Applicability of Harmonic Balance for the Determination of Blade Stability within the Prescribed Motion Approach

Kurzfassung

To predict blade aerodynamic damping during the design phase, unsteady linearized CFD methods are commonly used as they offer a reasonable accuracy at acceptable computational costs. However, for moderate blade oscillation amplitudes, nonlinear aerodynamic effects may appear, yielding eventually an evolution into a stable, limit cycle oscillation (LCO). In the perspective of raising performance and safety, identifying such scenarios might open new development possibilities. Therefore, a valuable alternative to expensive CFD time domain methods consists in applying the nonlinear frequency domain harmonic balance (HB) approach to determine the aerodynamic response. An appropriate number of higher harmonics have to be retained depending on the severity of the aerodynamic nonlinearity under consideration. This number can be identified using either a convergence study with an increasing number of harmonics, or a direct comparison with time-domain simulations. For weak to moderate aerodynamic nonlinearities, this work proposes a guideline to determine the number of harmonics without additional, comparative simulations. First, the HB convergence properties are derived using the wellknown Duffing oscillator. Next, the method is applied to a compressor rotor blade subjected to a prescribed harmonic motion for conditions with and without aerodynamic nonlinearities.