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Technical Brief

An Efficient Algorithm of Wiener–Hopf Method With Graphics Processing Unit for Duct Acoustics

[+] Author and Article Information
Hanbo Jiang

College of Engineering,
Peking University,
Beijing 100871, China
e-mail: jianghb@pku.edu.cn

Alex Siu Hong Lau

Mechanical and Aerospace Engineering,
Hong Kong University of Science and Technology,
Kowloon 100871, Hong Kong, China
e-mail: alexshlau@ust.hk

Xun Huang

Department of Mechanical and Aerospace Engineering,
The Hong Kong University of Science and Technology,
Kowloon 100871, Hong Kong, China;
Department of Aeronautics and Astronautics,
College of Engineering,
Peking University,
Beijing 100871, China
e-mails: huangxun@ust.hk; huangxun@pku.edu.cn

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 11, 2017; final manuscript received March 29, 2017; published online July 13, 2017. Assoc. Editor: Ronald N. Miles.

J. Vib. Acoust 139(5), 054501 (Jul 13, 2017) (8 pages) Paper No: VIB-17-1012; doi: 10.1115/1.4036471 History: Received January 11, 2017; Revised March 29, 2017

Acoustic liner optimization calls for very efficient simulation methods. A highly efficient and straightforward algorithm is proposed here for the Wiener–Hopf solver, which also takes advantage of the parallel processing capability of the emerging graphics processing unit (GPU) technology. The proposed algorithm adopts a simple concept that re-arranges the formulations of the Wiener–Hopf solver to appropriate matrix forms. This concept was often overlooked but is surprisingly succinct, which leads to a stunningly efficient computational performance. By examining the computational performance of two representative setups (lined duct and duct radiations), the current study shows the superior performance of the proposed algorithm, particularly with GPU. The much improved computational efficiency further suggests the potential of the proposed algorithm and the use of GPU for practical low-noise aircraft engine design and optimization.

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References

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Figures

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Fig. 1

A sketch of the axial-symmetrical, semi-infinitely lined duct problem [15], where ξl denotes the presumably straight and infinitely thin vortex sheet that develops from the lining surface. For clarity, ξl is shown here in an exaggerated way. In addition, the notations ξl+ and ξl− represent the upper and lower sides of the vortex sheet, respectively; M0 is the Mach number of the presumably uniform flow accommodated in the duct; and M1=0 is the Mach number of the boundary flow local to the lining surface. Other parameters are given in the main text.

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Fig. 2

(a) Schematic of the two complex half-planes R± and the overlapped strip when M = 0.3, as duplicated from Fig. 2 of our previous work [17]. (b) The path of integration (solid line) for Eq. (16) will be slightly deformed to around all possible acoustic zeros (“°”) and poles (x).

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Fig. 3

(a) The programming model of CUDA and (b) the programming flowchart for our work

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Fig. 4

The way matrix A in Eq. (22) is mapped to stream processors and simultaneously calculated on GPU

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Fig. 5

Computational costs for (a) the kernel factorization K+(μ) and (b) the calculation of the entire sound pressure field. Here, we consider both the proposed new algorithm and the old version algorithm, and compare the related costs on the CPU and GPU platforms, respectively. The horizontal axis is the matrix size. The vertical axes are the corresponding computational time in second: the left vertical axis of each panel is for the current proposed algorithm, while the right vertical axis displays the much longer computational time by using the old version algorithm with CPU. Other parameters of the test case are given in the main text.

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Fig. 6

Near-field sound pressure contours of a semi-infinitely lined cylindrical duct case, where the spinning mode is (m,n)=(4,1), the normalized acoustic impedance is Z=1+1i at ω = 10 and M0=0.5. (a) An instantaneous sound pressure and (b) the sound pressure level.

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Fig. 7

Sketch of the model setup for the classical test case from Munt [13]. M0 is the Mach number of the ambient flow, and Mj is the Mach number of the jet flow.

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Fig. 8

The near-field sound pressure contours. The Munt case [13]: ω = 10, Mode(4,1), and M0=0.5. (a) An instantaneous sound pressure field and (b) the sound pressure level.

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