We examine fundamental as well as application-specific research problems in turbulent compressible flows and turbomachinery, which have applications in energy systems and sustainable engineering. The research methodology is primarily experimental, using flow diagnostics like particle image velocimetry (PIV), high-speed imaging and probe measurements, with some supporting numerical tools like computational fluid dynamics (CFD). Innovative data analysis techniques are additionally explored for cost-effective experimentation. The research work is categorized into three verticals - high-speed flows, turbomachinery & power and experimental techniques.