High Rate Calculation
At higher burn rates, additional coolant is required to be buffered in coolant pipes between the reactor and the boiler or turbine (if water cooled). Theoretically there should be math to figure this out but no one seems to know it.
My 1st theory was that at higher rates, at any given tick, less and less cooled coolant is present in the reactor. This mathematically becomes a problem for sodium cooling due to the 10x higher heating rate than with water. What can happen is that there is not enough coolant left in the reactor since at any given tick it has to be in one of many places, and if its all been heated out of the cooled coolant tank of the reactor then there is nothing left to dissipate heat from the core. So lets find out what happens in our ticks.
- A tick of the reactor heats cooled coolant from the cooled coolant tank into the heated coolant tank
- A tick of a boiler moves coolant from its heated coolant tank to its cooled coolant tank
- A tick of a turbine is similar to the boiler in that it moves coolant as steam from its gas tank into water in its vent tank
- From what I can gather about pipe/tube/etc networks my guess is that coolant spends 1 tick a pipe if there is sufficient space at the acceptor end
Since in a sodium cooled reactor the boiler-turbine loop is separate from the reactor-boiler cooling loop, only a boiler OR a turbine needs to be accounted for in server ticks of the reactor cooling. If this hypothesis is correct then it would take 4 ticks for coolant to return to the cooled coolant tank of the reactor. Tick #1 would be the actual cooling process, then tick #2 to get to the boiler heated tank, tick #3 to cool into the cooled coolant tank of the boiler, and tick #4 back into the cooled coolant tank.
It appears the reactors start losing stability (core temp starts rising with a constant burn rate) after falling below about 27% cooled coolant tank fill. I was not able to get this to occur with a water cooled reactor, which makes sense given the math below showing the destabilizing threshold for water exceeding the max burn of the reactor (see estimated limit for water in the tables). For higher burn rates it just becomes a problem of water being an insufficiently efficient method of cooling so the core temp rises for that other reason. So, I will only be talking about sodium cooling for this issue, and it is the only type that will light up the startup rate high light on the reactor annunciator panel.
I performed some tests to test this hypothesis, data for the two reactor sizes are shown below.
Terms:
- AH: actual heating rate observed at the actual safe rate limit
- AC: actual coolant level observed at the actual safe rate limit
- ABR: actual burn rate (if it was 100% efficient) computed from actual heating rate
- ALIM: actual safe rate limit used in testing
- ELIM: estimated safe rate limit
The sodium/water per mB/t shows what burn rate would be required to instantly heat the entire coolant tank. I then divide that by the 4 ticks I estimated to get what burn rate should leave coolant in all stages of the loop.
This design I tested with both sodium and water cooling on the same biome. This found a maximum safe limit of 47.6 mB/t, producing a ratio of 3.603 instead of the expected 4.
This is one of my main sodium-cooled reactors in my nuclear power facility that was used for development. It is in a different biome type than the two 52 mB/t test reactors. Biomes matter slightly for thermal efficiencies, so some of then differences could be related to that, others due to proportions.
This design I tested with both sodium and water cooling on the same biome. This found a maximum safe limit of 143.9 mB/t, producing a ratio of 3.659 instead of the expected 4. This is different than the other reactor by a larger factor than I would assume is due to biome related temperature effects which can be seen by the ABR/ALIM. From just these two tests, it seems its around 3.6, but gets bigger for larger reactors?
I built this one as a single row of max height fuel assemblies. This reactor was not able to overheat at any rate, and mathematically by its coolant tank it shouldn't be able to, since the rate was larger than its max.
This was a standard cross pattern, and it did end up having a limit.
But finding a trend here is not proving to be very easy, so lets try a different approach.
Working with all this data, I found that a linear equation was the best fit for the data. But that little bump at the end, that's the issue. Two different reactors at different locations with identical builds have different maximum safe burn rates. I also noticed the boilers were running at different temperatures, but they had entirely different boiler builds. I feel like this shouldn't be the reason why this is occurring, but I'll do more investigation. What I do suspect is maybe the biome differences w/ environmental loss account for these slight differences.
Reactor #3 on its own had a "perfectly" linear formula, but it differed from the other reactors used.
Originally before I had tried the 175+ mB/t builds with reactor #3, I guessed that the error might be a parabola, but that did not turn out to be the case.
Something is causing this discrepancy between identical reactors, now to find out what it is.
Final Attempt (Chosen Implementation, KISS principle)
I suspected biome, since that has some effects, but it doesn't seem environmental loss will help me calculate this, as both 250mB/t test reactors rest at the same environmental loss percentage.
Final screenshot of excel workspace:
Looks like I've hit an impasse, so after reviewing all this data, the safest bet seems to just revert to the known fact: about 27% coolant causes overheating. With that, we can reverse calculate the burn rate that puts us at that level, and call that a high startup rate.
Where 200,000 is the heating rate for sodium reactors, and Vcool is defined as:
