A harmonic balance technique for modeling unsteady nonlinear ows in turbomachinery is presented. The analysis exploits the fact that many unsteady ows of interest in turbomachinery are periodic in time. Thus, the unsteady ow conservation variables may be represented by a Fourier series in time with spatially varying coef cients. This assumption leads to a harmonic balance form of the Euler or Navier-Stokes equations, which, in turn, can be solved ef ciently as a steady problem using conventional computational uid dynamic (CFD) methods, including pseudotime time marching with local time stepping and multigrid acceleration. Thus, the method is computationally ef cient, at least one to two orders of magnitude faster than conventional nonlinear time-domain CFD simulations. Computational results for unsteady, transonic, viscous ow in the front stage rotor of a high-pressure compressor demonstrate that even strongly nonlinear ows can be modeled to engineering accuracy with a small number of terms retained in the Fourier series representation of the ow. Furthermore, in some cases, uid nonlinearities are found to be important for surprisingly small blade vibrations.

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In this paper, we investigate non-synchronous vibrations (NSV) in turbomachinery, an aeromechanic phenomenon in which rotor blades are driven by a fluid dynamic instability. Unlike flutter, a self-excited vibration in which vibrating rotor blades and the resulting unsteady aerodynamic forces are mutually reinforcing, NSV is primarily a fluid dynamic instability that can cause large amplitude vibrations if the natural frequency of the instability is near the natural frequency of the rotor blade. In this paper, we present both experimental and computational data. Experimental data was obtained from a full size compressor rig where the instrumentation consisted of blade-mounted strain gages and case-mounted unsteady pressure transducers. The computational simulation used a three-dimensional Reynolds averaged Navier-Stokes (RANS) time accurate flow solver. The computational results suggest that the primary flow features of NSV are a coupled suction side vortex shedding and a tip flow instability. The simulation predicts a fluid dynamic instability frequency that is in reasonable agreement with the experimentally measured value.

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