Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach

Chen, T.; Vasanthakumar, P.; He, L.

doi:10.2514/2.5792

Cited by 79 publications

(27 citation statements)

References 17 publications

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“…sire high resolution capture of the SWBLI phenomena ¡ and higher if one were to attempt using hybrid LES approaches (coarser grids could be used, but there would be a risk of numerically dissipating turbulence to an unacceptable degree). The nonlinear harmonic (NLH) technique [25,26] was developed to obtain the deterministic stress terms for a multistage environment in an e©cient and accurate way. The researchers adopted a frequency-domain approach, where the NavierStokes equations are split into averaged and time-varying terms then time averaged, and a model is derived for resultant deterministic stress terms which depend on solution of unsteady disturbances.…”

Section: Motivationmentioning

confidence: 99%

Numerical analysis of three complex three-dimensional shock wave / turbulent boundary layer interaction flows

Grosvenor

Zheltovodov

Matheson

et al. 2013

Progress in Flight Physics

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A set of Reynolds-averaged NavierStokes (RANS) computations with turbulence closure provided by the SpalartAllmaras (SA) model have been carried out for prediction of shock-induced three-dimensional (3D) turbulent separated §ows. The experimental data for di¨erent aerodynamic test con¦gurations have been used for assessing credibility of the numerical method employed. Particularly, shock wave / turbulent boundary layer interactions (SWTBLI) in the vicinity of an asymmetric sharp double-¦n (DF) with di¨erent (7• and 11 • ) de §ection angles mounted on a §at plate and two conically sharp cylindrical bodies at varying interbody distances and nose cone angles 60• and 40• mounted over a §at plate at freestream Mach number 4, as well as a transonic fan stage operating in the near-stall regime are considered. The gas dynamic structure and topology of 3D separated §ows, surface §ow patterns, and pressure distributions as well as body aerodynamic force prediction are analyzed. A transonic fan stage operating in the near-stall regime and a possibility of applying §ow control is investigated. High Performance Computing was employed to make high resolution computations of these §ows possible, and advanced 3D visualization techniques were employed in order to improve understanding of the separating §ow phenomena.

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Section: Motivationmentioning

confidence: 99%

Numerical analysis of three complex three-dimensional shock wave / turbulent boundary layer interaction flows

Grosvenor

Zheltovodov

Matheson

et al. 2013

Progress in Flight Physics

View full text Add to dashboard Cite

show abstract

“…These terms effort to quantify the unsteady field effects on the time averaged solution. Ning et al [12], He et al [13] and Chen et al [14] also used averaging operators to form the deterministic stress terms and calculated these terms with a modified version of a linearized frequency domain solver. In deterministic-stress methods, no direct coupling between the harmonics is evident mathematically.…”

Section: Introductionmentioning

confidence: 99%

“…To overcome the error associated with the linearized form, seminonlinear and nonlinear forms of frequency domain approach have been developed. In [11][12][13][14][15] semi-nonlinear frequency domain analysis of periodic unsteady flow has been extended. Adamczyk [11] formed deterministic stress terms, using several different linearization and averaging operators and then modelled these terms.…”

Section: Introductionmentioning

confidence: 99%

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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“…Adamczyk proposed modeling these terms, but subsequent authors [2,3] proposed calculating these terms with a modified version of a linearized frequency domain solver, where the modes are coupled and require simultaneous solution of both the time-averaged and unsteady terms. Although some of the nonlinearities are addressed in the time-averaged solution, the higher order terms are still neglected in the solution of the unsteady modes.…”

Section: Introductionmentioning

confidence: 99%

Demonstration of Nonlinear Frequency Domain Methods

2006

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This paper demonstrates the accuracy of the nonlinear frequency domain method in applications to unsteady flow calculations. The basis of the method is a pseudospectral approach to recast a nonlinear unsteady system of equations in the temporal domain into a stationary system in the frequency domain. The nonlinear frequency domain method, in principle, provides the rapid convergence of a spectral method with increasing numbers of modes, and, in this sense, it is an optimal scheme for time-periodic problems. In practice it can also be effectively used as a reduced order method in which users deliberately choose not to resolve temporal modes in the solution. A variable-time-period method has been proposed such that the nonlinear frequency domain method can be applied to problems where the time period of the unsteadiness is either known or unknown a priori. To validate the latter case, results from this method have been compared with experimental results of vortex shedding in low Reynolds number flows past cylinders. Validation of the first case utilizes experimental data of a pitching airfoil in transonic flow. These comparisons demonstrate the efficiency of the nonlinear frequency domain method in representing complex nonlinear flow field physics with a limited number of temporal modes. = spatial dimension y = nondimensionalized distance from wall = ratio of specific heats ij = Kronecker delta = heat transfer coefficient = absolute viscosity = density = shear stress tensor = pseudotime

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Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach

Cited by 79 publications

References 17 publications

Numerical analysis of three complex three-dimensional shock wave / turbulent boundary layer interaction flows

Numerical analysis of three complex three-dimensional shock wave / turbulent boundary layer interaction flows

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

Demonstration of Nonlinear Frequency Domain Methods

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