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Research Papers

Investigations on Wave Propagation of the Pressure Pulsation in a Helmholtz-Type Hydraulic Silencer With a Hemispherical Vessel

[+] Author and Article Information
Takayoshi Ichiyanagi

Mem. ASME
Department of Mechanical Systems Engineering,
National Defense Academy,
1-10-20 Hashirimizu, Yokosuka,
Kanagawa 239-8686, Japan
e-mail: ichiyana@nda.ac.jp

Tetsuya Kuribayashi

Graduate School of Science and Engineering,
National Defense Academy,
1-10-20 Hashirimizu, Yokosuka,
Kanagawa 239-8686, Japan

Takao Nishiumi

Department of Mechanical Systems Engineering,
National Defense Academy,
1-10-20 Hashirimizu, Yokosuka,
Kanagawa 239-8686, Japan

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 29, 2016; final manuscript received August 10, 2016; published online September 30, 2016. Assoc. Editor: Ronald N. Miles.

J. Vib. Acoust 139(1), 011003 (Sep 30, 2016) (8 pages) Paper No: VIB-16-1151; doi: 10.1115/1.4034618 History: Received March 29, 2016; Revised August 10, 2016

The Helmholtz-type hydraulic silencer is one of the most practical silencers for attenuating pressure pulsations in hydraulic systems owing to its simple structure and reasonable cost. Maximum attenuation performance can be attained at the resonance frequency in accordance with the principle of Helmholtz resonance. Therefore, it is extremely important to precisely determine the resonance frequency at the design stage. It was clarified in our previous study that the shape of the volume vessel affects the resonance frequency of the silencer because of the wave propagation of pressure pulsation inside the volume vessel. In this study, the attenuation characteristics and wave propagation in a silencer with a hemispherical vessel are investigated. A mathematical model that takes into account the propagation of a one-dimensional wave in the radial direction of the hemispherical vessel is proposed and compared with the step section approximation model and the classic lumped parameter model. Furthermore, the effectiveness of the theoretical analysis is verified by experiments wherein the dimensional specifications of the vessel and neck are adjusted.

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References

Figures

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Fig. 1

Wave propagation of pressure pulsation in a cylindrical vessel (a) conventional shape and (b) flat shape

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Fig. 2

Helmholtz-type hydraulic silencer with a hemispherical vessel

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Fig. 3

Helmholtz-type hydraulic silencer with a hemispherical vessel

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Fig. 4

Modeling concept for wave propagation and the step section approximation model of the hemispherical vessel in the Helmholtz-type hydraulic silencer

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Fig. 5

Influence of number of divisions of step cylindrical sections (n) on resonance frequency fr (D = 115 mm, d = 12 mm, l = 101 mm)

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Fig. 6

TL of the three mathematical models (D = 115 mm, d = 12 mm, l = 101 mm)

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Fig. 7

Deviation Δf of resonance frequency between the lumped parameter model and distributed parameter model (d = 12 mm) (a) deviation Δf versus diameter D of the hemispherical vessel (b) deviation Δf versus resonance frequency fr of the lumped parameter model

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Fig. 8

Schematic of the experimental apparatus

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Fig. 9

Hydraulic circuit and hemispherical vessel of the test silencer (a) overview of the test rig and (b) hemispherical vessel (D = 115 mm)

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Fig. 10

Example of TL characteristics of test silencers with neck No. 2 (d = 12 mm, l = 101 mm) (LP: lumped parameter model, DP: proposed distributed parameter model, and SSA: step section approximation model) (a) D = 80 mm, (b) D = 115 mm, and (c) D = 170 mm

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Fig. 11

Influence of vessel diameter D on attenuation characteristics (a) resonance frequency (fr) and (b) peak transmission loss (TLr)

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Fig. 12

Relationship between neck dimensional index ε and attenuation characteristics (D = 80 mm) (LP: lumped parameter model, DP: proposed distributed parameter model) (a) resonance frequency (fr) and (b) peak transmission loss (TLr)

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Fig. 13

Influence of the neck diameter d on attenuation characteristics (under the conditions ε = 3.20 mm and D = 115 mm) (LP: lumped parameter model and DP: proposed distributed parameter model) (a) resonance frequency (fr) and (b) peak transmission loss (TLr)

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