Two-dimensional unsteady compressible flows are studied numerically, especially for the case of interactions between the steady flow and a periodically perturbed compressible flow at transonic speed. A LU-ADI finite difference method is employed, which has the following features; LU(lower & upper) decomposition for the speed acceleration and flux vector splitting & flux limiter for the shock capturing.
The numerical method is tested for the three basic flows with several different boundary conditions: a circular arc bump, two-dimensional shock tube and small perturbed wave propagations with & without the uniform flow. It turns out the method is appropriate to simulate the unsteady flows with low frequency motions including steady flows.
Finally, two different types of flow, composed of small unsteady perturbations and main flow fields, are calculated. The first type calculation is carried out by imposing the small perturbations at the inflow boundary condition in the circular arc bump channel at transonic speed. A periodic motion in the flow field including the shock is clearly observed for the harmonic perturbations at the inflow boundary. However, the flow field is dispersed due to the nonlinear and the geometric effect. The second type calculation is carried out by generating the small perturbation(acoustic wave) owing to the vortex shedding from the half wedge with a back step inside the duct. The periodic vortex sheddings are observed but the acoustic wave propagation is not shown in the calculation.
