A Nonreflecting Formulation for Turbomachinery Boundaries and Blade Row Interfaces

Applying a nonreflecting formulation of a boundary condition or blade row interface is sometimes of paramount importance for obtaining an accurate prediction of turbomachinery blade flutter or tonal noise, just to name a few examples. Although the theoretical foundations for these type of boundary conditions have existed for several decades, nonreflecting boundary conditions still remain an area of active research. Today, much focus appears to be put towards obtaining more generic, higher-order and numerically stable formulations. In this work, a quasi-three-dimensional nonreflecting formulation based on the exact, nonreflecting boundary condition for a single frequency and azimuthal wave number developed by Giles is presented. The proposed formulation is applicable without modifications to both steady and unsteady simulations. An implementation strategy which is consistent for both a boundary condition and blade row interface is also presented. This implementation strategy does also partly address the stability problems often encountered when the type of formulation considered in the presented work is used together with a pseudo-time integration approach for converging the flow residual. Results from a set of two-dimensional validation cases are also presented to verify the formulation.