Monday, March 30, 2015

Rockets IV: Thermal rockets, nuclear and otherwise

See also parts IIIIII, V, and VI.

Here we talk about applying some sort of external heat source to your propellant so it expands a bunch and then shoots out of the rocket.  Technically chemical rockets are thermal rockets too but I'm trying not to be pedantic here.   There are lots of things you can use as your source of heat.  NASA has done a lot of studies with using a nuclear reactor to heat some propellant directly.  If you've got a big parabolic mirror you can focus sunlight on your engine and heat it that way.  If you've got a friend nearby with a big laser they can use it the same way.

The constraints for these sorts of rockets aren't the same as for the last two sorts of rockets.  You don't have a fixed ratio of energy to propellant that chemical rockets have so the ve isn't fixed that way.  Energy is a concern as with electric rockets but not as large a one since its much easier to turn an energy source into heat than it is to turn it into electricity.  There's a more pressing limit, though.  When things get too hot they tend to melt and you probably don't want this to happen to your rocket. In the other sort of rockets you can have the engine itself be a lower temperature than the propellant but since thermal rockets transfer heat from the engine to the propellant thermodynamics means that the engine has to be hotter than the propellant.

We all know that things expand as they get hot and it stands to reason that really hot gasses will probably leave the rocket faster giving you a higher  ve.  There's an equation for this, of course, which is ½Mmv2 = 3/2 RT where Mm is the molar mas of the atoms or molecules making up the gas, R is the Molar Gas Constant (8.314 J/K*mol), and T is the temperature of the gas.  So the ve we get is proportional to the square root of the temperature of the gas divided by the mass of the particles in it.  Lets say we can get our engine up to 3,200 K.  That's pretty hot but not undoable.  If we've got steam coming out like the Space Shuttle did this means that our ve is going to be 2100 m/s.  That's a lot less than the 4600 m/s the Shuttle got.  Now, we do get to store our propellant as nice dense water at room temperature which will save us a lot of design hassle.  However we haven't explained how we're going to be heating up the water and that's probably going to take a lot of mass.  Also, did I mention that when you're talking about ve 2100 is a lot less than 4600?  Clearly there's a big advantage in only having your propellant rather than your entire engine get hot.

But since our propellant isn't the result of a chemical reaction nothing says that we have to use a big, heavy molecule like H20.  What if we just use pure hydrogen, H2 with a molecular weight of 2 rather than 18.  In that case suddenly our ve goes up to 6300 m/s.  That's certainly much nicer!  And at that temperature some of the hydrogen molecules will split apart and for monatomic hydrogen with an even lower molecular weight.  Most of the designs I've looked at for normal nuclear thermal engines like MITEE say they ought to get their ve up past 9000 m/s but I'm not conversant in all the math there.

People have come up with various ways to effectively increase the temperature of the engine by doing things like making part of it transparent to try to get the same differential heating you can get in chemical rockets.  Maybe you put your propellant behind a quartz window and put some carbon in to make it absorb the incoming energy more than the quartz.  There's an interesting design with this and gaseous uranium hexafloride called the nuclear lightbulb that's only somewhat crazy.

I've glossed over the problem of engine weight.  They generally range around 10 to 100 N/kg which is much better than the .005 you'd see for an electric rocket but much worse than the 700 to 1500 N/kg you see for a chemical rocket.  So maybe good for a second stage in your rocket but not your first.

A note on the radiation.  If you've got a high powered nuclear reactor or engine your going to be generating lots of neutrons and xrays that the crew will have to be shielded from.  Lots of neutrons will end up hitting the propellant but this isn't really a problem since hydrogen and a neutron just make deuterium which is pretty innocuous.  And if you fire it in the air you won't be making anything horrible from the oxygen and nitrogen either.  But if you launch one of these babies from the ground those neutrons will play havoc with various minerals and you'll have a serious cleanup problem.  So don't do that, ok?

Another option is to have a nuclear electric rocket but when you need the extra thrust just run your propellant through the reactor and get the full 500 kW of thermal power rather than the mere 100 kW of electricity it provides to the electric drive.  And the  ve is lower so the thrust is higher for the same energy too, giving you a wider range of tradeoff between thrust and efficiency than even a VASMIR can.

That's it for thermal rockets.  Tune in later for me talking about rockets that aren't actually rockets.

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