On the Stability of a Separation Bubble in a Supersonic Compression Ramp Flow

Linear stability of supersonic flows over short compression corners has been investigated using direct simulation Monte Carlo (DSMC) and global linear modal stability theory. Supersonic free stream at M=3, Re=1.1E4, and large ramp angles between 30 and 42° have been considered. Two-dimensional steady laminar base flows were generated with DSMC and exhibited large separation bubbles extending to the plate leading edge at all ramp angles. The recirculation strength is found to be higher than 10% for all the cases, and scaled angles calculated using triple deck theory (Egorov et al. DOI:10.2514/6.2011-730) are higher than 6.0. Both indicators could suggest self-excitation of steady three-dimensional global instabilities (Theofilis et al. DOI: 10.1098/rsta.2000.0706). However, solution of the BiGlobal eigenvalue problem that the known stationary three-dimensional global mode of separation is stable, but a previously unknown leading edge (LE) mode is unstable over a range of spanwise wavenumbers at the highest ramp angle. Close to the leading edge, the amplitude function of the LE mode peaks along the leading edge shock and the dividing streamline of laminar separation, while closer to the compression corner the two branches merge in a single periodic structure. The spatial structure and amplification rate of the LE mode are confirmed independently by three-dimensional (spanwise periodic) DSMC simulations. To the best of the authors' knowledge, the leading edge global mode of compression corners is identified for the first time in the present work.