Non-Reflecting Boundary Conditions for Time Domain Simulations of Unsteady Turbomachinery Flows

Abstract

This thesis presents the implementation of a spectral, non-reflecting boundary condition (NRBC) for time-marching, unsteady simulations of flows in turbomachinery components. It is well known that reflections from artificial boundaries can impair the prediction of unsteady flow phenomena. In the context of turbomachinery flows, some frequency domain methods for the most part overcome this problem using spectral NRBCs. Since these NRBCs are non-local in space and time, a transfer to time domain solvers is not straightforward. Challenges for a time domain implementation are highlighted and a detailed description of the underlying theory as well as of the specific implementation is given. This work particularly addresses time domain-related aspects of the implementation. The NRBC presented in this work is exact for two-dimensional flows that satisfy the linearized Euler equations. For three-dimensional, nonlinear, viscous flows, the NRBC is approximately non-reflecting. This work includes an extensive validation of the NRBC exhibiting substantially reduced reflections in comparison to widely-used, local approximations of this NRBC. The validation section comprises three basic, two-dimensional test cases: a transonic turbine cascade, the propagation of a single, acoustic mode in a circular duct and a popular flutter test case known as tenth standard configuration. Moreover, this thesis shows the application of the spectral NRBC to the flutter analysis of a transonic steam turbine blade and to blade row interactions in a modern, transonic compressor. These realistic configurations confirm the increased accuracy due to reduction of artificial reflections and additionally demonstrate the necessary stability of the implemented NRBC. Therefore, this thesis presents a reliable, accurate NRBC and, thus, offers a contribution to more accurate time domain simulations for real-world research and design tasks.