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Research Papers

Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part II: Time-Linearized Methods

[+] Author and Article Information
Christian Frey

e-mail: Christian.Frey@dlr.de

Graham Ashcroft

e-mail: Graham.Ashcroft@dlr.de

Hans-Peter Kersken

e-mail: Hans-Peter.Kersken@dlr.de
Institute of Propulsion Technology,
German Aerospace Center (DLR),
Linder Höhe,
Cologne 51147, Germany

Christian Weckmüller

Institute of Propulsion Technology,
German Aerospace Center (DLR),
Müller-Breslaustr. 8,
Berlin 10623, Germany
e-mail: Christian.Weckmueller@dlr.de

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Turbomachinery. Manuscript received August 2, 2012; final manuscript received April 26, 2013; published online September 26, 2013. Editor: David Wisler.

J. Turbomach 136(2), 021003 (Sep 26, 2013) (10 pages) Paper No: TURBO-12-1163; doi: 10.1115/1.4024649 History: Received August 02, 2012; Revised April 26, 2013

This is the second part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. It focuses on the application of linearized RANS methods to turbomachinery noise problems. The convective and viscous fluxes of an existing URANS solver are linearized and the resulting unsteady linear equations are transferred into the frequency domain, thereby simplifying the solution problem from unsteady time-integration to a complex linear system. The linear system is solved using a parallel, preconditioned general minimized residual (GMRES) method with restarts. In order to prescribe disturbances due to rotor stator interaction, a so-called gust boundary condition is implemented. Using this inhomogeneous boundary condition, one can compute the generation of the acoustic modes and their near field propagation. The application of the time-linearized methods to a modern high-bypass ratio fan is investigated. The tonal fan noise predicted by the time-linearized solver is compared to numerical results presented in the first part and to measurements.

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References

Saad, Y., 2003, Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM Society for Industrial and Applied Mathematics, Philadelphia, PA.
Pinelli, L., Poli, F., Marconcini, M., Arnone, A., Spano, E., and Torzo, D., 2011, “Validation of a 3D Linearized Method for Turbomachinery Tone Noise Analysis,” ASME Paper No. GT2011-45886. [CrossRef]
Kersken, H.-P., Frey, C., Voigt, C., and Ashcroft, G., 2012, “Time-Linearized and Time-Accurate 3D RANS Methods for Aeroelastic Analysis in Turbomachinery,” ASME J. Turbomach., 134(5), p. 051024. [CrossRef]
Nürnberger, D., Eulitz, F., Schmitt, S., and Zachcial, A., 2001, “Recent Progress in the Numerical Simulation of Unsteady Viscous Multistage Turbomachinery Flow,” Proceedings of the 15th International Symposium on Air Breathing Engines, Bangalore, India, September 2–7, ISABE Paper No. 2001-1081.
Roe, P. L., 1981, “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes,” J. Comp. Phys., 43, pp. 357–372. [CrossRef]
van Leer, B., 1997, “Towards the Ultimate Conservative Difference Scheme V. A Second-Order Sequel to Godunov's Method,” J. Comput. Phys., 135(2), pp. 229–248. [CrossRef]
Kügeler, E., 2005, “Numerical Method for the Accurate Analysis of Cooling Efficiency in Film-Cooled Turbine-Blades,” DLR-Forschungsbericht, Institute of Propulsion Technology, German Aerospace Center, Linder Höhe, Germany, Report No. 2005-11 (in German).
Clark, W. S., and Hall, K. C., 2000, “A Time-Linearized Navier–Stokes Analysis of Stall Flutter,” ASME J. Turbomach., 122, pp. 467–476. [CrossRef]
Giles, M. B., 1990, “Non-Reflecting Boundary Conditions for Euler Calculations,” AIAA J., 28(12), pp. 2050–2058. [CrossRef]
Enders, G., Dabrock, T., Voigt, C., Nicke, E., and Johann, E., 2012, “Experimental Investigations of a Four-Stage Axial Compressor Equipped With Casing Treatment Over Two Rows of Rotor Blades,” ASME Paper No. GT2012-68688.
Weckmüller, C., Guerin, S., and Ashcroft, G., 2009, “CFD/CAA Coupling Applied to the DLR UHBR-Fan: Comparison to Experimental Data,” Proceedings of the 15th AIAA/CEAS Aeroacoustics Conference, Miami, FL, May 11–13.
Ashcroft, G., Frey, C., Heitkamp, K., and Weckmüller, C., 2012, “Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery, Part I: Implicit Runge Kutta Schemes,” ASME Paper No. GT2012-69447.
Kaplan, B., Nicke, E., and Voss, C., 2006, “Design of a Highly Efficient Low-Noise Fan For Ultra-High Bypass Engines,” ASME Paper No. GT2006-90363. [CrossRef]
Tyler, J. M., and Sofrin, T. G., 1962, “Axial Flow Compressor Noise Studies,” Trans. SAE, 70, pp. 309–332.
Tapken, U., Raitor, T., and Enghardt, L., 2009, “Tonal Noise Radiation From an UHBR Fan—Optimized In-Duct Radial Mode Analysis,” Proceedings of the 15th AIAA/CEAS Aeroacoustics Conference, Miami, FL, May 11–13.

Figures

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Fig. 1

Prescribed acoustic wave in duct segment

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Fig. 2

Numerical dissipation error against grid resolution

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Fig. 3

Mach number distribution of mean flow through the DLR Rig 250 stator row

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Fig. 4

Real part of harmonic pressure on pressure (solid) and suction (dashed) side

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Fig. 5

Imaginary part of harmonic pressure on pressure (solid) and suction (dashed) side

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Fig. 6

Real part of harmonic pressure on pressure (solid) and suction (dashed) side. Perturbation amplitude has been increased by a factor of 4.

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Fig. 7

Imaginary part of harmonic pressure on pressure (solid) and suction (dashed) side. Perturbation amplitude has been increased by a factor of 4.

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Fig. 8

Real part of harmonic pressure on pressure (solid) and suction (dashed) side. Unsteady turbulence model versus constant eddy viscosity model.

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Fig. 9

Imaginary part of harmonic pressure on pressure (solid) and suction (dashed) side. Unsteady turbulence model versus constant eddy viscosity model.

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Fig. 10

Real part of harmonic pressure on pressure (solid) and suction (dashed) side. Two-dimensional nonreflecting boundary conditions are employed at outlets.

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Fig. 11

Imaginary part of harmonic pressure on pressure (solid) and suction (dashed) side. Two-dimensional nonreflecting boundary conditions are employed at outlets.

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Fig. 12

Model of the DLR–UHBR fan for the numerical simulations

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Fig. 13

Real part of second harmonic of axial velocity in the stator row. Time-linearized versus unsteady simulation.

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Fig. 14

Real part of second harmonic of blade surface pressure on suction side

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Fig. 15

Imaginary part of second harmonic of blade surface pressure on suction side

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Fig. 16

Real part of second harmonic of blade surface pressure on pressure side

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Fig. 17

Imaginary part of second harmonic of blade surface pressure on pressure side

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Fig. 18

Real part of harmonic surface pressure on stator caused by wave reflected at rotor blade row

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Fig. 19

Imaginary part of harmonic surface pressure on stator caused by wave reflected at rotor blade row

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Fig. 20

Real part of harmonic surface pressure on stator. Unsteady versus time-linearized solution using unsteady average.

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Fig. 21

Imaginary part of harmonic surface pressure on stator. Unsteady versus time-linearized solution using unsteady average.

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Fig. 22

Real part of the second harmonic of the pressure along the duct section

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Fig. 23

Sound pressure level of upstream acoustic mode of azimuthal order m = 6 and radial order n = 0, 1, 2. Time-linearized versus unsteady results and measurements.

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