Periodic Unsteady Flow Analysis Using a Diagonally Implicit Harmonic Balance Method

2011 ◽  
Author(s):  
Dongkyun Im ◽  
Jang-hyuk Kwon ◽  
Soo Hyung Park
Keyword(s):  
Unsteady Flow ◽  
Harmonic Balance ◽  
Flow Analysis ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Unsteady Flow Analysis

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

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

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.

scholarly journals Adjoint-Based Aeroelastic Design Optimization Using a Harmonic Balance Method

2020 ◽  
Author(s):  
Nitish Anand ◽  
Antonio Rubino ◽  
Piero Colonna ◽  
Matteo Pini
Keyword(s):  
Design Optimization ◽  
Harmonic Balance ◽  
Flow Analysis ◽  
Computational Cost ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Balance Method ◽  
Working Fluid ◽  
Compressor Cascade ◽  
Impulse Turbine

Abstract Turbomachinery blades characterized by highly-loaded, slender profiles and operating under unsteady flow may suffer from aeroelastic shortcomings, like forced response and flutter. One of the ways to mitigate these aeroelastic effects is to redesign the blade profiles, so as to increase aero-damping and decrease aero-forcing. Design optimization based on high-fidelity aeroelastic analysis methods is a formidable task due to the inherent computational cost. This work presents an adjoint-based aeroelastic shape-optimization framework based on reduced order methods for flow analysis and forced response computation. The flow analysis is carried out through a multi-frequency fully-turbulent harmonic balance method, while the forced response is computed by means of the energy method. The capability of the design framework is demonstrated by optimizing two candidate cascades, namely, i) a transonic compressor cascade and, ii) a supersonic impulse turbine rotor operating with toluene as working fluid, initially designed by means of the method of waves. The outcomes of the optimization show significant improvements in terms of forced-response in both cases as a consequence of aero-damping enhancement.

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