Exact and approximate gas dynamics using the tangent gas

Abstract

For the determination of aerodynamic characteristics such as lift, drag, and moment coefficients, it is crucial to compute the properties of steady flow past an airfoil. This investigation provides a set of flow dependent grid systems and initial flowfield guesses which substantially improve convergence rates when applied to the Euler equations for flows past an airfoil. The basic equations are examined, taking into account nonlinear equations which are difficult to solve. A good approximation to these equations under certain conditions can be obtained by introducing the so-called 'tangent gas approximation' considered by Woods (1961), in which the isentropic relation between rho and p is replaced by a tangent to a curve. Attention is given to the solution procedure, the analysis (direct) problem, and a comparison of the tangent gas solution with the converged Euler solution.