A discrete adjoint harmonic balance method for turbomachinery shape optimization

Huang, Huang; Ekici, Kivanc

doi:10.1016/j.ast.2014.05.015

Cited by 47 publications

(11 citation statements)

References 54 publications

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“…Later, Gopinath et al 12 performed a sliding mesh technique on the harmonic balance method to model the inter-row coupling interactions in multi-stage turbomachinery. 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.…”

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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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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“…wings or helicopter rotors. He and Wang (2011) as well as Huang and Ekici (2014) consider optimisation problems for a single blade row, e.g. for flutter stability.…”

Section: Introductionmentioning

confidence: 99%

Adjoint Process Chain for Forced Response Analysis Using a Harmonic Balance Method

Engels-Putzka

Frey

2017

European Conference on Turbomachinery Fluid Dynamics and Hermodynamics

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This paper describes the setup and validation of a process chain for aeroelastic sensitivity analysis using adjoint methods. In particular, the adjoint of an harmonic balance solver is applied to capture unsteady effects. The interaction between different blade rows is simulated by an "external" coupling of the adjoint harmonic balance solver with a steady adjoint solver. The adjoint process is applied to a turbine stage and the results are compared to finite differences of forward computations. KEYWORDS AEROELASTICITY, FORCED RESPONSE, HARMONIC BALANCE, ADJOINT METHODS NOMENCLATURE Symbols i complex unit F mod modal force F Fourier transform k harmonic index K number of higher harmonics m circumferential mode order N number of sampling points q vector of conservative flow variables x vector of grid coordinates ω angular frequency Abbreviations HB harmonic balance CEV constant eddy viscosity VEV variable eddy viscosity

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“…This is described in Choi et al [34] and in Mader and Martins [33] for helicopter applications, and in Huang and Ekici [35] in the context of turbomachinery. The adjoint development in these works is, however, limited to inviscid flows.…”

Section: Past Work On Adjoint For Aircraft and Rotorcraft Applicationsmentioning

confidence: 99%

Fully Implicit Discrete-Adjoint Methods for Rotorcraft Applications

2016

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This paper presents the development of a fully implicit, low-memory, discrete adjoint method by means of automatic source-code differentiation applied to the Helicopter Multi-Block computational fluid dynamics solver. The method is suitable for applications in flight mechanics as well as shape optimization, and is demonstrated in this paper for popular flow cases reported in the literature. In particular, adjoint CFD computations were undertaken for airfoils, wings and rotor blade cases, and the obtained results were found to agree well with published solutions and with finite differences of flow derivatives. The method has been demonstrated for inviscid and viscous cases and results suggest that the current implementation is robust and efficient. The cost of the adjoint computations is relatively low due to the employed source-code differentiation and most of the times it is no more than the cost of a steady-state flow solution.

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A discrete adjoint harmonic balance method for turbomachinery shape optimization

Cited by 47 publications

References 54 publications

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

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

Adjoint Process Chain for Forced Response Analysis Using a Harmonic Balance Method

Fully Implicit Discrete-Adjoint Methods for Rotorcraft Applications

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