Accuracy and Efficiency Assessment of Harmonic Balance Method for Unsteady Flow in Multi-Stage Turbomachinery

2020 ◽  
Vol 29 (6) ◽  
pp. 1569-1580
Author(s):  
Zhen Zhang ◽  
Can Ma ◽  
Xinrong Su ◽  
Xin Yuan
2020 ◽  
Vol 12 (3) ◽  
pp. 168781401989721 ◽  
Author(s):  
Haiou Sun ◽  
Meng Wang ◽  
Zhongyi Wang ◽  
Song Wang ◽  
Franco Magagnato

To improve the understanding of unsteady flow in modern advanced axial compressor, unsteady simulations on full-annulus multi-stage axial compressor are carried out with the harmonic balance method. Since the internal flow in turbomachinery is naturally periodic, the harmonic balance method can be used to reduce the computational cost. In order to verify the accuracy of the harmonic balance method, the numerical results are first compared with the experimental results. The results show that the internal flow field and the operating characteristics of the multi-stage axial compressor obtained by the harmonic balance method coincide with the experimental results with the relative error in the range of 3%. Through the analysis of the internal flow field of the axial compressor, it can be found that the airflow in the clearance of adjacent blade rows gradually changes from axisymmetric to non-axisymmetric and then returns to almost completely axisymmetric distribution before the downstream blade inlet, with only a slight non-axisymmetric distribution, which can be ignored. Moreover, the slight non-axisymmetric distribution will continue to accumulate with the development of the flow and, finally, form a distinct circumferential non-uniform flow field in latter stages, which may be the reason why the traditional single-passage numerical method will cause certain errors in multi-stage axial compressor simulations.


2020 ◽  
Vol 32 (12) ◽  
pp. 126103
Author(s):  
Di Zhou ◽  
Zhiliang Lu ◽  
Tongqing Guo ◽  
Guoping Chen

AIAA Journal ◽  
2012 ◽  
Vol 50 (3) ◽  
pp. 741-745 ◽  
Author(s):  
Dong-Kyun Im ◽  
Jang Hyuk Kwon ◽  
Soo Hyung Park

Author(s):  
Chad H. Custer ◽  
Jonathan M. Weiss ◽  
Venkataramanan Subramanian ◽  
William S. Clark ◽  
Kenneth C. Hall

The harmonic balance method implemented within STAR-CCM+ is a mixed frequency/time domain computational fluid dynamic technique, which enables the efficient calculation of time-periodic flows. The unsteady solution is stored at a small number of fixed time levels over one temporal period of the unsteady flow in a single blade passage in each blade row; thus the solution is periodic by construction. The individual time levels are coupled to one another through a spectral operator representing the time derivative term in the Navier-Stokes equation, and at the boundaries of the computational domain through the application of periodic and nonreflecting boundary conditions. The blade rows are connected to one another via a small number of fluid dynamic spinning modes characterized by nodal diameter and frequency. This periodic solution is driven to the correct solution using conventional (steady) CFD acceleration techniques, and thus is computationally efficient. Upon convergence, the time level solutions are Fourier transformed to obtain spatially varying Fourier coefficients of the flow variables. We find that a small number of time levels (or, equivalently, Fourier coefficients) are adequate to model even strongly nonlinear flows. Consequently, the method provides an unsteady solution at a computational cost significantly lower than traditional unsteady time marching methods. The implementation of this nonlinear harmonic balance method within STAR-CCM+ allows for the simulation of multiple blade rows. This capability is demonstrated and validated using a 1.5 stage cold flow axial turbine developed by the University of Aachen. Results produced using the harmonic balance method are compared to conventional time domain simulations using STAR-CCM+, and are also compared to published experimental data. It is shown that the harmonic balance method is able to accurately model the unsteady flow structures at a computational cost significantly lower than unsteady time domain simulation.


2011 ◽  
Vol 50-51 ◽  
pp. 583-588
Author(s):  
Yong Qiang Shi ◽  
Qing Zhen Yang ◽  
Xin Hai Zhou

A harmonic balance approach has been developed to compute nonlinear viscous unsteady flows around oscillating blades. The computed results using two orders harmonic balance method are compared with those by conventional dual-time stepping method. Results obtained with the present method agree well with those from dual-time stepping method, which demonstrate the ability of the present analysis method to model accurately the unsteady flow. Furthermore,the present method is highly efficient. It is about 36 times fast than conventional dual-time stepping method in the present computation. Then the effects of oscillation amplitude and reduced frequency on unsteadiness of flows are studied. The analysis exploits the fact that, (1) the hysteresis effect of unsteady flow is hardly affected by oscillation amplitude, but the first harmonic unsteady pressure across the blade is proportional to oscillation amplitude; (2) the higher the reduced frequency, the wider the range of unsteady aerodynamic forces, the more intense the hysteresis effect.


Sign in / Sign up

Export Citation Format

Share Document