A small-disturbance model for transonic flow of a real gas around a thin airfoil

A small-disturbance model for a steady transonic flow of a real gas around a thin airfoil is presented. The model explores the nonlinear interactions among the near-sonic speed of the flow, the small thickness ratio and angle of attack of the airfoil, and the upstream properties of the gas. The flow thermodynamic properties are described by a general equation of state. The asymptotic analysis provides the similarity parameters that govern the flow problem. Also, the flow field can be described by a transonic small-disturbance (TSD) equation. The approach is applied to the perfect gas, van der Waals and Redlich-Kwong gas models and the relationships between these cases are explored. An iterative numerical scheme that is based on the Murman & Cole's (1971) method for the solution of the TSD equation is developed. The computed results describe the effect of the upstream flow pressure and temperature on the fields of flow properties and the on aerodynamic performance of airfoils.