Fission Reactor Design

[Imperial528]

Hello SLAM,

So, as a project I've been looking into designing a realistic (read: achievable to known science and possibly engineering) long-range spacecraft. To that end I decided on fission reactors for the power plant. Partway into the initial concepts I realized today that if I'm going to do this right, I'll need to design it from the ground up. Which means starting with the reactor.

Which means designing the reactor.

Now, I understand the basic theory of fission, but the only actual academic knowledge I have that even approaches what is required for this comes from the radiation chapter of high school chemistry.

To get around this I decided to browse through the various types of nuclear reactors (generations II and III mostly) to find a suitable design to adapt. It was my hope that I'd be able to find diagrams describing the size of fuel rods and overall efficiency, heat output, etc. of the plant so that I could construct a crude model that has the ideal power output per rod and heat output per rod, and go from there. Sadly my research abilities are weak, so I didn't get very far.

The type most attractive for my purposes is gas-cooled, but really any data on fuel rods would work as well. Or the mathematical models used to design fuel rods.

Also, any fellow space geeks are free to critique or comment on my choice of power source, offer alternatives, and bring up existing engines. I have admittedly looked at atomic rockets for inspiration for this, though they did not have any reactor math suitable.

[Simon_Jester]

Just for the record, designing nuclear reactors and predicting their performance is really hard. If you want actual pictures, an ability to say "this is the reactor, it weighs X tons and outputs Y megawatts of electricity," your only real hope is to go digging through existing design studies until you find a reactor that has those characteristics and say "it'd look like this."

Note that most real-world reactors rely on a steady stream of coolant water flowing into the power plant, because they're built next to a river, or float in the ocean, or something. A spacecraft cannot depend on this and must be closed-cycle.

[Dass.Kapital]

Real designs you might ant to look up can be found all through the 'Atomic Rockets' web page. From the NERV to the simple put-put Orion.

Best of luck.

[TimothyC]

Your best bet might be to clone the Light Weight Nuclear Propulsion system that Westinghouse developed in the 1970s, and is based on 1950s era airborne reactor designs. The only major problems you'll have then is the generator selection, and the limited fuel life in the stock design. This design does have an advantage that the coolant loop is a Helium Brayton cycle - and thus a closed loop.

[Imperial528]

Just for the record, designing nuclear reactors and predicting their performance is really hard. If you want actual pictures, an ability to say "this is the reactor, it weighs X tons and outputs Y megawatts of electricity," your only real hope is to go digging through existing design studies until you find a reactor that has those characteristics and say "it'd look like this."

Note that most real-world reactors rely on a steady stream of coolant water flowing into the power plant, because they're built next to a river, or float in the ocean, or something. A spacecraft cannot depend on this and must be closed-cycle.

I've mostly been looking to keep it as simple as possible, so instead of looking for exact performance I've been looking for the heat produced by the reaction, and then simplifying that to a rough heat produced per rod(s) in whatever configuration. I'd imagine that the curve is non-linear of course as adding more fuel rods will increase the criticality of the reactor though I'd expect it to plateau at some point or become linear.

From that data I could design a coolant system and figure out roughly how much energy will go into the propellant. Which has the added benefit of going back into realms of science I've had more experience of, namely thermal systems. There's also more resources available out on the net for thermal problems as well.

For cooling purposes the image in my head was to have a closed-cycle system that will maintain the reactor while it is idling, and use the propellant as an open-cycle coolant during engine operation.

[Magis]

I can give you some information just for you to get started and to clear up any misconceptions.

I've mostly been looking to keep it as simple as possible, so instead of looking for exact performance I've been looking for the heat produced by the reaction, and then simplifying that to a rough heat produced per rod(s) in whatever configuration. I'd imagine that the curve is non-linear of course as adding more fuel rods will increase the criticality of the reactor though I'd expect it to plateau at some point or become linear.

A reactor is, always, by design, exactly critical. So no matter how much fuel mass there is, and no matter what their configuration, the reactor has a criticality of precisely 1.0, by design. Also, a critical reactor can operate at any power from a nuclear reaction point of view.

In practice, what puts a limit on reactor design power is the rate of heat transfer from the fuel to the coolant and the shape of the power distribution within the core. Clearly, whatever fission power that is produced in the fuel needs to be transferred to the coolant, and there will be a temperature gradient inside the fuel material - the rod will be coolest near its outer surface where it meets the coolant, and the rod will be hottest in the center of the rod. That steady-state centerline temperature is a function of the fission power in the rod, the rod diameter, the thermal conductivity of the rod material, and the heat transfer coefficient from the rod to the coolant (this is neglecting additional complexity added by the fuel rod sheathing, which may not be necessary for a reactor in space). For the reactor to function, that centerline temperature has to be less than the melting temperature of the fuel material, which is normally UO2, which melts at about 2,865 °C. Therefore, the fission power per unit length per rod depends on the materials and cooling system design, and not the nuclear reaction per se, and it is therefore a fluid dynamics and heat transfer problem rather than a reactor physics one.

If you want a rough number, civilian commercial power reactors using UO2 fuel, sheathed fuel rod diameters of about 1.0 to 1.5 cm, and cooled by forced convection to liquid water, can achieve maximum linear element ratings on the order of 100 to 200 kW/metre.

[Imperial528]

Ah, yes, thank you. I can work with that.

So, assuming a sheath made of zirconium alloy (I used the thermal properties of just zirconium, but may use the density of the alloy for the design purposes) with a total diameter of 1.25cm, split as a 1cm pellet diameter and 0.25cm sheath thickness, and assuming an output of 150kw with a high temperature of 1800 C I've derived an external temperature of 1377 C.

Now, converting the rod dimensions to the nearest Imperial units the final rod is described as follows; Diameter of 1/2", sheath thickness of 3/32", rod length of 3', and output of 146kw per rod, roughly, with identical temperature range. The pellets are 5/16" diameter and 1/2" long, and there are 72 pellets per rod. The fully assembled rod has a mass of 2.119 pounds.

Now I'll see if I can make a reactor assembly out of this.

[energiewende]

SLAM is air-breathing, and nuclear powered airplane experiments generated electricity to drive a turbine. Neither good for spacecraft.

Generally there is some trade-off between thrust and specific impulse (fuel efficiency); nuclear propulsion suffers from it less badly, but still, you said long range so let's simplify things by building the craft in space.

You want high as possible exhaust velocity. Energy is not likely to be the limiting factor, rather reaction mass to shoot out the back, so to get the largest momentum change from a given mass you want highest velocity. This means high temperatures. The buzzword you are looking to google is probably "nuclear thermal rocket"; specifics how to make as high as possible temperature reactor are sketchy because no one serious was really interested in this problem for some time.

[Imperial528]

SLAM is air-breathing, and nuclear powered airplane experiments generated electricity to drive a turbine. Neither good for spacecraft.

Generally there is some trade-off between thrust and specific impulse (fuel efficiency); nuclear propulsion suffers from it less badly, but still, you said long range so let's simplify things by building the craft in space.

You want high as possible exhaust velocity. Energy is not likely to be the limiting factor, rather reaction mass to shoot out the back, so to get the largest momentum change from a given mass you want highest velocity. This means high temperatures. The buzzword you are looking to google is probably "nuclear thermal rocket"; specifics how to make as high as possible temperature reactor are sketchy because no one serious was really interested in this problem for some time.

SLAM was a reference to the sub-forum Science, Logic, And Morality.

Indeed, I am designing an NTR. However, I am starting from scratch. I'm not even at the point of determining exhaust velocity or even propellant material. My starting point is designing the reactor itself and then tweaking from there, which means I need some understanding of the mathematical models that apply to nuclear fission reactors and most importantly the behavior of the fuel rods. So far I've tried to rig up a basic coolant requirement from Magis' advice however I have also been looking for ways of modeling the energy produced during fission per amount of fuel material.

Essentially, I am doing the Bad/Lazy Engineer's method. Cobble together a prototype that works barely and use that as a basis for something that was actually designed.

[Admiral Valdemar]

You would be better having an MHD turbine for an SSTO. The idea would be better with an aneutronic fusion reactor like the Focus Fusion one Lockheed is backing, but it basically acts like the engines in Macross fighters. A turbine is used to get up, heating the air via high ionisation processes, then it converts to a ramjet/scramjet to get to hypersonic speeds and finally shuts the intakes and starts heating propellant like H2O or H2 to work in rocket mode.