Archimerged has not given up on submerged air containers, but he is down on air entrained in water. Unless some polymer could form a skin around the bubbles which somehow anchors the bubble to the water flow. Maybe a long hydrophobic chain connected to a longer hydrophilic chain, like soap except instead of a single charged acid group, it has long polarized tails extending into the bulk water. But forget that for the moment. Today he is thinking about big wheels and chains of buckets pulling cold air down a column of cold water while expanding hot air in another chain of buckets pulls on the wheel while moving up through a column of hot water.
Imagine swinging buckets on a completely submerged water wheel, a WaterAirWheel, so to speak. That gets rid of the chains but requires a very big wheel. Looking broadside onto the counter-clockwise turning wheel, the left side is in a deep pool of cold water and the right side is in a deep pool of hot water. The two pools are separated by the hub of the wheel and a wall of stationary insulation which fits closely to the wheel to prevent water flow. The wheel and buckets are coated with insulation so heat doesn’t flow into the wheel on the hot side or out of the wheel on the cold side. The buckets are carefully designed so that no cold water or air is carried over to the hot side at the bottom, and no hot water or air is carried over to the cold side at the top. Unlike the TrombePump, the WaterAirWheel doesn’t need to repeatedly heat and cool the water, but it does need a long flexible partition which rubs against the walls of the wheel to keep water from flowing from one tank to the other.
On the hot side, hot compressed air bubbles up into buckets near the bottom of the wheel, and escapes at the top when the bucket tips upward. On the cold side, cold atmospheric pressure air is captured at the top. The buckets are shaped so the compressed cold air escapes upward into a fixed inverted collector just before reaching the bottom of the wheel and the insulated wall between the cold and hot tanks. A solid cylinder fills the buckets at the bottom, displacing cold compressed air and water as the bucket envelops the cylinder and swings around it. As the bucket pulls away from the cylinder, hot water and some hot compressed air flows into the bucket which is now tilted to hold the air in as it rises.
That’s rather complicated and very big. On second thought, Archimerged begins to like chains of buckets with idler wheels at top and bottom, and a large gear transmitting force from the hot idler to the cold idler. That reduces the size of the water tanks and allows them to be arbitrarily deep with only a linear increase in cost instead of a quadratic increase. The width and breadth of the tanks is constant with increasing depth, instead of constant breadth with width equal to depth. Since this still has a (relatively) big wheel, Archimerged figures he can still call this modified version a WaterAirWheel.
In the cold tank, buckets carry cold air downward, compressing it, and return full of water. In the hot tank, they descend full of water but return full of expanding hot air.
A large countercurrent heat exchanger cools hot atmospheric pressure air at constant pressure while warming cold high pressure air at constant pressure. The hot heat source keeps the hot water hot, and the cold heat sink keeps the cold water cold. The machine can turn an additional load at the wheel, or it can admit additional atmospheric pressure air and output high pressure cold or hot air.