How fast does a blastwave travel?

[Baluncore]

But don't both Glasstone and Kinney suggest that, if anything, the back of the blast wave travels more slowly than the shock front, causing the back of the blast wave to lag further and further behind the shock front, rather than catch up as the blast wave travels away from the blast?

It seems you insist on confusing the back of the shock-front with the back of the blast-wave. Are you a troll?

All your attached plots show the supersonic shock-front as a singular step function of pressure. That maintains its steepness, but the step is reduced in height as energy is lost. Later, things will happen at subsonic speeds.

You need to stop insisting, that the complex system must fit into your oversimplified model. If the theory is too complex for you, then walk away before your head explodes.

 

[Squizzie]

It seems you insist on confusing the back of the shock-front with the back of the blast-wave. Are you a troll?

I am trying desperately not to be.
I think of the shock front as the time and location of the arrival of the blast wave. It is an instant in time after which the air pressure starts to rise abruptly from ambient to an overpressure value above ambient.
The size of this overpressure depends on a number of factors including the nature of the explosion and the distance from the source.
The increase in pressure occurs over a very short distance and period of time: it is shown in the images posted at #34 as being vertical, but, as we know, it can't be exactly vertical, but its duration is smaller than the resolution of the plots. Unfortunately the plots have no scale on either axis, so it's hard to tell from the plots.
Kinney and Graham, when discussing "Thickness of the Shock Front" describe a shock plane and suggest:
"A representative thickness for a shock plane, as given by equation (4-23) for Mx= 2, is about 0.00025 mm. From equation (4-24), this corresponds to about twice the mean free path for a molecule in the upstream air."
I am confused about your interpretation of "shock front" in your post #88: "The back of the shock-front is hotter than the front of the shock-front"
[EDIT]
I read further in Kinney p. 50, that :
"The shock front of a blast wave is in many ways a determining factor in its behavior. The concern here is with shock fronts in air, which for present purposes may be considered as conforming to the specification of an ideal gas. The physical feature which uniquely characterizes a shock phenomenon is its abrupt occurrence in a Iamina of effectively zero thickness."
This seems to suggest and accord between "shock plane" and "shock front".

 

[Drakkith]

The increase in pressure occurs over a very short distance and period of time: it is shown in the images posted at #34 as being vertical, but, as we know, it can't be exactly vertical, but its duration is smaller than the resolution of the plots. Unfortunately the plots have no scale on either axis, so it's hard to tell from the plots.

For the 100g to 400g charges in my first reference in post #90 the rise time was less than 1 μs.

 

[Baluncore]

The increase in pressure occurs over a very short distance and period of time: it is shown in the images posted at #34 as being vertical, but, as we know, it can't be exactly vertical, but its duration is smaller than the resolution of the plots.

The front of that shock is in ambient air, while less than ¼ um behind, (one nanosecond later), the back is subjected to full pressure. If it is not vertical, then it will make itself vertical, because the back will overtake the front.

 

[Squizzie]

For the 100g to 400g charges in my first reference in post #90 the rise time was less than 1 μs.

I noted from the reference that :"The width of the shock front is only very small ",
and that :
"The transducers have a measuring range of 344.7 kPa, rise time less than 1 μs",
but I didn't see any specific reference to the size of the shock front. I am not familiar with the specification of transducers, so do I understand correctly that that implies that the duration of the shock front had to be less than 1 μs?
I have no doubt that the shock front has a very short duration, but 1 μs does seem a bit short!
In just one of the plots I can detect a 1 px step in the shock front, but the resolution of the plot is not high enough to ascertain if it indicates a slope in the line, or is an artefact of the image production.

 

[Squizzie]

But this whole concentration on the characteristics of the shock front has diverted from my search for a reason for the source of the condensation cloud's "negative overpressure" that we digressed from after post #60.

 

[Drakkith]

I have no doubt that the shock front has a very short duration, but 1 μs does seem a bit short!
In just one of the plots I can detect a 1 px step in the shock front, but the resolution of the plot is not high enough to ascertain if it indicates a slope in the line, or is an artefact of the image production.

My mistake, I didn't look closely enough. Looking closer now, I can see a step in the vertical line on the 100g charge too. A quick and totally non-rigorous count gives me about 16 steps over about 0.5 ms, or about 30 microseconds per step. Does a 50 microsecond rise time sound more reasonable?

 

[Baluncore]

I have no doubt that the shock front has a very short duration, but 1 μs does seem a bit short!

Does a 50 microsecond rise time sound more reasonable?

Over 40 years ago, when I was measuring the velocity of Mach 7+ shock fronts in a reaction tube. I used resistive sensors made from 0.2 mm wide gold leaf, mounted flush against the wall of the shock tube. The gauges were heated by the shock front as it passed, with their resistance rising in proportion to absolute temperature. The speed was measured accurately by the elapsed time between sensors.

It took about 100 ns for the narrow shock-front to cross the 0.2 mm wide sensor. The step transition then took another 50 ns to complete, as it was limited by the speed of the electronics.

As computed in chapter 4, of Kinney and Graham, I would expect the rise-time of the shock-front to be closer to 1 ns. The instrumentation is much slower than the shock front.

 

[Squizzie]

Folks, this analysis of the shock front is fascinating, but could I implore you to return to the question of the source of the low pressure in the back of the blast wave?
Contributors to this thread have provided evidence that It appears in all the experimental papers (Glasston, Kinney & Graham, Filice & collaborators), it is visible as a condensation (or Wilson) cloud in videos including the Beirut explosion, and is closely modelled with the Friedlander equation.
It has been suggested that it is the expression of a heavily damped oscillation, which is interesting, but there seems to be little independent evidence for that and the absence of an oscillating term in Friedlander equation would not support that view.
The plots of the experimental data would indicate the locus of the low pressure approaching atmospheric pressure asymptotically with time.
@renormalize queried my view that the presence of this low pressure was counterintuitive, by analogy with a pressure wave in a fluid, but as I said, there appears to be no evidence of an oscillation in the experimental results or the mathematical modelling.
I would expect the high pressure in the blast wave to decay exponentially to atmospheric pressure, but it doesn't, and I have yet to discover why.

 

[Drakkith]

I would expect the high pressure in the blast wave to decay exponentially to atmospheric pressure, but it doesn't, and I have yet to discover why.

Is that not what the graph in post #90 is showing?

Folks, this analysis of the shock front is fascinating, but could I implore you to return to the question of the source of the low pressure in the back of the blast wave?

In a normal sound wave, the compression and expansion phases have negligible energy transfer and the entire cycle of the wave leaves the medium with virtually no gain or loss of energy. I suspect that a blast wave is somewhat different as some form of energy loss has to occur for the air to cool and moisture to condense. Radiative losses maybe?

On the topic of blast waves, I stumbled across this extremely in depth report on nuclear detonations from Los Alamos from the 1940's. It may or may not be of use but I thought it was interesting and related to the topic. Here's the link: https://apps.dtic.mil/sti/tr/pdf/ADA384954.pdf

 

[Baluncore]

Folks, this analysis of the shock front is fascinating, but could I implore you to return to the question of the source of the low pressure in the back of the blast wave?

I deal in provable facts, not negotiated settlements. Everything follows on from the shock front. If you cannot, or will not, accept the shock wave model, then there is no hope for understanding the things that follow.

The condensation cloud is mostly irrelevant to the blast damage. It occurs at less than atmospheric pressure in cool air, after the out-rush of the blast wave. The local temperature and humidity make a big difference to when and how it will appear. It is simply an indicator of a momentary situation, there is no massive flow associated with it, if it comes, then it will go.

It has been suggested that it is the expression of a heavily damped oscillation, which is interesting, but there seems to be little independent evidence for that and the absence of an oscillating term in Friedlander equation would not support that view.

The Friedlander equation is a model for blast damage. It says nothing about any momentary condensation that may appear later. Models come with assumptions. Do you need independent evidence that mountains cause wave clouds?

So long as you reject the science of blast waves, and probe the irrelevancies of the pretty looking subsonic distractions, (that you once thought were a Mack 1.0 shock front), your private investigation will lead to a fiction. Disputing, or casting doubt on the facts, will not help in understanding the science.

The science is known. Read and accept Kinney and Graham. Stop trying to invent an alternative story, for your arbitrary and postmodernist, alternative private universe.

 

[Squizzie]

Is that not what the graph in post #90 is showing?

No, it's showing the pressure dropping below Atm.

But it's not showing the recovery to Atm that appears in the texts, so I'm not sure about its reliability

 

[snorkack]

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.

 

[Squizzie]

In a normal sound wave, the compression and expansion phases have negligible energy transfer and the entire cycle of the wave leaves the medium with virtually no gain or loss of energy. I suspect that a blast wave is somewhat different as some form of energy loss has to occur for the air to cool and moisture to condense. Radiative losses maybe?

Possibly, and that is the piece I'd like to explore more deeply

 

[Squizzie]

On the topic of blast waves, I stumbled across this extremely in depth report on nuclear detonations from Los Alamos from the 1940's. It may or may not be of use but I thought it was interesting and related to the topic. Here's the link: https://apps.dtic.mil/sti/tr/pdf/ADA384954.pdf

Looks interesting, thanks, a little more reading.

 

[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.