Just looking for a little input from those that are drinking a completed Vessi brew. Curious what you may have brewed and how long was it in the Vessi before you found it drinkable. I just tasted a bit of my cider (1st ever cider and 1st Vessi brew) and after 30+ hr. cold crash to 35 deg it's still relatively cloudy and yeasty tasting. I'm certainly not expecting a fully aged cider at this point (2 weeks in) and cloudy doesn't bother me as long as it's not yeast still in suspension. I may have to use something to drop the yeast further. It started at 1.062 and finished at 1.000 so it's relatively dry and I had to back sweeten with 2 cans frozen concentrate.
On another note, I haven't sorted out how the brew in the vessel gets to the dispensing tap. I haven't looked real close inside but I hadn't noticed a port anywhere near the bottom.
There is a port, just above where the tri clamp fitting is at the bottom. Easy to miss, it looks just like the CO2 outlet at the top, slightly rounded. The vessel only leaves a few inches of liquid in it which is a nice feature when cleaning.
From what I can tell looking in the back of the machine, there must be push fit tubing or bev tubing like the CO2 runs on and a tee valve to split the liquid to either the kegging/bottling port or to the tap. I didn't feel adventurous enough to take apart the machine housing and look through it yet.
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I have just completed a pale lager for my first brew, and my experience is much the same as yours. I have dumped yeast twice but still have a hazy, slightly yeasty brew at 12 days post-pitch. I think I will try filtering, but you could also try gelatin or the like to drop the yeast. It will naturally clear, generally, within two or so weeks of conditioning time. I plan to keg mine so I can start the next batch - so I will let it clear and mature and get my Cider started!