Optimal Airfoil Shapes for Viscous Transonic Flows of Dense Gases

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 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 fluids, can exhibit nonclassical gasdynamic behaviors in the transonic and supersonic regimes, such as the disintegration of compression shocks. Utilizing dense 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. I. Introduction ENSE gases are single-phase vapors operating close to saturation conditions, at temperatures and pressures of the order of magnitude of the critical ones. At these conditions, real gas effects play a crucial role in the dynamic behavior of the fluid. The study of the complicated dynamics of compressible flows of dense gases is strongly motivated by their potential technological advantages, as working fluids, in energy-conversion cycles. Specifically, such fluids possess large heat capacities compared to their molecular weight, which makes them excellent heat transfer fluids in Organic Rankine Cycles (ORCs). Specific interest has been developed in a particular class of dense gases, known as the Bethe-Zel’dovichThompson fluids 1 , which exhibit nonclassical gasdynamic behaviors in a range of thermodynamic conditions above the liquid/vapor coexistence curve, such that the Fundamental Derivative of Gasdynamics:

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