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My fluid flywheel is a solid case full of water. It has baffles so the water has to spin at the same speed as the case. It has a port at the centre where air can enter to displace the water, and another port at the centre, linked to the outer rim of the flywheel, where displaced water can exit. If the
flow is in the reverse direction, the water can displace air. The moment of inertia varies with the amount of water in the case.
As well as pumping compressed air in or out, you can also apply torque to the flywheel with a mechanical connection.
Ideally we'd use something incompressible instead of air, so a light hydraulic fluid could be used instead. The trade off is that we also want it to be much lighter than the fluid we use as the main flywheel mass. I'm going to approximate it as both massless and incompressible.
Here's a cyclical process using the flywheel:
Start with the flywheel stationary or at low speed, full of water.
A: Apply torque to spin it up to high speed with an electric motor/generator functioning as a motor.
B: Pump in compressed air to displace the water, until the moment of inertia is very low. This takes energy from the compressed air source that could be turned into rotational energy. Also, the smaller moment of inertia could increase the speed. Instead, keep the speed constant with the electric motor/generator.
C: Use the motor/generator to slow down flywheel either to zero or a low speed.
D: Let water displace the compressed air until the flywheel's full. Use the electric motor to keep speed constant.
Step B had to displace water against high centrifugal force, so took more pneumatic energy than is recovered in step D.
By conservation of energy, the cycle puts that extra energy into the electric motor/generator.
I think of it as being analogous to a thermodynamic cycle.
Thermodynamic processes can be adiabatic, or at constant pressure, or constant temperature, or constant volume.
Analogously, the by combining torque and pneumatic flow in various ratios, the processes of the flywheel can be:
1: applied torque with constant moment of inertia (no pneumatic flow)
2: pneumatic flow with no applied torque from the mechanical connection.
3: constant pressure from the pneumatic source.
4: constant speed
Various cycles can be devised that either convert energy from the torque connection to pneumatic output, or vice versa.
The pneumatic system may be most conveniently operated at either roughly constant pressure (attached to a large container of compressible gas, or some sort of spring system) or zero flow (closed port)
The torque connection may be most conveniently at no torque (disconnected) or roughly constant speed, e.g. attached to a much larger inertial mass - a larger flywheel or a car's wheels and therefore the car's movement. Attaching at different gear ratios allows different speed constants.
Roughly constant pressure at roughly constant speed can be achieved by only having a shallow pool of water around the edge of a large diameter flywheel, e.g. varying between empty and 1 cm of water in a 10 cm radius flywheel case. The trade off here is you can't get as much mass increase with the smaller amount of water.
variable moment flywheel
variable_20moment_20flywheel
Mechanical type variable moment flywheel [caspian, Oct 31 2009]
A Related Problem
http://www.physicsf...ghlight=tether+ball
Physics of a tetherball [sninctown, Nov 01 2009]
Angular Momentum (Wikipedia)
http://en.wikipedia...ki/Angular_momentum
[sninctown, Nov 01 2009]
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I'm not sure I understand the basic assumption here, but
first: Any spinning liquid, however, even one that is
closely compartmentalized, is going to dissipate more
energy as heat than the equivalent solid mass. |
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Is the idea that you get the wheel up to speed, then pump
the water in towards the center which increases the
speed. Then you maintain the speed with a power take
off? If so, then the net result is no different than running
the fly-wheel normally and running a separate air-powered
generator, just with a much more complicated system. |
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If I understand this: you're trying to //convert pressurized fluid to rotary motion//, so instead of running the fluid through a turbine, you use it to push water through your flywheel system. |
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Energy goes into spinning up the flywheel with water,
then you use your compressed air to pump the water towards the axis of the flywheel,
then you spin down the flywheel, taking out the energy you put in plus the energy from the compressed air minus inefficiencies,
then you move the water back away from the axis of rotation. |
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There's a problem here, though: moving the mass inward toward the axis of rotation does not increase the angular momentum of the flywheel (assuming I'm not too sleepy)!
The equation is:
(Angular Momentum) = (radius vector) crossed with (momentum vector)
L=r x m*v
So, decreasing the radius will decrease the angular momentum, not increase it! |
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From link for the similar tetherball problem, pg. 4: //As stated many times before me: angular momentum is not conserved, but energy is. The ball thus stays at constant velocity throughout the whole motion as would be expected.// Kinetic energy must be conserved, so the velocity of the water stays the same, even as the radius changes. |
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I won't drop a bad science tag on this one because I'm confused. Good job. [+] [edit: now [] because I conclude it is bad science] |
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[MechE] Yes, it's essentially a much more complicated air motor (or hydraulic motor, I can't decide), with a flywheel thrown in. But while the system as a whole is more complex, there's a couple of tricky bits of a normal air motor that it avoids. Unlike a piston air motor, it doesn't need sliding piston seals. And unlike an air turbine, it doesn't have fluid moving at high speed past stationary walls or differently-moving blades. Both of these require accurate tolerances and cause friction. |
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There may be some trickiness in rotating seals to let the air and water flow, unless the holding containers for them can be rotating too. |
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The water's spinning by itself won't dissipate energy when everything's rotating at the same rate and otherwise unmoving. It's only the motion relative to that that will dissipate enrergy - the connections at the axis and the relatively slow motion of incoming or outgoing water. |
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[sninctown] Interesting thread. I thought about using a tetherball system but couldn't think of a good way to switch between pulling the weight in, letting it out, and holding it steady. As stated in that thread, there are two similar but different types of systems - the ones where energy is applied to pull in the weights, and angular momentum is conserved (but the energy input increases kinetic energy), and ones where torque but not energy is applied while pulling in the weights. My idea is more like the first one, where you sit on a rotating stool, holding weights in outstretched arms, then pull them in. I add the energy by pumping in light fluid (air) to displace heavy fluid (water). Since I'm adding energy from outside the subsystem, it isn't conserved within the subsystem. |
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Anyone got any suggestions for replacing the heavy and light fluids so they're both incompressible, but still of greatly different densities? A minimum density ratio of 2:1 would be tolerable, though more would be better, and there's no hard cut-off point. The combination that keeps occurring to me is mercury for the dense one and oil for the light one, but I don't like poisonous mercury. Non-standard temperature and pressure are acceptable, depending on how impractical you want to be.
How much density difference could I get with other liquids at standard temperature and pressure? |
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//adding energy// Yes, the flywheel will rotate faster when the weight is moved in, because the water will keep the same speed (and kinetic energy) but travel around a smaller radius. However, moving the water inward actually decreases the angular momentum (L=r x m*v) because m and v stay the same while r decreases (see link). |
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The energy in the system is unchanged:
Work = Force *distance
or torque * angle.
With the mass closer to the center, changing its angular velocity requires less torque (mass has smaller moment) but a greater angle (because it's spinning faster), so the work is the same. |
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Yay, physics isn't broken. Unfortunately, your proposed system would be, I think? Does this make sense? |
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Not sure about good fluids to use. |
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[bigsleep] it's like sucking up water with a straw: most of the surface area of the water is in a cylinder shape with air 'above' it to the centre. The air connects to a hole at the centre of one side of the case. A disc separates off a small volume on the other side of the case, which is connected to another hole in the case. This small volume is always filled with water, and is analogous to the inside of a straw. The water gets sucked up by the relatively low pressure. The two volumes are only connected at the outer rim, and you make sure not to push air in that far. |
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[sninctown] conservation of energy doesn't work by adding energy to a system and the the system having the same amount of energy as before. Note that in the tether ball example energy wasn't added. Also that the wikipedia article has an example iceskater where kinetic energy is not conserved, but angular momentum is. My idea's like that |
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