A method enables the operation of a gas turbine engine. The method comprises channeling airflow into a cooling passageway defined between the combustor casing and an inner liner of the combustor, wherein the inner liner is fabricated from a plurality of panels coupled together, channeling airflow into a cooling passageway defined between the combustor casing and an outer liner of the combustor; wherein the outer liner is fabricated from a plurality of panels coupled together, and channeling dilution airflow into a combustion chamber defined between the inner and outer liners, through a plurality of openings formed within at least one panel within at least one of the inner liner panels and the outer liner panels, wherein the plurality of openings are non-circular.