Comparison of Linear and Nonlinear Frequency Domain Methods for Flutter Analysis

2018 ◽  
Author(s):  
Hans-Peter Kersken ◽  
Graham Ashcroft ◽  
Christian Frey ◽  
Nina Wolfrum ◽  
Oliver Pütz
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance Method ◽  
Frequency Domain Method ◽  
Nonlinear Frequency ◽  
Solution Approach ◽  
Time Solution ◽  
Domain Method ◽  
Frequency Domain Methods ◽  
Flutter Analysis ◽  
Linear And Nonlinear

Both linear and nonlinear frequency domain methods have been applied successfully to the investigation of time-periodic phenomena in turbomachinery. Linear methods allow to perform flutter analysis of turbomachinery blade rows very efficiently. Nonlinear frequency domain method can be applied to flutter analysis as well. If a pseudo-time solution algorithm is employed as a solver the nonlinear frequency domain method takes advantage of the stabilizing effect of the nonlinear coupling of the harmonics. Additionally, it allows studying the influence of nonlinear effects on the flutter stability. A linear GMRes based method and a harmonic balance method using a pseudo-time solution approach are compared with respect to computational efficiency when applied to the flutter analysis of blades of a stationary gas turbine and a low pressure turbine of a jet engine. It is shown that both methods have their merits and limitation depending on the type of problem at hand.

On the Application of Frequency-Domain Methods to Multistage Turbomachinery

2015 ◽  
Author(s):  
Laura Junge ◽  
Graham Ashcroft ◽  
Peter Jeschke ◽  
Christian Frey
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Harmonic Balance ◽  
Axial Compressor ◽  
Harmonic Balance Method ◽  
Nonlinear Frequency ◽  
Solution Quality ◽  
Multi Stage ◽  
Frequency Domain Methods ◽  
Blade Row

Due to the relative motion between adjacent blade rows the aerodynamic flow fields within turbomachinery are normally 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 capturing or modelling flow nonlinearity. Central to the efficiency and accuracy of such frequency-domain methods is the selection of the frequencies and the circumferential modes to be resolved in simulations. Whilst trivial in the context of the simulation of a single compressor- or turbine-stage, the choice of solution modes becomes substantially more involved in multi-stage configurations. In this work the importance of mode scattering, in the context of the unsteady aerodynamic field, is investigated and quantified. It is shown that scattered modes can substantially impact the unsteady flow field and are essential for the accurate modelling of wake propagation within multistage configurations. Furthermore, an iterative approach is outlined, based on the spectral analysis of the circumferential modes at the interfaces between blade rows, to identify the dominant solution modes that should be resolved in the adjacent blade row. To demonstrate the importance of mode scattering and validate the approach for their identification the unsteady blade row interaction within a 4.5 stage axial compressor is computed using both the harmonic balance method and, based on a full annulus midspan simulation, a time-domain method. Through the inclusion of scattered modes it is shown that the solution quality of the harmonic balance results is comparable to that of the nonlinear time-domain simulation.

Non-Linear Time and Frequency Domain Methods for Multi-Row Aeromechanical Analysis

2012 ◽  
Author(s):  
M. T. Rahmati ◽  
L. He ◽  
D. X. Wang ◽  
Y. S. Li ◽  
R. G. Wells ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Computational Models ◽  
Linear Time ◽  
Navier Stokes ◽  
Frequency Domain Method ◽  
Domain Method ◽  
Frequency Domain Methods ◽  
Blade Row ◽  
Nonlinear Time Domain

An unsteady Navier-Stokes solution system for aeromechanical analysis of multiple blade row configurations is presented. A distinctive feature of the solver is that unified numerical methods and boundary condition treatments are consistently used for both a nonlinear time-domain solution mode and a frequency-domain one. This not only enables a wider range of physical aeromechanical problems to be tackled, but also provides a consistent basis for validating different computational models, identifying and understanding their relative merits and adequate working ranges. An emphasis of the present work is on a highly efficient frequency-domain method for multi-row aeromechanic analysis. With a new interface treatment, propagations and reflections of pressure waves between adjacent blade rows are modeled within a domain consisting of only a single passage in each blade row. The computational model and methods are firstly described. Then, extensive validations of the frequency-domain method against both experimental data and the nonlinear time-domain solutions are described. Finally the computational analysis and demonstration of the intra-row reflection effects on the rotor aerodynamic damping are presented.

On the Development of Harmonic Balance Methods for Multiple Fundamental Frequencies

2018 ◽  
Author(s):  
Laura Junge ◽  
Graham Ashcroft ◽  
Hans-Peter Kersken ◽  
Christian Frey
Keyword(s):  
Frequency Domain ◽  
Fundamental Frequency ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Cross Coupling ◽  
Nonlinear Frequency ◽  
Fundamental Frequencies ◽  
Frequency Domain Methods ◽  
Sampling Points ◽  
The Common

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.

scholarly journals Comparison of Frequency Domain and Time-Domain Methods for Aeromechanical Analysis

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
M. T. Rahmati
Keyword(s):  
Unsteady Flow ◽  
Frequency Domain ◽  
Time Domain ◽  
Solution Method ◽  
Frequency Domain Method ◽  
Physical Conditioning ◽  
Domain Method ◽  
Frequency Domain Methods ◽  
Phase Solution ◽  
Nonlinear Time Domain

Unsteady flow around an oscillating plate cascade and that through a single compressor rotor subject to vibration have been computationally studied, aimed at examining the predictive ability of two low fidelity frequency methods compared with a high fidelity time-domain solution method for aeroelasticity. The computational solutions demonstrate the capabilities of the frequency domain methods compared with the nonlinear time-domain solution method in capturing small perturbations in the unsteady flow. They also show the great advantage of significant CPU time saving by the frequency methods over the nonlinear time method. Comparisons of two different frequency methods, nonlinear harmonic and phase solution method, show that these methods can produce different results due to the differences in numeric and physical conditioning. The results obtained using phase solutions method are in better agreement with the nonlinear time-domain solution. This is because the same numeric and physical conditioning are used in both the nonlinear time-domain method and phase solution frequency domain method.

Nonlinear Time and Frequency Domain Methods for Multirow Aeromechanical Analysis

2013 ◽  
Vol 136 (4) ◽  
Author(s):  
M. T. Rahmati ◽  
L. He ◽  
D. X. Wang ◽  
Y. S. Li ◽  
R. G. Wells ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Computational Models ◽  
Navier Stokes ◽  
Frequency Domain Method ◽  
Domain Method ◽  
Frequency Domain Methods ◽  
Blade Row ◽  
Consistent Basis ◽  
Nonlinear Time Domain

An unsteady Navier–Stokes solution system for aeromechanical analysis of multiple blade row configurations is presented. A distinctive feature of the solver is that unified numerical methods and boundary condition treatments are consistently used for both a nonlinear time-domain solution mode and a frequency-domain one. This not only enables a wider range of physical aeromechanical problems to be tackled, but also provides a consistent basis for validating different computational models, identifying and understanding their relative merits and adequate working ranges. An emphasis of the present work is on a highly efficient frequency-domain method for multirow aeromechanical analysis. With a new interface treatment, propagations and reflections of pressure waves between adjacent blade rows are modeled within a domain consisting of only a single passage in each blade row. The computational model and methods are firstly described. Then, extensive validations of the frequency-domain method against both experimental data and the nonlinear time-domain solutions are described. Finally, the computational analysis and demonstration of the intrarow reflection effects on the rotor aerodynamic damping are presented.

scholarly journals Modeling of thermoacoustic systems using the nonlinear frequency domain method

2015 ◽  
Vol 138 (3) ◽  
pp. 1241-1252 ◽  
Author(s):  
J. A. de Jong ◽  
Y. H. Wijnant ◽  
D. Wilcox ◽  
A. de Boer
Keyword(s):  
Frequency Domain ◽  
Frequency Domain Method ◽  
Nonlinear Frequency ◽  
Domain Method
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