A combustor assembly for a turbine engine includes a cap assembly which gradually increases the volume of compressed air provided to the combustor assembly, and which slows the compressed air in a controlled manner before delivering the compressed air into a combustor area. The cap assembly includes inner and outer sleeves which are mounted in a concentric fashion. The annular space formed between the inner and outer sleeves gradually increases from an aft end to a forward end. A stepped portion is formed on the inner sleeve of the cap assembly, and this stepped portion is joined to a corresponding combustor liner.