The Isothermal piston ball heat engine extracts work from available temperature differences using solid metal spheres as pistons in expansion and compression tubes shaped according to the equation of state of the working gas.
See the earlier Isothermal bubble pump heat engine design which uses liquid pistons.
Having observed that a lot of heat can flow through the tubing walls even with big tubes (depending on tube wall thickness), I am thinking about tubes several inches in diameter, and about how to manage the piston balls. This machine isn't really a bubble pump, but I call it one because it is a modification of the earlier bubble pump design. The pressure exerted by solid balls works quite differently in detail from pressure exerted by liquid. It depends on the number of balls in the tubing above, together with the angle of the tube, so pressure still goes roughly as height. But with a liquid, the diameter of the tube and the total weight of the fluid does not affect the pressure, while with solid balls, the total weight of the balls matters.
The tubes could be fabricated from two sheets of metal. The lower sheet (the ball race) would be thick steel formed with hyperbolic troughs, and would not need to transmit heat to speak of. The upper sheet would be thin copper separating the ball race from the refrigerant plenum. Or thin copper tubes bent in the appropriate hyperbolic curve could be supported by troughs made of steel or cast in place of concrete. By hyperbolic, I mean shaped like the curve y = -k/x for k and x positive.
The hot expansion tubes will naturally cool as the gas inside expands. In order to achieve isothermal expansion, the tubes are heated by refrigerant vapor condensing on the copper surface. A sealed evacuated plenum covers the tubes and contains the refrigerant. The condensed liquid flows down between the tubes to the hot heat source located at the bottom of the plenum, below the expansion tubes. The refrigerant evaporates off the heat source and carries more heat to the expansion tubes.
The cold compression tubes have a different arrangement for the refrigerant. Liquid refrigerant needs to be in contact with the copper, but it must not develop any substantial head of hydrostatic pressure. Probably the best approach is to bond a wicking material to the surface of the copper. Vapor rises to the cold heat sink at the top of the plenum, and condensed liquid flows back down over the wick.
In the case of a heat pipeline leading to a snow-capped mountain, the plenum is directly connected to the opening of a large diameter pipeline leading all the way to the cold sink at the top of the mountain. Since the walls of the pipeline are insulated, they will heat up slightly as vapor condenses and runs back down. The hottest surface will be the copper compression tube surface, which rises in temperature because heat from compressing gas is flowing through it. The pipeline walls will be warmer than the cold heat sink but cooler than the copper tube surface. At steady state, the vapor will flow rapidly to the top where it condenses on the cold heat sink. This creates a partial vacuum, and there will be a steady flow of vapor up the pipeline. The cold heat sink is arranged so the condensed liquid flows away from the vapor pipeline to the cold refrigerant drain pipeline, which is also insulated and carries a stream of rapidly flowing cold liquid down to the cold compression tubes.
The minimum temperature difference between the cold heat sink at the top of the mountain and the evaporating liquid at the bottom is influenced by the height of the mountain. The pressure of the vapor is higher at the bottom than the top because of gravitational effects, so the temperature at which the liquid will evaporate is a little higher at the bottom than the temperature at which it condenses at the top.
One important consideration is whether the balls will be heated and cooled repeatedly, or whether two separate sets of balls are used. Using two separate sets requires a complicated mechanical setup and a mechanism for removing the balls from the gas pressure environment and returning them after they are raised or lowered on a wheel.
Using a single set requires a large countercurrent heat exchanger for the balls, and a large inventory of additional balls which are held up in the exchanger. There is a constant unavoidable flow of heat from hot source to cold sink through the balls which does not accomplish any work. Also, the balls are constantly expanding and contracting, leading to wear.
So, today I work out a method to get the balls in and out of the machine without losing gas pressure. In this design, there is no need for a fluid countercurrent heat exchanger, since hot and cold fluid flow in separate circuits. Also, there is a wheel which raises cold piston balls while lowering hot piston balls, and work can be extracted from it because there are more balls to be lowered than raised since the volume of gas entering the bottom of the hot expansion tubes is larger than the volume of the same gas when it exits the bottom of the cold compression tubes at the same pressure.
Transferring fluid and balls in and out of the machine turns out not as difficult as it might seem, because the fluid is not compressible. A lock mechanism is used for entry and exit. It consists of a tilted segment of tube long enough to hold many piston balls, with "ball valves" at each end, the sort which when fully open present a smooth cylinder indistinguishable from the tube itself. They are so named because the rotating mechanism is a ball with a hole drilled through it, but the name is also appropriate because a ball valve will pass a piston ball without leaking fluid past the ball. There are also side ports at each end where fluid can enter and exit through smaller diameter tubes.
At the entrance, which is the top of the cold compression tubes and the bottom of the hot expansion tubes, one end of the lock opens to ambient pressure, and the other end leads directly into a compression or expansion tube. To admit piston balls and fluid to the system, the valves are set so ambient pressure fluid and balls roll in through the outside ball valve by gravity, and fluid flows out to the ambient pressure reservoir through the side ports at the inside end. After the lock is filled with fluid and piston balls, flow stops because there is no room for fluid to flow around the balls and the inside ball valve is still closed. The outside ball valve and inside fluid valve are closed, and the inside ball value and outside fluid valve are opened. This admits high pressure fluid behind the balls and forces them up and out into the receiving chamber, which is larger than the balls so they roll freely over a hump and through high pressure gas and fluid to the other end. Once the last ball has cleared the lock, the valves are reversed and the process continues as more balls arrive from the wheel. It is important that no gas from the receiving chamber enter the lock. The bottom of the receiving chamber has to be higher than the top of the lock.
At the exit, which is at the top of the hot expansion tubes and the bottom of the cold compression tubes, a similar lock is used. An exit chamber collects piston balls as they arrive out of the tubes. Gas at pressure flows out the top of the exit chamber to the countercurrent heat exchanger, while the balls roll to the entrance of the lock. To begin a cycle, the inside ball valve and the outside fluid valve are opened. Fluid inside the lock flows out the fluid valve while balls and fluid flow into the lock. When the balls hit the outside ball valve, flow stops because there is no space for fluid to flow around the balls. Then, the inside ball valve and the outside fluid valve are closed and the inside fluid valve and the outside ball valve are opened. The balls roll out by gravity into ambient pressure fluid, where they are picked up one-by-one by the wheel as it turns past. The fluid which flows in through the inside fluid valve to replace the balls is mostly the same fluid which flowed out the outside fluid valve as the balls were entering the lock.
The expansion tubes have a problem when starting the machine from a standstill. This will be solved by small diameter tubes attached at intervals along the top of the expansion tubes, which will admit air from reservoirs separately maintained at the appropriate pressure for the height. At first, this will be inadequate to lift all of the balls in the tube, because they may be tightly packed, but it will lift the balls at the top. As they are lifted, the downward pressure due to gravity will decrease and additional balls will begin rising. Eventually the flow will be established, and little if any gas will flow through the small tubes because the expansion tube pressures at the junctions will remain near the reservoir pressures.
The mechanism for air separation is very simple: when a ball exits at the bottom of the compression tube into the lower separation chamber, the air simply rises to the top and flows into the cold high-pressure input port of the countercurrent heat exchanger. The cold fluid and balls exit through the lock and are lifted on the wheel back to the top of the compression tube by the force of gravity on the hot balls and fluid descending on the other side. There will be excess power available at the wheel because the hot fluid and balls will be travelling around the hot circuit at a higher rate since the same gas at the same pressure occupies a larger volume when hot.
The situation is exactly the same for the expansion tube: when a ball exits at the top of the expansion tube into the upper separation chamber, air rises to the top and flows into the hot low-pressure input port of the countercurrent heat exchanger. The fluid and balls exit through the lock and provide the motive power to turn the wheel as they are lowered to the bottom of the expansion tube.
The mechanism for capturing air between piston balls is also rather simple. At the top of the compression tube, gas from the low-pressure cold output port of the countercurrent heat exchanger holds the fluid level well below the top of the flared entry tube. When a ball rolls down into the tube, it necessarily captures a substantial volume of gas in front of it because the tube is nearly level, and the maximum fluid level is well below the top. The exact volume of gas is controlled by the length of the nearly level straight segment of tube, and by the spacing enforced between entering balls.
At the bottom of the expansion tube, gas from the high-pressure hot output port of the countercurrent heat exchanger fills the top half of the flared entry chamber. When fluid and balls are admitted from the lock, the amount of fluid is only enough to partly fill the entry chamber. As balls roll down the entry chamber to the bottom of the expansion tube, they are in contact with each other. High pressure hot gas fills part of the space between balls, while fluid fills the remainder. After passing the low point, the expansion tube curves sharply upward. The downward pressure on the lowest ball decreases as the earlier balls rise and part of the gravitational force is borne by the walls of the expansion tube, which is shaped like a hyperbola. When the downward pressure on a ball is less than the gas pressure below the ball, the gas below it will expand and push the ball upward.