explosive thermal interactions between molten lava and water

Explosive Thermal Interactions between Molten Lava and Water

G. Friihlich IKE, University of Stuttgart, Stuttgart, FRG

B. Zimanowski

V. Lorenz Institute of Geology, University of Wfirzburg, Wiirzburg, FRG

i The most effective volcanic eruptions are the phreatomagmatic explosions. In such eruptions, magma and groundwater come into contact with each other, leading to explosions. A reproduction of such explosive interactions between lava (produced by remelting of volcanic rocks) and water in the laboratory was carried out, in which water was injected into molten lava. The amount of lava that was involved in the interactions, the so-called interactive lava mass, was determined. The influences of chemical composition and temperature of the melt and the injection velocity of water were also investigated.

Experiments show that an enhancement of the injection velocity of the water leads to more violent explosions. This is obviously due to an enlarge- ment of the mixing region between water and molten lava in the crucible. Raising the temperature of the lava melt leads also to a greater impulse but not to an increase in the interactive masses as is found in connection with the water injection velocity. That means that the conversion ratio will be larger for higher lava temperatures than for lower ones.

By a fitting calculation with the measured curve of the force history of an explosive thermal interaction, the mass of water that was evaporated by the thermal interaction was estimated. In the same calculation the superheating temperature of this evaporated water can be determined. Furthermore, the amount of energy released by the explosive thermal interactions was calculated by using the measured impulse and determined fragment mass in fragmentation analysis.

Keywords: thermal interaction, vapor explosion, steam explosion, fuel coolant interaction, rapid heat transfer, experimental volcanology, phreatomagmatism

I N T R O D U C T I O N

Investigations were carried out to produce explosive thermal interactions between molten lava and water in the laboratory. Such thermal interactions did not occur when molten lava was poured into a container filled with water. In this case a vapor film forms at the interface between lava and water and a crust forms at the surface of the lava melt. When water was injected into a crucible filled with molten lava, again no explosive thermal interactions occurred. In this case the injected water rose upwards in the molten lava toward the surface and vaporized relatively slowly at the surface of the mol ten lava. Hence a stable vapor film at the interface between lava and water pre- vented an explosive thermal interaction.

When the tempera ture of a melt is between 300 and 500°C, a spontaneous thermal interaction between the melt and water can take place. But with tin melt (m.p. 232°C) or with other materials having low melting points, spontaneous interactions have often been observed [1-4]. The vapor film is unstable in this t empera ture region and collapses easily, leading to direct contact between the melt

and water and to the formation of a large interface and thus very fast heat transfer from the hot melt to the water. This fast heat transfer leads to a superheat ing of the water, which then causes an explosive vaporization.

Besides the above-ment ioned spontaneous thermal interactions, tr iggered thermal interactions are also observed. In cases where a stable vapor film prevents a spontaneous thermal interaction (melt tempera ture > 500°C), an external trigger can be used to induce a thermal interaction. Af ter the enforced collapse of the vapor film, provoked by the external trigger, the mechanism of interaction follows the same sequence as in the case of spontaneous thermal interactions: direct contact, frag- mentat ion, large interface, heat transfer, superheating, explosive vaporization. Such tr iggered interactions have been carried out in laboratories, for instance with water and molten copper, aluminum oxide, and iron oxide [5-8].

But such tr iggered interactions with lava are not easily carried out in the laboratory because of the crust formation and low heat conductivity of lava. Fr6hlich et al were the first to achieve steam explosions with molten lava and water in the laboratory [9]. An ent rapment configuration

Address correspondence to Dr. G. Fr6hlich, IKE, University of Stuttgart, Pfaffenwaldring 31, D-7000 Stuttgart 80, Germany.

Experimental Thermal and Fluid Science 1993; 7:319-332 © 1993 by Elsevier Science Publishing Co., Inc., 655 Avenue of the Americas, New York, NY 10010 0894-1777/93/$6.00

319

320 G. Fr6hlich et al.

was used to avoid crust formation, with a small amount of water injected into a crucible filled with molten lava. Before the injected water could reach the lava surface, a thermal interaction was triggered by a shock wave generated by the impact of a bullet fired from an air gun onto the melt surface. To improve the reproducibility of the triggered thermal interactions of the molten lava and water, an automation of the experimental procedures was attempted.

E X P E R I M E N T A L SETUP (TEE-HAUS)

The setup in Fig. 1, called TEE-Haus, was constructed to enable quantitative investigations of the interactions between molten lava and water. Here TEE is an abbrevia- tion for Thermal Explosion Experiment. The German word Haus is synonymous with the English word "house" and is used to indicate that the containment surrounding the explosion center is relatively large.

The TEE-Haus covers an area of 3 m x 3 m, and its inner ceiling height ranges between 1 m and 1.8 m. Its base is 0.5 m above the laboratory floor. The heating arrangements and measurement recorders are placed underneath the base of the housing. The internal volume of the TEE-Haus was dimensioned large enough to allow the fragments of lava produced during the steam explo- s i ons -wh ich are ejected out of the experimental crucible and are still partly in the liquid s t a t e - - to cool to below their melting point before they strike the walls of the housing. Thus the fragments are not deformed at all (or at most very slightly) by their impact with the walls.

Figure 1 also shows the substructure recording device (1), which will be described in more detail later. A steel crucible is placed inside a coil. The coil is connected to a 30 kW middle frequency generator by the railing (2). This generator feeds a 10 kHz alternating current into the coil. An air gun was installed and used as a triggering device (5). Its release mechanism is activated through the use of an eccentric disk driven by an electric motor. The experimental process was recorded and monitored by a video camera (4). In addition, a high speed camera was used to record sequences at rates of 6000 pictures/s.

Figure 1. Sketch of the outer view of the TEE-Haus.

The water injection device ran over two L-shaped railings (3a) in the first version. In the second version these railings were replaced by railings implanted onto the floor of the TEE-Haus. A new water injection device was constructed that can be moved on these new railings by a cogwheel drive (3b). This new water injection device and the railings were covered by a tunnel as further protection against the fragments flying out of the crucible.

Water Inject ion Device

Figure 2 shows the water injection device constructed according to the first version. This device can be moved along the railings and positioned over the crucible with the help of an adjustable stop pin. The lower portion of the device can then be lowered with the help of a mounted motor unit, so that the injection pipe descends to the desired depth in the crucible. The injection motor unit pushes the piston downwards at an adjustable speed, thus enabling the injection of water into the crucible at various desired speeds. The speed of the injection of water is recorded on an inductive recording device. The speed of the injection of water depends on the applied motor voltage as well as on the inner diameter of the injection pipes used.

In order to provide an undisturbed melt and fragment eruption out of the crucible, an improved injection device was constructed (Fig. 3) in such a way that only the injection pipe was positioned directly over the crucible. The device in this arrangement moves over railings at the level of the floor of the TEE-Haus, driven with the help of variable-geared motors, and enables the injection pipe to be positioned directly above the crucible.

Substructure and Recording Device with Steel Crucible and Induct ion Coils

A recording device is used to measure the force during the time of explosion. The recording device along with the steel crucible and induction coils are presented in Fig. 4. The recording device is positioned underneath the cru-

Side view Suspenders J % j

vlounted motor .

ljection motor " "

Inductive path recorder

Front view

-Jiiiiii!iiiiiiiiiiiijiiL

- I n j ec t ion - - , .

Injection pipe -

Figure 2. Device for injection of water (first version).

Explosive Thermal Interactions--Lava and Water 321

5 CR I I

(7)

~ ( 2 ) _

_ (1)

Figure 3. Device for injection of water (second version). (1) Main motor; (2) Mounted motor; (3) injection motor; (4) injection; (5) injection pipe with bow; (6) inductive path recorder; (7) resistance path recorder.

cible and the induction coils. For thermal protection of the force transducers (see next subsection), the crucible is placed on a heat-insulating ceramic plate. Below this plate is a stainless steel sheet, which protects the force transducer and its cables against the heat of radiation from the crucible. A cooling arrangement underneath the crucible consists of a stainless steel cylinder into which copper cooling pipes have been soldered, and water flowing through this arrangement transports the rest of the heat conducted downwards from the crucible. The temperature near the recording device is thus only in the neighborhood of 50°C, although the crucible may reach temperatures up to 1800°C. Its upper edge is made level with the internal floor of the TEE-Haus by an adjusting mechanism (height adjuster).

Force Transducers

When a steam explosion occurs, the melt in the crucible is accelerated by the expanding steam. The time-dependent force F generated thereby is measured with the help of two piezoelectric force transducers (supplied by Kistler Company) that are positioned beneath the cooling arrangements (Fig. 5).

Piezoelectric force transducers have the remarkable characteristic that despite their small physical size they can endure large forces (up to about 60 or 120 kN used here) and possess a high force sensitivity (of the order of

i Crucible Inducl

Protecl

Arl

Force

Hek, Figure 4. Substructure recording device with steel crucible and induction coils.

0.01 N in the whole region of measurement), and due to their high rigidity (of the order of 6 or 9 kN//zm) they are extremely suitable for measuring abruptly changing processes. The response time for force measurements is of the order of 1 /xs. Two transducers were used to enable covering high sensitivity with one and low sensitivity with the other. The violence of an explosion is unpredictable because steam explosions show large fluctuations.

Control and Recording Instruments

All the control and measurement instruments are installed on a trolley (Fig. 6). These instruments are used for driving the experimental units and for processing and recording the measurements. The individual instruments on this device are

• A computer for controlling the experimental timing • Three power supply units • A remote control for the magnetic tape recorder • A charge amplifier for each of the force transducers • A digital recording oscilloscope with an integrated

disk drive unit • An analog multichannel magnetic tape recorder • A recording oscilloscope • A temperature recording device

"2 crn"

Cooling System Spherical Plate ~ ~ . , ~

Force Transducer Kistler 9031 , ~ /

Intermediary ~ ~ connecting piece ~ ~

Force Transducer ~ Kistler9051 ~ ~ ~ r

Pressure ~ distr!buting ~-- ~

nng Base

Figure 5. Sketch of force transducers as installed.


Coeputer PoMer supply unit for Nater injectim device Renote control for Data Magnetic band recorder

Charge amplifiers fo Force Transducer

~O cM m . I ! I

Data Recorder

Registering Oscilloscope

PoNer supplg unit for nounted Motor

PoNer supplu unit foe trigger

Tenperature neasuring device

Figure 6. Trolley with control and measurement instruments.

With the help of a computer, the desired duration and delay time were regulated and controlled for the chrono- logically successive individual steps in each experimental process (time delay after the end of sinking of the injection pipe before beginning water injection, duration of water injection). The triggering of the steam explosion in the modified version must occur at an exact predeter- mined time, as the amount of water available for a steam explosion depends on the time interval between the beginning of the injection of water and the onset of triggering.

EXPERIMENTS WITH MOLTEN LAVA AND WATER

Most of the experiments were carried out with lava obtained from the volcanic region of Sternberg, which is situated in the Swabian mountains (a mountain range located in the southern part of Germany). The lava was an olivine-melilitite. This is a lava with a relatively low SiO 2 content (36 wt %) but a relatively high alkaline earth content (35 wt %) and therefore belongs to the type of magmatic melts with low viscosity. The quality of reproduction of the thermal interaction depends on the quality of the preset initial conditions and on the system immanent fluctuations (fluctuations during the mixing of the injected water into melt in the crucible). The quality of the presetting of the initial conditions has been brought up to a high standard by using the TEE-Haus. It is not possible to govern the system immanent fluctuations, so experiments had to be carried out often under the same initial conditions to form average values, in order to eliminate the influence of these fluctuations to a large extent. An experiment with preset parameters that gave reliable and violent explosive interactions was designated a standard experiment, so the results could be used for the purpose of comparison with other experiments having different parameters. In the standard experiment, Stern- berg lava with a melt temperature of 1350 + 5°C was used; the injection velocity was 4.8 + 0.1 m/s , and the duration from the beginning of water injection to the time of bullet impact onto the melt surface, the so-called trigger instant, was 450 ms. The internal diameter of the injection pipe was 3.5 mm, and the depth of immersion of the injection pipe into the melt was 60 ram. The results

and parameters of the experiments carried out are listed in Table l. In these experiments the dependence of the force on time was measured by the force transducers (see Fig. 7). The uncertainties in measuring the force with the transducers is of the order of 0.01 N in the whole region of the measurement (see earlier), which is negligible com- i~ared to the fluctuations of the interactions. The values of the force maxima, the width of the base of the curve, and the integral of the force-time curves, that is, the impulse, were determined from these curves and are listed in Table 1.

Furthermore, all the fragments ( < 1.4 ram) produced in the TEE-Haus experiments were collected, weighed (uncertainty + 0.01 g), and analyzed to determine the mass of the interactive fragments. This interactive mass arises from the amount of melt that came into direct contact with water and produced steam. These fragments could be distinguished from the other fragments by their specific shape and size. As the thermally produced fragments that form the interactive lava mass show characteristic features (sizes and shapes that are coarse and fine), they could be identified by a high resolution digital picture analysis with an uncertainty of 0.02 g.

RESULTS

All experimental results are presented in Table 1. The values of impulse and interactive mass of each experiment are presented in Fig. 8. As can be seen from the dashed line, there is an approximately linear increase of the impulse with the interactive lava mass in the range between 2 and 18 g.

Experiments with magmatic melts of varying chemical compositions were carried out. The results are listed in Table 1 and presented in Fig. 9 using the following abbre- viations: SB = Sternberg (olivine-melilitite), HB = Hirschberg (basaltic andesite), WB = Weyersbach (melilitite-nephelinite), JU = Jusi (olivine-melilitite), GB = Goosberg (olivine-nephelinite), KG = K~segrotte (basanite), BB = Bad Bertrich (basanite), LO1 = Londorf 1 (olivine-basalt), LO2 = Londorf 2 (olivine-tholeyite), SP = Suc de Pertuis (phonolite), DB = Donnersberg (rhyo- lite), and DF = Drosselfels (dacite). Figure 9 shows the ranges of the impulses determined for the various types of melts. Types HB, LO1, LO2, SP, DB, and DF produced


Table 1. Results and Parameters of Experiments with Volcanic Melts*

Melt Injection Trigger Force Exp. Temp. t Velocity Instant Maxima No. (°C) (m / s) (ms) (kN)

CuFue Base Impulse F r a g m e n t s Interactive Width fFdt < 1.4 mm Mass (ms) (N" s) (g) (g)

SB T-1 1350 1.60 600 SB T-2 1350 1.60 600 SB T-4 1350 1.60 600 SB TI.1 1350 2.90 350 SB T1.2 1350 2.90 350 SB T1.3 1350 2.90 350 SB T1.4 1350 2.90 350 SB T1.5 1350 2.90 350 SB T1.6 1350 2.90 350 SB T1.7 1350 2.90 350 SB T2.2 1350 2.90 350 SB T2.4 1350 2.90 350 SB T2.6 1350 2.90 350 SB T3.3 1350 2.90 350 SB T3.4 1350 2.90 350 SB T3.5 1350 2.90 350 SB T4.1 1350 2.90 450 SB T4.3 1350 2.90 450 SB T4.4 1350 2.90 450 SB T4.5 1350 2.90 450 SB T5.1 1350 2.90 550 SB T5.2 1350 2.90 550 SB T5.3 1350 2.90 550 SB T5.4 1350 2.90 550 SB T5.5 1350 2.90 550 SB T6.1 1350 2.90 650 SB T6.2 1350 2.90 650 SB T6.3 1350 2.90 650 SB T6.4 1350 2.90 650 SB T6.5 1350 2.90 650 SB T7.1 1350 2.90 750 SB T7.2 1350 2.90 750 SB T7.5 1350 2.90 750 SB T8.1 1350 2.90 850 SB TF1A 1350 2.90 450 SB TF1B 1350 2.90 450 SB TFI.1 1350 2.90 450 SB TF1.2 1350 2.90 450 SB TF1.3 1350 2.90 450 SB TF1.4 1350 2.90 450 SB TF1.5 1350 2.90 450 SB TF1.6 1350 2.90 450 SB TF2.1 1350 2.90 450 SB TF2.2 1350 2.90 450 SB TF2.3 1350 2.90 450 SB TF2.4 1350 2.90 450 SB TF2.5 1350 2.90 450 SB TF3.1 1350 2.90 450 SB TF3.2 1350 2.90 450 SB TF3.3 1350 2.90 450 SB TF3.4 1350 2.90 450 SB TF3.5 1350 2.90 450 SB TF3.6 1350 2.90 450 SB TRI.1 1350 1.75 450 SB TR1.2 1350 1.75 450 SB TR1.3 1350 1.75 450

6.1/3.8 1.58 4.38 76.80 3.42 4.9 1.59 3.57 58.44 2.10 1.6 37.80 0.54 1.9 2.45 1.64 15.92 0.74 1.8 2.50 1.93 9.90 0.63

3.3/2.4 2.14 2.93 57.90 1.62 1.25 3.23 1.43 10.05 0.48 2.2 2.40 2.17 15.20 1.00

4.4/2.5 1.45 2.89 34.00 0.91 5.1/3.1 1.45 3.30 50.30 1.96

3.5 2.15 2.83 38.13 0.96 5.1 1.82 3.57 45.80 1.79

0.65 3.10 0.90 9.70 0.25 0.95 4.30 1.37 9.70 0.35 0.55 4.10 1.11 7.30 0.36 0.70 2.80 0.94 7.01 0.35

6.8/5.8 2.22 5.57 73.81 3.69 4.2 2.75 4.35 84.32 2.92

18.4/13.7/10.6 1.75 11.94 146.74 13.56 12.6/8.5 1.73 7.96 110.30 8.82

1.2 2.30 1.31 24.21 0.55 6.5/4.8 2.20 5.08 73.30 3.21 6.0/6.5 2.15 6.26 98.40 7.06 4.2/2.6 2.55 3.06 63.50 1.61

1.5 1.85 1.15 7.82 0.32 2.1 1.65 1.50 17.83 0.50

5.3/3.4 1.55 3.35 36.50 1.49 2.4/1.35 1.55 1.66 28.12 0.49 3.5/3.1 1.58 2.82 94.40 2.12

2.2 1.32 1.19 11.73 0.30 2.0 30.20 0.62 2.6 1.95 1.86 36.35 0.89 1.2 1.55 0.92 10.01 0.45

4.5/3.1 1.90 3.42 75.85 2.63 1.00 2.30 1.40 2.30 1.95 1.90 1.42 1.30 1.90 1.00

7.7/5.2 1.70 5.21 161.32 6.69 1.70 1.85 1.29 2.50 1.74 1.72 1.30 1.70 0.90 1.90 2.03 1.72 71.55 0.76 0.80 1.80 0.66 1.00 1.68 0.78 1.40 1.85 1.14 1.20 1.76 0.88 1.40 1.92 1.24 1.80 1.76 1.50 43.22 0.93 1.10 82.58 2.56 4.10 1.67 3.29 84.70 3.82 1.90 1.78 1.38 1.80 1.70 1.35 6.70 1.45 4.21 103.17 6.51

12.3/8.2 1.62 7.99 160.80 9.56 9.1/5.1 1.49 5.17

324 G. FriShlich et al.

Table 1. (Continued)

CuFue Melt Injection Trigger Force Base Impulse Fragments Interactive

Exp. Temp. t Velocity Instant Maxima Width f Fdt < 1.4 mm Mass No. (°C) (m / s) (ms) (kN) (ms) (N. s) (g) (g)

SBTR1.5 1350 1.75 450 SBTR1.6 1350 1.75 450 SBTR1.7 1350 1.75 450 SB TR1.8 1350 1.75 450 SB TR1.9 1350 1.75 450 SBTR2.0 1350 1.75 450 SBTR2.1 1350 1.75 450 SB TR2.2 1350 1.75 450 SBTR2.3 1350 2.50 450 SBTR2.4 1350 2.50 450 SB TR2.5 1350 2.50 450 SB TR2.6 1350 2.50 450 SB TR2.7 1350 2.50 450 SB TR2.8 1350 2.10 450 SB TR2.9 1350 1.75 450 SBTR3.0 1350 1.75 450 SBTR3.1 1350 1.75 450 SB TR3.2 1350 3.50 450 SB TR3.3 1350 3.50 450 SB TR3.4 1350 3.50 450 SB TR3.5 1350 3.50 450 SB TR3.6 1350 3.50 450 SB TR3.7 1350 3.50 450 SB TR3.8 1350 3.50 450 SB TR3.9 1350 3.50 450 SB TR4.0 1350 3.50 450 SB TR4.1 1350 3.50 450 SB TR4.2 1350 3.50 650 SB TR4.4 1350 3.50 650 SB TR4.5 1350 3.50 650 SB TR4.6 1350 6.30 450 SB TR4.8 1350 4.80 450 SB TR4.9 1350 4.80 450 SB TR5.0 1350 4.80 450 SB TR5.1 1350 4.80 450 SB TR5.2 1350 4.80 450 SB TR5.3 1350 4.80 450 SB TR5.4 1350 4.80 450 SB TR5.5 1350 4.80 450 SB TR5.7 1350 4.80 450 SBTR5.8 1350 4.80 450 SB TR5.9 1350 4.80 450 SB TR6.0 1350 4.80 450 SBTR6.1 1350 4.80 450 SB TR6.3 1350 4.80 450 SB TR6.4 1350 4.80 450 SB TR7.0 1350 4.8 450 SB TR7.1 1350 4.8 450 SB TR7.2 1350 4.8 450 SB TR7.3 1350 4.8 450 SB TR7.4 1350 4.8 450 SB STI.0 1350 4.8 450 SB STI. 1 1350 4.8 45{) SB STI.2 1350 4.8 450 SB ST1.3 1350 4.8 450 SB ST1.4 1350 4.8 450

1.2 1.52 1.2 1.42 2.0 1.77 1.63 1.3 1.44

0.95 1.45 1.2 1.40 1.1 1.37 1.1 1.38

5.5/4.5 1.73 4.79 1.5 1.38 2.4 1.33 1.53 0.8 1.40 1.35 1.77 1.1 1.38

1.25 1.32 1.65 1.40 1.21

2.6/1.6 1.34 1.89 2.8/3.2 1.80 2.94 9.7/9.2 1.58 7.67 1.9/1.5 1.82 1.80 1.4/1.45 2.29

1.50 1.51 3.4/5.1 2.15 4.62 3.7/3.9 1.43 3.43 5.5/7.7 1.69 5.83 2.0/2.5 2.11 2.95

13.3/11.2/12.6 1.53 10.37 2.9/4.2 1.87 3.98 2.3/1.0 1.26 1.3 3.8/3.2 1.43 2.57 1.0/2.8 3.65 4.87

9.6/8.7/10.5 1.60 8.79 5.2/5.9 1.58 4.67

10.4/9.4/11.4 1.73 9.58 13.2/10.5/11.8 1.51 9.51

3.4/5.2 1.82 4.76 3.5/4.3 1.68 3.5 4.0/5.0 2.03 4.63

4.25/5.5 1.91 4.92 2.3/2.6 1.78 2.41

1.6 1.77 1.54 2.5/3.3 1.54 2.85

2.05/2.1 1.69 1.74 1.2 2.60 1.5 1.58 1.3 1.42

6.7/6.9/9.1 1.57 7.39 5.0/6.5 1.65 5.46

5.55/6.5 1.65 5.25 3.7/4.0 1.66 3.12 3.0/1.0 3.85 4.82

1.3 1.36 0.6 1.70 1.5 1.43 0.8 1.40 0.8 1.40

165.59 157.00 143.15 129.15 110.14

8.82 5.82 3.68 2.75 1.48

Table 1. (Continued)


CuFue Melt Injection Trigger Force Base Impulse Fragments Interactive

Exp. Temp. t V e l o c i t y Instant Maxima Width f Fdt < 1.4 mm Mass No. (°C) (m / s) (ms) (kN) (ms) (N. s) (g) (g)

SB ST1.6 1350 4.8 450 1.7/2.0/1.0 2.10 2.32 85.09 1.73 SB ST1.7 1350 4.8 450 1.25 1.61 SB ST1.8 1350 4.8 450 3.1/3.35 1.80 3.71 SB ST1.9 1380 4.8 450 3.8 3.10 5.25 SB ST2.0 1360 9.0 250 11.25 1.93 10.13 SB ST2.1 1360 9.0 250 0.9 1.80 SB ST2.2 1360 9.0 250 11.8 1.92 11.06 243.63 14.80 SB ST2.3 1360 9.0 250 8.0/14.0 1.83 11.58 173.92 15.37 SB ST2.4 1360 9.0 250 2.9/3.15 1.72 3.01 SB ST2.5 1360 9.0 250 2.7/4.1 1.90 3.85 SB ST2.6 1360 9.0 250 1.2/0.7/0.6 2.30 SB ST2.7 1360 9.0 250 1.1 1.65 SB ST3.0 1360 4.80 450 3.35/3.8 1.84 3.83 SB ST3.3 1360 4.80 450 0.75/1.7 6.60 SB ST3.4 1360 4.80 450 3.8 3.40 6.30 SB ST3.7 1360 4.80 450 3.3/3.0 3.30 6.14 SB ST3.8 1360 4.80 450 2.1/2.3 2.44 3.04 SB ST3.9 1360 4.80 270 4.4/6.0 2.00 5.99 SB ST4.0 1360 4.80 270 4.4 1.50 4.12 SB ST4.2 1360 4.80 270 8.5/10.4 1.68 9.41 SB ST4.3 1360 4.80 270 13.7/14.6 1.58 13.19 SB ST4.4 1360 4.80 270 5.7 2.81 5.91 SB ST4.5 1360 4.80 270 6.60/6.00 1.63 5.96 SB Q1.0 1360 4.80 280 8.70 1.78 8.14 174.04 10.10 SB QI.1 1360 9.0 280 1.00 1.58 0.81 17.55 0.67 SB Q1.2 1410 9.0 280 6.30 2.10 6.21 160.49 9.98 HB TR1.2 1410 9.0 280 0.70 1.53 0.52 5.45 0.15 HB TR1.3 1410 9.00 350 0.50 1.90 0.48 3.30 0.10 HB TR2.0 1410 4.80 350 0.9/0.75 1.55 0.86 HB TR2.1 1650 4.80 350 1.90 2.29 2.12 20.22 0.69 WB TRI.1 1350 4.80 350 1.10 2.90 1.44 26.15 0.44 WB TR1.2 1350 4.80 350 2.90 2.19 2.76 68.86 1.54 WB TR1.3 1350 4.80 350 2.7/2.2 1.93 2.45 38.14 1.12 JU TR1.0 1350 4.80 350 12.8/12.7 1.70 10.70 178.53 13.76 JU TRI.1 1350 4.80 350 4.6/5.1 1.87 4.58 122.77 6.59 JU TR1.2 1350 4.80 350 6.3/5.7 1.90 5.85 155.18 7.59 JU TR1.3 1350 4.80 350 1.60 1.71 1.39 64.41 1.07 GB TR1.0 1350 4.80 350 1.45 2.85 1.57 20.44 0.70 GB TRI.1 1350 4.80 350 1.40 1.68 1.11 24.70 0.56 GB TR1.2 1350 4.80 350 2.75/3.40 1.67 2.74 51.67 0.97 GB TR1.3 1350 4.80 350 2.2/1.65 1.61 1.67 30.80 0.54 GB TR1.4 1350 4.80 350 2.95/3.55 1.71 2.71 45.82 0.92 KG TR1.0 1350 4.80 350 1.00 1.30 0.78 KG TRI.1 1350 4.80 350 1.45 1.50 1.14 KG TR1.2 1350 4.80 350 1.80 1.40 1.38 22.33 0.81 BB TR1.0 1350 4.80 350 1.00 1.54 0.85 BB TRI.1 1350 4.80 350 1.10 1.58 0.99 BB TR1.2 1350 4.80 350 1.85 1.52 1.48 42.16 0.89 LO1S TRI.1 1350 4.80 350 0.60 1.62 0.49 3.62 0.08 LO1SBTR1.3.0 1350 4.80 350 1.80/1.35 4.00 3.96 104.00 2.94 LO1SBTR1.4.0 1350 4.80 350 1.65/1.20 1.41 1.29 LO T-1 1350 4.80 350 3.30/2.30 1.93 2.57 36.90 1.03

*In a number of experiments carried out with the melt types LO2, SP, DB and DF and in some with melt types SB, HB, WB, and LO1, no explosive interactions were obtained. These experiments are not included in this table.

First two letters of Exp. No. give origins of lava types (see text).


8

7 -

6 - t 5 - Z

4 -

3 - , , _ o

2 -

1 -

0 -

-1

-0 .5

I I I I I

v,

o

I I I I I 0 0 .5 1.0 1.5 2 .0

t ime / ms

m

n

2.5

Figure 7. Force-time curve of an interaction between Stern- berg melt and water.

either very low values of impulses or no thermal explosions. These are the melts with high S i O 2 c o n t e n t (50-75%) and low content of alkaline earths (0-18%). Types SB, WB, JU, GB, KG, and BB gave measurable explosive interactions. They have relatively low SiO 2 content (35-43%) and a relatively higher alkaline earth content (24-34%). In general, an increase of the S i O 2 con - t en t increases the viscosity of the melt whereas an increase of the oxides of alkaline earth content decreases it. Explosive interactions occurred only below a certain threshold value of viscosity of the melt. Unfortunately, this threshold value is unknown because measurements of viscosities for such melts with temperatures of more than 1200°C are difficult and expensive. The results of Fig. 9 were obtained using melt temperatures in the range of 1350-1410°C.

Experiments with higher magmatic melt temperatures show that the interactions were more violent (compare, in Table 1, the force maxima of HBTR2.1 with HBTR1.2 to 2.0), as the value of the threshold viscosity is temperature-dependent. The bigger circles in Fig. 10 represent the average values of the force maxima at each injection velocity. With increasing injection velocity, these average values increase also (lower curve in Fig. 10). Also, the highest values of the force maximas increase with increasing injection velocity (see upper curve in Fig. 10). The large fluctuation of the experimental values in Fig. 9 as well as in Fig. 10 can be explained as being due to the gas bubbles escaping from the magmatic melt during heating.

A large number of bubbles can diminish the force of an explosion or even completely hamper it. High values of force maxima are obtained if the melt is homogenized by constant heating for a sufficiently long time before triggering.

DISCUSSION

Besides carrying out the experiments, we have undertaken to develop a coarse model. A comparison of the results calculated from modeling with the experimental results should lead to further conclusions.

Modeling

In order to get a first approximation of the explosion process, it has been split up into two imaginary steps. In the first step, water and melt are assumed to mix under isochore conditions, from which the temperature of the mixture, TM, can be calculated:

CpsmsTs + Cp mwTw T M = ( l )

Cram , + Cpwmw

15 - . . . 14

- , 12 11

• 19

[

8 0

I I I I I I I I I I ! I I I I I I

oS 0 0 0 . ~

1 2 ~ 4

. .0" "

o o ~ - ~ , o

, , " 0 " o 0 0

: °

0 0 O. ~ . 0 " "

I I i I I I i l I I I i I I

5 5 ? 8 ~ 18 11 12 1~ 14 15 15 17 18 interactive lava aass / g

Figure 8. The impulse for all successfully ignited experiments with magmatic melts and their dependence on the analytically determined interactive masses.

1 1 - 1 0 -

I

: ~ 7 - " 6 ~ 5

4

2 i

0

i I I

I , , , 1 1 1 I

SB HB WB JU GB KG BB LO1 LO2 SP DB OF

Figure 9. Ranges of impulses determined for the different melt types.

where T~, Cps, and m s are the initial temperature, the specific heat at constant pressure, and the amount of melt involved in the reaction, and T w, Cp, and m w are the corresponding values for water.

In the second step, there is adiabatic expansion of the vaporized water. It was assumed that only a thin layer of water inside the crucible evaporates and that evaporation is spread out uniformly over the entire cross section of the crucible. Nevertheless it can be taken as a rough approximation, since the water jet is injected parallel to the floor of the crucible in a nearly even plane into the melt. The plug of melt lying above this layer of vapor is ejected out of the crucible and disintegrates (see Fig. 11). The plug of melt below the steam, on the other hand, undergoes only a compression. The assumed model is undoubtedly a very idealized picture of the ejection process.

The amount of water present in this narrow layer should evaporate adiabatically after it has been heated up to the temperature T M, that is,

dH - Vdp = mwCp~ dT + h,. d m o - Vdp = 0 (2)


where H is enthalpy, V is volume, p is pressure, Cpw is the specific heat at constant pressure, T is temperature, h~ is the heat of vaporization of the water, and m D is the amount of steam. The Clausius-Clapeyron relation

dT RT 2 (a)

dp hvp

where R is the absolute gas constant, can be applied to eliminate dp in Eq. (2) on condition that the volume of water is negligible compared to the volume of vapor. In this way Eq. (2) becomes

hL, dmD= ( -~hL , -mwCpw)dT (4)

An integration of Eq. (4) from T M to T leads to

hL.m o = mwCp T ln(TM/T) (5)

where T M is the temperature of the superheated water after its mixture with the melt.

Assuming that the ideal gas law is applicable,

V = A T X = m D R T / p (6)

where A r is the cross-sectional area of the crucible and x is the vertical coordinate of the expansion of the steam (see Fig. 12), elimination of m D in Eq. (5) by using Eq. (6) leads to the relationship

T 2 T M ATh,,x = mwC p R - - In - - (7) w p T

Differentiation of Eq. (7) with respect to time t leads to

dx ( T(dT/dP) [21n( T M - l ] A Th,, - ~ = p --T )

T) 2 TM ~ dp - ( p ln---T-ImwCpR-d-; (8)

I

"7, E QJ i . J t _ O

14 . . . . . . . . . . i . . . . . . . . . . i . . . . . . . . . . . i . . . . . . . . . . . ~ i . . . . . . . . . . . i . . . . . . . ! . . . . . . . . . . 2 . . . . . . . . . . . . . . ii . . . . . . . . . . . . . . . . . . , . . .

- ,4 , r

le . . . . . . . . . . :- . . . . . . . . . . i . . . . . . . . . . . ] . . . . . , : . , ~ . . . ] . . . . . . . . .o.. ] . . . . . . . . . . i . . . . . . . . . . i . . . . . . . . . . :: . . . . . . . . . . 8 . . . • o] . o i i !

8 . . . . . . . . . . ! . . . . . . . . . . ! . . . . . . . . . ~ ! . . . . . ~ . . . . . ! . . . . . . . . . . . ! . . . . 8 . . . . . : . . . . . . . . . . : . . . . . . . . . . : . . . . . . . . . . : . . . o i o i i o i o i i i i

' ......... :: ....... i..:: .... .o...:: ........ ! .... .I ..... i .......... i .................... I .... I i I I I I I I I

90 1 2 : ; 4 5 5 7 8 9

i n j ec t ion ve loc i tU / n /s

Figure 10. Dependence of the force maxima on the injection velocity.


~e jet disintegration d fragmentation due Helmholtz Instability

E E 8

Fragmentation front of the Taylor Instability

Expanding steam + melt fragments

Crucible 80 mm m Melt

Figure 11. Illustration of the condition inside the crucible.

A further differential equation is obtained for the movement of the melt plug, of weight mp (see Fig. 12):

d2x p A T = m p - ~ + m p g (9)

where g is the acceleration due to gravity. The process of change of pressure p as a function of

time can be calculated numerically using both of the coupled equations (8) and (9). Although the amount of melt being heated in the crucible, ms0, and the amount of water injected into the crucible, m w , are known, only a

0 .

small fraction of these masses take part in the reaction, and not the whole amount of melt is catapulted out of the

crucible as a plug mass. A coefficient f was therefore introduced so that each unknown mass could be coupled with the known mass as follows:

mp =fpmso (10)

m r = L m s o ( l l )

m w = f w m w o (12)

Although the coefficients fp, fs, and fw are unknown, their values can be varied within the range 0-1 such that the calculated curves can be fitted to the experimentally obtained force curves. For that purpose, it was assumed that corresponding to the model (see Fig. 12), the experimentally obtained values of force F can be transformed to values of pressure p, using the known crucible cross section Av, according to the equation

p = F / A T (13)

It was observed in the curve-fitting calculations that ideal heat transfer does not take place between the reacting melt and the reacting water as assumed in relation (1). This leads to a lowering of the mixing temperature T g . The reduced mixing temperature T M is coupled to th~ mixing temperature T g through the r~lation

TM, =fTTM (14)

in which the correction factor f T can assume values between 0 and 1.

Fitting the Individual Measured Force Curves

The procedure followed in curve fitting is demonstrated on the basis of the curve obtained in experiment SB T4.4 using Sternberg lava (see Fig. 13). This force curve shows three maxima. This means that three successive explosions

[" 80 mm "I

B B Crucible

Melt

Steam

Figure 12. Model of melt-water interaction inside the crucible.

20 18 16 14 12 10 8 6 4 2 0 -2

-0.5

• i ! a

t z

o o

I I I I

0 0.5 1.0 1.5 2.0 time / ms

Figure 13. Qualitative illustration of the splitting of the force-time curve of a melt-water interaction with a number of maxima into the individual force-time curves corresponding to the successive explosions (Expt. SB T4.4).


took place. Such a curve can be resolved into partial curves according to the principle developed by Vaidya and Hester [10]. The force-t ime curve belonging to each of the individual explosive interactions in this experiment were thus obtained using this method, as shown in Fig. 13.

Only the descending arms of the curves were considered for the curve-fitting calculations, since the model cannot calculate the rise in pressure or force as it is based on the assumption of a mixing of the water and melt under isochore conditions. Thus only the force maxima and the adiabatic pressure drop have been considered. A good fitting of these curves (the partial curves of Fig. 13) has been achieved, as shown in Fig. 14a-c.

In principle all three coefficients f and the correlation factor fr can vary from 0 to 1, but such variations seldom lead to a good fitting of the curves. In practice, good fittings were achieved only by adjusting fw and fr and using the experimentally obtained fragments (< 1.4 mm) corresponding to m e and the determined interactive fragments corresponding to m r Thus, for instance, in Experi- ment SB T4.4, the mass of 146.7 g of fragments smaller than 1.4 mm (see Table 1) was split in proportion to the values of maxima obtained in Fig. 13. The so obtained fragment mass of each of the three individual explosive interactions was divided by ms0 to get the individual coefficient fp. In a similar manner, the individual coefficients fs are obtained from the value 13.56 g of the interactive mass (see the last column for SB T4.4 in Table 1). The coefficients fT and after that fw were varied, and, if still necessary, fine adjustments o n fp and fs were carried out. The calculations were performed with the values C, = 1000 J / ( k g . K) and Cp = 4200 J / ( k g . K) for the s~cific heat capacity of lava [11] and water [12], respectively.

R e s u l t s o f the F i t t ing M o d e l

In Table 2 the results of curve fitting for four experiments are listed, among them the results for the experiment discussed above (SB T4.4). The most interesting values are the estimated water masses that were thermally reacting with molten lava during interactions and the estimated temperature of the superheated water, because these values are difficult to obtain by measurements. Also, in the TEE-Haus the interacting water mass and the temperature of the superheated water cannot be measured. In the model an isochore heating of the melt-water mixture is assumed that leads to superheated water. This assumption is made because of the rapid heat transfer from melt to water during the fragmentation process.

The number in parentheses appended to the experiment number in the first column of Table 2 denotes an individual explosive interaction in this experiment--(1) first, (2) second, (3) third. In most entrapment experiments performed here, the first explosive interaction of an experiment was the most violent one (see the fifth column in Table 1). Therefore in each of the four experiments selected for curve fitting (see Table 2), the first individual explosive interaction was the most violent. Its violence can be characterized by the maximum force K(0) of each individual explosive interaction. If these most violent explosive interactions of the four experiments are compared with the corresponding values of the temperature of the superheated water [compare column TM. with K(0) in

20.0 ' I ' I ' I ' I '

Z °

~ 16.0

0 12.0

8.0

4.0

0.0 "1 ' I ' I ' I ' I '

0.0 0.2 0.4 0.6 0.8 1.0 t i m e / m s

a

8.0 Z

¢ 6.0 P 0 LL

4.0

2.0

0.0

b

4.0

Z " 3.0

~_ 2.0

1.0

' I ' I ' I ' I '

' I ' I ' I ' I '

0.0 0.2 0.4 0.6 0.8 1.0

t i m e / m s

t ' I ' I ' I ' I '

0.0 ' I ' I ' I ' I '

0.0 0.2 0.4 0.6 0.8 1.0

c t i m e / m s

Figure 14. Fitted curves (solid lines) and the partial curves resolved from the experimental force-time curve (dashed lines).

Table 2], it is found that the superheating temperatures of the interacting water are proportional to the force maxima.

Also the ratio of the interacting fragment mass [obtained from Eq. (11) and column fs in Table 2] to the interacting water mass [obtained from Eq. (12) and column fw in Table 2] correlates with the violence of the explosive interactions. This ratio, ms/m w, is bigger in the

330 G. FrBhlich et al.

Table 2. Results of Calculations with the Fitting Model for Four Experiments with mso = 333 g and mwo = 10.9 g

K(O) TM Expt. No. (kN) fs " E - 3 fp f r f~ (o~)

SB T4-4(1) 18.4 26.50 0.28 0.49 0.10 579.4 SB T4-4(2) 7.2 10.20 0.11 0.56 0.09 518.4 SB T4-4(3) 3.0 4.17 0.05 0.42 0.02 472.4 SB T4-5(1) 12.49 19.60 0.24 0.50 0.10 552.6 SB T4-5(2) 4.52 7.18 0.09 0.39 0.02 492.6 SB T6_5( 1 ) 2.06 1.21 0.03 1.00 0.07 455.0 SB T6_5(2) 0.45 0.11 0.01 1.00 0.01 397.8 GB TRI_I(1) 1.38 1.48 0.06 0.80 0.05 438.3 GB TRI_I(2) 0.26 0.13 0.29 0.01 0.53 397.7

case of violent interactions (> 4) and smaller in the case of weak explosions (< 1).

PRACTICAL SIGNIFICANCE

Laboratory experiments with molten lava and water gen- erally allow the investigation of phreatomagmatic processes that cannot be directly observed in nature because the sites of explosions in nature are below the surface of the earth. Only the aftermath of the explosions--the eruption of lava at the surface of the earth--can be studied in nature. The laboratory experiments reported here allow the investigation of the force transients and various aspects of the physical processes (fragmentation and expansion) that take place during the explosion. If the physical processes in a small volume can be adequately apprehended, they can then be scaled to larger volumes (deduced from Fig. 8) with the help of models. This statement holds if thermal detonation does not occur. Several thermal detonation models are already developed, but no real proof of a thermal detonation has been obtained from experiments. In our opinion, all experimental results can be explained without a detonation model.

The spectrum of phreatomagmatic volcanism observed in nature shows that the mechanism of the explosion is largely independent of the chemical composition of the magma, thus making it possible for physical investigations to yield an understanding of these mechanisms. In this respect the experiments reported here can be considered to be of fundamental importance. See, for instance, the HB TR experiments of Table 1. In all four experiments the chemical composition of lava was the same. In Experi- ment HB TR 2.1 the temperature was enhanced to 1650°C, and this physical variation led to a more violent explosion than in the other three experiments. In this case the value 1.90 kN for the force maximum cannot be put down to the fact of immanent fluctuations although for some lava types the values of the fluctuations were much larger as can be seen in Fig. 9. The viscosity in the HB TR experiment with melt temperature of 1650°C was much smaller than with a melt of 1410°C, which was noticeable by stirring of the melt. The mechanism of the explosion depends sensitively on viscosity in the range of the threshold viscosity. Therefore the value of viscosity is important. Chemical composition is less important because several chemical compositions can have the same viscosity. Chem- ical composition plays only an indirect role in the mechanism of thermal explosions, as in its influence on the

melting point and the decomposition of the melt at the conditions of state employed.

Remelted lava from a particular site as used in the experiments is not identical with magma from the same site. This is because from magma to solidified lava it has undergone changes in chemical composition due to aging processes and the remelted lava has undergone dehydra- tion, oxidation, and degassing during remelting. The re- sulting effects on the physical properties are of a complex nature, but aside from viscosity, physical properties do not have a significant influence on the violence of the explosions. Comparisons show that the viscosity of remelted lava is higher than that of magma, because magma is under higher system pressure (0.3-3 MPa) and a higher water partial pressure, which results in a considerable decrease in viscosity. A corresponding decrease in viscosity in laboratory experiments can be achieved by increasing the melt temperature to approximately 200 K above the temperature measured in the natural lava streams. Contemplating the results from this point of view, the values obtained experimentally can be transferred to volcanic scenarios.

The force transients measured during explosions in laboratory experiments can be used to derive the transient initial pressures, which is necessary for the calculation of the rise of magma in volcanic columns (ie, volcanic eruptions). A paper that describes a volcanic eruption caused by a thermal explosion is in preparation.

The fragments of lava produced in the experiments can be compared with the fragments produced in volcanic eruptions. The shapes and sizes of thermally produced fragments in both cases are identical because these thcr- real fragments originate in the same manner after direct contact between melt and water. During direct contact of molten lava and water, a fragmentation process takes place that is governed by local parameters and not by global conditions (assuming that thermal detonation does not occur). In addition to thermally produced fragments there are also hydrodynamically produced ones. Similar to the experiments in which thermally produced fragments can be separated from other fragments by their characteristic features, in the ashes of volcanic eruptions, thermally produced fragments can be separated from other fragments.

The hydrodynamically produced fragments are influ- enced by the acceleration and velocity of the erupted or expelled melt. As the acceleration and velocity of the melt in the case of experimental crucibles are much lower than


those within volcanic columns, the fragments obtained in the laboratory are larger than those in volcanic eruptions.

If thermally produced fragments are observed after volcanic eruptions, they are definite evidence that such eruptions originate from phreatomagmatic explosions. It is therefore essential that the characteristics of thermally produced fragments be determined by experiments.

Values of the released energy can be calculated from the measured impulse and erupted fragment masses. The ratio of the released energy to the mass of erupted fragments for the case of Krakatoa volcanic explosions (taken from Ref. 13) compared to the experimentally obtained ratio of the released energy and expelled fragments are found to be of the same order. In experiment SB T4-4 (see Table 1), the released energy was 486 J and the fragment mass was 146.74 g. According to Williams and McBirney [14], the released energy in the Krakatoa eruption was 1018 J. Corresponding to the data of experiment SB T4-4, an energy release of 10 TM J leads to 3 x 1011 metric tons of fragment masses, which corresponds to a volume of 111 km 3. In Ref. 15 a value of 20 km 3 of pumice and ashes has been given for Krakatoa eruptions; that is, the ratio of the released energy to the erupted fragment mass is of the same magnitude in experiments as in volcanic eruptions. This indicates that the thermal detonation is not relevant in volcanoes.

The experiments with hot melts and water also yield new information with regard to accidents involving steam explosions, especially for the expected pressure and energy release. Furthermore, investigations of the physical mechanism of steam explosions have additional aspects, for instance, that there is an increase of force maxima with an increase of injection velocity of water or that the ratio of interactive fragment mass and the calculated interacting water mass is bigger in the case of violent interactions than in the case of weak explosions.

RECOMMENDATIONS FOR FUTURE RESEARCH

The viscosity of the melt is important for the explositivity of a melt-water combination. Therefore measurements of viscosity of various types of molten lava at several states are recommended to determine the value for the threshold above which thermal explosions cannot be triggered. For these experiments a rotation viscometer can be used. The rotation cylinder should be constructed of a plat- inum-rhodium alloy because molten lava is chemically aggressive.

In nature, molten lava or magma often come into contact with salt water. Laboratory experiments with molten lava and salt water have not yet been performed. Such experiments could investigate the influence of salt content on the explosion violence.

For studying the scaling effect, experiments in the TEE-Haus should be performed with crucibles of various dimensions, increasing the diameter at constant crucible height and increasing the height at constant diameter. Also, for constant crucible dimensions, the diameter of the pipe for the water injection should be varied.

Obviously, high system pressures suppress phreatomagmatic explosions because eruptions of magma on the bottom of a deep sea lead to pillow lava (lava that is solidified in the shape of pillows). Fine fragments of lava,

which should be found if phreatomagmatic explosions have occurred, have not been observed. That means that phreatomagmatic explosions do not occur above a threshold of the ambient pressure. Therefore, experiments are recommended in which the system pressure is increased to the threshold value. The TEE-Haus is not suitable for such experiments, but experiments in tank geometry as performed in Ispra (Italy) at Euroatom in the frame of nuclear safety research.

SUMMARY AND CONCLUSIONS

Fr6hlich and coworkers were the first who were successful in igniting thermal interactions between remelted lava and water in laboratory experiments. In order to carry out a series of experiments, a largely automated experimental arrangement called the TEE-Haus (Thermal Explosion Experiment) was constructed in which the mechanism involved in the time-dependent explosion process could be exactly recorded.

The time-dependent force generated during the explosive interactions was recorded, and the mass of interactive fragments produced during the explosions was determined by an analysis of the total mass of fragments collected from the TEE-Haus after an explosion. These interactive fragments are the fragments that came into direct contact with the water and supplied the heat necessary for the explosive vaporization. A linear increase of the impulse with increasing interactive mass was found.

The lava melts used could be divided into explosive and nonexplosive types on the basis of experimental results. Explosive magmatic types had relatively low SiO 2 contents ( < 43%) and relatively high alkaline earth contents (> 24%). The violence of the interactions depends on the magmatic types as well as on the temperature and the gas content of the melt. An increase in temperature leads to an increase in explosive violence, and higher gas content leads to a reduction or even hindrance of the explosion.

The amount of water participating in the thermal interaction and the superheat temperature were approximated by comparing the experimentally obtained force-time curves with the curves obtained through calculations based on a coarse model. In violent thermal interactions the superheating temperature of the water and the ratio of the interacting melt mass to the mass of interacting water must be high.

The resulted force maxima of triggered thermal interactions tend to increase with an increase in injection velocity. But even the maximum injection velocities (9 m / s ) did not trigger an interaction between water and lava. For triggering, a shock wave was necessary, but even a shock wave produced by an air gun projectile of a kinetic energy of 8 J was sufficient. Therefore it can be concluded that the distortion of the steam film is due to condensation of steam at the steam-water interface.

The nature of the fragmentation process is to a large extent still unknown. It may be that the Marangoni effect (convective flows or vortices at the interface caused by the surface tension gradients) is involved in the process of micromixing. Further experimental and theoretical investigations are necessary in this field. Therefore, proper con- stitutive equations describing melt-water interactions cannot be presented yet.

The experiments reported here allow some conclusions with respect to real-scale explosions and thus also to


phreatomagmatic explosions: The energy required for ig- nition of a steam explosion (trigger energy) is small ( < 10 J). Bubbles of a noncondensible gas hinder or prevent a steam explosion. The impulse of a steam explosion tends to correlate with the amount of fragmented mass. Interac- tive fragments that are formed by thermal fragmentation should have the same characteristic shapes and sizes in laboratory steam explosions as in phreatomagmatic explosions. Therefore fragments with such shapes should be found in volcanic areas.

For future research in phreatomagmatic explosions, viscosity measurements are recommended to determine the threshold value above which explosions between molten lava and water cannot be triggered. Furthermore, laboratory experiments with molten lava and salt water are of interest. Also the scaling effect should be studied by changing the dimensions of the crucible and the water pipe. Obviously, a threshold also exists for ambient pressure above which phreatomagmatic explosions do not occur. Therefore the performance of experiments with molten lava and water in which the system pressure is increased is recommended.

NOMENCLATURE

A r cross section of crucible, m 2 Cp specific heat at constant pressure, J / ( k g . K) F force, N f coefficient, dimensionless

fT correction factor for temperature, dimensionless g acceleration due to gravity, m / s 2

H enthalpy, J h , heat of vaporization of water, J / k g

m mass, g p pressure, Pa R absolute gas constant, J / ( K . mol) t time, s

T temperature, °C TMr reduced mixing temperature, °C

V volume, m 3

x vertical coordinate, m

D steam M mixture p plug s melt w water

Subscripts

REFERENCES

I. Cho, D. H., and Gunther, W. H., Fragmentation of Molten Materials Dropped into Water, Trans. Am. Nucl. Soc., 16, 185 186, 1973.

2. Frost, D. L., and Ciccarelli, G., Dynamics of Explosive Interac- tions Between Multiple Drops of Tin and Water, presented at the llth Int. Colloquium on Dynamics of Explosions and Reac- tive Systems, Warsaw, Poland, Aug. 2-7, 1987.

3. Frost, D. L., and Ciccarelli, G., Propagation of Explosive Boiling in Molten Tin Water Mixtures, ASME Proc. 1988 Natl. Heat Transfer Conf, HTD-96, 2, 539-547, 1973.

4. Fr6hlich, G., Propagation of Fuel-Coolant Interactions in Multi- Jet Experiments with Molten Tin, Nucl. Eng. Design, 131, 209 221, 1991.

5. Zyskowski, M., Experimental Investigation of Fuel Coolant Inter- action, Nucl. Technol., 33, 40-59, April 1977.

6. Ando, M., Experimente zur getriggerten Fragmentation an einem schmelzfliissigen Kupfertropfen in Wasser, Karlsruhe, Universitfit Karlsruhe, Dissertation KIK 3667, 1983.

7. Peppier, W., and Till, W., Experimentelle Arbeiten zur BNR, Versuche mit A120 3 und Wasser, KFK Prim~irbericht 01.02.12p08A, December 1986.

8. Nelson, L. S., Duda, P. M., Fr/Shlich, G., and Anderle, A., Photographic Evidence for the Mechanism of Fragmentation of a Single Drop of Melt in Triggered Steam Explosion Experiments, J. Non-Equilibr. Thermodyn., 13, 27-55, 1988.

9. Fr6hlich, G., Zimanowski, B., Lorenz, V., Bayer, V., v. Berg, E., Khan, M., and Schindler, M., Experimente zur Simulation phreatomagmatischer Explosionen und vergleichende Unter- suchungen, Institut fiJr Kernenergetik und Energiesysteme, Uni- versit/it Stuttgart, IKE 2-97, May 1992.

10. Vaidya, R. A., and Hester, R. D., Deconvolution of Overlapping Chromatographic Peaks Using Constrained Nonlinear Optimiza- tion, J. Chromatogr., 287, 231-244, 1984.

11. Swanson, D. G., Castle, J. N., Anderson, P. D., and Catton, I., Core-Melt Materials Interaction Evaluations, NUREGCR-3299, Final Rep., p. 262, September 1983.

12. Kohlrausch, F., Praktische Physik, Band 3, p. 45, B. G. Teubner, Stuttgart, 1968.

13. Rast, H., Volcanoes and Volcanism, p. 179, F. Enke Verlag, Stuttgart, 1980.

14. Williams, H., and McBirney, A. K., Volcanology, p. 93, Freeman, Cooper, San Francisco, 1979.

15. Francis, P., and Self, S., The Eruption of Krakatau, Sci. Am., 249(5), 146-170, (1983).

Received April 27, 1993; revised August 2, 1993

explosive thermal interactions between molten lava and water

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