A method and apparatus to facilitate reducing NOx emissions in turbine engines is provided. The method includes providing an annular shell including a plurality of circumferentially extending panels. The plurality of circumferentially extending panels includes a first panel positioned at an upstream end of the shell and a second panel positioned downstream from, and adjacent to, the first panel. The method also includes forming a plurality of primary dilution holes in the first panel and forming a plurality of secondary dilution holes in the second panel. The dilution holes are configured to discharge dilution air into the shell.