Transonic flows of single-phase supercritical fluids over thin airfoils

摘要

A small-disturbance model for a steady, two-dimensional, inviscid and transonic flow of a single-phase real gas around a thin airfoil is presented. The approach explores the nonlinear interactions among near-sonic speed of the flow, small thickness ratio of the airfoil and upstream properties of the fluid. The gas thermodynamic properties are related by a general equation of state. Information about thermodynamic modelling of the gas is lumped into one similarity parameter, K-G, related to the fundamental derivative of gas dynamics. The flow field is described by a modified transonic small-disturbance problem. The theory applies to any working fluid of interest. Model problems are derived for steam flows described by the perfect, van der Waals, virial and Redlich-Kwong gas equations of state. Predictions are compared according to the various gas models under various free-stream operating conditions from low subcritical to high supercritical thermodynamic states to gain insights into the sensitivity of the small-disturbance problem solution to thermodynamic modelling of the gas. Results show that transonic flows are independent of gas modelling at low subcritical thermodynamic conditions. However, at near-critical and supercritical thermodynamic conditions, transonic flow behaviour is significantly sensitive to gas modelling and variations of K-G. The upstream flow critical Mach number increases as the flow approaches thermodynamic critical state and a wider range of upstream Mach numbers can be found where pressure drag is zero. However, at supercritical conditions, K-G increases, resulting in lower critical Mach numbers and higher pressure drags.