AN APPROXIMATE MODEL OF UNSTEADY AERODYNAMICS FOR HYPERSONIC PROBLEMS AT HIGH ALTITUDE

The paper introduces a local piston theory with viscous correction for the prediction of hypersonic unsteady aerodynamic loads at high altitude where viscous interaction cannot be ignored. A semi-empirical relation for the determination of effective shape for this method at high Mach number and high altitude is presented based on steady Navier-Stokes equations, and validation of the relation is also completed by numerical method. Furthermore, a series of two-dimensional numerical examples with various Mach numbers, angles of attack and operating altitudes for typical thin airfoil and typical blunt airfoil are provided. The unsteady aerodynamic force coefficients are in well agreement with the unsteady Navier-Stokes predictions with altitude in the range of 40 to 70 km and Mach number in the range of 10 to 20. Compared with classical piston theory and local piston theory based on steady Euler equations, this model performs much better at high Mach number and high altitudes when the viscous interaction effects are strong. This model can be applied in supersonic/hypersonic problems with wide range of Mach number, angle of attack and altitude, and has much higher computational efficiency than unsteady Navier-Stokes equations.