The broad research interest of the Turbomachinery and Heat Transfer Laboratory is to enhance the understanding of complex physics in coupled flow solutions relevant to turbomachinery and high speed propulsion. Our research interests guide us towards a deeper understanding, characterization and modeling of the inherently unsteady and coupled solutions in various propulsion applications, such as aero-aero, aero-thermal, aero-acoustic and aero-mechanical interactions. Even as computational resources become available to do full unsteady three-dimensional viscous solutions, a significant amount of simplified modeling is required when considering such utility as a design tool. In addition, there is much contribution to be made in not only identifying the key physics, but determining new metrics and analysis methods that allow complex sets of results to be digested in a useful way.