Turbine engine with a fuel injector

A turbine engine having a compression section, combustion section, and turbine section is serial flow arrangement, the turbine engine comprising:

• a fuel injector comprising:
• an outer wall in annular arrangement extending from a forward end to an outlet, the outer wall surrounding an interior having a non-swirling air passage, and the outer wall defining a central longitudinal axis;
• a centerbody positioned within the interior and defining a centerbody passage that extends through the centerbody, the centerbody passage being coaxially aligned with the central longitudinal axis and configured to introduce a first flow of air into the interior;
• a fuel passage fluidly coupled to the interior;
• and
• a set of air passages in annular arrangement about and extending through the outer wall and fluidly coupled to the interior aft of the fuel passage, wherein the set of air passages are arranged tangentially relative to the outer wall to impart a swirl to a second flow of air provided from the set of air passages to the interior,
• wherein the fuel passage is configured to introduce fuel radially into the non-swirling air passage upstream of the set of air passages.