Analysis of Spectral Non-Reflecting Boundary Conditions for Unsteady Simulations of Turbomachinery Flows in Terms of Predictive Quality and Computational Effort

Kurzfassung

The correct numerical representation of unsteady flow phenomena is becoming ever more important, for the design of increasingly performant turbomachines. The mathematical representation of fluid dynamics requires an appropriate definition of boundary conditions to resolve the governing differential equations. In the optimal case, the boundaries of the computational domain are positioned far away from area of interest. Due to the compact architecture of turbomachines, the boundaries need to be positioned close to the blades. This leads to unsteady fluctuation being reflected form the boundaries. These reflections can severely deteriorate the solution. In the flow solver TRACE, spectral boundary conditions have been implemented to prevent reflections. These non-reflecting boundary conditions take advantage of the fact that turbomachinery flows are dominated by periodic phenomena. At the boundaries, the flow field is decomposed into the spectral domain and incoming perturbations are suppressed. However, spectral non-reflecting boundary conditions are non-local in time and space. This results in high computational cost. One possibility to increase efficiency is to include only the relevant portion of the spectrum in the spectral boundary conditions with regards to the simulated configuration. In this work a concept for a reduced set of harmonics for the spectral non-reflecting boundary conditions is developed. Using Q3D simulations of 1.5 compressor stages the analysis of unsteady fluctuations at each harmonic reveals that only harmonics of the blade passing frequencies of rows rotating with different rotational speeds than the boundaries produce relevant reflections. A setup including only these harmonics in the boundary conditions is simulated. The results show that spectral boundary conditions using reduced set of harmonics yield very good results, at significantly lower computational costs. The concept is applied to a steam turbine stage. The results validate that a correct reduction of the set of harmonics does not affect the prediction quality of the solution, but significantly reduces the computational cost of the spectral boundary conditions. Finally, a method is presented that allows for an a posteriori analysis of the quality of the set of harmonics.