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

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A quantitative analysis of two imaging modalities, shadowgraphy and x-ray imaging, is presented in the framework of void fraction determination. The need for this arises from the fact that shadowgraphs are sometimes utilized to quantify void fraction profiles, which is an unproven method. Time-averaged x-ray images are used to evaluate the performance of the time-averaged shadowgraphs. The case of a cavitating flow through an axisymmetric converging-diverging nozzle (‘venturi’) is considered, for three separate cavitation numbers. The complex nature of the cavitating flow through the venturi manifests itself in the occurrence of three distinct regimes: a swarm of tiny bubbles; a large, coalesced cavity near the wall; and a drifting/collapsing cavity. The flow regime governs the performance of shadowgraphy for void fraction determination, with two of the three regimes deemed acceptable for shadowgraphy. The quantitative comparison exemplifies that sole reliance on shadowgraphy may lead one to draw improper conclusions on the void fraction distributions, even at a qualitative level.

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