Numerical solution of periodic transonic flow through a fan stage

Erdos, John; Alzner, E.; Mcnally, W. D.

doi:10.2514/6.1976-369

Cited by 23 publications

(24 citation statements)

References 3 publications

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“…While linearised methods allow calculations on a single blade passage for any interblade phase angle, non-linear methods need to include a number of blade passages, if not the whole annulus, unless some additional assumption are made. The pioneering work by Erdos et al (1977) presented a two-dimensional, unsteady, inviscid flow calculation of a fan stage with unequal pitches using a phase-shifted periodicity condition. Hodson (1985) modified the algorithm by Denton (1983) and used Erdos' technique to investigate wake/rotor interactions in a low speed turbine.…”

Section: Time-marching Methods For Non-linear Unsteady Aerodynamicsmentioning

confidence: 99%

Transonic Rotor/Stator Interaction Using a 3-D Linearised Unsteady Viscous Flow Model

Sbardella

Imregun

2002

International Journal of Computational Fluid Dynamics

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The paper first summarizes the forced response problem in turbomachinery and reviews various numerical methods for the simulation of unsteady flows. A particular technique, based on the linearisation of the unsteady Favre-averaged Navier -Stokes equations on three-dimensional mixedelement grids of tetrahedra, hexahedra and wedges, is described in some detail. The methodology was applied to a NGV/rotor interaction benchmark case for which detailed steady and unsteady flow measurements are available. The steady-state flow, calculated using a non-linear viscous representation, was described in detail with emphasis on features such as separation, horseshoe and passage vortices, tip leakage and shock structure since these are likely to influence the unsteady flow. The sources of unsteadiness on the rotor passage were evaluated from the steady-state solution at the NGV outlet. The disturbances were split into vortical, entropic and potential waves, the Fourier components of which were considered separately. The summation of the vortical and entropic waves was used as a rotor inlet boundary condition in order to assess the wake/rotor unsteady interaction. Similarly, potential waves were used to study the potential/rotor interaction. The results obtained from these two types of unsteady interactions were superimposed and compared with experimental data. Good qualitative and, in most cases, quantitative agreement was obtained, a finding which suggests that the unsteady flowfield generated by the relative blade motion can be considered to be a quasi-linear phenomenon for the particular HP turbine studied. Finally, the mechanisms of wake/rotor and potential/rotor interactions were studied in some detail and it was concluded that the former was strong in the crown of the blade while the latter was dominant in the leading edge region.

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Section: Time-marching Methods For Non-linear Unsteady Aerodynamicsmentioning

confidence: 99%

Transonic Rotor/Stator Interaction Using a 3-D Linearised Unsteady Viscous Flow Model

Sbardella

Imregun

2002

International Journal of Computational Fluid Dynamics

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“…Starting with the work of Erdos, Alzner, and McNally (1977), unsteady nonlinear CFD methods were developed and applied to the computation of rotor/stator interaction (Hah et al 1997;Chen et al 2001;Gerolymos, Michon, and Neubauer 2002a). There are mainly two different approaches for the computation of time-periodic unsteady flows in turbomachinery (He 2010), the time-marching methods (Erdos et al 1977), which time-integrate the flow equations, and the nonlinear harmonic (Chen et al 2001;He 2008;McMullen, Jameson, and Alonso 2006) and harmonic-balance (Hall et al 2002;Hall 2007, 2008) methods, which solve a coupled set of timeindependent problems to determine the Fourier coefficients of the decomposition of the flow into harmonics, eventually with multiple fundamental frequencies (He 1992;Li and He 2002;Ekici and Hall 2008).…”

Section: Introductionmentioning

confidence: 99%

“…There are mainly two different approaches for the computation of time-periodic unsteady flows in turbomachinery (He 2010), the time-marching methods (Erdos et al 1977), which time-integrate the flow equations, and the nonlinear harmonic (Chen et al 2001;He 2008;McMullen, Jameson, and Alonso 2006) and harmonic-balance (Hall et al 2002;Hall 2007, 2008) methods, which solve a coupled set of timeindependent problems to determine the Fourier coefficients of the decomposition of the flow into harmonics, eventually with multiple fundamental frequencies (He 1992;Li and He 2002;Ekici and Hall 2008). The introduction of nonlinearity, through coupling between the equations for various harmonics (Hall et al 2002), is essential to resolve the instability problems observed in the fully linearised harmonic approaches Giles 2003, 2004;Agarwal, Morris, and Mani 2004;Chassaing and Gerolymos 2008), by nonlinear saturation of the amplitude of instabilities, as shown in He (2008), who analyses the nonlinear harmonic method Ning and He 1998).…”

Section: Introductionmentioning

confidence: 99%

Filtered chorochronic interface as a capability for 3-D unsteady throughflow analysis of multistage turbomachinery

Gerolymos

2013

International Journal of Computational Fluid Dynamics

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This note reviews the widely used phased-lagged [Erdos, J. L., E. Alzner, and W. McNally. 1977. AIAA Journal 15: 1559-68.] approach and corresponding chorochronic interface relations [Gerolymos G. A., G. J. Michon, and J. Neubauer. 2002. Journal of Propulsion and Power 18: 1139-52.] and explores its potential extension to the approximate unsteady throughflow analysis of multistage turbomachinery. The basic relations pertaining to the binary blade-row interaction case, for which chorochronic periodicity is exact in a phase-averaged RANS framework, are briefly formulated, and selected computational examples illustrate the application of the method. Then, the filtered chorochronic interface is defined as the unsteady counterpart of the well-known mixing-plane concept. This interface takes into account only those tθ-waves which are compatible with the interaction of the immediately upstream and downstream blade-rows. The concept, which is similar to the decompositionand-superposition method [Li, H. D., and L. He. 2005. ASME Journal of Turbomachinery 127: 589-98.], is illustrated by 3-D computations of a 1 2 -stage transonic compressor.Nomenclature f frequency (Hz) f frequency (Hz) associated with the rotational speed | | = 2πf f n BR ,m BR frequency associated with the chorochronic periodicity of the binary interaction between blade-rows n BR and m BR (5a) BR grid-block index (a block may contain several domains, all associated with the pitch and rotational speed of the same blade-row) L θ number of nonzero θ -harmonics retained in the chorochronic series, used in the computations and postprocessing N B number of blades in a blade-row n BR blade-row index N BR total number of blade-rows n D grid-domain index n t time-harmonic index N t number of t-harmonics used in the computations and postprocessing n θ azimuthal harmonic index (2π -periodic) N PP number of points-per-period defining the time-step for the unsteady simulations (4, 7) m massflow (kg s −1 ) m WL working-line massflow (kg s −1 ) M Mach-number * Email: georges.gerolymos@upmc.fr p pressure (Pa) s entropy (J kg −1 K −1 ) t time (s) t COMP time duration simulated by the unsteady computation V absolute-flow velocity (m s −1 ) v(t, x, R, θ) flow-variables vector at (t, x, R, θ ) v n BR ,m BR unsteady-interaction flowfield, associated with the binary interaction between bladerows n BR and m BR in the decompositionand-superposition technique for predicting flows with multiple frequencies of He (1992), used in the formulation of multistage filtered chorochronic periodicity (6) v tθ -harmonics (chorochronic harmonics) of the flow-variables vector v (2, 3) w n BR ,m BR x-wise weight-function used (6) to filter out, at the chorochronic interface between blade-rows n BR and m BR , frequencies and phase-lags other than those associated with the binary interaction a FLTR fraction of blade-chord, defining the filterwidth (6c) (x, R, θ ) cylindrical system-of-coordinates (x is the engine axis) (x, y, z) corresponding Cartesian system-ofcoordinates (x is the engine a...

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“…At the azimuthal boundaries, phase-lag conditions [20] are used to take into account for the space-time periodicity.…”

Section: Numerical Setupmentioning

confidence: 99%

“…To efficiently apply the HB approach to turbomachinery configurations, phase-lag boundary conditions [20] are used to cut down the mesh size by using a grid that spans only one blade passage per row. The phase-lag boundary conditions are twofold: i) the azimuthal boundaries of a passage and ii) the blade row interface which must handle different row pitches on either sides (Fig.…”

Section: Extension Of the Harmonic Balance Approach To Turbomachinerymentioning

confidence: 99%

Convergence of Fourier-based time methods for turbomachinery wake passing problems

Gomar

Bouvy

Sicot

et al. 2014

Journal of Computational Physics

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Numerical solution of periodic transonic flow through a fan stage

Cited by 23 publications

References 3 publications

Transonic Rotor/Stator Interaction Using a 3-D Linearised Unsteady Viscous Flow Model

Transonic Rotor/Stator Interaction Using a 3-D Linearised Unsteady Viscous Flow Model

Filtered chorochronic interface as a capability for 3-D unsteady throughflow analysis of multistage turbomachinery

Convergence of Fourier-based time methods for turbomachinery wake passing problems

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