Solution Stabilization and Convergence Acceleration for the Harmonic Balance Equation System

[+] Author and Article Information
Ding Xi Wang

School of Power and Energy Northwestern Polytechnical University 127 Youyixi Road, Xi’an, 710072,China
dingxi wang@nwpu.edu.cn

Xiuquan Huang

School of Power and Energy Northwestern Polytechnical University 127 Youyixi Road, Xi’an, 710072,China
xiuquan huang@nwpu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4035912 History: Received January 16, 2017; Revised January 25, 2017


The paper presents an efficient approach for stabilizing solution and accelerating convergence of a harmonic balance equation system for turbomachinery flutter and blade row interaction. The proposed approach combines the Runge-Kutta method with the Lower Upper Symmetric Gauss Seidel (LU-SGS) method and the block Jacobi method. The LU-SGS method, different from its original application as an implicit time marching scheme, is used as an implicit residual smoother with under relaxation, allowing big CFL numbers (in order of 100s), within the Runge-Kutta explicit time marching loops. The block Jacobi method is introduced to implicitly integrate the time spectral source terms of a harmonic balance equation system, in order to reduce the complexity of the direct implicit time integration by the LU-SGS method. The implicit treatment of the time spectral source term by the block Jacobi method greatly augments the stability region of a harmonic balance equation system with grid reduced frequency well above 10. Validation of the harmonic balance flow solver was carried out using linear cascade test data. Flutter analysis of a transonic rotor and blade row interaction analyses for a transonic compressor stage were presented to demonstrate the stabilization and acceleration effect by the combination of the LU-SGS and the block Jacobi methods. The influence of the number of Jacobi iterations on solution convergence is also investigated showing that the two Jacobi iterations are sufficient for stability purpose, which is much more efficient than existing methods of its kind in the open literature.

Copyright (c) 2017 by ASME
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