Chew down means to chew something vigorously or with great effort. If you're looking for synonyms for this phrase, you can consider words like munch, chomp, gnaw, and devour. Munch implies a quieter, less aggressive form of chewing while chomp suggests a more forceful and noisy action. Gnaw is often used to describe the action of a small animal like a rodent while devour implies a sense of urgency and eagerness in eating. Other synonyms include bite, nibble, grind, and masticate. All these words may convey different shades of meaning, but they all depict the act of chewing food with the teeth.