processes ranging from a point explosion model to a shock tube model and the validity of these models, or a mixture of these procedures, would be identified by comparison between in situ overpressure measurement and numerically predicted measurements. If the result of numerical simulations agrees with the measurements, then the eruption model can be specified. This will also allow us to estimate what is happening in magmatic conduits.
Acknowledgements The authors would like to express their gratitude to H. Ojima and T. Ogawa of the Shock Wave Research Center, Institute of Fluid Science, Tohoku University, for their devotion to this project, to Professor P.A. Voinovitch, visiting professor to SWRC, for his collaboration in the numerical simulation and to Dr H. Babinsky for his help in developing the system for reading the contour lines on topographical maps. The authors wish to acknowledge Professor N. Fujii of
.
Nagoya University, Professor H. Taniguchi of Tohoku University and Dr H. Mader of Bristol University for their discussion of this project. This project was in part supported under the Grant-in-Aid for Scientific Research on Priority Area—the Dymanics of Vapour Explosions by the Ministry of Education, Science and Culture, Japan.
References [1] OJI Seminar, The Physics of Vapor Explosions, October 1993, pp. 25 – 29. [2] Annual Progress Report on Research on the Dynamics of Vapor Explosions, The Research Group on the Dynamics of Vapor Explosions, Under the Grant-Aid for Scientific Research Priority Area, From the Ministry of Education, Science and Culture, 1994. [3] Annual Progress Report on Research on the Dynamics of Vapor Explosions, The Research Group on the Dynamics of Vapor Explosions, Under the Grant-Aid for Scientific Research Priority Area, From the Ministry of Education, Science and Culture, 1995. [4] O. Onodera et al., Proc. Conf. Japan Society of Metals and Engineering, Ichinoseki, Japan, 1995, pp. l04 – 106. [5] T. Saito et al., Shock Waves, Proc. 19th ISSW, 1994, pp. 385 – 390. [6] H. Taniguchi et al., Volcanoes, vol. 39-6, 1995, pp. 257–266. [7] K. Yamada et al., Proc. 7th Annual Meeting , Institute of Fluid Science, Tohoku University, Japan, 1995, pp. 154 – 156. [8] K. Yamada, PhD thesis, Tohoku University, Japan, 1995. [9] H. Taniguchi, et al., Jpn. Geophys. Res. Lett. 20 (1993) 89-92. [10] Textbook for Practical Training and Manufacturing Technique of Pressure Transducer, in: Fluids Engineering Conf., Japan Society of Metals and Engineering, No. 940 – 66, 1994. [11] S. Hayakawa, Proc. 7th Annual Meeting, Institute of Fluid Science, Tohoku University, 1995, pp. 148 – 153. [12] A. Harten, J. Comp. Phys. 49 (1983) 357 – 393. [13] K. Ishihara, J. Geodyn. 3 (1981) 327 – 349. [14] B. Sturtebant et al., Shock Waves, Proc. 18th ISSW, 1992, pp. l29 – 140. [15] R.S.J. Sparks et al., Review in Mineralogy, Volatiles in Magmas, vol. 30, 1994, pp. 413 – 445. [16] P. Voinovich, E. Timofeev, K. Takayama, T. Saito, A. Galyukov, AIAA Paper 98 – 0540 (1998).
Application of shock wave research to geophysics K. Takayama a,*, O. Onodera a, T. Saito b a b
Tohoku Uni6ersity, Institute of Fluid Science, Shock Wa6e Research Center, 2 -1 -1 Katahira, Aoba-ku, Sendai 980 -77, Japan Shock Wa6e Research Center, Institute of Fluid Science, Tohoku Uni6ersity Nihon Silicon Graphics Cray K.K., Tohoku, Japan
Abstract This is a report describing an ambitious application of shock wave research to volcanology. In the explosive eruption of a volcano, a shock wave or a blast wave is created, which as it propagates, exhibits characteristics related to the nature of the pressure release at the mouth of the volcano. Hence, it was decided that it would be worthwhile to measure its overpressure in situ via a pressure transducer installed at a point not very far away from its mouth and then to use the measured data to validate a numerical scheme which, to identify the initial energy release of the eruption, was constructed for shock wave propagation over the three-dimensional geometry. The Shock Wave Research Center, Institute of Fluid Science, Tohoku University began a project in 1995 to study the shock wave dynamics of volcanic eruption, by measuring the time variation of blast wave overpressures in situ at Mount Aso near Kumamoto. This paper describes the preparation of the overpressure measurement, still awaiting an eruption, and the result of a three-dimensional fine numerical simulation, which is ready to be compared with the measured data. © 1999 Published by Elsevier Science S.A. All rights reserved. Keywords: Volcanic eruption; Blast wave; Pressure measurement; Pressure transducer
1. Introduction In general, shock waves produced by explosions induce high speed flows and are traditionally called blast waves. Large scale blast waves created by nature are those generated at the explosive eruption of a volcano. The time variation of blast wave overpressures possibly appearing at eruption will be recorded by the installation of a pressure transducer at the mouth of Mount Aso Nakadake. The results of a finite difference numerical scheme are compared with the expected overpressure data. This is an interdisciplinary project between shock wave dynamics and volcanology with the aim of understanding the mechanism of volcanic eruptions, from the shock wave dynamic point of view, as a large scale explosion. When energy is released in a very short period of time, a shock or blast wave is formed, whose overpressures are intimately affected by the gas dynamic process of the pressure release at the volcano mouth and that of wave interactions in the volcano shaft [1 – 3]. Therefore, it is considered that the time history of the blast wave * Corresponding author. Fax: [email protected]
+81
22
2277390;
e-mail:
overpressure produced at the volcanic eruption can provide a clue to understanding its dynamic mechanism. In the field of volcanology, the overpressures of the blast wave are traditionally monitored by using microphones which have very low frequency responses suited to measuring mostly very weak atmospheric pressure variation at a relatively distant location from the volcano. Its frequency response is usually of the order of tens of Hertz, so that these microphones cannot detect such steep overpressures of blast waves, whose rise time is typically less than 1 ms. In the Shock Wave Research Center (SWRC), a pressure transducer suited for this project was designed and manufactured. The pressure transducer, which uses a PVDF piezofilm as the pressure sensitive material, was calibrated and installed at the edge of the crater of Mount Aso Nakadake. The pressure transducer can quantitatively measure high frequency pressure variations [4]. For comparison with the measured result, three-dimensional numerical simulations of blast wave propagations induced by possible eruptions of Mount Aso Nakadake are also carried out at the SWRC [5,6], taking its topographical three-dimensional geometry into account. To initiate the eruption numerically, both a point source explosion model and a shock tube model
0924-0136/99/$ – see front matter © 1999 Published by Elsevier Science S.A. All rights reserved. PII S0924-0136(98)00244-1
K. Takayama et al. / Journal of Materials Processing Technology 85 (1999) 4–10
5
Fig. 1. PVDF pressure transducer. Fig. 3. Transmission of measured data.
are assumed as eruption models [7,8]. The quantitative comparison between the measured overpressure history and the numerical results obtained from these eruption models provided not only the validation of the eruption model, but also the mechanism of the pressure release at the volcanic mouth.
2. Installation of a pressure transducer at Mount Aso Nakadake Mount Aso Nakadake, 1238 m high, the world’s largest active volcano located very close to modern civilization, is one of the tourist attractions of Kyushu. Although this volcano is not necessarily ideally suited
to the measurement of blast waves occurring during its eruption, its crater lake is continuously monitored by two TV cameras, each of which is installed in a concrete bunker built at the edge of its crater and hanging over the lake. The size of the actual eruption site is expected to be about 10 m in diameter, while the diameter of the crater is approximately 200 m. The exact position of the eruption is readily identified visually from the live TV image. This information becomes particularly useful when setting up the initial and boundary conditions for numerical simulations of the eruption. The bunker is equipped with an electric power supply for the TV camera and other purposes. The TV signals are converted into optical signals and transmitted to the Volcano Museum located at about 4 km
Fig. 2. Installation of the PVDF pressure transducer (right) and signal converter (left).
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K. Takayama et al. / Journal of Materials Processing Technology 85 (1999) 4–10
Fig. 4. Contour lines.
from the crater. Here, the images from the TV cameras are displayed on monitor screens. It should again be emphasized that the visual and correct identification of the volcanic mouth inside such a large crater is the most important merit of Mount Aso. A pressure transducer is installed in one of the bunkers which is relatively easy to reach from the Volcano Museum at the side of the TV camera called the A-camera.
2.1. Pressure transducer Blast-wave overpressures are generally measured by low frequency microphones and thus far, to the best of the authors’ knowledge, no pressure transducers commonly used for shock wave research have been applied to the measurement of blast wave overpressures. However, during the eruption of Mount Unzen Hugen, a blast meter was used for the first time to detect the impulse of the blast waves. A blast meter is a kind of useful detector which records the deformation of a metal plate exposed to the overpressures of blast waves commonly caused by explosions. Hence, it measures the impulse of blast waves and usually consists of a lead plate with various thicknesses and a metal holder facing the center of the explosion. The lead plate is so soft that it is readily deformable by the blast waves. Blast wave peak overpressures can be deducted from its deformation. Blast meters were first used in volcanology during the Mount Unzen Hugen eruption [9]. This method is often used in the field testing of large scale explosions, but is unknown in the volcanology field tests, since it is believed that significant differences exists between blast waves created by the explosion of explosives and during volcanic eruptions. In particular, they have very a different time history of energy release. The blast meters were usually calibrated by exposing them to a known amount of TNT exploded at various distances in order to determine the relationship between the deformation of lead plates and the overpressure history loaded onto them. Studies are necessary to determine whether the blast meter is a reliable means of measuring the blast wave created by volcanic eruptions.
A blast meter was placed on the north-east slope of Unzen Hugendake at 2.7 km from the eruption center and noticeable deformation was indeed found immediately after the second eruption of June 8, 1991. Later, from this dent the peak overpressure of the blast wave was estimated to be approximately 0.3 atm. The blast meter was also calibrated by the dynamic loading shock waves of known strength emitted from a shock tube [9]. The three-dimensional numerical simulation of the second eruption on June 8 of Mount Unzen Hugen was carried out by taking the real ground geometry into consideration. The result showed a peak overpressure of 0.5 atm at the same location [5]. The measured overpressure was found to be significantly different from that predicted by the point explosion theory. Hence, this implies that the effect of the topography should not be neglected in estimating the overpressure. It also indicates that measurement of the time variation of the blast wave overpressure in situ is important. Consequently, it is necessary to use a pressure transducer with a high frequency response in order to compensate for the shortcomings of low frequency microphones or blast meters. Fig. 1 shows a pressure transducer designed for the current study [10] and manufactured in the machine shop of the Institute of Fluid Science, Tohoku University. The pressure sensitive material is piezo film (Polyvinylidenefluoride, Solvay) 20 mm in diameter and 0.024 mm in thickness is placed in a stainless steel housing, as shown in Fig. 1. The film is so thin that a very high frequency response is obtained. Frequency responses of up to 10 MHz were possible in the underwater shock wave study and frequencies ranging from 1–0.1 MHz were reported for gases, whereas where piezoceramics were used as the pressure sensitive material, the frequency response is known to be as good as this PVDF pressure transducer. Being so thin however, its sensitivity is not very high, so that in order to secure relatively higher output signals against weak blast wave loading, the use of a larger pressure sensitive area is nearly compulsory According to the manufacturer’s nominal value of the charge production per the stress
K. Takayama et al. / Journal of Materials Processing Technology 85 (1999) 4–10
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Fig. 5. Process of determining contour lines on computer.
loaded on the film, its pressure sensitive area is determined to be 20 mm in diameter., since the maximum overpressure of the blast waves which occurred during the last 10 years was estimated to be 0.4 MPa when evaluated at the position of the A-camera. Hence, the Mach number of the blast wave corresponding to this overpressure value is about 2.0 in air. This is a very strong shock wave. The film was tightly sandwiched between a stainless steel diaphragm 0.5 mm thick and another metal rod whose end surface was well polished and supported the film. The diameter of this diaphragm was approximately 50 mm. The metal rod, insulated from the stainless steel housing, became the electrode and was connected to a BNC terminal, while the housing itself was grounded. The output voltage signal was then transformed proportionally to the overpressure loaded onto it. Although the structure of this pressure transducer is straightforward, care must be taken in its manufacture. To secure a very tight contact between the film surface and the metal surfaces, the assemblage of these components was carried out under a vacuum environment. This is to prevent layers or pockets of air being trapped between these contact surfaces [4,10]. The entire housing of this pressure transducer is sealed with an O-ring in a container of 70 mm diameter and is accommodated in the end of a stainless steel pipe 30 mm in diameter and 1 m in length. This assemblage was located beside the TV camera facing towards the crater, as shown in Fig. 2. The position of the pressure transducer was so fixed that, knowing the angle between the direction of the blast wave propagation and the face normal of the pressure transduced from the relative position of the spot of the eruption detected from the TV camera image, its output signal would be correctly re-evaluated from this geometrical information. It should be mentioned that the pressure transducer is continuously exposed to a very corrosive environment, the atmosphere being filled with rich sulfur dioxide and other corrosive gases. The inside of the pressure transducer therefore, was carefully sealed from the atmosphere. However,
in the spring of 1997, 1 year after its installation, the pressure transducer was recovered for the firs time and replaced with a second one. Outwardly, the transducer appeared very badly corroded, but no sign of corrosion was found inside the transducer accommodated in the stainless steel pipe. However, a loose connection of the electrode was discovered. This is probably the result of minor shaking over the course of the year, presumably due to wind and underground volcanic activity. The pressure transducer was calibrated by explosing it to spherical shock waves produced by 10 mg lead azide pellets.
2.2. Transmission of measured signals The electrical signal from the pressure transducer is converted to a light signal by means of an electro/optical signal converter. The TV signal was also thus converted and transmitted through an optical-fiber cable to the Volcano Museum about 4 km from the volcanic crater. This conversion prevented electrical noise which otherwise caused interference during the transmission of electrical signals through cables when eruptions take place. Fig. 3 shows a schematic diagram of the signal transmission. At the Volcano Museum, the optical signal was reconverted to the electrical signal and recorded by the transient recorder (Iwatsu DM2350). The data were then transferred to a personal computer (Apple PowerBook 150) through GPIB interface (National Institute GPIB-SCSI/MacA) and stored on the hard disk. The transient recorder could store data at the sampling rate of 1–2 ms per word for approximately 1–2 s. This measuring system was adjusted to be triggered automatically upon any signal exceeding the threshold pressure value. These measuring and data acquisition systems were remotely controlable. The personal computer installed at the Volcano Museum was linked to that at the Shock Wave Research Center in Sendai, via the NTT telephone network using modems (Microcom V.34 ESII). The network communications software, ARA (apple remote access) and Timbuktu Pro (Falcom), are used to link these personal computers.
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Fig. 6. Three dimensional view from the east of Mount Aso, displayed on computer.
It takes about 10 s to transmit the measured data from Mount Aso to Sendai at approximately 1600 km distance, with a transmission rate of, in most cases, 26.4 kbyte s − 1. The time intervals of each eruption are expected to be much longer than 10 s, so the present data transmission rate is sufficiently long to rest the system for the next eruption when Mount Aso produces more frequent eruptions. Although the system must be maintained once or twice a year, it is basically fully automated and waiting for eruptions to occur. The PVDF piezofilm is reported to lose its sensitivity if heated over about 400 K. It is well known that during eruptions, the crater lake disappears and its dry basin sometimes becomes red hot. Hence, the temperature of the pressure transducer may exceed this critical temperature, due to radiation from the crater basin. To protect the system from this risk, proper methods of reducing the temperature of the pressure transducer, such as water-cooling of the stainless steel housing, are now being considered. Another concern is for the long term degradation of the sensitivity of the piezofilm due to leakage of charges. The effect can be compensated for by changing the circuit constants. This sensitivity degradation however, was not observed when the pressure transducer was inspected 1 year after its installation.
Fig. 7. Time variation of overpressure at the A-camera location.
3. Numerical simulations of blast wave generated by Mount Aso eruptions Before starting the numerical simulation of blast wave propagation over Mount Aso Nakadake, it was decided that the three-dimensional geometry of its topography should be stored on a supercomputer. It has not been an easy task to convert the contour lines of, for example scaled topographical maps issued by the Geographical Survey Institute (Ministry of Construction) into the numerical memory. A system of conversion of contour lines of a ground geometry into its corresponding numerical grid system was established in the Shock Wave Research Center. Three-dimensional numerical grids were then constructed for Mount Aso and finite difference numerical simulations were carried out over these three-dimensional meshes by using a finite volume method [11].
3.1. Grid generation of the ground shape A 1:5,000 scaled map of Mount Aso issued by the Geographical Survey Institute (Ministry of Construction) was used initially. First, the marks and other unnecessary information on the map, except the contour lines, were erased by hand. A scanner (Canon Pixcel Jet) was then used to read the processed map and
Fig. 8. Overpressure distribution on the ground surface 0.95 s after the explosion.
K. Takayama et al. / Journal of Materials Processing Technology 85 (1999) 4–10
Fig. 9. 3-D representations of the jet flow and the induced blast wave.
the digitized data was stored on the hard disk of a personal computer (Macintosh Quadra800). Fig. 4 shows the original map and its processed contour line map. In previous work, the contour lines were read manually by using a digitizer. This was a tedious task and took several days to process; for example, it took 4 – 5 days to digitize a piece of 1:25000 scaled map of the Sakurajima. In the current study, a newly developed system could handle the contour lines in such a way that they could be digitized almost automatically. The scanned map consists of pixels with 256 different grey levels. Those pixels representing contour lines have higher grey levels and the background pixels have lower grey levels. The algorithm of reading contour lines recognizes first the difference between these grey levels, as shown in Fig. 5 as follows. An arbitrary point on a contour line is chosen by a computer mouse. Then, another point in the vicinity of the first point in the tracing direction is chosen, Fig. 5(a). This initiates the automatic tracing of the contour line. The grey levels of pixels around the first point are compared in the selected direction as in Fig. 5(b). The pixel having the highest grey level is chosen as the point on the same contour line and its position is recorded, as seen in Fig. 5(c). The grey level of the chosen pixel is reset to zero in order to avoid any confusion which may occur in tracing the next point, Fig. 5(d). In principle, a contour line is traced automatically, repeating the previous process. In some cases, when the contour lines are not clearly identified, such as in cases of obscured lines and merging lines, which represent steep or overhanging cliffs on the maps, the searching process is interrupted. The process must then be restarted manually by indicating the next point on the contour line.
3.2. Numerical simulations The basic equations of the numerical simulations are the three dimensional nonstationary Euler equations. These are solved by a finite volume method, with second order accuracy in both space and time [5,6,12].
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The calculated area ranges for 1350 m from east to west and for 2000 m from south to north, as shown in Fig. 6. The number of grid points used on the ground surface is 270 and 400, respectively. In the vertical direction, 65 grid points are used in order to calculate blast wave propagation above the ground surface. Fig. 6 shows an aerial view from the east. The mouth of Aso-Nakadake is seen on the right hand side of Fig. 6 and an arrow indicates the location of the A-camera and pressure transducer. The eruption model was similar to a point explosion in which the finite volume of high pressure and high temperature air is suddenly released at a specified eruption point. The pressure and temperature are 400 MPa and 1200 K, respectively. The volume of the energy source in the current simulation was set at 10 ×10×8 m. The total energy of this eruption model is chosen just to produce the shock Mach number of 2.0 at the location where the pressure transducer was set. Its total energy corresponds to that of 154 t of TNT. This model appears to be too simple to represent an actual volcanic eruption, but in order to validate the usefulness of the present scheme, it would be worth using as the first step in a series of numerical simulations. Fig. 7 shows the numerical pressure history at the A-camera location. The ordinate is the overpressure of the blast wave in MPa and the abscissa is the time in seconds. In Fig. 7, a shock wave of Mach number 1.98 arrives 0.13 s after the eruption. The pressure history appears to be somewhat similar to one predicted by a point source explosion over a flat ground surface. However, its fine structure shows irregular pressure variations which clearly indicate the surrounding topography. The pressure history is strongly affected by the eruption model. One of the objectives of the numerical simulations is to determine the eruption model. If, for specified initial conditions and eruption model, the numerical result agrees with the measured pressure history, not only the initial condition but also the assumed eruption model would be acceptable. Fig. 8 shows the numerical pressure distribution at the A-camera location at 0.95 s after the eruption. Unlike explosions on flat ground, local reflections and diffractions of shock waves over the three-dimensional geometry are readily seen. Depending upon the incidence angles of blast waves with the ground geometry, the pattern of their reflected blast waves would be either Mach reflection or regular reflection. Regions behind the Mach stems would show higher pressures than those in the regular reflections. In particular, inside the inner wall of the crater, the blast wave would reflect from its vertical cliff and create a high pressure. However, in the analytical survey of reflected shock wave in three-dimensional geometry, its three-dimensional characteristics are not yet clear-cut. A more realistic eruption model may be the shocktube model in which a foreign gas at high temperature
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and pressure is released suddenly from a vertical shaft [13 – 15]. Fig. 9 gives one of the numerical results obtained with such an eruption model [16].
4. Conclusions Preparation of overpressure measurements of blast waves possibly produced by eruptions of Mount Aso Nakadake and their corresponding numerical simulation is described. At present, this project is still waiting for an eruption; the preparation for numerical simulations aiming to compare their result with that of the overpressure measurement are complete. This project is based upon the premise that the mechanism of volcanic eruptions is a result of nonstationary energy release on a gigantic scale, which is in principle represented by the processes ranging from a point explosion model to a shock tube model and the validity of these models, or a mixture of these procedures, would be identified by comparison between in situ overpressure measurement and numerically predicted measurements. If the result of numerical simulations agrees with the measurements, then the eruption model can be specified. This will also allow us to estimate what is happening in magmatic conduits.
Acknowledgements The authors would like to express their gratitude to H. Ojima and T. Ogawa of the Shock Wave Research Center, Institute of Fluid Science, Tohoku University, for their devotion to this project, to Professor P.A. Voinovitch, visiting professor to SWRC, for his collaboration in the numerical simulation and to Dr H. Babinsky for his help in developing the system for reading the contour lines on topographical maps. The authors wish to acknowledge Professor N. Fujii of
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Nagoya University, Professor H. Taniguchi of Tohoku University and Dr H. Mader of Bristol University for their discussion of this project. This project was in part supported under the Grant-in-Aid for Scientific Research on Priority Area—the Dymanics of Vapour Explosions by the Ministry of Education, Science and Culture, Japan.
References [1] OJI Seminar, The Physics of Vapor Explosions, October 1993, pp. 25 – 29. [2] Annual Progress Report on Research on the Dynamics of Vapor Explosions, The Research Group on the Dynamics of Vapor Explosions, Under the Grant-Aid for Scientific Research Priority Area, From the Ministry of Education, Science and Culture, 1994. [3] Annual Progress Report on Research on the Dynamics of Vapor Explosions, The Research Group on the Dynamics of Vapor Explosions, Under the Grant-Aid for Scientific Research Priority Area, From the Ministry of Education, Science and Culture, 1995. [4] O. Onodera et al., Proc. Conf. Japan Society of Metals and Engineering, Ichinoseki, Japan, 1995, pp. l04 – 106. [5] T. Saito et al., Shock Waves, Proc. 19th ISSW, 1994, pp. 385 – 390. [6] H. Taniguchi et al., Volcanoes, vol. 39-6, 1995, pp. 257–266. [7] K. Yamada et al., Proc. 7th Annual Meeting , Institute of Fluid Science, Tohoku University, Japan, 1995, pp. 154 – 156. [8] K. Yamada, PhD thesis, Tohoku University, Japan, 1995. [9] H. Taniguchi, et al., Jpn. Geophys. Res. Lett. 20 (1993) 89-92. [10] Textbook for Practical Training and Manufacturing Technique of Pressure Transducer, in: Fluids Engineering Conf., Japan Society of Metals and Engineering, No. 940 – 66, 1994. [11] S. Hayakawa, Proc. 7th Annual Meeting, Institute of Fluid Science, Tohoku University, 1995, pp. 148 – 153. [12] A. Harten, J. Comp. Phys. 49 (1983) 357 – 393. [13] K. Ishihara, J. Geodyn. 3 (1981) 327 – 349. [14] B. Sturtebant et al., Shock Waves, Proc. 18th ISSW, 1992, pp. l29 – 140. [15] R.S.J. Sparks et al., Review in Mineralogy, Volatiles in Magmas, vol. 30, 1994, pp. 413 – 445. [16] P. Voinovich, E. Timofeev, K. Takayama, T. Saito, A. Galyukov, AIAA Paper 98 – 0540 (1998).