Comparing heat exchangers of thermacoustic prime movers with a Van der Pol model

ORAL

Abstract

A thermoacoustic standing-wave prime mover is a self-sustained oscillator whose initial growth of acoustic pressure into amplitude saturation can be modeled by the Van der Pol equation. The nonlinear Van der Pol equation is calculated computationally, using 4$^{th}$ order Runge-Kutta. The Van der Pol model gives quantitative loss and gain parameters, when using a best-fit with experimental data. The engines tested in this study have an average frequency of 2700 Hz, which suggests that the first second of oscillations when using the Van der Pol model can reveal information about the steady-state performance of the device. This model is applied to studying the effect of different heat exchanger sizes. All sixteen possible permutations were tested using different copper wire mesh dimensions: 24X24, 40X40, 60X60, and 80X80 for the hot and cold heat exchangers (where {\#}{\#}X{\#}{\#} indicates wires per inch). Plotting the steady-state acoustic pressure as a function of the gain term divided by the loss term shows roughly, a linear relationship. The engine with the highest gain term and smallest loss term was using 80X80 for the hot heat exchanger combined with the 24X24 for the cold heat exchanger and is consistent with the highest steady-state pressure achieved. The modeling process has been very successful and fits the Van der Pol equation.

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Authors

  • I. Cox

    Utah Valley University

  • Andrew Polemi

    Utah State University, Brigham Young University, University of Pennsylvania, Lawrence Livermore National Laboratory, Los Alamos National Laboratory, High Altitude Observatory, University of Colorado at Boulder, Massachutes Institute of Technology, Utah Valley University, University of New Hampshire, Applied Physics Laboratory, Johns Hopkins University, University of Montana, Southwest Research Institute, University of Southern California, Lockheed Martin Advanced Technology Center, University of Chicago, Massachusetts Institute of Technology, SciPrint.org, Centre National de la Recherche Scientifique, Colorado State University, V. Alecsandri College, Bacau, Romania, Colorado School of Mines, National Renewable Energy Laboratory, Utah State University, Department of Physics, Brigham Young University, Provo, Huntsman Cancer Institute, Brigham Young University - Idaho, University of Arizona, Florida State University, Weber State University, Brigham Young University - Provo, New Mexico State University, Colorado State University, Fort Collins, CO 80523

  • Andrew Polemi

    Utah State University, Brigham Young University, University of Pennsylvania, Lawrence Livermore National Laboratory, Los Alamos National Laboratory, High Altitude Observatory, University of Colorado at Boulder, Massachutes Institute of Technology, Utah Valley University, University of New Hampshire, Applied Physics Laboratory, Johns Hopkins University, University of Montana, Southwest Research Institute, University of Southern California, Lockheed Martin Advanced Technology Center, University of Chicago, Massachusetts Institute of Technology, SciPrint.org, Centre National de la Recherche Scientifique, Colorado State University, V. Alecsandri College, Bacau, Romania, Colorado School of Mines, National Renewable Energy Laboratory, Utah State University, Department of Physics, Brigham Young University, Provo, Huntsman Cancer Institute, Brigham Young University - Idaho, University of Arizona, Florida State University, Weber State University, Brigham Young University - Provo, New Mexico State University, Colorado State University, Fort Collins, CO 80523