Sugar is used for adding gravity to a beer without increasing the final gravity, this will dry out the beer. It can also be used to add flavor, mostly done in Belgian styles with dark candy sugars. I have heard that adding at flameout or at high krausen makes little difference in the flavor. So, the deciding factor for me is the initial yeast pitch rate, if you add sugar at flameout, you'll have to pitch more yeast.
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Pimary #1: Trippel
Primary #2: Summer Berliner Weisse
Primary #3: Belgian Quad
Souring: Sour Red, Sour White, Sour Black, Saison brett, Farmhouse Saison
Bottled: Saison, Nelson saison, Sour Brett Saison
Waiting: Dubbel, Belma Pale, Dark Saison