On the performance of harmonic balance method for unsteady flow with oscillating shocks

2020 ◽  
Vol 32 (12) ◽  
pp. 126103
Author(s):  
Di Zhou ◽  
Zhiliang Lu ◽  
Tongqing Guo ◽  
Guoping Chen
Keyword(s):  
Unsteady Flow ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method

Periodic Unsteady Flow Analysis Using a Diagonally Implicit Harmonic Balance Method

AIAA Journal ◽  
2012 ◽  
Vol 50 (3) ◽  
pp. 741-745 ◽  
Author(s):  
Dong-Kyun Im ◽  
Jang Hyuk Kwon ◽  
Soo Hyung Park
Keyword(s):  
Unsteady Flow ◽  
Harmonic Balance ◽  
Flow Analysis ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Unsteady Flow Analysis

Unsteady Simulation of a 1.5 Stage Turbine Using an Implicitly Coupled Nonlinear Harmonic Balance Method

2012 ◽  
Author(s):  
Chad H. Custer ◽  
Jonathan M. Weiss ◽  
Venkataramanan Subramanian ◽  
William S. Clark ◽  
Kenneth C. Hall
Keyword(s):  
Unsteady Flow ◽  
Time Domain ◽  
Harmonic Balance ◽  
Fourier Coefficients ◽  
Fluid Dynamic ◽  
Time Derivative ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Computational Domain

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.

Application of Harmonic Balance Method to Numerical Model Unsteady Viscous Flow around Oscillating Cascade

2011 ◽  
Vol 50-51 ◽  
pp. 583-588
Author(s):  
Yong Qiang Shi ◽  
Qing Zhen Yang ◽  
Xin Hai Zhou
Keyword(s):  
Unsteady Flow ◽  
Harmonic Balance ◽  
Present Method ◽  
Oscillation Amplitude ◽  
Harmonic Balance Method ◽  
Hysteresis Effect ◽  
Balance Method ◽  
Time Stepping ◽  
Reduced Frequency ◽  
Dual Time Stepping

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.

Numerical simulation of transonic compressor under circumferential inlet distortion and rotor/stator interference using harmonic balance method

2018 ◽  
Vol 32 (12n13) ◽  
pp. 1840021
Author(s):  
Ziwei Wang ◽  
Xiong Jiang ◽  
Ti Chen ◽  
Yan Hao ◽  
Min Qiu
Keyword(s):  
Numerical Simulation ◽  
Unsteady Flow ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Transonic Compressor ◽  
Inlet Distortion ◽  
Speed Up ◽  
Computational Resources ◽  
Optimizing Algorithm

Simulating the unsteady flow of compressor under circumferential inlet distortion and rotor/stator interference would need full-annulus grid with a dual time method. This process is time consuming and needs a large amount of computational resources. Harmonic balance method simulates the unsteady flow in compressor on single passage grid with a series of steady simulations. This will largely increase the computational efficiency in comparison with the dual time method. However, most simulations with harmonic balance method are conducted on the flow under either circumferential inlet distortion or rotor/stator interference. Based on an in-house CFD code, the harmonic balance method is applied in the simulation of flow in the NASA Stage 35 under both circumferential inlet distortion and rotor/stator interference. As the unsteady flow is influenced by two different unsteady disturbances, it leads to the computational instability. The instability can be avoided by coupling the harmonic balance method with an optimizing algorithm. The computational result of harmonic balance method is compared with the result of full-annulus simulation. It denotes that, the harmonic balance method simulates the flow under circumferential inlet distortion and rotor/stator interference as precise as the full-annulus simulation with a speed-up of about 8 times.

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