Research Papers

Efficient Impedance Eductions for Liner Tests in Grazing Flow Incidence Tube

[+] Author and Article Information
Hanbo Jiang

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

Xun Huang

Department of Mechanical and
Aerospace Engineering,
The Hong Kong University of Science
and Technology,
Kowloon, Hong Kong, China
e-mail: huangxun@ust.hk;
Department of Aeronautics and Astronautics,
College of Engineering,
Peking University,
Beijing 100871, China
e-mail: 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 July 25, 2016; final manuscript received December 5, 2016; published online March 16, 2017. Assoc. Editor: Sheryl M. Grace.

J. Vib. Acoust 139(3), 031002 (Mar 16, 2017) (7 pages) Paper No: VIB-16-1371; doi: 10.1115/1.4035485 History: Received July 25, 2016; Revised December 05, 2016

This paper presents an efficient impedance eduction method for grazing flow incidence tube by using a surrogating model along with the Wiener–Hopf method, which enables rapid acoustic predictions and effective impedance eductions over a range of parametric values and working conditions. The proposed method is demonstrated by comparing to the theoretical results, numerical predictions, and experimental measurements, respectively. All the demonstrations clearly suggest the capability and the potential of the proposed solver for parametric studies and optimizations of the lining methods.

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Grahic Jump Location
Fig. 1

The case setups (not to scale) for (a) NASA's grazing flow incidence tube experiments [7] and (b) the efficient, Wiener–Hopf based solver. A vortex sheet is presumably developed from the hard–soft interface to enable the modeling of the lining surface. The thickness of the vortex sheet is presumably infinitely thin, i.e., the kinetic displacement of the vortex sheet infinitely approaches the upper wall.

Grahic Jump Location
Fig. 2

Argand diagram of u shows the two complex half-planes, which are defined as: ±Imag(u−u0±)<∓ tan(ε)Real(u−u0±), respectively, where tan(ε)=Imag(u)/Real(u) and u0±=±1/(1±M0). The integral path inside the overlapped strip moves back to the horizontal axis with ε → 0, except a slight distortion [31] around the origin to avoid any possible singular point.

Grahic Jump Location
Fig. 4

Comparisons of the SPL results at y = 0, with (a) f = 1.0 kHz, M0 = 0, and Z = 0.46 + 0.03i and (b) f = 2.0 kHz, M0 = 0.079, and Z = 1.26 − 1.53i, where WH denotes the results of the Wiener–Hopf based solver, and numerical results are calculated by the commercial solver

Grahic Jump Location
Fig. 5

Comparisons of the SPL results across the test points at y = 0, where () NASA's experimental results, and (−) the analytical predictions from our solver. M0 = 0.335.

Grahic Jump Location
Fig. 6

The root-mean-squared differences between the experimental datasets and the predictions from our solver at various setups

Grahic Jump Location
Fig. 7

Comparison of the impedance eduction results at certain working conditions using the proposed Wiener–Hopf method and the computational method [7]

Grahic Jump Location
Fig. 3

Instantaneous sound pressure field at the frequencies between f = 0.5 kHz and 3.0 kHz with M0 = 0.079. The normalized pressure contour is shown between ±0.9 to make the largely attenuated waves in the lined region at x ≥ 0 still visible. The lining surface at x ≥ 0 is represented by the bold, dashed line, and for simplicity, which is only shown here in the top panel.




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