Theoretical and experimental investigation of ultrasound propagation in packed beds

Karakaş, Zeynep
Ultrasound propagation through porous medium is investigated theoretically and experimentally in this study. Allowing measurements with opaque medium, giving fast measurements, requiring low cost and being non-invasive make the use of ultrasound based techniques convenient. Propagation of sound is directly related to the physical properties of a porous medium such as porosity, bulk modulus of medium, density of medium, particle size and physical properties of sound such as frequency. Therefore, it becomes possible to characterize a porous medium by using ultrasonic techniques provided that useful models capturing the sound propagation through such medium are readily available. Newton – Laplace equation is available for the investigation of ultrasound propagation through porous medium. According to Newton-Laplace equation, as porosity increases, sound velocity shows a negative dispersion as expected. Since this equation includes only the bulk modulus, density and porosity, dependence of the sound speed on different characteristics of porous medium, such as particle size, cannot be captured. Therefore, Biot model is used to investigate frequency effect on sound speed. In Biot model, frequency range is in between 1 to 200 kHz for water saturated medium sand medium in which wavelength to grain size ratio is changing between 375 and 18.75. For the water saturated glass beads media, lower limit of frequency again set as 1 kHz but upper limit is changing due to wavelength to grain size ratio. For that reason, upper limits of frequency are selected as 400 kHz, 1 MHz and 3.5 MHZ, where wavelength to grain size ratio are 3.75, 2.14 and 1.6, for the porous media with size of grains 1 mm, 700 microns and 300 microns, respectively. In all porous media, phase velocity shows positive dispersion. Also investigation of attenuation coefficient shows that it increases with frequency up to a value; however it starts to decrease from that point. Since decrease in attenuation coefficient is an unexpected results, it is concluded that Biot model is not applicable for high frequency values. That’s why experimental studies are needed to be conducted for the investigation of high frequency effect on sound velocity. Frequency values, f, used in the experiments are 1 MHz, 2 MHz and 4 MHz. Size of medium sand is 400 microns and glass beads are 1 mm, 700 microns and 300 microns. In all cases, wavelength to grain size ratio is very small which means value of wavelength is similar to grain size. Even for the frequency value of 4 MHz, grain size values are larger than wavelength. It is observed that phase velocity shows negative dispersion for each medium. Opposite to literature, deviation in sound speed has the lowest value for the medium with the highest grain size. Similarly, in contrast to literature, frequency dependency has the lowest value in the medium with the highest grain size. This is because of this medium having the higher grain size than wavelength.


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Citation Formats
Z. Karakaş, “Theoretical and experimental investigation of ultrasound propagation in packed beds,” M.S. - Master of Science, Middle East Technical University, 2016.