Injecting bubbles into moving fluid

The isothermal bubble pump is very simple, but not so flexible. There is no control over the spacing or size of bubbles once they are created when the machine is manufactured. So I propose a machine made of two hyperbolic segments of bubble pump with injectors at the inputs and collectors at the exits. The injectors are under automatic control. One injector feeds cold low-pressure gas bubbles into the downward moving fluid stream at the nearly horizontal top of the cold compression hyperbola. The other feeds hot high-pressure gas bubbles into the upward moving fluid stream in the nearly vertical bottom of the hot expansion hyperbola.

Alternating slugs of fluid and gas flow through the two hyperbolas, but elsewhere in the machine, flows of fluid and gas are separate. Heat is exchanged between high and low pressure fluid using a fluid-only countercurrent heat exchanger. Since there is no gas involved, a U tube easily brings the hot low-pressure fluid down to the level of the high-pressure fluid and returns the cold low-pressure fluid to the original level. Incidentally, inside the heat exchanger the fluids have equal hydrostatic pressure; importantly, the pipes are in direct thermal contact.

Separately, heat is exchanged between high and low pressure gasses in a gas-only countercurrent heat exchanger which can be placed anywhere in any orientation. Typically, it would comprise a series of insulated low pressure tanks of descending temperature, filled with coils of high-pressure pipes flowing in the opposite direction so cold gas enters the coldest low pressure tank, absorbs some heat, flows to the next warmer low pressure tank, absorbs more heat, etc. The volume of these tanks is unimportant so long as very little heat is lost and there is very little net heat flow in or out either end. The amount of heat gained by the high pressure gas should be essentially equal to the heat lost by the low pressure gas. The more tanks provided, the longer the gas stays in the tanks, and the larger the volume (so the relative surface area is lower) the better this goal is achieved. A single heat exchanger can serve many pairs of bubble pump hyperbolas.

This machine does not require a jump-start because the bubble injectors and collectors are inherently irreversible, and it cannot function as a heat pump unless the temperatures of the heat reservoirs are reversed. The liquid always flows down the compressor and up the expander, heat always flows from heat source to heat sink, and the motor always runs forward, but if the heat source is colder than the heat sink, forcing the motor to turn forward will pump heat from the cold source to the hot sink. Forcing the motor to turn backward will just pump fluid around the circuit with no gas flow.

The bubble collectors are simply vertical tubes leading to gas reservoirs. These tubes have such large diameters that the bubbles detatch from the walls of the tube and float freely (and irreversibly) upward. The gas pressures are always high enough to prevent fluid flow upward, so fluid never fills the gas reservoirs or flows into the gas-only tubes above the reservoirs. Hot fluid leaving the nearly horizontal upper end of the hot expansion hyperbola takes a sharp bend downward to the hot input port of the fluid countercurrent heat exchanger, but the bubbles escape upward into a short vertical pipe leading up to a gas reservoir. Cold fluid and bubbles arriving at the bottom of the cold compression hyperbola flow around a sharp bend from nearly vertical to horizontal. After a short horizontal segment, the bubbles escape up into the high pressure gas reservoir while the fluid flows to the cold input port of the fluid countercurrent heat exchanger.

Hot gas from the hot low-pressure reservoir and cold gas from the cold high-pressure reservoir flow slowly through the gas countercurrent heat exchanger and into the cold low-pressure reservoir and hot high-pressure reservoir. From there, the hot high-pressure gas feeds the bubble injector at the nearly vertial bottom of the hot expansion hyperbola, and the cold low-pressure gas feeds the bubble injector at the nearly horizontal top of the cold compression hyperbola.

A positive displacement pump somewhere in the fluid-only circuit converts fluid flow to rotary motion or rotary motion to fluid flow, always in the forward direction (the pump cannot run backward). A motor-generator converts electricity to or from shaft motion.

Thinking of gas at the level of moving molecules, one can imagine how and why the expansion hyperbola provides motive force to the liquid. At the bottom where the gas bubbles are injected, the hydrostatic pressure is so high that the bubbles are just big enough to touch the walls of the tube, and they are not expanding. But the fluid is moving upward in the nearly vertical hyperbolic tube, and the hydrostatic pressure drops as the amount and weight of the fluid above decreases. So the gas expands, doing work on the slug of liquid behind and ahead. Molecules of gas collide with the liquid, accelerating the liquid and decelerating the gas molecules, so the temperature and pressure drop. Molecules of gas also collide with the hot walls of the tube, gaining energy so the temperature and pressure of the gas rise. The faster heat flows into the gas, the more work it can do on the liquid and the faster the liquid moves. Nearer the top of the hyperbola, the slope of the tube decreases, so that a larger increase in volume is permitted without reducing the pressure so much. The goal is isothermal expansion: the pressure-volume product is constant and all of the energy removed from the hot walls of the tube is used to accelerate the moving fluid while the gas stays at constant temperature.

Thus, if no energy were being extracted from the fluid motion, the fluid would continue to accelerate. This is generally true of heat engines — they speed up as long as heat (microscopic disordered kinetic energy) is supplied faster than energy is removed, storing the excess as macroscopic ordered kinetic energy. Here, the moving fluid plays the role of a flywheel.

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