Interesting that "no grill" is always the most quiet, is there no configuration possible (or has never been explored) where the air flows in such a way that sound waves cancel each other out? I.e., even holes emit noise 1/2 phase changed from the uneven ones? Would be a nice area of research. Perhaps it exists, I'm lazy (some 5 mins of searching gave me nothing).
I'm just speculating here, but the grill is the source of the additional noise, rather than something that attenuates noise already present in the airflow. Therefore, to get two holes to emit sound out of phase, the mechanism by which they generate sound must be synchronized somehow.
One way that such synchronization can occur is by the blades passing the holes, and I suppose that the high noise of the 'turbine' grill is caused or exacerbated by the blades alternately aligning with the holes and the ribs. I recently learned that tire treads are made with a pseudo-randomized block size, as with a same size all around the sounds each makes as it contacts the road would be periodic, producing a siren-like sound with a definite pitch.
The swirl pattern presumably mitigates this effect by having little variation in the overall blade/rib alignment through one revolution. There are also tire treads like this.
The difficulties of using interference in reducing fan noise are that it becomes less effective the whiter the noise is, and that destructive interference somewhere usually creates constructive interference elsewhere else.
For passive noise cancellation you would need to add material that absorbs/dampens sound, or you would create a baffle/muffler of some sort. The only alternative I know of is ANC.
Not what you describe, but that reminds me. There are panels that 'cancel' (some of) the noise by guiding the air through foam channels. Had never heard of such thing before, personally.
