Research Papers

Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part I: Implicit Runge–Kutta Schemes

[+] Author and Article Information
Graham Ashcroft

e-mail: Graham.Ashcroft@dlr.de

Christian Frey

e-mail: Christian.Frey@dlr.de

Kathrin Heitkamp

e-mail: Kathrin.Heitkamp@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 December 17, 2012; published online September 26, 2013. Editor: David Wisler.

J. Turbomach 136(2), 021002 (Sep 26, 2013) (9 pages) Paper No: TURBO-12-1164; doi: 10.1115/1.4023904 History: Received August 02, 2012; Revised December 17, 2012

This is the first part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. In this part, the stability, accuracy, and efficiency of implicit Runge–Kutta schemes for the temporal integration of the compressible Navier–Stokes equations are investigated in the context of a CFD code for turbomachinery applications. Using two model academic problems, the properties of two explicit first stage, singly diagonally implicit Runge–Kutta (ESDIRK) schemes of second- and third-order accuracy are quantified and compared with more conventional second-order multistep methods. Finally, to assess the ESDIRK schemes in the context of an industrially relevant configuration, the schemes are applied to predict the tonal noise generation and transmission in a modern high bypass ratio fan stage and comparisons with the corresponding experimental data are provided.

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Fig. 1

Comparison of numerical and analytical solutions of the Liniger problem

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Fig. 2

Dependance of error on integration scheme and temporal resolution

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Fig. 3

UHBR fan: installation in the M2VP test facility

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Fig. 4

Computational mesh and block topology in the meridional plane in the rotor blade row

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Fig. 5

Computational mesh and block topology near midspan in the rotor blade row

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Fig. 6

Global performance curves of the fan stage from steady and unsteady simulations

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Fig. 7

Real component of pressure at the second harmonic of the BPF on the stator

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Fig. 8

Real component of the pressure fluctuations at the second harmonic of the BPF on the stator blade at 85% blade height

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Fig. 9

Variation of error with time-integration method and number of time steps per period

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Fig. 10

Real component of pressure at the second harmonic of the BPF along the duct casing

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Fig. 11

Real component of pressure at the second harmonic of the BPF in a meridional plane

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Fig. 12

Comparison of the amplitudes of three upstream propagating acoustic duct modes

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Fig. 13

Variation of the amplitude of the acoustic mode (m,n) = (+6,0) with time-integration method and number of time steps per period

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Fig. 14

Error in the predicted amplitude of the acoustic mode (m,n) = (+6,0) as a function of computational cost for each time-integration method




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