Catalyzes the NAD-dependent oxidation of glycerol to dihydroxyacetone (glycerone). Allows microorganisms to utilize glycerol as a source of carbon under anaerobic conditions (By similarity). glycerol + NAD(+) = dihydroxyacetone + H(+) + NADH Binds 1 zinc ion per subunit. Polyol metabolism; glycerol fermentation; glycerone phosphate from glycerol (oxidative route): step 1/2. Belongs to the iron-containing alcohol dehydrogenase family.