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TECHNICAL PAPERS

A Numerical Investigation on the Influence of Lateral Boundaries in Linear Vibrating Cascades

[+] Author and Article Information
Roque Corral

Industria de TurboPropulsores S.A., 28830 Madrid, Spaine-mail: Roque.Corral@itp.es

Fernando Gisbert

School of Aeronautics, UPM, 28040 Madrid, Spain

J. Turbomach 125(3), 433-441 (Aug 27, 2003) (9 pages) doi:10.1115/1.1575255 History: Received June 11, 2001; Online August 27, 2003
Copyright © 2003 by ASME
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References

Bölcs, A., 1983, “A Test Facility for the Investigation of the Steady and Unsteady Transonic Flows in Annular Cascades,” ASME Paper 83-GT-34.
Buffum, D. H., and Fleeter, S., 1991, “Linear Oscillating Cascade Unsteady Aerodynamic Experiments,” in the 6th International Symposium on Unsteady Aerodynamics, Aeroelasticity and Aeroacoustics of Turbomachines, Ed. Atassi, September 15–19.
Fransson, T. H., and Verdon, J. M., 1992, “Standard Configurations for Unsteady Flow Through Vibrating Axial-Flow Turbomachine-Cascades,” KTH Technical Report TRITA/KRV/92-009.
Bell,  D. L., and He,  L., 2000, “Three-Dimensional Unsteady Flow for an Oscilatting Turbine Blade and the Influence of the Tip-Clearance,” ASME J. Turbomach., 122(1), Jan., pp. 93–101.
Bölcs, A., Fransson, T. H., and Schlafli, D., 1989, “Aerodynamic Superposition Principle in Vibrating Turbine Cascades,” AGARD, 74th Specialists’ Meeting of the Propulsion and Energetics Panel on Unsteady Aerodynamic Phenomena in Turbomachines, Luxembourg, August 28–September 1.
Chima, R. V., McFarland, E. R., Wood, J. R., and Lepicovsky, J., 2000, “On Flowfield Periodicity in the NASA Transonic Flutter Cascade, Part II-Numerical Study,” ASME Paper 2000-GT-0573.
Lepicovsky, J., McFarland, E. R., Chima, R. V., and Wood, J. R., 2000, “On Flowfield Periodicity in the NASA Transonic Flutter Cascade, Part I—Experimental Study,” ASME Paper 2000-GT-0572.
Ott, P., Norryd, M., and Bölcs, A., 1998, “The Influence of Tailboards on Unsteady Measurements in a Linear Cascade,” ASME Paper 98-GT-0572.
Hall, K. C., 1999, “Linearized Unsteady Aerodynamics,” in Aeroelasticity in Axial Flow Turbomachines VKI Lecture Series 1999-05.
Jameson,  A., Schmidt,  W., and Turkel,  E., 1981, “Numerical Solution of the Euler Equations by Finite Volume Techniques Using Runge-Kutta Time Stepping Schemes,” AIAA Pap. No. 81–1259.
Roe,  P., 1981, “Approximate Riemman Solvers, Parameters, Vectors and Difference Schemes,” J. Comput. Phys. 43, pp. 357–372.
Swanson,  R. C., and Turkel,  E., 1992, “On Central-Difference and Upwinding Schemes,” J. Comput. Phys. 101, pp. 292–306.
Corral, R., Burgos, M. A., and Garcı́a, A., 2000, “Influence of the Artificial Dissipation Model on the Propagation of Acoustic and Entropy Waves,” ASME Paper 2000-GT-563.
Giles,  M. B., 1990, “Non-Reflecting Boundary Conditions for Euler Equation Calculations,” AIAA J., 28(12), pp. 2050–2057.
Burgos, M. A., and Corral, R. 2001, “Application of the Phase-Laged Boundary Conditions to Rotor/Stator Interaction,” ASME Paper 2001-GT-586.
Corral,  R., and Fernández-Castañeda,  J., 2001, “Surface Mesh Generation by Means of Steiner Triangulations,” AIAA J., 39(1), Jan., pp. 176–180.
Whitehead, D. S., 1987, “Classical Two-Dimensional Methods,” Chapt. 2, AGARD Manual on Aeroelasticity in Axial Flow Turbomachines: Unsteady Turbomachinery Aerodynamics, Vol. 1, eds., M. F. Platzer and F. O. Carta, AGARD-AG-298.
Wood, J. R., Strasizar, T., and Hathaway, M., 1990, “Test Case E/CA-6 Subsonic Turbine Cascade T106,” Test Cases for Computation of Internal Flows in Aero Engine Components, AGARD-AR-275, July.

Figures

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Typical hybrid-cell grid and associated dual mesh
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Comparison against LINSUB (solid line) of the unsteady pressure amplitude of the different airfoils (×) of a cascade of nine flat plates vibrating in traveling-wave mode (σ=160 deg)
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Scheme and nomenclature of a linear flat plate cascade with five passages
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Comparison with LINSUB (solid line) of the unsteady pressure amplitude (top) and phase (bottom) obtained with the current method for the baseline case (M=0.5,St=5,s/c=0.5, θ=30 deg, σ=0 deg) with two different grids.
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Comparison against LINSUB (solid line) of the unsteady pressure amplitude in the influence coefficient (top) and traveling-wave (bottom) forms of a cascade of five flat plates vibrating in a blade alone mode computed using periodic (×) and inviscid wall (○) boundary conditions in the lateral walls
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Comparison against LINSUB (solid line) of the unsteady pressure amplitude expressed in form of traveling-waves of a cascade of nine flat plates vibrating in blade alone mode computed using periodic (×) and inviscid wall (○) boundary conditions in the lateral walls
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Nondimensional work-per-cycle obtained from LINSUB (○) and from a cascade of nine flat plates vibrating in blade alone mode computed using solid lateral walls
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Comparison with LINSUB (solid line) of the unsteady pressure amplitude (top) and phase (bottom) obtained with the current method for the baseline case (M=0.5,St=5,s/c=0.5, θ=30 deg) and two different interblade phase angles (σ=0 deg and σ=π)
Grahic Jump Location
Comparison with LINSUB (○) of the influence coefficients obtained with the current method (×) for the baseline case (M=0.5,St=5,s/c=0.5, θ=30 deg) and N=21
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Comparison with LINSUB (solid line) of the unsteady pressure amplitude (top) and phase (bottom) obtained with the current method using nine blades (M=0.5,St=1,s/c=0.5, θ=30 deg, σ=0 deg)
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Influence coefficients obtained with the LINSUB with nine blades (N=9) for the baseline case (M=0.5,s/c=0.5, θ=30 deg) and two reduced frequencies St=1 and St=5
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Comparison against LINSUB (solid line) of the unsteady pressure amplitude of the different airfoils (×) of a cascade of nine flat plates vibrating in traveling-wave mode (σ=0 deg)
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Instantaneous isocontour lines of static pressure of a linear cascade of nine flat plates vibrating in traveling-wave mode; left: σ=0 deg, right: σ=160 deg
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Comparison of the unsteady pressure amplitude (top) and phase (bottom) obtained with the current method using the twm mode and a cascade of nine blades with solid lateral walls for the 10th standard configuration and two interblade phase angles σ=0 deg (left) and σ=160 deg (right)
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Isomach lines of the 10th standard configuration computation in the sidewall region
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Comparison of the unsteady pressure amplitude (top) and phase (bottom) obtained with the current method using the twm mode and a cascade of nine blades with solid lateral walls for the T106 blade and two interblade phase angles σ=0 deg (left) and σ=160 deg (right)

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