The harmonic balance method with arc-length continuation in blade-tip/casing contact problems

2021 ◽  
Vol 502 ◽  
pp. 116070
Author(s):  
Y. Colaïtis ◽  
A. Batailly
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Contact Problems ◽  
Balance Method ◽  
Arc Length ◽  
Blade Tip

Development of a Harmonic Balance Method-Based Numerical Strategy for Blade-Tip/Casing Interactions: Application to NASA Rotor 37

2021 ◽  
Author(s):  
Yann Colaïtis ◽  
Alain Batailly
Keyword(s):  
Harmonic Balance ◽  
Time Integration ◽  
Harmonic Balance Method ◽  
Gibbs Phenomenon ◽  
Contact Forces ◽  
Balance Method ◽  
Blade Tip ◽  
Model Reduction Technique ◽  
Predictor Corrector ◽  
Numerical Strategy

Abstract In this study, a frequency-domain approach based on the harmonic balance method coupled to a predictor-corrector continuation algorithm is implemented for the qualitative analysis of blade-tip/casing contacts in aircraft engines. Unilateral contact and dry friction are taken into account through a regularized penalty law. To enhance the robustness of the methodology, particular attention is paid to the mitigation of the Gibbs phenomenon. To this end, the employed Alternating Frequency/Time scheme features a Lanczos σ-approximation so that spurious oscillations of the computed nonlinear contact forces become negligible. This approach is applied in combination with a model reduction technique on an industrial compressor blade: NASA rotor 37. In order to assess the influence of both the contact law regularization and the Lanczos σ-approximation, obtained results are thoroughly compared to an existing time integration-based numerical strategy relying on a Lagrange multiplier-based approach for contact treatment and that was previously confronted to experimental results. Presented results underline the very good agreement between the proposed methodology and the reference time integration numerical strategy. The proposed developments thus complement existing results on blade-tip/casing contact adding a much needed qualitative understanding of the interaction and an accurate assessment of the contact stiffening phenomenon.

On the Extension of a Harmonic Balance Method for the Simulation of Compressor Casing Treatments

2016 ◽  
Author(s):  
Christian Voigt ◽  
Graham Ashcroft
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Nonlinear Frequency ◽  
Transonic Compressor ◽  
Frequency Domain Methods ◽  
Blade Tip ◽  
The Time Domain ◽  
Casing Treatments

In recent years both linear and nonlinear frequency domain methods have become increasingly popular in the simulation and investigation of time-periodic flows in turbomachinery. In this work the extension of an alternating frequency/time domain Harmonic Balance method to support arbitrary inter-domain block interfaces, with possibly different frames of reference, is described in detail. The approach outlined is based on the time-domain, area-based interpolation algorithm originally developed for the investigation of casing treatments. In this paper, it is shown that by solving the domain coupling problem in the time-domain it is possible to accurately and efficiently capture the flow physics of such complex, nonlinear problems as blade tip interaction with casing treatments in transonic compressors. To demonstrate and verify the basic algorithm the advection of a simple entropy disturbance in a subsonic duct flow is first computed. Secondly, unsteady flow due to rotor-stator interaction in a transonic compressor stage is simulated and the data compared with reference numerical methods. Finally, to validate the method a single stage transonic axial compressor with casing treatments is simulated and the results are compared with previously published time-domain simulations as well as experimental data based on particle image velocimetry measurements in the blade tip region.

Development of a Harmonic Balance Method-Based Numerical Strategy for Blade-Tip/Casing Interactions: Application to NASA Rotor 37

2021 ◽  
Author(s):  
Yann Colaïtis ◽  
Alain Batailly
Keyword(s):  
Harmonic Balance ◽  
Time Integration ◽  
Harmonic Balance Method ◽  
Gibbs Phenomenon ◽  
Contact Forces ◽  
Balance Method ◽  
Blade Tip ◽  
Model Reduction Technique ◽  
Predictor Corrector ◽  
Numerical Strategy

Abstract In this study, a frequency-domain approach based on the harmonic balance method coupled to a predictor-corrector continuation algorithm is implemented for the qualitative analysis of blade-tip/casing contacts in aircraft engines. Unilateral contact and dry friction are taken into account through a regularized penalty law. To enhance the robustness of the methodology, particular attention is paid to the mitigation of the Gibbs phenomenon. To this end, the employed Alternating Frequency/Time scheme features a Lanczos σ-approximation so that spurious oscillations of the computed nonlinear contact forces become negligible. This approach is applied in combination with a model reduction technique on an industrial compressor blade: NASA rotor 37. In order to assess the influence of both the contact law regularization and the Lanczos σ-approximation, obtained results are thoroughly compared to an existing time integration-based numerical strategy relying on a Lagrange multiplier-based approach for contact treatment and that was previously confronted to experimental results. Presented results underline the very good agreement between the proposed methodology and the reference time integration numerical strategy. The proposed developments thus complement existing results on blade-tip/casing contact adding a much needed qualitative understanding of the interaction and an accurate assessment of the contact stiffening phenomenon.

scholarly journals Convergence Acceleration of the Harmonic Balance Method Using a Time-Level Preconditioner

AIAA Journal ◽  
2020 ◽  
Vol 58 (11) ◽  
pp. 4908-4922
Author(s):  
Daniel Lindblad ◽  
Niklas Andersson
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Convergence Acceleration ◽  
Balance Method ◽  
Time Level

Some Remarks on the Harmonic Balance Method for Mixed-Parity Non-Linear Oscillations

1994 ◽  
Vol 170 (4) ◽  
pp. 571-576 ◽  
Author(s):  
A.Venkateshwar Rao ◽  
B.Nageswara Rao
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Non Linear
Sign in / Sign up

Export Citation Format

Share Document