A turbomachine includes a rotating group with a turbine wheel. The turbomachine also includes a housing that houses the rotating group, wherein the housing defines a turbine outlet passage for exhaust from the turbine wheel. The turbine outlet passage is directed in a downstream direction along an axis of the turbine outlet passage. The turbomachine includes an air bearing system with at least one bearing component that supports the rotating group for rotation relative to the housing. The air bearing system includes a bearing cooling path that is fluidly connected to the at least one bearing component and that has a bearing air line outlet. The bearing air line outlet is fluidly connected to the turbine outlet passage and is directed in the downstream direction along the axis.