The inviscid transonic flow about a cylinder

Abstract

The two-dimensional inviscid transonic flow about a circular cylinder is investigated. To do this, the Euler equations are integrated numerically with a time-dependent technique. The integration is based on an high-resolution finite volume upwind method.Time scales are introduced and the flow at very short, short and large times is studied. Attention is focused on the behaviour of the numerical solution at large times, after the breakdown of symmetry and the onset of an oscillating solution have occurred. This solution is known to be periodic at Mach number between 0.5 and 0.6.At higher speed, however, a richer behaviour is observed. As the Mach number is increased from 0.6 to 0.98 the numerical solution undergoes two transitions. Through a first one the periodical, regular flow enters a chaotic, turbulent regime. Through the second transition the chaotic flow comes back to an almost stationary state. The flow in the chaotic and in the almost stationary regimes is investigated. A numerical conjecture for the behaviour of the solution at large times is advanced.