This can be accomplished using CLR (a ZEP product - find at Home Depot) to dissolve the carbon. Soak the inside of the suppressor in ZEP CLR and flush it every day for several days. Alternating with an Ultrasonic cleaner can help to break up stubborn carbon. Do not use CLR in an ultrasonic cleaner - it will damage the tank.
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For ULTRA series suppressors, CLR should not soak the "Direct Thread Insert" for Direct Thread ULTRA suppressors. The best way to accomplish this is to have the thread end up and fill the suppressor up to just short of the direct thread insert, or about 1.25" into the suppressor.