Properties of Explosives and Their Application Part 3

Energetic materials in general and explosives in particular are incredibly important to an industrial/technological society. For propellants it's their ability to produce large volumes of gas in a short time frame during combustion. Rocket motors put our satellites in space that provide us with other forms of important technology. The airbags in your car are nothing more than an energetic material undergoing rapid combustion to fill the bag. I don't think you want to know what energetic material is probably in there.

The usefulness of explosives comes from the fast generation of gas, on the microsecond timeframe or less, that provides a large power density and amount of work available. This allows us to do extensive momentum transfers for a relatively low cost (blasting for mining and construction). The metals production industry, and subsequent manufacturing industries heavily depend on the low cost production of raw materials. The power densities in explosives allow for the high velocity acceleration of metals which produces the shaped charge effects needed in oil and gas well completion.

So, I've done a cylinder expansion test and I have the wall velocity. This velocity is primarily due  to the expansion of the high temperature-high pressure gas behind the supersonic front described in an earlier post. The characteristic velocity described would be the detonation velocity and is unique and constant for a given explosive material.

Wall Velocity from a Cylex Experiment.

Now I  need to convert that to something useful for the calculations and models I will be using. That post on going down the Rabbit Hole wasn't a complete Fool's Errand. What I end up with is an equation of state of the detonation products. This equation of state relates pressure (P), volume (V), temperature (T), and energy (E). Typically, simplifying assumptions are made so that we end up just using a relationship between pressure and volume (P-v). After numerous calculations I end up with:

Full Scale Pressure-Volume.

At different scales:

High Pressure Region Pressure-Volume.

Low Pressure Region Pressure-Volume.

The solid line is known as the Rayleigh line and is tangent to the curve at the state describing the detonation front. The dashed lines are the data and the curve fit in P-v space I've done. The upper part of the curve and the detonation state is important for determining the motion of metal in contact with the explosive. Down at larger volumes the gas is at much lower pressure and is the region of interest for moving large amounts of earth and rock for mining and construction.

I'll have to go into developing the equation of state of the gas in a separate post. I've been working on a Windows based application for directly taking cylinder test data and using that to output the P-v relationship. I hope to have that completed for inclusion in the downloads section when I do that post, we'll see.

I haven't done Windows development in a long time, and Microsoft has made a few changes in their Visual Studio since the last time I messed about in it. Good grief, that's an understatement. To think I started out with FORTRAN 77. Some of my code is still in that, even though my FORTRAN compiler uses a hand crank to run it.

OK, we have an explosive let's use it. The next posts on this matter will be using explosives in several industrial applications. They are: shaped charge design for oil well perforation; explosive cladding of dissimilar metals; rock and earth blasting for mining.