Harmonic Balance Analysis of Forced Response in a Transonic Compressor

A harmonic balance technique for the analysis of nonlinear forced response phenomenon in a two-row transonic compressor is presented. Using the present approach, each blade row is modeled using a computational grid spanning a single blade passage regardless of the the actual blade counts. In the harmonic balance analysis several sub-time level solutions that span a single time-period are stored. These sub-time level solutions are related to each other through the time derivative term, which is approximated by a pseudo-spectral operator in the governing equations, and through boundary conditions. The complex periodicity conditions connect the sub-time levels within a blade passage, and inter-row boundary conditions connect the solutions among blade rows. Because of the fact that the resulting discretized equations are mathematically steady, the flowfield can be solved very efficiently using multi-grid acceleration and local time-stepping techniques. In this paper, we apply the harmonic balance technique to an inlet guide vane (IGV) and rotor interaction problem and illustrate that quite accurate solutions can be obtained very efficiently. I. Nomenclature Ak,Bk kth temporal Fourier coefficient