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Cross-flow fans are mostly used for the even "curtain" of airflow produced that is as wide as they are long. They are also used when a product's form factor favours their long, narrow shape. The problem is that they are not particularly efficient by any measure. I have contemplated a few variations
around optimizing individual blade pitch. The result is improved efficiency at the cost of increased complexity and weight. Other possible variables include optimal rotational speed and noise levels.
I will start with the least complex variation. Each blade of the fan pivots independently with the pitch determined by a sprung linkage that follows a cam on the hub of the fan barrel. In this way the blades can be pitched to draw in air on the intake side and push out air on the exhaust side.
Next alternative is a gearset to rotate the blades counter to and at exactly half the frequency of the fan barrel.
An advanced variation would be flexible blades and an additional mechanism to reverse the orientation of the aerofoil to capture extra lift forces.
The engineering maths is beyond me but I might build a model one day. I found one design online that used a similar concept except purposed for wind power generation and will link to it below.
Novel Vertical Axis Wind Turbine
Development and Analysis of a Novel Vertical Axis Wind Turbine [matman, Feb 20 2007]
idea for fan with rotating blades [xaviergisz, Feb 20 2007]
||Rotating blades are an interesting concept.
However I think you'd get a lot of parasitic
turbulence which might lead to
inefficiency. Not to mention, ball bearings
are usually the primary noise generators,
so one per blade is probably not a good
recipe for silent cooling.
||Are you talking about reducing noise by having the blades turn to line up with the circumference of their travel during part of the rotation? Because if you are, that would be pretty fun to watch. Do it right, and it could also reduce power usage, since during part of the rotation, each individual blade is essentially "idling," coasting through the air in a lower-drag configuration.
||So it's a Voith Schneider propeller/cyclorotor, used as a fan?
||The simplest-at-first-glance pitch mechanism I've seen those use is a rod connected to each blade, offset somewhat from the blade's axis of rotation, all connected at the other end to an axle offset from the whole rotor's axis of rotation, that offset being adjustable in two axes to control the thrust vector. But this mechanism has a crankshaft passing problem.