A system includes a a combustor cap configured to be coupled to a plurality of mixing tubes of a multi-tube fuel nozzle, wherein each mixing tube of the plurality of mixing tubes is configured to mix air and fuel to form an air-fuel mixture. The combustor cap includes multiple nozzles integrated within the combustor cap. Each nozzle of the multiple nozzles is coupled to a respective mixing tube of the multiple mixing tubes. In addition, each nozzle of the multiple nozzles includes a first end and a second end. The first end is coupled to the respective mixing tube of the multiple mixing tubes. The second end defines a non-round outlet for the air-fuel mixture. Each nozzle of the multiple nozzles includes an inner surface having first and second portions, the first portion radially diverges along an axial direction from the first end to the second end, and the second portion radially converges along the axial direction from the first end to the second end.
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH & DEVELOPMENT
 This invention was made with Government support under contract number DE-FC26-05NT42643 awarded by the Department of Energy. The Government has certain rights in the invention.