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 Dual Time Stepping Algorithms With the High Order Harmonic Balance Method for Contact Interfaces With Fretting-Wear

2011 ◽  
Author(s):  
Loi¨c Salles ◽  
Laurent Blanc ◽  
Fabrice Thouverez ◽  
Alexander M. Gouskov ◽  
Pierrick Jean
Keyword(s):  
Frequency Domain ◽  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Contact Forces ◽  
Balance Method ◽  
Fretting Wear ◽  
Rate Equations ◽  
Time Stepping ◽  
Dual Time Stepping

Contact interfaces with dry friction are frequently used in turbomachinery. Dry friction damping produced by the sliding surfaces of these interfaces reduces the amplitude of bladed-disk vibration. The relative displacements at these interfaces lead to fretting-wear which reduces the average life expectancy of the structure. Frequency response functions are calculated numerically by using the multi-Harmonic Balance Method (mHBM). The Dynamic Lagrangian Frequency-Time method is used to calculate contact forces in the frequency domain. A new strategy for solving non-linear systems based on dual time stepping is applied. This method is faster than using Newton solvers. It was used successfully for solving Nonlinear CFD equations in the frequency domain. This new approach allows identifying the steady state of worn systems by integrating wear rate equations a on dual time scale. The dual time equations are integrated by an implicit scheme. Of the different orders tested, the first order scheme provided the best results.

scholarly journals Dual Time Stepping Algorithms With the High Order Harmonic Balance Method for Contact Interfaces With Fretting-Wear

2011 ◽  
Vol 134 (3) ◽  
Author(s):  
Loïc Salles ◽  
Laurent Blanc ◽  
Fabrice Thouverez ◽  
Alexander M. Gouskov ◽  
Pierrick Jean
Keyword(s):  
Frequency Domain ◽  
Dry Friction ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Contact Forces ◽  
Balance Method ◽  
Fretting Wear ◽  
Rate Equations ◽  
Time Stepping ◽  
Dual Time Stepping

Contact interfaces with dry friction are frequently used in turbomachinery. Dry friction damping produced by the sliding surfaces of these interfaces reduces the amplitude of bladed-disk vibration. The relative displacements at these interfaces lead to fretting-wear which reduces the average life expectancy of the structure. Frequency response functions are calculated numerically by using the multi-harmonic balance method (mHBM). The dynamic Lagrangian frequency-time method is used to calculate contact forces in the frequency domain. A new strategy for solving nonlinear systems based on dual time stepping is applied. This method is faster than using Newton solvers. It was used successfully for solving Nonlinear CFD equations in the frequency domain. This new approach allows identifying the steady state of worn systems by integrating wear rate equations a on dual time scale. The dual time equations are integrated by an implicit scheme. Of the different orders tested, the first order scheme provided the best results.

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.

scholarly journals Simulation of a Centrifugal Pump by Using the Harmonic Balance Method

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Franco Magagnato ◽  
Jinfeng Zhang
Keyword(s):  
Centrifugal Pump ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Flow Simulation ◽  
Flow Fields ◽  
Balance Method ◽  
Proper Number ◽  
Dual Time Stepping ◽  
Flow Phenomena ◽  
Calculation Results

The harmonic balance method was used for the flow simulation in a centrifugal pump. Independence studies have been done to choose proper number of harmonic modes and inlet eddy viscosity ratio value. The results from harmonic balance method show good agreements with PIV experiments and unsteady calculation results (which is based on the dual time stepping method) for the predicted head and the phase-averaged velocity. A detailed analysis of the flow fields at different flow rates shows that the flow rate has an evident influence on the flow fields. At 0.6Qd, some vortices begin to appear in the impeller, and at 0.4Qdsome vortices have blocked the flow passage. The flow fields at different positions at 0.6Qdand 0.4Qdshow how the complicated flow phenomena are forming, developing, and even disappearing. The harmonic balance method can be used for the flow simulation in pumps, showing the same accuracy as unsteady methods, but is considerably faster.

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