Modern desire to have turbomachines perform over a large range of conditions raises concerns as to their susceptibility to potentially harmful vibrations induced by the unsteady flows encountered at conditions far from the design point. Machines demonstrating this type of behavior may be damaged by fatigue or be subject to catastrophic failure. Due to these concerns and the relative expense and difficulty in obtaining accurate experimental data for fluid-structure interaction in turbomachines, computations have been and will continue to be an indispensable part of the design and research efforts focused on avoiding such phenomena. While the traditional computational analysis considering a single isolated blade row can aid in understanding the mechanisms that initiate vibrations in turbomachines, study of multiple blade rows may be necessary to completely model the underlying causes of these vibrations.;In the present work, the mixing-plane and sliding-mesh methods are used to simulate both steady and unsteady multi-stage transonic compressor flows. The simulations conducted here include the solution of the compressible unsteady Reynolds Averaged Navier Stokes (RANS) Equations. The Spalart Almaras model is used to simulate the effects of turbulence in the flow field. A modal superposition method is used to model fluid-structure interaction resulting from blade vibration.;Steady flow through the NASA Stage 35 transonic compressor is computed using the mixing-plane method, and reasonable agreement is obtained with experimental data and previous computations. Steady and unsteady computations are also performed for a modern 1.5-stage transonic compressor design provided by Siemens. For this case, experiments indicate the appearance of low frequency, large amplitude flow oscillations which could potentially lead to unwanted structural vibration. In performing unsteady computations for the Siemens compressor, effects of the periodic domain size for the sliding-mesh computations are considered by doubling and tripling the initial domain size. Computations performed on the triple-sized domain show a qualitatively different character than those performed with the two smaller domains. While this result cannot guarantee that the large domain has fully resolved the unsteady flow, it provides a strong argument that the two smaller domains have not, and highlights the need to clearly identify the circumferential wavelengths expected in an unsteady multi-stage flow. Fluid-structure interaction computations for this case show very small amplitude vibrations.
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