Interaction of a Weak Shock with Freestream Disturbances

摘要

A new transonic smatl-disturbancc model to analyze the interactions of freestream disturbances with a weak shock has been developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustic equation that describes the propagation of sound beams with a narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing effects, and induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite difference algorithm to solve the mixed-type elliptic/hyperbolic flows around the shock wave has also been developed. Numerical calculations of shock wave interactions with various deterministic vorticity and temperature disturbances result in complicated shock wave structures and describe peaked as well as rounded pressure signatures across the shock front, as were recorded in experiments of sonic booms running through atmospheric turbulence.