Bubble pumps and trompe compressors do not depend on “slug” flow

See the "trompe" article from Mother Earth News (1977), and also the article in Appleton's' Cyclopedia of Applied Mechanics (c.1880). Searching for Catalan forge water bellows leads to some interesting sites including photos of what might be a trompe.

maybe a trompe?

Another early reference suggests that the name trombe comes from the French for the "meteorological phenomenon which we call the water-spout" and cites other references I haven't looked up yet.

Update:  it's not clear that "trumpet shaped tube" is what a trompe was named for, and actually I'm not sure about how I need the shape to vary to get optimum efficiency. 

It appears that a system consisting of a trompe (trumpet shaped tube) with cold water flowing downward rapidly enough to carry bubbles with it will do work compressing cold air independent of the amount of water flowing. But that doesn't matter in a closed loop water system because neglecting friction, the water flow does not consume any energy.

The heat engine described here appears to be remarkably efficient and very simple. If large insulated water tanks are used, the engine automatically stores heat as hot water during the day and stores "cold" in the cold water at night, using the stored water as the heat source and sink. The refrigerant mediated heat exchanger serves as a "heat diode" which prevents heat loss when the hot heat source stops providing heat during the night, and which prevents loss of "cold" when the cold heat sink warms up during the day.

Let me describe a heat engine using small bubbles carried down a wide tube for compression and rising up a wide tube for expansion. At the bottom of the trompe, the tube makes a sharp bend and the water and bubbles enter the cold input plenum where the flow velocity is much less because the cross section is much larger, and the air separates. The cold input plenum ends in a flat wall pierced by many small thin tubes with adequate total cross section for slow flow. Each tube is sealed to the wall.

The counter-current heat exchanger comprises two sets of these tubes and a series of refrigerant tanks enclosing the tubes. The water and gas in the upper set of tubes flows from the cold side to the hot side, while the lower set flows in reverse. Heat flows from the lower tubes to the upper tubes, carried by refrigerant which evaporates from the lower tubes and condenses on the upper tubes. Each refrigerant tank is made from one tub-shaped sheet with one hole for each tube provided in the tub bottom. The lower (hotter) pipes are surrounded by wick material ensuring that liquid refrigerant will be in contact with all of the hotter pipes. The pipes are inserted into the holes, the sheet is slid along the pipes and sealed to the pipes and to the previous sheet, forming a gas-tight tank. The tank is evacuated and back-filled with enough refrigerant to keep the wick and the hotter pipes wet with liquid refrigerant. More refrigerant may be required for the hotter tanks as the refrigerant vapor pressure will be higher in those tanks. This process continues until the pipes are completely covered by refrigerant tanks. Finally, the hot output plenum is sealed to the top half of the last tank, the hot gas input plenum and the hot water input plenum are sealed to the bottom half of the last tank. All of the gas and water flowing from the heat exchanger pipes comes together in the hot output plenum.

The reverse flow (hot to cold) uses separate plenums for gas and water, because the gas is at low (atmospheric) pressure while the water is at the hydrostatic pressure dictated by the height of the water columns.

There are two trumpet shaped water columns which carry water and gas bubbles, each connected by an inverted U at the top to a straight column which carries only water in the opposite direction. The straight tubes have the same diameter as the widest part of the trumpet bell. Cold water flows out of the cold water output plenum of the heat exchanger into the bottom of the straight cold water column, up and around the U-bend into the bell of the trumpet. There, low pressure air flows in because the hydrostatic pressure at that point is even lower than that of the low pressure air. The downward flow of water carries the bubbles along with it. As the bubbles descend, their volume decreases because the pressure increases. The trumpet shape is designed so that the cross sectional area occupied by water will be constant all the way down, so that the average density of the bubble filled fluid is constant along the tube.

The top of the cold U-bend can be up to 30 feet higher than the hot U-bend, because there is no air in the cold U-bend. In that case, the hydrostatic pressure at the top of the U-bend would be near vacuum and bubbles of water vapor could form. The bubble injector tubes must be at about the same level as the water surface in the hot U-bend, to prevent formation of very large bubbles. They must not be too low, or the air pressure will be too low and water will flow into the bubble injector tubes instead of air flowing out.

Since the air bubbles are moving upward in the hot trompe, there is air at the top of the hot U-bend, and the hydrostatic pressure at the surface is equal to the air pressure. This pressure will be at least atmospheric, because there is a check valve to admit atmospheric pressure air at the top of the hot U-bend if the pressure should drop below atmospheric.

At the bottom of the cold trompe, the flow enters the cold input plenum. Air separates and enters the upper heat exchanger tubes while water enters the lower tubes. At the opposite end, the heated air and water enter the hot output plenum. Air from the top of the plenum flows into bubble injector tubes which lead into the trumpet tube a little ways up, where the hydrostatic pressure is a little lower. Hot water flows directly into the narrow part of the trumpet tube, which is narrower than the plenum so the flow is faster.

At the top of the hot trumpet, low pressure air separates and flows up a pipe to a U-bend and from there down to the hot low pressure air input plenum of the heat exchanger. A check valve admits atmospheric pressure air if the pressure is below atmospheric. The water flows out the wide end of the trumped, around a U-bend and down the straight tube to the hot water input plenum of the heat exchanger.

The cold air output plenum has a condensed water sump, because the hot air has more water vapor, which condenses inside the tubes of the heat exchanger. A water pump returns this water to the top of the cold trumpet. The cold air flows up a separate tube to the bubble generator at the top of the cold trumpet. Whenever the pressure is lower than atmospheric pressure, additional air is admitted through a check valve in the hot air input plenum. Excess cold compressed air is stored in a large tank at the level of the cold input plenum.

Additional heat from the hot heat source is added to the system at the hot end of the heat exchanger, and excess heat is carried away to the cold heat sink at the cold end of the heat exchanger.

That completes the description of the whole heat engine. Excess energy results in accumulation of excess compressed air, or if the air is allowed to enter the bubble pump, in faster water flow and a larger difference in the water level between the top of the hot trumpet and the top of the cold trumpet.

Water flows not because moving bubbles carry it along, but because bubbles injected into the bottom of the hot expansion trumpet reduce the average density of the water in the column, and hence reduce the hydrostatic pressure at the bottom. The higher hydrostatic pressure of the water exiting the heat exchanger leads to flow up the trumpet. The bubbles increase in diameter as the pressure decreases, but the flare of the trumpet is designed to compensate for this so that the average density of the air and water remains constant. The larger the volume of air introduced at the bottom of the hot expansion trompe, the lower the hydrostatic pressure due to the column of water, and the faster the flow. The level of the water surface at the top (where the air bubbles separate) will rise, as will the hydrostatic pressure at the bottom of the straight tube, which contains no air bubbles.

Hot water leaves the heat exchanger, enters the hot expansion trumpet where bubbles are injected, rises to the top where bubbles separate, and descends to the hot input plenum and enters the heat exchanger. The water is cooled, and leaves the exchanger, rises to the top of the straight tube and flows around the U-bend into the cold compression trompe, where cold air enters and flows downward with the water. If too much air is admitted, the hydrostatic pressure at the bottom of the compression trompe will decrease and the flow rate will decrease. If no air is admitted (so the bubbles added to the expansion trompe come from stored compressed air), the flow will be maximum.

The hotter the hot water, the larger the volume of gas available to form bubbles from the same number of moles of gas. Thus, the water will flow faster when a larger temperature difference is available because there will be a larger difference in the density of the bubble and water mixture in the cold and hot trompes.

As the hot air expands in the rising water, it does work on the water. None of this work is wasted, as the result is to reduce the hydrostatic pressure exerted by the column of water and increase the rate of flow. This results in a taller column of water which exerts a larger pressure at the bottom of the trompe. But this also causes a higher pressure at the bottom of the straight tube, so that the pressure in the hot water input plenum is higher than the pressure in the cold water output plenum.

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