Ultrasonic particle volume fraction profiling: an evaluation of empirical approaches

Abstract

We discuss empirical techniques to extract quantitative particle volume fraction profiles in particle-laden flows using an ultrasound transducer. A key step involves probing several uniform suspensions with varying bulk volume fractions from which two key volume fraction dependent calibration parameters are identified: the peak backscatter amplitude (acoustic energy backscattered by the initial layer of the suspension) and the amplitude attenuation rate (rate at which the acoustic energy decays with depth owing to scattering losses). These properties can then be used to reconstruct spatially varying particle volume fraction profiles. Such an empirical approach allows circumventing detailed theoretical models which characterize the interaction between ultrasound and suspensions, which are not universally applicable. We assess the reconstruction techniques via synthetic volume fraction profiles and a known particle-laden suspension immobilized in a gel. While qualitative trends can be easily picked up, the following factors compromise the quantitative accuracy: (1) initial reconstruction errors made in the near-wall regions can propagate and grow along the reconstruction direction, (2) multiple scattering can create artefacts which may affect the reconstruction, and (3) the accuracy of the reconstruction is very sensitive to the goodness of the calibration. Despite these issues, application of the technique to particle-laden pipe flows shows the presence of a core with reduced particle volume fractions in laminar flows, whose prominence reduces as the flow becomes turbulent. This observation is associated with inertia-induced radial migration of particles away from the pipe axis and is observed in flows with bulk volume fractions as high as 0.08. Even transitional flows with low levels of intermittency are not devoid of this depleted core. In conclusion, ultrasonic particle volume fraction profiling can play a key complementary role to ultrasound-based velocimetry in studying the internal features of particle-laden flows. Graphic abstract

Ultrasound imaging velocimetry in particle-laden flows: counteracting attenuation with correlation averaging

“…An example where this might not hold true is when particle migration occurs. At low Reynolds numbers for semi-dilute suspensions, inertial migration has been reported (Ardekani et al 2018;Dash et al 2021;Yousefi et al 2021). We compare SNR patterns in Fig.…”

“…In this section, we incorporate a simple, lumped model of ultrasonic backscattering in a suspension, which we evaluated in an earlier study (Dash et al 2021), into the cross-correlation theory developed for single-exposure, double-frame PIV systems (Keane and Adrian 1992). While Sect.…”

“…Experimental observations are complemented and supported by a modified cross-correlation theory for UIV in particle-laden flows. This modified theory is obtained by incorporating a lumped model of ultrasonic scattering in a suspension (Dash et al 2021) in the cross-correlation theory developed for PIV by Keane and Adrian (1992). This allows us to form heuristic arguments on the performance of UIV for particle-laden flows.…”

Characterizing Flocculated Mineral Sediments with Acoustic Backscatter, Using Solid and Hybrid Scattering Models

“…Additionally, inversion methods are increasingly being applied to derive mean size or concentration profiles, both for complex sediments in estuarine environments 29−32 and industrially, 6,33,34 using either a single frequency 4 or dualfrequency inversion methods. 20 The advantage of multifrequency methods are that they can reduce numerical instabilities in the far field.…”

“…Additionally, inversion methods are increasingly being applied to derive mean size or concentration profiles, both for complex sediments in estuarine environments − and industrially, ,, using either a single frequency or dual-frequency inversion methods . The advantage of multifrequency methods are that they can reduce numerical instabilities in the far field. , However, a more complete understanding of the frequency ratio is required, and the concentration limitations of these inversions for flocculated systems are often unknown.…”