TL;DR

Does using a Lilly impeller create space for vacuum accumulation in an inverted vacuum chamber half submerged in water?

Also, we do not allow AI as a reference in the technical forums, so your 3rd attachment will likely be deleted, modulo your response to my first question.

Welcome to PF.

From a quick Google search on that phrase, his work appears to be crackpottery. What is your goal in trying to make this unit?

Also, we do not allow AI as a reference in the technical forums, so your 3rd attachment will likely be deleted, modulo your response to my first question.

Ah, yes, that is true. https://en.wikipedia.org/wiki/Vacuum_cooling

What is the "vortex" part all about? Is that supposed to increase the efficiency somehow?

I see no way that a liquid, such as water alone, could be cooled by passage through a vortex or an eddy in a two port chamber. Since the two ports are the same size, the water velocity will be the same at inlet and outlet. If anything, the water would be heated by the internal turbulence, the heat energy flux in watts, being the product of the differential pressure in pascals, by the volumetric flow in m³/s.

The linked [questionable link redacted by the Mentors] website raises many red flags, that tell me it is bunkum. There will be new-age crystal healers who swear by it. For the true believers, the placebo effect may well be worth the investment.

Vortex cooling of air or a gas, is well established and widely used.
https://en.wikipedia.org/wiki/Vortex_tube

I see no way that a liquid, such as water alone, could be cooled by passage through a vortex or an eddy in a two port chamber. Since the two ports are the same size, the water velocity will be the same at inlet and outlet. If anything, the water would be heated by the internal turbulence, the heat energy flux in watts, being the product of the differential pressure in pascals, by the volumetric flow in m³/s.

The linked [questionable link redacted by the Mentors] website raises many red flags, that tell me it is bunkum. There will be new-age crystal healers who swear by it. For the true believers, the placebo effect may well be worth the investment.

There is a pressure at which water boils, determined by temperature. That is the vapour pressure of water. If you draw water vapour from a closed container, more water will boil off as steam, stabilising the pressure at that temperature. The water that boils will be from the liquid surface, as the deeper water below is under greater hydrostatic pressure. If you then create a rotation in the water about the vertical axis, the liquid surface will take up a parabolic shape, but the volumes of water and steam will not change. Within the container, we can assume the same pressure and temperature exists across the entire liquid-gas contact surface.

An air drier can operate by cooling a flow of air, then pumping out the liquid water that condenses, before allowing the air to warm again. The cooling and the warming of the air can be done efficiently in a counter-flow heat exchanger. The pressure can remain close to constant throughout the air flow. The liquid water that is pumped out will be at the temperature of the cold chamber, but you will need to pay for the cooling of the chamber, and of the liquid water that is extracted. The minimum partial pressure of water possible is about 0.611 kPa, or 0.089 psi, set by ice formation that may block the air flow through the cold chamber at 0°C.

Considering you need at least the vacuum pump, a water pump, and piping that will withstand being lowered to round-about a half atmosphere, I'm going to guess your build costs are not going to be a lot lower than that $500. And the first time you draw water into your vacuum pump you might be very unhappy.

As to keeping the water clean and hygenic, that is a question best asked of somebody with some solid authority. I don't know exactly who to ask. Possibly someboy who does hydrotherapy? It might be as simple as the case for a pool at more ordinary temperatures.