Shock Waves (1998) 8: 55 61
Behavior of detonation waves at low pressures
K. Ishii1, H. Gr�nig2
1
Department of Mechanical Engineering and Materials Science, Faculty of Engineering, Yokohama National University, 79-5 Tokiwadai,
Hodogaya-ku, Yokohama, 240 Japan
2
Stosswellenlabor, RWTH Aachen, Templergraben 55, D-52056 Aachen, Germany
Received 10 March 1997 / Accepted 8 June 1997
Abstract. With respect to stability of gaseous detonations, detonation (Nettleton 1987) and its propagating manner has
unsteady behavior of galloping detonations and re-initiation been studied by using schlieren photographs (Saint-Cloud
process of hydrogen-oxygen mixtures are studied using a et al. 1972) and microwave interferometry (Edwards et al.
detonation tube of 14 m in length and 45 mm i.d. The ar- 1974; 1977). Lee et al. (1995) characterized several prop-
rival of the shock wave and the reaction front is detected agation modes of near-limit detonations from velocity pro-
individually by a double probe combining of a pressure and files measured by a modified microwave interferometer. This
an ion probe. The experimental results show that there are method is practical for detections of galloping detonations
two different types of the re-initiation mechanism. One is because of its high spatial resolution and enables to obtain
essentially the same as that of deflagration to detonation detailed velocity profiles. Since a microwave is reflected
transition in the sense that a shock wave generated by flame mostly from an ionization front, the velocity measured by
acceleration causes a local explosion. From calculated values the microwave interferometer can identify the movement of
of ignition delay behind the shock wave decoupled from the the reaction front which contains much more ionized species
reaction front, the other is found to be closely related with than the shock front. Recently, Williams et al. (1996) indi-
spontaneous ignition. In this case, the fundamental propaga- cated, by using numerical simulations, that slow chemistry
tion mode shows a spinning detonation. in the gas heated by the separated shock front eventually
leads to re-ignition. This suggests that the gas condition be-
Key words: Detonation re-initiation, Galloping detonation, hind the shock front has a close relation to the re-initiation
Near-limit detonation, Spontaneous ignition process.
For the purpose of clearing the propagation mechanism
of the galloping detonation, the present work focuses on the
behavior of a shock wave and a reaction front which re-
sult from detonation decoupling. The shock and the reaction
1 Introduction
front are detected individually at a position by the double
probe which is composed of a pressure and an ion probe.
It is well known that detonation waves show unstable behav-
Experimental results obtained in the present work show that
ior under near-limit conditions (Gordon et al. 1959; Manson
two different types of the re-initiation mechanism exist. Ac-
et al. 1963; Munday et al. 1968). Investigation of instabilities
cording to the classification proposed by Lee et al. (1995),
of detonations is practically important from safety reasons
one corresponds to  galloping detonation and the other to
in terms of detonability limits. From the empirical fact that
 stuttering one .
a detonation wave cannot propagate in small tubes whose
diameter is dependent on the type of mixtures and initial
conditions, a number of attempts have been made to deter-
2 Experimental apparatus
mine detonability limits for various mixtures. On the basis
2.1 Detonation tube
of recent successful estimations of the detonation cell size
which becomes an index of the detonability of mixtures,
The schematic of the experimental set-up is shown in Fig. 1.
Dupr� et al. (1986; 1991) studied the critical tube diameter
The experiment was carried out in a stainless tube of about
using combination of tubes of various sizes.
14 m in length and of 45 mm i.d. A detonation wave
The unstable detonation, which is usually accompanied
was generated by igniting a stoichiometric hydrogen-oxygen
by large velocity fluctuations, is referred to as a galloping
mixture in a 2 mlong driver section equipped with a con-
Correspondence to: Kazuhiro Ishii ventional spark plug. A Shchelkin spiral was inserted in
56
Fig. 1. Experimental set-up
Fig. 3. Measured arrival time of shock and the reaction fronts by
the double probe
Fig. 2. Structure of the double probe
arrival of these fronts individually at one position, a double
probe was used which was composed of the combination of
the driver section to shorten the deflagration-to-detonation
a pressure probe made from piezoceramic disks and of an
transition (DDT) process. The driver and the test section
ion probe. The schematic of the double probe is shown in
was separated by a 10 �m thick polyethyleneterephthalate
Fig. 2. The structure of the pressure probe was essentially
(Hostaphan) diaphragm. The initial pressure in the driver
the same as that developed by Willmarth (1958). The piezo-
section is in the range from 250 mbar to 300 mbar in most
ceramic disks were 4 mm in dia. and 1 mm in thickness
experiments. Stoichiometric hydrogen-oxygen mixtures with
and their surfaces were coated with nickel. One of the disks
and without nitrogen were introduced into the evacuated test
had a drilled hole, through which a thin wire was soldered
section.
to the electrode surface of the other disk. The inner sur-
Smoked foils recorded the detonation front structure.
faces had a same polarity to double the sensitivity. These
Aluminum sheets, 0.1 mm thick and 500 mm long, were
two disks were glued together using electroconductive paint
placed inside the test section so as to fit them tightly on its
and were set in the recess of the brass holder with the paint
wall. Their inner surfaces were uniformly coated with soot
so as to ensure a stable ground connection. After drying the
produced with a propane-butane burner. These smoked foils
paint, the outer surface of the probe was coated thinly with
were inserted maximal at 10 positions in the test section.
an electroconductive adhesive for the sake of sealing, pro-
tection from heating and securing the ground connection.
The brass holder was then fit into the electrode holder made
2.2 Double probe
of delrin so that the mechanical vibration did not affect the
Under near-limit conditions, a detonation wave is decou- probe. After the completion of the pressure probe, two stain-
pling into a shock wave and a reaction front. To detect the less steel electrodes of 0.5 mm in dia. were adhered to the
57
Fig. 5. Velocity-distance plots during the re-initiation process of a
Fig. 4a,b. Velocity and pressure profiles during the re-initiation
galloping detonation (2H2+O2, p0 = 20 mbar). VR: Velocity of the
process of a galloping detonation (2H2+O2, p0 = 20 mbar)
reaction front; VG: Velocity of the gas behind the primary shock
front
delrin holder and were bent so as to form a gap width of
about 0.2 mm.
Its performance was examined by choosing a steady spin- velocity and pressure profiles of the re-initiation process of
ning detonation as a benchmark test problem. The structure
the galloping detonation for a mixture of 2H2+O2 at p0 of
of the spinning detonation has been investigated by many re- 20 mbar.
searchers (Schott 1965; Voitsekhovskii et al. 1969), and it is
From Fig. 4(b), one sees that the decoupling occurs at a
known that the distance between the shock and the reaction
distance xd of about 4.2 m from the diaphragm. Although
front is relative long compared to that of multi-head deto- the shock and reaction fronts decelerate, the velocity of the
nations. Figure 3 shows an example of arrival time of the
reaction front becomes lower than that of the primary shock
spinning detonation front measured by the double probe. The
front. Afterwards, at xd of about 7.3 m, the reaction front
pressure history as shown in Fig. 3 is peculiar to the spinning
accelerates. At the early stage of the acceleration phase, it is
detonation (Voitsekhovskii et al. 1969), namely the second
observed that compression waves follow the primary shock
pressure rise which corresponds to a transverse wave fol- front as shown in the upper pressure history of Fig. 4(a).
lows the primary shock front. Since low eigenfrequencies of
Compression waves generated by the flame acceleration pre-
the pressure probe often caused oscillations behind a sudden
cede the reaction front and both strength and velocity of the
pressure rise, quantitative measurements of pressure were
compression wave increase. It eventually forms a secondary
rather difficult. However, the present agreement on the spin
shock wave which is strong enough to cause local explosions
structure indicated that the double probe was very useful to
and consequently a detonation wave is initiated again. These
distinguish the shock from the reaction front. For the quan- velocity and the pressure profiles indicate that the re-initiated
titative measurement of pressures, a conventional pressure
detonation is initially overdriven.
transducer (Kistler 603B) was used.
In the re-initiation process, the origin of the primary
shock wave is different from the precursor shock wave in
DDT processes (Urtiew and Oppenheim 1966), although
3 Results and discussion
these heat up the mixture to some extent before the arrival
of the detonation. In the present work, the following two
3.1 Galloping detonation cases are found: The re-initiation occurs (1) before the sec-
ondary shock wave overtakes the primary shock; (2) after
Just after the rupture of the diaphragm, the detonation wave the secondary shock wave coalesces into the primary shock.
in the test section propagates in an overdriven state. The Sometimes the re-initiation was due to the second flame ac-
detonation velocity decreases until it attains a steady state celeration, although the first one also causes compression
and propagates with constant speed which is close to the waves as shown in Fig. 4(a). The flame acceleration which
Chapman-Jouget velocity VCJ. Under near-limit conditions, appears a few times during the re-initiation process is also
as is well known, a spinning detonation occurs whose veloc- stated by Edwards et al. (1977).
ity is somewhat lower than VCJ. In the present detonation Figure 5 shows velocity of the reaction front VR and
tube a steady spinning detonation is observed for a mixture the gas velocity VG behind the primary shock front, where
of 2H2+O2 at an initial pressure p0 of 30 mbar. At lower VG is calculated from the measured velocity of the primary
pressures the detonation wave is decoupled into a primary shock front. Since the location where the detonation front is
shock and a reaction front. Figure 4 shows an example of decoupled differs in every experiment, the set of data were
58
Fig. 7. Smoked foil record ahead of the re-initiation point (2H2+O2
+7N2, p0 = 85 mbar)
structure disappears almost coincides with that of the shock-
reaction front decoupling. No trace at all can be seen on
the smoked foil in the region where the shock and reaction
fronts were found to separate.
At the location of the re-initiation, some different pat-
terns of the imprint are observed. Figure 6 shows examples
of the smoked foil records for the mixture of 2H2+O2 at
p0 of 20 mbar. The detonation moves from left to right
in each record. In Fig. 6(a), there are a large number of
Fig. 6a,b. Smoked foil records at the re-initiation point (2H2+O2,
fine cell structures which characterize an overdriven deto-
p0 = 20 mbar)
nation. In Fig. 6(b) relative large scale structures are observ-
able even at the re-initiation point as compared to Fig. 6(a).
The triple points move diagonally forming mesh-patterns. In
shifted in the axial direction of the tube so that the profiles
these cases, the cell size increases toward downstream di-
of VG coincides with each other. In Fig. 5, VR and VG have
rection and eventually turns into the spin structure. Before
almost the same value from the distance x between 4 mand
the re-initiation, many thin scratch-like lines almost parallel
6 m, which suggests that the burning velocity of the mixture
to the tube axis appear as seen in Fig. 6. These lines are cre-
behind the primary shock front is much lower than the gas
ated not due to fragments of the ruptured diaphragm, because
velocity. However, VR increases rapidly from x of about
such lines were not observed upstream. If it were created by
6 m to 3000 m/s. In a shock tube, from a certain distance
the fragments, the scratch lines should have appeared every-
xR behind the incident shock wave, the thickness of the
where. Moreover, for a mixture of 2H2+O2+7N2, a vortex-
boundary layer becomes as thick as the tube radius. If the
like structure is observed ahead of the re-initiation point as
distance from the shock wave is greater than xR, the whole
shown in Fig. 7. In the present experiment, there is a ten-
flow region becomes turbulent. Generally xR depends on the
dency that dilution of nitrogen spoils the sharpness of the
shock strength and the initial conditions, and xR/D ranges
imprint. The viscosity of nitrogen and its temperature de-
from 20 to 100 for 10 pendence are larger than those of hydrogen, which causes
diameter and p21 is pressure ratio across the shock wave
to increase in friction between the gas flow and the smoked
(Oertel 1966). From this expression, xR can be estimated
foil. Thus it is concluded that the scratch-like lines are cre-
to range from 0.9 m to 4.5 m. For the case of Fig. 4, the
ated due to gas motion induced by the accelerating flame and
maximum separation distance between the shock and the
that the vortex-like structures are traces of turbulent flows.
reaction front is about 1 m. Some parts of the flows are,
From these results, the re-initiation process of the gal-
therefore, at least turbulent, which make the burning velocity
loping detonation is essentially the same as DDT process in
even higher and lead to rapid flame acceleration.
the sense that a shock wave generated by flame acceleration
Smoked foils were used to record the trajectories of the
leads to local explosions. One difference is that the flame
triple point and inserted on the inner surface of the detona-
in the re-initiation process propagates in a flowing mixture
tion tube. Just behind the diaphragm station in the test sec-
behind the primary shock wave.
tion, small cell structures were identified on the smoked foil
because of the overdriven state. Under near-limit conditions
the cell size increases as the detonation moves downstream
3.2 Stuttering detonation
until it shows a spin structure. As Schott (1965) reported,
the spin head has a ribbon-like structure containing several The general pressure and velocity profiles of the stuttering
triple points inside. In the case of an unsteady spinning det- detonation are shown in Fig. 8 for a mixture of 2H2+O2+3N2
onation, the number of these triple points decreases with the at p0 of 30 mbar. Two cycles of acceleration-deceleration
deceleration of the propagation velocity, and the imprint of are usually observed for this initial condition. Such type of
the spin structure becomes faint. The location where the spin velocity fluctuations are referred to as  stuttering in the
59
Fig. 8a,b. Velocity and pressure profiles of a stuttering detonation
(2H2+O2+3N2, p0 = 30 mbar). �SR: Separation time between shock
and reaction fronts
Table 1. Propagation modes in different mixtures: 1, 2H2+O2; 2,
2H2+O2+3Ar; 3, 2H2+O2+3N2; 4, 2H2+O2+7N2; C, Compression
wave resulting in no re-initiation; F, Failure; St, Stuttering; Ga,
Galloping; and S, Stable
Mixtures
Fig. 9a e. Sketch of smoked foil records (2H2+O2+3N2, p0 = 30
p0 (mbar) 1 2 3 4
mbar)
100 S
90 Ga
main features of the traces are presented as sketched in
80 C, Ga
Fig. 9 which is obtained from the smoked foil records of
70 C, F
the same experiment shown in Fig. 8. The spinning detona-
50 S S F
tion in Fig. 9(a) corresponds to the first accelerating phase.
40 S S
The spin head shows a more complicated structure than in
35 S
the following decelerating phase as shown in Fig. 9(b). The
30 S S F, St
trace of the spin is very weak and inner structures are not
25 Ga F F
observed. In Fig. 9(c), no trace is found beyond xd of 8.2
23 Ga
20 C, Ga F F m. Occasionally weak imprints of slapping waves are found
18 C, Ga
in Fig. 9(d), until strong trajectories of the spinning detona-
15 F F
tion appears again. At xd of 9.7 m, one triple point branches
into two paths: One forms a spinning detonation and the
other one fails gradually. This branching is also found dur-
classification of Lee et al. (1995). In Fig. 8, at the position ing the transition from an unsteady two-head to a spinning
of A and C the pressure profiles are characteristic of usual detonation. In Fig. 9(e) the spin head moves with a rotation
steady detonations. In particular at the position C, it is seen in the opposite direction from the previous one. From the
that a spinning detonation passed the pressure probe, since fact that a spinning detonation only occurs under near-limit
the second pressure rise owing to the strong transverse wave conditions, it is understandable that the stuttering detonation
follows the first shock wave. At the position B, namely in a imprints a spin structure on the smoked foils.
low velocity phase, the pressure profile is similar to that of The ignition delay during the whole phase is plotted in
a shock wave except that a cyclic fluctuation still remains Fig. 10 as a function of the shock velocity. Different from
owing to the transverse wave. This type of pressure profile �SR which is in the laboratory time, the ignition delay re-
is also obtained just after the shock-reaction fronts decou- ferred to here denotes the particle time, i.e. the time required
pling during the re-initiation process. The behavior of the for a heated gas volume element moving along the particle
detonation velocity agrees well with �SR, which denotes the path to reach the reaction front in the x-t diagram. Numer-
separation time between the primary shock and the reaction ical calculation was also made to obtain the ignition delay
front and is obtained from an xd - t diagram. using a reaction system of hydrogen-oxygen mixtures (Maas
At low initial pressures the imprint of the triple point and Warnatz 1988) including 9 species and 38 elementary
on the smoked foil is weak compared with those of cell reactions. The ignition delay is defined in the calculation as
structures of multi-head detonations. For this reason, the the time required for maximum change in OH concentra-
60
was found after the shock-reaction separation. It should be
noted that there is ambiguity in the definition of the failure
mode because of the limited length of the test tube. To define
detonability limits more accurately or to confirm the initial
pressure ranges at which the galloping detonation occurs,
one has to use even longer tubes.
4 Conclusions
Unsteady behavior of detonations and the detonation re-
initiation process of hydrogen-oxygen systems have been
studied on the basis of the propagation of shock and reaction
Fig. 10. Ignition delay behind the shock front (2H2+O2+3N2, p0 =
fronts resulted from the decoupling of the detonation wave.
30 mbar)
The arrival of shock and reaction fronts is detected individ-
ually by double probes which are composed of a pressure
and an ion probe. From the experimental results, there are
two types of the re-initiation mechanism. They correspond
to  galloping and  stuttering detonation. The re-initiation
process of the former is essentially the same as that of DDT
in the sense that a shock wave generated by flame acceler-
ation causes a local explosion. On smoke foils records, just
before the re-initiation point where a number of fine cell
structures are found, vortex-like imprints are observed ow-
ing to turbulent flames. Under near limit conditions a shock
wave is formed which is not strong enough to cause a local
Fig. 11. Velocity profile of shock and reaction front (2H2+O2+3Ar,
explosion and yields a failure in the re-initiation. The stutter-
p0 = 20 mbar)
ing detonation shows a spinning detonation as a fundamental
propagation mode. It was found that its re-initiation mecha-
nism is different from that of the galloping detonation, since
tion. Figure 10 indicates that the reaction is induced by the
shock wave during the whole phase of the stuttering deto- the reaction induced by the preceding shock governs the
whole phase.
nation, contrary to the re-initiation process of the galloping
detonation.
Acknowledgement. The present work was carried out when one of
the authors was a research fellow of the Alexander von Humboldt
3.3 Effect of dilution
Foundation. The author is grateful for support during his stay in
Germany.
As Edwards et al. (1977) stated, no galloping detonation nor
re-initiation was found also in the present experiment, when
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