Let's talk about [old] submarine propeller designs (nothing confidential)

[speed150mph]

I believe they hit the nail on the head. The ring on the 688 prop is most likely for reducing blade tip cavitation noise at slow to moderate speeds. This feature is what gives the 688 class it's somewhat higher silent speed. The Russians main focus with propeller design was speed first and foremost, and ducting the propellers on the diesel boats like the tango was more for protection when operating in shallow water then silencing. We are only now seeing the use of pump jets coming into Russian designs, such as the Borie and the Yasen-m class subs.

In response to the fella who brought up the Alrosa, she was a test bed for pump jets on diesel electric subs. Now pump jets are very effective at dampening noise and cavitation at moderate speeds, but only have a marginal effectiveness at slow crawling speeds. This makes them rather useless on conventional diesel electrics like the kilo as they are generally quiet enough on battery to avoid detection, and more importantly, they are pretty well forced to operate at slow speeds to have adequate range on their batteries.

As mentioned the pump jet comes into it's own at moderate speeds, which diesel patrol subs hardy ever operate at. The Russians deemed it to not be work the higher costs to install it on the subs for so little reward which is the reason why they didn't continue with it. They no doubt however worked the design into their SSN and SSBN designs, since they can operate at the moderate speeds where pump jets become most efficient without worrying about battery life.