Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique

Hall, Kenneth C.; Thomas, Jeffrey P.; Clark, William S.

doi:10.2514/2.1754

Cited by 572 publications

(311 citation statements)

References 18 publications

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“…Finally, a recently developed technique is the harmonic balance (HB) method, proposed by Hall et al [5] for time-periodic flows. This method can be viewed as an equivalent in the time domain of the frequency-domain approach proposed by He and Ning [6].…”

mentioning

confidence: 99%

Contrasting the Harmonic Balance and Linearized Methods for Oscillating-Flap Simulations

Dufour¹,

Sicot²,

Puigt³

et al. 2010

AIAA Journal

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In the framework of unsteady aerodynamics, forced-harmonic-motion simulations can be used to compute unsteady loads. In this context, the present paper assesses two alternatives to the unsteady Reynolds-averaged Navier-Stokes approach, the linearized unsteady Reynolds-averaged Navier-Stokes equations method, and the harmonic balance approach. The test case is a NACA 64A006 airfoil with an oscillating flap mounted at 75% of the chord. Emphasis is put on examining the performances of the methods in terms of accuracy and computational cost over a range of physical conditions. It is found that, for a subsonic flow, the linearized unsteady Reynolds-averaged Navier-Stokes method is the most efficient one. In the transonic regime, the linearized unsteady Reynolds-averaged Navier-Stokes method remains the fastest approach, but with limited accuracy around shocks, whereas a oneharmonic harmonic balance solution is in closer agreement with the unsteady Reynolds-averaged Navier-Stokes solution. In the case of separation in the transonic regime, the linearized unsteady Reynolds-averaged Navier-Stokes method fails to converge, whereas the harmonic balance remains robust and accurate.

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mentioning

confidence: 99%

Contrasting the Harmonic Balance and Linearized Methods for Oscillating-Flap Simulations

Dufour¹,

Sicot²,

Puigt³

et al. 2010

AIAA Journal

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“…(11) directly a pseudo-time derivative can be added to the unsteady residual. The application of the pseudo-time derivative is consistent with established convergence acceleration techniques used to solve steady-state problems [16]. Adding this term, a time-stepping approach can be employed to numerically integrate the resulting Eq.…”

Section: Pseudo-time Derivativesmentioning

confidence: 90%

“…Here is a problem of expressing each k R in terms of all coefficients, Ŵ k Hall proposed two approaches to calculate these coefficients [16]. In the first approach k R is directly calculated from all Ŵ k using a complex series of convolution sums, which has a massive complexity and computational cost.…”

Section: Transformation Of Equations Into Frequency Domainmentioning

confidence: 99%

“…1. The spatial operators computational cost in pseudospectral approach is the product of one steady-state spatial operator cost and the number of time instances used to represent the solution, N. Also, the cost of FFT is proportional to Nln(N) [16]. So, for more practical values…”

Section: Solution Proceduresmentioning

confidence: 99%

“…An efficient periodic solution of fully non-linear system of equations was first proposed by Hall et al [16] using the harmonic balance technique on 2-D turbomachinery cascades. McMullen et al [17][18][19] also proposed a nonlinear frequency domain method (NLFD) which represents a form of residual in the frequency domain.…”

Section: Introductionmentioning

confidence: 99%

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Time-periodic incompressible flow simulation using non-linear frequency domain approach

2017

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Original scientific paper The capability of nonlinear reduced frequency domain (NLFD) approach in predicting the flow field of time-periodic incompressible flow is investigated. The efficient NLFD method uses Fourier series representation in time considering the assumption of solution periodicity and the resulting nonlinear equations are solved using pseudo-spectral approach. In this manner, the desired periodic solution can directly be obtained without the need to solve the initial transient part. Thus, without loss of generality a considerable computational cost reduction can be achieved in comparison with the common timeaccurate methods. In the present algorithm (INLFD) the NLFD approach is used to solve the flow field in an incompressible formulation and the validation is performed using some periodic test cases with analytical solutions. The results show that capturing only a limited number of temporal modes can provide an accurate estimation of the flow field. Finally, the computational costs of the INLFD and a time-accurate method are also compared which demonstrate the efficiency of the INLFD method in representing nonlinear flow field physics by savings in computational time up to 50 percent. Keywords: incompressible flow; non-linear reduced frequency; pressure Poisson; pseudo-spectral; time-periodic Simulacija vremenski periodičnog nestlačljivog toka pristupom ne-linearnog područja frekvencijeIzvorni znastveni članak Istražuje se mogućnost predviđanja polja protoka vremenski periodičnog nestlačljivog toka pristupom područja nelinearne smanjene frekvencijenonlinear reduced frequency domain (NLFD). Učinkovita NLFD metoda koristi predstavljanje Fourierovih serija u vremenu smatrajući da se pretpostavka periodičnosti rješenja i rezultirajuće nelinearne jednadžbe rješavaju pseudo-spektralnim pristupom. Na taj se način željeno periodičko rješenje može dobiti direktno bez potrebe rješenja inicijalnog tranzijentnog dijela. Tako se može postići značajno smanjenje troška bez gubitka generalizacije u usporedbi s uobičajenim vremenski preciznim metodama. U postojećem algoritmu (INLFD), NLFD pristup je primijenjen za rješavanje polja protoka u nestlačljivoj formulaciji a validacija se obavlja primjenom nekih periodičnih slučajeva ispitivanja s analitičkim rješenjima. Rezultati pokazuju da se obuhvatom samo ograničenog broja temporalnih načina može osigurati točna procjena polja protoka. Konačno, troškovi izračuna INFLED-a i vremenski točne metode također su uspoređeni i pokazuju učinkovitost INFLED metode u predstavljanju fizike nelinearnog polja protoka uštedom vremena izračuna do 50 posto.

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Turbomachinery Aeroelasticity

Bendiksen¹,

Kielb²,

Hall³

2010

Encyclopedia of Aerospace Engineering

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This paper focuses on the validity of the used assumptions in the development of the Decoupled approaches which predict the aeroelasticity behavior of turbomachinery blades. A Decoupled approach is employed to evaluate the aerodynamic damping and the forced response of a low pressure compressor BluM T M induced by low engine order excitations. The validity of the assumptions like superposition principle, linearity of aerodynamic damping forces and the blade-motion independency of the aerodynamic forces are verified by employing the TWIN approach. Extensive experiments are also carried out to evaluate the overall performance of the approaches.

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Computation of Unsteady Nonlinear Flows in Cascades Using a Harmonic Balance Technique

Cited by 572 publications

References 18 publications

Contrasting the Harmonic Balance and Linearized Methods for Oscillating-Flap Simulations

Contrasting the Harmonic Balance and Linearized Methods for Oscillating-Flap Simulations

Time-periodic incompressible flow simulation using non-linear frequency domain approach

Turbomachinery Aeroelasticity

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