## Relating a Change in Power Density to Fissile Content

Lindsay
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### Relating a Change in Power Density to Fissile Content

For a situation where we are trying to scale from one condition to another, how does fissile concentration vary with power density?

For example if we have a core operating at 79kW/L with 0.60 mole % U233 as the fissile, all other things being equal, what fissile content is required to double the power density to 158 kW/L? and if possible how does one do the calculations for that?

jaro
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### Re: Relating a Change in Power Density to Fissile Content

Lindsay wrote:For a situation where we are trying to scale from one condition to another, how does fissile concentration vary with power density?

For example if we have a core operating at 79kW/L with 0.60 mole % U233 as the fissile, all other things being equal, what fissile content is required to double the power density to 158 kW/L? and if possible how does one do the calculations for that?
The only reason fissile concentration would vary with power density is if "all other things being equal" is no longer valid.
For example, ORNL's Fireball aircraft reactor project expected to operate the core from zero power, to something close to a megawatt per litre.
As long as that doesn't significantly change the fuel density and other reactor parameters (ie. all other things being equal), the fissile fraction does not need to change either.
Of course to avoid changing the fuel density, it means that heat must be removed at a corresponding rate to maintain constant temperature.
Eventually though - at some ridiculously high power density - radiolytic efects may have an effect on fuel desity by way of bubble formation at a rate that may exceed a system's ability to remove them (actually I'm not sure if this effect is applicable to molten salts....)

Lars
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### Re: Relating a Change in Power Density to Fissile Content

For what its worth here is my amateur attempt at this tradeoff.

In other words, the maximum power density is set by removing the heat.
For a FLiBe the minimum fuel salt temperature is set by the salt getting more viscous as you come close to freezing - your minimum temperature is around 50 degrees C above the freezing temperature. The maximum salt temperature is set by the vessel and plumbing - for HastalloyN this is 704C.
This gives you a deltaT. Combine that with the fuel salt heat capacity and you can calculate the required fuel salt flow rate for a given power level.

So, suppose you had one design with the deltaT already at its maximum and you want doubling the power density - all other things being equal.
This means you need to double the flow rate of the salt through the core.
The chemical processing needs to happen at 2x the rate.
The lifetime of the neutron exposure limited parts (graphite if present and first wall if a 1.5 or 2 fluid reactor) will be half.

One way would be to keep the flow rate the same through the pumps and HX's.
This means 2x the pumps, HXs, secondary HXs, turbines, and generators.
However, it also means 2x the fuel salt outside the core - and that brings some trouble for stability as we really like those delayed neutrons so that we are still critical but have more margin for prompt criticality. The general assumption is 1/3 the fluid outside the core but the French feel we can go as high as 1/2.

Another way would be to double the flow rate through the pumps and HX's.
This means more head loss (not sure if that would be 2x or 4x - does it scale with velocity or velocity square), and more trouble with vibration in the HX piping.
You could compensate some for this by tolerating a larger deltaT between the fuel salt and the secondary salt.

A better HX or a higher top temp (say using TZM rather than Hastalloy) would allow higher power density and likely a lower cost reactor.

Note that along with that higher power density comes a bigger challenge to passively cool the thing when you shut it down.

Cyril R
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### Re: Relating a Change in Power Density to Fissile Content

In addition to Lars' excellent summary of thermophysical issues, there are some other effects as well.

Losses to protactinium increase with higher power density. This affects breeding ratio, now if I understand correctly, if you can still breakeven on breeding then you might decide to suffer that, if not you have to increase fissile content in order to still breakeven, or run as a converter reactor. The fourth option is to have faster protactinium removal.

What about the salt? With a higher power density you have less salt. That means less losses to the salt, so either higher breeding or lower fissile startup. If you use an alternate salt I think this is even more important (bigger capture in the salt). Again if I understand this correctly you can compensate by increasing fissile startup as above.

ORNL tested fluoride in molten form to extremely high power densities (unbelievably high, I don't know how they even got such high fluxes). Nothing happened!! 100 kilowatts per liter or 100 megawatts (!) per liter, it doesn't seem to matter. So the limit will not be the salt itself.

USPWR_SRO
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### Re: Relating a Change in Power Density to Fissile Content

IIRC, head loss is a square function, power input required varies as power of 3. So twice the flow is 4 times the head loss, and 8 times the power required. At least for water, and Flibe at operating temperature is very close to water hydraulically.

The other issue with very high power density is the system would be extremely sensitive to primary to secondary power mismatch events. E.g., a generator trip or sudden turbine runback would cause a rapid primary side heat up. The amount of that heat up spike would probably be limiting to how much power density you can tolerate.

jaro
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### Re: Relating a Change in Power Density to Fissile Content

Some additional insight may be gleaned from info on the Fireball reactor thread: the power density limit estimated by ORNL was based on the time required for the liquid fuel to traverse the core (i.e. flow velocity and core size), combined with a guesstimated temperature increase limit of some 1000F to 2000F per second....

Lindsay
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### Re: Relating a Change in Power Density to Fissile Content

Thanks guys, much appreciated. My gut feel was something along those lines, very small changes, most managed by changing operating conditions.

Cheers