Combustion, Explosion, and Shock Waves, Vol. 37, No. 4, pp. 451 454, 2001
Passage of a Bubble-Detonation Wave
into a Chemically Inactive Bubble Medium
A. I. Sychev1 UDC 534.222.2:532.529
Translated from Fizika Goreniya i Vzryva, Vol. 37, No. 4, pp. 96 99, July August, 2001.
Original article submitted June 6, 2000.
Passage of detonation waves from a chemically active bubble medium into a chemically
inactive bubble medium is studied experimentally. The structure of incident (deto-
nation) and transmitted (post-detonation) waves is investigated, and the pressures of
these waves for different parameters of bubble media are measured. The evolution
of post-detonation waves is traced. Decay constants of post-detonation waves are
determined. The speeds of propagation of detonation and post-detonation waves are
measured. The energy-dissipation mechanisms for detonation and post-detonation
waves in bubble media are analyzed qualitatively.
Detonation is a dissipative process. The energy We studied the passage of detonation waves from
losses of a detonation wave are compensated for by the a chemically active bubble medium (VM-3 mineral vac-
chemical energy contained in the medium. When a det- uum oil with oxygen bubbles) into a chemically inac-
onation wave passes from a chemically active medium tive bubble medium [70% (by volume) glycerin solu-
into an inactive medium, the energy losses of the wave tion in water with oxygen bubbles]. A solution of this
remain uncompensated, and the wave decays due to dis- composition was chosen to provide for approximately
sipative processes. equal gas bubble rise velocities in both liquids, which is
The goal of the present work was to study the pas- achieved for close viscosities of the liquids (28.2 · 10-3
sage of a detonation wave from a chemically active bub- and 27.1 · 10-3 Pa · sec are viscosities of VM-3 oil and a
ble medium into a chemically inactive bubble medium. 70% glycerin solution in water, respectively).
Experiments were conducted in a vertical hydrody- The parameters of incident (detonation) and trans-
namic shock tunnel 4.3 m high with an inner diameter mitted (post-detonation) waves at various distances x
40 mm [1]. The column of the bubble medium was from the interface were measured by four piezoelec-
3.6 m high. The gas-phase concentration was varied in tric pressure transducers, whose signals were recorded
the range of 1/8 ²0 4%. The diameter of gas bub- by two S9-16 oscillographs. A post-detonation wave
bles was (2.5 Ä… 0.1) mm. The pressure on the surface of (like a detonation wave) has a pulsating pressure pro-
the bubble medium was equal to atmospheric pressure. file (Fig. 1). The duration of pressure pulsations is
Detonation waves were initiated by shock waves 4 6 µsec. The stochastic nature of pressure pulsations
generated in the bubble medium by combustion of a sto- is due to the chaotic distribution of bubbles in the liq-
ichiometric acetylene oxygen mixture. The amplitude uid. Thus, the propagation of detonation and post-
of the initiating shock waves was varied by changing detonation waves is accompanied by high-frequency
the initial pressure of the explosive gas mixture. Bub- wave perturbations.
ble detonation can be initiated by shock waves with Averaging of the pressure pulsations gives an effec-
an amplitude higher than the critical value p", which tive pressure profile of detonation and post-detonation
1
depends on the parameters of the bubble medium and waves. Bubble-detonation waves and transmitted waves
increases with rise in ²0. In the bubble media studied, with averaged pressure pulsations are solitary waves,
p" = 17 34 atm. and the pressure behind them is close to the pressure
1
1
Lavrent ev Institute of Hydrodynamics, Siberian Division,
Russian Academy of Sciences, Novosibirsk 630090.
0010-5082/01/3704-0451 $25.00 © 2001 Plenum Publishing Corporation 451
452 Sychev
Fig. 1. Oscillograms of pressures of detonation (I) and transmitted (II IV) waves before averaging (a) and
after averaging (b) over pressure pulsation; ²0 = 1/2% and x = 0.055 (II), 0.115 (III), and 0.185 m (IV).
before them [see Fig. 1]. Signals from the pressure trans- Figure 2 shows measured detonation-wave pres-
ducers were averaged over 10 points by the normal pro- sures p1 averaged over pulsations (each point is an av-
cedure of an S9-16 oscillograph with a time interval be- erage of 10 20 measurements). The value of p1 depends
tween points of 1 µsec (discretization time). on the parameters of the bubble medium: although
To describe the detonation and transmitted waves, at ²0 > 2%, the pressure can be considered approxi-
we introduce the following characteristics: p is the mately constant, at smaller gas-phase concentrations,
wave amplitude (pressure) at the maximum averaged the wave pressure decreases. The considerable spread
over pulsations (p1 and p2 refer to the detonation and of detonation-wave amplitudes results from the chaotic
transmitted waves, respectively); the wave duration Ä distribution of gas bubbles in the liquid [2].
is a time characteristic determined at the zero level of
the pulsation-averaged signal from the pressure trans-
ducer (Ä1 and Ä2 refer to the detonation and transmitted
waves, respectively); the linear extent (wavelength) ,
which is determined by the wave duration Ä and the
wave velocity D (1 = D1Ä1 for the detonation wave
and 2 = D2Ä2 for the transmitted wave, where D1
and D2 are the wave velocities).
Figure 1 shows the evolution of the transmitted
wave into which the detonation wave transforms after
passing through the boundary between the active and
inactive bubble media. It can be seen that as the trans-
mitted wave propagates, its pressure decreases.
Fig. 2. Curve p1(²0).
Passage of a Bubble-Detonation Wave into a Chemically Inactive Bubble Medium 453
Fig. 5. Curves of D(²0).
Fig. 3. Curve of ln(p2/p1)(x).
on detonation-wave velocity in the VM-3 oil O2 system
at larger gas-phase concentrations are given in [3].)
The lengths of detonation and transmitted waves
depend on the parameters of the system because
they are determined by the wave velocity and dura-
tion. According to the data shown in Fig 5, the
detonation-wave velocity changes over a wide range
(D1 = 650 1150 m/sec at 1/8 ²0 4%), and the
duration of detonation waves does not depend on the
gas-phase concentration and is equal to (80 Ä… 20) µsec.
Thus, the detonation wavelength is 1 = 0.05 0.09m at
1/8 ²0 4%.
Fig. 4. Curve of k(²0).
The duration of a transmitted wave is equal to
the duration of a detonation wave near the boundary
Measured transmitted-wave pressures p2 averaged between the media and increases slightly as the wave
over pulsations are shown in Fig. 3 in the form of a log- propagates: Ä2 = (70 Ä… 20) µsec at x = 0.20 m. Thus,
arithmic dependence of p2/p1 on the distance x (each the length of transmitted waves propagating at constant
point is an average of 10 15 measurements). The depen- speed is equal to the detonation wavelength near the
dence of the relative pressure of the transmitted wave boundary between the media, and at wave paths of up
on distance is expressed by p2/p1 = exp(-kx), where to x = 0.20 m, it decreases up to 2 0.91.
k is the attenuation constant (decay coefficient) of the Decay of transmitted waves is caused by dissipative
transmitted wave. processes. In bubble media, energy dissipation occurs
Figure 4 shows values of k. The attenuation con- by various mechanisms [4]. Thus, there are heat losses
stant increases with increase in gas-phase concentration of gas bubbles through the gas liquid interface, which
(each point is an average of 10 15 measurements). increase when the gas bubble surface is distorted during
Figure 5 shows measured transmitted-wave veloc- compression and when the cumulative liquid jet formed
ities (each point is an average of several experiments). during compression is dispersed in the bubble volume.
The wave velocity was measured by pressure transduc- In addition, the detonation-wave energy is expended in
ers placed in two sections of the shock tunnel with radiation of short-duration shock waves (see Fig. 1).
bases "x = 0.13 m. In the examined range of distances The chemical energy released during ignition of gas
from the interface, the transmitted-wave velocity was bubbles compensates for the energy losses of detona-
constant. For comparison, Fig. 5 gives detonation-wave tion waves. In the case of post-detonation waves, the
velocities. We note that detonation waves exist at an ex- energy losses are not compensated for, and, hence, post-
tremely low gas-phase concentration ²0 = 1/8%. (Data detonation waves decay.
454 Sychev
Thus, the present experiments on passage of deto- Bubble media are widely used in various indus-
nation waves from a chemically active bubble medium tries: they are necessary for some technological pro-
into a chemically inactive bubble medium showed that cesses (for example, liquid-phase hydrocarbon oxida-
both detonation and post-detonation waves have pul- tion), are formed during certain processes (e.g., trans-
sating pressure profiles. Bubble detonation waves and portation of oil products), and are employed as protec-
post-detonation waves with averaged pressure pulsa- tive elements in explosion-proof systems (liquid back-
tions are solitary waves. The detonation-wave pres- pressure valves). Therefore, results of studying bubble
sure increases with increase in gas-phase concentration. detonation can be used to develop scientific basis for
The transmitted-wave pressure decreases with increase explosion prevention during operation of liquid back-
in wave path and is described by an exponential de- pressure valves and to choose explosion-proof regimes
pendence. The pressure behind a detonation wave, as for technological processes that occur in bubble media.
well as that behind a post-detonation wave, relaxes to This work was supported by the Russian Foun-
the value of the pressure before the waves. The atten- dation for Fundamental Research (Grant No. 98-03-
uation constant (decay coefficient) of post-detonation 32325).
waves increases as the gas-phase concentration rises.
In the examined range of distances from the interface,
REFERENCES
the transmitted-wave velocity is constant and decreases
with increase in gas-phase concentration. The length of
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transmitted waves decreases slightly as the wave prop-
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agates. Attenuation of post-detonation waves is caused
117 (1993).
by dissipative processes in bubble media.
2. A. I. Sychev,  Structure of a bubble-detonation wave,
In conclusion, we note that detonation in gas me-
Fiz. Goreniya Vzryva, 30, No. 4, 119 124 (1994).
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and shock waves in bubble media have certain special characteristics, Fiz. Goreniya Vzryva, 31, No. 5, 83 91
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