Archimerged has done some calculations regarding how much gravitational energy is available to a turbine installed in the liquid return pipe of a heat pipeline running 2 km up a mountain. It seems that there is about 54 kW gravitational power for every MW heat power carried up the 2km mountain by a propane heat pipeline. This is about 10 kW gravitational power for every liter per second propane liquid flowing down the mountain. The propane vapor flowing upward needs a larger pipeline, perhaps 15 times larger than the liquid pipeline. The liquid return pipeline must be very well insulated. The vapor pipeline does not need as much insulation, but calculations are needed for that.
Archive for the ‘Uncategorized’ Category
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.
I wrote a post and pressed publish without ever having previewed it. They asked "are you sure you want to do this?" so I answered "no" thinking maybe it would be a good idea to preview it. A "post saved" line came up, but the post wasn't saved. I can't find it anywhere.
I tried doing that with this post, and it got posted with no confirmation dialog. I'll write it again later. Using the Firefox back button returned to the "write post" page but the text was gone.
First, it occurred to me that it is possible to avoid making the hot air subject to direct compression by expanding bubbles. There was no good reason for the gas output of the CCHEX to be connected to the same plenum as the water output. The revised design separates the cold water from the cold gas before they enter the CCHEX, and the hot gas enters the hot water flow at the bubble injectors. Therefore, aside from a very small exposure at the bubble injectors, there is no place where the water can do work on the hot gas after the CCHEX. The downward force from expanding bubbles is transmitted through water to the cold air collecting at the bottom of the trompe.
Unfortunately, some of the force also continues up the trompe, around the inverted U siphon tube, down through the hot to cold water CCHEX, and pushes up on water in the air-free column of hot water which flows out of the bubble pump.
Is this force mostly a balanced force which does no work?
The reason the bubble expands is that the weight of the water above it is less than the force exerted by the gas. This happens because the bubble has moved and is at a shallower depth. But it is also easier for the bubble to push the water down, because there is more water below counterbalancing the water in the downflow column. The hydrostatic pressure pushing upward equals the hydrostatic pressure pushing downwards.
However, this is dynamics, not statics. The mass of the large quantity of water below dictates that an equal force pushing downward will decelerate the large mass below much less than the upward force accelerates the smaller mass of water above. The equal forces act through different distances. More work is done on the water above than on the water below.
(Given equal forces pushing a big mass and a small mass, more work is done on the small mass because the force can act through a larger distance. This is in contrast to gravity, which applies equal acceleration, not equal force, to different masses).
My conclusion is that the small bubble design (which easily achieves isothermal expansion because of the large thermal mass of the water) captures nearly all of the work done by the expanding hot gas and stores it as gravitational potential energy in water moved from the top of the rising bubble-filled column over to the top of the heavier air-free column. From there, gravity does work on the water again, accelerating it. A force appears at the top of the bubbles of cold air, compressing them.
Of the smaller fraction of work done by expanding gas on the hot water below the bubbles, most results in compressing the cold air already at the bottom of the trompe. A smaller amount acts to compress cold air bubbles descending in the trompe. An even smaller amount acts to decelerate hot water flowing downward in the air-free column on the bubble pump output.
And there is a final triumph. It looks to me like even that small amount of work ends up compressing cold gas, because what difference is there between water which went up the bubble pump and over to the heavy column, or water which was pushed backward up the heavy column? So long as the surface of the hot water isn't rising and doing work on atmospheric pressure air, I see none. And actually, the surface is not rising.
I seem to be reaching the point where I can design an experiment to test this theory out.
Update: probably most of the inefficiency in a bubble pump occurs when raised water falls back down when dynamics is being relied on to do the pumping rather than statics. If the bubble pump is just supposed to raise the water a tiny amount, it should be quite efficient, even if the input side is not sealed, according to Archimerged's latest thinking… Need to do some experiments…
This design uses water and air and ignores any difficulties with water vapor and other than perfect slug flow in the tubes. Also, it aims for the given arbitrary target of 30kW gross heat flow into the expansion process. The available work will depend on the temperature difference, and on efficiencies. However, 30kW of heat flow ought to be enough to produce 1kW of work, which is probably enough for one family. Note that the amount of work you can extract from a given amount of compressed air depends on how much heat you put into it during expansion, and the starting temperature. Here, the work represents how much work went into compressing the air, not how much might come out of it.
We assume a pressure ratio of 2: the low pressure reservoir is at half the pressure of the high pressure reservoir. If the machine is 30 feet tall, the pressures are 13 psi and 26 psi. Higher pressures with a 30 foot machine would reduce the pressure ratio.
The required moles per second of air to handle 30kW of heat flow is 30kW = nRT ln(pressure ratio). Using gnu units, this gives
- 30kW / (R 300K ln(26psi/13psi)) = 17.351613 mol / s
- (29 g / mol) (30kW / (R 300K ln(26psi/13psi))) = 0.50319679 kg / s.
- 30kW / (R 300K ln(100psi/87psi)) = 86.363948 mol / s
Substituting this formula for the number of moles (which assumes isothermal expansion) into V = nRT/P, the temperature and gas constant cancels out, and the volume per second at a given pressure is just
- volume / second = power / (P ln(ratio)).
- 30kW / (26 psi ln(26psi/13psi)) = 241.4368 liters / second
- 30kW / (100 psi ln(100psi/87psi)) = 312.44202 liters / second
This is the required air flow volume into the expansion hyperbola at the high-pressure end. The gas expands throughout the hyperbola so the total volume will be larger. This value can be used as volume per unit height, as the expansion is accomodated by bending the tube to be more nearly horizontal. The space required for the slugs of liquid is accomodated in the same way. A reasonable minimum amount of liquid would provide equal volume slugs of gas and liquid at the low-pressure end.
The required volume of the expansion hyperbola depends on the expected rate of heat flow per unit area of hyperbola tubing surface, or on the maximum velocity of the fluid and gas, whichever gives the more stringent limit.
Considering 1 meter / second (2.2 mph) a reasonable velocity for the fluid, and 30 feet (9.14 meters) a reasonable height, we first need the hyperbola length.
Still working on this…
Patents and copyrights have many things in common with slavery. For example, all three were sanctioned by the original U.S. constitution. It took the civil war to get slavery removed from the constitution. What will it take to get rid of patents and copyrights?
But I am getting ahead of myself. All three institutions involve artificial ownership: of human beings, of methods of doing something, or of words and sounds and images. All were controversial when incorporated into the constitution. All have evil effects on individuals for the benefit of the so-called owners. And all are unnecessary.
It is for this reason that I do not patent my inventions or apply restrictions to the use of my writing. I find the above self-evident, but I expect it may be a long time before patents and copyrights cease to exist. But clear thinking people can refuse to participate in artificial ownership which places restrictions on the freedom of others.
While wordpress was down yesterday I lost a little work on the previous article because of a bad interaction between Firefox and the partly down wordpress server. The browser back button did not return to a page where I could save my text. Firefox had forgotten it after sending it to the server and receiving an updated page (showing an empty blog), and the server had no record of the text. So I started working on the article at renewableenergy.wikia.com. I hate re-doing things, but it all came out for the best because I finally got the design right.
Please refer to the image of the tanks, pipes, valves, and reservoirs.
The article is still in a state of flux, but I believe I now have all of the elements of a workable design. I figured out how to make the water motion reversible: water is moved between many pairs of low-pressure tanks at different elevations by adjusting the air pressure difference so that water flows either up or down through a U tube (with valve) connecting each tank of a pair. The pressure difference is coupled to the hydrostatic pressure applied to pairs of high-pressure tanks so that expansion of many different levels of high-pressure gas exerts a low pressure force raising water from many lower tanks to many higher tanks at once, while the pressure generated by water flowing downward from many pairs of higher and lower tanks together creates an increase in the hydrostatic pressure of a column of water feeding the high-pressure tanks, which compresses the air.
This machine is so simple it is amazing. It isn't quite obvious, but it will seem so once built. During compression, the slight pressure created by water flowing downward in many pairs of tanks at once is combined and applied to the space above an enclosed water reservoir at about the same height as the upper lake. The level of the enclosed reservoir is restored to the level of the upper lake after every step. (I call it a step rather than a cycle, because this machine completes one trip around the thermodynamic cycle each day). Thus, water descending in many pairs of tanks at different elevations generates air pressure which combines to push down on the top of a column of water, which compresses air at many different pressures simultaneously.
During expansion, the air pressure inside the hydrostatic tanks causes air flow until the hydrostatic pressures equal the air pressures inside all tanks. This causes an increase in the height of the water in the enclosed top reservoir, a decrease in the available volume for the enclosed air, and an increase in the air pressure. This air pressure appears in the lower tank of a pair of low-pressure tanks, and forces water down through the U tube and up into the upper tank of the pair. Thus, expanding gas pumps water.
The enclosed reservoir drain can be connected to either the even or odd hydrostatic manifold, while the upper lake is connected to the other one. The even hydrostatic manifold connects to the drain ports on the even numbered hydrostatic tanks, while the odd manifold connects to the odd numbered tanks. The manifolds are completely filled with water from the surface of the upper lake or reservoir to the water surface inside those tanks which contain air, or else to the top of the tanks. So the hydrostatic pressure at the surface of the water equals the vertical distance from the reservoir surface to the water surface inside the tank. Water will flow and air will compress or expand until the air pressure equals the hydrostatic pressure. This can't take very long because the pressures are never very far apart.
Recently I've been thinking about a cylindrical machine tilted at about 45 degrees which is all one piece, as described in the last post. It feeds hot water in at top center, and the water flows through and finally out at middle outside. There are two heat exchangers, both water to air, instead of one air to air. This avoids the need for high pressure piping because the high pressure air stays in deep water where its pressure equals the ambient. Near the surface, hot low pressure air is cooled by cold water, and at the maximum depth, cold high pressure air is warmed by hot water.
Last post I asked what's the difference between the helix and a countercurrent heat exchanger? The purpose of the low pressure exchanger is to be sure the air is as cold as possible before any work is expended compressing it. If the exchanger has flexible walls, this means the air has to be at constant depth. The heat exchanger looks like a conical hat on the cylinder. With the cylinder axis at 45 degrees, the cone has a right angle at apex. The highest surface of the cone is horizontal. As the cylinder rotates about its axis, that surface will be vertical after 1/2 turn. The air stays under the horizontal part.
The cone has two parallel surfaces, top and bottom. (Really two cones). The space between is filled mostly with water, and an air pocket at minimum depth. The top surface has a spiral wall which leads the air toward the axis as the rotor turns. Since the air pocket is horizontal (45 degree cone tilted at 45 degrees), the air stays at constant pressure as it moves toward the axis. The water flow needs to be in the opposite direction, from axis toward the outer edge. There will be a second pair of surfaces in which the air moves away from the axis and the water moves toward the axis.
Archimerged now has a free account named “Archimedes Underall” in the Second Life virtual community. First attempt to use the Linux port failed due to lack of GLX library… He hopes to find some interested helpers there.
I used inkscape to create some simple scale geometric drawings with labels. I discovered that inkscape doesn’t support nested coordinate systems: I couldn’t create a coordinate system for the geometric drawing separate from the coordinates of the image itself. At least not explicitly. What I ended up doing was ignoring the drawing boundaries completely and laying out the image as needed. Then I grouped everything, copied it, and pasted into a new image which I then sized to fit around the drawing, and saved. Then I converted that to png using gimp.
I discovered that the best way to put points where you want them is to use guidelines. Finding out how to create guidelines is not easy. But creating them is. You drag from the ruler to the drawing, and a guideline appears. To place it at a precise location, use the XML edit window, where you can edit the property and store the exact location.
In file/document preferences, you can select “snap to guides” and points and line endpoints stay where you want them.
I also discovered quite by accident that the xml file includes the full path name of where inkscape saved the file. Not good. An information leak if you didn’t intend to publish your username on the system where you edited the file.
See the post on krazyletter. Well, maybe I’ll get back to working on the heat engine P vs. V, T vs. S diagram, in SVG…