Heat produced by Focus Fusion and cooling

[Allan Brewer]

I have been reading the “How will we get there from here?” text linked from the FFS home page, and in particular the section about yield and efficiency.
To paraphrase: we put in 100KJoules per shot, and create an extra 33KJoules by fusion, but lose around 10-20% of the whole through inefficiency.

On those figures and assuming all the loss appears as heat then, per shot, we recover our 100KJoules for the next shot, we generate 6-20KJoules of new electricity and 13-26KJoules of heat.

Assuming a cycling rate of 300 per second that gives us approximately 2-6 MWatts of electricity and 4-8 MWatts of heat.

My gut feeling is that it would be impossible to cool away 4-8 MWatts of heat from such a small device???

Is my lack of engineering knowledge making me pessimistic, or am I missing something else?

[jamesr]

The core of a conventional fission reactor, such as a PWR has around 3500MW being produced in a volume of around 3 cubic meters. A fast breeder reactor is even smaller – hence they need to use a more efficient coolant (liquid sodium). But you can get that order of head out of a small volume. It’s just a case of pumping through a large enough volume of coolant fast enough.

A PWR for example pumps around 11tonnes of water through it ever second!

[Breakable]

I am not an engineer, but I would expect that the first prototypes and production units would function at a much lower shot frequency allowing for easy thermal management.
Maybe after this technology is tried and proven we can have world class scientists and engineers work out more efficient cooling and energy conversion methods.

[Allan Brewer]

It’s just a case of pumping through a large enough volume of coolant fast enough

.

That’s reassuring, but where does most of the heat arise?
Presumably we can’t pump water or sodium through the anode or cathode as that would make the coolant electrically live?
Would coolant around the vacuum chamber block the X-rays to the onion?
Are there any tentative plans as to how cooling could be done?

[jamesr]

The anode would have helium gas pumped through, in order to keep its surface below 800K or so. The outside of the vacuum chamber and other parts (eg. the capacitors) can be conventionally water cooled.

[rashidas]

Any surplus heat from Aneutronic Fusion need not be wasted. Instead it can be used directly for space heating in winter and air conditioning in summer. Many European cities have central space heating systems. It can also be used to heat/cool greenhouses and for aquaculture, especially in cold climates. If FF is safe enough to be built in urban/suburban areas space heating and cooling would be both easy and economical and would improve the economics of a FF power plant.

[belbear]

Allan Brewer wrote:
That’s reassuring, but where does most of the heat arise?
Presumably we can’t pump water or sodium through the anode or cathode as that would make the coolant electrically live?
Would coolant around the vacuum chamber block the X-rays to the onion?
Are there any tentative plans as to how cooling could be done?

Contrary to common belief, water CAN be used to cool electrically live components. Unlike tap water, fully deionized water is nonconductive. This is standard technology in high-powered transmitters that use triodes or klystrons, where the bare anodes, carrying up to 40KV, are in direct contact with the coolant water. A short length of glass or ceramic pipe is used to connect the HV component, for the rest ordinary metal pipes do the job. Saw it with my own eyes.

Disadvantages of water are its viscosity when liquid, its low boiling point and its corrosiveness when gaseous at high temperature. Helium has none of these drawbacks, so it may be a better primary coolant.

The X-ray “onion” has to be put inside the vessel, and cooled as well. Again, for cooling the X_ray converter, helium coolant is ideal because it does not block X-rays.
For the vacuum vessel and other electrical components (capacitors, switches, beam converter, transformers), ordinary water cooling can be used.

[vansig]

jamesr wrote: The anode would have helium gas pumped through, in order to keep its surface below 800K or so. The outside of the vacuum chamber and other parts (eg. the capacitors) can be conventionally water cooled.

for 5MW of cooling to an exit temperature of 800K, I’m getting that ~2 kg/s of helium gas would need to be pumped.

delta-T = 527° (800K – 373K, if the secondary coolant is water);
Helium heat capacity = 20.786 J·mol−1·K−1
5MW / 20.786 J·mol−1·K−1 / 527° = 456 mol/s
= 1.8 kg/s

If the anode is constructed to enable co-axial flow, of cool helium up through the centre (~1cm diameter “artery”), and to exit back down along the adjacent layer, closer to the surface (“veins”), what is the max flow rate?

[jamesr]

vansig wrote:

The anode would have helium gas pumped through, in order to keep its surface below 800K or so. The outside of the vacuum chamber and other parts (eg. the capacitors) can be conventionally water cooled.

for 5MW of cooling to an exit temperature of 800K, I’m getting that ~2 kg/s of helium gas would need to be pumped.

delta-T = 527° (800K – 373K, if the secondary coolant is water);
Helium heat capacity = 20.786 J·mol−1·K−1
5MW / 20.786 J·mol−1·K−1 / 527° = 456 mol/s
= 1.8 kg/s

If the anode is constructed to enable co-axial flow, of cool helium up through the centre (~1cm diameter “artery”), and to exit back down along the adjacent layer, closer to the surface (“veins”), what is the max flow rate?

I love this kind of quick & dirty calculation. It lets you get a grasp on what are fairly intangible concepts and bring them into reality.

The outer surface or the anode would get that hot, but there would be a steep thermal gradient down to the cooling “veins” running through it. So their inner wall temperature, even if they are only 1mm below the surface would be quite a bit less. Hence the volume of coolant, I reckon, would probably be a bit more than your estimate.

[vansig]

Ok. but i’m using the exit temperature of the helium, and holding that at 800K for these calculations. so the anode surface will climb a little higher than 800K.

next, i’m getting that at 373K, the volume of 456 mol/s helium is ~14 m³/s (at ~1atm pressure), which would need to become supersonic to pass through the artery.

PV=nRT
= (456) (8.314) (373)
= 1.414 x 10^6 m³ Pa
= 13.9 m³ x 1 atm

(edit: corrected)
speed of sound in helium = ~1137 m/s at 373K;
1137 m/s x Area = 14 m³/s
Area = 0.0122 m²;
= a 12.5 cm diameter tube. since the injection nozzle is smaller, so then the pressure must increase until enough coolant goes through.

Seems like pressure will climb to ~175 atmospheres (the typical pressure in a fuel injector), and/or the gas velocity will become supersonic.
Can it do this?

Or will that exceed the structural strength of the beryllium anode?

[digh]

jamesr wrote: The anode would have helium gas pumped through, in order to keep its surface below 800K or so. The outside of the vacuum chamber and other parts (eg. the capacitors) can be conventionally water cooled.

Perhaps the heat energy could be recaptured for helium cooling with a Brayton closed cycle gas turbine.

[jamesr]

I think, for a Brayton cycle you would need the helium temperature to be higher.

This may be eventually achievable with some fancy materials technology to allow the anode surface to run hotter without boiling off.

[vansig]

digh wrote:
Perhaps the heat energy could be recaptured for helium cooling with a Brayton closed cycle gas turbine.

possibly. note, that the temperature ratio is 800:373, just over 2:1, which i’m not sure is all that good, but the pressure ratio could be increased with intercooling… “wherein the working fluid passes through a first stage of compressors, then a cooler, then a second stage of compressors before entering the combustion chamber.” in this case, what they call the “combustion chamber” is the space inside the anode just beneath the tip, where the cooled, high-pressure helium gas squirts from the artery.

some people might quibble about terms, since this is not really internal heat generation, (meaning internal to the working fluid), but it’s all based on the same principles.

also, the turbine could run the compressor pumps, and further heat be rejected with combined cycle, using water and steam, running counter-current to the higher-temperature helium flow. it all seems very expensive, though.

the compressor, even a compact one, will be bulky. check http://www.grcompressor.com/

[vansig]

jamesr wrote: I think, for a Brayton cycle you would need the helium temperature to be higher.

This may be eventually achievable with some fancy materials technology to allow the anode surface to run hotter without boiling off.

curiously, 565°C (838K) is the usual upper limit for the Rankine cycle, due to the creep strength of stainless steel.
— http://www.engineersedge.com/material_science/creep.htm

to run the anode surface hotter, creep limit is really the property we want to know. for 90-day service, that would be specified as something like “creep rate of 0.01 in 2000 hours at operating temperature of X”

[Allan Brewer]

Really exciting posts guys – I am not an engineer but hope this helps:

“Creep characteristics of beryllium have been determined in the temperature range 600–800°C and the stress range 0.25–5 kgf/mm2. The rate of the process is controlled by the Herring —Nabarro mechanism in the range of stresses less than 1 kgf/mm2. The creep activation energy (39±1 kcal/mole) hence agrees with the energy of self-diffusion. The creep rate for stresses greater than 1 kgf/mm2 is determined by the simultaneous progress of dislocation creep and slip, where the slip contribution grows with the increase in stress. An approximate picture of the deformation mechanisms of creep is constructed.”

http://www.springerlink.com/content/g78658x377h72768/fulltext.pdf

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