Do those cylindrical sails actually work?

hen I first saw that story about those cylindrical sails supposedly used to power a ship, I thought it must be a joke. I am still trying to understand how these devices are going to provide enough thrust to replace 90% of the energy to move a ship.

First some background. It's well established that air blowing across a rotating cylindrical surface causes lift. A non-rotating cylinder has zero lift and zero drag according to the inviscid flow theory, which ignores viscosity. This is called d'Alembert's paradox, but in fact it's a failure of the theory. Drag exists, and it's caused by viscous effects, which generate shear stress at the body surface and cause the flow to separate from the surface at the back of the body. These viscous effects must be calculated by computational fluid dynamics or CFD; inviscid theory, while much simpler, doesn't account for them.

Inviscid lift theory

Purely in terms of lift, a rotating cylinder has the greatest amount of lift of any airfoil shape. Is it enough to power a ship? Let's look at a rotating cylinder of radius R.

One aerodynamics text says:^[1]

Friction between the fluid and the surface tends to drag the fluid near the surface in the same direction as the rotational motion. . . . the extra velocity con­tribution [caused by spinning] creates higher-than-usual velocity at the top of the cylinder and a lower-than-usual velocity at the bottom.

So the lift is L^′ = ρ_∞V_∞Γ. In other words, the lift L is directly proportional to the circulation Γ. ρ_∞ is the density of air = 1.225 kg/m³ at sea level and 15°C. This is the Kutta-Joukowski theorem. CFD will show that there is drag as well, but the lift formula is reasonably accurate.

This is called the Magnus effect. A typical rotation speed is such that surface velocity is 3 × V_∞. However, the drag is also much higher than for a normal airfoil, so it is not used for powered flight.

The formula for lift is
where c_l (lower case 'c' is per unit span; upper case is per airfoil) is the coefficient of lift,
and V_∞ is the freestream velocity in air (at 'infinity', that is, before the air encounters the airfoil), ρ_∞ is the density of air, S is the planiform area, and Γ is the 'circulation.'

So, for example, if the cylinder had a diameter of 0.5 m, the freestream velocity is 25 m/s (48 knots), and the maximum surface velocity of the cylinder is 75 m/s (145 knots), we would get a lift of 892 N/m or 200 pounds of force per meter (1 Newton = 1 kg m/s²). Let's say there are two of these cylinders counter-rotating so as not to add any angular momentum, and they are 10 meters tall. You'd have 17,840 Newtons of thrust for the ship.

That's not a whole lot. Thrust requirement increases nonlinearly with the desired speed. A cargo ship might need 67,000 hp or 50 MW to produce enough. So, if the target speed is 20 kt (10.28889 meters/sec), then you would need 4,859,611 Newtons of thrust to maintain it. Ignoring aerodynamic drag, those cylinders would reduce your power requirements by one part in 292, or 0.36%.

Even so, in the 1920s, Anton Flettner was the first to use it to propel a sailboat, and was able to steer by rotating two cylinders in opposite directions. The technology was abandoned because of the difficulty in rotating those cylinders. It's not used on airplanes because the enormous drag makes them useless.

What about the CoFlow scheme?

The CoFlow scheme does away with rotation. Instead, it has an impeller that sucks a small amount of air in on one side and blows it out on the other side. The idea seems to be that this eliminates the need for wind and, it is claimed, generates “a pressure imbalance and a considerable amount of thrust.”

On a ship, the air would have to blow from port to starboard or vice-versa (most likely they'd use two cylinders blowing in different directions). This creates “lift” as the ship would be pulled toward the lower air pressure, i.e. forward.

The questions are: first, does V_∞ have to be external, or can you use a fan? And second, how could it be more efficient than just using the air jet itself for thrust? It would be like attaching a fan in front of an airplane wing and hoping the plane would fly straight up like a helicopter. This would be so useful there must be a good reason why it's not done. Suppose you're holding a fan in one hand and and a vacuum cleaner in the other. Could you levitate yourself this way? (Assume a cylindrical cow . . . .)

Experiment

Shopvac aerodynamics experiment

Just because I was really bored yesterday, I tested that by placing a Shopvac (0.43 meters in diameter, air velocity about 100 feet/second or Mach 0.088) on a dolly in my garage so it could move easily. I then directed the hose through a duct so that the air from the exhaust flowed toward the suction end over the surface of the shopvac. The formulas say it should have accelerated across the floor and smashed into my car. Instead it rotated counterclockwise. No amount of encouragement could get it to move toward the area of lower pressure. This crude test confirms that the jet effect is much stronger than the aerodynamic effect, at least in my setup.

I could only find one non-paywalled article ^[2] on the subject. It's a computer CFD simulation. In their paper, the authors calculate drag and lift by subtracting the reactive force caused by the air jet, thus obtaining a ‘corrected aerodynamic efficiency.’ In their simulations, they use air at Mach 0.063 (42 knots). The standard measure of efficiency of an airfoil is C_l / C_d . The simulations in the paper show a maximum ratio of C_l / C_{d corrected} about 6:1. On their website, they claim C_l of 15. In a white paper on the website ^[3] they describe wind tunnel tests on an airplane wing at Mach 0.1 and 0.729. There's no indication on their website that the company has yet done a proof-of-principle test.

It sounds like they'd have a better result by just directing the air from their impeller toward the stern. Even so, radical new ideas are always welcome, and bear in mind that even a 1 or 2% reduction in fuel costs might make them cost-effective. And, as the company's website emphasizes, it is “green,” at least theoretically, so the PR value might make it worth the cost even if it slows the ship down.

Perhaps rotating cylinders underwater would work better. Or use a supercavitating propeller system to blast the ship at 100 knots. It may or may not be cost-effective, and it might have trouble navigating through the Panama Canal at that speed, but it would be interesting to watch.

Disclaimer: I'm not an expert in hydrodynamics. Maybe I'm wrong and the ship will go into orbit. But it seems to me they'll have to go back to rotating the cylinders. The drawback to that is they'll have to wait for the wind.

aug 06 2024, 5:26 am