### Abstract

It is widely known that losses due to viscous, thermal and molecular relaxation play an important role in sound propagation. Traditionally, acoustics is concerned with the treatment of the fluid as a (linear) continuum using macroscopic quantities such as velocity and pressure as dependent variables. However, the continuum model has its limitations and the model breaks down for Knudsen numbers (Kn) greater than roughly 0.05, where Kn is defined as the ratio of mean free path to wavelength. Particle or Boltzmann equation methods are necessary for, but not limited to, problems with Kn > 0.05. In our studies we have used a particle method, Bird's direct simulation Monte Carlo method, to study acoustics which allows us to simulate real gas effects for all values of Kn with a molecular model that continuum methods cannot offer. Direct simulation Monte Carlo allows us to explore acoustics at varying temperatures, molecular composition, Knudsen numbers, and amplitude. Our current simulations of gas mixtures have employed different methods to model the internal degrees of freedom in molecules and the exchange of translational, rotational and vibrational energies in collisions. One of these methods is the fully classical rigid-rotor/harmonic-oscillator model for rotation and vibration developed by Borgnakke and Larsen. A second takes into account the discrete quantum energy levels for vibration with rotation treated classically. This method gives a more realistic representation of the internal structure of diatomic and polyatomic molecules. In our studies, we have investigated the application of these methods with the direct simulation - at the molecular level - of the propagation of sound and its attenuation along with their dependence on temperature for diatomic nitrogen systems.

Original language | English (US) |
---|---|

Title of host publication | 14th International Congress on Sound and Vibration 2007, ICSV 2007 |

Pages | 2604-2611 |

Number of pages | 8 |

Volume | 3 |

State | Published - Dec 1 2007 |

Event | 14th International Congress on Sound and Vibration 2007, ICSV 2007 - Cairns, QLD, Australia Duration: Jul 9 2007 → Jul 12 2007 |

### Other

Other | 14th International Congress on Sound and Vibration 2007, ICSV 2007 |
---|---|

Country | Australia |

City | Cairns, QLD |

Period | 7/9/07 → 7/12/07 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Acoustics and Ultrasonics

### Cite this

*14th International Congress on Sound and Vibration 2007, ICSV 2007*(Vol. 3, pp. 2604-2611)

}

*14th International Congress on Sound and Vibration 2007, ICSV 2007.*vol. 3, pp. 2604-2611, 14th International Congress on Sound and Vibration 2007, ICSV 2007, Cairns, QLD, Australia, 7/9/07.

**Investigation of quantum and classical models for molecular relaxation using the direct simulation Monte Carlo method.** / Hanford, Amanda D.; O'Connor, Patrick D.; Long, Lyle Norman; Anderson, James B.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Investigation of quantum and classical models for molecular relaxation using the direct simulation Monte Carlo method

AU - Hanford, Amanda D.

AU - O'Connor, Patrick D.

AU - Long, Lyle Norman

AU - Anderson, James B.

PY - 2007/12/1

Y1 - 2007/12/1

N2 - It is widely known that losses due to viscous, thermal and molecular relaxation play an important role in sound propagation. Traditionally, acoustics is concerned with the treatment of the fluid as a (linear) continuum using macroscopic quantities such as velocity and pressure as dependent variables. However, the continuum model has its limitations and the model breaks down for Knudsen numbers (Kn) greater than roughly 0.05, where Kn is defined as the ratio of mean free path to wavelength. Particle or Boltzmann equation methods are necessary for, but not limited to, problems with Kn > 0.05. In our studies we have used a particle method, Bird's direct simulation Monte Carlo method, to study acoustics which allows us to simulate real gas effects for all values of Kn with a molecular model that continuum methods cannot offer. Direct simulation Monte Carlo allows us to explore acoustics at varying temperatures, molecular composition, Knudsen numbers, and amplitude. Our current simulations of gas mixtures have employed different methods to model the internal degrees of freedom in molecules and the exchange of translational, rotational and vibrational energies in collisions. One of these methods is the fully classical rigid-rotor/harmonic-oscillator model for rotation and vibration developed by Borgnakke and Larsen. A second takes into account the discrete quantum energy levels for vibration with rotation treated classically. This method gives a more realistic representation of the internal structure of diatomic and polyatomic molecules. In our studies, we have investigated the application of these methods with the direct simulation - at the molecular level - of the propagation of sound and its attenuation along with their dependence on temperature for diatomic nitrogen systems.

AB - It is widely known that losses due to viscous, thermal and molecular relaxation play an important role in sound propagation. Traditionally, acoustics is concerned with the treatment of the fluid as a (linear) continuum using macroscopic quantities such as velocity and pressure as dependent variables. However, the continuum model has its limitations and the model breaks down for Knudsen numbers (Kn) greater than roughly 0.05, where Kn is defined as the ratio of mean free path to wavelength. Particle or Boltzmann equation methods are necessary for, but not limited to, problems with Kn > 0.05. In our studies we have used a particle method, Bird's direct simulation Monte Carlo method, to study acoustics which allows us to simulate real gas effects for all values of Kn with a molecular model that continuum methods cannot offer. Direct simulation Monte Carlo allows us to explore acoustics at varying temperatures, molecular composition, Knudsen numbers, and amplitude. Our current simulations of gas mixtures have employed different methods to model the internal degrees of freedom in molecules and the exchange of translational, rotational and vibrational energies in collisions. One of these methods is the fully classical rigid-rotor/harmonic-oscillator model for rotation and vibration developed by Borgnakke and Larsen. A second takes into account the discrete quantum energy levels for vibration with rotation treated classically. This method gives a more realistic representation of the internal structure of diatomic and polyatomic molecules. In our studies, we have investigated the application of these methods with the direct simulation - at the molecular level - of the propagation of sound and its attenuation along with their dependence on temperature for diatomic nitrogen systems.

UR - http://www.scopus.com/inward/record.url?scp=84881436252&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84881436252&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781627480000

VL - 3

SP - 2604

EP - 2611

BT - 14th International Congress on Sound and Vibration 2007, ICSV 2007

ER -