If you could get the water to swirl it would be cause it would result in a longer contact time with the water. But I have never had a problem with my "normal" reactors. But the very nature of fluid flow means that it will take the path of least resistance. The only way you will get fluid to swirl in a pipe is to deflectors in the pipe.
The swirling thing works quite well in very wide container with very high capacity pumps. In fact it's how they separate wort from the solids in a brewery. But the pumps in that case are huge. Imagine 8000 gallons of liquid in a brewing tun (about 20 feet across) swirling around the outside edge so fast that it's almost leaving a dry spot in the middle.
This whole thing reminds me of a common myth among cigar smokers. That if you cut the foot of a pyramid cigar at an angle it will direct the smoke at your upper palette.
That doesn't work either as the smoke is going to take the path of least resistance towards the vacuum.
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