In a 100 MW BFR (Bussard Fusion Reactor) with 20 % area intercept, back of the envelope calculations show that Heat Load on the MaGrid will be about 1 Mw / sq m. About the limit of current technology. .3 Mw / sq m is common.
Above 100 Mw unless we can reduce the size of the coils, power output can only increase as the square of the radius. That is rather unfavorable.
The implication for space travel is that fusion reactors of the Bussard design may not have the power density for boost to LEO.
Heat Transfer Limitations Re: Power Plants and Rockets
Heat Transfer Limitations Re: Power Plants and Rockets
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Yes.93143 wrote:I suppose we'll just have to advance the state of the art.
I believe the Space Shuttle Main Engines with LH cooling max out at 1 to 2 Mw/sq m.What if you did something dumb like using high-pressure supercritical hydrogen instead of water?
Engineering is the art of making what you want from what you can get at a profit.
It is very straight forward.
Assume a power. Assume a core radius. Assume a 20% power intercept. Assume an area for heat transfer of pi times the intercept area. Actually a factor of 2X is more likely due to variations of power/area over the surface of the toroid. This is helped to some extent by getting "backside" flows to swirl around to the front. Vanes at appropriate places in the piping.
Area of a sphere is 4*pi*r^2.
Assume a power. Assume a core radius. Assume a 20% power intercept. Assume an area for heat transfer of pi times the intercept area. Actually a factor of 2X is more likely due to variations of power/area over the surface of the toroid. This is helped to some extent by getting "backside" flows to swirl around to the front. Vanes at appropriate places in the piping.
Area of a sphere is 4*pi*r^2.
Engineering is the art of making what you want from what you can get at a profit.
What I see:
4*(1.5m)^2*pi = 28.3 m^2
100MW*.2/28.3m^2=700 kW/m^2
for a 1.5m radius reactor, about the size Bussard suggested would be necessary for p-11B fusion. (Of course, there's far more variables involved in that.) Not sure where you get the pi multiplication factor; either you have 20% of the energy intercepted at the magrid or you don't.
For a .75m radius reactor sufficient for D-D fusion,
4*(.75m)^2*pi=7.07m^2
100MW*.2/7.07m^2=2.8 MW/m^2
Much worse for the smaller reactor. Of course, the actual heat generated may be wildly different depending on things like neutron interception (much worse for D-D, which was already bad thanks to the smaller radius) and whether the MaGrid converts those electrically.
4*(1.5m)^2*pi = 28.3 m^2
100MW*.2/28.3m^2=700 kW/m^2
for a 1.5m radius reactor, about the size Bussard suggested would be necessary for p-11B fusion. (Of course, there's far more variables involved in that.) Not sure where you get the pi multiplication factor; either you have 20% of the energy intercepted at the magrid or you don't.
For a .75m radius reactor sufficient for D-D fusion,
4*(.75m)^2*pi=7.07m^2
100MW*.2/7.07m^2=2.8 MW/m^2
Much worse for the smaller reactor. Of course, the actual heat generated may be wildly different depending on things like neutron interception (much worse for D-D, which was already bad thanks to the smaller radius) and whether the MaGrid converts those electrically.
The actual pipe area will be approximately 2 pi times the intercept area because of the toroidal nature of the magnet. Assuming skinny toroids.
The intercept area is a projection of the pipe area.
I'm assuming 1 pi because I look at only the impingement side of the pipe. Then I cut that down some more because not all the pipe will be receiving maximum flux so you have a peak to average problem.
As I said. This gives you an idea of the problem.
Three things to do:
1. Make the magnet structure smaller.
2. Increase heat transfer capabilities
3. Make the magnets strong enough to deflect 3 MeV alphas
Note: #3 is in conflict with #1 - so there are tradeoffs.
The intercept area is a projection of the pipe area.
I'm assuming 1 pi because I look at only the impingement side of the pipe. Then I cut that down some more because not all the pipe will be receiving maximum flux so you have a peak to average problem.
As I said. This gives you an idea of the problem.
Three things to do:
1. Make the magnet structure smaller.
2. Increase heat transfer capabilities
3. Make the magnets strong enough to deflect 3 MeV alphas
Note: #3 is in conflict with #1 - so there are tradeoffs.
Engineering is the art of making what you want from what you can get at a profit.
Room temperature hydrogen at 200 psi is supercritical. The question is, how much heat capacity can you pump through the coil sheath without destroying it? Hydrogen is less dense than water, but its specific heat is three and a half times higher - the highest of any known substance, probably of any substance period. As a gas, its viscosity is quite low (at SATP it has half the viscosity of air, and even well into the supercritical regime the viscosity should be lower than that of liquid water), making it potentially easier to pump.scareduck wrote:Solutions that require being at Jupiter's core are non-starters.
I can't really see using cryogenic liquid for the outer sheath, so I came up with a compromise off the top of my head.
You know, for a large reactor we can probably afford to have several layers, rather than just three or four. This could increase the power scaling from r^2 to closer to r^3 with no additional advances. We're still talking about at least a tenfold increase in required heat removal rate per unit area for a 6 GW reactor, but it's starting to sound possible.
I find this encouraging, even though it's not directly related: http://www.reactionengines.co.uk/he_man.html
Apparently they've manufactured and tested a piece, and it works. The improvement is about what we're looking at over previous state of the art.
I only took one course that actually focused exclusively on heat transfer, and it was a while back. Bear with me here...
EDIT: changed the factor of improvement in Cp between water and hydrogen - I accidentally compared gaseous hydrogen with air, and in terms of heat capacity gaseous hydrogen REALLY kicks the #@$& out of air...
Last edited by 93143 on Mon Feb 25, 2008 1:54 am, edited 1 time in total.
Seriously?
Even a p-11B reactor would generate significant enough neutrons to make life very unhealthy for any humans nearby. You couldn't exactly open a hole on one side of the reactor and launch a rocket that way. Humans in the payload (not to mention anything that doesn't like neutrons, which covers a lot of stuff) would require a pretty significant amount of shielding.
This is one part of Bussard's claims where I think he really let his imagination get way, way ahead of him.
Even a p-11B reactor would generate significant enough neutrons to make life very unhealthy for any humans nearby. You couldn't exactly open a hole on one side of the reactor and launch a rocket that way. Humans in the payload (not to mention anything that doesn't like neutrons, which covers a lot of stuff) would require a pretty significant amount of shielding.
This is one part of Bussard's claims where I think he really let his imagination get way, way ahead of him.
I think that if you're running a horizontal-takeoff-and-landing spaceplane (reduced gravity losses) with combined-cycle QED engines (ie: airbreathing below some substantial fraction of orbital velocity), your SSTA should be capable of lofting a reasonable boronated-water shadow shield.
Say... if we're using liquid hydrogen for propellant, maybe we could carry some liquid oxygen for the orbital insertion and boost the vacuum thrust/Isp beyond QED nominal...
In the air, of course, it doesn't matter; we're probably talking about an Isp of a trillion seconds or something like that, because no propellant is expended and the thrust per unit energy is so high.
Say... if we're using liquid hydrogen for propellant, maybe we could carry some liquid oxygen for the orbital insertion and boost the vacuum thrust/Isp beyond QED nominal...
In the air, of course, it doesn't matter; we're probably talking about an Isp of a trillion seconds or something like that, because no propellant is expended and the thrust per unit energy is so high.
Use the reaction mass as shielding.scareduck wrote:Seriously?
Even a p-11B reactor would generate significant enough neutrons to make life very unhealthy for any humans nearby. You couldn't exactly open a hole on one side of the reactor and launch a rocket that way. Humans in the payload (not to mention anything that doesn't like neutrons, which covers a lot of stuff) would require a pretty significant amount of shielding.
This is one part of Bussard's claims where I think he really let his imagination get way, way ahead of him.
Here is how you do it.
1. Reaction mass moderates neutrons. If the neutrons are moderated down to 5K all the better. A few inches (4" to 6") of reaction mass will get all the neutrons thermalized.
2. Thin layer of B10 - 1 mm absorbs all the neutrons.
3. Thin layer of ??? absorbs 500 KeV gammas
I like the maglev slingshot idea. Start off at Mach .8
Engineering is the art of making what you want from what you can get at a profit.
These guys claim they can get 2 Mw per sq m
http://www.delftoutlook.tudelft.nl/info ... ArtID=4242
http://www.efda.org/news_and_events/dow ... 005_05.pdf
http://www.brightsurf.com/news/headline ... nents.html
http://www.delftoutlook.tudelft.nl/info ... ArtID=4242
The above from:In fusion devices of the next generation, such as ITER and Wendelstein 7-X, the thermal load on the divertor regions will be appreciable. Powers of up to 10 megawatts per square metre, with transients much higher, are expected. The development of suitable divertor components is to be supported by tests on the GLADIS heat test facility at Garching. “We had the good fortune,” states project head Henri Greuner, “of being able to enlist existing powerful components for building GLADIS and thus save costs.
http://www.efda.org/news_and_events/dow ... 005_05.pdf
http://www.brightsurf.com/news/headline ... nents.html
Engineering is the art of making what you want from what you can get at a profit.
Wow, is it really that high? I assumed the coils were 10% of the space or less.Assume a 20% power intercept.
Hmm? Am I missing something here? How do we go from to R^7 to R^2? (Okay, it's really R^3 * B^4, but still).Above 100 Mw unless we can reduce the size of the coils, power output can only increase as the square of the radius.
Edit: Oh, duh, the radiative square law, so the heat load doesn't grow over that limit. Yeah, shrinking the coils would help a lot.
Still, how bad is r^2 over 100MW? Even if the engine mass is growing at r^3 while power grows at r^2, given how mass/energy-efficient the fuel is it seems like there ought to be a size that produces enough power for LEO. Has anyone done back of the envelope calcs on mass/thrust?