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On the Development of Harmonic Balance Methods for Multiple Fundamental Frequencies

Junge, Laura and Kersken, Hans-Peter and Frey, Christian and Ashcroft, Graham (2018) On the Development of Harmonic Balance Methods for Multiple Fundamental Frequencies. In: Proceedings of the ASME Turbo Expo. ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, 11.-15. Jun. 2018, Oslo, Norwegen. doi: 10.1115/GT2018-75495. ISBN 978 0 7918 5101 2.

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Due to the relative motion between adjacent blade rows the aerodynamic flow fields within turbomachinery are usually dominated by deterministic, periodic phenomena. In the numerical simulation of such unsteady flows, (nonlinear) frequency-domain methods are therefore attractive as they are capable of fully exploiting the given spatial and temporal periodicity, as well as modelling flow nonlinearities. A nontrivial issue in the application of frequency-domain methods to turbomachinery flows is to simultaneously capture disturbances with multiple fundamental frequencies in one relative system. In case of harmonically related frequencies, the interval spanned by the sampling points typically resolves the common fundamental frequency. To avoid signal aliasing the highest harmonic of the common frequency should be sampled with an appropriate number of sampling points. However, when the common fundamental frequency is very low in relation to the frequencies of primary interest, equidistant time sampling leads to a high number of sampling points, hence frequency-domain methods can become computationally inefficient. Furthermore, when a problem can no longer be described by harmonic perturbations that are integer multiples of one fundamental frequency, as it may occur in two-shaft configurations, the standard discrete Fourier transform is no longer suitable and the basic harmonic balance method requires extension. In this article two nonlinear frequency-domain approaches for dealing with the accounted issues are demonstrated and compared. The first approach is a generalized harmonic balance method based on almost periodic Fourier transforms with non-equidistant time sampling. Then the so-called harmonic set approach, developed by the authors, is evaluated. Based on the neglection of the nonlinear, quadratic cross-coupling terms between higher harmonics of different fundamental frequencies, the harmonic set approach allows the superposition of periodic disturbances with different fundamental frequencies as well as the separated, equidistant sampling of the highest harmonic of each base frequency. The aim of this paper is to compare the computational efficiency and accuracy of the two methods and assess the impact of neglecting the quadratic cross-coupling terms.

Item URL in elib:https://elib.dlr.de/140602/
Document Type:Conference or Workshop Item (Speech)
Title:On the Development of Harmonic Balance Methods for Multiple Fundamental Frequencies
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Kersken, Hans-PeterUNSPECIFIEDhttps://orcid.org/0000-0003-4203-6450134615951
Frey, ChristianUNSPECIFIEDhttps://orcid.org/0000-0003-0496-9225UNSPECIFIED
Date:June 2018
Journal or Publication Title:Proceedings of the ASME Turbo Expo
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:No
ISBN:978 0 7918 5101 2
Keywords:Nonlinear Frequency-Domain Methods, Harmonic Balance, Unsteady CFD, Turbomachinery
Event Title:ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition
Event Location:Oslo, Norwegen
Event Type:international Conference
Event Dates:11.-15. Jun. 2018
Organizer:The American Society of Mechanical Engineers
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:propulsion systems
DLR - Research area:Aeronautics
DLR - Program:L ER - Engine Research
DLR - Research theme (Project):L - Virtual Engine and Validation methods (old)
Location: Köln-Porz
Institutes and Institutions:Institute of Propulsion Technology > Numerical Methodes
Deposited By: Junge, Laura
Deposited On:25 Jan 2021 09:56
Last Modified:09 May 2023 09:39

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