The first one that comes to mind is Texas A&M University. Their emphasis is on mechanical aspects of turbomachinery (rotor dynamics, seals), but that is not to the exclusion of fluids/thermo/aero. They are the "host" of a significant symposium, often simply referred to as the Texas A&M TurboShow. In fact, it occurs in early September every year. It is more focused on industry activities (rather than other universities), but might still be useful for you in your explorations.
Some others that I've come across recently (mostly for aerodynamics research) are:
Mississippi State Univ.
Univ. of Milwaukee
Massachusetts Inst. of Technology
Univ. of Cambridge (UK)
Univ. of Durham (UK)
There are others, of course. I suggest that you do a web-search - some "advanced search" option - where you can enter enough keywords to limit the search to your particular area of interest.
Research goes where the money is, especially in academe. I'm not sure what you mean by "unconventional".