Optimal airfoil shapes for viscous transonic flows of Bethe–Zel’dovich–Thompson fluids

High-performance airfoils for transonic viscous flows of dense gases are constructed using an efficient high-order accurate flow solver coupled with a multi-objective genetic algorithm. Dense gases are theoretically characterized by reversed behavior of the speed of sound in isentropic perturbations for a range of temperatures and pressures in the vapor phase. A class of dense gases, namely the so-called Bethe–Zel’dovich–Thompson (BZT) fluids, might exhibit nonclassical gasdynamic behaviors in the transonic and supersonic regimes, such as the disintegration of compression shocks. Utilizing BZT gases as working fluids may result in low drag exerted on airfoils operating at high transonic speeds thanks to an increase in the airfoil critical Mach number. This advantage can be further improved by a proper design of the airfoil shape, also leading to the enlargement of the airfoil operation range within which BZT effects are significant. Such a result is of particular interest in view of the exploitation of BZT fluids for the development of high-efficiency turbomachinery.