Dynamical Systems Analysis of Thermoacoustics Stacks

ORAL

Abstract

Thermoacoutics is the science of interconversion between disorganized heat energy and organized sound energy. The effect was observed centuries ago with ceremonial rice cookers in China and may be easily observed by heating a wire mesh in a pipe. Time series gas pressures may be measured with a piezoelectric sensor embedded in the resonator of a thermoacoustic engine. The emergent resonant frequency of the sound produced depends on the working fluid and dimensions of the apparatus. A plot of time series data reveals an initial region of random pressure variation followed by a region of growing pressure amplitude together with interspersed regions of random and chaotic motion. Thermoacoustics has traditionally been modeled using fluid dynamics and acoustics theory. The purpose of the research reported here is to explore modeling thermoacoustics phenomena using the analysis tools of dynamical systems theory. This approach is capable of describing various regions of organized and disorganized behavior and produces mathematical models designed to describe observed data. The time series data suggest a sigmoid growth curve moderated by a periodic oscillation model. We have assumed a simple logistic growth curve having a single adjustable parameter (representing growth rate) multiplied by a simple sine curve having an observed resonant frequency of 2.28 kHz. It is found that a nonlinear least squares fit of the logistic/sine model parameters reproduces the observed behavior of the various regions reasonably well.

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Authors

  • Robert Stoddard

    Utah Valley University

  • William Stockwell

    Logan High School, University of Tsukuba, Department of Physics, University of Texas at El Paso, El Paso, TX, Division of Engineering, Mayo Clinic, Rochester, MN, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Utah Valley University, University of New Mexico, Brigham Young University, Moxtek, INC, New Mexico State University, Oak Ridge National Laboratory, Oak Ridge TN 37830, USA, Los Alamos National Laboratory, Argonne National Laboratory, Embry-Riddle Aeronautical University, University of Newcastle, University of Sydney, Brigham Young University Provo, Rice University, Perimeter Institute and University of Guelph, University of Reims Champagne-Ardenne, France, Texas A&M University, University of Illinois at Urbana-Champaign, University of Valencia, Spain, None, University of Texas at El Paso, Universidad Simon Bolivar, Universidad Autonoma de Ciudad Juarez, Brigham Young University - Provo, Morgan High School - Morgan, UT, Utah State University, University of Tsukaba, Chemistry Research Center, US Air Force Academy, USAFA, JILA, University of Colorado Boulder, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, El Paso, TX, Department of Orthopedics, Mayo Clinic, Rochester, MN, Colorado State University, National Research Tomsk Polytechnic University \& New Mexico State University,, National Institute of Standards and Technology Center for Neutron Research, Oak Ridge National Laboratory, Huazhong University of Science and Technology, U of Utah, NMSU, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Chemical Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA, INM - Leibniz Institute for New Materials, Saarbrucken, Germany, Department of Physics, The University of Texas at El Paso, El Paso, Texas, 7996, UTEP, Arizona State University, The University of Texas at El Paso, none, National Renewable Energy Laboratory, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, Division of Engineering, Mayo Clinic, Department of Neurologic Surgery, Mayo Clinic, Department of Physics & Astronomy, Texas A&M University, Commerce,TX-75428, USA., INFN, Sezione di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy, Texas A&M University Commerce, Commerce, Texas-75429, Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, Texas 75429, USA, Cyclotron Institute, Texas A&M University, College Station, Texas 77843, USA, Department of Physics, University of Texas at El Paso, University of Delaware, IIT INDORE, UT AUSTIN, Idaho Accelerator Center, Brigham Young University, Physics and Astronomy, Univesidad de Guanajuato, Fermilab, École Polytechnique Fédérale de Lausanne, RadiaSoft, LLC, Weber State University, University of Texas at Dallas, National High Magnetic Field Laboratory, University of Texas Southwestern Medical Center, University of Alabama in Huntsville, Marshall Space Flight Center, NASA, Howard University

  • William Stockwell

    Logan High School, University of Tsukuba, Department of Physics, University of Texas at El Paso, El Paso, TX, Division of Engineering, Mayo Clinic, Rochester, MN, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Utah Valley University, University of New Mexico, Brigham Young University, Moxtek, INC, New Mexico State University, Oak Ridge National Laboratory, Oak Ridge TN 37830, USA, Los Alamos National Laboratory, Argonne National Laboratory, Embry-Riddle Aeronautical University, University of Newcastle, University of Sydney, Brigham Young University Provo, Rice University, Perimeter Institute and University of Guelph, University of Reims Champagne-Ardenne, France, Texas A&M University, University of Illinois at Urbana-Champaign, University of Valencia, Spain, None, University of Texas at El Paso, Universidad Simon Bolivar, Universidad Autonoma de Ciudad Juarez, Brigham Young University - Provo, Morgan High School - Morgan, UT, Utah State University, University of Tsukaba, Chemistry Research Center, US Air Force Academy, USAFA, JILA, University of Colorado Boulder, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, El Paso, TX, Department of Orthopedics, Mayo Clinic, Rochester, MN, Colorado State University, National Research Tomsk Polytechnic University \& New Mexico State University,, National Institute of Standards and Technology Center for Neutron Research, Oak Ridge National Laboratory, Huazhong University of Science and Technology, U of Utah, NMSU, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Rochester, MN, Chemical Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA, INM - Leibniz Institute for New Materials, Saarbrucken, Germany, Department of Physics, The University of Texas at El Paso, El Paso, Texas, 7996, UTEP, Arizona State University, The University of Texas at El Paso, none, National Renewable Energy Laboratory, Division of Engineering, Department of Neurologic Surgery, Mayo Clinic, Department of Physics, Border Biomedical Research Center, University of Texas at El Paso, Division of Engineering, Mayo Clinic, Department of Neurologic Surgery, Mayo Clinic, Department of Physics & Astronomy, Texas A&M University, Commerce,TX-75428, USA., INFN, Sezione di Pisa, Largo Pontecorvo 3, 56127 Pisa, Italy, Texas A&M University Commerce, Commerce, Texas-75429, Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, Texas 75429, USA, Cyclotron Institute, Texas A&M University, College Station, Texas 77843, USA, Department of Physics, University of Texas at El Paso, University of Delaware, IIT INDORE, UT AUSTIN, Idaho Accelerator Center, Brigham Young University, Physics and Astronomy, Univesidad de Guanajuato, Fermilab, École Polytechnique Fédérale de Lausanne, RadiaSoft, LLC, Weber State University, University of Texas at Dallas, National High Magnetic Field Laboratory, University of Texas Southwestern Medical Center, University of Alabama in Huntsville, Marshall Space Flight Center, NASA, Howard University