Investigation of BZT transonic flows past an airfoil using a 5^TH power virial equation of state

Dense Gasdynamics studies the flow of gases in a thermodynamic region close to the liquid-vapour critical point. In recent years, great attention has been paid to certain substances, known as the Bethe-Zel'dovich-Thompson (BZT) fluids, that exhibit in the vapour phase, for a whole range of temperatures and pressures above the upper saturation curve, negative values of the Fundamental Derivative of Gasdynamics. This can lead to nonclassical gasdynamic behaviors, such as rarefaction shock waves, mixed shock/fan waves, shock splitting and other. The uncommon behavior of BZT fluids can find application in technology, in particular to reduce losses due to wave drag and shock/boundary layer interaction in turbines and nozzles. The present work presents a detailed numerical study of transonic BZT fluid flows past a NACA0012 airfoil. The compressible Euler equations are solved using a third-order accurate centred scheme, and the fifth virial power equation of Martin and Hou is used to model the thermodynamic behavior of the fluid. A parametric study of the influence of free-stream thermodynamic conditions has been performed for a typical BZT gas flowing past a NACA0012 in transonic regime, at fixed Mach number and angle of attack. The objective is to investigate the influence of BZT effects on the airfoil performance and to demonstrate the possible gains with respect to a classical perfect gas flow past the same configuration.