APMR

Acoustical Porous Material Recipes

The tables reported below present, for a large number of models, the parameters they require to describe the visco-thermal dissipation effects when sound waves propagate through a porous medium.

This empirical model based on measurements results for fibrous materials should not be used without corrections proposed by Miki (see Delany-Bazley-Miki model below).

Parameter(s) | Usual notation |
---|---|

Static air flow resistivity | $\sigma$ |

This empirical model may be used to described fibrous material behaviors.

Parameter(s) | Usual notation |
---|---|

Static air flow resistivity | $\sigma$ |

The year he published his corrections of Delany-Bazley expressions (1990), Miki also presented a 3-parameter model.

Parameter(s) | Usual notation |
---|---|

Static air flow resistivity | $\sigma$ |

Open porosity | $\phi$ |

High frequency limit of the tortuosity | $\alpha_{\infty}$ |

This semi-phenomenological model may be used to described the dissipation behavior of fibrous materials or materials with arbitrary pore shapes without important pore section variations.

Parameter(s) | Usual notation |
---|---|

Static air flow resistivity | $\sigma$ |

Open porosity | $\phi$ |

High frequency limit of the tortuosity | $\alpha_{\infty}$ |

Viscous characteristic length | $\Lambda$ |

Thermal characteristic length | $\Lambda'$ |

This semi-phenomenological model may be used to described the dissipation behavior of materials with arbitrary pore shapes without important pore section variations.

Parameter(s) | Usual notation |
---|---|

Static air flow resistivity | $\sigma$ |

Open porosity | $\phi$ |

High frequency limit of the tortuosity | $\alpha_{\infty}$ |

Viscous characteristic length | $\Lambda$ |

Thermal characteristic length | $\Lambda'$ |

Static thermal permeability | $k'_{0}$ |

This semi-phenomenological model may be used to described the dissipation behavior of materials with arbitrary pore shapes and important pore section variations.

Parameter(s) | Usual notation |
---|---|

Static air flow resistivity | $\sigma$ |

Open porosity | $\phi$ |

High frequency limit of the tortuosity | $\alpha_{\infty}$ |

Viscous characteristic length | $\Lambda$ |

Thermal characteristic length | $\Lambda'$ |

Static thermal permeability | $k'_{0}$ |

Static viscous tortuosity | $\alpha_0$ |

Static thermal tortuosity | $\alpha_0'$ |

This semi-phenomenological model may be used to described the dissipation behavior of fibrous materials or materials with arbitrary pore shapes without important pore section variations.

Parameter(s) | Usual notation |
---|---|

High frequency limit of the dynamic density | $\rho_{\infty}$ |

Vorticity-mode relaxation time | $\tau_{\textrm{vor}}$ |

High frequency limit of the bulk modulus | $K_{\infty}$ |

Entropy-mode relaxation time | $\tau_{\textrm{ent}}$ |