Sound propagation in porous media : upscaling methods,
optimization and validation
Citation for published version (APA):
Vafadari Komarolia, R., Dommelen, van, J. A. W., Geers, M. G. D., & Roozen, N. B. (2010). Sound propagation in porous media : upscaling methods, optimization and validation. Poster session presented at Mate Poster Award 2010 : 15th Annual Poster Contest.
Document status and date: Published: 01/01/2010 Document Version:
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Mechanics of Materials
Sound Propagation in Porous Media:
Upscaling Methods, Optimization and
Validation
R. Vafadari, J. A. W. van Dommelen, M. G. D. Geers, N. B. Roozen
/department of mechanical engineering
Introduction
Noise reduction is a key issue for High-tech and high precision instruments. To reduce the noise levels emitted by internal or external sources, porous materials can be used for acoustic shielding. The acoustic wave penetrates into the pore network, and part of its energy is dissipated as heat by viscous friction and thermal-elastic damping, material mechanical damping and Helmholtz type resonators [1]. Therefore acoustic properties of porous materials are highly sensitive to geometrical and mechan-ical properties of the microstructure.
Objective
The objective of this work is building relationships between mi-croscopic and mami-croscopic acoustic properties of porous mate-rials, based on physical models of geometrical features and ma-terial characterizations of the porous medium at micro-level. In this way, it will be feasible to optimize the local geometry of the medium for improving its sound absorption performance.
Preliminary Strategy
- Acquisition and Modeling
The acquisition of the 3D local geometry of the porous medium is obtained by X-ray computed tomography at micro-level. Once the 3D observation at the microscale is made, either the direct meshed model or simplified interpretation of the complicated mi-crostructure can be produced.
Fig. 1 Local geometrical features acquisition based on X-ray com-puted tomography.
- Pore Scale Formulation
A micro-structural model based on the material characteristics and the local geometrical features aims at describing the de-tailed sound propagation phenomena. This model incorporates fluid-structure infarction and the pertinent thermodynamics. - Scale Bridging
A proper scale bridging method is needed to transfer the micro-scale response to macro-micro-scale at the least computational cost.
There are several upscaling methods utilized for poroelastic ma-terials in the literature like: volume averaging and asymptotic homogenization [2]. Also there are some phenomenological ap-proaches like Biot’s theory [3]. Unaddressed in the literature so far are multilevel finite element (FE2) scale bridging method and
statistical multi-scale modeling for wave propagation in porous media.
- Validation
To validate the reliability of the multi-scale scheme, numerical simulation results will be compared with experimental data. To this end, the acoustic absorption coefficient of the sample is measured using an impedance tube (standing wave or Kundt’s tube) [4].
Fig. 2 Sample placed in a standing wave tube, where sound absorption as a function of frequency is measured.
- Optimization
The validated multi-scale scheme can be applied for microstruc-ture optimization of highly porous materials.
Challenges
Computational Resource Extremely large number of ele-ments, due to complex microstructure and considering air gaps as the second phase.
Multi-scale Scheme Resolving time-scale details (frequency dependency) and considering boundary effects on micro-macro bridging.
Macro-model Based Optimization Design variables determi-nation, Design space reduction and Optimal sequencing of multilayered covers.
References:
[1] Lu, T.J., Hess, A., Ashby, M.F.: J. Applied Physics, 1999, 85, 41-52.
[2] Gilbert, R.P., Mikelic, A.: Nonlinear Analysis, 2000, 40, 185-211. [3] Biot, M.A.: J. Acoust. Soc. Am., 1962, 34, 1254-1264.
[4] Song, B.H., Bolton, J.S.: J. Acoust. Soc. Am., 2000, 107, 1131-1152.