When Gas Dynamics strikes: the West, Texas fertilizer explosion

Gas dynamics and combustion (accidentally) at work

A few notes:

  • The events that predicated this post are extremely tragic. Condolences to those affected.
  • This post is by no means a manual or instruction set for creating incendiary devices of any sort. It only provides some technical explanation of the effects of explosions.
  • Do not under any circumstances attempt to recreate the effects described here. You risk death or serious injury to yourself and others, not to mention trouble with law enforcement.
  • This discussion is very simple, rough, and high level.
  • Some level of morbid humor is required beyond this point, because of the reference to conditions generally unsurvivable by unprotected humans.

The West, Texas fertilizer plant explosion got me thinking about the physics behind explosions in general, and in particular about several classes I took (yes, I’m so lame there’s a list of all my classes on the Internet) which cover these principles:

  • MECH 591 (Rice University graduate level class) – Gas Dynamics – Study of the fundamentals of compressible, one-dimensional gas flows with area change, normal shocks, friction, and heat addition. Includes oblique shocks, Prandtl-Meyer flows expansions, and numerical techniques.
  • EML 5714 (University of Florida graduate level class) – Introduction to Compressible Flow – One-dimensional and quasi-one-dimensional compressible fluid flows. Mach waves, normal shocks, oblique shocks, Prandtl-Meyer expansions, isentropic flow with area change, Fanno flow, Rayleigh flow.
  • EML 5131 (University of Florida graduate level class) – Combustion – Chemical thermodynamics, chemical kinetics, flame propagation, detonation and explosion, combustion of droplets and spray.

Don’t worry about the big words in the above. Basically the first 2 classes cover shock waves and the conditions they create, while the third class covers how things burn to create said shock waves.

How things (fuels) burn

The technical term for anything that burns is a fuel.

Generally speaking there are 2 methods of burning:

  1. Deflagration: in this method, a flame front moves progressively through the fuel. An example of deflagration is the flame observed by lighting a pool of kerosene (DO NOT ATTEMPT) or candle wick. You will notice that the flame spreads slower than the speed of sound
  2. Detonation: in this method, the flame front spreads faster than the speed of sound.

How detonations cause damage

Both of the above produce heat directly, which usually results in other things catching fire. Detonation has the added effect of creating a shock wave that travels outwards from the point of detonation. A shock wave isn’t so much a tangible thing as it a border or demarcation line. In front of the shock wave, gas (e.g. the air around you) conditions are normal. Behind the shock wave, temperature and pressure increase by multiples of their original values. It is this increase that results in the extreme destruction visible in the case of the fertilizer plant explosion.

Generally, the faster the shockwave, the larger the pressure and temperature difference between the region in front of it and that behind it is. For example, a shockwave that travels at twice the speed of sound (Mach 2) produces a pressure behind it that is 4.5 times the pressure in front of it.*

Let’s do some quick math to approximate the effects of the pressure rise by itself:

Imagine a 2 m x 1 m (~6 ft by 3 ft) door. Normal atmospheric pressure is 100 kPa, or 100 000 newtons per square meter.  A Mach 2 normal shock wave hitting the door would produce a net pressure on it of 4.5 – 1 = 3.5 times atmospheric pressure, 350 000 newtons per square meter (350 kPa). Since the door’s area is 2 m * 1 m = 2 square meters, the net force on the door is 2 * 350 000 = 700 000 newtons. That’s ~157 000 lbs or 70 tons of force, many times what most home structures were built to handle. For the record, eardrum damage occurs at ~34.5 kPa pressure difference, while lung damage occurs at ~103 kPa. Besides the sudden force, there’s also blast wind, but that’s beyond the scope of this discussion. You can read more about it here.

The bottom line here is that detonations cause more damage via kinetic action (movement of air) than heat and fire. This explains the attractiveness of detonation devices to those who deliberately use them: because the shock wave moves outwards in all directions, there’s less need for specific placement of the device than there is for directed projectiles. Anything within the detonation’s (unobstructed) blast radius will experience the pressure effects above, even if it escapes the heat resulting directly from the detonation itself.

Also, because shock waves are supersonic – a shock wave moving at Mach 2 is traveling at 0.68 km/s at sea level – it is nearly impossible for observers on the ground to outrun them (contrary to what is seen in movies). Ergo, it’s good to be as far as possible from a possible detonation situation, because once it happens, it WILL catch up to you if you’re within the blast range. There won’t be time for you to take cover, as this guy filming the fertilizer plant fire found out the hard way:

How to tell when detonation might be possible

Fortunately, although detonations may be accidental, they don’t happen by magic. Besides the obvious cases of explosives/highly unstable substances, detonation risk increases when a fuel is finely dispersed (i.e. well-mixed in air). Examples of this include fuel vapor clouds and even various forms of dust – even aluminum and sawdust become explosive as dispersed powders. From the vapor clouds link:

Saturated hydrocarbons containing only hydrogen and carbon (e.g. methane, ethane, propane, butane, pentane, hexane, etc. are more to result in deflagration if completely unconfined. Olefins are more likely to detonate (overpressure produced from combustion products). If the fuel is reactive (e.g. acetylene) or contains oxygen (e.g. ethers, ethylene oxide) it is even more likely to detonate. Any nearby structures including the ground which provides a barrier to the combustion front can result in the buildup of overpressures resulting in a blast front.

Of course, detonations aren’t the only way to create shock waves outside of a lab. Another method is to have an object travel faster than the speed of sound, thus resulting in a shock wave associated with said object. NASA has an extensive article (unfortunately and anachronistically written in outdated Imperial units) on that here. Let’s just say you probably don’t want a large supersonic aircraft flying at low altitude to pass directly over you. I heard stories of this effect being used against enemy positions by B-1 Lancer pilots in Afghanistan, but those might just be hearsay.

*This is a back-of-the-envelope estimate for a normal shock with some simplifying assumptions. Pressure difference factor computed here.

Author: jdrch

ISTJ, Rice Owl, UF Gator, mechanical engineer. STEM, sports, music, movies, humor. Account mine only & unaffiliated.

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