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Time domain modelling of sound attenuation in porous materials

Full details of EPSRC grant

Research team: Diego Turo, Olga Umnova

Summary from final report

The main aim of this project was to develop a reliable and computationally robust time domain model which describes propagation of acoustic pulses of different durations and amplitudes in rigid porous materials.

The main outcomes of the project are the following:

  1. We have developed a semi-empirical relaxational model for low amplitude sound propagation in rigid porous materials. It is based on two simple pore geometries (cylindrical pores of two different sizes in "parallel" and "in series") and is able to approximate porous materials with the whole range of shape factors. The new model requires a usual set of macroscopical independently measurable material parameters and can be analytically formulated in time domain. The numerical procedure has been developed to effectively solve the time domain equations which account for both viscous and thermal interactions of sound with porous materials. It has been demonstrated that the model provides an excellent agreement with the data for both long and short pulses. It is proven to be especially useful for the materials with shape factors very different from unity, i.e. when there are pores with very different characteristic sizes. This fact makes the model suitable for the naturally occured granular porous materials like for instance gravel where shape factor value is higher than 10.
  2. We have developed a semi-empirical time domain model to describe high amplitude sound propagation in porous materials. In this case the properties of the material change with the amplitude, i.e. it can become strongly nonlinear. The major advantage of the new model is that it incorporates both viscous and memory effects and so is suitable for both long and short pulses interacting with rigid porous material. To validate the model we have performed a series of measurements using pulses generated in a shock tube and with a sparker source. The pulse durations were ranging from several microseconds to tens of milliseconds to cover different regimes of sound interaction with porous materials. The amplitudes of the pulses were in the range from 100Pa to 40kPa. It has been demonstrated that the new model has a significant advantage over the others for short pulses of moderate amplitude when both Forchheimer's nonlinearity and the memory effects have to be accounted for simultaneously.

Journal publications

  • O.Umnova, D.Turo “Time domain formulation of the equivalent fluid model for rigid porous materials”, Journal of the Acoustical Society of America, 125, 1860-1863 (2009).
  • D.Turo, O.Umnova “Time domain modelling of sound propagation in porous media and the role of shape factors”, Acta Acustica united with Acustica, 96, 225-238 (2010).
  • D.Turo, O.Umnova “Influence of Forchheimer’s nonlinearity and transient effects on pulse propagation in air saturated rigid granular materials”, Journal of the Acoustical Society of America, 134, 4763-4774 (2013).