<div>Enhancements of gas turbine engines efficiency are critical for the development of the next generation of clean and efficient aircraft. With the increase in combustion temperatures, cooling of the turbine blades poses one of the most important thermal management issues. The current and most adopted solution is to flow cooling air bled from the compressor through channels inside turbine blades. Fuel preheating, meant to increase combustion efficiency, could be used to cool such air flow in fuel-air heat exchangers. However, when fuel thermodynamic states approach supercritical pressures and temperatures, large amplitude oscillations have been known to occur with catastrophic hardware failures. For this reason, the use of supercritical fuels in fuel-air heat exchangers has been avoided, thereby reducing the fuel's cooling potential and the overall efficiency of the aircraft. Engine manufacturers desire a model capable of predicting the onset of such disruptive thermoacoustic oscillations. To this goal, we study theoretically and numerically transcritical thermoacoustic oscillations, i.e., thermoacoustic instabilities manifesting themselves when a fluid is heated close to its critical point, where abrupt changes of thermodynamic properties appear. Details of this work will be on the development of a transcritical thermoacoustic theory and on numerical results from linear stability analysis and high-fidelity Navier-Stokes simulations. Meeting the needs of industry and with the intent of pushing technological and scientific barriers, we propose to exploit such powerful oscillations for energy conversion through the use of the first-ever-built transcritical thermoacoustic engine.</div>