Combustion, Explosion, and Shock Waves, Vol. 38, No. 2, pp. 215 218, 2002
Passage of a Bubble-Detonation Wave into a Liquid
A. I. Sychev1 UDC 534.222.2:532.529
Translated from Fizika Goreniya i Vzryva, Vol. 38, No. 2, pp. 99 103, March April, 2002.
Original article submitted April 6, 2001; revision submitted June 26, 2001.
The passage of a detonation wave from a chemically active bubble media into a chem-
ically inert medium (liquid) is studied experimentally. The structure of the transmit-
ted wave and the wave reflected from the butt-end of a shock tube (post-detonation
waves) is investigated, and the pressures of these waves for different liquids are mea-
sured. The evolution of the post-detonation waves is traced, their velocities are
measured, and the attenuation constants of these waves are determined. The energy-
dissipation mechanisms for post-detonation waves in liquids are analyzed qualitatively.
Chemically active bubble media exemplify physical
systems with potential (internal) energy. A detonation
wave accomplishes release of the chemical energy of the
medium. The released energy compensates for the en-
ergy losses of the detonation waves and thus ensures
wave propagation. If a detonation wave passes from a
chemically active medium into an inactive medium, the
energy losses of the wave remain uncompensated, and
the wave decays due to dissipative processes.
The wave disturbances into which detonation waves
transform after passing into chemically inactive (inert)
media will be referred to as post-detonation waves.
In particular, post-detonation waves are formed
when a bubble-detonation wave passes into a chem-
ically inactive bubble medium [1] or when a bubble-
detonation wave is reflected from a rigid boundary [2].
Another example of post-detonation waves is a wave
that appears when a bubble-detonation wave passes into
a liquid.
The goal of the present work was to study the pas-
sage of a detonation wave from a chemically active bub-
ble medium into a chemically inert liquid. We studied
experimentally the passage of detonation waves from a
Fig. 1. Diagram of the experimental setup: high-
chemically active bubble medium of type I [3] (chem-
and low-pressure sections (1 and 3, respectively),
ically inert liquid bubbles of an explosive gas) into a
rupture diaphragm (2), capillaries (6) and piezoelec-
tric pressure transducers (4, 5, and 7 10).
chemically inactive medium (inert liquid). The liquid
was aqueous glycerin solutions with volumetric con-
The experiments were conducted in a vertical shock
centrations of glycerin Ä… = 0, 0.25, and 0.5 (viscosi-
tube 4.3 m high with an inner diameter of 40 mm [4].
ties of the solutions µ = 1.01 · 10-3, 2.27 · 10-3, and
The tube consisted of high- and low-pressure sections
6.84 · 10-3 Pa · sec, respectively), and the gas was a sto-
separated by a rupture diaphragm (Fig. 1). The low-
ichiometric acetylene oxygen mixture C2H2 + 2.5O2.
pressure section was filled with a liquid and a bub-
1
ble medium. Bubbles 2.5 Ä… 0.1 mm in diameter were
Lavrent ev Institute of Hydrodynamics, Siberian Division,
Russian Academy of Sciences, Novosibirsk 630090. formed upon passage of the gas through a system of cap-
0010-5082/02/3802-0215 $27.00 © 2002 Plenum Publishing Corporation 215
216 Sychev
Fig. 2. Pressure oscillograms for the detonation wave (1), transmitted wave (2), and the wave reflected from the
shock-tube butt-end (3) before averaging (a) and after averaging (b) of the pressure oscillations (Ä… = 0.25 and
²0 = 1/4%): signals I and II refer to x = -0.070 and 0.060 m, respectively.
illaries placed in the liquid perpendicular to the shock- detonation waves. The bubble-detonation, transmitted,
tube wall. The gas-phase concentration of the bubble and reflected waves with averaged pressure pulsations
medium was varied within the range of 1/4 d" ²0 d" 4%. are solitary waves, and the pressure behind them is
The column of the liquid and bubble medium was 3.6 m close to the pressure in front of them (see Fig. 2). Sig-
high. The pressure on the surface of the bubble medium nals from the pressure transducers were averaged over
was equal to atmospheric pressure. 10 points by the normal procedure of an S9-16 oscil-
Detonation waves were initiated by shock waves lograph with a time interval between points of 1 µsec
generated in the bubble medium upon combustion of (discretization time).
a stoichiometric acetylene oxygen mixture in the high- To describe the detonation and post-detonation
pressure section [5]. The intensity of the initiating shock waves, we find the wave amplitude (pressure) as the
waves was varied by changing the initial pressure of the pressure at the maximum averaged over pulsations (P1,
explosive gas mixture. In the bubble media examined, P2, and P3 for the detonation wave, transmitted wave,
the critical amplitude of the initiating shock waves was and the wave reflected from the shock-tube butt-end,
"
P1 = 17 34 atm. respectively).
Passing through the interface between the chem- Figure 3 shows the evolution of the post-detonation
ically active bubble medium and the inert liquid, the wave after passage of the detonation wave through the
detonation wave transforms (Fig. 2). This gives rise to interface (the oscillograms show averaged signals from
a transmitted wave, which propagates in the liquid. No pressure transducers obtained in one experiment): as
wave reflected from the interface and propagating in the the transmitted wave propagates, its pressure decreases.
bubble medium is observed.
The parameters of the incident (detonation) and
transmitted (post-detonation) waves at various dis-
tances x from the interface between the bubble media
and the liquid were measured by piezoelectric pressure
transducers (see Fig. 1), whose signals were recorded by
two S9-16 oscillographs.
The post-detonation wave (as the detonation
waves) has a pulsating pressure profile (see Fig. 2). The
amplitude of pressure pulsations, which have a sawtooth
profile, reaches 150 300 atm. The duration of pressure
pulsations is 4 6 µsec. Figure 2 also shows the post-
detonation wave reflected from the shock-tube butt-end
(distance from the interface to the reflecting surface
xt = 0.54 m). As the post-detonation (transmitted and
reflected) waves propagate, the amplitude of pressure
Fig. 3. Averaged oscillograms of pressures P2 (1),
pulsations decreases. Thus, the post-detonation wave is
P3 (2), and P2-3 (1 2) for Ä… = 0.5 and ²0 = 1/4%:
an aggregation of sawtooth -shaped waves.
signal I refers to x = 0.270, II to 0.310, III to 0.330,
Averaging of the pressure pulsations gives an ef-
and IV to 0.336 m; xt = 0.336 m.
fective pressure profile of the detonation and post-
Passage of a Bubble-Detonation Wave into a Liquid 217
This figure also shows the process of transformation exp(-k ·x), where k is the attenuation constant (damp-
of the transmitted wave to the reflected wave: when ing factor) of the post-detonation waves (P1 = 150 atm
the transmitted wave interacts with the reflecting rigid for Ä… = 0.5 and ²0 = 1/4% [2]).
surface (the butt-end of the shock tube), the transmit- An analysis of the data in Fig. 4 shows that a
ted and reflected waves are superimposed. The pres- wave reflected from the shock-tube butt-end is actu-
sure of the wave formed as a result of superposition ally a transmitted wave: after interaction with the rigid
of the transmitted and reflected waves (P2-3) is ap- boundary, the transmitted wave disappears and a re-
proximately twice that of the transmitted wave P2: flected wave appears which is identical to the wave that
P2-3 = (2.0 Ä… 0.1)P2. Further, the transmitted and re- disappeared. During further propagation, the parame-
flected waves are separated in time. At small distances ters of the reflected wave change with time under the
from the butt-end of the shock tube, the reflected-wave law established for the transmitted wave. (Below, the
pressure is equal to the transmitted-wave pressure be- difference between the transmitted wave and the wave
fore interaction with the reflecting surface: in a sense, reflected from the shock-tube butt-end is ignored, and
the post-detonation wave behave as a particle. Thus, the path length of the post-detonation wave is the sum
when the detonation wave passes through the bubble- of the distance traveled by the transmitted wave to the
medium liquid interface, a post-detonation transmit- shock-tube butt-end and the distance then traveled by
ted wave is formed, whose pressure decreases as the the reflected wave.)
wave propagates; the interaction of the transmitted In systems with Ä… = 0, 0.25, or 0.5, the attenua-
wave with the reflecting surface is similar in nature to tion constant of post-detonation waves (k) is (0.9Ä…0.2),
an elastic impact. (1.2Ä…0.3), or (2.1Ä…0.4) m-1, respectively, and the prop-
The results of measurements of the pulsation- agation velocity of post-detonation waves is (1370Ä…50),
averaged pressure of the transmitted (P2) and reflected (1480Ä…50), or (1550Ä…50) m/sec, which is approximately
(P3) post-detonation waves are shown in Fig. 4 as a equal to the speed of sound in liquids [(1380 Ä… 50),
logarithmic dependence of the ratio Pj/P1 on the dis- (1470Ä…50), or (1580Ä…50) m/sec in systems with Ä… = 0,
tance x (Pj is the transmitted-wave pressure for j = 2 0.25, or 0.5, respectively]. The speed of sound in the
or the reflected-wave pressure for j = 3; each point is examined liquids was determined from the propagation
the result of averaging over 10 15 measurements). The velocity of weak shock waves (the measurements were
character of the given dependence (straight line passing performed at T = 15ć%C).
through the coordinate origin) suggests that the trans- The values obtained for the speed of sound in liq-
mission constant of the bubble-medium liquid inter- uids are somewhat lower than those given in reference
face is equal to unity for the detonation wave, and the books. Thus, according to [6], the speed of sound in dis-
reflection coefficient is zero (see Fig. 2). tilled water is 1467.5 m/sec (at T = 15ć%C). The differ-
Thus, the dependence of the relative post- ence between these data is due to the following reasons:
detonation pressure (both the transmitted wave and the The propagation of detonation [7, 4], post-detonation,
wave reflected from the butt-end of the shock tube) on and shock waves is accompanied by the formation of
the distance from the interface is written as Pj/P1 = cavitation bubbles <0.5 mm in diameter (cavitation
bubbles were observed in the liquid during evacuation
of the shock tube after the experiment). After evacua-
tion of the shock tube, a number of small bubbles can
be present in the liquid during 10 15 min. The pres-
ence of even a small number of gas bubbles in the liquid
decreases the velocity of acoustic waves significantly. In
addition, in the examined liquids, one can see suspended
solid particles formed upon ignition of gas bubbles in the
detonation wave (soot particles). The presence of solid
particles in a liquid also leads to a decrease in the speed
of sound [8].
The attenuation constant and velocity of post-
detonation waves depend on the properties of the liquid
(in particular, viscosity) and do not depend on the pa-
Fig. 4. Curve ln(Pj/P1)(x) for Ä… = 0.5 and ²0 =
rameters of the post-detonation waves proper (the char-
1/4: points 1 refer to the transmitted wave (j = 2)
acteristics of post-detonation waves specified by detona-
and points 2 refer to the wave reflected from the butt-
tion waves, whose parameters, in turn, depend on the
end of the shock tube (j = 3).
218 Sychev
properties of the bubble media were varied over a wide Thus, the experiments on passage of detona-
range: the gas-phase concentration of the bubble media tion waves from a chemically active bubble medium
was varied in the range of 1/8 d" ²0 d" 4%). into a chemically inert liquid showed that both post-
The duration of the transmitted wave Ä2 (time detonation (transmitted waves and the waves reflected
characteristic determined at the zero level of the aver- from the shock-tube butt-end) and detonation waves
aged signal of a pressure transducer: Ä1, Ä2, and Ä3 for have pulsating pressure profiles. Bubble detonation
the detonation wave, transmitted wave, and the wave waves and post-detonation waves with averaged pres-
reflected from the shock-tube butt-end, respectively) sure pulsations are solitary waves. The pressure of post-
is equal to the duration of a detonation wave [Ä1 = detonation waves decreases as the wave propagates and
(70 Ä… 20) µsec] near the interface and decreases slightly is described by an exponential dependence. The pres-
as the wave propagates (see Fig. 2): Äj = (50Ä…10) µsec sure behind the post-detonation wave as well as be-
at x = 0.96 m (Äj is the duration of the transmitted hind the bubble detonation waves is close to the initial
wave for j = 2 or the duration of the reflected wave pressure. The attenuation constant (damping factor)
for j = 3). Thus, the linear extent of the transmitted of post-detonation waves increases with increase in the
waves (wavelength), determined by the wave duration viscosity of the liquid. The velocity of post-detonation
Ä2 and the wave velocity D2 (2 = D2 · Ä2), is H"10 cm waves is equal to the speed of sound in the liquid. The
near the interface and it decreases slightly as the wave duration and linear extent of post-detonation waves de-
propagates. crease slightly as the wave propagates. Attenuation of
Post-detonation waves decay due to dissipative pro- post-detonation waves (decrease in pressure) is caused
cesses. The dependence of the attenuation constant on by dissipative processes.
the viscosity of the liquid indicates that there is vis- Passage of a detonation wave from a bubble
cous energy dissipation. In addition, the presence of medium into a liquid can be used to generate wave dis-
cavitation bubbles and suspended particles also con- turbances with varying parameters in liquids.
tributes to wave attenuation [8]. The work was supported by the Russian Foun-
We note that the attenuation constant of post- dation for Fundamental Research (Grant No. 01 03
detonation waves in liquids is considerably smaller than 32351).
that in bubble media [1, 2], i.e., the energy dissipation
of post-detonation waves in bubble media is largely due
to the presence of gas bubbles in the liquid.
REFERENCES
It is important to note special features of post-
detonation waves that distinguish them from the well- 1. A. I. Sychev, Passage of a bubble-detonation wave into
known wave disturbances, for example, solitary waves. a chemically inactive bubble medium, Combust. Expl.
A solitary wave exists when the dispersion and nonlin- Shock Waves, 37, No. 4, 451 454 (2001).
2. A. I. Sychev, Reflection of a bubble-detonation wave
ear characteristics of a medium are in equilibrium. The
from a rigid obstacle, Combust. Expl. Shock Waves, 36,
solitary-wave velocity decreases with decrease in its am-
No. 3, 384 389 (2000).
plitude. Because of dissipative processes, the solitary-
3. A. I. Sychev, Shock wave ignition of liquid gas-bubble
wave amplitude and, hence, its velocity decrease as the
systems, Combust. Expl. Shock Waves, 21, No. 2, 250
wave propagates.
253 (1985).
A post-detonation wave is a dissipative solitary
4. A. I. Sychev, Detonation waves in multicomponent bub-
wave with a pulsating pressure profile. In the case of
ble media, Combust. Expl. Shock Waves, 29, No. 1, 104
a detonation wave, the energy losses are compensated
110 (1993).
for by the energy released into the medium as the wave
5. A. I. Sychev, Detonation waves in a liquid gas bubble
propagates. In contrast, in a post-detonation wave, the
system, Combust. Expl. Shock Waves, 21, No. 3, 365
energy losses remain uncompensated, and the wave am-
372 (1985).
plitude decreases due to dissipative processes. In this
6. G. Ebert, Desk Reference Book on Physics [in Russian],
case, the post-detonation waves formed upon passage
Gos. Izd. Fiz.-Mat. Lit., Moscow (1963).
of a bubble detonation wave into a chemically inactive,
7. A. V. Pinaev and A. I. Sychev, Structure and properties
bubble medium [1] or into an inert liquid or upon re-
of detonation in a liquid gas bubble system, Combust.
flection of a detonation wave from a rigid obstacle [2]
Expl. Shock Waves, 22, No. 3, 360 367 (1986).
propagate at constant velocities that do not depend on
8. N. I. Brazhnikov, Ultrasonic Methods [in Russian],
their amplitudes.
Énergiya, Moscow (1965).
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