Consistent non-refleflecting boundary conditions for both steady and unsteady flow simulations in turbomachinery applictations

Abstract

This paper presents the implementation of a non-reflecting boundary condition for steady and unsteady turbomachinery flow computations. Here, the truncation of the computational domain can lead to spurious numerical reflections due to artificial open boundary surfaces. To face this issue, Giles introduces a popular set of non-reflecting boundary conditions for turbomachinery applications. Whereas the steady formulation is exact within the linearisation approach, Giles suggests an approximate boundary condition for unsteady simulations. Resulting from this approximation, the unsteady boundary conditions are not perfectly non-reflecting. Thus, steady and time averaged unsteady flow solutions do not necessarily coincide, even if the flow field contains no unsteadiness. We suggest a single boundary condition formulation suitable for steady and unsteady simulations. This approach applies a modal decomposition and, thus, undesired incoming modes can easily be ruled out. Steady modes can be handled as in the steady case. Apart from the assumptions made by starting from the linearised, two-dimensional Euler equations, this ap- proach does not require any further approximation, and, therefore, the time-averaged unsteady and the steady solutions coincide in the limit of steady flows. We apply and assess the presented boundary condition in steady and unsteady computations of two turbomachinery test cases.