Time-Domain Harmonic Balance Method for Turbomachinery Aeroelasticity

Sicot, Frédéric; Gomar, Adrien; Dufour, Guillaume; Dugeai, Alain

doi:10.2514/1.j051848

Cited by 22 publications

(10 citation statements)

References 42 publications

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“…If the number of harmonics used in eq. (18) is N H , the structural degree-of-freedom (DOF) is N s , then the fluid system needs to be evaluated (N s [(2N H + 1) × 2] + 1) times to form J. As long as the initial guess is good enough, the Newton-Raphson method usually achieves converged solutions rapidly and efficiently.…”

Section: A Prediction Of Limit-cycle Oscillationsmentioning

confidence: 99%

“…(23) and eq. (18). If the LCO frequency, ω, is given beforehand, then the coupling itself becomes a fixed point iteration process which is extensively used for static aero-elastic problems in its time domain counterpart.…”

Section: A Prediction Of Limit-cycle Oscillationsmentioning

confidence: 99%

“…These methods have been successful in predicting unsteady flows efficiently in diverse applications: forced motions, 14,15 helicopter rotors, 16 turbomachinery. 12,17,18 Thomas et al extended the HB formulation to predict Limit Cycle Oscillations for fixed wing aircraft. 3 Ekici and Hall further reduced the computational cost of predicting LCOs with HB methods, by proposing a one-shot method to analyze 1-DOF LCO in turbomachinery flows.…”

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confidence: 98%

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Prediction of Transonic LCO using an Harmonic Balance Method

Yao

Marques

2014

44th AIAA Fluid Dynamics Conference

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This work proposes a novel approach to compute transonic Limit Cycle Oscillations using high fidelity analysis. CFD based Harmonic Balance methods have proven to be efficient tools to predict periodic phenomena. This paper's contribution is to present a new methodology to determine the unknown frequency of oscillations, enabling HB methods to accurately capture Limit Cycle Oscillations (LCOs); this is achieved by defining a frequency updating procedure based on a coupled CFD/CSD Harmonic Balance formulation to find the LCO condition. A pitch/plunge aerofoil and delta wing aerodynamic and respective linear structural models are used to validate the new method against conventional timedomain simulations. Results show consistent agreement between the proposed and timemarching methods for both LCO amplitude and frequency, while producing at least one order of magnitude reduction in computational time. * Research Fellow, MAIAA † Lecturer, MAIAA 1 of 20 Downloaded by UNIVERSITY OF TENNESSEE on August 8, 2015 | http://arc.aiaa.org | Nomenclature A = Harmonic Balance frequency domain matrix b, c = aerofoil semi-chord and chord, respectively D = Harmonic Balance operator matrix E = energy E = Tranformation matrix between frequency and time domains f = fluid force acting on structure F, G, H = convective fluxes for fluid equations h = plunge coordinate I = HB residual K = structure stiffness matrix L = frequency updating figure of merit M = structure mass matrix p = pressure R = vector of fluid and/or structural equation residual t = time step U ∞ = free-stream velocity u, v, w = fluid cartesian velocity components V, V s = reduced velocity and velocity index W = vector of fluid unknowns x, y = vector of structural unknowns α = angle of attack ω, κ = frequency and reduced frequency, κ = 2ω U∞c ρ = density τ = pseudo-time step

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Section: A Prediction Of Limit-cycle Oscillationsmentioning

confidence: 99%

Section: A Prediction Of Limit-cycle Oscillationsmentioning

confidence: 99%

mentioning

confidence: 98%

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Prediction of Transonic LCO using an Harmonic Balance Method

Yao

Marques

2014

44th AIAA Fluid Dynamics Conference

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“…Then, Huang and Ekici 13,14 applied the harmonic balance method on investigations of the unsteady flow in turbomachinery caused by self-excited vibrations and shape optimization of compressor cascades. Sicot and colleagues [15][16][17] modeled the rotor/stator interactions in turbomachinery using the harmonic balance method. More recently, a similar method is adopted by many other researchers to investigate various problems.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of the non-uniform flow in a full-annulus multi-stage axial compressor with the harmonic balance method

Sun

Wang

et al. 2020

Advances in Mechanical Engineering

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To improve the understanding of unsteady flow in modern advanced axial compressor, unsteady simulations on full-annulus multi-stage axial compressor are carried out with the harmonic balance method. Since the internal flow in turbomachinery is naturally periodic, the harmonic balance method can be used to reduce the computational cost. In order to verify the accuracy of the harmonic balance method, the numerical results are first compared with the experimental results. The results show that the internal flow field and the operating characteristics of the multi-stage axial compressor obtained by the harmonic balance method coincide with the experimental results with the relative error in the range of 3%. Through the analysis of the internal flow field of the axial compressor, it can be found that the airflow in the clearance of adjacent blade rows gradually changes from axisymmetric to non-axisymmetric and then returns to almost completely axisymmetric distribution before the downstream blade inlet, with only a slight non-axisymmetric distribution, which can be ignored. Moreover, the slight non-axisymmetric distribution will continue to accumulate with the development of the flow and, finally, form a distinct circumferential non-uniform flow field in latter stages, which may be the reason why the traditional single-passage numerical method will cause certain errors in multi-stage axial compressor simulations.

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“…The HB method was afterwards adapted for simulating aeroelastic flows in turbomachinery using a predefined frequency [34] or set of frequencies [73,74] that were deduced from the blade passage pattern. In both cases, however, since the frequencies are fixed, the aeroelastic analysis is unidirectional: the motion is prescribed based on the structural mode shapes with a given amplitude, and combined structural and aerodynamic damping is assessed afterwards and employed in an aeroelastic stability analysis.…”

Section: Aeroelastic Solutions Using Frequency-domain Methodsmentioning

confidence: 99%