How fast does a blastwave travel?

[Baluncore]

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.

You are ignoring the rise in temperature of the air due to the shock front pressure rise. The speed of sound in hot air is greater than in ambient air. So the average speed of the molecules in the shock front is supersonic, >M1.
Indeed, all shock fronts that arise from an explosion are supersonic.
See: Kinney and Graham; Equation 4-34 .

 

[Squizzie]

You are ignoring the rise in temperature of the air due to the shock front pressure rise.

But isn't it the drop in temperature to below the dew point (and below ambient) in the negative phase that causes the condensation?

 

[Baluncore]

But isn't it the drop in temperature to below the dew point (and below ambient) in the negative phase that causes the condensation?

That does not happen at, nor in, the shock front.
After the explosion, the outward momentum of the shock front, and the blast wave, have removed most of the combustion products and air from the site of the explosion. That volume is cooling and contracting to create the partial vacuum with condensation. The speed of the condensation wave front is slower than M1 because the front is hotter than the rear, which makes a ramp, not a step.

The blast wave will reverse at some point, flowing back in to fill the condensing gas and the partial vacuum that also causes. The wave that flows back in may again develop a step shock front, since it raises the pressure and temperature again at the site of the original explosion. That second wave is closer to ambient pressure and temperature, so the speed does not rise anywhere near the original explosive shock front.

Do not mix your viewpoints. You must decide to observe and discuss the shock front from a fixed position relative to the explosion, or travelling with the front itself, from the point of the greatest pressure step.

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

Do not forget that a rise in pressure, causes a rise in temperature, which causes the speed of sound to increase, which steepens the pressure step of a shock front.

 

[Squizzie]

That does not happen at, nor in, the shock front.

Correct, and I am not suggesting that it does. Recall fig 6-32 from Kinney:

The negative phase ("-")is behind the positive phase (+) which commences at the instantaneous shock front at time t_a.

 

[Baluncore]

... , according to statistical mechanics, the molecules are individually moving in random directions at a mean speed of around Mach 1, ...

That is a truism. I wonder what you really mean there by Mach 1.
The mean speed is temperature dependent.

The speed of sound at any temperature is Mach 1. If a vehicle travels at twice the (temperature dependent) speed of sound, it is doing Mach 2.

Indeed, I would argue that every pressure disturbance travels through the air at Mach 1, the speed of sound, corrected for the immediate local temperature.

A shock front travels at the speed of sound at its peak absolute temperature. That temperature is greater than the ambient atmosphere it propagates through, or it would not remain as an almost instant shock-step.

We need to restrict the use of the Mach scale to objects moving through a fluid, and avoid the use of Mach 1 to mean the speed of sound at STP.

 

[Squizzie]

I wonder what you really mean there by Mach 1.

I am using Mach 1 in its standard physics context: the speed of sound in the medium that is under discussion. In air at STP, the speed is around 340 m/s. At different temp's and pressures, and in different gases, it's different. And, for the purpose of this thread, I would like the discussion to address gases in particular, not fluids in general.
I assure you I am not re-defining the Mach scale.

 

[Baluncore]

I assure you I am not re-defining the Mach scale.

Every pressure disturbance must propagate at Mach 1, so why do you need to use the dimensionless term "Mach" anywhere in this discussion.

 

[snorkack]

You are ignoring the rise in temperature of the air due to the shock front pressure rise. The speed of sound in hot air is greater than in ambient air. So the average speed of the molecules in the shock front is supersonic, >M1.
Indeed, all shock fronts that arise from an explosion are supersonic.
See: Kinney and Graham; Equation 4-34 .

Does the shock front ever become subsonic? If yes, how?
It is clear how the bullet becomes subsonic. It is actually moving its bulk relative to air and experiencing drag even when subsonic. A bullet that moved at 400 m/s and has decelerated to 350 m/s will go on experiencing drag to decelerate to 340 m/s, then 330 m/s, 300 m/s, 30 m/s et cetera. The drag decreases but it does not jump to zero at nonzero speed.
But the muzzle blast?
If the ambient air ahead of the bang is at 101 325 Pa and the muzzle blast is at 201 325 Pa, rather hotter and supporting higher sound speed behind the shock than ahead, the shock peak clearly catches up with the shock front, and the pressure jumps over air molecule free path (micrometres?).
But when the muzzle blast spreads out, the pressure drops. The sound speed behind the shock front decreases as the pressure in the peak decreases - from 440 m/s to 350 m/s to 341 m/s to 340,01 m/s - but it still remains higher or equal than the sound speed ahead of the front. 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?

 

[Squizzie]

Every pressure disturbance must propagate at Mach 1

Not only pressure disturbance, but density and conduction temperature disturbances as well.
I suspect the reason that blast waves move faster than Mach 1 (of the ambient air) in the milliseconds immediately after the detonation could be due to local heating of the air due to the radiant heat (infra red) from the explosion raising the air temperature and thus the speed of sound in the immediate vicinity.

 

[Squizzie]

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?

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.
The Fourier analysis of a sharp wave form (square , triangle etc) reveals a lot of high frequency signals are required to maintain the sharpness. I suspect those high frequencies decay more quickly over time and distance than the low frequency ones, which would tend to smooth out the wave form. And of course the energy of the wave diminishes due not just to the square root of the distance, but also the absorption of the energy by the stuff in its way.

 

[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.