On the Development of an Efficient Sliding Mesh Interface for the Harmonic Balance Method, Part I: Implementation and Verification

In recent years the Harmonic Balance method has become a popular tool in the field of turbomachinery design. While it can efficiently capture nonlinear effects in time-periodic flows, its application to complex configurations such as cavities or casing treatments requires sophisticated domain coupling methods. To address this topic, in a series of two papers, we present and validate an algorithm for the coupling of non-conforming mesh topologies across domain boundaries. In this first paper the basic algorithm and its verification are presented in detail. In the second paper the method is applied to analyze the impact of a casing treatment on blade flutter in a compressor stage. It is shown in this paper that memory layout can have a strong impact on memory usage and CPU time. To handle indexed modes, i.e., modes with the same frequency but different inter-blade phase angles, we introduce virtual passage segments on which the required spatial Discrete Fourier Transform (DFT) is performed. Using Almost Periodic Fourier Transforms (APFT) to transfer the temporal solution harmonics we show that the computational overhead can be significantly reduced when compared to a standard temporal DFT ansatz. In this context a simple, but robust algorithm is proposed to determine the temporal sampling interval and distribution of the sampling points such that a bound on the condition number of the resulting APFT matrix is satisfied. The method is verified and analyzed using three academic test cases: the propagation of an entropy wave across moving interfaces in an empty duct with a rotating mean flow; the aerodynamic excitation of a simple rotor blade exposed to a time-periodic gust disturbance; and the flow in a duct with an attached cavity.