Lagrangian study of entrainment for confined vortex rings in dense suspensions using echo-LPT

An ultrasound-based Lagrangian particle tracking (echo-LPT) method is used to investigate path-dependent quantities for confined vortex rings in dense suspensions with volume fractions up to 40%. The echo-LPT measurement technique is successfully validated through a close comparison of the pixel displacements collected with established ultrasound image velocimetry methods. The carrier phase of the suspension is tracked through the vortex ring in transitional and turbulent circulation-based Reynolds numbers of \(Re_{\mathrm {\Gamma }}=2.4\) $R{e}_{\mathrm{\Gamma }}=2.4$ ,  \(4.2\times 10^{4}\) $4.2\times {10}^4$ . Furthermore, fluid transport and residence time are obtained using pathline extension techniques for entrained and recirculating particles in order to compare with traditional Eulerian analysis. The fluid transport and residence time results show that the entrained fluid originates from similar locations and generally indicate that there is no dependence or effect of changing volume fraction. These results show that the convective entrainment mechanisms for the forming vortex rings are insensitive to changes in \(Re_{\mathrm {\Gamma }}\) $R{e}_{\mathrm{\Gamma }}$ and volume fraction. Exceptions are found for the volume fraction 40% cases where increases in nonlinear fluid behaviour and particle–particle interaction are thought to inhibit vortex-ring roll-up and reduce entrainment.