Light Mill results

by Greg Egan

This page shows some results computed with the Light Mill applet (follow that link for the applet itself, along with details of the toy model that the applet simulates).

Locked rotor

Snapshot for locked rotor

The snapshot on the right shows the results when the rotor is locked, by setting the friction to “infinite”; the particle/container friction is also set to “infinite” to limit the build-up of angular momentum. The particles have been removed from the snapshot, allowing a clearer view of the flow lines.

In the second histogram at the bottom, we see that near the centre of the vanes the forces on either side are nearly identical. However, near the edges there is a significant failure of cancellation between the opposing forces, with the force on the black side stronger. The third histogram makes this clearer by showing the difference between the momentum delivered to the two sides.

The approximate cancellation near the centres of the vanes reflects the fact that the hotter gas on the black side expands to become less dense than the cooler gas on the white side. The first histogram at the bottom shows a clear excess in the number of collisions on the white side, reflecting the greater density there, but each collision on the black side imparts more momentum.

Varying the rotor’s outer radius

The plots below show the effect of varying the outer radius of the rotor, while holding the inner radius fixed at the minimum value. The “average angular momentum to t=100” in the second plot is calculated by multiplying the average angular velocity (i.e. the net rotation at t=100, divided by 100) by the rotational inertia of the rotor.

Because the rotor here extends down to the minimum value of 10%, when the outer radius reaches 100% the particles are sealed off into four disconnected chambers, with no possibility of a circulating current encompassing the whole container.

Net rotation vs outer radius

Average angular momentum vs outer radius

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Science Notes / Light Mill results / created Wednesday, 6 August 2008 / revised Thursday, 28 August 2008
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Copyright © Greg Egan, 2008. All rights reserved.