Sit down comfortably, relax, and admire, because I've found ZE solution.
Well, maybe it exists already, but as usual I didn't check, so interested people should.
I propose to control the aerostat's buoyancy through the temperature of a gas, but with little heat expense and a short reaction time, by using a heat storer-exchanger about as a Stirling engine does.
Such a storer-exchanger has a a warm and a cold side and let's the fluid flow from cold to warm to warm it, and in the reverse direction to cool it.
- Heat removed from the fluid gets back in the storer-exchanger for re-use;
- The fluid has everywhere nearly the temperature of the storer-exchanger, avoiding losses;
- The same fluid gives and receives heat at different times. No need to withstand pressure nor transmit heat through a wall. The exchange surface is easily made huge.
By moving a gas through a storer-exchanger in one direction or the other, its temperature and volume hence buoyancy is controlled quickly and reversibly: very nice for the aerostat. Heat is lost only through technological imperfections or if the aerostat delivers cargo higher than it picked it.
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The gas can be helium (needs less heat for being monoatomic), air, or an other, even heavier than air.
The insulating envelope, the storer-exchanger... can be outside or within the aerostat's main hull, and might even be the main hull. If within the main hull, heat leaks through the insulating envelope don't reduce immediately the total buoyancy - but they affect the buoyancy's control range.
On the sketch, the storer-exchanger itself moves in a stiff insulating envelope, but this envelope could be deformable, or a separate piston could move the gas - combine several methods if you like worries.
Smooth operation, including stability, wants to keep the warm gas at nearly the warmer temperature of the storer-exchanger. The gas can be blown, or rely on natural convection, for instance if it's above the storer-exchanger.
A very intimate contact between the gas and the storer-exchanger is compatible with a small pressure drop. It needs finely divided gas channels, suggesting a clean gas. Many narrow and short capillaries, fed in parallel by arteries, arterioles, veinules and veins like for blood, possibly in different directions, make a superior organisation. One example is a porous ceramic with in and out channels on a chessboard pattern, but stapled sheet would achieve it too, as would loose powder, or a metal or ceramic mesh, or thin nickel that separates the gas from a heat storing liquid - and more possibilities.
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For the storer-exchanger, water possibly mixed with antifreeze, brine (of LiF better than NaCl?), and other materials like liquid or solid paraffins (polyolefins) have a big heat capacity but a limited temperature range - as may the insulating envelope. A liquid, or solid-liquid transitions preferably at successive temperatures, should be immobilized to preserve a warm and a cold side.
Take again a 2kN (200kg) buoyancy control. 625m3 of helium getting 80K would need ~500kg of brine to lose 20K.
A bigger relative temperature variation in the storer-exchanger is acceptable if:
- Gas exiting it doesn't mix, so gas' temperature corresponds to the storer-exchanger when it enters again;
- Sections of the storer-exchanger are switched so its extreme temperatures correspond to the gas at both sides;
or use solid-liquid transitions, with proper regulation.
Metal, ceramic... enable a hotter storer-exchanger but offer only some 800W/kg/K. Li, Be, B bring more but have drawbacks.
The storer-exchanger can be heated before flight, possibly outside the main envelope, by a combustion, electricity, Sunlight... and be further heated or not during flight.
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A stiff insulating envelope can consist of foam, or a possibly multilayer honeycomb with organic spacer... They can be filled with a better insulator than helium, like argon or vacuum. Aramide, polyimide have good heat resistance - and a ceramic foam would be welcome.
If flexible, the insulating envelope might use a foam as well, or mesh between several films... Roll it like a toothpaste tube?
If surrounding the warmer gas mainly by the storer-exchanger, for instance as two big pistons in a short cylinder, then leaks decrease.
Marc Schaefer, aka Enthalpy