Archive for the ‘TrombePump’ Category

Nearly stationary bubbles don’t separate easily during horizontal motion

2006-07-04

Archimerged has found some data for air bubble behavior. There is a graph of bubble size vs velocity on page 67 of this pdf file. Very slow bubble rise is possible for 100 micron bubbles. The problem is those bubbles also don’t rise after leaving the bubble pump and trompe. It becomes clear that either some mechanism to trigger bubble separation is needed, or a large separation chamber is needed at the top of the bubble pump and the bottom of the trompe. But at least, if the separation chamber is very shallow and wide, the forward flow velocity need not drop much while the distance the bubble needs to rise to reach the surface can be just a few cm. Bubbles rising at 10 cm/s would reach the surface in under a second, meaning the separation chamber needs to be under ten meters long. Inconvenient but not impossible.

The ratio of water speed to bubble rise speed would apparently be a lower bound on inefficiency: if the bubbles rise in still water at 1% of the speed of the water, e.g. 0.1 m/s vs. 10 m/s, then in the bubble pump the water rises at 10 m/s while the bubbles rise at 10.1 m/s and in the trompe, the water descends at 10 m/s while the bubbles descend at 9.9 m/s. Then the bubble pump and the trompe both lose 1% efficiency, leading to at most 98% efficiency, while break even would be around 95%.

So maybe we need slower than 1 in 100. Bubbles 0.2 mm in diameter rise at about 2 cm/s. With water moving 10 m/s, that is 2 in 1000, and the bubble speed accounts for an efficiency loss of 0.4%. The separation chamber must spread out so widely that that the water is only 2 cm thick and it must be 10 meters long. Actually, that might make it wider than it is long, depending on the volume. And it has to be well insulated, and the separation chamber must be at around atmospheric pressure: the bubbles have to separate before the water descends to the heat exchanger.

At the top of the bubble pump tower, that is kind of inconvenient, to say the least. Some more clever ideas are needed…

It begins to sound like the bubble pump is made of fairly small diameter pipe, say 10 cm, and multiple pipes are used to increase the power.  Maybe we are back with the hyperbolic shaped tubing which tilts to nearly horizontal at the top.  This allows the water to continue at constant speed say 10 m/s (need to check the hydrodynamic drag to pick actual pipe sizes and water speeds) while the vertical velocity component slows to zero. Note well, the bubbles are confined by the top wall of the tilted pipe so their rise is slowed.  Also they start getting separated before reaching the top of the bubble pump.

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Let’s try something solid once again: the WaterAirWheel

2006-06-29

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.

What goes down must come up

2006-06-27

Archimerged has been thinking about why he believes the TrombePump should efficiently convert hot compressed air into an equal volume and a greater number of moles of cold compressed air. He assumes that the countercurrent heat exchanger can be made to operate efficiently so that not much heat flows from the hot source to the cold sink without heating expanding air, and that turbulence can be reduced to tolerable levels. The question is about how bubbles that don’t even look like they can push water ahead of them should raise water.

Well, the bubbles don’t push water up. The water is moving and will tend to continue to move. In the steady state, the volume of air in the bubble pump equals the volume in the trompe and the hydrostatic forces exactly balance. Adding a little air to the bubble pump will reduce the weight of water above and cause an imbalance of forces so that water in the bubble pump moves a little faster. And adding more air to the trompe will similarly reduce the weight of water in the trompe and reduce the downward force, slowing the watter a little.

From another viewpoint, the water which goes down the trompe has nowhere to go but back up the bubble pump, and vice-versa. We aren’t raising any more water than we let down. The mass of water balances.

If too much compressed air is released into the bubble pump, the excess energy goes into accelerating the water. If too much air goes into the trompe, excess energy to compress it comes from the kinetic energy of the flowing water, which must slow down because there is more hydrostatic pressure coming down the bubble pump than down the trompe and the net force is backwards, slowing the water.

So, Archimerged concludes that the apparent ability of water to flow around the bubbles is not a problem. The bubbles don’t push the water. Gravity pulls the water downward as far as it can go, as usual.

Revised:  Archimerged has thought about this some more, and realized that he was wrong.  Gravity pulls water down in both tubes, with the flow in the trompe and against the flow in the bubble pump.  Bubbles will tend to rise due to water flowing from along side to underneath them.  This slows the descent in the trompe and speeds the ascent in the pump.  Thus, to keep the same average density in both tubes, more gas flow by volume is required in the pump than in the trompe.

So Archimerged is now looking for more information about how bubbles behave.  Do tiny bubbles move more slowly?  What is the effect of detergent in the water?  Does fast moving water reduce the effect or leave it alone?

Rapid flow countercurrent heat exchanger

2006-06-25

Efficiency considerations are crucial to the TrombePump or any heat engine operating on low ΔT heat. For example, operating on 30K ΔT with a 300K hot heat source (and therefore a 270K cold heat sink) means at most 10% of the heat accepted from the hot heat source can be converted to work by a heat engine operating on a closed cycle, while at least 90% must be rejected to the cold sink.

Consider a cycle using isothermal expansion, isobaric cooling and compression, isothermal compression, and isobaric heating and expansion of the working gas. The system includes a store of internal energy. For the cycle to close, the working gas must return to the initial pressure, volume, and temperature, and the internal energy store must contain exactly as much energy as it started with. The isobaric steps cancel out, absorbing or rejecting the same amount of heat and increasing or decreasing the internal energy by the same amount. The isothermal expansion converts all of the input heat to internal energy of the system, while the isothermal compression converts 90% of the internal energy to heat and rejects it. The unused 10% is output as useful work in order to return the system to the initial state.

In this cycle, the working gas repeatedly moves between two pressures and volumes. The expansion step absorbs enough heat to allow the gas to reach the final low pressure and high volume, storing the work done as internal energy, while the compression step uses enough internal energy to return the gas to the initial high pressure and low volume. The isobaric steps change the temperature and volume while leaving the pressure constant. The isobaric cooling and compression step uses internal energy to do work on the gas, while the isobaric heating and expansion step stores the work done by expanding gas as internal energy.

The above describes a piston engine. In a continuous cycle engine such as the TrombePump, some working gas is expanding while some is being compressed, some is warming and some is cooling. The isobaric steps exchange heat with each other but not with the external heat source and sink. In that case, ideally the system is in a steady state where the amount of gas in each condition is constant and the amount of heat in the heat exchanger is constant. Actually, the situation is more complicated, but results for the ideal case should be good enough.

When the processes are inefficient, the expansion step converts less than 100% of the input heat to internal energy, and the compression step uses more internal energy than the expected 90% of the input heat to return the working gas to the high pressure and low volume. Now when the system returns to its initial state, the working gas must be at the initial pressure, volume, and temperature, and the internal energy must return to its initial value. This last adjustment is made by letting the system do work if it has excess internal energy, or by doing work on the system if it has a deficit.

Well, it can easily happen that after recompressing the working gas, the internal energy of the system is lower than the starting point. This is known as operating at a loss. The system does not produce any work, but instead consumes work.

In the TrombePump system, losses can occur at many places. Archimerged is particularly worried about what happens to the kinetic energy of rapidly moving water when it flows out of the narrow trompe into the wide heat exchanger and decelerates. He now thinks the energy must be going to heat without doing any useful work, and therefore has concluded that a design change is necessary to eliminate this loss.

He also thinks he ought to calculate how much energy this would be, but is too lazy just now.

The new principle for TrombePump V0.2 will be that the water runs at constant speed all the way around the cycle, through tubes with a constant cross sectional area devoted to water. When air and water flow together, the cross section will be larger to allow for the air volume. Because it takes a long time for heat to flow, the countercurrent heat exchanger must be very long so that rapidly moving water will remain in the exchanger long enough to be warmed or cooled.

There will be no baffles inside the water channels of the heat exchanger. Recall that the heat exchanger is also a series of temperature reservoirs, and uses gravity feed heat pipes to prevent heat flow in undesired directions. The diameter of the tubes will need to be rather low so that water in the center will also exchange heat. It may be necessary to add a polymer to the water to reduce friction losses and achieve laminar flow. Also, the heat exchanger might be wide and thin instead of cylindrical, and the heat pipe might be integrated so that a single metal wall separates the water from the refrigerant.

… expect revisions to this post…

Ambient temperature energy collection

2006-06-21

All heat engines operate by transferring energy from a hot heat source to a cold heat sink, while diverting a fraction of the input energy into useful work. The fraction passed through to the cold sink (or otherwise dissipated) can never be less than the cold temperature divided by the hot temperature, both expressed on an absolute temperature scale such as the Kelvin scale.

Thus, it appears useless to worry with operating heat engines when the hot source is not much hotter than the cold sink. We who pay for gasoline, natural gas, and electricity should wonder whether this is like scoffing at a 1% share of something vs. a 100% share of something else, when it might turn out that "something" is very much more than 100 times larger than "something else."

Archimerged knows it is possible (and believes it is practicable):

  • To extract heat energy from ambient temperature air and store it up in a temperature reservoir whenever the air is hotter than the reservoir.
  • To reject heat from a reservoir to ambient air whenever the ambient is colder than the reservoir. (Of course, one would only want to do this when there is no possible use for the heat, which is to say, heat would be rejected only from the coldest reservoir).
  • To use these same reservoirs to store energy arriving as sunlight on sunny days.
  • To reject heat from the coldest reservoir to other cold objects such as cold river water or cold road surfaces.
  • To extract latent heat from moist ambient temperature air whenever the air is warmer than the surface of a heat pipe leading up to a temperature reservoir, by condensing water on the heat pipe surface. (This is where the water dripping from an air conditioner comes from).
  • To reject heat by evaporating water, adding latent heat to cool dry ambient air.

The TrombePump described earlier uses a countercurrent heat exchanger with many temperature large reservoirs between the flow channels. Here Archimerged indicates how to design these reservoirs so that it is possible to feed ambient temperature energy into them and possble to reject heat from the coldest reservoir to ambient temperature.

A temperature reservoir is always "full" of heat at its current temperature. It is never possible to add more heat from ambient unless the ambient temperature is more than the reservoir temperature. The closer the temperatures are, the longer it takes for heat to flow in. This is why the countercurrent heat exchanger for a TrombePump must be so large, so that when heat which entered the water from the hottest reservoir does not find its way into expanding air, it has a chance of re-entering the hottest reservoir or the next cooler one. When the water moves very slowly through the exchanger, there is more time for heat to flow into a reservoir which is only slightly cooler than the water itself.

The coldest temperature reservoir clearly needs to be somewhat larger than the others, and it receives heat only from the water being cooled prior to ascending the trompe tower and descending through the narrow trompe tube. It might also receive heat extracted from water as it descends the trompe tube.

In order to make use of ambient heat of all temperatures, Archimerged has thought of a clever idea (even if he does say so himself) which one would hope has been thought of before. In addition to the water flowing through the hot to cold channel of the countercurrent heat exchanger, surrounding heat pipes leading up into the temperature reservoirs, he adds another channel with a separate set of heat pipes leading upward into all of the temperature reservoirs but the last (and coldest) one. Ambient temperature air flows through this channel. If the air is moist, additional heat is available when water condenses on cool heat pipes. The output air will be somewhat cooler and dryer than the input air.

It is counterproductive to remove heat from any reservoirs except the coldest, because that heat would otherwise go to warming up the cold water after it has descended the trompe and must be heated. Any heat removed from the reservoirs that serve to warm that water represents heat that must otherwise come from a higher temperature reservoir. So only the coldest reservoir is cooled further by ambient, and obviously that happens only when ambient is colder than the coldest reservoir. Heat pipes leading up out of the coldest reservoir are exposed to ambient air. When the ambient air is dry, these heat pipes may be covered with a wick soaked in water so that evaporating water will cool the heat pipes colder than ambient air.

Because very little heat flows downward through heat pipes, it is perhaps unnecessary to close off the ambient air flow when the temperature is too high to achieve any cooling, but certainly one would want to do so when it is very hot, so it should be possible to do so.

Direct solar heat can be used in a number of ways. Liquid from a solar collector could flow through yet another channel with heat pipes feeding up into the heat reservoirs. Or hot liquid could flow through tubes running through the water rising in the bubble pump tower. In that case some fraction of the direct solar energy finds its way into expanding air (and from there into gravitational potential energy used to raise the water to the top of the trompe). If the liquid is really hot, some water boils and the steam bubbles act to raise water so that no compressed air need be released into the bubble pump. The solar energy which does not get captured quickly ends up in the hottest temperature reservoirs as the hot water is cooled (and water vapor is condensed) after descending from the bubble pump tower.

TrombePump countercurrent heat exchanger design

2006-06-19

If you look at the drawing (link now works), it is apparent that the machine can be built quite large. There is no need for the trompe tower to be anywhere near the bubble pump tower. There is need for a quite large heat exchanger, with a volume many times that of the towers, so that the flow velocity through the exchanger can be very slow.

I present a perhaps overly concrete (!) design which is not informed by much knowledge of construction practices.

  • Heat flow is always upward, carried by many small diameter heat pipes, made from evacuated metal tubing back-filled with some refrigerant and permanently sealed. Replacing the heat pipes is probably not feasible and they should be designed for the expected lifetime of the machine. The heat pipes are provided with fins.
  • Regularly spaced baffles with perhaps 50% of the area occupied by holes are attached to the walls of the water channels to restrict flow from one chamber to the next. The water in each chamber will tend to stay at a constant temperature. This divides the heat exchanger into perhaps hundreds of segments.
  • A deep trench is excavated between the sites of the trompe tower and the bubble pump tower. This provides insulation and permits other uses for the land over the heat exchanger.
  • The bottom and sides of the trench will be filled with insulating material.
  • Forms are built to define the inside surfaces of the lower water channel.
  • Expansion joints and baffle mounting hardware are provided for. The joints must be well sealed and designed for the hydrostatic pressure which will be created by the trompe and bubble pump towers.
  • Heat pipes are held in place by the forms, extending from the bottom of the lower channel to the top of the upper channel.
  • The entire bottom channel is poured of concrete, one expansion segment at a time, casting the hardware and heat pipes in place.
  • Baffles and the atmospheric pressure air pipe are installed as each segment is cast.
  • A large volume of high heat-capacity material is filled above the bottom channel around the heat pipes with good thermal conductivity to them, forming a large heat reservoir between the lower and upper water channels. Insulating baffles prevent heat flow along the length of the heat reservoir, so that each short segment can maintain a different temperature without short-circuit losses.
  • Forms for the upper water channel are built and the channel is cast over the heat reservoir.

Note that there is no provision for a separate hot and cold heat reservoir. Instead, the outer segments of the heat exchanger serve this purpose. Additional heat is added to water in the bubble pump tower and heat is removed from water in the trompe pump tower whenever external conditions permit, probably using a separate system of heat pipes.

A no-moving-parts isothermal / isobaric cycle heat engine

2006-06-18

The sun delivers 62 million gigawatts to the land and water of the earth. That same energy is re-radiated out into space. We can capture tiny amounts using machines such as the air compressor described here.

Please digg this. Thanks.

Well, we're coming up on 24 hours on the digg queue, and absolutely no one has dugg the story. At least I got some traffic here: apparently about 12 people clicked 4 links each from the Renewable Energy Design article. I can't tell how people got to Renewable Energy Design, because wikia.com doesn't release referrer data, or actually, any page view data at all (since they use a proxy that hides all activity from the MediaWiki software). But I suspect that the traffic came from the heat engine related yahoo groups and other blogs I posted the story on, and not from digg.

read more | digg story

Version 0.1 of Archimerged’s TrombePump drawing

2006-06-17

See also the TrombePump article on Renewable Energy Design Wikia, which you can edit. Also, please digg the story.

Archimerged has completed the first revision of his TrombePump drawing, and uploaded it to wordpress. The original is an svg image, designed for 640×480 pixels, and the image here was rendered by the gimp, flattened, and saved as png. Sorry, I haven't figured out how to make wordpress allow wide images, but if you click on the image you get the original size png. I'm going to upload it to other places and link it as well. Update: I re-rendered it in gimp at 450×338, and it looks a lot better here. SVG is good stuff.
Archimerged's TrombePump V0.1.450x338.png

Water powered water pump vs. heat exchanger

2006-06-16

The TrombePump design involves using gravitational potential energy stored in a descending column of bubble-free hot water to compress cold air bubbles in a descending column of cold water, and subsequently using hot compressed air to raise hot water in a bubble pump. There are two ways to do this. Either use a countercurrent heat exchanger to change the hot water into cold water and vice-versa, or use a water-powered water pump to lower the hot water and raise an equal mass of cold water. Either should work. It is a question of cost effectiveness. The countercurrent heat exchanger can be made arbitrarily efficient if it is made larger (and therefore more expensive and bulky). I'm not sure exactly how efficient a water-powered water pump can be. If the water is flowing rapidly, two turbines on a single shaft might achieve efficiency comparable to the heat exchanger, and if attached to a motor-generator, the TrombePump could produce electricity rather than compressed air.

Work done by small expanding bubbles in TrombePump

2006-06-16

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…