0
Research Papers

Resonant Gas Oscillations in a Linear Area Variation Cavity: Rectangular Versus Circular Cross Section

[+] Author and Article Information
Sonu K. Thomas

Department of Aerospace Engineering,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: thomas.sonu91@gmail.com

T. M. Muruganandam

Associate Professor
Department of Aerospace Engineering,
Indian Institute of Technology Madras,
Chennai 600036, India
e-mail: murgi@ae.iitm.ac.in

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 3, 2015; final manuscript received July 3, 2015; published online October 20, 2015. Assoc. Editor: Theodore Farabee.

J. Vib. Acoust 138(1), 011006 (Oct 20, 2015) (5 pages) Paper No: VIB-15-1070; doi: 10.1115/1.4031521 History: Received March 03, 2015; Revised July 03, 2015

Resonant gas oscillations in a linear area variation closed cavity are investigated, for two duct cross sections: rectangular and circular. The resonance frequencies were similar for both the ducts. Increased drive amplitude produced higher distortions in the waveform. It was found that both resonators exhibited commensurate behavior. This is opposed to noncommensurate behavior observed in nonuniform circular cross section resonators. The rectangular section duct had higher energy than circular section duct, in second harmonic for the same drive amplitude. The results reveal that in order to achieve shockless high amplitude pressure oscillations in a duct, both nonuniform area variation and circular cross section are required.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Ilgamov, M. A. , Zaripov, R. G. , Galiullin, R. G. , and Repin, V. R. , 1996, “ Nonlinear Acoustic Oscillations of a Column of Gas in a Tube,” ASME Appl. Mech. Rev., 49(3), pp. 137–154. [CrossRef]
Saenger, R. A. , and Hudson, G. E. , 1960, “ Periodic Shock Waves in Resonating Gas Columns,” J. Acoust. Soc. Am., 32(8), pp. 961–970. [CrossRef]
Nguyen, N. T. , and Wereley, S. T. , 2002, Fundamentals and Applications of Microfluidics, Artech House, Boston.
Nguyen, N. T. , Huang, X. Y. , and Toh, K. C. , 2002, “ MEMS-Micropumps: A Review,” ASME J. Fluids Eng., 124(2), pp. 384–392. [CrossRef]
Ockendon, H. , and Ockendon, J. R. , 2001, “ Nonlinearity in Fluid Resonances,” Meccanica, 36(3), pp. 297–321. [CrossRef]
Mortell, M. P. , and Seymour, B. R. , 2004, “ Nonlinear Resonant Oscillations in Closed Tubes of Variable Cross-Section,” J. Fluid Mech., 519, pp. 183–199. [CrossRef]
Lawrenson, C. C. , Lipkens, B. , Lucas, T. S. , Perkins, D. K. , and Van Doren, T. W. , 1998, “ Measurement of Macrosonic Standing Wave in Oscillating Closed Cavities,” J. Acoust. Soc. Am., 104(2), pp. 623–636. [CrossRef]
Ilinskii, Y. A. , Lipkens, B. , Lucas, T. S. , Van Doren, T. W. , and Zabolotskaya, E. A. , 1998, “ Nonlinear Standing Waves in an Acoustical Resonator,” J. Acoust. Soc. Am., 104(5), pp. 2664–2674. [CrossRef]
Ilinskii, Y. A. , Lipkens, B. , and Zabolotskaya, E. A. , 2001, “ Energy Losses in an Acoustical Resonator,” J. Acoust. Soc. Am., 109(5), pp. 1859–1870. [CrossRef] [PubMed]
Hamilton, M. F. , Ilinskii, Y. A. , and Zabolotskaya, E. A. , 2001, “ Linear and Nonlinear Frequency Shifts in Acoustical Resonator With Varying Cross Section,” J. Acoust. Soc. Am., 110(1), pp. 109–119. [CrossRef]
Sugimoto, N. , Masuda, M. , Hashiguchi, T. , and Doi, T. , 2001, “ Annihilation of Shocks in Forced Oscillations of an Air Column in a Closed Tube,” J. Acoust. Soc. Am., 110(5), pp. 2263–2266. [CrossRef] [PubMed]
Sugimoto, N. , Masuda, M. , and Hashiguchi, T. , 2003, “ Frequency Response of Nonlinear Oscillations of Air Column in a Tube With an Array of Helmholtz Resonators,” J. Acoust. Soc. Am., 114(4), pp. 1772–1784. [CrossRef] [PubMed]
Masuda, M. , and Sugimoto, N. , 2005, “ Experiments of High-Amplitude and Shockfree Oscillations of Air Column in a Tube With Array of Helmholtz Resonators,” J. Acoust. Soc. Am., 118(1), pp. 113–123. [CrossRef] [PubMed]
Huang, P. T. , and Brisson, J. G. , 1997, “ Active Control of Finite Amplitude Acoustic Waves in a Confined Geometry,” J. Acoust. Soc. Am., 102(6), pp. 3256–3267. [CrossRef]
Li, X. , Finkbeiner, J. , Raman, G. , Danielsb, Ch. , and Steinetz, B. M. , 2004, “ Optimized Shapes of Oscillating Resonators for Generating High-Amplitude Pressure Waves,” J. Acoust. Soc. Am., 116(5), pp. 2814–2821. [CrossRef]
Cervenka, M. , and Bednarik, M. , 2013, “ On the Optimization of an Acoustic Resonator Shape With Respect to Acoustic Pressure Amplitude,” Acta Acust. Acust., 99(2), pp. 183–191. [CrossRef]
Cervenka, M. , and Bednarik, M. , 2014, “ Optimal Shaping of Acoustic Resonators for the Generation of High-Amplitude Standing Waves,” J. Acoust. Soc. Am., 136(3), pp. 1003–1012. [CrossRef] [PubMed]
Mortell, M. P. , and Seymour, B. R. , 1972, “ Pulse Propagation in a Nonlinear Viscoelastic Rod of Finite Length,” SIAM J. Appl. Math., 22, pp. 206–224. [CrossRef]
Luo, C. , Huang, X. Y. , and Nguyen, N. T. , 2005, “ Effect of Resonator Dimensions on Nonlinear Standing Waves,” J. Acoust. Soc. Am., 117(1), pp. 96–103. [CrossRef] [PubMed]
Luo, C. , Huang, X. Y. , and Nguyen, N. T. , 2007, “ Generation of Shock-Free Pressure Waves in Shaped Resonators by Boundary Driving,” J. Acoust. Soc. Am., 121(5), pp. 2515–2521. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Linear area variation resonator shapes: (a) rectangular cross section and (b) circular cross section where L = 200 mm and area at small end A1 = 1000 mm2 and area at large end A2 = 5500 mm2

Grahic Jump Location
Fig. 2

Schematic of the experimental apparatus

Grahic Jump Location
Fig. 3

Pressure waveforms for three different drive amplitudes (7.5, 22.5, and 31 V) for rectangular cross section (black) and circular cross section (gray) resonators

Grahic Jump Location
Fig. 4

Pressure waveforms at small end PA (solid line) and large end PB (dashed line), for rectangular cross section and circular cross section duct for 31 V driving voltage

Grahic Jump Location
Fig. 5

Pressure waveforms and its corresponding spectra at (a) 7.5 V, (b) 22.5 V, and (c) 31 V driving voltage. Data for rectangular section is in the left column and the circular section data is in the right.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In