You could do the equation yourself. My assumption has been that only the air closest to the envelope gets perturbed by the envelope. If the envelope was a smooth cylinder this boundary layer might only be a few centimeters. The more uneven the cylinder, the faster it is spinning, the more viscous the fluid, the greater the height of this boundary layer I think. Perhaps the equation in the paper is the correct one to calculate it, or has some of the right variables.
I don’t know if the paper is applicable though as there the particles are forced to move, while in your case they only move if they are within the boundary layer
A separate question is how this boundary layer interacts with the natural convection inside the balloon, and how that depends on the strength/size of either.
What would happen if there were no convection and the fluid was very viscous and the cylinder was very small and was spinning very fast, and what would happen in the opposite case?
But say you attach baffles to the inside of the envelope that rotate with it. Or say you are only interested in the air within the boundary layer, now you can calculate the ratios of the centrifugal and buoyancy forces, if you make some assumptions about rotation speeds and temperature differences.
Now if you know the ratios of the forces you can decide if adding the baffles helps or not, or where you should put them.
A publication which is also available on Researchgate provides interesting figures 3 and 4:
Margarita Khusnutdinova, Aigul Haibullina, Alex Sinyavin and Aidar Hayrullin
Kazan State Power Engineering University, 51 Krasnoselskaya Street, Kazan, 420066, Russia
Many parameters remain to be known to know if a Magnus effect-based balloon could improve the insulation of contained heated air: the volume, the diameter, the angular speed, the temperature gradient, the degree of interference between the layers according to these parameters …
However, I would make a remark: we can predict that the effect would be limited during pumping mode cycles due to the variation in the rotation speed going as far as its stopping or even its reversal. It is the reason why I rather see an use in static mode (which is mentioned in the preprint), i.e. for Is an electrically heated balloon lift support for AWES possible? And for gigantic balloons the time to achieve stability of the maximal heat could be very long, perhaps several hours or even days. But there are only hypotheses.
A heating wire (like below) with adapted electrical resistance and battery could be settled in the middle of a balloon. Then measuring the aerostatic force when rotating (and the time to achieve maximal heat) and when not rotating and comparing.
Thermography of a filled and ready to go hot air balloon.
Now I would wish to see the image of the same balloon when rotating.
Hot air balloons sometimes use rotation vents (see below). Would the (low) rotation speed be sufficient to see if the colder layers are against the walls inside, and after how long, and at what speed of rotation?
ROTATION VENTS
Rotation vents enable the balloon to be turned so that it is correctly orientated for landing. When flying a partitioned basket or one with a door , rotation vents are mandatory.
That said, the measurements would be distorted because of temperature exchanges due to the vents.
The temperature in a hot air balloon is far higher (about 70 to 100 degrees more in relation to the outside temperature) than that of the intended Magnus effect-based balloon (2 to 10 degrees according to the dimensions of the balloon). This must be taken into consideration. Perhaps also the horizontal axis of rotation of a Magnus effect-based balloon leads to some differences.
As I mentioned above the static mode would be required to keep the benefit of insulation by the rotation, above all if along time is necessary to achieve it. Flettner balloon and VAWT side by side leads to a static (stationary) operation. If the results are better known, some designs of hot air with central heating cables could be introduced in the designs mentioned in the preprint Vertical axis wind turbine(s) connected to Flettner or Sharp balloons, avoiding helium or hydrogen and their respective issues.
An advantage compared to other yo-yo AWES including parasails: the alternating phases of reel-in and reel-out do not change the structural configuration through folding or other depowering techniques, but only the velocity (and perhaps the direction) of the rotation. That could mitigate the wear due to the terrible yo-yo mode. This is likely a small advantage, nothing more.
