Filtering Mixing Planes for Low Reduced Frequency Analysis of Turbomachines

A class of problems in turbomachinery is characterized by unsteady interactions at low reduced frequencies. These interactions are often the result of perturbations with length-scale on the order of the machine circumference and examples include axial compressors operating with inlet distortion, fans with downstream pylons, and turbine rotors downstream of midframe struts. Typically, this unsteadiness is accompanied by higher frequency fluctuations caused by perturbations with a length-scale on the order of a blade pitch. Conventional numerical analysis of this class of problem requires computations with a time step governed by the high-frequency content but a greatly reduced run time could be achieved if the time step was dictated solely by the low reduced frequency, long length-scale, interaction of interest. In this paper, a filtering mixing plane technique is proposed that removes unwanted short length-scale perturbations at the interfaces between blade rows. This approach gives the user control over the amount of mixing that occurs at these interfaces with the limits being fully mixed-out to pitchwise uniformity (conventional mixing plane) or no mixing (conventional sliding plane). By choosing to retain only enough harmonics to resolve the low reduced frequency interaction of interest, an order of magnitude reduction in run time can be achieved.