How fast does a blastwave travel?

[Squizzie]

Source of the low pressure seems intuitively obvious to me.
When a bomb is initially exploded, the whole explosive turns into high pressure but stationary gas. No low pressure yet.
Then the exploded smoke and the surrounding air are accelerated outwards.
But as the explosion products and air have completed acceleration, at some point the explosive fragments and air in front are all travelling outwards at some speed... with inertia.
And that inertia means that the outward movement cannot instantly stop when the initial overpressure has been relaxed. So a lowered pressure region must form as everything around is travelling out by inertia.

This may well be the case, and I'm not saying you are wrong, but are you able to support it with some published studies?

 

[Baluncore]

This may well be the case, and I'm not saying you are wrong, but are you able to support it with some published studies?

The partial vacuum that follows an explosion is well known and accepted. It is, in effect, a simple harmonic motion, like ripples in a pond.

Fuel-air bombs, vacuum bombs, and thermobaric weapons, deliberately fill the vacuum with an air-fuel mix, that is then ignited as a second, more powerful explosion.

W. E. Baker. Blast Pressure Effects: An Overview
https://pubs.acs.org/doi/pdf/10.1021/bk-1987-0345.ch001

 

[Squizzie]

Source of the low pressure seems intuitively obvious to me.
When a bomb is initially exploded, the whole explosive turns into high pressure but stationary gas. No low pressure yet.
Then the exploded smoke and the surrounding air are accelerated outwards.
But as the explosion products and air have completed acceleration, at some point the explosive fragments and air in front are all travelling outwards at some speed... with inertia.
And that inertia means that the outward movement cannot instantly stop when the initial overpressure has been relaxed. So a lowered pressure region must form as everything around is travelling out by inertia.

I am working through https://apps.dtic.mil/sti/tr/pdf/ADA384954.pdf and came across this by John Von Neumann p. 27,:
"As the pressure wave expands spherically through the atmosphere it is diluted over spherical shells of ever-increasing radii, and hence its intensity (the density of energy, and with it the over- pressure) decreases continuously also. This pressure wave is known (both theoretically and experimentally) to consist at all times of a discontinuous shock wave at the head, and to weaken gradually as one goes backward from that head."
Note: "weaken gradually", not reduce to below atmospheric pressure before returning to Atm.
I suspect he would find the "negative overpressure" counterintuitive

 

[Baluncore]

I am working through https://apps.dtic.mil/sti/tr/pdf/ADA384954.pdf and came across this by John Von Neumann p. 27,:
"As the pressure wave expands spherically through the atmosphere it is diluted over spherical shells of ever-increasing radii, and hence its intensity (the density of energy, and with it the over- pressure) decreases continuously also. This pressure wave is known (both theoretically and experimentally) to consist at all times of a discontinuous shock wave at the head, and to weaken gradually as one goes backward from that head."
Note: "weaken gradually", not reduce to below atmospheric pressure.
I suspect he would find the "negative overpressure" counterintuitive

You are butchering the science.
It is not your place to put thoughts into the mind of someone who's intelligence far exceeds yours.
https://en.wikipedia.org/wiki/Dunning–Kruger_effect

 

[renormalize]

I am working through https://apps.dtic.mil/sti/tr/pdf/ADA384954.pdf and came across this by John Von Neumann p. 27,:
"As the pressure wave expands spherically through the atmosphere it is diluted over spherical shells of ever-increasing radii, and hence its intensity (the density of energy, and with it the over- pressure) decreases continuously also. This pressure wave is known (both theoretically and experimentally) to consist at all times of a discontinuous shock wave at the head, and to weaken gradually as one goes backward from that head."
Note: "weaken gradually", not reduce to below atmospheric pressure before returning to Atm.
I suspect he would find the "negative overpressure" counterintuitive

How much did you bother to even read of this Los Alamos report? Are you making an honest enquiry or just cherry-picking quotes that you think support your position?
From that report's chapter 1 by Hans Bethe, regarding numerical simulations of the Trinity blast wave, he states on pg. 15:

A representative graph from chapter 6 by Klaus Fuchs (!!!):

Will you continue to question the existence of a low-pressure region behind a blast-wave shock?

 

[bdrobin519]

When I said the "detonation front", I was referring to the C4 detonation, not the bullet. At 8:09 they display the speed of the explosion at 3326 m/s , that's around Mach 10 in air at STP, and the speed of the bullet at 387 m/s , which is Mach 1.1

I don't have the energy to produce the numerical explanation through calculations right now however this is complicit with supersonic principles. C4 is used for the rapid vaporization from solid to gas. The ratio from mass to gas I'm sure is drastic compared to other thermal expansions, thus reaching a plasma state while expanding against surroundings. However the fact it goes almost straight from solid to gas means the surrounding environment ( via. Earth atmosphere) resists exponentially when displaced. Matter displacing Earth's troposphere to the tenth degree while vaporizing from a solid state in any time frame has to eventually be absorbed by the surrounding media and is eventually restricted to their relativity. I'm comparing this to the same way a jet undergoes thermal and kinetic stress after piercing the sound barrier.

Thank you for any insights,

Just hoping to learn from people willing to discuss.

Thank you.

 

[renormalize]

However the fact it goes almost straight from solid to gas means the surrounding environment ( via. Earth atmosphere) resists exponentially when displaced. Matter displacing Earth's troposphere to the tenth degree while vaporizing from a solid state in any time frame has to eventually be absorbed by the surrounding media and is eventually restricted to their relativity.

For us slow learners, is it possible to re-express these statements more clearly, preferably in terms of some equations?

 

[Squizzie]

Will you continue to question the existence of a low-pressure region behind a blast-wave shock?

Please, read my post #44.
I am not questioning the existence of the low pressure region. I know it's there. The Wilson cloud in the Beirut video, the texts by Glasston, Kinney and the technical reports from Los Alamos all describe it.
It exists.
Can I encourage your to read my post #44 to understand what it is that I am looking for?

 

[Baluncore]

Can I encourage your to read my post #44 to understand what it is that I am looking for?

From post #44, we see you refuse to accept earlier language, until you have dragged the member trying to help you, through every possible misinterpretation of a text. That is the behaviour of a troll.

In post #108, you quoted John Von Neumann, who was following the "maximum damage" peak pressure as the radius increased. You then twisted that to claim his statement referred to a time series passing a fixed radius. If you will not accept a text, without throwing a tantrum, there can be no hope for this thread. You are wasting too much of our time by playing the part of a troll.

 

[Squizzie]

What dissatisfies you with Kinney‘s description?

Thank you for your research, I had missed that section. We appear to be working from different editions. Mine is Second Edition, and handles the material slightly differently. Your copy has:
"It can be noted that the inertial effects responsible for the negative phase could give rise to additional pressure reversals an to pressure oscillations in the atmosphere. Such reversals are important in underwater explosions, but not ordinarily observed or reported in explosions in air..."

In my copy the reference to inertial effects is slightly more developed :
p. 90:
"On further expansion inertial effects produce overexpansion and a consequent rarefaction at the explosion center."
The reference to oscillations in underwater explosions appears 12 lines further down the page.

It is the physics of these "inertial effects" and the idea that there is a "rarefaction at the explosion centre" which bothers me.
[EDIT] and, at the risk of repetition, I am not denying the existence of the negative phase, I am curious as to its cause.

 

[Squizzie]

Why?

For me, and my acquaintances, the appearance of the cloud, and its formation due to a low pressure region behind the shock front is counterintuitive. We would expect the overpressure behind the shock to decay asymptotically to zero, not, as we now know, to below zero before then rising asymptotically back up to zero.
The literature describes the phenomenon but only in the case of Kinney and Graham (that I can find), is any cause of this negative overpressure provided, and that is in very general terms of "inertial effects".
Contributors to this thread have offered various theories, but none of these appear to be based on what PF refers to as "acceptable sources".
That bothers me.

 

[Squizzie]

Look at page 149-150 of Blast Wave.

Well spotted. I will see if I can get my head around Chapter 5. I do note your reference at the end of 5.6:
"The shock wave must consist of a phase of positive a (overpressure) and a phase of negative or (underpressure) such that the impulses of the two phases cancel each other in first approximation. This argument is also a proof of the existence of the negative phase; it was first given by Penney using the energy rather than the amount of material."
so I'll have some work to do. Thanks

 

[Squizzie]

Well spotted. I will see if I can get my head around Chapter 5. I do note your reference at the end of 5.6:
"The shock wave must consist of a phase of positive a (overpressure) and a phase of negative or (underpressure) such that the impulses of the two phases cancel each other in first approximation. This argument is also a proof of the existence of the negative phase; it was first given by Penney using the energy rather than the amount of material."
so I'll have some work to do. Thanks

Does anyone have a link to Penney's paper?
[EDIT] is it this one?

 

[Drakkith]

I'm unsure of what you want. A mathematical explanation of the negative phase? A plain-English explanation? A full derivation? I feel like most of these have been given already, either in the posts themselves or in their references. 'Inertial effects' is a pretty good explanation to me. What is confusing about it? The blast throws material outwards, leaving a rarified section until the material can be slowed down and its direction reversed. What more do you want?

And I'm sorry you think most of the explanations don't meet PF rules for acceptable references. As far as I can tell, all the references provided in this thread are just fine. Most of the explanations typed out are based on those references. If you think they aren't, please make a report and the moderators will look into it.

 

[Baluncore]

In an ideal fluid, the explosive impulse will generate a cosine pressure wave, with the shock step at time zero, followed by the rarefaction centred at 3π/2. That is SHM.

In a real fluid, the cosine wave will decay, and can be approximated by the exponential terms of the Friedlander equations.

Both approaches demonstrate a rarefaction.

 

[Squizzie]

I'm unsure of what you want. A mathematical explanation of the negative phase? A plain-English explanation? A full derivation? I feel like most of these have been given already, either in the posts themselves or in their references. 'Inertial effects' is a pretty good explanation to me. What is confusing about it? The blast throws material outwards, leaving a rarified section until the material can be slowed down and its direction reversed. What more do you want?

The range of “explanations” on his thread so far indicates a lack of consensus on the matter, merely suggesting several alternative and contradictory descriptions of the effect (ranging from “the partial vacuum pulled by the outward momentum“, to “inertia”, to “simple harmonic motion”.)
I'm looking for an explanation which uses standard physics terms and which is consistent with modern scientific theory.

 

[renormalize]

I'm looking for an explanation which uses standard physics terms and which is consistent with modern scientific theory.

In an attempt to enlighten @Squizzie, I present here a proof that blast waves always include regions of low pressure. (Inspired by the reasoning used by Penney and Bethe in https://apps.dtic.mil/sti/tr/pdf/ADA384954.pdf.)

For simplicity, consider the case of a spherically-symmetric explosion into a static atmosphere of uniform density $\rho_0$. Denote by $\text{X}$ the center of the explosion and draw around it a spherical outer surface of arbitrary radius $r=R_o$, as shown in the following figure:

Before the explosion, the total mass of atmosphere contained within the outer surface is simply:$$M_{o}^{\text{BE}}=\frac{4\pi}{3}\rho_{0}R_{o}^{3}\tag{1}$$Now trigger the explosion to produce a blast wave (BW), that is, a spherical shell of disturbed atmosphere of fluctuating density $\rho\left(r\right)$, propagating outward and characterized by a leading and a trailing edge. Focus on the instant that the leading edge of the BW reaches the outer surface, and label the radius of the trailing-edge at that instant to be $R_i$, as depicted here:

For $r<R_i$, the atmosphere is undisturbed and has settled back to its prior uniform density $\rho_0$. (Similarly, for radii larger than $R_o$, the atmosphere is undisturbed and uniform because the leading edge of the BW has not yet reached there.) In contrast, for the region $R_i<r<R_o$ within the blast wave, the atmospheric density $\rho\left(r\right)$ is unknown without solving a complex problem in fluid dynamics. But even so, after the explosion it's still possible to formally express the the total atmospheric mass within the outer surface as:$$M_{o}^{\text{AE}}=\frac{4\pi}{3}\rho_{0}R_{i}^{3}+4\pi\intop_{R_{i}}^{R_{o}}\rho\left(r\right)r^{2}dr$$$$=\frac{4\pi}{3}\rho_{0}R_{i}^{3}+\frac{4\pi}{3}\overline{\rho}_{\text{BW}}\left(R_{o}^{3}-R_{i}^{3}\right)\tag{2}$$in terms of the average density $\overline{\rho}_{\text{BW}}$ within the blast wave, defined as:$$\overline{\rho}_{\text{BW}}\equiv\frac{\intop_{R_{i}}^{R_{o}}\rho\left(r\right)r^{2}dr}{\frac{1}{3}\left(R_{o}^{3}-R_{i}^{3}\right)}\tag{3}$$Everything to this point is just describing the system and performing some simple math manipulations. But now enters the single fact from physics that is crucial to the proof: conservation of matter as applied to the atmosphere. That is, both theory and experiment dictates that a disturbance like a blast wave can neither create nor destroy atmospheric material. In particular, this means the total mass of the atmosphere is unchanged by a BW, which says in our notation:$$M_{o}^{\text{BE}}=M_{o}^{\text{AE}}\tag{4}$$Putting eqs.(1), (2) into this gives:$$\frac{4\pi}{3}\rho_{0}R_{o}^{3}=\frac{4\pi}{3}\rho_{0}R_{i}^{3}+\frac{4\pi}{3}\overline{\rho}_{\text{BW}}\left(R_{o}^{3}-R_{i}^{3}\right)$$or more simply:$$\overline{\rho}_{\text{BW}}=\rho_{0}\tag{5}$$In other words, no matter how wildly the density varies inside a blast wave from point to point, the average density is always exactly the same as that of the undisturbed atmosphere. In particular, maintaining this average within a BW requires that every region of compression (higher density/above atmospheric pressure) must be balanced by one or more regions of rarefaction (lower density/below atmospheric pressure). That's why in an earlier post I drew a comparison to sound waves, where each compression is always followed by rarefaction. All due to conservation of (fluid) matter!

 

[snorkack]

In an attempt to enlighten @Squizzie, I present here a proof that blast waves always include regions of low pressure. (Inspired by the reasoning used by Penney and Bethe in https://apps.dtic.mil/sti/tr/pdf/ADA384954.pdf.)

But now enters the single fact from physics that is crucial to the proof: conservation of matter as applied to the atmosphere. That is, both theory and experiment dictates that a disturbance like a blast wave can neither create nor destroy atmospheric material. In particular, this means the total mass of the atmosphere is unchanged by a BW, which says in our notation:

In other words, no matter how wildly the density varies inside a blast wave from point to point, the average density is always exactly the same as that of the undisturbed atmosphere. In particular, maintaining this average within a BW requires that every region of compression (higher density/above atmospheric pressure) must be balanced by one or more regions of rarefaction (lower density/below atmospheric pressure). That's why in an earlier post I drew a comparison to sound waves, where each compression is always followed by rarefaction. All due to conservation of (fluid) matter!

But this is manifestly false!
Because when a bomb goes off, the explosive, previously solid or liquid, becomes gas. Thereby causing increase of atmospheric mass in any volume enclosing the bomb.

However, rarefaction might indeed happen in case of sufficient inertia.
Suppose that you fire a gun but the bullet is stuck in the barrel. Then there will be a high pressure in the chamber when the powder has turned into gas. The pressurized gas would leak out of the chamber slowly, through the touchhole; but there would never be a rarefaction. The pressure inside the chamber would approach the external pressure asymptotically from above - but it would never fall below the external pressure.
However, if there is enough inertia... Suppose the bullet is free to travel but the charge is insufficient to fill the barrel. Then the bullet is accelerated along the barrel, but as the gases expand, their pressure drops (also the air in barrel ahead of bullet is compressed), so eventually the pressure in chamber drops below the pressure ahead and starts to decelerate the bullet.
Now, in free air, the pressure behind the bullet equalizes with the ambient pressure when the bullet stops, so the bullet will remain at rest there. Not so in a barrel, because the barrel cannot be emptied or refilled except by moving the bullet - if the bullet stops in the barrel because the charge does not fill the barrel, the bullet would be sucked back into the barrel. And depending on the means of damping (side friction, gas leaks...) the bullet might oscillate repeatedly.

Just as the rarefaction behind a bullet in flight will NOT exist when the cartridge is first fired (the explosion gases are at high pressure throughout, if the charge is sufficient then rarefaction will form only when the bullet flies ahead of muzzle blast), an explosion propelling ambient gas only will start out as pure overpressure. Its evolution to contain one or several underpressure zones will happen by inertia and will depend on the relation of inertia and friction (sufficient friction will prevent any underpressure occurring).

 

[renormalize]

But this is manifestly false!
Because when a bomb goes off, the explosive, previously solid or liquid, becomes gas. Thereby causing increase of atmospheric mass in any volume enclosing the bomb.

True enough. But fortunately, an explosion freely expanding into the atmosphere rapidly dilutes the combustion gas to irrelevance within a relatively short distance. For example, consider a hypothetical detonation that releases a gas mass $M_{X}=\text{100 US tons}$. (Note that this represents several times the mass of the "Gadget" bomb and support tower that were vaporized in the Trinity test.) The ratio of $M_{X}$ to atmospheric mass $M_{A}=\frac{4\pi}{3}\rho_{0}R^{3}$ versus $R$ is shown below:

At just $130\:\text{m}$ from the blast center, the explosive gas component comprises less than $1\%$ of the total atmosphere and rapidly becomes negligible further out.

So beyond some minimal distance, I stand by my "conservation of mass" proof of low pressure regions in a blast wave.

 

[Squizzie]

A colleague has drawn my attention to Springer Link Shock Waves Journal and The International Shock Wave Institute. It seems most of the publications are behind a paywall which limits their accessibility to citizen scientists, but I suspect we are just scratching the surface of the problem.
Is this an "acceptable source" for PF? Is it worth further investigation?

 

[Squizzie]

I haven't fully digested this paper yet, but a scan of the figures and a text search fails to reveal any "negative overpressure" in their experiments.
I am not denying the existence of negative overpressure - the Beirut explosion and atomic blasts clearly indicate its presence.
I wonder if there is a missing controlling influence? Critical size of the blast, type of explosive, distance from blast centre, ...?

 

[berkeman]

A colleague has drawn my attention to Springer Link Shock Waves Journal and The International Shock Wave Institute. It seems most of the publications are behind a paywall

Can you see if your local library can help you gain temporary access to those resources? They may be able to help arrange an inter-library loan or similar.

 

[Squizzie]

Can you see if your local library can help you gain temporary access to those resources? They may be able to help arrange an inter-library loan or similar.

I have found some open access papers in their collection, and an interesting one noted above.

 

[hmmm27]

Your wonderment at water condensing from the air, and negative pressure gradients can mostly be answered by looking in Wikipedia for articles related to "weather" and "sound", respectively.

 

[Squizzie]

Your wonderment at water condensing from the air, and negative pressure gradients can mostly be answered by looking in Wikipedia for articles related to "weather" and "sound", respectively.

Thanks, but that is not my wonderment.
The creation of the cloud, as explained here, is not, in itself complicated, as it is due to the adiabatic cooling of the humid air in the low pressure region, leading to condensation.
My wonderment is the cause of the "negative overpressure" itself.

 

[hmmm27]

My wonderment is the cause of the "negative overpressure" itself.

Doesn't seem complex : air behind the wavefront is colder than the wavefront, so has a lower speed of sound... it literally can't keep up with the wavefront, thus underpressure. I guess you can add that one to the list of possibilities.

What does Kinney have to say about it ?

 

[Squizzie]

What does Kinney have to say about it ?

"the inertial effects responsible for the negative phase " Kinney & Graham referenced in #116

 

[snorkack]

Doesn't seem complex : air behind the wavefront is colder than the wavefront, so has a lower speed of sound... it literally can't keep up with the wavefront, thus underpressure. I guess you can add that one to the list of possibilities.

In case of a live load, the muzzle blast is pressing and accelerating the bullet out of the barrel. But soon after the bullet exits the muzzle, the blast spreads out and is slowed, while the bullet is not spread out and for that reason is not slowed so much.
How about the case of blank load? The smoke will undergo adiabatic cooling. When the pressure of the smoke comes to match that of ambient air, is the temperature of the smoke lower than that of ambient air, or still higher?
What happens to the clean air that was in the barrel before shooting the blank? It must have been compressed and heated adiabatically when pushed ahead of the smoke. When the blast exits the muzzle, is the (adiabatically heated) clean air hotter or cooler than the (adiabatically cooled) smoke?

 

[Squizzie]

Does anyone have access to this paper by Rigby et. al? The Negative Phase of the Blast Load.?
From the summary, I think it might be interesting:
"Following the positive phase of a blast comes a period where the pressure falls below atmospheric pressure known as the negative phase. Whilst the positive phase of the blast is well understood, validation of the negative phase is rare in the literature, and as such it is often incorrectly treated or neglected altogether. Herein, existing methods of approximating the negative phase are summarised and recommendations of which form to use are made based on experimental validation. Also, through numerical simulations, the impact of incorrectly modelling the negative phase has been shown and its implications discussed."

Rigby SE, Tyas A, Bennett T, Clarke SD, Fay SD. The Negative Phase of the Blast Load. International Journal of Protective Structures. 2014;5(1):1-19. doi:10.1260/2041-4196.5.1.1

 

[renormalize]

Does anyone have access to this paper by Rigby et. al? The Negative Phase of the Blast Load.?

Try here:
https://eprints.whiterose.ac.uk/782...14 - The Negative Phase of the Blast Load.pdf

 

[Squizzie]

Brilliant, many thanks.

 

[Squizzie]

The closest the Rigby paper comes to providing an explanation in which uses standard physics terms and which is consistent with modern scientific theory is, in the introduction:
"Following the positive phase comes a period of ‘negative’ pressure (below atmospheric); a partial vacuum caused by over-expansion of the shocked air" (my emphasis)
Which raises the question: what is meant by "over-expansion"? I have written privately to Dr. Rigby for elucidation.
[EDIT] Doesn't the ideal gas law insist that the adiabatic expansion of air will generate a low pressure, and vice versa: an adiabatic lowering of the pressure of air will be associated with its expansion?
Is that not just a restatement of the ideal gas law, rather than an explanation of the phenomenon of the "'negative' pressure"?

 

[snorkack]

Consider the case of the squib again.
If the bullet seizes at the breech then there would be no blastwave: the overpressure in the chamber would leak out gradually through touchhole and windage and asymptotically approach ambient pressure from above.
If the bullet moves along the barrel then as the bullet moves, the smoke behind the bullet expands and the air ahead of the bullet is compressed. But if the pressure of the expanding smoke becomes equal to pressure of air ahead while the bullet is in the barrel, at that point the bullet only stops accelerating but is at top speed. Therefore the smoke goes on expanding, and the inertia of bullet in barrel can cause the smoke to expand till its pressure is below ambient.

 

[Squizzie]

Consider the case of the squib again.
If the bullet seizes at the breech then there would be no blastwave: the overpressure in the chamber would leak out gradually through touchhole and windage and asymptotically approach ambient pressure from above.

No, the gun explodes.

 

[Squizzie]

The closest the Rigby paper comes to providing an explanation in which uses standard physics terms and which is consistent with modern scientific theory is, in the introduction:
"Following the positive phase comes a period of ‘negative’ pressure (below atmospheric); a partial vacuum caused by over-expansion of the shocked air" (my emphasis)
Which raises the question: what is meant by "over-expansion"? I have written privately to Dr. Rigby for elucidation.

He has replied with a description as follows:
"The negative phase is really just a response (of the air) to the positive phase. The two are interlinked.
Consider a point in free air, some distance from the centre of an explosive. Let's define a frame of reference where "forwards" is the direction of travel of the blast wave, and "backwards" is back towards the explosive.
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. So all the while the positive phase is acting, our point is moving away from the explosion centre. Once the positive phase has completed, that point temporarily reaches ambient pressure, but since it has moved away from the blast, the air between it and the blast centre has overexpanded, therefore reduced in pressure, and left a partial vacuum.
The negative phase sees the "blast wind" changing direction and the particle rushing back to where it came from, to equilibrate. "

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."

I'll keep you posted.