How is combustion speed regulated in solid propellants?

Question

My question on Space.SE didn't yield anything I didn't know already: the secondary regulation mechanism – grain (cross-section shape) of the propellant, changing the area of open surface of the propellant as it burns away; the combustion occurs only on the surface, travels inwards only as much as the surface burns away, and produces uniform amount of exhaust gasses per unit of area of open surface; the variance in surface area is what changes the overall thrust.

But I'm currently interested in what is done to composition and/or inner structure of the propellant, so that it burns uniformly on the surface, at predictable (and quite slow) pace, instead of, say, exploding all at once, or at least deflagrating at shocking speed, like common explosives (of very similar composition!) do. What property or reaction keeps the combustion to the surface and makes it progress inwards only so slowly – in case of the Space Shuttle, 290 seconds to burn through about 1.5 m of the propellant.

Answer 1

(I apologize for being too lazy to find all of the citations for my answer. However, I have a fair amount of experience as an organic chemist, at one point worked in an underground mine with explosives and have built (for entertainment) a solid fuel composite propellant)

1. Why does propellant "burn" instead of detonating like similar explosives?

A typical solid composite propellant looks like this: (1) mainly ammonium nitrate (oxidizer) + "fuel" (typically aluminum flake or magnesium) + binder (polymer + perhaps plasticizer) + (maybe) catalysts OR substitute ammonium perchlorate for ammonium nitrate.

The most similar mining explosive is ANFO or variants thereof: ammonium nitrate + diesel fuel (possible sensitizing substitutions are... some ammonium perchlorate for the ammonium nitrate, some aluminum in addition to fuel, partially oxidized "fuels" such as hexamine nitrate, nitromethane, possibly a small percentage of a secondary explosive such as TNT or RDX, or addition of plastic "bubbles" to simulate the bubbles that sensitize pure nitroglycerine.

The key point is that the latter mining explosive is called a blasting agent. The taxonomy of high explosives looks like this: primary explosives can be easily DETONATED (as opposed to deflagration, which is a type of "burning", detonation involves a supersonic thin region of reaction that moves through the explosive, giving it brisance that can shatter rock). Primary explosives are used in primers, and can be detonated with sparks, physical shocks, etc. Secondary explosives (dynamites, TNT, PETN) need to be detonate with a primary explosive. They are relatively insensitive to other means of initiation (one measure of this is the deflagration to detonation distance, which really is the amount of explosive that can burn before detonation takes place. It is usually quite large). You can often shoot or burn secondary explosives without them detonating.

Finally, blasting agents are quite hard to detonate. They require a booster that is a secondary explosive. Blasting agents are very insensitive and can be burned without detonating, especially if not completely confined.

This answers your first question... we should not expect solid propellants to detonate without a booster (actually I'd guess that solid propellants are even harder to initiate, as ANFO variants are usually oxygen balanced so that all of the fuel is oxidized, whereas propellants appear to be a bit carbon rich).

Note that blasting agents and solid propellants share the property that the oxidizer and fuel form distinct particles, as opposed to explosives such as nitroglycerine, which are self-oxidizing within the molecule. The low explosive gunpowder shares the property of having a mixture of discrete particles of oxidizer and fuel, and it merely deflagrates.

TLDR: The explosives that are most similar to solid composite propellants are difficult to detonate, so it isn't a surprise that they burn instead.

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2. How is the burn rate controlled? (note, I use burn as burn typically is decomposition at a rate of a few cm per second, while deflagration is at a rate of many meters per second. Detonation is thousands of meters per second).

A:

All propellant mixtures have (approximately) a burn rate that is a function of pressure. This approximation is called Vieille's Law. The formula is

$rate = {rate}_0 + aP^\beta$

where $P$ is the pressure. Thus, as pressure increases in the rocket motor, burn rate increases. Ideal values of $\beta$ are between 0.5 and 0.8, otherwise initiation can be difficult or else a slight overpressure could be amplified to cause the pressure to increase dramatically and destroy the rocket. What seems to affect the burn rate? I'll list a few:

(1) Ammonium perchlorate burns much faster than ammonium nitrate.

(2) Generally, the rate limiting property of a propellant is the particle size of the oxidizer, so more finely divided oxidizer means faster burn rate.

(3) The geometry of the propellant is important. The burning tends to occur at the exposed surface, so wide and not very long propellant castings will produce more thrust.

(4) Metallic catalysts increase burn rate, such as iron oxides and chromates.

(5) I've heard that a small amount of carbon black increases burn rate by increasing infrared absorption in the casting. It also makes it look cooler.

(6) Not so good: cracks and voids in the casting will increase burn speed, as they lead to more exposed area. That's why typical binders are rubbers, often including plasticizers, as these are less likely to crack under pressure.

Here's a couple of citations:

A amateur rocketry site

metallic wires as a burn rate catalyst

Rocket engine mathematics

Answer 2

Ask your question the other way. What is required for a material to burn to detonation. Most explosives will burn as propellants, it is only when you confine them and the combustion pressure increases that they risk burning to detonation. Very few materials can burn to detonation without confinement; these are called primary high explosives (eg Lead Azide).

Answer 3

For most propellants and explosives the speed of reaction is a function of the compound and its physical properties

You make an incorrect assumption when you assume that the primary reaction in propellants and explosives is burning. It isn't. Explosives and propellants are usually designed so they react without needing an external oxidiser. Explosives, some of which can also be used as propellants, are usually built from oxygen and nitrogen-rich chemicals that fall apart into gaseous products when given the right impetus. No external oxygen is required. Some are mixtures containing a fuel and an oxidant where the oxidant contains all the required oxygen to create a gaseous product and/or a great deal of heat when reacting with the fuel.

Whether a propellant reacts controllably or not is, to a large extent, a property of the material. The difference between detonation (very fast reaction) and deflagration (slower) is whether the reaction travels faster than the speed of sound in the bulk material (see this answer on explosives). Not all explosives detonate. For example, the explosives used in guns and artillery to drive the shells need to deflagrate to create a relatively slow reaction driving a controlled propulsion of the shell from the gun barrel. Rockets are just a carefully controlled version of this principle.

So, the dominant requirement for a solid rocket fuel is a substance or mixture where the reaction proceeds at a relatively slow pace in the bulk compound (and there may not be much you can do about this except to select the right chemical or chemical mixture). Having said that, you can influence the pace to some extent by changing the physical makeup of the compound, especially where the propellant is a mixture not a pure substance.

The boosters on the space shuttle used a mixture of ammonium perchlorate and aluminium. To some extent the propellant properties can be modified by both the physical makeup of the propellant (e.g. the grain size) but also by the addition of additives to modify the bulk properties of the mixture (both the binders used to hold the mixture together and some catalysts can modify the reaction speed). Some control can also be exercised by the overall shape of the propellant mass. Some military rockets use the explosive HMX as a fuel (it has a higher specific thrust than the fuel used in the space shuttle's boosters but is also more dangerous).

But the dominant characteristic is the bulk physical properties of the substance (which determine how fast the reaction proceeds in the bulk compound). So your primary choice as an engineer is which propellant to pick. You can modify that a bit but you can't fundamentally change the basic chemistry and physics.