What areas of maths and physics do I need to understand explosion physics?

[Ax_xiom]

Give me a day or two.

Alright, thanks!

 

[Frabjous]

Kinney "Explosive Shocks in Air" 1962

 

[Frabjous]

Kinney and Graham "Explosive Shocks in Air" 1985

 

[Ax_xiom]

Kinney and Graham "Explosive Shocks in Air" 1985

View attachment 363608View attachment 363609View attachment 363610View attachment 363611

Interesting. For smaller distances my model aligns with the data fairly well (although the trend seems to be slightly less than cubic) but for larger distances the pressure values seem to follow a completely different relationship entirely.

 

[Frabjous]

What does the mach number comparison look like?

 

[Ax_xiom]

What does the mach number comparison look like?

Do you mean compare overpressure to the mach number of the shockwave?

 

[Frabjous]

Try to follow the analysis in the paper.
It starts with z vs t
Then comes mach number.
Then comes pressure.

 

[Ax_xiom]

Try to follow the analysis in the paper.
It starts with z vs t
Then comes mach number.
Then comes pressure.

Isn't that what I did when I got the result I'm currently testing? I took the result for $\frac{dz}{dt}$ and changed it to an expression of the mach number, then used that expression to calculate the pressure (and overpressure)

 

[Frabjous]

Isn't that what I did when I got the result I'm currently testing? I took the result for $\frac{dz}{dt}$ and changed it to an expression of the mach number, then used that expression to calculate the pressure (and overpressure)

You want to see where the disagreement starts. Then you try to figure out the discrepancy there.

 

[Ax_xiom]

You want to see where the disagreement starts. Then you try to figure out the discrepancy there.

So plot overpressure against mach number?

 

[Frabjous]

No. Start with position vs time. Figure 3 of the paper.

 

[Ax_xiom]

Ok, is $t_0$ or $t_d$ the column I should be looking at for this?

 

[Frabjous]

Diaz eventually published a journal paper
https://link.springer.com/article/10.1007/s00193-022-01089-z

 

[Frabjous]

t_a
Use the nondimensional forms like in the paper.

 

[boneh3ad]

Thanks for citing the Diaz & Rigby paper. We had a poster some time back who vehemently insisted that a blast-wave shock-front could propagate at the speed-of-sound $c$ and cited data from the 2020 Beirut chemical explosion to back his claim. But the analysis in this paper clearly demonstrates that the Beirut shock front traveled supersonically and only approached $c$ ("acoustic wave") as $t\rightarrow\infty$:
View attachment 363466

I mean, the definition of a blast wave requires it to be supersonic. It will eventually weaken into an acoustic wave. So that was pretty silly by said poster.

 

[hunt_mat]

The topic you should study is called "Compressible reactive flow". This is a branch of fluid dynamics which combines chemical reactions with fluid mechanics. There is a short introduction to it in the Book, "Applied Mathematics" and "nonlinear partial differential equations" by Logan.

 

[Ax_xiom]

Hello, it's been a while, and I've decided to revisit this topic. I have a quick question: when dealing with partial derivatives, is it fine to treat them as ordinary derivatives if the values depend only on one variable?

I'm trying to derive the expressions in the paper from the ones in the video and I noticed that velocity, pressure and density only depend on velocity and many of the equations have partial derivatives in respect to just r

Edit: Just realised that they also depend on time aswell. Fortunately, the thing I was trying to do (product rule) works the same way in multivariable calculus as in single variable calculus