Quasi-Homogeneous and Pseudospin Modes of Zirconium-Wire Combustion in Air, CHEMIA I PIROTECHNIKA, Chemia i ...

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Combustion, Explosion, and Shock Waves, Vol. 39, No. 1, pp. 59{63, 2003
Quasi-Homogeneous and Pseudospin Modes
of Zirconium-Wire Combustion in Air
S. G. Vadchenko
1
UDC 546
Translated from Fizika Goreniya i Vzryva, Vol. 39, No. 1, pp. 69{73, January{February, 2003.
Original article submitted January 22, 2002.
A novel experimental technique is proposed for examining the transition mechanism
from quasi-homogeneous to heterogeneous combustion | burning of a variable-pitch
spring. Depending on the pitch of air-combustible zirconium springs, two combus-
tion modes are possible. Quasi-homogeneous (layer-by-layer) combustion is observed
in the case of small-pitch springs; as the spring pitch increases, quasi-homogeneous
combustion transforms into heterogeneous (pseudo-spin) combustion. Conditions for
the occurrence of various combustion modes, depending on the spring diameter and
pitch, are studied.
Key words: heterogeneous combustion, spin, zirconium oxidation.
In the present-day theory of heterogeneous com-
bustion, studying of burning features of specially con-
structed heterogeneous model systems is of great inter-
est. For instance, combustion in multilayered systems
composed by combustible and inert layers was studied in
[1, 2]; the theory of such processes was given in [3{6]. In
these works, concepts of primary importance concern-
ing quasi-homogeneous and relay modes of combustion
were developed. Another heterogeneous model struc-
ture composed by thin alternating fuel and oxidant lay-
ers (for instance, metal and nonmetal layers or layers
of two dissimilar materials) was proposed in [7, 8]. In
these works, the possibility of \high-velocity" combus-
tion modes was demonstrated.
In the present article, a new heterogeneous model
(spring) is proposed and examined; this model also per-
mits various combustion modes | solitary waves of the
spin type [9] or collective waves resulting from thermal
interaction of spring coils.
Fig. 1. Experimental scheme: 1) specimen holder;
2) initial wire; 3) combustion front; 4) combustion
products; 5) video-camera; 6) igniting wire.
EXPERIMENTAL PROCEDURE
ten wire diameters. The spring is ignited by a 0.1-mm
diameter molybdenum lament heated by a short elec-
tric pulse. The limiting case of spring combustion (for
h !1) is combustion of a straight wire. Combustion
can be initiated in the upper or lower part of the spec-
imen. The process is registered by a video-camera, and
the combustion mode and front velocity U
f
are found
from the video-recording.
The experiments were performed in air under at-
mospheric pressure.
0010-5082/03/3901-0059 $25.00
c
2003
Plenum Publishing Corporation
The scheme of the experiments is shown in Fig. 1.
The specimens are springs of diameter D = 0:3{1:1 mm,
wound from zirconium wire of diameter d = 0:09 mm
with a xed pitch h. The minimum spring length is
1
Institute of Structural Macrokinetics and Material
Science Problems, Russian Academy of Sciences,
Chernogolovka 142432; vadchenko@mail.ru.
59
60
Vadchenko
Fig. 2. Straight-wire burning rate versus the angle ':
negative inclination angles refer to combustion initi-
ation from below, ' = 0 to the horizontal position of
the wire, and positive inclination angles to combus-
tion initiation from above.
Fig. 3. Frontal (U
f
) and predicted frontal (U
0
f
) burning
rates versus the angle '.
EXPERIMENTAL RESULTS
AND DISCUSSION
lowed us to reveal the existence of two combustion
modes | quasi-homogeneous combustion and pseu-
dospin combustion. In the rst case, the combustion
front exerts a layer-by-layer motion, without any sub-
stantial delays in going over from one coil to the other.
This mode is typical of dense, small-pitch springs. In
the second case, starting from a certain coil, combus-
tion propagates along the wire and is visually observed
as a heat-source motion during spin combustion. In the
latter case, the main spring-combustion features (a de-
crease in the frontal and circumferential burning rates
with increasing spring diameter) are in good qualitative
agreement with the features of ordinary spin combus-
tion [7].
Combustion-Front Velocities and Time
Shift. Figure 3 shows the combustion-front velocity
(U
f
) as a function of the angle ' between the spring-
coil tangent line and the combustion-front velocity for
various spring diameters. The angle ' was calculated
by the formula
Inuence of Gravitational Convection and
Edge Eects. Figure 2 shows the straight-wire burn-
ing rate U versus the angle of wire deection from the
horizontal line (' = 0). Engaging attention is the
burning-rate minimum for a position of the wire close
to the horizontal one, caused by variation of the ef-
fective cross section of the convective airow aecting
heat transfer from the combustion front. A study of the
burning-rate distribution over the length of a straight
vertical wire as a function of combustion-wave propa-
gation direction showed that, if combustion is initiated
from above, the steady-state combustion-front velocity
is established over a wire length approximately three
times as short as that in the case of initiating combus-
tion from below. The observed burning rate diers from
the steady-state value over the starting length of the
wire because of the additional heating from the igniting
wire and at the end of the wire because of conductive
heat transfer into the specimen holder.
The steady-state burning rate of the spring as a
function of the spring diameter and pitch was stabilized
after 1 to 5 spring coils were burnt and remained con-
stant almost up to the end of the process.
To exclude the inuence of convection and edge
eects (additional heat ux from the igniting wire and
heat transfer to the specimen holder) on the process,
we conducted tests with initiation of the reaction from
above; measurements were performed over the length of
the spring with an established burning rate.
Modes of Spring Combustion. Video-recording
of propagating combustion waves along the spring al-
' = arctan
h
(Dd)
:
(1)
Here the angle ' is chosen as an argument since it is
a universal value for springs of various diameters and
pitches, permits a comparison between the burning rate
of springs and the straight-wire burning rate (h !1),
and provides a convenient scale of values for spring
pitches varying from zero to innity.
The following specic features of the curves U
f
(')
are worth noting:
| no substantial burning-rate discontinuity occurs
as the quasi-homogeneous combustion mode gives way
to the pseudospin one;
Quasi-Homogeneous and Pseudospin Modes of Zirconium-Wire Combustion in Air
61
Fig. 4. Time shift versus the angle '.
Fig. 5. Unit-length burn-up time versus the angle '.
| starting from a certain angle ', the spring burn-
ing rate becomes higher than the straight-wire burning
rate (the dashed curve in Fig. 3);
| the burning rate displays a maximum at a cer-
tain angle '.
By analogy with the combustion-wave propagation
process in a system of plates [1], one can also introduce
the time shift t
sh
, being the time required for one spring
coil to burn out completely:
t
sh
= h=U
f
:
(2)
The dependences t
sh
(') are shown in Fig. 4.
Such representation of data reveals several character-
istic zones, most distinctly observed during combustion
of small-diameter springs. In the quasi-homogeneous
combustion-mode region, as the angle ' (of individual
coils) increases, the time t
sh
remains approximately con-
stant. The transition to the pseudospin regime is rst
accompanied by the growth of t
sh
; afterwards, a plateau
is observed in the t
sh
curve up to a certain value of
the angle '; and, nally, the time t
sh
monotonically in-
creases. With increasing spring diameter, the length of
the plateau decreases.
Circumferential Burning Rate and Unit-
Length Burn-up Time. From the combustion-front
velocity, one can calculate the corresponding circumfer-
ential burning rate
Fig. 6. Domains of existence of various combustion
modes: the angle at which the transition from the quasi-
homogeneous to pseudospin combustion mode is ob-
served (1), the angle at which the frontal burning rate is
higher than the straight-wire burning rate (2), the an-
gle '
lim
(3), and the angle below which the dependences
t
sh
(') display the plateau (4).
small-diameter springs, these curves display an inec-
tion point. With increasing spring diameter, the max-
imum degenerates into a plateau (D = 0:58 mm), and
for the diameter D = 1:1 mm, the time t
s
monotonically
increases with increasing angle '.
Parametric Domains of Existence of Vari-
ous Combustion Modes. A number of factors aect
the combustion modes and burning rate; these factors
partially mask the observed eects. These factors in-
clude heat transfer to the ambient medium, diusion-
limited transport of oxygen to the wire surface, and non-
equal accessibility of dierent parts of the wire at spring
sections with dierent spring diameters and pitches.
r
((Dd))
2
h
2
U
f
sin '
U
s
= U
f
+ 1 =
(3)
or the unit-length burn-up time t
s
= 1=U
s
(in the
present study, we assume the unit length to equal
1 mm). It should be noted that the quantities U
s
and
t
s
in the quasi-homogeneous combustion mode are c-
titious. The curves t
s
(') are shown in Fig. 5. For
62
Vadchenko
Nonetheless, using the experimental data, we built a
parametric diagram of the domains of various combus-
tion modes in the \angle ' (spring pitch){spring diam-
eter" coordinates (Fig. 6). From the left and below, the
diagram is bounded by the limiting values of the angle
' given by the formula
conductive heat transfer along the wire. The number of
heated coils is given by the formula
n =
l cos '
(Dd)
(5)
'
lim
= arctan
d
(Dd)
:
(4)
and ranges from n = 4:5 (D = 0:3 mm and ' = 8:6
)
to 0:47 (D = 1:1 mm and ' = 60
). Thus, due to con-
ductive heat transfer along the wire, combustion always
occurs at the initial temperature of spring coils higher
than the ambient temperature.
Owing to conductive and radiative heat transfer
through the gas gap between the coils, the initial tem-
perature of the wire additionally rises, causing an as-
sociated increase in the burning rate; as a consequence,
the length of the heated zone of the wire and the frontal
heating length of the spring also undergo changes.
We measured the straight-wire burning-rate tem-
perature coecient in the temperature range from 293
to 533 K. The curve obtained can be tted by the for-
mula
The whole combustion domain can be divided into
two subdomains, diusion and kinetic ones. The po-
sition of the dividing curves between the subdomains
can be roughly estimated from the intersection points
of the curve U
f
(') and the straight-wire burning-rate
curve. These points give the maximum values of the
angle ' at which the reaction is still limited by oxygen
transport to the reaction zone. The minimum values of
the angle ' can be found as angles corresponding to the
end of the plateau in the t
sh
(') curves, at which the
time t
sh
starts increasing. Since the oxygen transport
to the wire surface is diusion-controlled, one of the
reasons for the occurrence of the plateau in the t
sh
(')
curves or inection points in the t
s
(') curves may be
the transition from the diusion region of the reaction
to its kinetic region.
Thus, the quasi-homogeneous combustion is ob-
served in the diusion region, while the pseudospin com-
bustion both in the diusion and kinetic regions.
Eect of Initial Temperature. Obviously, the
combustion-front velocity should tend to the straight-
wire burning rate with increasing spring pitch or in-
creasing angle '; hence, this velocity should contin-
uously increase. For conditions without heat trans-
fer between spring coils, the straight-wire burning rate
can be used to estimate the ctitious combustion-front
velocity, which is independent of the spring diameter,
by the formula U
0
f
= U sin ' (the calculated curve is
shown in Fig. 3). However, because of the interaction
between spring coils (heating of the next coil by the
previous, burning one), the experimentally measured
combustion-front velocity exceeds the predicted burn-
ing rate in the quasi-homogeneous combustion mode by
a factor of 2:5{5; as the angle ' increases, the measured
and predicted values come closer and closer together.
Apparently, the combustion-front velocity in the
pseudospin-mode domain depends on the circumferen-
tial velocity. As was noted above, the study of the varia-
tion of the burning rate along a straight wire revealed a
strong inuence of heat transfer to the specimen holder;
this eect was observed at a nal section of the wire of
length 3 mm, or 30 wire diameters. This distance can
be identied as the heating-zone length in the straight-
wire combustion wave. As the wire is coiled into a
spring, there arise coils heated only at the expense of
k
T
0
=
d ln U
dT
0
= 2:45 10
3
K
1
:
Comparing the dependences U(T
0
) and U
f
('), one
can conclude that, for the maximum observed excess
of the combustion-front velocity over the straight-wire
burning rate (D = 0:4 mm and ' = 57
), it suces to
heat the spring coils to the temperature T
0
= 390 K,
which may well be the case due to heat transfer along
the wire and across the gas phase.
As was noted above, the plateau in the t
sh
(')
curves or the inection point in the t
s
(') curves, indica-
tive of a relative growth in the circumferential burning
rate, may be caused by the transition from the diu-
sion region of the reaction to its kinetic region. Another
possible reason for the increase in the burning rate in a
certain range of angles ' may be approaching of com-
bustion conditions for xed-pitch springs to conditions
of the super-adiabatic mode of combustion theoretically
substantiated in [3{5]. The actual reason for the plateau
can be established by studying zirconium-wire combus-
tion in oxygen or using, in the experimental procedure
described above, wires capable of self-sustained com-
bustion in inert media, such as nickel-coated aluminum
wires.
The author thanks Academician A. G. Merzhanov
for his valuable advice concerning the experimental
scheme and for discussion of the results obtained.
This work was supported by the Russian Founda-
tion for Fundamental Research (Grants Nos. 99-03-
32392 and 99-03-32020).
Quasi-Homogeneous and Pseudospin Modes of Zirconium-Wire Combustion in Air
63
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