It's interesting to mention the three T's.
As far as turbulence, if there is any it must be microscopic. The flame burns as smoothly as if it were a solid object. It makes me think there are ways other than turbulence to achieve the same goal.
Temperature is supposedly higher in the Sans Rival, as many people claim to see a whiter light, though I haven't seen any spectrograph measurements or anything.
Time is interesting. They claim the Sans Rival creates a stronger draft. I am not sure that is not just an assumption since it burns more cleanly and at a higher flame output. I have seen no measurements of the flow. It would seem counterintuitive based on its shape (for a chimney roughly the same height), but it could be like the dimples on a golf ball I guess. They also claim the font remaining cooler as evidence of greater draft, though I wonder if the restructuring of the flame could also simply be moving the heat further from the burner and font instead.
I really don't know what is going on, but it clearly works. I bought one, and it works exactly as advertised. As I imagine it, there are probably three main things at play:
1. Its shape physically changes the shape of the flame. The original chimneys had a sharp pinch similar to the Sans Rival. This takes the cylindrical flame to more of a cone shape, which I assume helps better incorporate the air in the center into the flame. Burning without a chimney, or with a large, fat chimney like would be used with a flat wick, the flame cannot be very high or it will smoke. I'm not sure about there being two pinches. It looks to me like there is one pinch and then two bulges above it in what would be the straight part of a normal chimney. The pinch reminds me of the similar one in a batch box.
2. The varying diameters will create different speeds at different parts of the flame. I assume this is part of what helps structure the flame, and I wonder if it somehow helps improve combustion.
3. If speed is changing, then Bernoulli's Principal also comes into play. I wonder if changing from fast, slow, fast, slow, fast varies the pressure
enough to somehow improve combustion.
I think the most important part is the flame control area. It would be fairly simple to make with wool, and maybe even with brick could be made, though not quite as smoothly. I don't think it would even need to be cylindrical. I imagine a square cross section would work as well. Castable refractory could obviously be made any shape. Though I wonder about how the dimensions might scale changing it to a much larger system.