Aerodynamic Approximations for Unsteady Supersonic Flow Through Ducts of Revolution

Supersonic flow of a perfect, inviscid gas through a finite, flexible duct of revolution is considered. Internal equivalents to Lighthill’s piston theory and Ackeret’s strip theory are derived and compared. The comparison shows that for low reduced frequencies of the duct wall the two internal theories coincide. Using “internal strip theory”, the flutter bounds for a circular cylindrical duct are calculated. The results demonstrate that, as the effective duct aspect ratio becomes large, the flutter bounds are asymptotic to those predicted by using classical strip theory for internal flow.