This paper presents an efficient approach for stabilizing solution and accelerating convergence of a harmonic balance equation system for an efficient analysis of turbomachinery unsteady flows due to 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 Courant–Friedrichs–Lewy (CFL) numbers (in the order of hundreds), leading to significant convergence speedup. The block Jacobi method is introduced to implicitly integrate the time spectral source term 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 thus greatly augments the stability region of a harmonic balance equation system in the case of grid-reduced frequency well above ten. 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 stabilization is also investigated, showing that two Jacobi iterations are sufficient for stability purpose, which is much more efficient than existing methods of its kind in the open literature.
Skip Nav Destination
Article navigation
September 2017
Research-Article
Solution Stabilization and Convergence Acceleration for the Harmonic Balance Equation System
Ding Xi Wang,
Ding Xi Wang
School of Power and Energy,
Northwestern Polytechnical University,
127 Youyixi Road,
Xi'an 710072, China
e-mail: dingxi_wang@nwpu.edu.cn
Northwestern Polytechnical University,
127 Youyixi Road,
Xi'an 710072, China
e-mail: dingxi_wang@nwpu.edu.cn
Search for other works by this author on:
Xiuquan Huang
Xiuquan Huang
School of Power and Energy,
Northwestern Polytechnical University,
127 Youyixi Road,
Xi'an 710072, China
e-mail: xiuquan_huang@nwpu.edu.cn
Northwestern Polytechnical University,
127 Youyixi Road,
Xi'an 710072, China
e-mail: xiuquan_huang@nwpu.edu.cn
Search for other works by this author on:
Ding Xi Wang
School of Power and Energy,
Northwestern Polytechnical University,
127 Youyixi Road,
Xi'an 710072, China
e-mail: dingxi_wang@nwpu.edu.cn
Northwestern Polytechnical University,
127 Youyixi Road,
Xi'an 710072, China
e-mail: dingxi_wang@nwpu.edu.cn
Xiuquan Huang
School of Power and Energy,
Northwestern Polytechnical University,
127 Youyixi Road,
Xi'an 710072, China
e-mail: xiuquan_huang@nwpu.edu.cn
Northwestern Polytechnical University,
127 Youyixi Road,
Xi'an 710072, China
e-mail: xiuquan_huang@nwpu.edu.cn
1Corresponding author.
Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received January 16, 2017; final manuscript received January 25, 2017; published online April 11, 2017. Editor: David Wisler.
J. Eng. Gas Turbines Power. Sep 2017, 139(9): 092503 (9 pages)
Published Online: April 11, 2017
Article history
Received:
January 16, 2017
Revised:
January 25, 2017
Citation
Wang, D. X., and Huang, X. (April 11, 2017). "Solution Stabilization and Convergence Acceleration for the Harmonic Balance Equation System." ASME. J. Eng. Gas Turbines Power. September 2017; 139(9): 092503. https://doi.org/10.1115/1.4035912
Download citation file:
Get Email Alerts
Shape Optimization of an Industrial Aeroengine Combustor to reduce Thermoacoustic Instability
J. Eng. Gas Turbines Power
Dynamic Response of A Pivot-Mounted Squeeze Film Damper: Measurements and Predictions
J. Eng. Gas Turbines Power
Review of The Impact Of Hydrogen-Containing Fuels On Gas Turbine Hot-Section Materials
J. Eng. Gas Turbines Power
Effects of Lattice Orientation Angle On Tpms-Based Transpiration Cooling
J. Eng. Gas Turbines Power
Related Articles
Accounting for Unsteady Interaction in Transonic Stages
J. Eng. Gas Turbines Power (May,2015)
A Nonlinear Numerical Simulator for Three-Dimensional Flows Through Vibrating Blade Rows
J. Turbomach (April,1999)
A New Approach to the Experimental Study of Turbomachinery Flow Phenomena
J. Eng. Power (January,1977)
A Navier–Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping
J. Turbomach (January,1997)
Related Chapters
Cavitating Structures at Inception in Turbulent Shear Flow
Proceedings of the 10th International Symposium on Cavitation (CAV2018)
Dynamic Behavior of Pumping Systems
Pipeline Pumping and Compression Systems: A Practical Approach
Antilock-Braking System Using Fuzzy Logic
International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3