FAST MOVING SUB-SUBSONIC SHOCKS IN CLOSED-END TUBES

The problem of the detection, formation, and propagation of a fast moving shock in a wholly subsonic environment inside a closed-end tube is solved by a finite-difference integration method belonging to the family of shock-fitting techniques. The shock is fitted by locally combining the method of characteristics with the Rankine-Hugoniot relations, while the regions of smooth flow are solved via a λ scheme. A special attention is devoted to the problems related to shock detection and formation and to the treatment of the reflection of the shock at the boundaries. The pressure oscillation data demonstrate that the shock transition remains sharp and oscillation-free even after many wave cycles. The spectral analysis performed on these data shows that the energy distribution among modes is in good agreement with the analytical solution. These results point out the characteristics of low dissipation and dispersion of the method. For these reasons, the proposed integration technique is particularly well suited for the study of nonlinear axial mode instabilities (usually referred to as “triggered instabilities”) in combustion chambers.