Harmonic balance analysis of limit cycle oscillations in turbomachinery
A harmonic balance technique for the analysis of limit cycle oscillations (LCO) of turbomachinery blades is presented. This method couples a computational fluid dynamics (CFD) model to a single-degree of freedom structural dynamic model of the turbomachinery blades. The CFD solver uses a nonlinear frequency-domain (harmonic balance) approach that allows one to model the blade row of a turbomachine on a computational grid spanning a single blade passage. Using the harmonic balance approach, several solutions, each one corresponding to a different subtime level of the periodic unsteady flow, are computed simultaneously. These subtime level solutions are coupled to each other in the computational field by a spectral approximation of the time derivative term in the Navier-Stokes equation, and also by application of far-field and periodic boundary conditions. The structural dynamic model is based on a similar approach where a single vibratory mode of interest is modeled using the harmonic balance technique. The two solvers are coupled together through the upwash condition on the surface of the blade and the resulting generalized aerodynamic forces. In the proposed approach, the limit cycle oscillation frequency is treated as another unknown, which is solved iteratively together with the governing equations of fluid flow and structural dynamics, thereby driving the residual of the aeroelastic problem to zero in a single CFD run. The accuracy of the new method is compared to two other techniques and it is shown to offer significant computational savings. Copyright © 2010 by Kivanc Ekici and Kenneth C. Hall.
