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By second ferment, do you mean for bottle conditioning? If you want a tripel, then I would recommend using a tripel yeast (w big starter) at the outset, to ensure you get the flavor profile you want.
Unless you cold crashed it, you'd likely get enough yeast in the bottles to get some minor refermentation in the bottles. If you successfully got a 1.080 tripel down to 1.011 FG, then you won, and you'd likely have difficulties getting a new (regular) yeast to start up against 8.5% ABV, little food, low pH, and no oxygen.
I used WLP 530 Abbey yeast for my Tripel for 3 weeks ago. Went from 1076 to 1012 in 10 days time without any problems (pitched with a yeast starter 2L).
Not bottled yet, but secondary allready gave a very nice Tripel taste and flavour with this yeast.
Pitch the Abbey yeast at end of wort cool. Ferment 7 days.
Pitch the Trappist yeast at 7 days and ferment another 14 days.
Rack to bottling bucket, seal, add blow-ff and let settle at 60 degrees for another 7 days.
Prime LIGHTLY and bottle.
Bottle condition for 30 days.
Follow the advice of Maltlicker. And if you use a kind of normal Tripel profile, go for one type of yeast. After you pitched with a big starter aerate 2 times properly during the first 24hrs. Fermentation at 19c (66/67F) and be patience. Don't focus too much on rigid fermentation schemes (7 days primary, 7 days secondary etc.) but measure and observe what your beer is doing. It takes the time that it takes. It's just like Belgium Beer the spectrum is large Good luck!
When I suggested a "tripel yeast" I didn't intend to suggest there's only one yeast for that. Both big yeast houses have several, and some are called Abbey, but if you Google up the actual Belgian tripels, you'd find that many use one of two strains that seem to be the traditional tripel yeasts.
To me anyway, tripel is one of those styles that is instantly recognizable by its distinctive aroma.