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High-fidelity simulation of a standing-wave thermoacoustic–piezoelectric engine

Published online by Cambridge University Press:  26 October 2016

Jeffrey Lin ,
Carlo Scalo  and
Lambertus Hesselink
Jeffrey Lin*
Affiliation:
Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
Carlo Scalo
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Lambertus Hesselink
Affiliation:
Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: [email protected]
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Abstract

We have carried out wall-resolved unstructured fully compressible Navier–Stokes simulations of a complete standing-wave thermoacoustic–piezoelectric engine model inspired by the experimental work of Smoker et al. (J. Appl. Phys., vol. 111 (10), 2012, 104901). The model is axisymmetric and comprises a 51 cm long resonator divided into two sections: a small-diameter section enclosing a thermoacoustic stack and a larger-diameter section capped by a piezoelectric diaphragm tuned to the thermoacoustically amplified mode (388 Hz). The diaphragm is modelled with multi-oscillator broadband time-domain impedance boundary conditions (TDIBCs), providing higher fidelity over single-oscillator approximations. Simulations are first carried out to the limit cycle without energy extraction. The observed growth rates are shown to be grid convergent and are verified against a numerical dynamical model based on Rott’s theory. The latter is based on a staggered grid approach and allows jump conditions in the derivatives of pressure and velocity in sections of abrupt area change and the inclusion of linearized minor losses. The stack geometry maximizing the growth rate is also found. At the limit cycle, thermoacoustic heat leakage and frequency shifts are observed, consistent with experiments. Upon activation of the piezoelectric diaphragm, steady acoustic energy extraction and a reduced pressure amplitude limit cycle are obtained. A heuristic closure of the limit cycle acoustic energy budget is presented, supported by the linear dynamical model and the nonlinear simulations. The developed high-fidelity simulation framework provides accurate predictions of thermal-to-acoustic and acoustic-to-mechanical energy conversion (via TDIBCs), enabling a new paradigm for the design and optimization of advanced thermoacoustic engines.

JFM classification

Acoustics: Acoustics Mathematical Foundations: Computational methods Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Papers
Information
Journal of Fluid Mechanics , Volume 808 , 10 December 2016 , pp. 19 - 60
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Copyright
© 2016 Cambridge University Press 

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Lin et al. Movie 1

Instantaneous visualizations of fluid temperature (see colorbar) surrounding the stack, showing streaming of hot fluid out of the stack, and of high vorticity magnitude (white), showing entrance effects. Data taken under limit cycle conditions for temperature setting 5, grid-resolution/stack-type C/I.

Download Lin et al. Movie 1(Video)
Video 8.4 MB

Lin et al. Movie 2

Instantaneous visualizations of fluid temperature (see colorbar) surrounding the resonator area change, showing streaming of hot fluid, and of high vorticity magnitude (white), showing entrance effects. Data taken under limit cycle conditions for temperature setting 5, grid-resolution/stack-type C/I.

Download Lin et al. Movie 2(Video)
Video 1.4 MB