0
Research Papers

Onset of Oscillations in Traveling Wave Thermo-Acoustic-Piezo-Electric Harvesters Using Circuit Analogy and SPICE Modeling

[+] Author and Article Information
M. Nouh

Mechanical Engineering Department,
University of Maryland,
College Park, MD 20742

O. Aldraihem

Mechanical Engineering Department,
King Saud University,
Riyadh 11421, Saudi Arabia;
King Abdulaziz City of Science and Technology,
Space Research Institute,
Riyadh 11421, Saudi Arabia

A. Baz

Mechanical Engineering Department,
University of Maryland,
College Park, MD 20742
e-mail: baz@umd.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 29, 2013; final manuscript received July 16, 2014; published online August 8, 2014. Assoc. Editor: Qingze Zou.

J. Dyn. Sys., Meas., Control 136(6), 061005 (Aug 08, 2014) (10 pages) Paper No: DS-13-1045; doi: 10.1115/1.4028050 History: Received January 29, 2013; Revised July 16, 2014

Equations governing different physical fields such as mechanical, acoustical, and electrical are inherently similar. This enables mechanical, thermal, and acoustical networks to be fully described with analogous electric networks. For thermo-acoustic-piezo-electric (TAP) harvesters, such a modeling approach allows the whole system to be characterized in the electrical domain and facilitates the understanding of the underlying physics. In this paper, a traveling wave thermo-acoustic-piezoelectric (TWTAP) energy harvester is considered which converts thermal energy, such as solar or waste heat energy, directly into electrical energy without the need for any moving components. The input thermal energy generates a steep temperature gradient along a porous regenerator. At a critical threshold of the temperature gradient, self-sustained acoustic waves are developed inside an acoustic resonator. The associated pressure fluctuations impinge on a piezo-electric diaphragm, placed at the end of the resonator, to generate electricity. The acoustic pressure oscillations are amplified by a specially designed acoustic feedback loop that introduces appropriate phasing to make the pulsations take the form of traveling waves. The behavior of this TWTAP is modeled using electrical circuit analogy. The developed model combines the descriptions of the acoustic resonator, feedback loop, and the regenerator with the characteristics of the piezo-electric diaphragm. With the help of a simulation program with integrated circuit emphasis (SPICE) code, the developed electric circuit is used to analyze the system’s stability with regard to the input heat and hence predict the necessary temperature ratio required to establish the onset of self-sustained oscillations inside the harvester’s resonator. The predictions are compared with published results obtained using root locus and numerical methods and validated against experiments. This approach provides a very practical approach to the design of TAP energy harvesters both in the time and frequency domain. Such capabilities do not exist presently in the well-known design tool design environment for low-amplitude thermo-acoustic energy conversion (DeltaEC) developed at Los Almos National Laboratory which is limited to steady-state analysis. This is in contrast to the present approach which can be applicable to both steady as well as transient analysis.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Swift, G., 2002, Thermoacoustics: A Unifying Perspective for Some Engines and Refrigerators, Acoustical Society of America, American Institute of Physics Press, New York, Chaps. 1 and 8.
Swift, G., 1988, “Thermoacoustic Engines,” J. Acoust. Soc. Am., 84(4), pp. 1145–1180. [CrossRef]
Backhaus, S., and Swift, G., 2000, “A Thermoacoustic-Stirling Heat Engine: Detailed Study,” J. Acoust. Soc. Am., 107(6), pp. 3148–3166. [CrossRef] [PubMed]
Backhaus, S., and Swift, G., 1999, “A Thermoacoustic-Stirling Heat Engine,” Nature, 399, pp. 335–338. [CrossRef]
Hartley, R., 1951, “Electric Power Source,” U.S. Patent No. 2,549,464.
Marrison, W., 1958, “Heat-Controlled Acoustic Wave System,” U.S. Patent No. 2,836,033.
Ceperley, P. H., 1979, “A Pistonless Stirling Engine—The Traveling Wave Heat Engine,” J. Acoust. Soc. Am., 66, pp. 1508–1513. [CrossRef]
Ceperley, P. H., 1982, “Resonant Traveling Wave Engine,” U.S. Patent No. 4,355,517.
Feldman, K. T., Jr., 1968, “Review of the Literature on Sondhauss Thermoacoustic Phenomena,” J. Sound Vib., 7(1), pp. 71–82. [CrossRef]
Regan, T. F., Gerber, S. S., and Roth, M. E., 2004, “Development of a Dynamic, End-to-End Free Piston Stirling Convertor Model,” Glenn Research Center, Report No. NASA/TM—2004-212941.
Wakeland, R. S., 2000, “Use of Electrodynamic Drivers in Thermoacoustic Refrigerators,” J. Acoust. Soc. Am., 107(2), pp. 827–832. [CrossRef] [PubMed]
Tu, Q., Gusev, V., Bruneau, M., Zhang, C., Zhao, L., and Guo, F., 2006, “Experimental and Theoretical Investigation on Frequency Characteristic of Loudspeaker-Driven Thermoacoustic Refrigerator,” Cryogenics, 45, pp. 739–746. [CrossRef]
Fan, L., Zhang, S., and Wang, B., 2006, “Coupling Between Thermoacoustic Resonance Pipes and Piezoelectric Loudspeakers Studied by Equivalent Circuit Method,” J. Acoust. Soc. Am., 120(3), pp. 1381–1387. [CrossRef]
Tu, Q., Li, Q., Wu, F., and Guo, F. Z., 2003, “Network Model Approach for Calculating Oscillating Frequency of Thermoacoustic Prime Mover,” Cryogenics, 43, pp. 351–357. [CrossRef]
Aldraihem, O., and Baz, A., 2012, “Onset of Self-Excited Oscillations of Traveling Wave Thermo-Acoustic-Piezoelectric Energy Harvester Using Root-Locus Analysis,” ASME J. Vib. Acoust., 134(1), p. 011003. [CrossRef]
de Waele, A. T. A. M., 2009, “Basic Treatment of Onset Conditions and Transient Effects in Thermoacoustic Stirling Engines,” J. Sound Vib., 325, pp. 974–988. [CrossRef]
Nagel, L. W., and Pederson, D. O., 1973, “SPICE (Simulation Program With Integrated Circuit Emphasis),” University of California, Berkeley, Memorandum No. ERL-M382.
Martini, W. R., Johnson, R. P., and White, M. A., 1974, “Stirling Engine Power System and Coupler,” U.S. Patent No. 3,833,388.
Keolian, R. M., and Bastyr, K. J., 2006, “Thermoacoustic Piezoelectric Generator,” U.S. Patent No. 7,081,699.
Symko, O. G., Abdel-Rahman, E., Kwon, Y. S., Emmi, M., and Behunin, R., 2004, “Design and Development of High-Frequency Thermoacoustic Engines for Thermal Management in Microelectronics,” Microelectron. J., 35, pp. 185–191. [CrossRef]
Symko, O., and Abdel-Rahman, E., 2007, “High Frequency Thermoacoustic Refrigerator,” U.S. Patent No. 7,240,495.
Matveev, K. I., Wekin, A., Richards, C. D., and Shafrei-Tehrany, N., 2007, “On the Coupling Between Standing-Wave Thermoacoustic Engine and Piezoelectric Transducer,” ASME International Mechanical Engineering Congress and Exposition, IMECE2007, Seattle, WA, Nov. 11–15, Paper No. IMECE2007-41119. [CrossRef]
Smoker, J., Nouh, M., Aldraihem, O., and Baz, A., 2012, “Energy Harvesting From a Standing Wave Thermoacoustic-Piezoelectric Resonator,” J. Appl. Phys., 111(10), p. 104901. [CrossRef]
Nouh, M., Aldraihem, O., and Baz, A., 2012, “Energy Harvesting of Thermoacoustic-Piezo Systems With a Dynamic Magnifier,” ASME J. Vib. Acoust., 134(6), p. 061015. [CrossRef]
Nouh, M., O., Aldraihem, O., and Baz, A., 2013, “Analysis and Optimization of Thermoacoustic-Piezoelectric Energy Harvesters: An Electrical Circuit Analogy Approach,” Proceedings of the SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring, San Diego, CA, Mar. 10, Vol. 8688, p. 86880L. [CrossRef]
Zhao, D., and Chew, Y., 2012, “Energy Harvesting From a Convection-Driven Rijke-Zhao Thermoacoustic Engine,” J. Appl. Phys., 112(11), p. 114507. [CrossRef]
Zhao, D., 2013, “Waste Thermal Energy Harvesting From a Convection-Driven Rijke–Zhao Thermo-Acoustic-Piezo System,” Energy Convers. Manage., 66, pp. 87–97. [CrossRef]
Nilsson, J., and Riedel, S., 2011, Electric Circuits, 9th ed., Prentice Hall, Upper Saddle River, NJ, Chap. 4.
Roshwalb, A., 2011, “Traveling Wave Thermoacoustic-Piezoelectric Energy Harvester: Theory and Experiment,” M.S. thesis, University of Maryland, College Park, MD.
Ward, B., Clark, J., and Swift, G., 2012, “Design Environment for Low-Amplitude Thermoacoustic Energy Conversion DeltaEC,” Version 6.3b11, Users Guide, Los Alamos National Lab, Feb. 13, 2012, http://www.lanl.gov/thermoacoustics/

Figures

Grahic Jump Location
Fig. 2

Electric circuit equivalent of a TWTAP harvester

Grahic Jump Location
Fig. 3

Ltspice schematic of open-ended traveling wave thermo-acoustic engine

Grahic Jump Location
Fig. 4

Ltspice schematic of a TWTAP energy harvester

Grahic Jump Location
Fig. 5

Root locus plot for open-ended traveling wave thermo-acoustic engine [15]

Grahic Jump Location
Fig. 6

Stable, unstable and marginally stable pressure pulsations vt in the open-ended traveling wave engine obtained by (a) Laplace solution of governing differential equation and (b) Ltspice model

Grahic Jump Location
Fig. 7

Frequency response of the pressure vt of the open-ended resonator obtained through an AC sweep in Ltspice (resonant frequency ≈ 103 Hz)

Grahic Jump Location
Fig. 8

Magnitude and phase comparison of vc, I1, Iinput, and I4 in an open-ended traveling wave thermo-acoustic engine obtained via Ltspice

Grahic Jump Location
Fig. 9

Pressure drop across inertance Δvinert for an open-ended traveling wave thermo-acoustic engine obtained via Ltspice

Grahic Jump Location
Fig. 10

Root locus plot for a TWTAP harvester [15]

Grahic Jump Location
Fig. 11

Stable, unstable, and marginally stable pressure pulsations vt in a TWTAP harvester obtained by (a) Laplace solution of governing differential equation and (b) Ltspice model

Grahic Jump Location
Fig. 12

Frequency response of the pressure vt of the TWTAP harvester obtained through an AC sweep in Ltspice (resonant frequency ≈ 228 Hz)

Grahic Jump Location
Fig. 13

Magnitude and phase comparison of vc, I1, Iinput, and I4 in a TWTAP harvester obtained via Ltspice

Grahic Jump Location
Fig. 14

Pressure drop across inertance Δvinert for a TWTAP harvester obtained via Ltspice

Grahic Jump Location
Fig. 15

Effect of resonator length on (a) onset temperature ratio, (b) resonant frequency, and (c) dimensionless frequency for an open-ended traveling wave thermo-acoustic engine

Grahic Jump Location
Fig. 16

Effect of resonator length on (a) onset temperature ratio, (b) resonant frequency, and (c) dimensionless frequency for a TWTAP harvester

Grahic Jump Location
Fig. 17

Experimental prototype of a TWTAP harvester

Grahic Jump Location
Fig. 18

(a) Close-up images of the ambient heat exchanger and (b) the regenerator screen

Grahic Jump Location
Fig. 19

Hot end temperature and piezo-output voltage variation with time for the TWTAP harvester when (a)T≤Tonset and (b) T≥Tonset

Grahic Jump Location
Fig. 20

Electrical analog of the piezo-electric diaphragm

Grahic Jump Location
Fig. 21

Simplified electrical analog of the piezo-electric diaphragm

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