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Post by zuthal on Nov 11, 2016 21:17:27 GMT
qswitched wrote on his blog that: I respectfully disagree, if you make sufficient assumptions. These are that the thermocouple exit temperature can be adjusted more or less freely for a given core temperature and electric output power, without significant mass penalties. Solving the Carnot efficiency equation and the Stefan-Boltzmann law yields these graphs. A few conclusions are readily apparent: 1) You should always run your core as hot as possible 2) There is a single optimum radiator temperature, and it is always three quarters of the thermocouple inlet temperature. |
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Post by dragonkid11 on Nov 11, 2016 23:25:34 GMT
SCIENCE!!!
Thanks a lot though, pal
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Post by Crowne on Nov 12, 2016 1:26:39 GMT
Math.
What's there not to like?
Good job though, will keep in mind.
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Post by goduranus on Nov 12, 2016 5:28:33 GMT
I don't get this, shouldn't the energy density of the reactor, area density of the radiator, and the total size of your craft be factors of consideration?
If total radiator mass needed is tiny relative to the craft, you'd opt for low temperature outlet because weight penalty wouldn't matter much but increased thermocouple efficiency means a smaller reactor is needed.
If total radiator mass needed is huge relative to the craft, you'd opt for high temperature outlets to minimize radiator size in order to increase payload.
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Post by paleblackdot on Nov 12, 2016 6:49:51 GMT
I don't get this, shouldn't the energy density of the reactor, area density of the radiator, and the total size of your craft be factors of consideration? If total radiator mass needed is tiny relative to the craft, you'd opt for low temperature outlet because weight penalty wouldn't matter much but increased thermocouple efficiency means a smaller reactor is needed. If total radiator mass needed is huge relative to the craft, you'd opt for high temperature outlets to minimize radiator size in order to increase payload. Not quite. A lower radiator temperature makes more efficient use of available power, but it severely limits what that available power can be. In steady-state operation, generator power must be equal to power radiated (or else the ship heats up, and it's not steady-state). In the end, a higher radiator temperature is less efficient, but it allows for more source-heat from the reactor, and can brute-force its way to higher electric-power. As an extreme example, imagine a (non-realistic) theoretical radiator at 0K. 100% thermal efficiency, but radiates 0.0 Watts steady steady state; so is limited to 0.0W reactor power and 0.0W electric power. Not desirable for power output. Atomic Rockets has a derivation of the equations from the first post. Under "Optimal Radiator Temperature" The is all valid for optimizing just on poweroutput - I could envision other design factors that could drive you towards temperatures not constrained by the 3/4 value. For example, if you prioritized delta-V in a design, higher radiator temperature (and lower associated radiator area/mass) might make it perform its overall mission better. |
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Post by n2maniac on Nov 12, 2016 8:06:51 GMT
qswitched wrote on his blog that: I respectfully disagree, if you make sufficient assumptions. These are that the thermocouple exit temperature can be adjusted more or less freely for a given core temperature and electric output power, without significant mass penalties. Solving the Carnot efficiency equation and the Stefan-Boltzmann law yields these graphs. A few conclusions are readily apparent: 1) You should always run your core as hot as possible 2) There is a single optimum radiator temperature, and it is always three quarters of the thermocouple inlet temperature. Thermocouple stresses from thermal expansion limit the maximum delta T available across the thermocouple, and thus the efficiency. I think most people have settled on Tungsten + Tantalum thermocouples with about 500K delta T. This... actually gets surprisingly close to the optimum you computed. |
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Post by zuthal on Nov 12, 2016 11:24:52 GMT
I don't get this, shouldn't the energy density of the reactor, area density of the radiator, and the total size of your craft be factors of consideration? If total radiator mass needed is tiny relative to the craft, you'd opt for low temperature outlet because weight penalty wouldn't matter much but increased thermocouple efficiency means a smaller reactor is needed. If total radiator mass needed is huge relative to the craft, you'd opt for high temperature outlets to minimize radiator size in order to increase payload. If you have a certain reactor design (core mass, moderator mass, control rod mass), you can adjust the available thermal power almost freely via the neutron flux, and increasing or decreasing the turbopump speed (to regulate core temp) is almost free too, in general. The radiators will usually end up making up the majority of the mass of your power system. qswitched wrote on his blog that: I respectfully disagree, if you make sufficient assumptions. These are that the thermocouple exit temperature can be adjusted more or less freely for a given core temperature and electric output power, without significant mass penalties. Solving the Carnot efficiency equation and the Stefan-Boltzmann law yields these graphs. A few conclusions are readily apparent: 1) You should always run your core as hot as possible 2) There is a single optimum radiator temperature, and it is always three quarters of the thermocouple inlet temperature. Thermocouple stresses from thermal expansion limit the maximum delta T available across the thermocouple, and thus the efficiency. I think most people have settled on Tungsten + Tantalum thermocouples with about 500K delta T. This... actually gets surprisingly close to the optimum you computed. Of course, you sadly cannot reach that optimum at the reactor temperatures that would be most ideal (not that a reactor that is only 100 K away from meltdown would ever be approved by any safety officer anyways). Though fortunately, due to the quartic scaling in the Kevin-Boltzmann law, the region of "acceptable" radiator efficiency isn't too narrow. |
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Post by cuddlefish on Nov 12, 2016 13:00:43 GMT
100K away? Luxury! Hardcore Nuke Jockeys size their coolant systems to only be below the melt-line by 10 K, even at maximum capacity, if they can get away with it. What could possibly go wrong?
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Post by apophys on Nov 13, 2016 15:05:55 GMT
On the other hand, it's easy to take an existing design that courts meltdown on a knife's edge (such as any 2500K reactor around on the forum) and drop the coolant loop temperature by a few hundred degrees to give it a safety margin.
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Post by qswitched on Nov 13, 2016 23:18:10 GMT
qswitched wrote on his blog that: I respectfully disagree, if you make sufficient assumptions. These are that the thermocouple exit temperature can be adjusted more or less freely for a given core temperature and electric output power, without significant mass penalties. Solving the Carnot efficiency equation and the Stefan-Boltzmann law yields these graphs. A few conclusions are readily apparent: 1) You should always run your core as hot as possible 2) There is a single optimum radiator temperature, and it is always three quarters of the thermocouple inlet temperature. Some issues with this. 1) None of the reactors in game run at Carnot efficiency. Doing so is thermodynamically impossible, and all reactors run below that. 2) You're assuming the final goal is to minimize radiator area. This is not necessarily the case. For instance, colder radiators can take laser and nuclear damage far better than hotter ones. Additionally, colder radiators will yield overall less waste heat, which can be a major consideration for flare decoys. 3) You can't necessarily assume you can set your output temperature arbitrarily. One such limitation is thermocouple stress. Having too great of a temperature may not be possible, or the materials might be too expensive to do so. 4) The reactors bleed power out of both turbocompressors. This further drags your efficiency down from the Carnot efficiency, even possibly bringing it negative. Arbitrarily controlling the output temperature can cost you more power than it gives you back. TL;DR Your ideas work if your reactor is a spherical cow. The details end up being a touch messier. Edit: Forgot about one more thing. Radiators do not perfectly follow the Stefan-Boltzmann law, because you can't simply pump 2000 K coolant in and suddenly your radiator is 2000 K. They have an additional efficiency coefficient based on a slew of factors like the heat transfer coefficient, thickness, coolant, etc. So again, radiators are not spherical cows either. |
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Post by n2maniac on Nov 14, 2016 0:47:10 GMT
colder radiators can take laser and nuclear damage far better than hotter ones That ... is an interesting note... |
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Post by zuthal on Nov 14, 2016 14:51:02 GMT
Some issues with this. 1) None of the reactors in game run at Carnot efficiency. Doing so is thermodynamically impossible, and all reactors run below that. 2) You're assuming the final goal is to minimize radiator area. This is not necessarily the case. For instance, colder radiators can take laser and nuclear damage far better than hotter ones. Additionally, colder radiators will yield overall less waste heat, which can be a major consideration for flare decoys. 3) You can't necessarily assume you can set your output temperature arbitrarily. One such limitation is thermocouple stress. Having too great of a temperature may not be possible, or the materials might be too expensive to do so. 4) The reactors bleed power out of both turbocompressors. This further drags your efficiency down from the Carnot efficiency, even possibly bringing it negative. Arbitrarily controlling the output temperature can cost you more power than it gives you back. TL;DR Your ideas work if your reactor is a spherical cow. The details end up being a touch messier. Edit: Forgot about one more thing. Radiators do not perfectly follow the Stefan-Boltzmann law, because you can't simply pump 2000 K coolant in and suddenly your radiator is 2000 K. They have an additional efficiency coefficient based on a slew of factors like the heat transfer coefficient, thickness, coolant, etc. So again, radiators are not spherical cows either. 1) True, though I am assuming (somewhat naïvely) that reactor efficiency as a percentage of Carnot efficiency is roughly constant with temperature - though I will be open to being corrected on that. 2) They can indeed, but materials are available (like the various allotropes of carbon) which have a margin over the typical coolant temperatures at the high-temperature end (on the order of 2500 K) of over 1000 K before they melt/sublimate. And needing less radiator area allows you to have more redundant radiators, allowing them to sustain more damage before your reactor is disabled. 3) Indeed, that is an issue especially at the high-temperature end - a tantalum-tungsten thermocouple, which is the standard high-temperature solution, seems to have a maximum temperature drop of ~500 K, though due to the nature of quartic functions, that is still close to the optimum radiator area. 4) They do indeed, and increasing coolant flow to reduce output temperature does increase the amount of power needed for the turbopumps. However, in my experience, it seems that the turbopumps only take up a small percentage of the total output power for large (multi-MW and beyond) reactors. And regarding the non-ideal radiators, that is true, however experiments have shown that as the game is currently, if you use materials that have sufficiently high heat transfer coefficients, you can achieve significant additional armour thickness without losing efficiency - for example, a 1 mm thick diamond radiator keeps its full efficiency up to an additional armour thickness of ~7 mm. Though I feel that diamond's transparency should have an impact on its use as a radiator - you would in effect have significant emission directly from the coolant. |
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Post by Rocket Witch on Nov 19, 2016 23:40:41 GMT
colder radiators can take laser and nuclear damage far better than hotter ones. Oh? I remember a comment from you before about the fact the heat is radiated away very quickly and the only reason they don't visually dim in seconds is for performance reasons (though engines start/stop glowing in realtime when working and that's not taxing?). I would intuitively expect the temp to be higher than the melting point for a moment, ablating away the surface of the radiator, but I took up the implication that it wasn't a serious concern at least for nukes. |
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Post by amimai on Nov 20, 2016 0:41:01 GMT
i did some experimentation on this a while back using a spread of reactors 2500-2800 outlet temperatures, here is a quick and dirty summary of it:
(I use diamond radiators because of structural strength and cheapness to armour efficiently)
<2400: civilian boat territory, only way this thing will work is with radiators that have 100nm armour and are big enough to be used as solar sails
2500 : efficient for civilian ship with armoured radiators(2cm) with 1 redundancy - this thing might win vs a pure laser boat if its lucky
2600 : best for medium combat ships with 2-4 set of redundant radiators with medium armour(<8cm) - can survive a light peppering of kinetic ammo
2700 : an in between reactor use as and when
2800+ : best for mele brawlers with 5+ sets of redundant and heavy armour on radiators (>8cm) - bring on the rain for I fear no railgun!
I should probably test if its possible to make a 3000k outlet radiators but when I tried efficiency drops were harsh
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Post by n2maniac on Nov 22, 2016 22:20:38 GMT
i did some experimentation on this a while back using a spread of reactors 2500-2800 outlet temperatures, here is a quick and dirty summary of it: (I use diamond radiators because of structural strength and cheapness to armour efficiently) <2400: civilian boat territory, only way this thing will work is with radiators that have 100nm armour and are big enough to be used as solar sails 2500 : efficient for civilian ship with armoured radiators(2cm) with 1 redundancy - this thing might win vs a pure laser boat if its lucky 2600 : best for medium combat ships with 2-4 set of redundant radiators with medium armour(<8cm) - can survive a light peppering of kinetic ammo 2700 : an in between reactor use as and when 2800+ : best for mele brawlers with 5+ sets of redundant and heavy armour on radiators (>8cm) - bring on the rain for I fear no railgun! I should probably test if its possible to make a 3000k outlet radiators but when I tried efficiency drops were harsh Since the reactor can't run above 3200K hot side, the thermocouple's best efficiency is at 500K dT, and the mathematical optimum radiator temperature suggests ~2400K, I would expect going above 2700K will only increase radiator area for a given electrical power output. Do you observe differently? |
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