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Special Section Articles

Time Domain Wave Packet Method and Suppression of Instability Waves in Aeroacoustic Computations

[+] Author and Article Information
Fang Q. Hu

Department of Mathematics
and Statistics,
Old Dominion University,
Norfolk, VA 23529
e-mail: fhu@odu.edu

X. D. Li

School of Jet Propulsion,
Beihang University,
Beijing 100191, China
e-mail: lixd@buaa.edu.cn

X. Y. Li

School of Jet Propulsion,
Beihang University,
Beijing 100191, China
e-mail: lixiaoyan2001@googlemail.com

M. Jiang

School of Jet Propulsion,
Beihang University,
Beijing 100191, China
e-mail: jm3304420@sjp.buaa.edu.cn

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 6, 2012; final manuscript received October 3, 2013; published online April 28, 2014. Assoc. Editor: Ye Zhou.

J. Fluids Eng 136(6), 060905 (Apr 28, 2014) (12 pages) Paper No: FE-12-1559; doi: 10.1115/1.4025866 History: Received November 06, 2012; Revised October 03, 2013

A new time domain methodology for Computational Aeroacoustics (CAA) is proposed. The time domain wave packet (TDWP) method employs a temporally compact broadband pulse for acoustic sources. As the radiation and transmission of acoustic waves of all frequencies within the numerical resolution are embedded in the propagation of the wave packet, acoustic solution of the full spectrum become available at once. In addition, it becomes possible to separate the acoustic and instability waves in shear flows in the time domain wave packet method due to the compactness of the wave packet. The instability waves can further be suppressed by a source filtering technique, applied after the acoustic wave packet has propagated through the shear layers. Details on the source filtering technique used in the paper are presented. The TDWP method has been validated using a CAA Benchmark problem. The TDWP method is also applied to the NASA/GE Fan Noise Source Diagnostic Test (SDT) exhaust radiation problem.

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Figures

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Fig. 1

Schematics for a time signal of a sinusoidal wave (left) and a wave packet (right). A wave packet has a shorter time duration compared to that of a sinusoidal wave, and thus is more efficient in time domain simulations. A wave packet also contains a broad range of frequencies.

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Fig. 2

Illustration of Broadband Acoustic Test Pulse time function Ψ(t) and its spectrum, given in Eq. (4). The width of the spectrum can be controlled by parameter ω0.

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Fig. 3

Instantaneous Contours for an acoustic source located inside the jet, showing shear layer effects on the radiation of sound. Left: without suppression, showing the growth of Kelvin–Helmholtz instability wave; right: with TDWP method, obtained by FFT of the time domain solution at the given frequency.

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Fig. 4

Pressure contour history for the TDWP method. Left: without instability wave suppression, ε = 0; right: with source filtering suppression technique, α = 0.25, β = 0.75.

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Fig. 5

Pressure along y = 15, 50, and x = 100 for the Benchmark Problem shown in Fig. 4 Solid lines are the computation by TDWP method and circles are the analytical solution

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Fig. 6

Schematics showing the variation of hub-to-tip ratio h and mean flow Mach number M along the SDT flow path. Top: Variation of hub-to-tip ratio; bottom: variation of the mean flow Mach number.

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Fig. 7

A schematic of TDWP method for duct radiation computation. Source mode is introduced at the source plane. The radiated sound propagates through the exhaust shear layer to the far field. Suppression of the instability wave by source filtering technique is turned on after the front of the wave packet has propagated through the shear layer. As the propagation of duct modes is dispersive (Dispersion relation of a duct mode is also shown above), waves with higher frequencies arrive at the far field sooner than those with lower frequencies. Here ω0 denotes the minimum cut-on frequency and ω1, ω2, ω3, etc., indicate schematically a sequence of increasing frequencies.

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Fig. 8

Computational domain and mesh for time domain simulation. Every fifth grid lines are shown. Two zones of body fitted finite element meshes are used, with Perfectly Matched Layer at all nonreflecting boundaries.

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Fig. 9

Left: at approach condition, 61.7% of design speed, the dispersion relations show 5 cut-on radial modes at 2BPF when hub-to-tip ratio h = 0.529, M = 0.35. Right: the dispersion relations show 4 cut-on radial modes at 2BPF when hub-to-tip ratio h = 0.609, M = 0.4.

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Fig. 10

Top: sample pressure time history at a far field point, showing that the higher the frequency the earlier the arrival time, and the limiting frequency is ω0 as indicated in the dispersion relation curve shown in Fig. 7. Here, ω1, ω2, ω3, etc., indicate schematically a sequence of increasing frequencies. Bottom: FFT of the time signal shown in the top figure, showing the cut-off phenomenon of the duct mode propagation as indicated in Fig. 9 mode number (−10, 1).

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Fig. 11

Time history of pressure at a sample point inside the shear layer of the exhaust flow. Top: without suppression; bottom: with source filtering suppression technique.

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Fig. 12

Near-field pressure distribution (real part), mode (−10, 0) and (−10, 1) at 2BPF

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Fig. 13

Near-field pressure distribution (real part), mode (−10, 2) and (−10, 3) at 2BPF

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Fig. 14

Near-field pressure distribution (real part), mode (−10, 4) at 2BPF

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Fig. 15

Experimental (circle) and computed (square) sound pressure level in dB (ref. 20 μPa) for the exhaust radiation, where angle is measured from the inlet forward. The modal power levels used for the computation are W0 = 97 (dB), W1 = 61 (dB), W2 = 86 (dB), W3 = 91 (dB), and W4 = 52 (dB) (ref. 10 − 12 Watts).

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