Nonlinear Frequency-Domain Analysis of Unsteady Flows in Turbomachinery with Multiple Excitation Frequencies

A harmonic balance technique for the analysis of nonlinear unsteady flows in turbomachiney arising from several excitation sources, possibly with frequencies with irrational ratios, is presented in this paper. This method uses a mixed time-domain/frequencydomain approach that allows one to model the blade row on a computational grid spanning just a single blade passage, no matter the interblade phase angles of the original disturbances. Using this approach, we compute several solutions, each one corresponding to one of several times over one period for periodic flows, or over a representative time interval for aperiodic flows. These time levels are coupled to each other through a spectral time derivative operator in the interior of the computational domain, and through the far-field and periodic boundary conditions around the boundary of the domain. In this paper, we apply the method to the two-dimensional Euler equations (although the method can be applied to three-dimensional and viscous flows), and examine the nonlinear interaction of wake passing with blade vibration.