A simple scattering model for measuring particle mass fractions in multiphase flows

Abstract

In this paper we present a simple theoretical model of how pulsed ultrasound is attenuated by the particles in a solid/liquid flow. The theoretical model is then used to predict the attenuation of sound, given the mass fraction, the density, and the size distribution of the solid particles.The model is verified experimentally for suspensions of 0-10% (by mass) Dolomite ((Ca,Mg)CO 3 ) particles and water. The experimental results show that the attenuation of sound due to particles varies linearly with mass fraction, and that the proposed theoretical model can be used to predict this attenuation. In all experiments the transmitter and receiver array were clamped onto the pipe wall, thus providing a completely non-invasive and non-intrusive measurement technique. Ó

Experimental validation of acoustic inversions for high concentration profiling of spherical particles, using broadband technology in the Rayleigh regime

“…With respect to the 212 μm glass particles results (Figure 5 (c)), there is a clear concentration limit at which the measured attenuation is no longer proportional to concentration. A similar concentration limit in transmission measurements has been observed by both Stolojanu and Prakash [17] and Atkinson and Kytömaa [36] for glass particles in water, as well as other authors for differing particle systems [23], [25], [56], [57] and is widely attributed to an increase in multiple scattering effects [54]. It is also noted that both authors [23], [32], observed an increase in this non-monotonic behaviour as ka increases towards unity, an effect also observed in the experimental results in Figure 5.…”

“…In general, because fitting of the model was not computationally intensive and was easily implemented using MATLAB, it is recommended that the NFCF method presented here is incorporated whenever a transducer calibration is performed for a given set of probes, if measurements in the nearfield are to be used for further analysis. This procedure would subsequently improve measurements in zones close to the transducer such as in pipe flow applications [8], [54] and when taking backscatter measurements in highly attenuating or concentrated dispersions [19], [55]. The gradient dG/dr values versus concentration are presented in Figure 5 for the three particle types, with dashed linear interpolations indicating the fits taken to calculate the attenuation coefficient (Eqn.…”

Ultrasonic detection of slurry ice flows

“…For a given pulser -receiver unit with set signal gain and damping, signal amplitudes are reliable and directly comparable. At low solid fractions, attenuation can be modelled as a function of the percentage of solids in the fluid [16].…”

Application of Airborne Sound Waves to Mass Transfer Enhancement

“…Thus, Landau and Lifshits (Landau & Lifshits,1986) derived a formula which suggests that the intensity of scattering,I s is proportional to the sixth power of d and fourth power of f for the case of rigid particles suspended in a gas. The reported dependences of I s on C o are linear for both the gaseous (Temkin, 1998) and liquid mediums (Carlson & Martinsson, 2002). Therefore, the intensity of scattering becomes significant only at higher frequencies, generally in the MHz range and/or at larger volume fractions of particulates.…”