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
Highlights
Introduction and scopeDispersed multiphase systems are notoriously difficult to access by optical means
We describe the key ideas behind an empirical approach, which includes calibration in uniform suspensions (Sect. 2), followed by the application of inversion approaches in profiling non-uniform suspensions
Two cases are considered: one where the particle volume fraction profile resembles the radial migration of neutrally buoyant particles away from the axis (‘migrating’) and the other where the profile resembles the transport of dispersed particles heavier than the fluid (‘sedimenting’)
Summary
Experiments in Fluids (2021) 62:85 the continuous and dispersed phase) which leads to a quick extinction of light, for example in dense sprays (Coghe and Cossali 2012), fluidized beds (van Ommen and Mudde 2008) or bubbly flows (Mudde 2005). Semi-empirical approaches integrate the calibration data in the aforementioned rigorous, theoretical scattering models, i.e. the equation between the backscattered acoustic signal and the characteristics of the system. The calibration data are used directly to quantify volume fraction profiles in non-uniform suspensions (which is assumed to be composed of multiple, tiny, contiguous regions of uniform suspensions), without the aid of any theoretical scattering model. The approaches presented here are best applicable to (semi-)dilute suspensions and for size domains in the order of a few centimetres (laboratory-scale experiments and small/medium-scale industrial flows). In this manuscript, we describe the key ideas behind an empirical approach, which includes calibration in uniform suspensions We end by summarizing our key findings and discussing possible directions that can build up on the work presented here (Sect. 6)
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