Bathtub compressed air energy storage

Many toys are made to amuse kids, but not the engineers who build them. This one is dedicated to entertaining engineers !

Here is a short presentation video

I have long been fascinated by the idea of compressed air energy storage under deep water : storing gigantic amounts of energy under the depth of the ocean… Now you can see it at work in your bathtub, exploiting the pressure of this extensive, deep (sort of) stretch of water.

This is also a quite sophisticated way to make bubbles.

Principle

The idea of storing compressed air under deep water is to leverage the surrounding pressure, which increases roughly of 1 bar every 10 meters. So, a if compressed air is stored at this same pressure, the reservoir does not need to sustain the pressure.

If the reservoir is just filled by pushing air and letting water flow outside, according to Archimede's principle, a resulting force will tend to lift the reservoir upwards. So, instead, the water is pumped out of the reservoir as the air is pumped in, maintaining an air pressure which is equal to the pressure of water just above the reservoir, instead of the pressure corresponding to the water level in the reservoir. So, for a cylindrical reservoir, the pressure is the same on both sides of the roof, which does not sustain any resulting force, and the walls are pushed inward, according to the water level. And the reservoir stays at the bottom, Eureka!

Of course, in a bathtub, the pressure under 15cm of water will only be 1.5kPa more than the atmospheric pressure. As a consequence, the air can be considered to have a constant volume, it's not really "compressed" and energy is stored only by the displacement of water. While the air is pumped in at 1.5 kPa, the water is pumped out at 0 to 1 kPa as the water level in the tank decreases (the tank is about 10cm high).

Bathtub implementation

The system consists of an air reservoir with a transparent top (and without bottom), a pump which simultaneously blows air in and water out of the reservoir. The stored energy powers a pneumatic motor, which allows the cute little duck to happily travel across the bathtub. The pump and the reservoir are connected by two pieces of washing machine hose (24mm external diameter), and the motor to the reservoir by a third hose with a valve in between.

Air reservoir

The reservoir is a cylinder  with an outer diameter of 20cm, 4mm thick, and a height of 11cm, for an approximate 3l volume. With 25cm of water in the bathtub, the system has an impressive capacity of 4.5 joules! (Only the air pressure difference is used, the additional water pressure difference is “wasted” since there is only a pneumatic motor). The wall is 3d printed (takes 100g of PLA with one perimeter and 10% infill) and its bottom follows the curve profile of the bathtub. I wrapped it with adhesive tape since the 3d print is not really airtight, especially with a single perimeter. The top is a simple sheet of PE-LD (assembled with glue).

I printed a TPU gasket in order to make the bottom watertight. It has lips that were intended to fit around the cylinder's wall, but those didn't work as expected because the wall is not always orthogonal to the floor, since it is curved. So I removed the lips with a knife, and assembled the gasket with silicone “in place”: first I laid down the gasket in the bathtub, then I pressed the cylinder covered with silicone on top and let it cure overnight with weight on top.

This was quite hermetic (the gasket was printed on glass, so its bottom surface was really flat) but I later applied silicone bellow the gasket too to keep it in place (see bellow).

Pressure balancing

The pump replaces water in the reservoir by approximately the same volume of air (see bellow for the pump mechanism) which is made simpler by the fact that the air has almost a constant volume (due to the very low pressure difference). But for accurate pressure adjustment, the roof of a reservoir has a permeable membrane,  which is a fine sieve made by printing at 50% infill. When the pressure is identical on both sides, the water stays on top and the air on the bottom. If the pressure is too low in the reservoir, then it “rains” ; if it is too high, then it bubbles.

A little cheating

The TPU gasket part that I glued around the bottom for sealing proved unnecessary as I had to glue the reservoir at the bottom of the bathtub anyway (with silicone). The two small magnets that I had included to secure it on the bottom of the bathtub weren't enough. A simple solution was to add some ballast, for example put some big weight on top of the reservoir, but I opted for the silicon solution to make the video prettier.

It's not that the principle of pressure balancing doesn't work, but the printed reservoir is too light to sustain even the slightest disturbance (such as  the minor forces applied by the hoses, which are quite rigid, and float when filled with air), and the sieve on the top has some resistance : it only allows bubbles to escape if a slight pressure difference exists, which is enough to lift the reservoir. I also attached the pump will double-sided tape, and a piece of foam, since otherwise it would float too.

So, unless adding some ballast or attaching stronger magnets that come directly in contact with the bathtub (the 2mm gap coming from the gasket thickness is already a lot), this toy is not one that can simply be thrown in the bathtub every time you take a bath to play with it. And now I have to cleanup all this silicone bead at the bottom of my bathtub :-(.

Air and water pump

The same pump is used to displace the air and water at the same time, and at the same rate. 

Pump operation

In the cylinder, the water is below the piston, and the air is above. When the piston moves upwards the water is replaced with air in the reservoir, and when the piston moves downwards, the water is released in the bathtub, while air is sucked from the bathroom (through the pump handle).

Pump parts

The cylinder is a 10cm portion of a used silicon cartridge, closed by two printed parts at the ends. The piston is 3d printed (in PETG) and glued on a shaft which is a portion of plastic tubing of 16.5 external diameter which I had at hand. I also printed a gasket in PETG to use between the shaft and the top part, which is reasonably air tight without too much friction. The gasket is kept in place by a printed nut.

Four printed check valves are used to enforce air and water flow direction : two are connected on the bottom part, one on the top part, and the last one between the shaft and the handle, so the shaft is also the air intake.

Check valves

The first three check valves are identical, both ends of each valve have a 24mm inner diameter, which can be connected either to a piece of washing machine hose, or to the pump body (the fit is loose on the pump body, I used PTFE tape for sealing). The air intake valve is different only in that its input end is the pump handle and its output is the shaft.

A valve consists of the two ends which screw together, a pin to insert in the output end, a 24x15x2 gasket, and a spring. I initially used small steel springs of 6mm diameter, but I only had two, so I printed other springs in PETG using one of my previous designs. A bit of care is required when removing the integrated supports.

Pneumatic motor

The motor is a vane-type one, designed and printed specifically for this assembly. It has two pairs of vanes which are connected together, so that the vanes are always flushed against the casing, without relying on centrifugal force for this. The hose going to the motor is connected to the “membrane” part on the top of the reservoir.

A valve with a push button is put just before the motor. I lazily used a steel spring for this one. It's different from the other valves as the shaft is on the low pressure side, to be able to push it to actuate the motor.

The pulley is attached to the motor's hexagonal shaft, and winds the string, pulling the attached bird.

Conclusion

This was an interesting project to carry out, and it was great to see this work ! If anyone is interested in reproducing the experiment, it doesn't require a lot of hardware, almost everything is 3d printed (the pump's shaft and cylinder could even be printed too, but it was more convenient to use what I could salvage).

It doesn't raises much health concern, since I don't think anyone would actually take their bath with the system installed (I didn't). Anyway, I believe the used materials are safe, maybe with the exception of the silicon beads, which I'm not sure is meant to be immersed within the bathtub (at least within the 24 hours after application).

I hope this will inspire someone !