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Post by n2maniac on Dec 22, 2016 5:36:09 GMT
Gah, shurugal, you are right! I goofed up between heat input and waste heat. A Carnot engine operating between T1 and T2 in series with another Carnot engine operating between T2 and T3 will perform identically to a single Carnot engine operating between T1 and T3 (it must given they are all reversible + the 1st law of thermodynamics). A heat pump is just a heat engine operating in reverse (so a less efficient Carnot engine), so pumping the temperature back up will do no better than just exhausting at the higher temperature to begin with. For a Carnot engine approximation to the heat pump to pump 250MW of heat from 600K to 2400K (yay, nice round numbers), we have eff = 1-T"c" / T"h", but c and h are reversed. That computes to eff = 1 - 2400/600 = -3 (yes, negative 300%). It will take 750MW of work (electricity) and 250MW of input heat to exhaust 1GW at 2400K. Then that sequence with the reactor becomes: 1.25GW heat @ 3000K -> 250MW heat @ 600K + 1GW work 750MW work + 250MW heat @ 600K -> 1000MW heat @ 2400K total: 1.25GW heat @ 3000K -> 250MW work + 1GW heat @ 2400K2 (please continue to sanity check my numbers and keep me honest)
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Post by shurugal on Dec 22, 2016 17:50:08 GMT
Gah, shurugal , you are right! I goofed up between heat input and waste heat. A Carnot engine operating between T1 and T2 in series with another Carnot engine operating between T2 and T3 will perform identically to a single Carnot engine operating between T1 and T3 (it must given they are all reversible + the 1st law of thermodynamics). A heat pump is just a heat engine operating in reverse (so a less efficient Carnot engine), so pumping the temperature back up will do no better than just exhausting at the higher temperature to begin with. For a Carnot engine approximation to the heat pump to pump 250MW of heat from 600K to 2400K (yay, nice round numbers), we have eff = 1-T"c" / T"h", but c and h are reversed. That computes to eff = 1 - 2400/600 = -3 (yes, negative 300%). It will take 750MW of work (electricity) and 250MW of input heat to exhaust 1GW at 2400K. Then that sequence with the reactor becomes: 1.25GW heat @ 3000K -> 250MW heat @ 600K + 1GW work 750MW work + 250MW heat @ 600K -> 1000MW heat @ 2400K total: 1.25GW heat @ 3000K -> 250MW work + 1GW heat @ 2400K2 (please continue to sanity check my numbers and keep me honest) your numbers look better than mine for the heat pump, but does this not assume that we are working with fluids having the same heat capacity? IE: we extract heat from X tons of water, then try to put it back? For example, if we use Water in our turbine, it has a heat capacity of 4.18 kJ/kg*K, but radon only has a heat capacity of 93J/kg*K, would it not therefore take less power to pump radon up from, say, 280k (after using it to chill the water) to 2500k for considerably less power than to do the same with water? or do we just end up using a fuckton more radon to move the same heat energy, with no benefit to the heat pump?
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Post by newageofpower on Dec 22, 2016 18:28:07 GMT
Pumping heat from a lower level of saturation to a higher heat environment (basically, refrigeration and air conditioning applied large-scale) is inherently inefficient. I don't know the numbers off the top of my head so I can't say if n2's numbers look correct or not.
Either way, Turboelectric allows us to extract significantly more energy for a given level of reactor heat.
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Post by n2maniac on Dec 22, 2016 22:36:04 GMT
Gah, shurugal , you are right! I goofed up between heat input and waste heat. A Carnot engine operating between T1 and T2 in series with another Carnot engine operating between T2 and T3 will perform identically to a single Carnot engine operating between T1 and T3 (it must given they are all reversible + the 1st law of thermodynamics). A heat pump is just a heat engine operating in reverse (so a less efficient Carnot engine), so pumping the temperature back up will do no better than just exhausting at the higher temperature to begin with. For a Carnot engine approximation to the heat pump to pump 250MW of heat from 600K to 2400K (yay, nice round numbers), we have eff = 1-T"c" / T"h", but c and h are reversed. That computes to eff = 1 - 2400/600 = -3 (yes, negative 300%). It will take 750MW of work (electricity) and 250MW of input heat to exhaust 1GW at 2400K. Then that sequence with the reactor becomes: 1.25GW heat @ 3000K -> 250MW heat @ 600K + 1GW work 750MW work + 250MW heat @ 600K -> 1000MW heat @ 2400K total: 1.25GW heat @ 3000K -> 250MW work + 1GW heat @ 2400K2 (please continue to sanity check my numbers and keep me honest) your numbers look better than mine for the heat pump, but does this not assume that we are working with fluids having the same heat capacity? IE: we extract heat from X tons of water, then try to put it back? For example, if we use Water in our turbine, it has a heat capacity of 4.18 kJ/kg*K, but radon only has a heat capacity of 93J/kg*K, would it not therefore take less power to pump radon up from, say, 280k (after using it to chill the water) to 2500k for considerably less power than to do the same with water? or do we just end up using a fuckton more radon to move the same heat energy, with no benefit to the heat pump? You just use a fuckton more radon to move it. One of the fundamental laws regarding a Carnot engine is that no heat engine can do better than it in terms of efficiency. This would make sense since it is reversible and energy cannot be created from nothing (i.e. no perpetual motion / energy machines).
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Post by shurugal on Dec 23, 2016 0:03:44 GMT
your numbers look better than mine for the heat pump, but does this not assume that we are working with fluids having the same heat capacity? IE: we extract heat from X tons of water, then try to put it back? For example, if we use Water in our turbine, it has a heat capacity of 4.18 kJ/kg*K, but radon only has a heat capacity of 93J/kg*K, would it not therefore take less power to pump radon up from, say, 280k (after using it to chill the water) to 2500k for considerably less power than to do the same with water? or do we just end up using a fuckton more radon to move the same heat energy, with no benefit to the heat pump? You just use a fuckton more radon to move it. One of the fundamental laws regarding a Carnot engine is that no heat engine can do better than it in terms of efficiency. This would make sense since it is reversible and energy cannot be created from nothing (i.e. no perpetual motion / energy machines). Hmm. I would have expected that we would preserve thermodynamics by using less energy to heat a lower-heat substance. I suppose if all we were doing was heating an arbitrary amount of radon to 2500, we could just use a few grams and only need a dozen joules or so to do it. What i really want to crunch numbers on, now, is, first, how much water would be coming out of our carnot engine to be carrying 250MW @600k after expanding from 2400k@1.25 GW? Can anyone point me in the direction of the calculations for that? If i knew the flow rate at the exit, I could crunch numbers on how much radon flow would be needed to bring the radon from 203K to 279K, while dropping the water from 600K to 279K. My instinct tells me that there is still somewhere we can make this work, and until i can crunch numbers to prove it wrong, it's gonna bug me.
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Post by n2maniac on Dec 23, 2016 4:45:36 GMT
You just use a fuckton more radon to move it. One of the fundamental laws regarding a Carnot engine is that no heat engine can do better than it in terms of efficiency. This would make sense since it is reversible and energy cannot be created from nothing (i.e. no perpetual motion / energy machines). Hmm. I would have expected that we would preserve thermodynamics by using less energy to heat a lower-heat substance. I suppose if all we were doing was heating an arbitrary amount of radon to 2500, we could just use a few grams and only need a dozen joules or so to do it. What i really want to crunch numbers on, now, is, first, how much water would be coming out of our carnot engine to be carrying 250MW @600k after expanding from 2400k@1.25 GW? Can anyone point me in the direction of the calculations for that? If i knew the flow rate at the exit, I could crunch numbers on how much radon flow would be needed to bring the radon from 203K to 279K, while dropping the water from 600K to 279K. My instinct tells me that there is still somewhere we can make this work, and until i can crunch numbers to prove it wrong, it's gonna bug me. Basic heat capacity calculations hyperphysics has a quick intro. A fair warning: Carnot engines do not care what substance they are working with for a reason: it does not matter. Transferring heat between substances of different specific heat capacities will not get around the laws of thermodynamics.
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Post by shurugal on Dec 23, 2016 16:28:36 GMT
Hmm. I would have expected that we would preserve thermodynamics by using less energy to heat a lower-heat substance. I suppose if all we were doing was heating an arbitrary amount of radon to 2500, we could just use a few grams and only need a dozen joules or so to do it. What i really want to crunch numbers on, now, is, first, how much water would be coming out of our carnot engine to be carrying 250MW @600k after expanding from 2400k@1.25 GW? Can anyone point me in the direction of the calculations for that? If i knew the flow rate at the exit, I could crunch numbers on how much radon flow would be needed to bring the radon from 203K to 279K, while dropping the water from 600K to 279K. My instinct tells me that there is still somewhere we can make this work, and until i can crunch numbers to prove it wrong, it's gonna bug me. Basic heat capacity calculations hyperphysics has a quick intro. A fair warning: Carnot engines do not care what substance they are working with for a reason: it does not matter. Transferring heat between substances of different specific heat capacities will not get around the laws of thermodynamics. I suppose one critical point i am overlooking here is this: Do the laws of thermodynamics not operate in parallel with conservation of energy? I have been making my assumptions and crunching my numbers on the basis that so long as energy in == energy out, we're golden.
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Post by n2maniac on Dec 23, 2016 19:23:09 GMT
Basic heat capacity calculations hyperphysics has a quick intro. A fair warning: Carnot engines do not care what substance they are working with for a reason: it does not matter. Transferring heat between substances of different specific heat capacities will not get around the laws of thermodynamics. I suppose one critical point i am overlooking here is this: Do the laws of thermodynamics not operate in parallel with conservation of energy? I have been making my assumptions and crunching my numbers on the basis that so long as energy in == energy out, we're golden. Conservation of energy is correct, but alone insufficient. The efficiency limits of a Carnot engine are also critical here. Carnot's theorem is central. Hyperphysics and Wikipedia have info on the Carnot engine, but those get a little off into the weeds.
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Post by shurugal on Dec 23, 2016 20:18:39 GMT
I suppose one critical point i am overlooking here is this: Do the laws of thermodynamics not operate in parallel with conservation of energy? I have been making my assumptions and crunching my numbers on the basis that so long as energy in == energy out, we're golden. Conservation of energy is correct, but alone insufficient. The efficiency limits of a Carnot engine are also critical here. Carnot's theorem is central. Hyperphysics and Wikipedia have info on the Carnot engine, but those get a little off into the weeds. bleh. I suppose it wouldn't help to stick a resistive heating element in there, would it?
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Post by n2maniac on Dec 23, 2016 20:38:07 GMT
Conservation of energy is correct, but alone insufficient. The efficiency limits of a Carnot engine are also critical here. Carnot's theorem is central. Hyperphysics and Wikipedia have info on the Carnot engine, but those get a little off into the weeds. bleh. I suppose it wouldn't help to stick a resistive heating element in there, would it? A resistive heating element is less efficient than a heat pump, so no, you would be better off just operating the first heat engine at a higher exhaust temperature. For a given generator it would shrink the radiator area, but robs more output power than it is worth (at least compared to a one-stage heat engine with higher exhaust temperature).
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Post by shurugal on Dec 23, 2016 20:59:55 GMT
bleh. I suppose it wouldn't help to stick a resistive heating element in there, would it? A resistive heating element is less efficient than a heat pump, so no, you would be better off just operating the first heat engine at a higher exhaust temperature. For a given generator it would shrink the radiator area, but robs more output power than it is worth (at least compared to a one-stage heat engine with higher exhaust temperature). sounds like we need to go the other way: Liquid hydrogen cooled reactors at 3100k expanded to 4k in a turbine. 99.87% efficient. 1.0013GW in, 1GW out, waste heat... still way the fuck too much to radiate. damn.
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Post by newageofpower on Dec 23, 2016 21:36:34 GMT
sounds like we need to go the other way: Liquid hydrogen cooled reactors at 3100k expanded to 4k in a turbine. 99.87% efficient. 1.0013GW in, 1GW out, waste heat... still way the fuck too much to radiate. damn. At 99.87% efficiency, you use open cycle cooling. Forget radiators.
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Post by n2maniac on Dec 23, 2016 21:45:58 GMT
sounds like we need to go the other way: Liquid hydrogen cooled reactors at 3100k expanded to 4k in a turbine. 99.87% efficient. 1.0013GW in, 1GW out, waste heat... still way the fuck too much to radiate. damn. At 99.87% efficiency, you use open cycle cooling. Forget radiators. Going to re-suggest aiming for a radiator operating at 2100K to 2600K. The math/plot is here. Other than a few details (helium boils at 4K and absorbs almost no heat upon boiling) open cycle would work very well for a reactor that needed to operate for less than, say, 5 minutes. There is another thread on that topic elsewhere, but a larger delta-T heat engine would improve its case.
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Post by newageofpower on Dec 23, 2016 21:59:10 GMT
Going to re-suggest aiming for a radiator operating at 2100K to 2600K. The math/plot is here. Other than a few details (helium boils at 4K and absorbs almost no heat upon boiling) open cycle would work very well for a reactor that needed to operate for less than, say, 5 minutes. There is another thread on that topic elsewhere, but a larger delta-T heat engine would improve its case. -_- You wouldn't actually go to 4k for liquid helium, you'd go to liquid hydrogen (~20k) which has a decent specific heat of almost 10kj/kg. Obviously, you can't run your reactor 24/7, but long enough to destroy any target of your main laser? Perfectly viable. EDIT: I did read your discussion and math on the "How hot to run reactor" thread, btw. Good stuff.
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Post by fenrin49 on Dec 23, 2016 22:07:19 GMT
throw molten heat sinks at your enemys! on a more serious note being able to throw that heat into your propellant as a sort of closed cycle NTR would be useful. having ntr and resistojets always struck me as odd one has a reactor that is turned off half the time the other uses electricity to make heat and radiates a bunch of heat from the reactors as waste in order to make that heat.
so use that reactor to make some energy and use that waste heat to make some thrust(will probably need a little bit of power to get the heat up to useful levels). why use two reactors when you only need one? why radiate heat when you can make thrust with it? you still need radiators as back up to dump heat when not maneuvering or be limited in how much power you can use by thermal throttling.
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