Biglobal instability of compressible Taylor-Culick flow

The effects of compressibility on the hstability of axi-symmetric Taylor-Culick flow are investigated using isentropic compressible linear Navier-Stokes equations. The resulting eigenvalue problems are then solved using spectral collocation methods. Vortico- Acoustic and hydrodynamic modes are obtained simultaneously. Numeric results are validated by compared with analysable solutions. On the sound side, the eigenvalues are a little smaller than the classic values where no mean flow exists, and the mode shapes display the sound boundary layer effect obviously which plays an important role in estimating the total unsteady energy of solid rocket motors. On the hydrodynamic side, the mode shapes mildly differ from those when incompressible linear Navier-Stokes equations were adopted whereas eigenvalues show some obvious differences.