This is a really good question. The reason regular turbines and wind turbines are designed differently is because regular turbines have a small volume of fluid experiencing a large change in pressure while wind turbines have a large volume of fluid experiencing a small change in pressure. You see the exact same thing in fans - big ceiling fans look like wind turbines and air compressors look a lot like regular turbines.

I’m sure the cost of a casing plays into it, but its primarily about the energy efficiency of different blade shapes in different hydraulic conditions.

And if it were more efficient, there’s the the challenge of rotating the casing when the wind direction changes.

I mean the whole point of the casing as I understand it is to contain a flow at above ambient pressure - not something that even makes sense for wind. You could have different (more turbine-like) blade geometry without a casing.

There's a bunch of maths around Betz' law that dictates how the efficiency works, but it turns out that the theoretically optimal structure is a single blade: http://www.wind-works.org/cms/index.php?id=543

For mechanical engineering reasons, mostly to do with evening out the load at the point of blade attachment, the industry has mostly converged on three.

This is also linked to tip speed ratio: http://www.reuk.co.uk/wordpress/wind/wind-turbine-tip-speed-... ; the tip speed is usually several times faster than the wind speed.

Remember that the blades are aerofoils, effectively wings. They don't need to touch all the air in their swept area, their effect is given by redirecting the flow of the whole stream of air.

Casings are only useful for small turbines operating at high pressures, where the energy lost to spilling over the tip of the blade would be high.

> but it turns out that the theoretically optimal structure is a single blade

In Betz's own derivation, the ideal rotor is an "actuator disk", having an infinite number of blades, which have no drag.

Single bladers have - as do twin bladed machines horrific tower thump.

You've already received some good responses (particularly from /u/pjc50), but one particular point may not be real clear.

Generally speaking, the power a wind turbine can generated is proportional to the entire swept area. So, other things being equal, it is better to go for longer blades to increase the area, rather than trying to "capture all the wind" in a smaller cross-sectional area.

So the most efficient use of your wind turbine's mass (which is proportional to cost) is to make it as big as feasible.

For the same reason propellers aren't shaped like compressor blades inside a cylindrical encasing. The cylindrical encasing dramatically reduces air flow, but is necessary for large pressure changes. For a brayton cycle heat engine, like a jet engine, you need to maximize pressure gradient for optimal efficiency, but if you're not burning fuel then you want to minimize pressure gradient and maximize mass flow rate.

The Halcium Power Pod uses a casing to increase power generation by 40%: https://www.halcium.com/

I believe that if you consider the money it takes to add the conical casing, and instead just make a bigger tri-blade without a casing with that same money, you come out ahead.

It's not that. It's because they are optimized for low pressure differentials.

I'm sure both are true. It doesn't make physical sense or economic sense. Encasing the entire turbine with a shroud the diameter of the blades would be astronomically expensive.

However, there is no rule in physics that you can't 10x the windspeed with a focused inlet.

Natural mountain ranges around some farms have a similar effect to improve power output, but we would never consider building a natural mountain to improve turbine efficiency

> but we would never consider building a natural mountain to improve turbine efficiency

Maybe we could? Mining operations already produce huge volume of material from tailings and overburden. Not an outrageous idea to be more strategic in how and where that material is placed. Could create some artificial ranges with better wind properties.

I mean I think it's outrageous but I would be willing to look at a cost benefit analysis proving me wrong

Not an expert, but that rings true. Probably environmental impact of a huge volume of air sucked into the cone and fed into a high-speed grinder should be factored in as well.