How fast does a blastwave travel?

[Baluncore]

Since the wave started as a sudden increase across micrometres, does it remain such a sudden increase no matter how weak it gets? Or does it eventually spread out, and then how?

The explosion generates the heat and pressure. But once propagating outside the fireball, the shock front heat comes only from the pressure step. The shock front "self maintains" a step function until the temperature is attenuated sufficiently to approach the ambient speed of sound. The shock step then ceases to exist, as it becomes a gentle ramp.

A positive pressure step can become a self maintaining shock front. A negative pressure step cannot, it must always become a more gentle ramp as the speed of sound is falling.

 

[Baluncore]

As we have discussed on this thread, when the observer is close to an lightning strike, the sound is a crack. Further away, it becomes a rumble. I suspect the abrupt energy increase at the shock front becomes less and less sharp as the wave propagates outwards.

As the shock front propagates outwards, the energy density is falling continuously, and the step is reduced in amplitude over time. The virtually instant rise time of the step however, is maintained by the positive temperature step, so long as the wave remains a shock front.

The P and T step remains virtually instant and self-maintains that step, until the shock front slows to the speed of sound in ambient air. Only then does the step collapse into a sound wave ramp. If you are in the area covered by the shock step, you will hear only a click or a single crack as it passes.

If you examine Kinney and Graham, table XI, you will see the velocity of the shock front progressively falls to 343 m/s. The shock front step obviously ceases to exist at the end of that table.

In the atmosphere, high frequency sound is attenuated much more rapidly than low frequency sound. That is why distant thunder does not crack, it rumbles.

 

[snorkack]

As the shock front propagates outwards, the energy density is falling continuously, and the step is reduced in amplitude over time. The virtually instant rise time of the step however, is maintained by the positive temperature step, so long as the wave remains a shock front.

The P and T step remains virtually instant and self-maintains that step, until the shock front slows to the speed of sound in ambient air. Only then does the step collapse into a sound wave ramp.

But my point is that it should be impossible for the step to collapse, ever. Because so long as there is any wave at all, as long as there is any nonzero ΔP, then the wave crest should be travelling faster than the wave foot. When the sound gets weak and ΔP is small compared to total P then the speed of wave crest should approach that of wave foot, but not become lower. Since the wave starts as a steep step, it should remain a steep step. Collapsing a step into ramp would require the crest to travel slower than foot.

If you are in the area covered by the shock step, you will hear only a click or a single crack as it passes.

If you examine Kinney and Graham, table XI, you will see the velocity of the shock front progressively falls to 343 m/s. The shock front step obviously ceases to exist at the end of that table.

In the atmosphere, high frequency sound is attenuated much more rapidly than low frequency sound. That is why distant thunder does not crack, it rumbles.

Attenuation view gets an opposite result, yes. Since a steep step can be expressed as a sum of high frequency components, attenuating away these high frequency components should collapse step into ramp. The paradox here is that this model, reasonable taken alone, clashes with the model of speed/amplitude relations, which predicts no collapse. So how can a broken wave collapse?

 

[Baluncore]

Because so long as there is any wave at all, as long as there is any nonzero ΔP, then the wave crest should be travelling faster than the wave foot. When the sound gets weak and ΔP is small compared to total P then the speed of wave crest should approach that of wave foot, but not become lower.

We do not concern ourselves with the distortion of low energy audio waves in the atmosphere. An audio wave is different to a shock front. We assume an audio wave does not significantly change the air temperature as it passes. The shock front is assumed to have a temperature step sufficient to maintain that step. There will come a point where you must change your assumptions and terminology, where the shock front becomes an acoustic wave. You cannot extrapolate wave profile or behaviour across that transition.

The shock front step is a high frequency step, so it is attenuated by both the inverse square law, and by acoustic dispersion. So long as it has a sufficient temperature step, it will maintain that step.

The paradox here is that this model, reasonable taken alone, clashes with the model of speed/amplitude relations, which predicts no collapse. So how can a broken wave collapse?

The step collapses and begins to transform into a ramp, when the temperature step becomes insufficient to maintain that step. Based on our assumptions, that is when the shock front ceases, and the audio sound wave begins.

 

[snorkack]

We do not concern ourselves with the distortion of low energy audio waves in the atmosphere. An audio wave is different to a shock front. We assume an audio wave does not significantly change the air temperature as it passes. The shock front is assumed to have a temperature step sufficient to maintain that step. There will come a point where you must change your assumptions and terminology, where the shock front becomes an acoustic wave. You cannot extrapolate wave profile or behaviour across that transition.

The shock front step is a high frequency step, so it is attenuated by both the inverse square law, and by acoustic dispersion. So long as it has a sufficient temperature step, it will maintain that step. The step collapses and begins to transform into a ramp, when the temperature step becomes insufficient to maintain that step. Based on our assumptions, that is when the shock front ceases, and the audio sound wave begins.

But the thing is, wave profile and behaviour must be continuous across the transition, at least the lower derivatives. Both effects - self-sharpening due to amplitude dependent velocity and spreading due to preferential attenuation of high frequency - must be present on both sides of transition. So how do you analyze the balance of the two effects to predict exactly when the step collapses. What is the minimum temperature step for the shockwave to stay a step?

 

[Baluncore]

So how do you analyze the balance of the two effects to predict exactly when the step collapses. What is the minimum temperature step for the shockwave to stay a step?

You do not have to be exact. One model ends, another begins, wherever.
If it steps like a shock front, it is a shock front. Everything else is noise.

 

[Baluncore]

Both effects - self-sharpening due to amplitude dependent velocity and spreading due to preferential attenuation of high frequency - must be present on both sides of transition.

No. Self-sharpening due to temperature step dependent velocity is assumed to be absent in audio sound waves.

You have introduced a new term Spreading due to attenuation of high frequency; which suggests audio phase dispersion, which is present in acoustic waves.
https://en.wikipedia.org/wiki/Acoustic_attenuation

A shock front is not 100% efficient. Some energy is left behind, to become part of the following blast wave. That represents a loss of energy from the shock front, which reduces the step height, but not the step duration, as that is maintained by the temperature step while it continues to propagate.

It is the presence of a PT step that defines the presence of a shock front. That is fundamental to this discussion and cannot be denied, without departure from the observed reality.

 

[Squizzie]

Folks, can we take a pause and remind ourselves that unlike a water wave or the vibrations in a string, a pressure wave is a transverse wave and not a longitudinal wave. In a longitudinal wave the dimensions of wavelength and amplitude are the same: distance. In a transverse wave, like sound, they are different: distance and pressure respectively.
Whilst many analogies between the two are valid, not all are.

 

[Baluncore]

Folks, can we take a pause and remind ourselves that unlike a water wave or the vibrations in a string, a pressure wave is a transverse wave and not a longitudinal wave. In a longitudinal wave the dimensions of wavelength and amplitude are the same: distance. In a transverse wave, like sound, they are different: distance and pressure respectively.
Whilst many analogies between the two are valid, not all are.

I think you have that backwards.
A longitudinal wave is one where all the particles of the medium (such as gas, liquid or solid) vibrate in the same direction as the wave. Sound waves are longitudinal waves. When longitudinal waves travel through any given medium, they also include compressions and rarefactions.
Transverse waves do not travel through a gas.

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

Thread is reopened provisionally to see if OP @Squizzie understands the correction.

 

[Squizzie]

Thread is reopened provisionally to see if OP @Squizzie understands the correction.

Yes, I stand corrected. I had the terms backwards. The waves in water and a taut string are indeed transverse waves.
Sound waves through a solid, liquid or gas are longitudinal waves.
My apologies for the confusion and thank you for the opportunity to keep the thread active.
I have not heard back from Dr. Rigby on my request for clarification of his use of "particle velocity" in his explanation for the negative phase of the blast wave.

 

[Squizzie]

Here is a sloppy proof for a spherical sound wave, but it should give you the idea.
u is particle velocity,

Do you mean molecule velocity?

 

[Baluncore]

Do not mix your gas models. You must analyse the gas using statistical mechanics, or fluid mechanics.

Do you mean molecule velocity?

A "particle" of a fluid refers to a small volume, or parcel of the fluid, not to the statistical molecules that make up the fluid.

Your follow-up question to Dr. Rigby mixed the fields, which makes your question too complex to answer simply.

Please stay away from the statistical mechanics of molecules, while discussing the fluid dynamics of pressure waves. If you mix the statistical-micro-internal model, with the fluid-macro-external model, you will confuse yourself, and confuse the issue.

 

[Squizzie]

No, particle velocity. A sound wave moves at velocity c. It gives the air a particle velocity u at the continuum level.

Yes, a sound wave moves at velocity c, and that velocity is relative to an inertial frame of reference in which the medium is stationary.

Despite molecular theory and statistical mechanics establishing that the molecules are moving randomly at a mean speed of around Mach 1, with a mean free path of around 50 nm, the medium is considered to be stationary
In that frame of reference, air is considered as a continuum in which, to quote Gupta[1],
"This is called the continuum concept, that is, the matter is uniformly and continuously distributed and not made up of pebble-like molecules followed with space. "

There are clearly two realms in which the properties of gas, like air, can be studied: the thermodynamic, or "macroscopic" realm in which the gas behaves as a continuum and is described in terms of pressure, temperature, and density, and the molecular realm, in which it behaves like a collection of molecules and is described in terms of velocity, momentum, size and mean free path.

The two realms appear to be distinguished the size of the system under discussion relative to the mean free path of the molecules.
In the thermodynamic realm there is no useful concept of particles.
In molecular theory, the only particles are molecules. Therefore the use of particle velocity is not useful in the discussion of the velocity of sound waves in air.

In neither realm does it contain particles that are not molecules, so I am not sure in which context the term "particle velocity" is being used in the context of sound waves in air.

[1] Gupta S. C., (2011) Thermodynamics, Dorling Kindersley (India) Pvt. Ltd. p. 4

 

[Squizzie]

Your follow-up question to Dr. Rigby mixed the fields, which makes your question too complex to answer simply.

Yes I agree, but it was not me, but Dr. Rigby who appears to have mixed the fields by including "particle velocity" and "pressure" in the explanation.
I find it confusing, which is why I asked for clarification

 

[Baluncore]

Yes I agree, but it was not me, but Dr. Rigby who appears to have mixed the fields by including "particle velocity" and "pressure" in the explanation.

Dr. Rigby wrote: ..."The positive phase imparts a forwards particle velocity to the air. Pressure and particle velocity are two sides of the same coin, you can't have one without the other, so if a pressure is acting it is also moving the particles." ...

I believe you misinterpreted the term "particle" in the reply to mean "molecule", rather than "parcel". In doing that, you were confused by the answer, as it then mixed the models.

 

[Squizzie]

I believe you misinterpreted the term "particle" in the reply to mean "molecule", rather than "parcel". In doing that, you were confused by the answer, as it then mixed the models.

Nope, Dr Rigby used "particle" four times in his response. Here's a marked-up image of his email:

That's not me having "misinterpreted" him.
I suggested to him that the association with molecule would be incorrect.
I have not received further explanation of his use of the term molecule.

 

[Baluncore]

I suggested to him that the association with molecule would be incorrect.
I have not received further explanation of his use of the term molecule.

I do not see him use the term "molecule" anywhere in his reply. I think you are imagining it. That suggests that you have fixated in your head, that the term "particle" must, and can only mean, "molecule".

A large population, or a parcel of molecules, is one particle of fluid.

 

[Squizzie]

I suggested to him that the association with molecule would be incorrect.
I have not received further explanation of his use of the term molecule.

I have just noticed the error in my final sentence of post #160:

I have not received further explanation of his use of the term molecule

He didn't mention molecule. I didn't request clarification from him about the use of molecule - see my post #40:
"May I ask for clarification on your use of particle velocity please?"
The sentence should have read:
I have no received further explanation of his use of the term "particle".
That would explain the sceptical emojis from @weirdoguy and @Motore

 

[Drakkith]

I have replied:
"May I ask for clarification on your use of particle velocity please?
If you are referring to individual molecules as particles, then my understanding is that, according to statistical mechanics, the molecules are individually moving in random directions at a mean speed of around Mach 1, and that the pressure in the blast wave is being transmitted by the molecules imparting momentum to their neighbours through their collisions over the distance of the few nanometers of their mean free path. That is, the individual molecules don't travel any significant distances in the direction of the blast front, rather it is the transient concentration of these molecules that is the pressure wave that travels out from the blast centre."

Instead of a chemical explosion, imagine a spherical 'piston' that expands a short distance very rapidly, say at mach 5, pushing air out of the way and creating a spherical blast wave. There MUST be some way for this volume of displaced air to move outwards and dissipate into the rest of the air. This requires that some net molecular displacement occur. In other words, the average molecule MUST move some distance, perhaps a significant amount, away from the origin of the blast wave. This must occur not only near the piston's surface, but also much further away if the entire volume is to return to ambient pressure.

This would seem to imply that an outwards inertial effect exists, as there must be a net outwards molecules velocity (or else how could we have a net flow outwards to dissipate the high-density gas), resulting in an rarefaction and a negative phase to the pressure as the outwards moving gas has to be stopped and then compressed back to mean atmospheric pressure.

There is virtually no change with a chemical explosion. The rapid vaporization and combustion generates a high-pressure, high-temperature region that pushes outwards, just like the piston.

 

[Squizzie]

Instead of a chemical explosion, imagine a spherical 'piston' that expands a short distance very rapidly, say at mach 5, pushing air out of the way and creating a spherical blast wave.

Whilst there clearly are similarities between explosions and other methods of creating pressure waves, discussions about the differences can often lead to endless debates that do not apply to the subject at hand: explosive blast waves. At the risk of introducing one, the elephant in the room for me is that an explosion converts a very small volume of solid explosive into a massive volume of gas.
Please, may I request we stay on topic?

 

[Drakkith]

Whilst there clearly are similarities between explosions and other methods of creating pressure waves, discussions about the differences can often lead to endless debates that do not apply to the subject at hand: explosive blast waves. At the risk of introducing one, the elephant in the room for me is that an explosion converts a very small volume of solid explosive into a massive volume of gas.
Please, may I request we stay on topic?

It is on topic. The topic of this thread is not about the initiation of the blast wave, but how it propagates. It matters not whether it is generated mechanically, chemically, or thermally. I chose a slightly simpler example to minimize the number of factors to consider when illustrating my point.

At the risk of introducing one, the elephant in the room for me is that an explosion converts a very small volume of solid explosive into a massive volume of gas.

What about it?

 

[Squizzie]

It matters not whether it is generated mechanically, chemically, or thermally.

You may be right, you may be wrong, but don't you see that a discussion on this opens a further detour from the present subject which is the source of the negative phase of a blastwave, which is generally accepted to have been generated by a chemical or nuclear reaction?

 

[Baluncore]

At the risk of introducing one, the elephant in the room for me is that an explosion converts a very small volume of solid explosive into a massive volume of gas.

And that gas is very hot and expanded like a fireball. At first, it pushes air away from the site of the explosion, then the combustion products of the explosive cool and condense, and the air comes flowing back in.

 

[Squizzie]

And that gas is very hot and expanded like a fireball. At first, it pushes air away from the site of the explosion, then the combustion products of the explosive cool and condense, and the air comes flowing back in.

Are you offering this as a complete explanation for the source of the negative overpressure?

 

[Baluncore]

Are you offering this as a complete explanation for the source of the negative overpressure?

No. Just the part played by the fireball seen in the video of big explosions.

 

[snorkack]

I think that we could return to the example of squib load.
Yes, as you pointed out, if the bullet is stuck at the breech and the explosive load is normal then the pressure at the chamber will be above the normal live load pressure, which may result in barrel burst.
However, consider a squib which is a squib because it has abnormally small amount of explosive, but still some explosive. For example a cartridge that has just primer but no powder.

When the bullet is stuck at the breech and the explosion is not strong enough to either dislodge the bullet or burst the barrel, there will be no negative phase. Because the overpressure in the chamber will be released by slowly leaking out of the windage. Not enough inertia to produce overshoot and underpressure.
When the bullet slides freely but the explosion is too small to fill the length of the barrel, the bullet will travel partway along the barrel, and then continue travelling by inertia while underpressure is left behind. So the bullet is sucked back.

If the explosive load is sufficient then the smoke in the barrel is still under overpressure when the bullet exits the muzzle, and smoke will continue to exit the muzzle as a muzzle blast. But the inertia of muzzle blast will cause the smoke to overshoot, leading to underpressure in the barrel, after which air is sucked back into the barrel. This is demonstrated in that when a target is near the muzzle, pieces of target are sucked into the barrel, such as blood and pieces of brain.

 

[Squizzie]

I think that we could return to the example of squib load.

At the risk of repetition, can we keep to the topic: blastwaves?

 

[Squizzie]

No. Just the part played by the fireball seen in the video of big explosions.

I'm pretty sure that the condensation cloud does not appear until the blastwave has cleared the fireball.