Civil Aviation

It's a customer option (hush kit) for certain engine types, and it's supposed to reduce exhaust turbulence, thus reducing noise. However, it's usually the high pitched whine of the compressor that most people hear. Most companies don't want to pay for it unless they're required to fall under certain sound levels for certain airports at night. For those, it's often cheaper to not fly that route at night, or use a quieter airplane (such as a CRJ or ERJ with GE CF34 engines).

Every design is different, and every design choice has advantages and penalties. In short, Airbus doesn't use them because of increased fuel consumption, since they found other ways to reduce noise.