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Technical Brief

Synthetic Jet Actuator Cavity Acoustics: Helmholtz Versus Quarter-Wave Resonance

[+] Author and Article Information
Tyler Van Buren

Mechanical and Aerospace Engineering,
Princeton University,
Princeton, NJ 08544

Edward Whalen

Boeing Research and Technology,
Hazelwood, MO 63042

Michael Amitay

Professor
Mechanical Aerospace and Nuclear Engineering,
Center for Flow Physics and Control,
Rensselaer Polytechnic Institute,
Troy, NY 12180

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 25, 2014; final manuscript received February 20, 2015; published online April 27, 2015. Assoc. Editor: Theodore Farabee.

J. Vib. Acoust 137(5), 054501 (Oct 01, 2015) (5 pages) Paper No: VIB-14-1358; doi: 10.1115/1.4030216 History: Received September 25, 2014; Revised February 20, 2015; Online April 27, 2015

The impact of cavity geometry on the source of acoustic resonance (Helmholtz or quarter-wave) for synthetic jet type cavities is presented. The cavity resonance was measured through externally excited microphone measurements. It was found that, for pancake-shaped cavities, the Helmholtz resonance equation was inadequate (off by more than 130%) at predicting the acoustic cavity resonances associated with synthetic jet actuation, whereas a two-dimensional quarter-wave resonance was accurate to 15%. The changes in the geometry (cavity diameter, cavity height, and orifice length) could alter the cavity resonance by up to 50%, and a finite element solver was accurate at predicting this resonance in all cases. With better knowledge of the phenomena governing the acoustic resonance, prediction of the cavity resonance can become more accurate and improvements to current prediction tools can be made.

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Figures

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Fig. 1

Volume of fluid inside an ideal Helmholtz resonator (a) and a representative pancake-shape cavity (b) used in the experiments

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Fig. 2

Schematics of the SJA apparatus with common dimensions labeled. Two microphones (one inside and outside of the cavity) measured the output of an external speaker (not to scale).

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Fig. 3

Power spectral density of the microphones inside and outside of the cavity as they vary with frequency for apparatus A (a) with geometry: dc = 40 mm, hc = 1 mm, hn = 3 mm, lo = 6 mm, ho = 1 mm, and apparatus B (b) with geometry: dc = 80 mm, hc = 3 mm, hn = 3 mm, lo = 12 mm, ho = 1 mm. The peak of the inner and outer ratio, which is the cavity resonance, is marked with a dashed (apparatus A) and solid (apparatus B) line. SJA performance compared with cavity resonance results superimposed (dashed and solid lines) for the same cavity geometries. Taken from Van Buren [6], Fig. 3.28.

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Fig. 4

Differential pressure distribution of the first resonance mode different orifice lengths (a–c) and cavity heights (d–f). For the varying orifice length cases, lo = 3 mm (a), 9 mm (b), and 15 mm (c), at hn = 3 mm, ho = 1 mm, hc = 3 mm, and dc = 80 mm. For the varying cavity height cases, hc = 2 mm (d), 6 mm (e), and 10 mm (f) at hn = 3 mm, ho = 1 mm, lo = 12 mm, and dc = 80 mm.

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Fig. 5

The variation of the cavity resonance frequency with orifice length. Experimental results (symbols), acoustics FEM simulation (black lines), quarter-wave resonance (dark gray lines), and the Helmholtz resonance prediction (light gray lines) for a selected geometry of apparatus A: hc = 1 mm, hn = 2 mm, and apparatus B: hc = 3 mm, hn = 2 mm are presented.

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Fig. 6

Change in normalized cavity resonance frequency with orifice half-length and cavity height for apparatus A (a) and B (b) with common neck lengths of hn = 3 mm and orifice widths ho = 1 mm. The surface shade depicts ratio of measured frequency, fcav to Helmholtz, fH. Note that apparatus A and B are presented on different scales of hc/ho and lo/ho due to a limited range of available geometries.

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