From: ahahma@polaris.utu.fi (Arno Hahma)
Newsgroups: rec.pyrotechnics
Subject: Re: whistle compositions
Message-ID: <1991Feb15.221441.10738@polaris.utu.fi>
Date: 15 Feb 91 22:14:41 GMT

In article <6581@hplabsz.HP.COM> schediwy@hplabsz.HP.COM (Bic Schediwy) writes:
>

>any problems with using ammonium perchlorate instead of potassium
>perchlorate (particularly if used with sodium benzoate)?
>Specifically, are there safety problems. I'm thinking that
>ammonium perchlorate may have an advantage due to its potential
>for enhanced gas production.

>Since the literature makes no mention of the mixture my guess is
>that there is either a safety problem or it doesn't work as well.

I'd guess ammonium perchlorate wouldn't work, mixtures with it
have a low pressure exponent. Therefore the burning would tend to be
stable, not oscillating.

The burning is believed to be a oscillating series of small explosions
on the surface of the composition. A thin layer of the mixture explodes and
generates a fast flow of gas out of the tube. The inertia of the gas causes
a sudden pressure drop at the surface and the mixture is extinguished. Now the
pressure in the tube drops even more, since gas isn't produced any more.
As the underpressure turns the flow back into the tube, the hot gases ignite
the mixture again causing a new layer of crystals to explode/burn and the
cycle starts again.

This phenomenon closely resembles chuffing in a rocket engine. A high
exponent of pressure enhances this phenomenon, thus, AP probably will
make the whistle burn smoothly rather than oscillate. Potassium
perchlorate based mixtures invariably have a high pressure exponent and
a high minimal burning pressure - both facts favor the chuffing phenomenon.

______________________________________________________________________________

                              R'
                                \
                                 /======\
                               /          \        O
                             /     ArNO     \    //
                             \\        2    //--N+
                              \\          //     \
                                \\______//         O-
                               /
                             R

From: ahahma@kontu.utu.fi
Newsgroups: rec.pyrotechnics
Subject: Re: Fireworks, whistles go BOOM
Message-ID: <1991Apr23.155624.38244@kontu.utu.fi>
Date: 23 Apr 91 15:56:24 GMT

In article <1991Apr20.164853.3508@waikato.ac.nz>, chem2149@waikato.ac.nz
writes:

> On the subject of whistles, has anyone got a good mix that works for the
> small dia tubes, based on KClO4. I have one mix of this sort but it
> does'nt work for the small dia (1/2"), OK for 3/4" and larger.

Try sodium salicylate + KP (stoichiometric). This mixture has to be pressed
hard, the harder the better. At first, I was not able to make it whistle,
until I used about 5 tons of force to confine the mass. The diameter of
the PVC-tube I used was 16 mm (internal). These gave a louder sound
than 28 mm whistles and used about one fourth of the chemicals.

The mixture is hygroscopic. It is spoiled in a couple of days, if left in
the open.
                              R'
                                \
                                 /======\
                               /          \        O
                             /     ArNO     \    //
                             \\        2    //--N+
                              \\          //     \
                                \\------//         O-
                               /
                             R

From: ahahma@polaris.utu.fi (Arno Hahma)
Newsgroups: rec.pyrotechnics
Subject: Re: How do whistling compounds work?
Message-ID: <1991Dec9.220854.14584@polaris.utu.fi>
Date: 9 Dec 91 22:08:54 GMT

In article <31201@nntpd.lkg.dec.com> moroney@ramblr.enet.dec.com writes:

>In article <22810324@hpcvaac.cv.hp.com>, billn@hpcvaac.cv.hp.com (bill
>nelson) writes...

>>Ah, maybe the potassium perchlorate forms an mildly explosive mixture with
>>one of the products of the reaction. It would have to for the whistle to
>>work.

The whistle can not work with small explosions. Such a behaviour would
either lead to a full scale detonation or the whistle would
extinguish. I know this is the theory presented in the pyrotechnical
literature, but it is very hard to believe it.

This is easy to show, if you know about the theory of shock waves. If
not, it may be difficult to get a picture of the following:

Draw the Hugoniot curves of the combustion products of any energetic
material and for the material itself on the same picture. Then draw
the tangents (so called Rayleigh lines) from the initial state of the
unburnt material to the curve, corresponding to a deflagration (or
combustion) and detonation.  Between the tangent points on the curve
there is a forbidden area, on which the Rayleigh line can not go,
since that would give imaginary velocities for the combustion or
detonation. Thus, the combustion can not switch to a detonation
directly.

To switch from a combustion detonation, you would have to raise the
pressure of the unburnt material tremendously, i.e. go up along its
Hugoniot curve until the tangent corresponding to a combustion equals
that of the detonation. This means, you have to have a shock wave in
the material and its intensity has to _exceed_ that of the wave in the
burnt material. This is the case in the detonation.  This will not
happen easily with most materials, especially, it is difficult with
mixtures. The required shock wave typically (in the steady state
detonation) has a pressure more than 500 kilobar.

The theory of shock waves also states, that a shock wave within a gas
can never exceed a certain pressure. In air this limit is about 6
bar, i.e. a pressure difference over the shock wave front in air never
exceeds 6 bar. It should be clear now, that the gas phase
oscillations, even if they were shock waves, are not likely to trigger
a solid state detonation with a shock wave pressure of 500 kilobar.

If the whistle detonates, which is known to have happened, it is due to a
macroscopic, sudden compression of the mass. Should that happen, the
required, initial shock wave may be generated, if a crystal cracks or
hits another with a high velocity.

In the gas phase above the solid state combustion, the situation is
different. Here the Hugoniot curves are totally different and the
pressures are measured in bar instead of kilobar. Thus, an external
shock wave easily triggers a detonation in the gas phase, if the gas
phase contains a combustible mixture and even more easily, if this
combustible mixture is already hot. This is a well known phenomenon
with rocket fuels and colored stars. If a star hits ground while
burning, it often makes a small bang.

But, if this happens, the detonation will sweep the along the burning
surface (a so called surface detonation) of the mixture and shake the
reacting zone off.  The reacting zone is a region with molten, partly
decomposed, charred, etc.  material and it certainly can not take any
high stresses. As a result, the mixture will extinguish. If it has a
high thermal conductivity, it may even reignite, as is the case with
crackling strobe stars. However, this is rare.

>>ALL whistling compounds are sensitive to shock, to some degree or another.
>>That is why they whistle. I am surprised that any of the above resultant
>>compounds would be explosive.

They are shock sensitive. However, the shock sensitivity has no
influence on the capability to whistle. There may be a correlation,
but there is also no evidence that the mixture has to be shock
sensitive in order to whistle. Smokeless powder whistles louder than
any pyrotechnical whistle under proper conditions.

>25% sodium salicylate/75% potassium perchlorate mixture is a standard whistle
>mix.  I'm quite sure it will explode if confined.

Definitely. This mixture is at least as dangerous as flash powder. It
explodes easily and may even detonate, if packed as a loose powder.

>Potassium perchlorate and almost any organic in the proper ratio and extremely
>well mixed is a good bet to be explosive or nearly so.  A substance can be
>explosive without being a single compound, but a mixture of powders.  Flash
>powder is an excellent example.

True. At least, if ignited with a booster charge. Some mixtures do not
need even that, like flash powder and the whistle mixtures, loose.

>I'm quite sure that whistles operate by having a burn rate that depends greatl
>on the pressure.  Resonant sound waves in the tube vary the pressure at the

True. I think there are actually two requirements for the resonance to
happen.

One: the pressure exponent of the mixture has to be close to unity.
If it isn't, the burn rate variations and their influence on the
pressure wave will be less than the intensity of the pressure wave
itself. An oscillator has to have a positive feedback or the
oscillations will die out. Everyone who knows electronics knows this.
With pyrotechnical whistles there is also an upper limit. If the
pressure exponent is too high, the oscillations or even a single
oscillation will continue growing until a full scale detonation of the
mass occurs or if it is not possible, the burn extinguishes (a surface
detonation occurs). This happens, since there is almost no limit for
the power the mixture can supply. In electronics you can't have more
power in the oscillations than the power supply gives. This with the
losses keeps the intensity within definite limits.  With pyrotechnical
oscillators you have a very narrow area to operate in, unless:

Two: the burn rate is very likely to depend non-linearly of pressure.
If the dependence is linear, i.e. the pressure exponent is constant
over a wide pressure area, the whistle is not likely to work. This is
because it is not likely, that a mixture has a pressure exponent close
to one but not above, at least it is very difficult to find such
mixtures.  On the other hand, if the mixture has a pressure exponent
even over one at low pressures and the burn rate dependence becomes
smaller at high pressures, the situation is very favorable for steady
oscillations with a limited intensity. The sharpness of this change
would greatly affect the wave form the whistle gives - this may be the
reason, why different whistle mixtures give different sound.

The pressure at the burning surface rises sharply until the burn rate
no longer follows the pressure. As an underpressure wave is reflected
from the mouth of the resonant tube, it lowers the pressure at the
burning surface and the pressure-burn rate dependence (amplifier gain)
is returned to a value over 1,0 again. As the next pressure wave
arrives, the amplifier has been set to a high gain, the pressure wave
will collect more energy than it supplies and the process repeats
itself. This works like sort of an UJT oscillator - a very easy to
make oscillator but produces awful looking signal (definitely no sine
wave). Oscillographs of an pyrotechnical whistle greatly resemble that
of an UJT oscillator. An UJT has a non-linear gain just like the one
explained above.

>comps I've seen are a mixture of an oxidizer with an organic acid compound tha
>has a benzene ring and simple side groups, or its salt.  Benzoates, picrates,
>salicylates, gallic acid are all like this.

True. To give more evidence on my theory about the nonlinearity of the
pressure dependence: Lead and chromium salts of salicylic, benzoic,
phtalic, adipic and other carboxylic acids are used to lower the
pressure exponent of rocket propellants. All of these work at
different pressure areas, starting from 10..20 bar up to 300 bar.
They are particularly effective with smokeless powder and are being
used with it for rockets. This kind of powders have a high pressure
exponent at low pressures (even over 1,0) and the pressure
exponent drops continuously down to zero and even below, as the pressure
rises (plateau and mesa burning characteristics).

If this kind of powders are ignited at normal pressure, they very
often give off tremendously loud, high pitched and clear whistling
sounds. Also, cannon powders sometimes whistle, if burnt at
atmospheric pressure.  They, like all gunpowders, have a pressure
exponent very close to unity. At pressures slightly above atmospheric
it may be over that - the powders often crackle loud, as surface
detonations occur. If that happens, the grain will extinguish, until
another grain or other source of external heat ignites it again.

The reaction mechanism of the whistling composition may well be a two
phase reaction. Thus, the combustion would not be complete at once,
but yield an intermediate product. The primary reaction would then
have a low exponent of pressure, especially, if it is a solid or
liquid state reaction. If the secondary stage only would generate gas,
it only would be sensitive to changes in pressure. This kind of a
system would explain, why the exponent of pressure changes suddenly.
If the reaction rate of the intermediate exceeds that of the primary
reaction, the intermediate will soon be exhausted. As the
primary reaction generates no gas, it will not be any faster at a high
pressure than at a low. At low pressures, the limiting stage would be
the secondary one, leading to an accumulation of the intermediate.

So, at low pressure the system is "loading" itself and at high pressure
it gives off the energy, as the intermediate reacts.

Note, that all the whistling mixtures contain a metal salt of an
organic acid. This supports the theory of two phase reactions. The
first stage could be an intramolecular, exothermic decomposition or
even a rearrangement of the salt (no gases given off) and the second
stage the reaction between the oxidizer and the decomposition
products. Many carboxylic acid salt do indeed decompose exothermally.

>-Mike

ArNO
    2

From: ahahma@polaris.utu.fi (Arno Hahma)
Newsgroups: rec.pyrotechnics
Subject: Re: How do whistling compounds work?
Message-ID: <1991Dec10.090404.17472@polaris.utu.fi>
Date: 10 Dec 91 09:04:04 GMT

>itself. An oscillator has to have a positive feedback or the
>oscillations will die out. Everyone who knows electronics knows this.

To be more precise, the oscillator also has to have an amplification
more than 1,0. This is why the whistle has to have a pressure exponent
close to 1,0.

ArNO
    2

From: ahahma@polaris.utu.fi (Arno Hahma)
Newsgroups: rec.pyrotechnics
Subject: Re: How do whistling compounds work?
Message-ID: <1991Dec12.151802.12562@polaris.utu.fi>
Date: 12 Dec 91 15:18:02 GMT

In article <22810330@hpcvaac.cv.hp.com> billn@hpcvaac.cv.hp.com (bill nelson) writes:

>I assume you are talking about atmospheric pressure. If this is the case,
>then how can an explosion be propogated across an air gap? Is this due
>to high velocity particals from the initiating explosive?

A good point! This made me check my notes - indeed, I made an error here.
Bill, you should have noticed it ;-).

The relation is not 6 times the initial pressure but the initial
_DENSITY_. How did I not notice this even while replying the question
about it and stating the limit is due to heating of the gas? Also, I
wrote it inaccurately, the number is a ratio, not an absolute value.
That is, air can not be compressed more than about 6 times its initial
density by a shock wave. Such a compression naturally causes heating,
thus an increase in pressure.

Still, this does not change the situation much, the maximum reasonable
pressure for air at normal pressure is less than 100 bar (back of the
envelope calculation) for a density ratio of 5. Even this would heat
the air up to 5000+ K, so it would start dissociating. Thus, the
pressure jump is limited, although it really tends towards infinity,
as the density ratio tends towards (k + 2)/k(k - 1) (note: this may be
wrong, I don't have any references to check it now), k == polytropic
exponent of the matter, with gases the heat capacity ratio can be used
for rough evaluation. The exponent will grow, as the gas is heated,
thus, this approximation gives larger values than the actual limiting
density ratio.

For the question about the air gap, the explosion does not proceed
across it undisturbed. The acceptor charge actually undergoes a new
initiation sequence. The smaller the gap the faster this happens.
In fact, tiny bubbles may even accelerate the propagation of the
detonation. In this case the detonation will not be a wave front any
more, but also have depth.

The initiation of explosives is an area not well known, the theory
about air gaps or bubbles also leaves many questions. How does a
detonation develop if you don't have a shock initially? This is
another, unanswered question. Hypotheses exist, but none of them have
been verified, as far as I know.

This discussion has created more questions than it has answered and
the number of questions seems to increase faster than the number of
answers ;-).  I also got a lot of interesting and difficult questions
via e-mail. I try to answer as many as I can. No one actually _knows_
about this topic of discussion - so I may be wrong and you may be
right about it or vice versa, the point is on the word "may".

I'll be back later.

ArNO
    2

From: chem2149@waikato.ac.nz
Newsgroups: rec.pyrotechnics
Subject: Re: How do whistling compounds work?
Message-ID: <1991Dec13.163136.5873@waikato.ac.nz>
Date: 13 Dec 91 03:31:36 GMT

My feeling on the whistling process is that of a stop-start combustion.
When the whistle mix is ignited the layer begins to burn, the reaction zone
begins to deplete in one ingredient (oxidizer or fuel, this depends on which is
more easily decomposed). As the surface forms this layer the combustion process
slows down until the heat tranfer ignites the next layer. This process occurs
in the kHz range, which we hear as the whistle. I agree with Arno on the
pressure exponent of these compositions being very high, around 1.

As for a detonation type process, I dont like that one.  These whistle mixes
will detonate when confined lightly or ignited too strongly. When the
pressure/shock wave is high/strong enough the whole mix will detonate.
If not the mix will extinguish or continue burning.

I favour a combustion zone process over shock waves and detonation.

Any comments.

Dr Martin L. Van Tiel

From: ahahma@polaris.utu.fi (Arno Hahma)
Newsgroups: rec.pyrotechnics
Subject: Re: How do whistling compounds work?
Message-ID: <1991Dec13.110852.4348@polaris.utu.fi>
Date: 13 Dec 91 11:08:52 GMT

In article <1991Dec13.163136.5873@waikato.ac.nz> chem2149@waikato.ac.nz writes:

>My feeling on the whistling process is that of a stop-start combustion.
>When the whistle mix is ignited the layer begins to burn, the reaction zone
>begins to deplete in one ingredient (oxidizer or fuel, this depends on which is
>more easily decomposed). As the surface forms this layer the combustion process
>slows down until the heat tranfer ignites the next layer. This process occurs

>I favour a combustion zone process over shock waves and detonation.

This is exactly what I mean with the two phase reaction.

The whistle mix is an extreme example of a rocket fuel with a "cold"
fuel and "hot" oxidizer. The fuel decomposes very easily whereas the
oxidizer has a very high activation energy. Rocket propellants with a
similar composition (i.e. KP-propellants) tend to resonate and chuff
easily.  They also have a pressure exponent close to 1.

ArNO
    2

From: ahahma@polaris.utu.fi (Arno Hahma)
Newsgroups: rec.pyrotechnics
Subject: Re: How do whistling compounds work?
Message-ID: <1991Dec18.192208.12363@polaris.utu.fi>
Date: 18 Dec 91 19:22:08 GMT

Bill Nelson writes:

>Well, as you say, it is still being discussed. Wouldn't it be possible
>for a rarefaction zone, due to the reflected shock waves in the tube,
>to extinguish the detonation?

No. The pressure behind a shock front has no influence on
the shock, because the particle velocity is higher than the signal
velocity in this region (behind the C-J-plane, which is very close to
the shock front). The situation is just analogous to that of a
rocket nozzle, changing the outlet pressure has no influence on the
flow conditions in and before the throat. Detonation is a supersonic
flow (or analogous to it). If it is not supersonic, it is not a
detonation but a deflagration.

If the detonation travels towards the material, then the statement is
clear. If it travels away (very unlikely, since the initiation happens
at the surface) from it, then the rarefaction waves are already too
"late", they occur only as the detonation has already passed (i.e.
behind the shock front). This is because the detonation (assuming it
starts somewhere within the mixture) has to first pass through the
mixture before it can reflect anywhere in the tube.

This argument of yours would apply to a deflagration or combustion,
since they travel at subsonic speeds in any case.

>would not start out at the full propogation rate - most explosives
>start with a low order detonation that transitions to a high order
>detonation after a few microseconds delay.

True. Still, the low order detonation is travelling much faster than
sound in a gas.

>If the reflected rarefaction
>were traveling at the full detonation rate, then the detonation could
>be extinguished.

You mean the rarefaction would catch the detonation before it reaches
full velocity and quench it?  Reflected waves always travel at the
same or lower speed than the original one.  If the reflected wave
would accelerate, it should be gaining energy somehow. A rarefaction
wave is not going to do that.

>The main problem I see with the above is that I don't know if the
>initiating shock wave would slow down or weaken enough. I also wonder
>if the reflected rarefaction wave could be strong enough.

The initial shock would only be enhanced by any colliding shock
waves, since this would cause more energy to be transferred to the
reaction zone of the shock. The rarefaction wave (if such
interacted with the schock front) would have little influence. The
shock impedance would only be lowered by it, so the shock wave would
lose less energy for a while. On the other hand, it would also gain
less. As a result it might be dampened, but less than in a matter at
normal pressure and without any reactive species.

The absence of shock waves in the tube can also be seen, if you
measure the sonic output of a whistle. At a distance of 5 cm on the
side it may reach 130..140 dB. I can't remeber, what is the pressure
intensity for a 0 dB sound, it is very, very small anyhow. From this
you can calculate, what is the magnitude of the pressure differences
in the resonating tube. I am quite sure it is far from the intensities
of shock waves.

>>mixtures. The required shock wave typically (in the steady state
>>detonation) has a pressure more than 500 kilobar.

>Right. But I think you are considering the steady state condition of a
>material that is homogenous. The whistle compounds are heterogenous and
>will have a non uniform shock impedance. If we were talking about liquid
>explosives or single crystals, then I would agree without reservation.

Steady state, yes. It was easier to explain briefly than some
non-steady state condition.

For mixtures one can also calculate an average Hugoniot curve. You are
right that this can only handle the gross behaviour of the mixture, at
first sight. So, let's use the individual curves of the crystals in
the mixture. Still, for all these crystals the Rayleigh lines can not
switch from combustion to a detonation directly. However, the
necessary shock to initiate a detonation will be less than for a
homogeneous matter, since the individual curves will overlap. Also, the
forbidden region in the gross curve will probably involve conditions
on the individual ones.  This is the reason why heterogeneous
explosives detonate and transition into detonation easier than
homogeneous ones as long as the shock within a single crystal releases
energy.

In this case, it does not, except with picrate whistles (this is why
they are likely to detonate without warning, if they decide to do so
and the perchlorate mixtures may only crackle, if handled carelessly).
Since a shock within an individual crystal consumes energy instead of
releasing it, you have to combine enough of these to reach conditions,
where you start gaining energy, i.e. you can start using the gross
curve, which is a combination of the curves of the individual
crystals. In practice this means, that the detonation front has to
have at least as much depth as the particle size of the mixture. For a
100 mesh mixture this means about 0,2 mm.

How thick is the reacting zone in whistles, then? If the whistle
operates at 2500 Hz, it burns about 5 mm/s (K-benzoate/KP). Thus, for
one pulse only about 0,002 mm of the material is consumed.  That is
1/100 of the detonation front depth. Considering this, the detonation
is not a likely mechanism. Still, the particle size of 0,2 mm is small
enough for the whistle to work well.

>However, I have a few questions and some conjectures. I am sure it has
>been discussed somewhere before, but I have not run across it.

Neither have I, at least not about whistles.

>In a whistle compound, is it possible to have a condition where the
>shock wave is transmitted from a material with a higher shock impedance
>to a material with a lower shock impedance?

Of course. The mixture is very likely to contain voids, unless pressed
in an evacuated form and under a very high pressure.

>I would assume that the
>shock wave, entering the air gaps in the compound, would produce a
>rarefaction wave that would quench the existing explosive front. Is
>there enough air space in the whistling compound for this to occur.

There is probably enough air space for such rarefaction waves to
accur, at least within crystals. Also, similar rarefaction waves are
formed always, as the detonation passes through an interface. As
before, rarefaction waves in the gas phase are not likely to affect,
since their pressure can not go under zero and also, because such
waves always occur behind a detonation front. This can also be seen
from the conservation of momentum - there HAS to be such waves and the
flow direction also has to reverse at some point. On the other hand,
in a solid matter you can have "negative" pressures, if you also
consider the direction of the shock , the forces it induces and the
velocities of particles.

However, this is again of no significance.  If the crystal does not
take part into the reactions fast enough or if the reaction zone comes
far behind the shock, the the rarefaction and the shock itself can not
exit the crystal to go and suppress other shock waves (partly of
course, but the major part of it stays within the crystal). This is
simply because the shock impedances of a gas and a solid matter differ
too much (that is why the shock was reflected and a rarefaction
generated in the first place!).  The rarefaction reflects again and
another, weaker shock is generated, unless the crystal is already
turned into dust of high velocity towards to unreacted matter.  If the
crystal is reactive, i.e. the reaction zone follows within it, there
will be a gas phase rarefaction only. As before, this occurs behind
the shock front (the reaction zone lies there !) and has no influence.

The air spaces would actually have just the opposite effect you were
after: the detonation would only become easier. As the shock wave
compresses an air space (a small one) it is heated tremendously. As I
stated before, even a compression to a five fold density heats air up
to the dissociation temperature of the molecules. So, it is quite sure
such a temperature will induce new reactions. The gross detonation
velocity will be diminished, since the gross density is lower and thus
the gross initial conditions under the Hugoniot curve lie more to the
right. Also, the curve itself would be lower, if drawn on the same
scale as the curve of the void-free material.

>If it can, then the pressure of the transmitted wave is lower than when
>entered the explosive and the rarefaction wave would be away from the
>explosive towards the mouth of the tube. If the transmitted wave is not
>strong enough to sustain the detonation, then it would die out.

If the shock is strong enough to keep up a detonation even for a
little while, then it will compress the the air spaces in the matter
enough to initiate a new reaction zone and the shock would continue
there. The reflected wave is not likely to sustain detonation in any
case, since it is traveling away from the material. There is hardly
unreacted matter there.

>Another question - could the rarefaction wave, upon reaching the mouth of
>the tube and being reflected back toward the explosive, still have enough
>energy to trigger another explosion in the deflagrating compound?

For a gas phase detonation, unlikely, for a solid phase detonation,
definitely not. Even a gas phase _detonation_ will never reach
pressures high enough to trigger a solid phase detonation. If a
rarefaction wave reflects and causes a wave of condensation to form,
the condensation wave will be sonic, i.e. it is no longer a shock.
Also, it is travelling in a lower than normal pressure, that further
reduces the possible density and pressure difference. It also unlikely
to trigger even a gas phase detonation.

>If so, then you would have a series of explosions, each self extingushing
>because the transmitted shock wave was not strong enough to keep it going
>but the reflected rarefaction wave would reinitiate the explosion.

There is some contradiction in this, even if this could happen. If
the detonation starts at the surface, then it will be travelling
towards the composition, not away from it. Still, the transmitted
shock is travelling outwards? Also, if the stronger transmitted wave
can not sustain a detonation, how could a sonic wave reinitiate it then?

>There is another possibility - in some cases, shocks can be cumulative.
>In other words - one shock might not be enough, but all it would take
>to trigger the explosion in the shocked material is a small second shock.

Yes, this is possible, provided the shocks arrive within a few
microseconds or so. If not, the material will have time to cool down
and the next shock will have to "start from scratch". Of course, if
you had a very large number of shocks, this might be possible. But
then, as the material finally detonates, it would generate a very
strong shock wave compared to the triggering ones. The longer you have
to heat up the mixture the thicker layer of it is heated close to a
reaction temperature. Then, as the reaction starts, all of it reacts
at once. As a result, you'd have to use more shocks than you get.

>This second shock could be provided by the reflected wave from the mouth
>of the tube.  Now, the initial shock may only have penetrated into the
>compound a few molecules deep - due to the damping effect of the material.
>When those shocked crystals explode, they would "sensitize" another thin
>layer of crystals which would be initiated by the reflected wave - the
>process continuing in pulses.

This kind of a process would gradually lead to a full scale
detonation. If the weak, sonic pulse from the reflecting wave can
trigger a detonation or heat up material enough for the next pulse to
initiate it, then how about the much stronger detonation at the
surface? It causes a lot stronger shock, that would either consume all
of the available matter or sensitize a thicker layer than it used
itself. Thus, the reactive zone would become thicker and thicker until
the detonation has enough energy to blow the whole thing apart.

>The question here is - what causes the initial explosion? A superheated
>crystal fracture perhaps?

For example. Or in case of a surface detonation, you may have a
reaction with a high rate, activation energy and enthalpy. As the reaction
starts, it accelerates fast and transitions into a detonation.

>There is also the possibility that rarefaction waves from the walls of
>the container damp the explosion enough that to becomes to weak to be
>self-sustaining. As it dies, the rarefaction waves die and the deflagration
>could once again build back to a detonation.

The rarefaction waves would reach the surface only after the
detonation already has passed through it - too late. The deflagration
to detonation sequence is possible at the surface, but it would lead
to a more or less random bangs.

>Another possibility is the sensitivity of the explosive due to density.
>When an explosion occurs, the material is packed more densely. If the
>density becomes too high, the the explosion will quench - allowing the
>material to continue deflagration with consequent progression to
>detonation - the process being cyclical. This would be enhanced by the
>interstitial gases ahead of the exploding front (from the deflagration
>before detonation.

This is not likely, since in this would mean, that a weak shock would
initiate better than a strong one, that also causes a stronger
compression. The opposite is observed. If the density is low enough
for the detonation to occur, there will always be such a compression,
which in fact keeps the detonation going by heating the matter up to
its reaction temperature.  On the other hand, if the initial density
of the matter is higher than or very close to the density of the
reacted zone, the detonation will not occur at all.  In this case, it
can only propagate along the surface, in the gas phase above it.

Again, the Hugoniot curve gives a clue to this problem. If most of it
lies to the right or just above of the initial condition, it means the
density of the reacted zone is lower or the same than the initial
conditions. In this case, the whole curve is on the forbidden area,
where the Rayleigh line cannon go - i.e. the system does not detonate.
If the density is higher (the curve lies far enough to the left from
the initial conditions), then a full detonation is always possible.
There are no cases between these.

This is the situation with crackling twinklers. They are very dense
(made of minium and magnalium) so they can not detonate. As they burn,
the magnesium will react leaving highly porous aluminum and unreacted,
hot lead oxide as a layer on the surface. As this heats up to the
melting point of aluminum presumably, the layer detonates (it has a
low density and additionally, much small spaces). Since there is an
independent reaction going on deeper in the mass, where the detonation
cannot reach, the system will reignite after some time. The time only
is quite random, since the detonation will definitely do some damage
to the primary reaction zone also.

>>bar, i.e. a pressure difference over the shock wave front in air never
>>exceeds 6 bar. [6 times the density, with 5 times the density the
pressure is less than 100 bar and the temperature 5000+ K]

>I assume you are talking about atmospheric pressure. If this is the case,
>then how can an explosion be propogated across an air gap? Is this due
>to high velocity particals from the initiating explosive?

At atmospheric pressure, yes. But this is the condition with whistles,
the pressure in the tube is close to atmospheric. I just wanted to
show that a gas phase detonation can not couple with a solid phase
one directly. There is always a new initiation sequence.

<about the air gaps> If the explosive is insensitive enough or the air
gap is large, the reaction products of the detonation may reach the
explosive causing a new, high intensity shock, since their pressure is
still very high. In this case, you don't have a shock in air any more,
since you are adding extra gaseous material to the air gap. This also
limits the maximum temperature, since the very dense gases at the
shock front of the explosive will absorb any extra heat the
compression of the air causes. The detonation will transfer due to
high velocity particles, i.e. gas molecules from the donor charge.

If you place a disk on the donor charge, it will not compress air to
more than about 5 times its density and the pressure will also be less
than ~100 bar (maximum drag that air can induce). The pressure gradient
across the disk will be tremendous and it will probably break up very
fast. In this case the disk (of any heat resistant material) will hit
the acceptor charge and initiate it. Again, high velocity particles
cause the initiation.

The temperature at the disk front, where it compresses air will indeed
rise as high as the molecular dissociation limits it. This can be
easily verified. A bare charge of explosive hardly flashes, or if it
does, the flash is yellow to white in color and caused by the
combustion products. If you put a disk on the charge, it gives a very
intense, blue flash, exactly of the same color as an electric spark in
air.

If you take argon instead of air, you get much hotter, since argon is
monoatomic. Thus, it can only ionize or exite, if heated high enough.
Since the energies needed to this are far higher than those for
dissociation, the temperature will also reach very high values. If you
put a disk on a charge and detonate it in argon or even better,
helium, the flash will be extremely bright and most of the radiation
comes in ultraviolet region.

>>oscillations, even if they were shock waves, are not likely to trigger
>>a solid state detonation with a shock wave pressure of 500 kilobar.

>I am not sure I can agree here for a number of reasons. I don't think
>such pressures are necessary to initiate a gaseous detonation of the
>deflagration products. Correct me if I am wrong.

No. You are right, a gas phase detonation needs much less to happen,
depending on the gas mixture. Acetylene-oxygen, for example, will
detonate reliably with a blasting cap only.

>I seem to recall that the shock initiation threshold for TNT, one of the
>harder explosives to initate is somewhere around 50 kilobars for single
>crystals (as dense as you can get), but only about 10-20 kilobars for a
>density of 1 g/cc.

You are right (whether the values are correct, I don't know, I don't
have any gap test results with me), the initiation happens at much
less pressures than those at the steady state condition. I just wanted
to show the pressures in a gas phase and condensed phase differ with
several magnitudes.

>only describe the gross behavior of heterogenous explosives. They also
>assume that there is no chemical reaction at the front of the shock wave
>in the explosive - an assumption we cannot make with whistle compounds.

If such a reaction occured (it is quite common) it just causes the
detonation front to "rush" at that point. Air bubbles cause a similar
phenomenon. About the gross behaviour, see the beginning of the article.

>>If the whistle detonates, which is known to have happened, it is due to a

>Do they ever! Although I am not sure they are always high order detonations.

They are probably no high order detonations, since even flash powder
detonates with quite a low velocity, only about 2000..3000 m/s,
depending on confinement and initiation.  Whistles have detonated and
the whistle mix will do that, particularly as loose powder. In a
compacted state it might be very difficult.

>>with rocket fuels and colored stars. If a star hits ground while
>>burning, it often makes a small bang.

>I think some variation of this is what occurs with whistle compounds.

I don't, since the star and the rocket motor will extinguish or the
grain cracks => the rocket bursts, if that happens. Also, if the
sequence repeated itself (like with the crackling twinklers) it would
do so at irregular intervals.

>>But, if this happens, the detonation will sweep the along the burning
>>surface (a so called surface detonation) of the mixture and shake the
>>reacting zone off.  The reacting zone is a region with molten, partly

>But, what if the rarefaction waves from the wall prevent the complete
>removal of the reaction zone?  In other words, the surface deflagrates
>and progresses to detonation at the center of the surface. It progresses
>towards the edge of the material until the rarefaction wave prevents
>further initiation outward. The reacting zone is swept off the surface,
>but the deflagrating edges are still reacting to reignite the center.

Again, the rarefaction arrives far too late. The detonation will
definitely go faster at the surface than in the gas space further
above it. This is because it gains energy on the surface but not in
the gas far enough from it. If the detonation traveled slower at the
surface than in the gas phase, then the detonation would travel
exactly at the velocity in the gas phase. This is simply because it
would then travel there and the detonation at the surface would
be overdriven to this speed. Still, the detonation will arrive at the
edges before any rarefaction wave, since these rarefaction waves
travel at the same or less velocity. Also, the density of the reacting
zone is higher than that of the gas above it => faster detonation.
Thus, for many reasons there is no chance for a rarefaction wave to
reach the edges before or even at the same time as the detonation.

>>sensitive in order to whistle. Smokeless powder whistles louder than
>>any pyrotechnical whistle under proper conditions.

>Smokeless powders can also detonate under the proper conditions. I don't
>know if they can when they are used for whistles.

Yes, if it is porous, like pistol and shotgun powders. Or contains
enough nitroglycerine. However, these don't whistle, they are
_powders_. Large grains of powder, such as cannon powder or rocket
grains do whistle, often actually. They also do not usually detonate
even if tried with a large pile of TNT. Also, double base powders
resonate easier than single base, which in turn tend to crackle
easier. This is just an observation about what I have seen. As a side
note, it is quite a sight, when a few ten (metric) tons of old cannon
powder is being destroyed by burning it ;-).

>>One: the pressure exponent of the mixture has to be close to unity.
>>Two: the burn rate is very likely to depend non-linearly of pressure.

>Why couldn't the same be true for detonations at the surface of the
>mixture?

Since a detonation would consume everything at the surface and
slightly more ;-).  Only if the frequency of the reactions is slow
enough to allow enough heat to be transferred deeper into the material
and if the material is strong enough to withstand the mechanical
effects of the detonation, the detonations could repeat.  Whistle
mixtures do not fill either of these requirements. Also, the thermal
conductivity of whistle mixtures is not very good.

>Well, using Ockham's well known razor, your explanation should be the
>correct one.

What is that? Some kind of a general rule perhaps?

>>it may be over that - the powders often crackle loud, as surface
>>detonations occur. If that happens, the grain will extinguish, until
>>another grain or other source of external heat ignites it again.

>I've never had enough powder to try that. Doubt if I ever will.

The amount is not critical but the composition is. Handgun and
"civilian" powders are not likely to whistle or crackle, even if the
grains were larger. This is because they are made to be safer, i.e.
their pressure exponent is usually less than 0,8. Many military
powders have the exponent very close to 1, since that is the optimal
value you should aim at for a gun powder. Go over it and you have
trouble... With a cannon, you really want every m/s you can get.

>>So, at low pressure the system is "loading" itself and at high pressure
>>it gives off the energy, as the intermediate reacts.

>Same could happen with explosions. :-)

Possibly, but not because of them. That is, a detonation would tend to
stop this kind of an oscillating reaction rather than supporting it.

>How refreshing to be discussing practical pyrotechnics for a change, even
>if it is the theory behind why something works.

Practical? Well, this was quite theoretic, I think ;-).

>Thanks for responding to this thread Arno. I am looking forward to your
>response.

You're welcome! I would like to say the same about your response.
I am waiting to see more criticism and comments.

Next time, I think we should cut this long articles into a few smaller
ones. I'll try to avoid writing this large articles any more, who is
going to read them anyway ;-).

>Bill

ArNO
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